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major depressive disorder ( mdd ) and posttraumatic stress disorder ( ptsd ) have been associated with higher incidence of cardiovascular disease [ 14 ] and diabetes [ 5 , 6 ] .
one mechanism that may contribute to the comorbidity between psychopathology and adverse health outcomes is chronic inflammation , whose role in atherosclerosis is well established [ 7 , 8 ] .
c - reactive protein ( crp ) is a marker of systemic inflammation and provides a useful indicator of chronic inflammation . increased circulating concentrations of crp are associated with mdd [ 7 , 911 ] . increased circulating concentrations of crp have also been described in ptsd [ 1214 ] ; however , the relationship is not as clear as other data are equivocal [ 1517 ] . because inflammation may be a key factor in understanding the significant comorbidity between psychiatric disorders and physical diseases , establishing other psychological factors that help explain the relationship between inflammation and psychiatric disorders and how problems with inflammation may develop is critical .
ample evidence indicates that early life stress is associated with chronic inflammation in adulthood [ 18 , 19 ] , and this may be particularly true among african americans .
for example , a recent meta - analysis on the role of childhood maltreatment ( i.e. , childhood sexual , physical , and emotional abuse and physical and emotional neglect ) in inflammation in adulthood demonstrated a significant positive association between exposure to childhood trauma and higher circulating concentrations of crp .
childhood maltreatment exposure may be particularly detrimental to the immune system via problematic alterations in the function of the hypothalamic pituitary adrenal ( hpa ) axis , a major component of the body 's stress response system and a system that both modulates and is modulated by inflammatory processes [ 22 , 23 ] .
based on this evidence , some posit that chronic inflammation may be one mediator in the relationship between early trauma exposure and the later development of psychiatric disorders .
it is important to note that the results of the meta - analysis on childhood trauma and inflammation suggested a relatively subtle ( although significant ) effect of trauma exposure on inflammatory activation suggesting that there may be other important components to this pathway that should be considered .
emotion dysregulation , or deficits in awareness and management of intense negative emotional states , is a transdiagnostic risk factor for the development and maintenance of many psychological disorders , including depression and ptsd [ 23 , 24 ] , and may be another psychological factor that impacts chronic inflammation .
importantly , emotional development begins early in life and developmental research has shown a strong relationship between exposure to childhood maltreatment and the development of emotion regulation deficits in adolescence and adulthood [ 2527 ] .
this may occur in part because emotion regulation strategies are learned by caregivers and when family environments are harmful or unsupportive , children are less likely to be exposed to appropriate regulatory behavior and more likely to experience emotional invalidation where emotional expression is ignored , rejected , or punished .
therefore , emotion dysregulation may be an important mechanism by which early life adversity confers lifetime risk for psychological disorders [ 25 , 26 ] . based on the strong link between childhood maltreatment and emotion dysregulation
recent research in fact suggests that emotion functioning is related to inflammation . a longitudinal study examining emotional functioning in 7-year - old children showed that inappropriate self - regulation and distress proneness during childhood predicted higher circulating concentrations of crp in adulthood .
other cross - sectional research on adults looked specifically at emotion regulation and showed that reappraisal ( an adaptive emotion regulation skill ) was associated with lower circulating concentrations of crp while suppression ( a maladaptive emotion regulation skill ) was associated with elevated circulating concentrations of crp . taken together , these studies indicate that emotion dysregulation could be important in predicting chronic inflammation , although no studies to our knowledge have examined the specific association between emotion dysregulation and circulating concentrations of crp among traumatized adults with high rates of depression and ptsd .
one population at particular risk for elevated systemic inflammation is individuals with type 2 diabetes mellitus ( t2 dm ) .
multiple recent longitudinal studies show that elevated circulating concentrations of crp put individuals at greater risk of developing t2 dm [ 31 , 32 ] . understanding psychological factors that may be associated with increased inflammation levels in individuals with t2 dm could be useful when considering how to improve treatments .
therefore , the goal of the present study was to examine the differential associations between trauma exposure , emotion dysregulation , current mdd , current ptsd , and crp concentrations in a highly traumatized urban , minority sample of women with t2 dm . we hypothesized that emotion dysregulation would be associated with higher concentrations of crp independent of the effects of trauma exposure and current psychiatric diagnoses ( i.e. , ptsd and mdd ) .
participants were drawn from astudy of risk factors for the development of ptsd in a low socioeconomic , urban minority population .
participants were recruited from waiting rooms in the diabetic , gynecology , and primary care medical clinics at a publically funded hospital in atlanta , georgia .
we did not narrow recruitment to specific criteria but approachedany individual in the waiting room . to be eligible for participation , subjects had to be between the ages of 18 and 65 and able to give informed consent ( see for full details regarding study procedures ) .
the investigation was carried out in accordance with the latest version of the declaration of helsinki and informed consent of the participants was obtained after the nature of the procedures had been fully explained .
after signing the informed consent approved by the emory institutional review board and the research oversight committee of grady memorial hospital , an interview was administered with questionnaires regarding trauma history and psychological variables .
a subgroup of female participants with t2 dm was chosen for a separate associated study .
exclusion criteria included current bipolar or psychotic disorder diagnosis , alcohol or substance dependence , treatment for an autoimmune disorder , treatment with nonsteroidal anti - inflammatory , glucocorticoid , or anticonvulsant , and current treatment with an antipsychotic , benzodiazepine , or antidepressant .
on the morning of the interview , height and weight were measured for calculation of body mass index ( bmi ) and fasting blood samples were collected for later batch assessment of crp concentrations ( approximately 2 weeks after initial assessment ) .
the current study included 40 diabetic african - american women with a mean age of 51.88 years ( sd = 7.57 years , range = 3265 ) .
education levels were as follows : 18.8% reported less than high school education , 21.9% reported having a high school diploma or ged , 37.5% reported having some college or technical school education , and 21.9% reported graduating from technical school or college .
only 25.0% of participants were employed and 84.4% had a household monthly income of $ 1999 or less .
the ders is a 36-item psychometrically validated self - report measure of emotion regulation difficulties .
it measures several aspects of emotion regulation , including awareness and understanding of one 's emotions , acceptance of negative emotions , the ability to successfully engage in goal - directed behavior and control impulsive behavior when experiencing negative emotions , and the ability to use situationally appropriate emotion regulation strategies .
for the present study the overall scale , as well as six subscales , of emotion regulation was examined .
the internal consistency of the ders total scale was high ( = 0.92 ) .
it was administered to detail frequency and type of trauma(s ) experienced ; consistent with prior research , total level of trauma exposure was measured by a sum score reflecting the total frequency of different types of trauma ( e.g. , car accident , sexual assault ) a participant had been exposed to over the course of their life . for this study ,
the number of traumatic experiences reflects the total number of different types of events that an individual experienced or witnessed . in order to separate lifetime trauma exposure and childhood abuse
, we excluded the childhood abuse items from the tei ( i.e. , exposure to sexual abuse , physical abuse , and emotional abuse ) .
the ctq is a 25-item , reliable , and valid self - report instrument assessing sexual , physical , emotional abuse , and neglect in childhood ( = 0.92 in current study ) .
bernstein and fink established scores for none , mild , moderate , and severe for each type of abuse . for descriptive purposes , the data from the ctq were used to create a categorical variable to account for the presence or absence of moderate - to - severe reported exposure to emotional ( score 13 ) , physical ( score 10 ) , and sexual ( score 8) abuse in childhood ( 0 = none or mild abuse ; 1 = the presence of moderate or severe abuse scores for at least one of the three types of abuse ) . a continuous measure of overall severity of childhood abuse exposure was also calculated and used as the measure of child abuse severity in all analyses .
the caps is an interviewer - administered psychometrically validated diagnostic instrument measuring ptsd [ 37 , 38 ] .
it includes items that rate social and occupational functioning , global ptsd symptom severity , and the validity of participant 's responses .
the caps assesses current ptsd and was used to determine presence / absence of a ptsd diagnosis . mini is a structured diagnostic interview that assesses mood , anxiety , substance use , and psychotic disorders based on dsm - iv - tr criteria .
mini has shown good reliability and validity across different samples [ 39 , 40 ] .
for the present study , only the current major depression section was used to assess presence / absence of current mdd .
body mass index is calculated as bmi = body mass ( kg)/(height ( m ) ) .
mean bmi for this sample was 36.53 ( sd = 7.30 , range = 2153.80 ) .
serum samples were stored at 80c until the time of highly sensitive crp ( hscrp ) assay .
serum hscrp concentrations were determined using an immunoturbidimetric assay from sekisui diagnostics ( lexington , ma ) on the beckman au480 chemistry analyzer , with an interassay coefficient of variation ( cv ) of 5.2% and an intra - assay cv of 3.1% .
individuals with circulating concentrations of hscrp > 20 mg / l were excluded from analysis because hscrp > 20 mg / l suggests the presence of an active infection or other illnesses that could seriously confound study findings ( two individuals were excluded from analyses ( hscrp = 26.25 and 61.69 ) ) .
circulating concentrations of hscrp averaged 5.70 mg / l ( sd = 4.81 , range = 0.2318.43 ) .
glucose is measured by enzymatic methods on the beckman au480 using reagents from beckman coulter ( fullerton , ca ) .
average glucose level for this sample was 125.05 ( sd = 38.31 , range = 35.70208.15 ) .
hba1c was measured using high performance liquid chromatography by arup laboratories ( salt lake city , utah ) .
average hba1c for this sample was 7.61 ( sd = 1.71 , range = 4.9013.60 ) .
the overall analytic approach was to examine the predictive utility of trauma , current ptsd , current mdd , and emotion dysregulation on hscrp concentrations .
hscrp concentrations , trauma exposure , and emotion dysregulation variables were positively skewed . however , the level of skewness ( range : 0.321.96 ) in this sample fell within acceptable parameters for the sample size on all variables except child abuse severity and the difficulty with emotion regulation strategies dimension of emotion dysregulation .
each had one outlier which affected the level of kurtosis , but results remained the same with or without these outliers included and so they remained in the models presented .
differences in trauma level , emotion dysregulation , and bmi were also examined by both mdd and ptsd diagnoses using analysis of variance ( table 1 ) . for variables of interest , bivariate correlations ( continuous variables ) and a univariate analysis of variance ( categorical variables )
then , based on the results of the correlational analyses , a series of linear regression models was fit to examine the unique predictive value of child abuse , current mdd , and emotion dysregulation on hscrp .
potential covariates for regression analysis were first identified based on previous research suggesting associations with circulating concentrations of hscrp : age , income , bmi , hemoglobin a1c , and baseline blood glucose level [ 9 , 4245 ] . due to the small sample size and risk for low power in detecting significant effects ,
associations between hscrp and these potential covariates were first assessed to determine if their inclusion in the regression model was warranted .
no significant differences emerged between any of the variables and hscrp except for bmi ( r = 0.40 , p = 0.01 ) and therefore only bmi was included as a covariate in the regression analysis .
all analyses were conducted with spss 23.0 software package ( twelve primary analyses were conducted resulting in a bonferroni correction value of p < 0.004 ) .
this was a highly traumatized sample , with all participants reporting the experience of at least one type of trauma in their lifetime ( excluding child abuse ; m = 4.31 , sd = 2.28 ) .
many participants were also exposed to childhood abuse ( i.e. sexual , physical , or emotional abuse ) , with 35.0% of the sample reporting exposure to moderate - to - severe child abuse .
rates of depression and ptsd were also high in this sample , with 32.5% ( n = 13 ) meeting criteria for current mdd and 32.5% ( n = 13 ) meeting criteria for current ptsd . the majority of those individuals that met diagnostic criteria for at least one diagnosis in fact met diagnostic criteria for both mdd and ptsd ( 22.5% of overall sample , n = 9 ) .
as shown in table 1 , individuals with depression and ptsd were more likely to report higher levels of child abuse ( p < 0.01 and p < 0.001 , resp . ) and emotion dysregulation ( p <
0.01 and p < 0.05 , resp . ) . rates of other trauma exposure and bmi were not significantly different across groups . to determine the extent of association between trauma exposure , emotion dysregulation , and hscrp , we first calculated pearson correlation coefficients among our variables of interest ( see table 2 ) .
bmi was also included in these analyses to evaluate independent associations with the variables of interest .
overall emotion dysregulation was significantly positively correlated with hscrp concentrations ( p < 0.001 ) . when looking at the six dimensions of emotion dysregulation , all six were significantly positively correlated with difficulty controlling impulses and lack of emotion regulation strategies showing the strongest correlations ( p < 0.001 ) .
all significant associations except for lack of awareness of emotions would survive correction for multiple comparisons .
the association between child abuse severity and hscrp trended toward significance ( p = 0.067 ) .
however , overall trauma exposure ( excluding child abuse ) was not significantly correlated with hscrp . regarding associations between trauma exposure and emotion dysregulation ,
child abuse severity was associated with overall emotion dysregulation ( p < 0.05 ) as well as nonacceptance of emotions ( p = 0.01 ) and difficulty with goal - directed behavior in the presence of strong emotions ( p = 0.05 ) .
overall trauma exposure ( excluding child abuse ) was not associated with emotion dysregulation . however
, child abuse severity and overall trauma exposure ( excluding abuse ) were significantly correlated with each other ( p < 0.05 ) . regarding bmi , only one emotion dysregulation dimension
lack of awareness of emotions was significantly associated with bmi ( p < 0.05 ) .
univariate analysis of variance was then used to examine mean differences in hscrp by ptsd and mdd diagnosis .
as shown in figure 1 , univariate analysis of variance results showed that there was a significant increase in mean hscrp across current mdd diagnosis ( f = 19.12 , p < 0.001 ) but not current ptsd diagnosis ( f = 2.87 , p = 0.10 ) .
next , a series of linear regression models was run to test the differential associations of child abuse , current mdd , and emotion dysregulation with hscrp .
then , child abuse severity was entered into the second step of the regression model .
as shown in table 3 , when bmi was included in step 1 , higher bmi was significantly related to higher hscrp levels ( p < 0.05 ) .
when child abuse severity was included in step 2 , it was not significant in predicting hscrp .
in step 3 , when current mdd was entered into the regression model , mdd was significantly predictive of hscrp ( p < 0.01 ) , accounting for 13% of the variance in hscrp independent of bmi and child abuse severity .
when overall emotion dysregulation was included in the model in step 4 , emotion dysregulation was significantly predictive of hscrp ( p < 0.001 ) above and beyond bmi , child abuse severity , and current mdd , surviving correction for multiple comparisons and accounting for 25% of unique variance in predicting higher hscrp concentrations .
including ptsd in the model did not change the results ; a model was also run with continuous measures of depression ( mini ) and ptsd ( caps ) and significant results did not change .
to our knowledge , the current study is the first to evaluate the differential relationship between emotion dysregulation , trauma exposure , psychiatric disorders , and circulating crp concentrations in a traumatized sample of women . in support of our hypothesis , within this sample of african - american females with t2 dm , we found that emotion dysregulation was significantly associated with higher peripheral concentrations of crp .
this result is consistent with recent research which has shown that emotional functioning in childhood predicts elevated crp in adulthood and expands previous findings to demonstrate that emotion dysregulation was significantly predictive of elevated crp above and beyond already known risk factors , including bmi , trauma , and current mdd .
although all dimensions of emotion dysregulation measured were significantly related to higher crp , difficulty engaging in goal - directed behavior in the presence of strong emotions and a lack of strategies for managing strong negative emotions showed the strongest associations with elevated concentrations of crp .
these results indicate that heightened inflammation in those with high emotion dysregulation in the current study may be due to chronic activation of neuroendocrine and immune systems in response to chronic stress exposure as a result of a lack of effective strategies for managing negative emotions . indeed , exposure to repeating and unrelenting psychosocial stressors results in the dysregulation of the feedback mechanisms that regulate the activity of the hpa axis and the inflammatory system [ 21 , 22 ] . under normal conditions ,
glucocorticoids are released in response to stressors that act to inhibit the activity of the immune system .
however , overactivation of the hpa axis in response to chronic stress exposure leads to dysfunction of the hpa axis and glucocorticoid responsiveness that leads to an attenuation of glucocorticoid - induced inhibition of the inflammatory response .
thus , it is possible that an inability to manage negative emotions in response to psychosocial stressor exposure with adaptive strategies facilitates increased inflammation .
although the direction of causality can not be established from an association study , improving emotion regulation strategies and individuals ' ability to tolerate strong emotions and not act on them may be a useful area to focus on in treatment with individuals who have comorbid psychopathology and chronic inflammation .
future studies with a controlled experimental design are needed to assess whether improvements in emotional regulation can lead to reductions in inflammation .
it is also critical that more research be conducted to dissect the associations between the various dimensions of emotion dysregulation and chronic inflammation to inform treatment decisions .
consistent with previous research , we also found that current depression was associated with a proinflammatory state .
indeed , individuals with mdd have been shown in meta - analyses to have elevated crp [ 7 , 911 ] , as well as increased levels of interleukin-6 ( il-6 ) and tumor necrosis factor- ( tnf- ) [ 9 , 47 ] .
causal pathways between depression and inflammation have been debated and much of the evidence has focused on the role of proinflammatory cytokines in the development of depressive symptoms and sickness behavior ( e.g. , anhedonia , sleep , and appetite changes [ 4851 ] ) . however , not all individuals with depression show a heightened inflammatory state , and it is likely that in fact the positive association between depression and inflammation is a result of a complex and bidirectional process in which components of the central nervous system ( e.g. , hpa axis , autonomic nervous system ) alter inflammation and depression which in turn impact one another . our finding that current depression is associated with higher crp in females is helpful since some recent population - based studies found sex differences in associations between depression and crp , such that the relationship was only found for men [ 10 , 11 ] .
however , other studies looking specifically at women have found strong associations between mdd and higher levels of crp in women [ 52 , 53 ] , and our finding indicates further support for this relationship among women .
it will be important to continue evaluating sex differences in the association between inflammation and psychopathology as the type of population studied clearly impacts the interpretation and generalizability of the association .
while depression was significantly associated with crp , current ptsd was not , which contradicts some previous findings [ 1214 ] .
however , the literature on this association is mixed , with studies also showing a negative association between ptsd and crp or no association at all [ 16 , 17 ] .
it is likely that the specificity of our sample ( highly traumatized african - american females with t2 dm ) contributed to these results and therefore limits the generalizability of these results to other populations .
there may be other pathways associated with the stress response system and emotion dysregulation that may be more relevant to ptsd than inflammation , such as enhanced glucocorticoid negative feedback of the hpa axis and heightened activity of the sympathetic nervous system .
ongoing studies in our lab are beginning to examine how immune , neuroendocrine , and autonomic function all relate to ptsd and mdd in the context of acute stress .
it is possible that this is in part due to the fact that all women included in the study had been exposed to traumatic events ( mean = 4.23 types of events ) .
however , although not significant in this sample , we did see a trend toward a positive association between child abuse and peripheral concentrations of crp .
our small sample size made us underpowered to detect small effects , and it is likely that with more women included , this effect would be statistically significant .
this result would fit with previous research finding a relationship between child abuse exposure and inflammation in adulthood . of note
, emotion dysregulation and child abuse were significantly related , and based on the strong effect found between emotion dysregulation and crp , it is possible that emotion dysregulation is the mechanism by which early trauma contributes to chronic inflammation , although this could not be explored in this cross - sectional study .
more research is needed to determine potential risk pathways of trauma exposure and emotion regulation problems on the development of inflammation and should be examined in both traumatized and nontraumatized populations .
the current study has some limitations that should be kept in mind when interpreting the results .
first , the study was cross - sectional in nature , which does not allow for the determination of causality .
it is certainly possible that chronic inflammation leads to higher levels of emotion dysregulation , as some research has shown that inflammation can lead to mood and emotional changes .
however , the strong evidence that emotion dysregulation develops throughout childhood and is impacted by early life trauma [ 2527 , 5759 ] , along with initial evidence that the emotional functioning in childhood predicts adult crp concentrations , provides support for emotion dysregulation as an underlying mechanism that might lead to chronic inflammation and later health problems such as cardiovascular disease and diabetes . in addition
this means that participants needed to have insight into their emotion regulation difficulties in order to report them .
a lack of insight could have underestimated the severity of emotion dysregulation within this group of women .
however , the ders has shown good construct validity in its strong relationship with psychiatric symptoms and outcomes ( e.g. , ptsd symptoms , self - harm behavior [ 34 , 6062 ] ) .
recent research has also shown associations between the poor impulse control dimension of the ders and lower activation of the rostral anterior cingulate cortex during an impulse control task , suggesting that this self - report measure of emotion dysregulation is related to already known neural mechanisms associated with adaptive emotion regulation , thus further supporting its validity .
another limitation is that the homogeneity of the study population means that the results may not be generalizable to other samples .
this sample included all african - american women with t2 dm and high levels of trauma exposure , thus exceeding the rates of psychiatric disorders generally found in community samples .
however , the homogeneous sample is a strength as african - american women with t2 dm are clearly an at - risk sample that would benefit from improved interventions .
past research has shown increased inflammatory biomarkers in low - socioeconomic - status african - american communities [ 63 , 64 ] which is consistent with our sample of traumatized t2 dm women , as overall peripheral concentrations of crp in this sample were very high ( mean = 5.70 mg / l , sd = 4.80 ) .
finally , the small sample size of this study means that we may not have had enough power to detect small , yet clinically important associations between the variables examined .
this was evident in the association between child abuse severity and higher concentrations of crp ( r = 0.29 , p = 0.067 ) that was trending toward significance .
this is the first study to examine the complex relationships between trauma , psychiatric disorders , self - reported emotion dysregulation , and crp and therefore more research with larger sample sizes is needed to replicate these findings .
within at - risk groups it may be particularly beneficial to target psychological treatment interventions that may also then impact inflammation .
crp is easily measured and is a significant predictor of risk for serious physical conditions like cardiovascular disease .
future research should examine how psychological interventions for depression and/or ptsd might differentially affect emotion dysregulation and crp concentrations and whether changes in one might then influence the status of the other .
there is already some evidence that reductions in chronic inflammation can result from treating depression and that reducing inflammation decreases affective symptoms .
emotion dysregulation may be an even more useful treatment target since it cuts across psychiatric disorders and can be implemented in the context of various treatment modalities ( e.g. , cognitive - behavioral , acceptance and commitment , and dialectical behavior therapies ) and may be more easily integrated into nonpsychiatric settings ( e.g. , primary care and diabetes clinics ) where brief skills training is more feasible than long - term psychotherapy . | c - reactive protein ( crp ) , a marker of systemic inflammation , has been associated with major depressive disorder ( mdd ) and posttraumatic stress disorder ( ptsd ) .
emotion dysregulation is a transdiagnostic risk factor for many psychological disorders associated with chronic inflammatory state .
the objective of this study was to determine whether inflammation is associated with emotion dysregulation in women with type 2 diabetes mellitus ( t2 dm ) .
we examined associations between trauma exposure , mdd , ptsd , emotion dysregulation , and crp among 40 african - american women with t2 dm recruited from an urban hospital .
emotion dysregulation was measured using the difficulties in emotion regulation scale .
ptsd and mdd were measured with structured clinical interviews .
child abuse and lifetime trauma load were also assessed .
analyses showed that both emotion dysregulation and current mdd were significantly associated with higher levels of crp ( p < 0.01 ) .
current ptsd was not significantly related to crp . in a regression model , emotion dysregulation was significantly associated with higher crp ( p < 0.001 ) independent of body mass index , trauma exposure , and mdd diagnosis .
these findings suggest that emotion dysregulation may be an important risk factor for chronic inflammation beyond already known risk factors among women with t2 dm , though a causal relationship can not be determined from this study . | <s>[INST]major depressive disorder ( mdd ) and posttraumatic stress disorder ( ptsd ) have been associated with higher incidence of cardiovascular disease [ 14 ] and diabetes [ 5 , 6 ] .
one mechanism that may contribute to the comorbidity between psychopathology and adverse health outcomes is chronic inflammation , whose role in atherosclerosis is well established [ 7 , 8 ] .
c - reactive protein ( crp ) is a marker of systemic inflammation and provides a useful indicator of chronic inflammation . increased circulating concentrations of crp are associated with mdd [ 7 , 911 ] . increased circulating concentrations of crp have also been described in ptsd [ 1214 ] ; however , the relationship is not as clear as other data are equivocal [ 1517 ] . because inflammation may be a key factor in understanding the significant comorbidity between psychiatric disorders and physical diseases , establishing other psychological factors that help explain the relationship between inflammation and psychiatric disorders and how problems with inflammation may develop is critical .
ample evidence indicates that early life stress is associated with chronic inflammation in adulthood [ 18 , 19 ] , and this may be particularly true among african americans .
for example , a recent meta - analysis on the role of childhood maltreatment ( i.e. , childhood sexual , physical , and emotional abuse and physical and emotional neglect ) in inflammation in adulthood demonstrated a significant positive association between exposure to childhood trauma and higher circulating concentrations of crp .
childhood maltreatment exposure may be particularly detrimental to the immune system via problematic alterations in the function of the hypothalamic pituitary adrenal ( hpa ) axis , a major component of the body 's stress response system and a system that both modulates and is modulated by inflammatory processes [ 22 , 23 ] .
based on this evidence , some posit that chronic inflammation may be one mediator in the relationship between early trauma exposure and the later development of psychiatric disorders .
it is important to note that the results of the meta - analysis on childhood trauma and inflammation suggested a relatively subtle ( although significant ) effect of trauma exposure on inflammatory activation suggesting that there may be other important components to this pathway that should be considered .
emotion dysregulation , or deficits in awareness and management of intense negative emotional states , is a transdiagnostic risk factor for the development and maintenance of many psychological disorders , including depression and ptsd [ 23 , 24 ] , and may be another psychological factor that impacts chronic inflammation .
importantly , emotional development begins early in life and developmental research has shown a strong relationship between exposure to childhood maltreatment and the development of emotion regulation deficits in adolescence and adulthood [ 2527 ] .
this may occur in part because emotion regulation strategies are learned by caregivers and when family environments are harmful or unsupportive , children are less likely to be exposed to appropriate regulatory behavior and more likely to experience emotional invalidation where emotional expression is ignored , rejected , or punished .
therefore , emotion dysregulation may be an important mechanism by which early life adversity confers lifetime risk for psychological disorders [ 25 , 26 ] . based on the strong link between childhood maltreatment and emotion dysregulation
recent research in fact suggests that emotion functioning is related to inflammation . a longitudinal study examining emotional functioning in 7-year - old children showed that inappropriate self - regulation and distress proneness during childhood predicted higher circulating concentrations of crp in adulthood .
other cross - sectional research on adults looked specifically at emotion regulation and showed that reappraisal ( an adaptive emotion regulation skill ) was associated with lower circulating concentrations of crp while suppression ( a maladaptive emotion regulation skill ) was associated with elevated circulating concentrations of crp . taken together , these studies indicate that emotion dysregulation could be important in predicting chronic inflammation , although no studies to our knowledge have examined the specific association between emotion dysregulation and circulating concentrations of crp among traumatized adults with high rates of depression and ptsd .
one population at particular risk for elevated systemic inflammation is individuals with type 2 diabetes mellitus ( t2 dm ) .
multiple recent longitudinal studies show that elevated circulating concentrations of crp put individuals at greater risk of developing t2 dm [ 31 , 32 ] . understanding psychological factors that may be associated with increased inflammation levels in individuals with t2 dm could be useful when considering how to improve treatments .
therefore , the goal of the present study was to examine the differential associations between trauma exposure , emotion dysregulation , current mdd , current ptsd , and crp concentrations in a highly traumatized urban , minority sample of women with t2 dm . we hypothesized that emotion dysregulation would be associated with higher concentrations of crp independent of the effects of trauma exposure and current psychiatric diagnoses ( i.e. , ptsd and mdd ) .
participants were drawn from astudy of risk factors for the development of ptsd in a low socioeconomic , urban minority population .
participants were recruited from waiting rooms in the diabetic , gynecology , and primary care medical clinics at a publically funded hospital in atlanta , georgia .
we did not narrow recruitment to specific criteria but approachedany individual in the waiting room . to be eligible for participation , subjects had to be between the ages of 18 and 65 and able to give informed consent ( see for full details regarding study procedures ) .
the investigation was carried out in accordance with the latest version of the declaration of helsinki and informed consent of the participants was obtained after the nature of the procedures had been fully explained .
after signing the informed consent approved by the emory institutional review board and the research oversight committee of grady memorial hospital , an interview was administered with questionnaires regarding trauma history and psychological variables .
a subgroup of female participants with t2 dm was chosen for a separate associated study .
exclusion criteria included current bipolar or psychotic disorder diagnosis , alcohol or substance dependence , treatment for an autoimmune disorder , treatment with nonsteroidal anti - inflammatory , glucocorticoid , or anticonvulsant , and current treatment with an antipsychotic , benzodiazepine , or antidepressant .
on the morning of the interview , height and weight were measured for calculation of body mass index ( bmi ) and fasting blood samples were collected for later batch assessment of crp concentrations ( approximately 2 weeks after initial assessment ) .
the current study included 40 diabetic african - american women with a mean age of 51.88 years ( sd = 7.57 years , range = 3265 ) .
education levels were as follows : 18.8% reported less than high school education , 21.9% reported having a high school diploma or ged , 37.5% reported having some college or technical school education , and 21.9% reported graduating from technical school or college .
only 25.0% of participants were employed and 84.4% had a household monthly income of $ 1999 or less .
the ders is a 36-item psychometrically validated self - report measure of emotion regulation difficulties .
it measures several aspects of emotion regulation , including awareness and understanding of one 's emotions , acceptance of negative emotions , the ability to successfully engage in goal - directed behavior and control impulsive behavior when experiencing negative emotions , and the ability to use situationally appropriate emotion regulation strategies .
for the present study the overall scale , as well as six subscales , of emotion regulation was examined .
the internal consistency of the ders total scale was high ( = 0.92 ) .
it was administered to detail frequency and type of trauma(s ) experienced ; consistent with prior research , total level of trauma exposure was measured by a sum score reflecting the total frequency of different types of trauma ( e.g. , car accident , sexual assault ) a participant had been exposed to over the course of their life . for this study ,
the number of traumatic experiences reflects the total number of different types of events that an individual experienced or witnessed . in order to separate lifetime trauma exposure and childhood abuse
, we excluded the childhood abuse items from the tei ( i.e. , exposure to sexual abuse , physical abuse , and emotional abuse ) .
the ctq is a 25-item , reliable , and valid self - report instrument assessing sexual , physical , emotional abuse , and neglect in childhood ( = 0.92 in current study ) .
bernstein and fink established scores for none , mild , moderate , and severe for each type of abuse . for descriptive purposes , the data from the ctq were used to create a categorical variable to account for the presence or absence of moderate - to - severe reported exposure to emotional ( score 13 ) , physical ( score 10 ) , and sexual ( score 8) abuse in childhood ( 0 = none or mild abuse ; 1 = the presence of moderate or severe abuse scores for at least one of the three types of abuse ) . a continuous measure of overall severity of childhood abuse exposure was also calculated and used as the measure of child abuse severity in all analyses .
the caps is an interviewer - administered psychometrically validated diagnostic instrument measuring ptsd [ 37 , 38 ] .
it includes items that rate social and occupational functioning , global ptsd symptom severity , and the validity of participant 's responses .
the caps assesses current ptsd and was used to determine presence / absence of a ptsd diagnosis . mini is a structured diagnostic interview that assesses mood , anxiety , substance use , and psychotic disorders based on dsm - iv - tr criteria .
mini has shown good reliability and validity across different samples [ 39 , 40 ] .
for the present study , only the current major depression section was used to assess presence / absence of current mdd .
body mass index is calculated as bmi = body mass ( kg)/(height ( m ) ) .
mean bmi for this sample was 36.53 ( sd = 7.30 , range = 2153.80 ) .
serum samples were stored at 80c until the time of highly sensitive crp ( hscrp ) assay .
serum hscrp concentrations were determined using an immunoturbidimetric assay from sekisui diagnostics ( lexington , ma ) on the beckman au480 chemistry analyzer , with an interassay coefficient of variation ( cv ) of 5.2% and an intra - assay cv of 3.1% .
individuals with circulating concentrations of hscrp > 20 mg / l were excluded from analysis because hscrp > 20 mg / l suggests the presence of an active infection or other illnesses that could seriously confound study findings ( two individuals were excluded from analyses ( hscrp = 26.25 and 61.69 ) ) .
circulating concentrations of hscrp averaged 5.70 mg / l ( sd = 4.81 , range = 0.2318.43 ) .
glucose is measured by enzymatic methods on the beckman au480 using reagents from beckman coulter ( fullerton , ca ) .
average glucose level for this sample was 125.05 ( sd = 38.31 , range = 35.70208.15 ) .
hba1c was measured using high performance liquid chromatography by arup laboratories ( salt lake city , utah ) .
average hba1c for this sample was 7.61 ( sd = 1.71 , range = 4.9013.60 ) .
the overall analytic approach was to examine the predictive utility of trauma , current ptsd , current mdd , and emotion dysregulation on hscrp concentrations .
hscrp concentrations , trauma exposure , and emotion dysregulation variables were positively skewed . however , the level of skewness ( range : 0.321.96 ) in this sample fell within acceptable parameters for the sample size on all variables except child abuse severity and the difficulty with emotion regulation strategies dimension of emotion dysregulation .
each had one outlier which affected the level of kurtosis , but results remained the same with or without these outliers included and so they remained in the models presented .
differences in trauma level , emotion dysregulation , and bmi were also examined by both mdd and ptsd diagnoses using analysis of variance ( table 1 ) . for variables of interest , bivariate correlations ( continuous variables ) and a univariate analysis of variance ( categorical variables )
then , based on the results of the correlational analyses , a series of linear regression models was fit to examine the unique predictive value of child abuse , current mdd , and emotion dysregulation on hscrp .
potential covariates for regression analysis were first identified based on previous research suggesting associations with circulating concentrations of hscrp : age , income , bmi , hemoglobin a1c , and baseline blood glucose level [ 9 , 4245 ] . due to the small sample size and risk for low power in detecting significant effects ,
associations between hscrp and these potential covariates were first assessed to determine if their inclusion in the regression model was warranted .
no significant differences emerged between any of the variables and hscrp except for bmi ( r = 0.40 , p = 0.01 ) and therefore only bmi was included as a covariate in the regression analysis .
all analyses were conducted with spss 23.0 software package ( twelve primary analyses were conducted resulting in a bonferroni correction value of p < 0.004 ) .
this was a highly traumatized sample , with all participants reporting the experience of at least one type of trauma in their lifetime ( excluding child abuse ; m = 4.31 , sd = 2.28 ) .
many participants were also exposed to childhood abuse ( i.e. sexual , physical , or emotional abuse ) , with 35.0% of the sample reporting exposure to moderate - to - severe child abuse .
rates of depression and ptsd were also high in this sample , with 32.5% ( n = 13 ) meeting criteria for current mdd and 32.5% ( n = 13 ) meeting criteria for current ptsd . the majority of those individuals that met diagnostic criteria for at least one diagnosis in fact met diagnostic criteria for both mdd and ptsd ( 22.5% of overall sample , n = 9 ) .
as shown in table 1 , individuals with depression and ptsd were more likely to report higher levels of child abuse ( p < 0.01 and p < 0.001 , resp . ) and emotion dysregulation ( p <
0.01 and p < 0.05 , resp . ) . rates of other trauma exposure and bmi were not significantly different across groups . to determine the extent of association between trauma exposure , emotion dysregulation , and hscrp , we first calculated pearson correlation coefficients among our variables of interest ( see table 2 ) .
bmi was also included in these analyses to evaluate independent associations with the variables of interest .
overall emotion dysregulation was significantly positively correlated with hscrp concentrations ( p < 0.001 ) . when looking at the six dimensions of emotion dysregulation , all six were significantly positively correlated with difficulty controlling impulses and lack of emotion regulation strategies showing the strongest correlations ( p < 0.001 ) .
all significant associations except for lack of awareness of emotions would survive correction for multiple comparisons .
the association between child abuse severity and hscrp trended toward significance ( p = 0.067 ) .
however , overall trauma exposure ( excluding child abuse ) was not significantly correlated with hscrp . regarding associations between trauma exposure and emotion dysregulation ,
child abuse severity was associated with overall emotion dysregulation ( p < 0.05 ) as well as nonacceptance of emotions ( p = 0.01 ) and difficulty with goal - directed behavior in the presence of strong emotions ( p = 0.05 ) .
overall trauma exposure ( excluding child abuse ) was not associated with emotion dysregulation . however
, child abuse severity and overall trauma exposure ( excluding abuse ) were significantly correlated with each other ( p < 0.05 ) . regarding bmi , only one emotion dysregulation dimension
lack of awareness of emotions was significantly associated with bmi ( p < 0.05 ) .
univariate analysis of variance was then used to examine mean differences in hscrp by ptsd and mdd diagnosis .
as shown in figure 1 , univariate analysis of variance results showed that there was a significant increase in mean hscrp across current mdd diagnosis ( f = 19.12 , p < 0.001 ) but not current ptsd diagnosis ( f = 2.87 , p = 0.10 ) .
next , a series of linear regression models was run to test the differential associations of child abuse , current mdd , and emotion dysregulation with hscrp .
then , child abuse severity was entered into the second step of the regression model .
as shown in table 3 , when bmi was included in step 1 , higher bmi was significantly related to higher hscrp levels ( p < 0.05 ) .
when child abuse severity was included in step 2 , it was not significant in predicting hscrp .
in step 3 , when current mdd was entered into the regression model , mdd was significantly predictive of hscrp ( p < 0.01 ) , accounting for 13% of the variance in hscrp independent of bmi and child abuse severity .
when overall emotion dysregulation was included in the model in step 4 , emotion dysregulation was significantly predictive of hscrp ( p < 0.001 ) above and beyond bmi , child abuse severity , and current mdd , surviving correction for multiple comparisons and accounting for 25% of unique variance in predicting higher hscrp concentrations .
including ptsd in the model did not change the results ; a model was also run with continuous measures of depression ( mini ) and ptsd ( caps ) and significant results did not change .
to our knowledge , the current study is the first to evaluate the differential relationship between emotion dysregulation , trauma exposure , psychiatric disorders , and circulating crp concentrations in a traumatized sample of women . in support of our hypothesis , within this sample of african - american females with t2 dm , we found that emotion dysregulation was significantly associated with higher peripheral concentrations of crp .
this result is consistent with recent research which has shown that emotional functioning in childhood predicts elevated crp in adulthood and expands previous findings to demonstrate that emotion dysregulation was significantly predictive of elevated crp above and beyond already known risk factors , including bmi , trauma , and current mdd .
although all dimensions of emotion dysregulation measured were significantly related to higher crp , difficulty engaging in goal - directed behavior in the presence of strong emotions and a lack of strategies for managing strong negative emotions showed the strongest associations with elevated concentrations of crp .
these results indicate that heightened inflammation in those with high emotion dysregulation in the current study may be due to chronic activation of neuroendocrine and immune systems in response to chronic stress exposure as a result of a lack of effective strategies for managing negative emotions . indeed , exposure to repeating and unrelenting psychosocial stressors results in the dysregulation of the feedback mechanisms that regulate the activity of the hpa axis and the inflammatory system [ 21 , 22 ] . under normal conditions ,
glucocorticoids are released in response to stressors that act to inhibit the activity of the immune system .
however , overactivation of the hpa axis in response to chronic stress exposure leads to dysfunction of the hpa axis and glucocorticoid responsiveness that leads to an attenuation of glucocorticoid - induced inhibition of the inflammatory response .
thus , it is possible that an inability to manage negative emotions in response to psychosocial stressor exposure with adaptive strategies facilitates increased inflammation .
although the direction of causality can not be established from an association study , improving emotion regulation strategies and individuals ' ability to tolerate strong emotions and not act on them may be a useful area to focus on in treatment with individuals who have comorbid psychopathology and chronic inflammation .
future studies with a controlled experimental design are needed to assess whether improvements in emotional regulation can lead to reductions in inflammation .
it is also critical that more research be conducted to dissect the associations between the various dimensions of emotion dysregulation and chronic inflammation to inform treatment decisions .
consistent with previous research , we also found that current depression was associated with a proinflammatory state .
indeed , individuals with mdd have been shown in meta - analyses to have elevated crp [ 7 , 911 ] , as well as increased levels of interleukin-6 ( il-6 ) and tumor necrosis factor- ( tnf- ) [ 9 , 47 ] .
causal pathways between depression and inflammation have been debated and much of the evidence has focused on the role of proinflammatory cytokines in the development of depressive symptoms and sickness behavior ( e.g. , anhedonia , sleep , and appetite changes [ 4851 ] ) . however , not all individuals with depression show a heightened inflammatory state , and it is likely that in fact the positive association between depression and inflammation is a result of a complex and bidirectional process in which components of the central nervous system ( e.g. , hpa axis , autonomic nervous system ) alter inflammation and depression which in turn impact one another . our finding that current depression is associated with higher crp in females is helpful since some recent population - based studies found sex differences in associations between depression and crp , such that the relationship was only found for men [ 10 , 11 ] .
however , other studies looking specifically at women have found strong associations between mdd and higher levels of crp in women [ 52 , 53 ] , and our finding indicates further support for this relationship among women .
it will be important to continue evaluating sex differences in the association between inflammation and psychopathology as the type of population studied clearly impacts the interpretation and generalizability of the association .
while depression was significantly associated with crp , current ptsd was not , which contradicts some previous findings [ 1214 ] .
however , the literature on this association is mixed , with studies also showing a negative association between ptsd and crp or no association at all [ 16 , 17 ] .
it is likely that the specificity of our sample ( highly traumatized african - american females with t2 dm ) contributed to these results and therefore limits the generalizability of these results to other populations .
there may be other pathways associated with the stress response system and emotion dysregulation that may be more relevant to ptsd than inflammation , such as enhanced glucocorticoid negative feedback of the hpa axis and heightened activity of the sympathetic nervous system .
ongoing studies in our lab are beginning to examine how immune , neuroendocrine , and autonomic function all relate to ptsd and mdd in the context of acute stress .
it is possible that this is in part due to the fact that all women included in the study had been exposed to traumatic events ( mean = 4.23 types of events ) .
however , although not significant in this sample , we did see a trend toward a positive association between child abuse and peripheral concentrations of crp .
our small sample size made us underpowered to detect small effects , and it is likely that with more women included , this effect would be statistically significant .
this result would fit with previous research finding a relationship between child abuse exposure and inflammation in adulthood . of note
, emotion dysregulation and child abuse were significantly related , and based on the strong effect found between emotion dysregulation and crp , it is possible that emotion dysregulation is the mechanism by which early trauma contributes to chronic inflammation , although this could not be explored in this cross - sectional study .
more research is needed to determine potential risk pathways of trauma exposure and emotion regulation problems on the development of inflammation and should be examined in both traumatized and nontraumatized populations .
the current study has some limitations that should be kept in mind when interpreting the results .
first , the study was cross - sectional in nature , which does not allow for the determination of causality .
it is certainly possible that chronic inflammation leads to higher levels of emotion dysregulation , as some research has shown that inflammation can lead to mood and emotional changes .
however , the strong evidence that emotion dysregulation develops throughout childhood and is impacted by early life trauma [ 2527 , 5759 ] , along with initial evidence that the emotional functioning in childhood predicts adult crp concentrations , provides support for emotion dysregulation as an underlying mechanism that might lead to chronic inflammation and later health problems such as cardiovascular disease and diabetes . in addition
this means that participants needed to have insight into their emotion regulation difficulties in order to report them .
a lack of insight could have underestimated the severity of emotion dysregulation within this group of women .
however , the ders has shown good construct validity in its strong relationship with psychiatric symptoms and outcomes ( e.g. , ptsd symptoms , self - harm behavior [ 34 , 6062 ] ) .
recent research has also shown associations between the poor impulse control dimension of the ders and lower activation of the rostral anterior cingulate cortex during an impulse control task , suggesting that this self - report measure of emotion dysregulation is related to already known neural mechanisms associated with adaptive emotion regulation , thus further supporting its validity .
another limitation is that the homogeneity of the study population means that the results may not be generalizable to other samples .
this sample included all african - american women with t2 dm and high levels of trauma exposure , thus exceeding the rates of psychiatric disorders generally found in community samples .
however , the homogeneous sample is a strength as african - american women with t2 dm are clearly an at - risk sample that would benefit from improved interventions .
past research has shown increased inflammatory biomarkers in low - socioeconomic - status african - american communities [ 63 , 64 ] which is consistent with our sample of traumatized t2 dm women , as overall peripheral concentrations of crp in this sample were very high ( mean = 5.70 mg / l , sd = 4.80 ) .
finally , the small sample size of this study means that we may not have had enough power to detect small , yet clinically important associations between the variables examined .
this was evident in the association between child abuse severity and higher concentrations of crp ( r = 0.29 , p = 0.067 ) that was trending toward significance .
this is the first study to examine the complex relationships between trauma , psychiatric disorders , self - reported emotion dysregulation , and crp and therefore more research with larger sample sizes is needed to replicate these findings .
within at - risk groups it may be particularly beneficial to target psychological treatment interventions that may also then impact inflammation .
crp is easily measured and is a significant predictor of risk for serious physical conditions like cardiovascular disease .
future research should examine how psychological interventions for depression and/or ptsd might differentially affect emotion dysregulation and crp concentrations and whether changes in one might then influence the status of the other .
there is already some evidence that reductions in chronic inflammation can result from treating depression and that reducing inflammation decreases affective symptoms .
emotion dysregulation may be an even more useful treatment target since it cuts across psychiatric disorders and can be implemented in the context of various treatment modalities ( e.g. , cognitive - behavioral , acceptance and commitment , and dialectical behavior therapies ) and may be more easily integrated into nonpsychiatric settings ( e.g. , primary care and diabetes clinics ) where brief skills training is more feasible than long - term psychotherapy .[/INST]c - reactive protein ( crp ) , a marker of systemic inflammation , has been associated with major depressive disorder ( mdd ) and posttraumatic stress disorder ( ptsd ) .
emotion dysregulation is a transdiagnostic risk factor for many psychological disorders associated with chronic inflammatory state .
the objective of this study was to determine whether inflammation is associated with emotion dysregulation in women with type 2 diabetes mellitus ( t2 dm ) .
we examined associations between trauma exposure , mdd , ptsd , emotion dysregulation , and crp among 40 african - american women with t2 dm recruited from an urban hospital .
emotion dysregulation was measured using the difficulties in emotion regulation scale .
ptsd and mdd were measured with structured clinical interviews .
child abuse and lifetime trauma load were also assessed .
analyses showed that both emotion dysregulation and current mdd were significantly associated with higher levels of crp ( p < 0.01 ) .
current ptsd was not significantly related to crp . in a regression model , emotion dysregulation was significantly associated with higher crp ( p < 0.001 ) independent of body mass index , trauma exposure , and mdd diagnosis .
these findings suggest that emotion dysregulation may be an important risk factor for chronic inflammation beyond already known risk factors among women with t2 dm , though a causal relationship can not be determined from this study .</s> |
full - length human cxcr1 ( residues 1 to 350 ) was expressed with an n - terminal gst partner and a c - terminal his6 tag in e. coli bl21 cells .
isotopically labeled samples were obtained by growing bacteria in m9 media containing n labeled ammonium sulfate and c6-glucose or 2-c - glycerol ( cambridge isotope laboratories ) . a sample of selectively c / n - phe labeled cxcr1 was also prepared .
after cell lysis , the gst - cxcr1-his6 fusion protein was bound to ni - nta resin .
cxcr1 was separated from gst by incubation with thrombin and then purified and refolded in dmpc proteoliposomes by detergent dialysis .
the resulting proteoliposomes were suspended in buffer , isolated by ultra - centrifugation , and packed as a hydrated pellet into the mas rotor .
, cxcr1 proteoliposomes were incubated with varying concentrations of i - labeled and unlabeled il-8 , and bound il-8 was determined by measuring radioactivity in a scintillation counter after removing any free il-8 ligand ( supplementary fig .
cxcr1 proteoliposomes were reconstituted with gi / o protein trimer , and used to measure s - gtps binding as a function of agonist il-8 concentration ( supplementary fig .
refolded cxcr1 binds il-8 ( kd ~ 15 nm ) and activates g - protein in a ligand - dependent manner ( ec50 ~ 1 nm ) , with affinities similar to those reported in the literature .
nmr experiments , experimental parameters and measurements of restraints are described in supplementary information , including supplementary table 2 .
c chemical shifts were externally referenced to dss by setting the adamantane methylene carbons to a c chemical shift frequency of 40.48 ppm ; n chemical shifts were externally referenced to liquid ammonia by setting the ammonium sulfate nitrogen to 26.8 ppm .
fast rotational diffusion ( > 10 hz ) of the protein was verified by analysis of co powder pattern line shapes .
resonances from residues 20 - 325 of cxcr1 were all assigned , except for those corresponding to seven pro residues ( p22 , p93 , p170 , p180 , p185 , p214 and p257 ) and one arg ( r285 ) .
two disulfide bonds ( c30-c277 , c110-c187 ) were determined from the characteristic cb and ca chemical shifts that reflect the oxidation states of cys sites .
backbone dihedral angle ( , ) restraints were derived from the experimentally measured isotropic chemical shifts using cs - rosetta and talos .
values of the experimental h - n dc and h - ca dc used in the structure calculations were measured from the perpendicular edge frequencies of the respective rotationally averaged powder patterns . for each dc , the perpendicular edge frequency
was multiplied by 4 to obtain the frequency of dipolar splitting between the parallel edges of the pake doublet . in most measurements , the sign of the h - n dc could be determined unambiguously . in cases where this was not possible , and for all of the h - ca dc data ,
structure calculations were performed in three stages using the programs : cs - rosetta ; rosetta ( including both the coarse - grained and all - atom potentials as well as the implicit membrane potential available in rosetta version 3.2 ) ; and xplor - nih . in the first stage , we used cs - rosetta together with the amino acid sequence of cxcr1 and the assigned isotropic chemical shifts from ca , cb , co , and n protein sites , to generate a molecular fragment database , containing 67,784 9-residue fragments and 69,204 3-residue fragments . in the second stage , we used the resulting molecular fragment database , together with the experimental dc restraints and the structure of rhodopsin ( pdb i d : 1f88 ) as topology template , to fold 20,000 structural models with the coarse - grained and implicit membrane potentials of rosetta .
these coarse - grained structural models were evaluated according to their rosetta energy and backbone ca rmsd to the lowest energy structure .
the 1,000 lowest energy models were selected for further refinement using the all - atom energy function and implicit membrane environment of rosetta , together with the experimental dc restraints , and the experimentally determined disulfide bond restraints .
the rosetta all - atom relax protocol was implemented for 10 cycles with an increasing h - n dc restraint weighting factor ramped from 1 to 3 kcalmolhz .
structure refinement was performed using a simulated annealing protocol with xplor - nih internal variable molecular dynamics and all the experimental nmr restraints . during simulated annealing
, the temperature was lowered from 500 k to 50 k. experimentally determined disulfide bonds were included by explicit definition in the molecular structure file of cxcr1 .
backbone dihedral angles were imposed with a range of 2 for helices and 30 for loops , and a fixed force constant ( 1,000 kcalmolrad ) .
h - n dc restraints were imposed with a range of 2 khz and a ramped force constant ( 0.1 - 2.5 kcalmolkhz ) .
h - ca dc restraints were imposed with a range of 4 khz and a ramped force constant ( 0.05 - 1.25 kcalmolkhz ) .
the protocol also included a potential for knowledge - based torsion angles implemented with a dimensionless force constant ( 0.2 ) , a potential for the radius of gyration implemented for residues 28 to 325 with a fixed force constant ( 10 kcalmol ) , plus energy terms to enforce covalent geometry and prevent atomic overlap .
the magnitude and symmetry of the molecular alignment tensor were fixed , with values of the axial alignment ( da ) and rhombicity ( rh ) parameters set to 10.52 khz and 0 , respectively , as expected for a membrane protein in phospholipid bilayers with an order parameter of 1.0 and an amide nh bond length of 1.05 .
the h - ca dc alignment tensor was normalized to the maximum value of the h - n dc .
a total of 100 structures were calculated and the 10 lowest energy structures were selected as the structural ensemble for analysis ( fig . 1e , supplementary table 1 ) .
rmsds and r factors , reflecting correlations between experimentally observed values of the restraints and values calculated from the refined structure , were estimated as described .
full - length human cxcr1 ( residues 1 to 350 ) was expressed with an n - terminal gst partner and a c - terminal his6 tag in e. coli bl21 cells .
isotopically labeled samples were obtained by growing bacteria in m9 media containing n labeled ammonium sulfate and c6-glucose or 2-c - glycerol ( cambridge isotope laboratories ) . a sample of selectively c / n - phe labeled cxcr1 was also prepared .
after cell lysis , the gst - cxcr1-his6 fusion protein was bound to ni - nta resin .
cxcr1 was separated from gst by incubation with thrombin and then purified and refolded in dmpc proteoliposomes by detergent dialysis .
the resulting proteoliposomes were suspended in buffer , isolated by ultra - centrifugation , and packed as a hydrated pellet into the mas rotor .
to assay il-8 ligand binding , cxcr1 proteoliposomes were incubated with varying concentrations of i - labeled and unlabeled il-8 , and bound il-8 was determined by measuring radioactivity in a scintillation counter after removing any free il-8 ligand ( supplementary fig .
cxcr1 proteoliposomes were reconstituted with gi / o protein trimer , and used to measure s - gtps binding as a function of agonist il-8 concentration ( supplementary fig .
refolded cxcr1 binds il-8 ( kd ~ 15 nm ) and activates g - protein in a ligand - dependent manner ( ec50 ~ 1 nm ) , with affinities similar to those reported in the literature .
nmr experiments , experimental parameters and measurements of restraints are described in supplementary information , including supplementary table 2 .
c chemical shifts were externally referenced to dss by setting the adamantane methylene carbons to a c chemical shift frequency of 40.48 ppm ; n chemical shifts were externally referenced to liquid ammonia by setting the ammonium sulfate nitrogen to 26.8 ppm .
fast rotational diffusion ( > 10 hz ) of the protein was verified by analysis of co powder pattern line shapes .
resonances from residues 20 - 325 of cxcr1 were all assigned , except for those corresponding to seven pro residues ( p22 , p93 , p170 , p180 , p185 , p214 and p257 ) and one arg ( r285 ) .
two disulfide bonds ( c30-c277 , c110-c187 ) were determined from the characteristic cb and ca chemical shifts that reflect the oxidation states of cys sites .
backbone dihedral angle ( , ) restraints were derived from the experimentally measured isotropic chemical shifts using cs - rosetta and talos .
values of the experimental h - n dc and h - ca dc used in the structure calculations were measured from the perpendicular edge frequencies of the respective rotationally averaged powder patterns . for each dc , the perpendicular edge frequency
was multiplied by 4 to obtain the frequency of dipolar splitting between the parallel edges of the pake doublet . in most measurements , the sign of the h - n dc could be determined unambiguously . in cases where this was not possible , and for all of the h - ca dc data
structure calculations were performed in three stages using the programs : cs - rosetta ; rosetta ( including both the coarse - grained and all - atom potentials as well as the implicit membrane potential available in rosetta version 3.2 ) ; and xplor - nih . in the first stage , we used cs - rosetta together with the amino acid sequence of cxcr1 and the assigned isotropic chemical shifts from ca , cb , co , and n protein sites , to generate a molecular fragment database , containing 67,784 9-residue fragments and 69,204 3-residue fragments . in the second stage , we used the resulting molecular fragment database , together with the experimental dc restraints and the structure of rhodopsin ( pdb i d : 1f88 ) as topology template , to fold 20,000 structural models with the coarse - grained and implicit membrane potentials of rosetta .
these coarse - grained structural models were evaluated according to their rosetta energy and backbone ca rmsd to the lowest energy structure .
the 1,000 lowest energy models were selected for further refinement using the all - atom energy function and implicit membrane environment of rosetta , together with the experimental dc restraints , and the experimentally determined disulfide bond restraints .
the rosetta all - atom relax protocol was implemented for 10 cycles with an increasing h - n dc restraint weighting factor ramped from 1 to 3 kcalmolhz .
, structure refinement was performed using a simulated annealing protocol with xplor - nih internal variable molecular dynamics and all the experimental nmr restraints . during simulated annealing
, the temperature was lowered from 500 k to 50 k. experimentally determined disulfide bonds were included by explicit definition in the molecular structure file of cxcr1 .
backbone dihedral angles were imposed with a range of 2 for helices and 30 for loops , and a fixed force constant ( 1,000 kcalmolrad ) .
h - n dc restraints were imposed with a range of 2 khz and a ramped force constant ( 0.1 - 2.5 kcalmolkhz ) .
h - ca dc restraints were imposed with a range of 4 khz and a ramped force constant ( 0.05 - 1.25 kcalmolkhz ) .
the protocol also included a potential for knowledge - based torsion angles implemented with a dimensionless force constant ( 0.2 ) , a potential for the radius of gyration implemented for residues 28 to 325 with a fixed force constant ( 10 kcalmol ) , plus energy terms to enforce covalent geometry and prevent atomic overlap .
the magnitude and symmetry of the molecular alignment tensor were fixed , with values of the axial alignment ( da ) and rhombicity ( rh ) parameters set to 10.52 khz and 0 , respectively , as expected for a membrane protein in phospholipid bilayers with an order parameter of 1.0 and an amide nh bond length of 1.05 .
the h - ca dc alignment tensor was normalized to the maximum value of the h - n dc .
a total of 100 structures were calculated and the 10 lowest energy structures were selected as the structural ensemble for analysis ( fig . 1e , supplementary table 1 ) .
rmsds and r factors , reflecting correlations between experimentally observed values of the restraints and values calculated from the refined structure , were estimated as described .
| cxcr1 is one of two high - affinity receptors for the cxc chemokine interleukin-8 ( il-8 ) , a major mediator of immune and inflammatory responses implicated in many disorders , including tumor growth1 - 3 .
il-8 , released in response to inflammatory stimuli , binds to the extracellular side of cxcr1 .
the ligand - activated intracellular signaling pathways result in neutrophil migration to the site of inflammation2 .
cxcr1 is a class - a , rhodopsin - like g - protein - coupled receptor ( gpcr ) , the largest class of integral membrane proteins responsible for cellular signal transduction and targeted as drug receptors4 - 7 . despite its importance , its molecular mechanism is poorly understood due to the limited structural information available .
recently , structure determination of gpcrs has advanced by tailoring the receptors with stabilizing mutations , insertion of the protein t4 lysozyme and truncations of their amino acid sequences8 , as well as addition of stabilizing antibodies and small molecules9 that facilitate crystallization in cubic phase monoolein mixtures10 .
the intracellular loops of gpcrs are critical for g - protein interactions11 and activation of cxcr1 involves both n - terminal residues and extracellular loops2,12,13 .
our previous nmr studies indicate that il-8 binding to the n - terminal residues is mediated by the membrane , underscoring the importance of the phospholipid bilayer for physiological activity14 . here
we report the three - dimensional structure of human cxcr1 determined by nmr spectroscopy .
the receptor is in liquid crystalline phospholipid bilayers , without modification of its amino acid sequence and under physiological conditions
. features important for intracellular g - protein activation and signal transduction are revealed . | <s>[INST]full - length human cxcr1 ( residues 1 to 350 ) was expressed with an n - terminal gst partner and a c - terminal his6 tag in e. coli bl21 cells .
isotopically labeled samples were obtained by growing bacteria in m9 media containing n labeled ammonium sulfate and c6-glucose or 2-c - glycerol ( cambridge isotope laboratories ) . a sample of selectively c / n - phe labeled cxcr1 was also prepared .
after cell lysis , the gst - cxcr1-his6 fusion protein was bound to ni - nta resin .
cxcr1 was separated from gst by incubation with thrombin and then purified and refolded in dmpc proteoliposomes by detergent dialysis .
the resulting proteoliposomes were suspended in buffer , isolated by ultra - centrifugation , and packed as a hydrated pellet into the mas rotor .
, cxcr1 proteoliposomes were incubated with varying concentrations of i - labeled and unlabeled il-8 , and bound il-8 was determined by measuring radioactivity in a scintillation counter after removing any free il-8 ligand ( supplementary fig .
cxcr1 proteoliposomes were reconstituted with gi / o protein trimer , and used to measure s - gtps binding as a function of agonist il-8 concentration ( supplementary fig .
refolded cxcr1 binds il-8 ( kd ~ 15 nm ) and activates g - protein in a ligand - dependent manner ( ec50 ~ 1 nm ) , with affinities similar to those reported in the literature .
nmr experiments , experimental parameters and measurements of restraints are described in supplementary information , including supplementary table 2 .
c chemical shifts were externally referenced to dss by setting the adamantane methylene carbons to a c chemical shift frequency of 40.48 ppm ; n chemical shifts were externally referenced to liquid ammonia by setting the ammonium sulfate nitrogen to 26.8 ppm .
fast rotational diffusion ( > 10 hz ) of the protein was verified by analysis of co powder pattern line shapes .
resonances from residues 20 - 325 of cxcr1 were all assigned , except for those corresponding to seven pro residues ( p22 , p93 , p170 , p180 , p185 , p214 and p257 ) and one arg ( r285 ) .
two disulfide bonds ( c30-c277 , c110-c187 ) were determined from the characteristic cb and ca chemical shifts that reflect the oxidation states of cys sites .
backbone dihedral angle ( , ) restraints were derived from the experimentally measured isotropic chemical shifts using cs - rosetta and talos .
values of the experimental h - n dc and h - ca dc used in the structure calculations were measured from the perpendicular edge frequencies of the respective rotationally averaged powder patterns . for each dc , the perpendicular edge frequency
was multiplied by 4 to obtain the frequency of dipolar splitting between the parallel edges of the pake doublet . in most measurements , the sign of the h - n dc could be determined unambiguously . in cases where this was not possible , and for all of the h - ca dc data ,
structure calculations were performed in three stages using the programs : cs - rosetta ; rosetta ( including both the coarse - grained and all - atom potentials as well as the implicit membrane potential available in rosetta version 3.2 ) ; and xplor - nih . in the first stage , we used cs - rosetta together with the amino acid sequence of cxcr1 and the assigned isotropic chemical shifts from ca , cb , co , and n protein sites , to generate a molecular fragment database , containing 67,784 9-residue fragments and 69,204 3-residue fragments . in the second stage , we used the resulting molecular fragment database , together with the experimental dc restraints and the structure of rhodopsin ( pdb i d : 1f88 ) as topology template , to fold 20,000 structural models with the coarse - grained and implicit membrane potentials of rosetta .
these coarse - grained structural models were evaluated according to their rosetta energy and backbone ca rmsd to the lowest energy structure .
the 1,000 lowest energy models were selected for further refinement using the all - atom energy function and implicit membrane environment of rosetta , together with the experimental dc restraints , and the experimentally determined disulfide bond restraints .
the rosetta all - atom relax protocol was implemented for 10 cycles with an increasing h - n dc restraint weighting factor ramped from 1 to 3 kcalmolhz .
structure refinement was performed using a simulated annealing protocol with xplor - nih internal variable molecular dynamics and all the experimental nmr restraints . during simulated annealing
, the temperature was lowered from 500 k to 50 k. experimentally determined disulfide bonds were included by explicit definition in the molecular structure file of cxcr1 .
backbone dihedral angles were imposed with a range of 2 for helices and 30 for loops , and a fixed force constant ( 1,000 kcalmolrad ) .
h - n dc restraints were imposed with a range of 2 khz and a ramped force constant ( 0.1 - 2.5 kcalmolkhz ) .
h - ca dc restraints were imposed with a range of 4 khz and a ramped force constant ( 0.05 - 1.25 kcalmolkhz ) .
the protocol also included a potential for knowledge - based torsion angles implemented with a dimensionless force constant ( 0.2 ) , a potential for the radius of gyration implemented for residues 28 to 325 with a fixed force constant ( 10 kcalmol ) , plus energy terms to enforce covalent geometry and prevent atomic overlap .
the magnitude and symmetry of the molecular alignment tensor were fixed , with values of the axial alignment ( da ) and rhombicity ( rh ) parameters set to 10.52 khz and 0 , respectively , as expected for a membrane protein in phospholipid bilayers with an order parameter of 1.0 and an amide nh bond length of 1.05 .
the h - ca dc alignment tensor was normalized to the maximum value of the h - n dc .
a total of 100 structures were calculated and the 10 lowest energy structures were selected as the structural ensemble for analysis ( fig . 1e , supplementary table 1 ) .
rmsds and r factors , reflecting correlations between experimentally observed values of the restraints and values calculated from the refined structure , were estimated as described .
full - length human cxcr1 ( residues 1 to 350 ) was expressed with an n - terminal gst partner and a c - terminal his6 tag in e. coli bl21 cells .
isotopically labeled samples were obtained by growing bacteria in m9 media containing n labeled ammonium sulfate and c6-glucose or 2-c - glycerol ( cambridge isotope laboratories ) . a sample of selectively c / n - phe labeled cxcr1 was also prepared .
after cell lysis , the gst - cxcr1-his6 fusion protein was bound to ni - nta resin .
cxcr1 was separated from gst by incubation with thrombin and then purified and refolded in dmpc proteoliposomes by detergent dialysis .
the resulting proteoliposomes were suspended in buffer , isolated by ultra - centrifugation , and packed as a hydrated pellet into the mas rotor .
to assay il-8 ligand binding , cxcr1 proteoliposomes were incubated with varying concentrations of i - labeled and unlabeled il-8 , and bound il-8 was determined by measuring radioactivity in a scintillation counter after removing any free il-8 ligand ( supplementary fig .
cxcr1 proteoliposomes were reconstituted with gi / o protein trimer , and used to measure s - gtps binding as a function of agonist il-8 concentration ( supplementary fig .
refolded cxcr1 binds il-8 ( kd ~ 15 nm ) and activates g - protein in a ligand - dependent manner ( ec50 ~ 1 nm ) , with affinities similar to those reported in the literature .
nmr experiments , experimental parameters and measurements of restraints are described in supplementary information , including supplementary table 2 .
c chemical shifts were externally referenced to dss by setting the adamantane methylene carbons to a c chemical shift frequency of 40.48 ppm ; n chemical shifts were externally referenced to liquid ammonia by setting the ammonium sulfate nitrogen to 26.8 ppm .
fast rotational diffusion ( > 10 hz ) of the protein was verified by analysis of co powder pattern line shapes .
resonances from residues 20 - 325 of cxcr1 were all assigned , except for those corresponding to seven pro residues ( p22 , p93 , p170 , p180 , p185 , p214 and p257 ) and one arg ( r285 ) .
two disulfide bonds ( c30-c277 , c110-c187 ) were determined from the characteristic cb and ca chemical shifts that reflect the oxidation states of cys sites .
backbone dihedral angle ( , ) restraints were derived from the experimentally measured isotropic chemical shifts using cs - rosetta and talos .
values of the experimental h - n dc and h - ca dc used in the structure calculations were measured from the perpendicular edge frequencies of the respective rotationally averaged powder patterns . for each dc , the perpendicular edge frequency
was multiplied by 4 to obtain the frequency of dipolar splitting between the parallel edges of the pake doublet . in most measurements , the sign of the h - n dc could be determined unambiguously . in cases where this was not possible , and for all of the h - ca dc data
structure calculations were performed in three stages using the programs : cs - rosetta ; rosetta ( including both the coarse - grained and all - atom potentials as well as the implicit membrane potential available in rosetta version 3.2 ) ; and xplor - nih . in the first stage , we used cs - rosetta together with the amino acid sequence of cxcr1 and the assigned isotropic chemical shifts from ca , cb , co , and n protein sites , to generate a molecular fragment database , containing 67,784 9-residue fragments and 69,204 3-residue fragments . in the second stage , we used the resulting molecular fragment database , together with the experimental dc restraints and the structure of rhodopsin ( pdb i d : 1f88 ) as topology template , to fold 20,000 structural models with the coarse - grained and implicit membrane potentials of rosetta .
these coarse - grained structural models were evaluated according to their rosetta energy and backbone ca rmsd to the lowest energy structure .
the 1,000 lowest energy models were selected for further refinement using the all - atom energy function and implicit membrane environment of rosetta , together with the experimental dc restraints , and the experimentally determined disulfide bond restraints .
the rosetta all - atom relax protocol was implemented for 10 cycles with an increasing h - n dc restraint weighting factor ramped from 1 to 3 kcalmolhz .
, structure refinement was performed using a simulated annealing protocol with xplor - nih internal variable molecular dynamics and all the experimental nmr restraints . during simulated annealing
, the temperature was lowered from 500 k to 50 k. experimentally determined disulfide bonds were included by explicit definition in the molecular structure file of cxcr1 .
backbone dihedral angles were imposed with a range of 2 for helices and 30 for loops , and a fixed force constant ( 1,000 kcalmolrad ) .
h - n dc restraints were imposed with a range of 2 khz and a ramped force constant ( 0.1 - 2.5 kcalmolkhz ) .
h - ca dc restraints were imposed with a range of 4 khz and a ramped force constant ( 0.05 - 1.25 kcalmolkhz ) .
the protocol also included a potential for knowledge - based torsion angles implemented with a dimensionless force constant ( 0.2 ) , a potential for the radius of gyration implemented for residues 28 to 325 with a fixed force constant ( 10 kcalmol ) , plus energy terms to enforce covalent geometry and prevent atomic overlap .
the magnitude and symmetry of the molecular alignment tensor were fixed , with values of the axial alignment ( da ) and rhombicity ( rh ) parameters set to 10.52 khz and 0 , respectively , as expected for a membrane protein in phospholipid bilayers with an order parameter of 1.0 and an amide nh bond length of 1.05 .
the h - ca dc alignment tensor was normalized to the maximum value of the h - n dc .
a total of 100 structures were calculated and the 10 lowest energy structures were selected as the structural ensemble for analysis ( fig . 1e , supplementary table 1 ) .
rmsds and r factors , reflecting correlations between experimentally observed values of the restraints and values calculated from the refined structure , were estimated as described .
[/INST]cxcr1 is one of two high - affinity receptors for the cxc chemokine interleukin-8 ( il-8 ) , a major mediator of immune and inflammatory responses implicated in many disorders , including tumor growth1 - 3 .
il-8 , released in response to inflammatory stimuli , binds to the extracellular side of cxcr1 .
the ligand - activated intracellular signaling pathways result in neutrophil migration to the site of inflammation2 .
cxcr1 is a class - a , rhodopsin - like g - protein - coupled receptor ( gpcr ) , the largest class of integral membrane proteins responsible for cellular signal transduction and targeted as drug receptors4 - 7 . despite its importance , its molecular mechanism is poorly understood due to the limited structural information available .
recently , structure determination of gpcrs has advanced by tailoring the receptors with stabilizing mutations , insertion of the protein t4 lysozyme and truncations of their amino acid sequences8 , as well as addition of stabilizing antibodies and small molecules9 that facilitate crystallization in cubic phase monoolein mixtures10 .
the intracellular loops of gpcrs are critical for g - protein interactions11 and activation of cxcr1 involves both n - terminal residues and extracellular loops2,12,13 .
our previous nmr studies indicate that il-8 binding to the n - terminal residues is mediated by the membrane , underscoring the importance of the phospholipid bilayer for physiological activity14 . here
we report the three - dimensional structure of human cxcr1 determined by nmr spectroscopy .
the receptor is in liquid crystalline phospholipid bilayers , without modification of its amino acid sequence and under physiological conditions
. features important for intracellular g - protein activation and signal transduction are revealed .</s> |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Fisheries Restoration and Irrigation
Mitigation Act of 2007''.
SEC. 2. PRIORITY PROJECTS.
Section 3(c)(3) of the Fisheries Restoration and Irrigation
Mitigation Act of 2000 (16 U.S.C. 777 note; Public Law 106-502) is
amended by striking ``$5,000,000'' and inserting ``$2,500,000''.
SEC. 3. COST SHARING.
Section 7(c) of Fisheries Restoration and Irrigation Mitigation Act
of 2000 (16 U.S.C. 777 note; Public Law 106-502) is amended--
(1) by striking ``The value'' and inserting the following:
``(1) In general.--The value''; and
(2) by adding at the end the following:
``(2) Bonneville power administration.--
``(A) In general.--The Secretary may, without
further appropriation and without fiscal year
limitation, accept any amounts provided to the
Secretary by the Administrator of the Bonneville Power
Administration.
``(B) Non-federal share.--Any amounts provided by
the Bonneville Power Administration directly or through
a grant to another entity for a project carried under
the Program shall be credited toward the non-Federal
share of the costs of the project.''.
SEC. 4. REPORT.
Section 9 of the Fisheries Restoration and Irrigation Mitigation
Act of 2000 (16 U.S.C. 777 note; Public Law 106-502) is amended--
(1) by inserting ``any'' before ``amounts are made''; and
(2) by inserting after ``Secretary shall'' the following:
``, after partnering with local governmental entities and the
States in the Pacific Ocean drainage area,''.
SEC. 5. AUTHORIZATION OF APPROPRIATIONS.
Section 10 of the Fisheries Restoration and Irrigation Mitigation
Act of 2000 (16 U.S.C. 777 note; Public Law 106-502) is amended--
(1) in subsection (a), by striking ``2001 through 2005''
and inserting ``2008 through 2014''; and
(2) in subsection (b), by striking paragraph (2) and
inserting the following:
``(2) Administrative expenses.--
``(A) Definition of administrative expense.--In
this paragraph, the term `administrative expense'
means, except as provided in subparagraph (B)(iii)(II),
any expenditure relating to--
``(i) staffing and overhead, such as the
rental of office space and the acquisition of
office equipment; and
``(ii) the review, processing, and
provision of applications for funding under the
Program.
``(B) Limitation.--
``(i) In general.--Not more than 6 percent
of amounts made available to carry out this Act
for each fiscal year may be used for Federal
and State administrative expenses of carrying
out this Act.
``(ii) Federal and state shares.--To the
maximum extent practicable, of the amounts made
available for administrative expenses under
clause (i)--
``(I) 50 percent shall be provided
to the State agencies provided
assistance under the Program; and
``(II) an amount equal to the cost
of 1 full-time equivalent Federal
employee, as determined by the
Secretary, shall be provided to the
Federal agency carrying out the
Program.
``(iii) State expenses.--Amounts made
available to States for administrative expenses
under clause (i)--
``(I) shall be divided evenly among
all States provided assistance under
the Program; and
``(II) may be used by a State to
provide technical assistance relating
to the program, including any staffing
expenditures (including staff travel
expenses) associated with--
``(aa) arranging meetings
to promote the Program to
potential applicants;
``(bb) assisting applicants
with the preparation of
applications for funding under
the Program; and
``(cc) visiting
construction sites to provide
technical assistance, if
requested by the applicant.''. | Fisheries Restoration and Irrigation Mitigation Act of 2007 - Amends the Fisheries Restoration and Irrigation Mitigation Act of 2000 to direct the Secretary of the Interior, acting through the Director of the U.S. Fish and Wildlife Service, to give priority to any project that has a total cost of less than $2.5 million (currently, $5 million).
Authorizes the Secretary, without further appropriation and without fiscal year limitation, to accept any amounts provided to the Secretary by the Administrator of the Bonneville Power Administration.
Requires: (1) any amounts provided by the Bonneville Power Administration directly or through a grant to another entity for a project carried out under the Program to be credited toward the non-federal share of project costs; and (2) the Secretary's report on projects under such Act to be made after partnering with local governmental entities and the states in the Pacific Ocean drainage area (Oregon, Washington, Montana, and Idaho).
Authorizes appropriations for the Act through FY2014. Sets forth limits and requirements on the amount that may be used each fiscal year for federal and state administrative expenses of carrying out this Act. | <s>[INST]SECTION 1. SHORT TITLE.
This Act may be cited as the ``Fisheries Restoration and Irrigation
Mitigation Act of 2007''.
SEC. 2. PRIORITY PROJECTS.
Section 3(c)(3) of the Fisheries Restoration and Irrigation
Mitigation Act of 2000 (16 U.S.C. 777 note; Public Law 106-502) is
amended by striking ``$5,000,000'' and inserting ``$2,500,000''.
SEC. 3. COST SHARING.
Section 7(c) of Fisheries Restoration and Irrigation Mitigation Act
of 2000 (16 U.S.C. 777 note; Public Law 106-502) is amended--
(1) by striking ``The value'' and inserting the following:
``(1) In general.--The value''; and
(2) by adding at the end the following:
``(2) Bonneville power administration.--
``(A) In general.--The Secretary may, without
further appropriation and without fiscal year
limitation, accept any amounts provided to the
Secretary by the Administrator of the Bonneville Power
Administration.
``(B) Non-federal share.--Any amounts provided by
the Bonneville Power Administration directly or through
a grant to another entity for a project carried under
the Program shall be credited toward the non-Federal
share of the costs of the project.''.
SEC. 4. REPORT.
Section 9 of the Fisheries Restoration and Irrigation Mitigation
Act of 2000 (16 U.S.C. 777 note; Public Law 106-502) is amended--
(1) by inserting ``any'' before ``amounts are made''; and
(2) by inserting after ``Secretary shall'' the following:
``, after partnering with local governmental entities and the
States in the Pacific Ocean drainage area,''.
SEC. 5. AUTHORIZATION OF APPROPRIATIONS.
Section 10 of the Fisheries Restoration and Irrigation Mitigation
Act of 2000 (16 U.S.C. 777 note; Public Law 106-502) is amended--
(1) in subsection (a), by striking ``2001 through 2005''
and inserting ``2008 through 2014''; and
(2) in subsection (b), by striking paragraph (2) and
inserting the following:
``(2) Administrative expenses.--
``(A) Definition of administrative expense.--In
this paragraph, the term `administrative expense'
means, except as provided in subparagraph (B)(iii)(II),
any expenditure relating to--
``(i) staffing and overhead, such as the
rental of office space and the acquisition of
office equipment; and
``(ii) the review, processing, and
provision of applications for funding under the
Program.
``(B) Limitation.--
``(i) In general.--Not more than 6 percent
of amounts made available to carry out this Act
for each fiscal year may be used for Federal
and State administrative expenses of carrying
out this Act.
``(ii) Federal and state shares.--To the
maximum extent practicable, of the amounts made
available for administrative expenses under
clause (i)--
``(I) 50 percent shall be provided
to the State agencies provided
assistance under the Program; and
``(II) an amount equal to the cost
of 1 full-time equivalent Federal
employee, as determined by the
Secretary, shall be provided to the
Federal agency carrying out the
Program.
``(iii) State expenses.--Amounts made
available to States for administrative expenses
under clause (i)--
``(I) shall be divided evenly among
all States provided assistance under
the Program; and
``(II) may be used by a State to
provide technical assistance relating
to the program, including any staffing
expenditures (including staff travel
expenses) associated with--
``(aa) arranging meetings
to promote the Program to
potential applicants;
``(bb) assisting applicants
with the preparation of
applications for funding under
the Program; and
``(cc) visiting
construction sites to provide
technical assistance, if
requested by the applicant.''.[/INST]Fisheries Restoration and Irrigation Mitigation Act of 2007 - Amends the Fisheries Restoration and Irrigation Mitigation Act of 2000 to direct the Secretary of the Interior, acting through the Director of the U.S. Fish and Wildlife Service, to give priority to any project that has a total cost of less than $2.5 million (currently, $5 million).
Authorizes the Secretary, without further appropriation and without fiscal year limitation, to accept any amounts provided to the Secretary by the Administrator of the Bonneville Power Administration.
Requires: (1) any amounts provided by the Bonneville Power Administration directly or through a grant to another entity for a project carried out under the Program to be credited toward the non-federal share of project costs; and (2) the Secretary's report on projects under such Act to be made after partnering with local governmental entities and the states in the Pacific Ocean drainage area (Oregon, Washington, Montana, and Idaho).
Authorizes appropriations for the Act through FY2014. Sets forth limits and requirements on the amount that may be used each fiscal year for federal and state administrative expenses of carrying out this Act.</s> |
the 1g cosyntropin test has some advantages over the 250g test as a test of adrenal function .
one of the concerns regarding the 1 g test includes stability of the cosyntropin when reconstituted and stored . classically the 5 percentile responses to cosyntropin in normal individuals have been used to define a normal response .
we performed a 1g cosyntropin test using reconstituted and refrigerated ( 4 - 8 c ) cosyntropin in saline solution in 49 non pregnant adults who were apparently healthy and had no exposure to exogenous glucocorticoids .
we analysed the data for any association between duration of cosyntropin solution storage and the cortisol responses to cosyntropin administration .
the mean sd cortisol level at baseline , 30 and 60 min were-12.19 3 g / dl , 20.72 2.63 g / dl , 16.86 3.33 g / dl .
the 5 percentile cortisol response at 30 min was 16.5 g / dl ( 16.33 g / dl rounded off ) .
the correlation coefficients between number of days of cosyntropin solution storage and the cortisol responses at 30 and 60 min were ( spear mans rho = 0.06,-0.24 respectively ) ( p = 0.69 and 0.41 ) .
there were no differences in cortisol values whether the storage was for less than 30 days or more than 30 days ( mean difference 0.25 g / dl p = 0.44 ) .
the 5 percentile normative values determined for our assay is lower than what is currently being used clinically and in research publications .
prolonged refrigerated storage of cosyntropin solution does not affect the validity of the 1 g cosyntropin test .
the 250 g cosyntropin test has been conventionally used as a test for impaired adrenal reserve .
the cosyntropin that is commercially available is a 250 g preparation ; it contains the 1 - 24 amino acids of adrenocorticotropic hormone ( acth ) .
earliest studies with cosyntropin showed that responses to cosyntropin were similar to surgical stress or trauma . in a study comparing 250 g , 0.5 g , 1 g cosyntropin with insulin tolerance test ( itt ) in healthy volunteers , the 1 g test was found to produce plasma 1 - 24acth levels of 120 pmol / l , approximately twice as high than that of the itt but of the same order of magnitude .
the cortisol responses at 30 minute were comparable to that of the 250 g synacthen test .
pmol / l nearly 220 times that produced during insulin tolerance test ( itt ) or 1 g synacthen .
moreover 1 g synacthen test has been used in studies looking into milder degrees of hpa axis suppression , such as patients with asthma using inhaled corticosteroids ( ics ) .
receiver operator curve analyses which are classically used to assess the utility of clinical screening tests suggest that 1 g test is superior to 250 g test
. there has been some criticism of the 1 g test because the stability of reconstituted cosyntropin has been questioned and there has been one publication involving 8 normal individuals that suggests that cosyntropin if administered in small quantities produces false positive results presumably because it tends to adhere to plastic tubing used to administer the drug .
conflicting this report there is evidence in literature for the stability of reconstituted cosyntropin in saline for up to four months .
not withstanding these controversies 1 g cosyntropin test has been used widely in research protocols to identify impaired adrenal reserve both internationally and in india .
the cut offs for a clear pass response for the 1 and 250 g tests have been classically derived as a response above the 5 percentile response in a group of normal individuals for each test .
studies have pointed out the need for determining normative responses for the cortisol assay because of variability between different assay methods .
previous metanalyses have suggested a cut - off of 16 g / dl for the 30 min value while using the 1 g test when the test is used in patients with suspected adrenal insufficiency . despite this
we performed a pilot study using the 1 g cosyntropin test in 49 normal individuals in order to obtain the 5 percentile response for the test using an immuno chemiluminometric assay .
we also simultaneously tested the hypothesis that storage of synacthen in saline solution for up to 60 days does not affect cortisol responses .
forty nine non - pregnant volunteer normal adults were tested after institutional ethical review board clearance and informed consent .
following were the exctlusion criteria :
use of any oral / topical / inhaled glucocorticoid in the past 3 years for any durationhistory of hypothalamo pituitaryadrenal diseasehistory of head injury in the pasthistory of snake bitehistory of disseminated intravascular coagulation in the pastany history of diseases known to cause adrenal insufficiency.reconstitution and storage : synthetic acth124 1ml of solution 250 g / ml ( synacthen , novartis , manufactured by alliance pharmaceutical ltd chippenham , wiltshire u.k ) was diluted in 499 ml of 0.9% saline in plastic intravenous fluid container .
after reconstitution the solution was stored in refrigerator 2 - 8 for up to 60 days .
use of any oral / topical / inhaled glucocorticoid in the past 3 years for any duration history of hypothalamo pituitaryadrenal disease history of head injury in the past history of snake bite history of disseminated intravascular coagulation in the past any history of diseases known to cause adrenal insufficiency .
performance of the test : an i.v access with 21 gauge scalp vein set was obtained .
blood was taken at 08:00 hrs for basal cortisol , two ml of the reconstituted solution containing 1 g co - syntropin was administered intravenously through the same cannula .
the scalp vein set was flushed with 10 ml of normal saline following administration of cosyntropin .
an interim analysis showed that the 60 min value was significantly lower than the 30 min value .
since our aim was to identify the peak response we did not perform the 60 min cortisol test in remaining patients , to optimize use of resources available to us .
a note was made regarding the duration of storage of reconstituted co - syntropin at the time of the test .
cortisol assay was done using the automated immuno chemiluminometric access2 assay system ( beckmann- coulter gallaway , ireland ) .
cumulative coefficient of variation was 3.68% at 16.9 g / dl and 9.77% at 2.77 g / dl . internal quality control ( iqc ) material lypocheck immuno assay plus control lot no .
40240 from biorad laboratories with known cortisol concentrations were analyzed on the days of sample run .
the 1 g cosyntropin test was performed in 49 subjects , 38 male ( 77.6% ) .
the mean age of the subjects was 37.2 years , range ( 19 - 84 years ) .
majority of the subjects were young with 59.2% being 36 years or younger , 14.3% of subjects were 55 years or older[figure 1 ] .
the age distribution of studied subjects the mean cortisol values at three time points are depicted in table 1 .
the cortisol values at 30 min were significantly higher than the 0 min and 60 min value p < 0.001 for both .
the lowest and highest cortisol values at each time point and the fifth percentile cortisol value at each time point are depicted in table 1 .
the lowest four responses at 30 min were 13.86 g / dl , 16.07 g / dl , 16.60 g / dl and 17.47 g / dl .
the 5 percentile response was 16.33 g / dl - rounded off to 16.5 g / dl .
cortisol values at different time points for the group all values in g / dl mean and 95% ci values of coristol at baseline,30 min and 60 min the incremental cortisol response was 8.53 2.56 g / dl ( mean sd ) . ranging from 2.61 - 16.92 g / dl .
there was excellent correlation between the 30 min cortisol value and the incremental cortisol response pearsons r = 0.405 p = 0.004 .
the cortisol values at 30 and 60 min had no relationship with number of days of refrigerated storage of the prepared cosyntropin solution .
spear mans rho = 0.06,-0.24 and p = 0.69 , 0.41 for 30 min and 60 min cortisol respectively ( data not shown ) .
we divided the studied normal individuals into two groups one where the duration of reconstituted cosyntropin was stored < 30 days and another where duration of storage 30 days .
there was no difference in the mean 30 min cortisol response using the paired t test ( mean difference 0.25 g / dl p = 0.44 ) table 2 .
in our study we found that the 30 min cortisol response was higher than the 60 min cortisol response .
the value of cortisol corresponding to 5 percentile cortisol response in our study population was 16.5 g / dl . we also found that there was no association between duration of refrigeration of reconstituted synacthen and cortisol response for up to 60 days .
classical comparative studies showed similar 30 min responses to cosyntropin for the 1 and 250 g tests in the same individuals . in the 1 g test the cortisol values quickly reduce and the 60 min value is always lower than the 30 min value . the obvious clinical implication for this
will be that while using the 1 g ldsst test one needs to ensure that the 30 min sampling not be delayed by a few minutes as one can obtain a falsely low value for the cortisol response .
offs for adrenal insufficiency have been derived by investigators as a 5 percentile response in normal individuals . but this method has been disputed by some investigators who feel that the cut point for cortisol value in a stimulation test has to be derived by comparison with a gold standard usually the itt and doing a roc analysis . unfortunately in the most common clinical situation where stimulation testing is necessary- basal cortisol levels are equivocal with no clinical evidence of adrenal insufficiency and itt is not feasible- there is no gold standard for diagnosis of adrenal insufficiency . also in many cases
some centers follow the protocol of using a response above the 5 percentile of normal response as a cut - off to rule out hpa axis suppression , they also use the 2.5 to 5 percentile values as abnormal requiring steroid supplementation as required .
the practice of using 5 percentile responses and using them clinically is continuing with the understanding that the cut points so derived are only a guide to clinical decision making .
in a recent study klose et al . , showed that the 2.5 percentile response varied from 17.2 g / dl ( 475 nmol / l ) to 18.9 g / dl ( 523 nmol / l ) in three different contemporary assays and the stimulated cortisol values varied up to 110 nmol / l ( 3.98 g / dl ) in the same sample when assayed by different methods .
the tendency for a downward shift in cortisol values has been attributed to higher specificity for cortisol and lesser cross reactivity with intermediaries of cortisol metabolism . the use of 550 nmol / l ( 20 g / dl ) or 500 nmol / l ( 18 g / dl ) as a cut off would lead to substantial number of false positives .
our study we found that the 5 percentile cut - off was 16.5 g / dl this value is substantially lower than 18 g / dl being used clinically .
this figure is similar to 16 g / dl identified by roc curve analysis of patient level data of different published studies while using the 1 g cosyntropin test .
the contribution of our study is that we have demonstrated that stimulated cortisol cut - offs lower than the currently used cut point is probably warranted with our assay . in order to arrive at a clinically useful cut off we need to study cortisol values at 30 min in patients with clinically suspected cortisol insufficiency with a longitudinal follow - up .
we suggest that any cortisol value below 16.5 g / dl at 30 min while using the 1 g cosyntropin test will be suspicious of adrenal insufficiency based on our data alone .
one of the main criticisms against the 1 g cosyntropin test is that storage of prepared cosyntropin solution is not possible and it has to be used immediately upon reconstitution .
a previous study has shown stability of cosyntropin after storage for four months at 4c .
our study also had similar findings when we used the 30 min cortisol value as an indirect bioassay of the 1 - 24 acth levels , we found no difference in cortisol levels on storage up to 30 days or even longer .
this finding is of importance in a resource constrained country like ours where reconstituted cosyntropin can be used stored for up to two months and used in multiple patients .
measurement of 1 - 24 cosyntropin in the reconstituted solution and/or retesting in the same individuals after duration of storage could have better supported our hypothesis and these are shortcomings in our study . | background : the 1g cosyntropin test has some advantages over the 250g test as a test of adrenal function .
one of the concerns regarding the 1 g test includes stability of the cosyntropin when reconstituted and stored .
classically the 5th percentile responses to cosyntropin in normal individuals have been used to define a normal response .
recent studies have shown that these normative values should be determined for individual assays.materials and methods : we performed a 1g cosyntropin test using reconstituted and refrigerated ( 4 - 8 c ) cosyntropin in saline solution in 49 non pregnant adults who were apparently healthy and had no exposure to exogenous glucocorticoids .
the cosyntropin solution was stored for up to 60 days following reconstitution .
we analysed the data for any association between duration of cosyntropin solution storage and the cortisol responses to cosyntropin administration.results:the mean sd cortisol level at baseline , 30 and 60 min were-12.19 3 g / dl , 20.72 2.63 g / dl , 16.86 3.33 g / dl .
the 5th percentile cortisol response at 30 min was 16.5 g / dl ( 16.33 g / dl rounded off ) .
the correlation coefficients between number of days of cosyntropin solution storage and the cortisol responses at 30 and 60 min were ( spear mans rho = 0.06,-0.24 respectively ) ( p = 0.69 and 0.41 ) .
there were no differences in cortisol values whether the storage was for less than 30 days or more than 30 days ( mean difference 0.25 g / dl p = 0.44).conclusion : the 5th percentile normative values determined for our assay is lower than what is currently being used clinically and in research publications .
prolonged refrigerated storage of cosyntropin solution does not affect the validity of the 1 g cosyntropin test . | <s>[INST]the 1g cosyntropin test has some advantages over the 250g test as a test of adrenal function .
one of the concerns regarding the 1 g test includes stability of the cosyntropin when reconstituted and stored . classically the 5 percentile responses to cosyntropin in normal individuals have been used to define a normal response .
we performed a 1g cosyntropin test using reconstituted and refrigerated ( 4 - 8 c ) cosyntropin in saline solution in 49 non pregnant adults who were apparently healthy and had no exposure to exogenous glucocorticoids .
we analysed the data for any association between duration of cosyntropin solution storage and the cortisol responses to cosyntropin administration .
the mean sd cortisol level at baseline , 30 and 60 min were-12.19 3 g / dl , 20.72 2.63 g / dl , 16.86 3.33 g / dl .
the 5 percentile cortisol response at 30 min was 16.5 g / dl ( 16.33 g / dl rounded off ) .
the correlation coefficients between number of days of cosyntropin solution storage and the cortisol responses at 30 and 60 min were ( spear mans rho = 0.06,-0.24 respectively ) ( p = 0.69 and 0.41 ) .
there were no differences in cortisol values whether the storage was for less than 30 days or more than 30 days ( mean difference 0.25 g / dl p = 0.44 ) .
the 5 percentile normative values determined for our assay is lower than what is currently being used clinically and in research publications .
prolonged refrigerated storage of cosyntropin solution does not affect the validity of the 1 g cosyntropin test .
the 250 g cosyntropin test has been conventionally used as a test for impaired adrenal reserve .
the cosyntropin that is commercially available is a 250 g preparation ; it contains the 1 - 24 amino acids of adrenocorticotropic hormone ( acth ) .
earliest studies with cosyntropin showed that responses to cosyntropin were similar to surgical stress or trauma . in a study comparing 250 g , 0.5 g , 1 g cosyntropin with insulin tolerance test ( itt ) in healthy volunteers , the 1 g test was found to produce plasma 1 - 24acth levels of 120 pmol / l , approximately twice as high than that of the itt but of the same order of magnitude .
the cortisol responses at 30 minute were comparable to that of the 250 g synacthen test .
pmol / l nearly 220 times that produced during insulin tolerance test ( itt ) or 1 g synacthen .
moreover 1 g synacthen test has been used in studies looking into milder degrees of hpa axis suppression , such as patients with asthma using inhaled corticosteroids ( ics ) .
receiver operator curve analyses which are classically used to assess the utility of clinical screening tests suggest that 1 g test is superior to 250 g test
. there has been some criticism of the 1 g test because the stability of reconstituted cosyntropin has been questioned and there has been one publication involving 8 normal individuals that suggests that cosyntropin if administered in small quantities produces false positive results presumably because it tends to adhere to plastic tubing used to administer the drug .
conflicting this report there is evidence in literature for the stability of reconstituted cosyntropin in saline for up to four months .
not withstanding these controversies 1 g cosyntropin test has been used widely in research protocols to identify impaired adrenal reserve both internationally and in india .
the cut offs for a clear pass response for the 1 and 250 g tests have been classically derived as a response above the 5 percentile response in a group of normal individuals for each test .
studies have pointed out the need for determining normative responses for the cortisol assay because of variability between different assay methods .
previous metanalyses have suggested a cut - off of 16 g / dl for the 30 min value while using the 1 g test when the test is used in patients with suspected adrenal insufficiency . despite this
we performed a pilot study using the 1 g cosyntropin test in 49 normal individuals in order to obtain the 5 percentile response for the test using an immuno chemiluminometric assay .
we also simultaneously tested the hypothesis that storage of synacthen in saline solution for up to 60 days does not affect cortisol responses .
forty nine non - pregnant volunteer normal adults were tested after institutional ethical review board clearance and informed consent .
following were the exctlusion criteria :
use of any oral / topical / inhaled glucocorticoid in the past 3 years for any durationhistory of hypothalamo pituitaryadrenal diseasehistory of head injury in the pasthistory of snake bitehistory of disseminated intravascular coagulation in the pastany history of diseases known to cause adrenal insufficiency.reconstitution and storage : synthetic acth124 1ml of solution 250 g / ml ( synacthen , novartis , manufactured by alliance pharmaceutical ltd chippenham , wiltshire u.k ) was diluted in 499 ml of 0.9% saline in plastic intravenous fluid container .
after reconstitution the solution was stored in refrigerator 2 - 8 for up to 60 days .
use of any oral / topical / inhaled glucocorticoid in the past 3 years for any duration history of hypothalamo pituitaryadrenal disease history of head injury in the past history of snake bite history of disseminated intravascular coagulation in the past any history of diseases known to cause adrenal insufficiency .
performance of the test : an i.v access with 21 gauge scalp vein set was obtained .
blood was taken at 08:00 hrs for basal cortisol , two ml of the reconstituted solution containing 1 g co - syntropin was administered intravenously through the same cannula .
the scalp vein set was flushed with 10 ml of normal saline following administration of cosyntropin .
an interim analysis showed that the 60 min value was significantly lower than the 30 min value .
since our aim was to identify the peak response we did not perform the 60 min cortisol test in remaining patients , to optimize use of resources available to us .
a note was made regarding the duration of storage of reconstituted co - syntropin at the time of the test .
cortisol assay was done using the automated immuno chemiluminometric access2 assay system ( beckmann- coulter gallaway , ireland ) .
cumulative coefficient of variation was 3.68% at 16.9 g / dl and 9.77% at 2.77 g / dl . internal quality control ( iqc ) material lypocheck immuno assay plus control lot no .
40240 from biorad laboratories with known cortisol concentrations were analyzed on the days of sample run .
the 1 g cosyntropin test was performed in 49 subjects , 38 male ( 77.6% ) .
the mean age of the subjects was 37.2 years , range ( 19 - 84 years ) .
majority of the subjects were young with 59.2% being 36 years or younger , 14.3% of subjects were 55 years or older[figure 1 ] .
the age distribution of studied subjects the mean cortisol values at three time points are depicted in table 1 .
the cortisol values at 30 min were significantly higher than the 0 min and 60 min value p < 0.001 for both .
the lowest and highest cortisol values at each time point and the fifth percentile cortisol value at each time point are depicted in table 1 .
the lowest four responses at 30 min were 13.86 g / dl , 16.07 g / dl , 16.60 g / dl and 17.47 g / dl .
the 5 percentile response was 16.33 g / dl - rounded off to 16.5 g / dl .
cortisol values at different time points for the group all values in g / dl mean and 95% ci values of coristol at baseline,30 min and 60 min the incremental cortisol response was 8.53 2.56 g / dl ( mean sd ) . ranging from 2.61 - 16.92 g / dl .
there was excellent correlation between the 30 min cortisol value and the incremental cortisol response pearsons r = 0.405 p = 0.004 .
the cortisol values at 30 and 60 min had no relationship with number of days of refrigerated storage of the prepared cosyntropin solution .
spear mans rho = 0.06,-0.24 and p = 0.69 , 0.41 for 30 min and 60 min cortisol respectively ( data not shown ) .
we divided the studied normal individuals into two groups one where the duration of reconstituted cosyntropin was stored < 30 days and another where duration of storage 30 days .
there was no difference in the mean 30 min cortisol response using the paired t test ( mean difference 0.25 g / dl p = 0.44 ) table 2 .
in our study we found that the 30 min cortisol response was higher than the 60 min cortisol response .
the value of cortisol corresponding to 5 percentile cortisol response in our study population was 16.5 g / dl . we also found that there was no association between duration of refrigeration of reconstituted synacthen and cortisol response for up to 60 days .
classical comparative studies showed similar 30 min responses to cosyntropin for the 1 and 250 g tests in the same individuals . in the 1 g test the cortisol values quickly reduce and the 60 min value is always lower than the 30 min value . the obvious clinical implication for this
will be that while using the 1 g ldsst test one needs to ensure that the 30 min sampling not be delayed by a few minutes as one can obtain a falsely low value for the cortisol response .
offs for adrenal insufficiency have been derived by investigators as a 5 percentile response in normal individuals . but this method has been disputed by some investigators who feel that the cut point for cortisol value in a stimulation test has to be derived by comparison with a gold standard usually the itt and doing a roc analysis . unfortunately in the most common clinical situation where stimulation testing is necessary- basal cortisol levels are equivocal with no clinical evidence of adrenal insufficiency and itt is not feasible- there is no gold standard for diagnosis of adrenal insufficiency . also in many cases
some centers follow the protocol of using a response above the 5 percentile of normal response as a cut - off to rule out hpa axis suppression , they also use the 2.5 to 5 percentile values as abnormal requiring steroid supplementation as required .
the practice of using 5 percentile responses and using them clinically is continuing with the understanding that the cut points so derived are only a guide to clinical decision making .
in a recent study klose et al . , showed that the 2.5 percentile response varied from 17.2 g / dl ( 475 nmol / l ) to 18.9 g / dl ( 523 nmol / l ) in three different contemporary assays and the stimulated cortisol values varied up to 110 nmol / l ( 3.98 g / dl ) in the same sample when assayed by different methods .
the tendency for a downward shift in cortisol values has been attributed to higher specificity for cortisol and lesser cross reactivity with intermediaries of cortisol metabolism . the use of 550 nmol / l ( 20 g / dl ) or 500 nmol / l ( 18 g / dl ) as a cut off would lead to substantial number of false positives .
our study we found that the 5 percentile cut - off was 16.5 g / dl this value is substantially lower than 18 g / dl being used clinically .
this figure is similar to 16 g / dl identified by roc curve analysis of patient level data of different published studies while using the 1 g cosyntropin test .
the contribution of our study is that we have demonstrated that stimulated cortisol cut - offs lower than the currently used cut point is probably warranted with our assay . in order to arrive at a clinically useful cut off we need to study cortisol values at 30 min in patients with clinically suspected cortisol insufficiency with a longitudinal follow - up .
we suggest that any cortisol value below 16.5 g / dl at 30 min while using the 1 g cosyntropin test will be suspicious of adrenal insufficiency based on our data alone .
one of the main criticisms against the 1 g cosyntropin test is that storage of prepared cosyntropin solution is not possible and it has to be used immediately upon reconstitution .
a previous study has shown stability of cosyntropin after storage for four months at 4c .
our study also had similar findings when we used the 30 min cortisol value as an indirect bioassay of the 1 - 24 acth levels , we found no difference in cortisol levels on storage up to 30 days or even longer .
this finding is of importance in a resource constrained country like ours where reconstituted cosyntropin can be used stored for up to two months and used in multiple patients .
measurement of 1 - 24 cosyntropin in the reconstituted solution and/or retesting in the same individuals after duration of storage could have better supported our hypothesis and these are shortcomings in our study .[/INST]background : the 1g cosyntropin test has some advantages over the 250g test as a test of adrenal function .
one of the concerns regarding the 1 g test includes stability of the cosyntropin when reconstituted and stored .
classically the 5th percentile responses to cosyntropin in normal individuals have been used to define a normal response .
recent studies have shown that these normative values should be determined for individual assays.materials and methods : we performed a 1g cosyntropin test using reconstituted and refrigerated ( 4 - 8 c ) cosyntropin in saline solution in 49 non pregnant adults who were apparently healthy and had no exposure to exogenous glucocorticoids .
the cosyntropin solution was stored for up to 60 days following reconstitution .
we analysed the data for any association between duration of cosyntropin solution storage and the cortisol responses to cosyntropin administration.results:the mean sd cortisol level at baseline , 30 and 60 min were-12.19 3 g / dl , 20.72 2.63 g / dl , 16.86 3.33 g / dl .
the 5th percentile cortisol response at 30 min was 16.5 g / dl ( 16.33 g / dl rounded off ) .
the correlation coefficients between number of days of cosyntropin solution storage and the cortisol responses at 30 and 60 min were ( spear mans rho = 0.06,-0.24 respectively ) ( p = 0.69 and 0.41 ) .
there were no differences in cortisol values whether the storage was for less than 30 days or more than 30 days ( mean difference 0.25 g / dl p = 0.44).conclusion : the 5th percentile normative values determined for our assay is lower than what is currently being used clinically and in research publications .
prolonged refrigerated storage of cosyntropin solution does not affect the validity of the 1 g cosyntropin test .</s> |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``American Land Sovereignty Protection
Act''.
SEC. 2. FINDINGS AND PURPOSES.
(a) Findings.--Congress finds that--
(1) the power to dispose of and make all necessary rules
governing property belonging to the United States is vested in
Congress under section 3 of article IV of the Constitution;
(2) some Federal property designations under international
agreements concern land use policies and regulations for
property belonging to the United States that, under section 3
of article IV of the Constitution, can be implemented only by
an Act of Congress;
(3) some international property designations, such as those
under the United States Biosphere Reserve Program and the Man
and Biosphere Program of the United Nations Scientific,
Educational, and Cultural Organization, operate under
independent national committees, such as the United States
National Man and Biosphere Committee, that have no legislative
directive or authorization from Congress;
(4) actions by the United States in making such
designations may affect the use and value of nearby non-Federal
property;
(5) the sovereignty of the States is a critical component
of our Federal system of government and a bulwark against the
unwise concentration of power;
(6) private property rights are essential for the
protection of freedom;
(7) actions by the United States to designate property
belonging to the United States under international agreements
in some cases conflict with congressional constitutional
responsibilities and the sovereign powers of the States; and
(8) actions by the President in applying certain
international agreements to property owned by the United States
diminish the authority of Congress to make rules respecting the
property.
(b) Purposes.--The purposes of this Act are--
(1) to reaffirm the power of Congress under section 3 of
article IV of the Constitution over international agreements
that concern disposal, management, and use of property
belonging to the United States;
(2) to protect State powers not reserved to the Federal
Government under the Constitution from Federal actions
designating property under international agreements;
(3) to ensure that no United States citizen suffers any
diminishment or loss of individual rights as a result of
Federal action designating property under an international
agreement for the purpose of imposing restrictions on use of
the property;
(4) to protect private interests in property from
diminishment as a result of Federal action designating property
under international agreements; and
(5) to provide a process under which the United States may,
when it is desirable to do so, designate property under an
international agreement.
SEC. 3. CLARIFICATION OF CONGRESSIONAL ROLE IN WORLD HERITAGE SITE
LISTING.
Section 401 of the National Historic Preservation Act Amendments of
1980 (16 U.S.C. 470a-1) is amended--
(1) by striking ``Sec. 401. (a)'' and inserting the
following:
``SEC. 401. PARTICIPATION BY THE UNITED STATES.
``(a) In General.--'';
(2) in the first sentence of subsection (a)--
(A) by striking ``The Secretary of the Interior''
and inserting ``Subject to subsections (b), (c), (d),
and (e), the Secretary of the Interior (referred to in
this section as the `Secretary')''; and
(B) by inserting ``(referred to in this section as
the `Convention')'' after ``1973'';
(3) in subsection (b)--
(A) by striking ``(b) The Secretary of the
Interior'' and inserting ``(b) Nomination of Property
to World Heritage Committee.--The Secretary''; and
(B) in the fourth sentence--
(i) by striking ``Representatives and'' and
inserting ``Representatives,''; and
(ii) by inserting before the final period
``, and the appropriate State and local
governments'';
(4) in subsection (c), by striking ``(c) No non-Federal
property may be nominated by the Secretary of the Interior''
and inserting ``(c) Nomination of Non-Federal Property to World
Heritage Committee.--No non-Federal property may be nominated
by the Secretary''; and
(5) by adding at the end the following:
``(d) Requirements for Nomination of Properties.--The Secretary
shall not nominate a property under subsection (b) unless--
``(1) the Secretary publishes a proposed nomination in the
Federal Register and conducts a proceeding under sections 555,
556, and 557, of title 5, United States Code;
``(2) the Secretary, in carrying out the proceeding
described in paragraph (1)--
``(A) considers--
``(i) natural resources associated with the
property proposed to be nominated and other
property located within 10 miles of the
property to be nominated; and
``(ii) the impact that inclusion of the
property proposed to be nominated on the World
Heritage List would have on existing and future
uses of the property proposed to be nominated
or other property located within 10 miles of
the property to be nominated; and
``(B) determines that commercially viable uses (in
existence on the date of the nomination) of the
property proposed to be nominated and of other property
located within 10 miles of the property proposed to be
nominated will not be adversely affected by inclusion
of the property on the World Heritage List; and
``(3) the Secretary submits to Congress a report that--
``(A) contains the information described in
subparagraphs (A) and (B);
``(B) describes the necessity for including the
property on the list; and
``(C) proposes legislation authorizing nomination
of the property; and
``(4) the nomination is specifically authorized by an Act
of Congress enacted after the date of the report.
``(e) Objection to Inclusion of Property.--The Secretary shall
object to the inclusion of property in the United States on the list of
World Heritage in Danger established under Article 11.4 of the
Convention, unless--
``(1) the Secretary submits to Congress the report required
under subsection (d)(1)(C); and
``(2) the Secretary is specifically authorized to assent to
the inclusion of the property on the list by an Act of Congress
enacted after the date of submission of the report under
paragraph (1).
``(f) Decisionmaking.--Notwithstanding any provision of the
Convention, all land management decisions with respect to any Federal
or State land shall remain the responsibility of the land management
agency that administers the land.''.
SEC. 4. PROHIBITION AND TERMINATION OF UNAUTHORIZED UNITED NATIONS
BIOSPHERE RESERVES.
Title IV of the National Historic Preservation Act Amendments of
1980 (16 U.S.C. 470a-1 et seq.) is amended by adding at the end the
following:
``SEC. 403. PROHIBITION AND TERMINATION OF UNAUTHORIZED UNITED NATIONS
BIOSPHERE RESERVES.
``(a) In General.--No Federal official may nominate property in the
United States for designation as a Biosphere Reserve under the Man and
Biosphere Program of the United Nations Educational, Scientific, and
Cultural Organization unless--
``(1) the Secretary of State publishes a proposed
nomination in the Federal Register and conducts a proceeding
under sections 555, 556, and 557, of title 5, United States
Code;
``(2) the Secretary of State, in carrying out the
proceeding described in paragraph (1)--
``(A) considers--
``(i) natural resources associated with the
property proposed to be nominated and other
property located within 10 miles of the
property to be nominated; and
``(ii) the impact that inclusion of the
property proposed to be designated as a
Biosphere would have on existing and future
uses of the property proposed to be nominated
or other property located within 10 miles of
the property to be nominated;
``(B) determines that commercially viable uses (in
existence on the date of the nomination) of the
property proposed to be nominated and of other property
located within 10 miles of the property proposed to be
nominated will not be adversely affected by designation
of the property as a Biosphere; and
``(3) the Secretary of State submits to Congress a report
that--
``(A) contains the information described in
subparagraphs (A) and (B);
``(B) describes the necessity for including the
property in the program; and
``(C) proposes legislation authorizing nomination
of the property; and
``(4) the nomination is specifically authorized by an Act
of Congress enacted after the date of the report.
``(b) Objection to Inclusion of Property.--The Secretary of State
shall object to the designation of property in the United States as a
Biosphere Reserve under the Man and Biosphere Program of the United
Nations Educational, Scientific, and Cultural Organization, unless--
``(1) the Secretary of State submits Congress the report
required under subsection (a)(1)(C); and
``(2) the Secretary of State is specifically authorized to
assent to the inclusion of the property on the list by an Act
of Congress enacted after the date of submission of the report
under paragraph (1).
``(c) Properties Designated Before Date of Enactment.--Any
designation of property in the United States as a Biosphere Reserve
under the Man and Biosphere Program of the United Nations Educational,
Scientific, and Cultural Organization made before the date of enactment
of this section shall terminate on December 31, 2003, unless the
Biosphere Reserve--
``(1) is specifically authorized by a law enacted after the
date of enactment of this section and before December 31, 2003;
``(2) consists solely of property that on the date of
enactment of this section is owned by the United States; and
``(3) is subject to a management plan that specifically
ensures that the use of nearby non-Federal property is not
limited or restricted as a result of the designation.
``(d) Decisionmaking.--Notwithstanding any provision of the
Convention, all land management decisions with respect to any Federal
or State land shall remain the responsibility of the land management
agency that administers the land.''.
SEC. 5. TECHNICAL AMENDMENTS.
Title IV of the National Historic Preservation Act Amendments of
1980 (16 U.S.C. 470a-1 et seq.) is amended--
(1) in the last sentence of section 401(b), by striking
``Committee on Natural Resources'' and inserting ``Committee on
Resources''; and
(2) in section 402, by striking ``Sec. 402. Prior to the
approval'' and inserting the following:
``SEC. 402. MITIGATION OF ADVERSE EFFECTS OF FEDERAL UNDERTAKINGS
OUTSIDE THE UNITED STATES.
``Prior to the approval''. | American Land Sovereignty Protection Act - Amends the National Historic Preservation Act Amendments of 1980 to prohibit the Secretary of the Interior from nominating any non-federal property for inclusion on the World Heritage List unless the Secretary: (1) publishes a proposed nomination in the Federal Register and conducts required hearings; (2) considers natural resources in the area, as well as the impact that inclusion would have on existing and future property uses; (3) determines that commercially viable uses of the property and adjacent property within ten miles will not be adversely affected by inclusion; and (4) submits a report to Congress describing the necessity of such inclusion and proposing legislation authorizing such nomination.Requires the Secretary to object to inclusion of property on the World Heritage in Danger list unless the Secretary: (1) submits such report to Congress; and (2) is specifically authorized to assent to such inclusion by an Act of Congress.Prohibits any Federal official from nominating property for designation as a Biosphere Reserve unless the Secretary of State: (1) publishes such proposed nomination and conducts required hearings; (2) makes the same considerations and submits the same type of report as required of the Secretary for inclusion on the World Heritage List and the nomination is specifically authorized by an Act of Congress. Requires such Secretary to object to such a designation unless such report is submitted and such Secretary is specifically authorized to assent to such inclusion by an Act of Congress. Provides transitional provisions for property so designated before the enactment of this Act. | <s>[INST]SECTION 1. SHORT TITLE.
This Act may be cited as the ``American Land Sovereignty Protection
Act''.
SEC. 2. FINDINGS AND PURPOSES.
(a) Findings.--Congress finds that--
(1) the power to dispose of and make all necessary rules
governing property belonging to the United States is vested in
Congress under section 3 of article IV of the Constitution;
(2) some Federal property designations under international
agreements concern land use policies and regulations for
property belonging to the United States that, under section 3
of article IV of the Constitution, can be implemented only by
an Act of Congress;
(3) some international property designations, such as those
under the United States Biosphere Reserve Program and the Man
and Biosphere Program of the United Nations Scientific,
Educational, and Cultural Organization, operate under
independent national committees, such as the United States
National Man and Biosphere Committee, that have no legislative
directive or authorization from Congress;
(4) actions by the United States in making such
designations may affect the use and value of nearby non-Federal
property;
(5) the sovereignty of the States is a critical component
of our Federal system of government and a bulwark against the
unwise concentration of power;
(6) private property rights are essential for the
protection of freedom;
(7) actions by the United States to designate property
belonging to the United States under international agreements
in some cases conflict with congressional constitutional
responsibilities and the sovereign powers of the States; and
(8) actions by the President in applying certain
international agreements to property owned by the United States
diminish the authority of Congress to make rules respecting the
property.
(b) Purposes.--The purposes of this Act are--
(1) to reaffirm the power of Congress under section 3 of
article IV of the Constitution over international agreements
that concern disposal, management, and use of property
belonging to the United States;
(2) to protect State powers not reserved to the Federal
Government under the Constitution from Federal actions
designating property under international agreements;
(3) to ensure that no United States citizen suffers any
diminishment or loss of individual rights as a result of
Federal action designating property under an international
agreement for the purpose of imposing restrictions on use of
the property;
(4) to protect private interests in property from
diminishment as a result of Federal action designating property
under international agreements; and
(5) to provide a process under which the United States may,
when it is desirable to do so, designate property under an
international agreement.
SEC. 3. CLARIFICATION OF CONGRESSIONAL ROLE IN WORLD HERITAGE SITE
LISTING.
Section 401 of the National Historic Preservation Act Amendments of
1980 (16 U.S.C. 470a-1) is amended--
(1) by striking ``Sec. 401. (a)'' and inserting the
following:
``SEC. 401. PARTICIPATION BY THE UNITED STATES.
``(a) In General.--'';
(2) in the first sentence of subsection (a)--
(A) by striking ``The Secretary of the Interior''
and inserting ``Subject to subsections (b), (c), (d),
and (e), the Secretary of the Interior (referred to in
this section as the `Secretary')''; and
(B) by inserting ``(referred to in this section as
the `Convention')'' after ``1973'';
(3) in subsection (b)--
(A) by striking ``(b) The Secretary of the
Interior'' and inserting ``(b) Nomination of Property
to World Heritage Committee.--The Secretary''; and
(B) in the fourth sentence--
(i) by striking ``Representatives and'' and
inserting ``Representatives,''; and
(ii) by inserting before the final period
``, and the appropriate State and local
governments'';
(4) in subsection (c), by striking ``(c) No non-Federal
property may be nominated by the Secretary of the Interior''
and inserting ``(c) Nomination of Non-Federal Property to World
Heritage Committee.--No non-Federal property may be nominated
by the Secretary''; and
(5) by adding at the end the following:
``(d) Requirements for Nomination of Properties.--The Secretary
shall not nominate a property under subsection (b) unless--
``(1) the Secretary publishes a proposed nomination in the
Federal Register and conducts a proceeding under sections 555,
556, and 557, of title 5, United States Code;
``(2) the Secretary, in carrying out the proceeding
described in paragraph (1)--
``(A) considers--
``(i) natural resources associated with the
property proposed to be nominated and other
property located within 10 miles of the
property to be nominated; and
``(ii) the impact that inclusion of the
property proposed to be nominated on the World
Heritage List would have on existing and future
uses of the property proposed to be nominated
or other property located within 10 miles of
the property to be nominated; and
``(B) determines that commercially viable uses (in
existence on the date of the nomination) of the
property proposed to be nominated and of other property
located within 10 miles of the property proposed to be
nominated will not be adversely affected by inclusion
of the property on the World Heritage List; and
``(3) the Secretary submits to Congress a report that--
``(A) contains the information described in
subparagraphs (A) and (B);
``(B) describes the necessity for including the
property on the list; and
``(C) proposes legislation authorizing nomination
of the property; and
``(4) the nomination is specifically authorized by an Act
of Congress enacted after the date of the report.
``(e) Objection to Inclusion of Property.--The Secretary shall
object to the inclusion of property in the United States on the list of
World Heritage in Danger established under Article 11.4 of the
Convention, unless--
``(1) the Secretary submits to Congress the report required
under subsection (d)(1)(C); and
``(2) the Secretary is specifically authorized to assent to
the inclusion of the property on the list by an Act of Congress
enacted after the date of submission of the report under
paragraph (1).
``(f) Decisionmaking.--Notwithstanding any provision of the
Convention, all land management decisions with respect to any Federal
or State land shall remain the responsibility of the land management
agency that administers the land.''.
SEC. 4. PROHIBITION AND TERMINATION OF UNAUTHORIZED UNITED NATIONS
BIOSPHERE RESERVES.
Title IV of the National Historic Preservation Act Amendments of
1980 (16 U.S.C. 470a-1 et seq.) is amended by adding at the end the
following:
``SEC. 403. PROHIBITION AND TERMINATION OF UNAUTHORIZED UNITED NATIONS
BIOSPHERE RESERVES.
``(a) In General.--No Federal official may nominate property in the
United States for designation as a Biosphere Reserve under the Man and
Biosphere Program of the United Nations Educational, Scientific, and
Cultural Organization unless--
``(1) the Secretary of State publishes a proposed
nomination in the Federal Register and conducts a proceeding
under sections 555, 556, and 557, of title 5, United States
Code;
``(2) the Secretary of State, in carrying out the
proceeding described in paragraph (1)--
``(A) considers--
``(i) natural resources associated with the
property proposed to be nominated and other
property located within 10 miles of the
property to be nominated; and
``(ii) the impact that inclusion of the
property proposed to be designated as a
Biosphere would have on existing and future
uses of the property proposed to be nominated
or other property located within 10 miles of
the property to be nominated;
``(B) determines that commercially viable uses (in
existence on the date of the nomination) of the
property proposed to be nominated and of other property
located within 10 miles of the property proposed to be
nominated will not be adversely affected by designation
of the property as a Biosphere; and
``(3) the Secretary of State submits to Congress a report
that--
``(A) contains the information described in
subparagraphs (A) and (B);
``(B) describes the necessity for including the
property in the program; and
``(C) proposes legislation authorizing nomination
of the property; and
``(4) the nomination is specifically authorized by an Act
of Congress enacted after the date of the report.
``(b) Objection to Inclusion of Property.--The Secretary of State
shall object to the designation of property in the United States as a
Biosphere Reserve under the Man and Biosphere Program of the United
Nations Educational, Scientific, and Cultural Organization, unless--
``(1) the Secretary of State submits Congress the report
required under subsection (a)(1)(C); and
``(2) the Secretary of State is specifically authorized to
assent to the inclusion of the property on the list by an Act
of Congress enacted after the date of submission of the report
under paragraph (1).
``(c) Properties Designated Before Date of Enactment.--Any
designation of property in the United States as a Biosphere Reserve
under the Man and Biosphere Program of the United Nations Educational,
Scientific, and Cultural Organization made before the date of enactment
of this section shall terminate on December 31, 2003, unless the
Biosphere Reserve--
``(1) is specifically authorized by a law enacted after the
date of enactment of this section and before December 31, 2003;
``(2) consists solely of property that on the date of
enactment of this section is owned by the United States; and
``(3) is subject to a management plan that specifically
ensures that the use of nearby non-Federal property is not
limited or restricted as a result of the designation.
``(d) Decisionmaking.--Notwithstanding any provision of the
Convention, all land management decisions with respect to any Federal
or State land shall remain the responsibility of the land management
agency that administers the land.''.
SEC. 5. TECHNICAL AMENDMENTS.
Title IV of the National Historic Preservation Act Amendments of
1980 (16 U.S.C. 470a-1 et seq.) is amended--
(1) in the last sentence of section 401(b), by striking
``Committee on Natural Resources'' and inserting ``Committee on
Resources''; and
(2) in section 402, by striking ``Sec. 402. Prior to the
approval'' and inserting the following:
``SEC. 402. MITIGATION OF ADVERSE EFFECTS OF FEDERAL UNDERTAKINGS
OUTSIDE THE UNITED STATES.
``Prior to the approval''.[/INST]American Land Sovereignty Protection Act - Amends the National Historic Preservation Act Amendments of 1980 to prohibit the Secretary of the Interior from nominating any non-federal property for inclusion on the World Heritage List unless the Secretary: (1) publishes a proposed nomination in the Federal Register and conducts required hearings; (2) considers natural resources in the area, as well as the impact that inclusion would have on existing and future property uses; (3) determines that commercially viable uses of the property and adjacent property within ten miles will not be adversely affected by inclusion; and (4) submits a report to Congress describing the necessity of such inclusion and proposing legislation authorizing such nomination.Requires the Secretary to object to inclusion of property on the World Heritage in Danger list unless the Secretary: (1) submits such report to Congress; and (2) is specifically authorized to assent to such inclusion by an Act of Congress.Prohibits any Federal official from nominating property for designation as a Biosphere Reserve unless the Secretary of State: (1) publishes such proposed nomination and conducts required hearings; (2) makes the same considerations and submits the same type of report as required of the Secretary for inclusion on the World Heritage List and the nomination is specifically authorized by an Act of Congress. Requires such Secretary to object to such a designation unless such report is submitted and such Secretary is specifically authorized to assent to such inclusion by an Act of Congress. Provides transitional provisions for property so designated before the enactment of this Act.</s> |
Organizers of an effort to oust Wisconsin's Republican Gov. Scott Walker say they are submitting 1 million petition signatures, almost double the number needed to force a recall election.
Their effort was spurred by anger over Walker's efforts last year to reduce the bargaining power of public sector unions.
The Wisconsin elections board now must verify that there are enough valid signatures, a process expected to take several months.
In a recall election, voters can remove an elected official before the end of his or her term. In Wisconsin, those forcing the recall generally put up a candidate to face the official in a special eleciton.
An election may not happen until June or later.
Organizers also turned in on Tuesday about 305,000 more signatures than needed to force a recall election of Walker's lieutenant governor. ||||| • The Government Accountability Board has transported the boxes of recall petitions to a state-owned building in Madison. The location will not be made public until all the petitions have been scanned to digital files. Scanning is expected to take several days.
• The GAB has 31 days to validate the signatures, but officials have said they will be in court asking for an extension that could stretch well beyond 60 days. The GAB also will ask a judge that all of the recalls be held on the same day.
• Those wishing to challenge signatures have 10 days from when they receive copies of the recall signatures to file with the GAB. Republican Party spokesman Ben Sparks said the party has 5,000 volunteers ready to examine petitions.
• When election workers are finished verifying signatures and analyzing challenges, they will deliver a report to GAB board members.
• The board will then rule on the validity of the recalls. If it rules in favor, an election date will be set six weeks from that point. There is a high possibility of legal challenges, which could push the election date back even farther. | – Looks like Wisconsin Gov. Scott Walker will be facing a recall re-election. Leaders of the Democratic effort say they collected 1 million signatures for today's filing, about double the necessary amount. The figure represents about the same number of votes Walker received in the November 2010 election, notes the Wisconsin State Journal. The signatures will need to be verified by the state elections board, which could take months, reports AP. Earlier, the group trying to recall Senate Majority Leader Scott Fitzgerald said it would easily make its quota as well. The same applies to the lieutenant governor and three other state senators, all of them Republicans. The recall efforts stem from Walker's move last year to essentially eliminate the collective bargaining rights of public workers. | <s>[INST]Organizers of an effort to oust Wisconsin's Republican Gov. Scott Walker say they are submitting 1 million petition signatures, almost double the number needed to force a recall election.
Their effort was spurred by anger over Walker's efforts last year to reduce the bargaining power of public sector unions.
The Wisconsin elections board now must verify that there are enough valid signatures, a process expected to take several months.
In a recall election, voters can remove an elected official before the end of his or her term. In Wisconsin, those forcing the recall generally put up a candidate to face the official in a special eleciton.
An election may not happen until June or later.
Organizers also turned in on Tuesday about 305,000 more signatures than needed to force a recall election of Walker's lieutenant governor. ||||| • The Government Accountability Board has transported the boxes of recall petitions to a state-owned building in Madison. The location will not be made public until all the petitions have been scanned to digital files. Scanning is expected to take several days.
• The GAB has 31 days to validate the signatures, but officials have said they will be in court asking for an extension that could stretch well beyond 60 days. The GAB also will ask a judge that all of the recalls be held on the same day.
• Those wishing to challenge signatures have 10 days from when they receive copies of the recall signatures to file with the GAB. Republican Party spokesman Ben Sparks said the party has 5,000 volunteers ready to examine petitions.
• When election workers are finished verifying signatures and analyzing challenges, they will deliver a report to GAB board members.
• The board will then rule on the validity of the recalls. If it rules in favor, an election date will be set six weeks from that point. There is a high possibility of legal challenges, which could push the election date back even farther.[/INST]– Looks like Wisconsin Gov. Scott Walker will be facing a recall re-election. Leaders of the Democratic effort say they collected 1 million signatures for today's filing, about double the necessary amount. The figure represents about the same number of votes Walker received in the November 2010 election, notes the Wisconsin State Journal. The signatures will need to be verified by the state elections board, which could take months, reports AP. Earlier, the group trying to recall Senate Majority Leader Scott Fitzgerald said it would easily make its quota as well. The same applies to the lieutenant governor and three other state senators, all of them Republicans. The recall efforts stem from Walker's move last year to essentially eliminate the collective bargaining rights of public workers.</s> |
walter dandy was the first research to describe radicular pain as an extradural mass associated syndrome in 19293 ) .
mixter and barr , however , reported in 1934 that extruded disc materials cause sciatic pain and described the surgical approach11 ) .
intervertebral disc degeneration18 ) , smoking , occupational
and sports - related physical activity , microtrauma , such as obesity ,
environmental factors covered by the different forms of
life12 ) , genetic factors1 ) , congenital defects of vertebral formation16 )
are involved in the etiology of lumbar disc herniation .
the disc herniation depending on vertebral corpus developmental
anomaly is available only one case in english literature .
a thirty - year - old female patient was admitted to our clinic with complaints of low back and right leg pain after a fall 3 weeks ago .
physical examination was evaluated as normal and there were not any features identified in family history .
the neurological examination was described as right straight leg raising test positive at 45 degrees , full muscle strength , norm active tendon reflexes , right s1 dermatome hypoesthesia .
lumbar computed tomography ( ct ) was planned because s1 lumbar vertebra fracture was suspected in the lumbosacral graph ap / l ( fig .
1 ) based on history of trauma . lumbar magnetic resonance imaging ( mri ) was performed as fusion anomaly was detected but s1 vertebral corpus was not broken on the lumbar ct ( fig .
l5-s1 right paramedian disc herniation was detected with the precipitation of trauma on the lumbar mri ( fig .
development of the spinal canal due to congenital defects in the lumbar mr imaging was normal ( fig .
the patient did not consent to surgical treatment and was referred to physical therapy clinic for conservative treatment .
disc herniation occurs as a result of displacement of lumbar intervertebral disc annulus fibrosis and nucleus polyposis fibrosis in the vertebral canal7 ) .
lumbar disc herniation can be symptomatic as a result of compression on the spinal nerves or roots .
radicular symptoms occur due to generation of nerve root ischemia because of the direct mechanical effect of the herniated disc material , or with an inflammatory response and the effect of secondary edema and compression of vascular structures9 ) . in the etiology of the disease ,
cumulative microtrauma was held responsible and it is reported to be more frequently encountered in those driving motor vehicles , those with sedentary life style and in smokers12 ) .
these anomalies are classified as disorders of formation , segmentation disorders and the composition of the two complex disorders5 ) .
although the pathophysiology of spina bifida can be described , the embryological pathogenesis of vertebral corpus fusion anomaly is not fully known .
mesoderm structure emerges after the second week of embryological development of the vertebrae that make up the spine .
skeletal system develops from the para - axial mesoderm and the lateral plates ( somatic layer ) , and crista neuralis .
paraaxial mesoderm creates a series of segmented tissue block known as the somite towards caudal from both sides of the neural tube , somatomeres and occipital region .
the position of the sclerotome cells changes to surround the notochord and the spinal column in the fourth week of development .
this positional change occurs with the differentiation of surrounding structures and not the active migration of those sclerotome cells13 ) .
thus , the resulting mesenchymal column retains segmental traces by leaving less - dense areas containing intersegmental arteries of sclerotomies blocks .
the caudal part of each sclerotome segment is heavily divided and collected in the ongoing stages of development .
this division is so intense that it moves towards the environment intersegmental tissue and thus , a caudal part of the sclerotome is connected to cephalic part of another sclerotome .
thus , vertebral body becomes intersegmental with the connection of intersegmental tissue and the pre - cartilaginous vertebra body10 ) . among sclerotomes that are poor in cell count in cranial and rich in cell count in caudal forms , the one that contains the poo r area forms the intervertebral disc , while the one that contains the rich area constitutes a section of vertebral body10 ) .
these formation defects occurring in the embryological period cause anomalies regarding the vertebra and the disc10 ) . among congenital vertebral anomalies ,
double facet joint formation8 ) , the absence of pedicle17 ) , and absence of lumbar articular processes are reported ; however , vertebral corpus fusion defect as in our case was reported before only one time2 ) .
butterfly vertebra is an uncommon congenital disorder characterized by a symmetrical fusion defect resulting in a sagittal cleft vertebra2 ) .
intervertebral disc was filled due to the lack of development of annulus fibrosis in cavity associated with the defect of embryological development of the vertebral corpus and trauma as a result of weakness in our case and it caused the patient to develop lumbar disc hernia .
therefore disc herniation could occur more easily in patients with vertebral body defect than in patients with normal vertebral body .
congenital vertebra corpus fusion anomalies are typically asymptomatic . however , these anomalies incidentally detected during routine radiographic investigations and post - traumatic radiological evaluations6 ) .
the specific radiological examinations usually include direct roentgenogram , ct and mri15 ) . in our case ,
vertebral fusion defects were determined with lumbar radiograph performed due to back pain after trauma .
we thought that the defect occurred during the development in the embryological period of the vertebral body .
however , that intervertebral disc was the weakest link as sufficient circular annulus fibrosis had not developed here .
there were no other osseous pathologies such as spina bifida occulta , facet abnormalities , and/or pedicle anomaly in our case .
disc herniation in patients with congenital bone deformities associated with congenital developmental defects are considered related problems in the spinal canal . on the level of the patient 's filum terminale , whether tethered cord syndrome should be investigated14 ) .
there was not a congenital defect of development of the spinal canal in our case ( fig .
5 ) . presenting with similar symptoms , such as back and leg pain , especially adult clinical presentation patients with lumbar disc herniation group tethered cords can be confused with tethered cord . and
these types of cases after trauma can be misevaluated and overlooked as congenital malformation without treatment .
especially , patients with congenital malformations and an unusual clinic should be examined carefully with advanced radiological imaging techniques . | lumbar disc herniation is characterized with low back and leg pain resulting from the degenerated lumbar disc compressing the spinal nerve root .
the etiology of degenerative spine is related to age , smoking , microtrauma , obesity , disorders of familial collagen structure , occupational and sports - related physical activity .
however , disc herniations induced by congenital lumbar vertebral anomalies are rarely seen .
vertebral fusion defect is one of the causes of congenital anomalies .
the pathogenesis of embryological corpus vertebral fusion anomaly is not fully known . in this paper , a 30-year - old patient who had the complaints of low back and right leg pain after falling from a height
is presented .
she had right l5-s1 disc herniation that had developed on the basis of s1 vertebra corpus fusion anomaly in lumbar computed tomography .
this case has been discussed in the light of literature based on evaluations of lumbar computed tomography ( ct ) and magnetic resonance imaging ( mri ) .
this case is unique in that it is the first case with development of lumbar disc herniation associated with s1 vertebral corpus fusion anomaly .
congenital malformations with unusual clinical presentation after trauma should be evaluated through advanced radiological imaging techniques . | <s>[INST]walter dandy was the first research to describe radicular pain as an extradural mass associated syndrome in 19293 ) .
mixter and barr , however , reported in 1934 that extruded disc materials cause sciatic pain and described the surgical approach11 ) .
intervertebral disc degeneration18 ) , smoking , occupational
and sports - related physical activity , microtrauma , such as obesity ,
environmental factors covered by the different forms of
life12 ) , genetic factors1 ) , congenital defects of vertebral formation16 )
are involved in the etiology of lumbar disc herniation .
the disc herniation depending on vertebral corpus developmental
anomaly is available only one case in english literature .
a thirty - year - old female patient was admitted to our clinic with complaints of low back and right leg pain after a fall 3 weeks ago .
physical examination was evaluated as normal and there were not any features identified in family history .
the neurological examination was described as right straight leg raising test positive at 45 degrees , full muscle strength , norm active tendon reflexes , right s1 dermatome hypoesthesia .
lumbar computed tomography ( ct ) was planned because s1 lumbar vertebra fracture was suspected in the lumbosacral graph ap / l ( fig .
1 ) based on history of trauma . lumbar magnetic resonance imaging ( mri ) was performed as fusion anomaly was detected but s1 vertebral corpus was not broken on the lumbar ct ( fig .
l5-s1 right paramedian disc herniation was detected with the precipitation of trauma on the lumbar mri ( fig .
development of the spinal canal due to congenital defects in the lumbar mr imaging was normal ( fig .
the patient did not consent to surgical treatment and was referred to physical therapy clinic for conservative treatment .
disc herniation occurs as a result of displacement of lumbar intervertebral disc annulus fibrosis and nucleus polyposis fibrosis in the vertebral canal7 ) .
lumbar disc herniation can be symptomatic as a result of compression on the spinal nerves or roots .
radicular symptoms occur due to generation of nerve root ischemia because of the direct mechanical effect of the herniated disc material , or with an inflammatory response and the effect of secondary edema and compression of vascular structures9 ) . in the etiology of the disease ,
cumulative microtrauma was held responsible and it is reported to be more frequently encountered in those driving motor vehicles , those with sedentary life style and in smokers12 ) .
these anomalies are classified as disorders of formation , segmentation disorders and the composition of the two complex disorders5 ) .
although the pathophysiology of spina bifida can be described , the embryological pathogenesis of vertebral corpus fusion anomaly is not fully known .
mesoderm structure emerges after the second week of embryological development of the vertebrae that make up the spine .
skeletal system develops from the para - axial mesoderm and the lateral plates ( somatic layer ) , and crista neuralis .
paraaxial mesoderm creates a series of segmented tissue block known as the somite towards caudal from both sides of the neural tube , somatomeres and occipital region .
the position of the sclerotome cells changes to surround the notochord and the spinal column in the fourth week of development .
this positional change occurs with the differentiation of surrounding structures and not the active migration of those sclerotome cells13 ) .
thus , the resulting mesenchymal column retains segmental traces by leaving less - dense areas containing intersegmental arteries of sclerotomies blocks .
the caudal part of each sclerotome segment is heavily divided and collected in the ongoing stages of development .
this division is so intense that it moves towards the environment intersegmental tissue and thus , a caudal part of the sclerotome is connected to cephalic part of another sclerotome .
thus , vertebral body becomes intersegmental with the connection of intersegmental tissue and the pre - cartilaginous vertebra body10 ) . among sclerotomes that are poor in cell count in cranial and rich in cell count in caudal forms , the one that contains the poo r area forms the intervertebral disc , while the one that contains the rich area constitutes a section of vertebral body10 ) .
these formation defects occurring in the embryological period cause anomalies regarding the vertebra and the disc10 ) . among congenital vertebral anomalies ,
double facet joint formation8 ) , the absence of pedicle17 ) , and absence of lumbar articular processes are reported ; however , vertebral corpus fusion defect as in our case was reported before only one time2 ) .
butterfly vertebra is an uncommon congenital disorder characterized by a symmetrical fusion defect resulting in a sagittal cleft vertebra2 ) .
intervertebral disc was filled due to the lack of development of annulus fibrosis in cavity associated with the defect of embryological development of the vertebral corpus and trauma as a result of weakness in our case and it caused the patient to develop lumbar disc hernia .
therefore disc herniation could occur more easily in patients with vertebral body defect than in patients with normal vertebral body .
congenital vertebra corpus fusion anomalies are typically asymptomatic . however , these anomalies incidentally detected during routine radiographic investigations and post - traumatic radiological evaluations6 ) .
the specific radiological examinations usually include direct roentgenogram , ct and mri15 ) . in our case ,
vertebral fusion defects were determined with lumbar radiograph performed due to back pain after trauma .
we thought that the defect occurred during the development in the embryological period of the vertebral body .
however , that intervertebral disc was the weakest link as sufficient circular annulus fibrosis had not developed here .
there were no other osseous pathologies such as spina bifida occulta , facet abnormalities , and/or pedicle anomaly in our case .
disc herniation in patients with congenital bone deformities associated with congenital developmental defects are considered related problems in the spinal canal . on the level of the patient 's filum terminale , whether tethered cord syndrome should be investigated14 ) .
there was not a congenital defect of development of the spinal canal in our case ( fig .
5 ) . presenting with similar symptoms , such as back and leg pain , especially adult clinical presentation patients with lumbar disc herniation group tethered cords can be confused with tethered cord . and
these types of cases after trauma can be misevaluated and overlooked as congenital malformation without treatment .
especially , patients with congenital malformations and an unusual clinic should be examined carefully with advanced radiological imaging techniques .[/INST]lumbar disc herniation is characterized with low back and leg pain resulting from the degenerated lumbar disc compressing the spinal nerve root .
the etiology of degenerative spine is related to age , smoking , microtrauma , obesity , disorders of familial collagen structure , occupational and sports - related physical activity .
however , disc herniations induced by congenital lumbar vertebral anomalies are rarely seen .
vertebral fusion defect is one of the causes of congenital anomalies .
the pathogenesis of embryological corpus vertebral fusion anomaly is not fully known . in this paper , a 30-year - old patient who had the complaints of low back and right leg pain after falling from a height
is presented .
she had right l5-s1 disc herniation that had developed on the basis of s1 vertebra corpus fusion anomaly in lumbar computed tomography .
this case has been discussed in the light of literature based on evaluations of lumbar computed tomography ( ct ) and magnetic resonance imaging ( mri ) .
this case is unique in that it is the first case with development of lumbar disc herniation associated with s1 vertebral corpus fusion anomaly .
congenital malformations with unusual clinical presentation after trauma should be evaluated through advanced radiological imaging techniques .</s> |
in most current free space optical ( fso ) communication systems , for reasons of simplicity , intensity modulation with direct detection ( im / dd ) is used . to improve the spectral efficiency , we consider @xmath0-ary pulse amplitude modulation ( mpam ) here by presuming that the receiver photodetector will not be saturated by the impinging optical signal level that has the highest energy .
the transmitter side constellation is shown in fig .
[ fg : cons_tx ] , where @xmath1 denotes the minimum signal intensity distance and the transmitter average power is defined as @xmath2 . inside the receiver , as shown in fig .
[ fg : receiver ] , there is an integrator that integrates the photo current for each symbol period @xmath3 . for the @xmath4th symbol interval ( @xmath5 ) ,
the received electrical signal @xmath6 is obtained by sampling the integrator at time @xmath7 .
since the photo current can be assumed to be constant during the integration time , @xmath6 can be expressed as @xcite @xmath8 where @xmath9 is the responsivity of the photo detector and @xmath10 denotes the instantaneous channel gain .
the transmitted data symbol @xmath11 takes on any value from set @xmath12 with equal probability , and gray mapping of bits onto the levels is assumed . in practice , multiplying the received signal by the normalising basis @xmath13 , which is shown in fig .
[ fg : receiver ] , is not necessary .
we use it here because we want to simplify later performance analysis by normalizing the discrete additive white gaussian noise ( awgn ) term @xmath14 such that @xmath15=\delta _ { ij } { n_0}/{2 } $ ] conditioned on that the continuous noise term @xmath16 is an additive white gaussian random process with mean zero and two - sided spectral density @xmath17 . by defining @xmath18 as the instantaneous receiver - side electrical - domain minimum signal distance
, @xmath6 can be modelled as @xcite @xmath19 correspondingly , the receiver side constellation is shown in fig .
[ fg : cons_rx ] . since atmospheric turbulence and pointing errors cause fluctuations in the intensity of the received signal , i.e. , @xmath10 is time - varying ,
therefore , @xmath20 is time - varying and is modelled as @xmath21 where @xmath22 denotes the minimum signal distance when @xmath23 , i.e. , @xmath24 , which is related to the average transmit power @xmath25 , i.e. , @xmath26 for the on - off keying ( ook ) system that is considered as the simplest mpam ( @xmath27 ) case , the turbulence and pointing error induced fading is the major issue that degrades system performance .
thus , the accurate channel state information ( csi ) , i.e. , the accurate instantaneous value of @xmath10 , is required for properly adjusting the decision threshold . in previous studies , frequent insertions of pilot symbols
@xcite or co - propagating reference light @xcite is used to estimate the csi . in this paper ,
when it comes to pilot symbols , we specifically refer to pilot symbols used for channel estimation . in practice
, pilot symbols are also required for other purposes such as timing synchronization .
since pilot symbols do not carry data , the use of them results in a system spectral efficiency reduction and additional energy overheads .
therefore , we hope to minimize the amount of pilot symbols . the co - propagating reference light has the same problem , and besides , since it has a different frequency with the signal - bearing light , the estimation result may not be accurate . for mpam systems ( @xmath28 ) , to detect signals reliably , the requirement of accurate csi is more stringent .
the difficulty of accurate csi acquisition is the main reason that limits the use of mpam in practical systems . however , though these two above - mentioned methods can be extended to mpam systems , they are not so suitable in practice .
the receiver design problem remains challenged by the fact that the csi is hard to acquire at the receiver side if very few pilot symbols and no co - propagating reference light are used . since the channel coherence length
@xmath29 , defined as the number of consecutive data symbol intervals over which the channel gain @xmath10 can be considered to be constant , is a very large number ( @xmath30 ) for multi - gbps systems@xcite , the data and the csi can be jointly detected and estimated . in @xcite , for the 2-level pam system , i.e. , the ook system , based on the generalized likelihood ratio test ( glrt ) principle , we derived a maximum likelihood ( ml ) sequence detection receiver ( the glrt - mlsd receiver ) that jointly detects the data sequence and estimates the unknown channel gain . in @xcite , we have extended this glrt - mlsd receiver to multi - level pam systems . however , as we discussed in @xcite , the search complexity of the glrt - mlsd receiver increases with the modulation order @xmath0 almost quadratically .
therefore , in section ii of this paper , we derive a simpler decision - feedback ( dfb ) , symbol - by - symbol receiver , whose implementation complexity is independent of the modulation order @xmath0 .
it uses the most recently detected data symbols to help estimate the instantaneous channel gain . as the number of the detected data symbols used to estimate the channel increases , the bit error probability ( bep ) of this receiver approaches the genie bound , which is defined as the bep of detection with perfect csi ( pcsi )
we use @xmath31 to denote the decision on symbol @xmath11 and @xmath32 , @xmath33 , ... , @xmath34 $ ] to denote the decision on the subsequence @xmath35 , @xmath36 , ... , @xmath37 $ ] .
the glrt - mlsd receiver @xmath38 which was derived in @xcite for ook systems and generalised in @xcite for multi - level pam systems , has been shown to be able to achieve the genie bound . in
, @xmath39 is the decision metric and is given as @xmath40 where @xmath41 is the received signal subsequence with length @xmath42 , i.e. , @xmath43 , @xmath44 , ... , @xmath45 $ ] .
this glrt - mlsd receiver continuously and implicitly performs ml estimation of the @xmath10 by ( * ? ? ?
* eq . ( 16 ) ) . here , for any hypothesized subsequence @xmath46
, @xmath21 can be estimated similarly by performing @xmath47 our glrt - mlsd receiver has to evaluate the decision metrics of all possible subsequences and choose the one with largest metric value as the decision . in this section ,
based on , we develop a new simpler decision - feedback symbol - by - symbol receiver .
we first assume that at each time @xmath4 , all the past decisions before time @xmath4 have been completed , and we use @xmath48 $ ] to denote the subsequence whose first @xmath42 elements are @xmath49 , @xmath33 , ... ,
@xmath50 and last element is @xmath11 .
thus , at time @xmath4 , the detection rule given in can be considered as choosing the @xmath11 that maximizes the decision metric value of subsequence @xmath48 $ ] , i.e. , @xmath51 ) .
\label{eq : dfb_0}\ ] ] since @xmath52=\mathbf{r}(k , l+1)$ ] is independent of the detection result , after substituting into , is equivalent to @xmath53\|^2 - \lambda ( [ \hat{\mathbf{m}}(k-1,l),m(k ) ] ) \big ) \nonumber \\ = & \arg \min_{m(k ) }
\| [ \mathbf{r}(k-1,l ) , r(k ) ] \nonumber \\ & \qquad - \hat{a}([\hat{\mathbf{m}}(k-1,l),m(k ) ] ) [ \hat{\mathbf{m}}(k-1,l),m(k ) ] \|^2 .
\label{eq : dfb_deriviation0}\end{aligned}\ ] ] as discussed in section 2 , the channel coherence length @xmath29 is on the order of @xmath54 , which is a very large number .
the channel gain @xmath10 can be safely considered unchanged from time point @xmath55 to @xmath4 .
thus , we can use the ml estimation on @xmath56 based on @xmath57 , denoted by @xmath58 to approximate @xmath59)$ ] , with very high accuracy .
this enables us to further simplify the decision rule to .
@xmath60 - \hat{a}(\hat{\mathbf{m}}(k-1,l ) ) [ \hat{\mathbf{m}}(k-1,l),m(k ) ] \right\|^2 \nonumber \\
= & \arg \min_{m(k ) } \left ( \left\| \mathbf{r}(k-1,l ) - \hat{a}(\hat{\mathbf{m}}(k-1,l ) ) \hat{\mathbf{m}}(k-1,l ) \right\|^2 + \left\| r(k ) - \hat{a}(\hat{\mathbf{m}}(k-1,l ) ) m(k ) \right\|^2 \right ) .
\label{eq : dfb_deriviation2}\end{aligned}\ ] ] since term @xmath61 is independent of @xmath11 , we eliminate it and simplify the decision rule as @xmath62 in principle , to decide based on , one has to compute the value of @xmath63 for each @xmath64 and then choose the @xmath11 corresponding to the minimum @xmath63 value . since @xmath11 may take any value from set @xmath65 and there are totally @xmath0 entities in @xmath65 , for one symbol detection , @xmath0 evaluations of @xmath63are required
thus , the search complexity still increases with @xmath0 linearly . to reduce the complexity
, we can further simplify the decision rule as @xmath66 where @xmath67 is obtained from and @xmath68 is the floor function .
in contrast to implementing , implementing is much simpler .
first , we need to compare @xmath6 to 0 and @xmath69 . if @xmath70 or @xmath71 , the decision is made .
if @xmath72 , we can substitute @xmath6 into @xmath73 and obtain the decision .
totally , the computational complexity is much lower and is independent of the modulation order @xmath0 . after implementing , a reverse gray mapping
is then performed to recovery information bits .
if all the elements of the detected subsequence @xmath74 are zeros , the denominator of @xmath75 given in is zero , resulting in a channel estimation failure .
we propose here a _
selective store strategy _ ( sss ) : at each time @xmath4 , we only store the @xmath76 most recent received signals that have been detected to carry symbol @xmath77 .
since all the signals correspond to the same data symbol @xmath77 , store of detection results is unnecessary , and thus , the estimate of @xmath20 reduces to @xmath78 where @xmath79 is defined as the @xmath80th most recent received signal at time @xmath4 that is detected to carry data symbol @xmath77 . in this way ,
a zero - denominator of the channel estimator will never occur , leading to completely avoiding the channel estimation failure .
we assume all the decisions before time @xmath4 are correct . even in practice
, decisions can not be 100% correct , with a very low error probability , we can assume so when analysing system performance . in the later section that shows simulation results
, we do not assume 100% correct decision feedback .
thus , with the assumption , we have @xmath81 , where @xmath82 is the corresponding awgn term . substituting @xmath81 into and simplifying
, we have @xmath83 obviously , @xmath67 is a gaussian random variable and its mean and variance are the true value of @xmath20 and @xmath84 , respectively .
apparently , we have @xmath85 from ( * ? ?
14.1 ) , we see that for a random variable @xmath86 , if @xmath87 , where @xmath88 is a constant , the random variable @xmath86 equals @xmath88 with probability 1 .
thus , since @xmath89 , we have @xmath90 with probability 1 .
since the estimation of @xmath20 can approach the true value , we can say that the bep of our dfb receiver with sss approaches the genie bound as @xmath76 goes to infinity .
a more general sss is given as follows : we selectively store the @xmath76 most recent received signals and their corresponding detection results with the criterion @xmath91 , where @xmath92 takes value from set @xmath93 .
clearly , @xmath92 is an important parameter and the sss introduced in the previous two paragraphs is an extreme case with @xmath94 .
if @xmath95 , both detected data and corresponding signals are required to be stored , and the required memory length is @xmath96 ; if @xmath94 , since only signals that are detected to carry @xmath77 are required to be stored , the memory length is @xmath76 and the best memory efficiency is achieved .
also , with a fixed value of @xmath76 , a higher value of @xmath92 leads to better performance .
another aspect to consider is to keep the observation window length @xmath97 , which is on the order of @xmath98 , far smaller than the channel coherence length @xmath29 .
thus , to achieve the best performance with a fixed @xmath76 value , we can choose the highest value of @xmath92 that makes @xmath99 .
the bep of symmetric pam over the awgn channel has been studied and given in ( * ? ? ?
* eq.s ( 9 ) and ( 10 ) ) in terms of the average energy per bit @xmath100 and the awgn spectral density @xmath101 .
it should be noticed that @xcite assumed an electrical digital communication system and thus @xmath100 is the electrical - domain average energy per bit .
based on the mapping given in ( * ? ? ?
* eq . ( 2 ) ) which is from @xmath100 to the minimum signal distance @xmath22 , we can obtain its inverse . after substituting this inverse into ( * ? ? ? * eq.s ( 9 ) and ( 10 ) ) , we can derive the general bep expression in terms of the minimum signal distance @xmath20 and the awgn one sided spectral density @xmath101 as .
@xmath102 since is expressed in terms @xmath20 and @xmath101 , it applies to both symmetric and asymmetric pam signals over the awgn channel .
therefore , the bep of the pcsi receiver conditioned on a given value of @xmath10 is @xmath103 , and the average bep over all possible values of @xmath10 is given by @xmath104 this average bep , which is also referred to as the _ genie bound _ , is used as a benchmark when analysing other receivers . specifically ,
when discussing the bep of our receiver , we refer to the average bep over all possible channel states .
from , we see that the average bep is only related to @xmath22 , @xmath101 , @xmath0 and @xmath105 . thus , when the environment condition , i.e. , @xmath105 , the system modulation order @xmath0 and the receiver circuit awgn one - sided psd @xmath101 do not change , using different transmission rates ( different bandwidths ) , to achieve the same error probability
, we need to keep , @xmath106 unchanged . for conventional electrical digital communication systems
, we have @xmath107 which is equivalent to @xmath108 where @xmath100 denotes the electrical - domain energy per bit . from
, we see that when keeping the same level of error probability , @xmath100 is irrelevant to the transmission rate .
this means no matter how fast we transmit data , the energy consumed on each bit does not change , i.e. , to transmit the same amount of data , the total energy consumed is irrelevant to the transmission rate .
however , for optical systems , the situation is different .
the optical - domain energy consumed per bit @xmath109 can be calculated via @xmath110 according to , we have @xmath111 where @xmath112 is defined as the data rate .
we can see that the higher the transmission rate @xmath113 is , the lower the energy consumed on each bit transmission is .
therefore , we can say that , when @xmath22 , @xmath101 , @xmath0 and @xmath105 are unchanged , i.e. , the same level of error probability is retained , to transmit the same amount of data , using a larger data rate ( bandwidth ) is suggested since the total energy consumption is lower . this is because the amplitude of the photo detector output current is proportional to the incident light power @xcite . that means
if we increase the optical power by @xmath114 times , the electrical - domain signal amplitude is increased by @xmath114 times and the electrical - domain signal power is increased by @xmath115 times .
when we use a larger bandwidth , say @xmath116 times of before , to achieve a higher data rate , the noise power , which is the product of the noise power spectral density and the bandwidth , is increased by @xmath116 times . to keep the error probability same ,
the electrical - domain signal power is also required to be increased by @xmath116 times , corresponding to increasing the optical signal power by @xmath117 times . since the transmission rate is increased by @xmath116 times , the required time for transmitting the same amount of data is shortened to @xmath118 of before , and thus the total optical energy consumption is @xmath119 times of before . finally , our conclusion is that using a higher bandwidth is suggested since it saves energy .
it should be emphasized that all the analysis and conclusions in this subsection are based on several basic assumptions : * pin diode is used for photo detection , i.e.
, thermal noise can be regarded as the dominant noise souse and shot noise is negligible * the photo detector will never be saturated by the signal pulse that is with the highest power level * the photo detector can response as fast as the user requires , i.e. , the photo detector bandwidth is no less than the system symbol rate . *
the fso channel is always in a linear regime , where the output power is proportional to the input signal power . without any of the abovementioned assumptions
, the analysis and conclusions may not be true . as discussed in @xcite and @xcite , geometric spread and pointing errors @xmath120 , atmospheric turbulence @xmath121 , and path loss @xmath122 together
determine the overall channel gain @xmath10 .
the channel state @xmath10 is formulated as @xmath123 .
all these three parameters are time - varying for outdoor environments .
the path loss is related to the atmospheric phenomena , such as rain , fog and snow , and the distance between the transmitter and receiver .
therefore , if the distance between the transmitter and the receiver does not chain , @xmath122 changes much slower than @xmath121 and @xmath120 . in @xcite and @xcite , @xmath122 is considered as a deterministic variable while @xmath121 and @xmath120 are considered as random variable . in @xcite
, log - normal distribution is adopted to model @xmath121 for weak turbulence , gamma - gamma distribution for moderate to strong turbulence and the negative exponential distribution for strong turbulence . since in @xcite
, it has been shown that the gamma - gamma distribution can nicely fit the channel fading statistics of all turbulence regimes , in this paper , we only consider @xmath121 is a gamma - gamma distributed random variable , and the pdf of @xmath121 is @xmath124 where @xmath125 is the modified bessel function of the second kind , and @xmath126 and @xmath127 are the variances of the small and large scale eddies , respectively .
pointing error influence on an fso system is discussed in @xcite and @xcite , and we here use the model in @xcite where the pdf of @xmath120 is given as @xmath128 parameter @xmath129 is the fraction of the collected power when no pointing error occurs , and @xmath130 is the ratio between the equivalent beam radius at the receiver and the pointing error displacement standard deviation at the receiver@xcite . without loss of generality
, we can incorporate @xmath122 into @xmath121 which amounts to setting @xmath131 .
then for a turbulent channel with pointing errors , the channel gain is @xmath132 , and by using ( * ? ? ?
* example 13.1.10 ) , its pdf can be derived by @xmath133 full model details can be found in @xcite .
the system parameters of this paper are given as follows : for the weak turbulence channel , @xmath134 , @xmath135 and the corresponding @xmath136 ; for the strong turbulence channel , @xmath137 , @xmath138 and @xmath139 . according to ,
the turbulence with si=0.1244 , which is less than 1 , is in weak irradiance fluctuations regime ; and the turbulence with si=1.3890 , which is larger than 1 , is in moderate - to - strong irradiance fluctuations regime .
the pointing error parameters are chosen to be @xmath140 and @xmath141 . without loss of generality , the photo detector responsivity @xmath9 is assumed to be 1 and the expected channel gain @xmath142 $ ] is set to be 1 .
additionally , we assume the system data rate @xmath113 is on the order of 10 gbps , thus the symbol duration @xmath143 is on the order of @xmath144s and the channel coherence length @xmath29 can be safely regarded as @xmath54 data symbols .
we consider the typical thermal noise , which is -174dbm / hz , passing through a 50@xmath145 receiver circuit .
thus , the value of @xmath17 is @xmath146 , i.e. , @xmath147 . in fig .
[ fg : bep_vs_snr_sss2 ] , we plot the bep versus average receive power curves of our dfb receiver . since the implementation complexity of our dfb receiver is independent of @xmath0 , we show simulation results with up to @xmath148 .
we see that as the value of @xmath76 increases , the bep decreases . to achieve the genie bound ,
the required value of @xmath76 is 12 for the weak turbulence channel and no larger than 16 for the strong turbulence channel . from fig .
[ fg : bep_vs_snr_sss2 ] , we see that if we keep the data rate unchanged and increase @xmath0 to save bandwidth , to achieve the same error probability , we need to increase the transmit power .
this means bandwidth and power are a pair of contradictions .
we can hardly minimize both of them simultaneously , but we can select appropriate values according to practical requirements .
another interesting observation is that if we keep @xmath0 unchanged and use a larger bandwidth to achieve a higher data rate , to achieve the same level error probability , the multiple of the power growth is the square root of that of the data rate growth . specifically , from fig .
[ fg : bep_vs_snr_sss2 ] , we can see that for @xmath149 , if we increase the data rate from 10 gbps to 20 gbps , the corresponding power increment is less than 3db , approximately 1.5 db . to further study the receiver performance with more values of memory lengths , we plot fig .
[ fg : bep_vs_l ] . for the reason of space limit
, we only pick one ( @xmath0 , average receive power , data rate , si ) point here , which is ( @xmath150 , -1 dbm , 40 gbps , si=1.3890 ) .
clearly , as the value of @xmath76 increases , all the bep curve approach the corresponding genie bound . in fig .
[ fg : estimation ] , we plot the estimate of @xmath20 with different memory lengths .
we assume ook modulation and choose @xmath151 .
the numerical results given in fig .
[ fg : estimation ] completely agree with the theoretical analysis given in the previous section .
thus , we have shown that , by both theoretical analysis and simulation , with a higher value of @xmath76 , the estimation of @xmath20 is more accurate .
this enables the bep of our dfb receiver to approach the genie bound .
s ; @xmath150 , -1 dbm , 40 gbps , si=1.3890 . ]
when starting to operate our dfb receiver , @xmath76 pilot symbols are required to obtain an initial value of @xmath152 . unlike some other communication systems that require frequent insertion of pilot symbols to avoid burst errors , in our simulation , no burst errors are observed even with only @xmath76 pilot symbols for initializing and no further frequent insertions .
thus , the pilot - to - data ratio is far smaller than 1 , and we do not consider the power consumed by pilots when calculating the average snr per bit .
since the channel coherence length @xmath29 is very large , we can use the detected data symbols to estimate the unknown channel state instead of using pilot symbols which causes spectral efficiency reduction . in this paper , based on the decision metric of our previously proposed glrt - mlsd receiver ,
we propose a dfb symbol - by - symbol receiver , whose implementation complexity is much lower and is independent of the modulation order .
hence , it is efficient both spectrally and computationally .
we also propose a selective - store strategy , which can help avoid potential channel estimation failures and increase the system memory efficiency .
additionally , we derive a general bep expression for both symmetric and asymmetric m - pam signals , by using which as a benchmark , we have shown that as the number of the detected data symbols used to estimate the channel increases , the bep of our dfb receiver approaches the genie bound .
the authors would like to thank the support by the singapore moe acrf tier 2 grant moe2010-t2 - 1 - 101 . t. song and p .- y .
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_ , vol . 27 , no . 18 , pp . 3965 3973 , sep | to detect @xmath0-ary pulse amplitude modulation signals reliably in an fso communication system , the receiver requires accurate knowledge about the instantaneous channel attenuation on the signal . we derive here an optimum
, symbol - by - symbol receiver that jointly estimates the attenuation with the help of past detected data symbols and detects the data symbols accordingly .
few pilot symbols are required , resulting in high spectral efficiency .
detection can be performed with a very low complexity . from both theoretical analysis and simulation ,
we show that as the number of the detected data symbols used for estimating the channel attenuation increases , the bit error probability of our receiver approaches that of detection with perfect channel knowledge . | <s>[INST]in most current free space optical ( fso ) communication systems , for reasons of simplicity , intensity modulation with direct detection ( im / dd ) is used . to improve the spectral efficiency , we consider @xmath0-ary pulse amplitude modulation ( mpam ) here by presuming that the receiver photodetector will not be saturated by the impinging optical signal level that has the highest energy .
the transmitter side constellation is shown in fig .
[ fg : cons_tx ] , where @xmath1 denotes the minimum signal intensity distance and the transmitter average power is defined as @xmath2 . inside the receiver , as shown in fig .
[ fg : receiver ] , there is an integrator that integrates the photo current for each symbol period @xmath3 . for the @xmath4th symbol interval ( @xmath5 ) ,
the received electrical signal @xmath6 is obtained by sampling the integrator at time @xmath7 .
since the photo current can be assumed to be constant during the integration time , @xmath6 can be expressed as @xcite @xmath8 where @xmath9 is the responsivity of the photo detector and @xmath10 denotes the instantaneous channel gain .
the transmitted data symbol @xmath11 takes on any value from set @xmath12 with equal probability , and gray mapping of bits onto the levels is assumed . in practice , multiplying the received signal by the normalising basis @xmath13 , which is shown in fig .
[ fg : receiver ] , is not necessary .
we use it here because we want to simplify later performance analysis by normalizing the discrete additive white gaussian noise ( awgn ) term @xmath14 such that @xmath15=\delta _ { ij } { n_0}/{2 } $ ] conditioned on that the continuous noise term @xmath16 is an additive white gaussian random process with mean zero and two - sided spectral density @xmath17 . by defining @xmath18 as the instantaneous receiver - side electrical - domain minimum signal distance
, @xmath6 can be modelled as @xcite @xmath19 correspondingly , the receiver side constellation is shown in fig .
[ fg : cons_rx ] . since atmospheric turbulence and pointing errors cause fluctuations in the intensity of the received signal , i.e. , @xmath10 is time - varying ,
therefore , @xmath20 is time - varying and is modelled as @xmath21 where @xmath22 denotes the minimum signal distance when @xmath23 , i.e. , @xmath24 , which is related to the average transmit power @xmath25 , i.e. , @xmath26 for the on - off keying ( ook ) system that is considered as the simplest mpam ( @xmath27 ) case , the turbulence and pointing error induced fading is the major issue that degrades system performance .
thus , the accurate channel state information ( csi ) , i.e. , the accurate instantaneous value of @xmath10 , is required for properly adjusting the decision threshold . in previous studies , frequent insertions of pilot symbols
@xcite or co - propagating reference light @xcite is used to estimate the csi . in this paper ,
when it comes to pilot symbols , we specifically refer to pilot symbols used for channel estimation . in practice
, pilot symbols are also required for other purposes such as timing synchronization .
since pilot symbols do not carry data , the use of them results in a system spectral efficiency reduction and additional energy overheads .
therefore , we hope to minimize the amount of pilot symbols . the co - propagating reference light has the same problem , and besides , since it has a different frequency with the signal - bearing light , the estimation result may not be accurate . for mpam systems ( @xmath28 ) , to detect signals reliably , the requirement of accurate csi is more stringent .
the difficulty of accurate csi acquisition is the main reason that limits the use of mpam in practical systems . however , though these two above - mentioned methods can be extended to mpam systems , they are not so suitable in practice .
the receiver design problem remains challenged by the fact that the csi is hard to acquire at the receiver side if very few pilot symbols and no co - propagating reference light are used . since the channel coherence length
@xmath29 , defined as the number of consecutive data symbol intervals over which the channel gain @xmath10 can be considered to be constant , is a very large number ( @xmath30 ) for multi - gbps systems@xcite , the data and the csi can be jointly detected and estimated . in @xcite , for the 2-level pam system , i.e. , the ook system , based on the generalized likelihood ratio test ( glrt ) principle , we derived a maximum likelihood ( ml ) sequence detection receiver ( the glrt - mlsd receiver ) that jointly detects the data sequence and estimates the unknown channel gain . in @xcite , we have extended this glrt - mlsd receiver to multi - level pam systems . however , as we discussed in @xcite , the search complexity of the glrt - mlsd receiver increases with the modulation order @xmath0 almost quadratically .
therefore , in section ii of this paper , we derive a simpler decision - feedback ( dfb ) , symbol - by - symbol receiver , whose implementation complexity is independent of the modulation order @xmath0 .
it uses the most recently detected data symbols to help estimate the instantaneous channel gain . as the number of the detected data symbols used to estimate the channel increases , the bit error probability ( bep ) of this receiver approaches the genie bound , which is defined as the bep of detection with perfect csi ( pcsi )
we use @xmath31 to denote the decision on symbol @xmath11 and @xmath32 , @xmath33 , ... , @xmath34 $ ] to denote the decision on the subsequence @xmath35 , @xmath36 , ... , @xmath37 $ ] .
the glrt - mlsd receiver @xmath38 which was derived in @xcite for ook systems and generalised in @xcite for multi - level pam systems , has been shown to be able to achieve the genie bound . in
, @xmath39 is the decision metric and is given as @xmath40 where @xmath41 is the received signal subsequence with length @xmath42 , i.e. , @xmath43 , @xmath44 , ... , @xmath45 $ ] .
this glrt - mlsd receiver continuously and implicitly performs ml estimation of the @xmath10 by ( * ? ? ?
* eq . ( 16 ) ) . here , for any hypothesized subsequence @xmath46
, @xmath21 can be estimated similarly by performing @xmath47 our glrt - mlsd receiver has to evaluate the decision metrics of all possible subsequences and choose the one with largest metric value as the decision . in this section ,
based on , we develop a new simpler decision - feedback symbol - by - symbol receiver .
we first assume that at each time @xmath4 , all the past decisions before time @xmath4 have been completed , and we use @xmath48 $ ] to denote the subsequence whose first @xmath42 elements are @xmath49 , @xmath33 , ... ,
@xmath50 and last element is @xmath11 .
thus , at time @xmath4 , the detection rule given in can be considered as choosing the @xmath11 that maximizes the decision metric value of subsequence @xmath48 $ ] , i.e. , @xmath51 ) .
\label{eq : dfb_0}\ ] ] since @xmath52=\mathbf{r}(k , l+1)$ ] is independent of the detection result , after substituting into , is equivalent to @xmath53\|^2 - \lambda ( [ \hat{\mathbf{m}}(k-1,l),m(k ) ] ) \big ) \nonumber \\ = & \arg \min_{m(k ) }
\| [ \mathbf{r}(k-1,l ) , r(k ) ] \nonumber \\ & \qquad - \hat{a}([\hat{\mathbf{m}}(k-1,l),m(k ) ] ) [ \hat{\mathbf{m}}(k-1,l),m(k ) ] \|^2 .
\label{eq : dfb_deriviation0}\end{aligned}\ ] ] as discussed in section 2 , the channel coherence length @xmath29 is on the order of @xmath54 , which is a very large number .
the channel gain @xmath10 can be safely considered unchanged from time point @xmath55 to @xmath4 .
thus , we can use the ml estimation on @xmath56 based on @xmath57 , denoted by @xmath58 to approximate @xmath59)$ ] , with very high accuracy .
this enables us to further simplify the decision rule to .
@xmath60 - \hat{a}(\hat{\mathbf{m}}(k-1,l ) ) [ \hat{\mathbf{m}}(k-1,l),m(k ) ] \right\|^2 \nonumber \\
= & \arg \min_{m(k ) } \left ( \left\| \mathbf{r}(k-1,l ) - \hat{a}(\hat{\mathbf{m}}(k-1,l ) ) \hat{\mathbf{m}}(k-1,l ) \right\|^2 + \left\| r(k ) - \hat{a}(\hat{\mathbf{m}}(k-1,l ) ) m(k ) \right\|^2 \right ) .
\label{eq : dfb_deriviation2}\end{aligned}\ ] ] since term @xmath61 is independent of @xmath11 , we eliminate it and simplify the decision rule as @xmath62 in principle , to decide based on , one has to compute the value of @xmath63 for each @xmath64 and then choose the @xmath11 corresponding to the minimum @xmath63 value . since @xmath11 may take any value from set @xmath65 and there are totally @xmath0 entities in @xmath65 , for one symbol detection , @xmath0 evaluations of @xmath63are required
thus , the search complexity still increases with @xmath0 linearly . to reduce the complexity
, we can further simplify the decision rule as @xmath66 where @xmath67 is obtained from and @xmath68 is the floor function .
in contrast to implementing , implementing is much simpler .
first , we need to compare @xmath6 to 0 and @xmath69 . if @xmath70 or @xmath71 , the decision is made .
if @xmath72 , we can substitute @xmath6 into @xmath73 and obtain the decision .
totally , the computational complexity is much lower and is independent of the modulation order @xmath0 . after implementing , a reverse gray mapping
is then performed to recovery information bits .
if all the elements of the detected subsequence @xmath74 are zeros , the denominator of @xmath75 given in is zero , resulting in a channel estimation failure .
we propose here a _
selective store strategy _ ( sss ) : at each time @xmath4 , we only store the @xmath76 most recent received signals that have been detected to carry symbol @xmath77 .
since all the signals correspond to the same data symbol @xmath77 , store of detection results is unnecessary , and thus , the estimate of @xmath20 reduces to @xmath78 where @xmath79 is defined as the @xmath80th most recent received signal at time @xmath4 that is detected to carry data symbol @xmath77 . in this way ,
a zero - denominator of the channel estimator will never occur , leading to completely avoiding the channel estimation failure .
we assume all the decisions before time @xmath4 are correct . even in practice
, decisions can not be 100% correct , with a very low error probability , we can assume so when analysing system performance . in the later section that shows simulation results
, we do not assume 100% correct decision feedback .
thus , with the assumption , we have @xmath81 , where @xmath82 is the corresponding awgn term . substituting @xmath81 into and simplifying
, we have @xmath83 obviously , @xmath67 is a gaussian random variable and its mean and variance are the true value of @xmath20 and @xmath84 , respectively .
apparently , we have @xmath85 from ( * ? ?
14.1 ) , we see that for a random variable @xmath86 , if @xmath87 , where @xmath88 is a constant , the random variable @xmath86 equals @xmath88 with probability 1 .
thus , since @xmath89 , we have @xmath90 with probability 1 .
since the estimation of @xmath20 can approach the true value , we can say that the bep of our dfb receiver with sss approaches the genie bound as @xmath76 goes to infinity .
a more general sss is given as follows : we selectively store the @xmath76 most recent received signals and their corresponding detection results with the criterion @xmath91 , where @xmath92 takes value from set @xmath93 .
clearly , @xmath92 is an important parameter and the sss introduced in the previous two paragraphs is an extreme case with @xmath94 .
if @xmath95 , both detected data and corresponding signals are required to be stored , and the required memory length is @xmath96 ; if @xmath94 , since only signals that are detected to carry @xmath77 are required to be stored , the memory length is @xmath76 and the best memory efficiency is achieved .
also , with a fixed value of @xmath76 , a higher value of @xmath92 leads to better performance .
another aspect to consider is to keep the observation window length @xmath97 , which is on the order of @xmath98 , far smaller than the channel coherence length @xmath29 .
thus , to achieve the best performance with a fixed @xmath76 value , we can choose the highest value of @xmath92 that makes @xmath99 .
the bep of symmetric pam over the awgn channel has been studied and given in ( * ? ? ?
* eq.s ( 9 ) and ( 10 ) ) in terms of the average energy per bit @xmath100 and the awgn spectral density @xmath101 .
it should be noticed that @xcite assumed an electrical digital communication system and thus @xmath100 is the electrical - domain average energy per bit .
based on the mapping given in ( * ? ? ?
* eq . ( 2 ) ) which is from @xmath100 to the minimum signal distance @xmath22 , we can obtain its inverse . after substituting this inverse into ( * ? ? ? * eq.s ( 9 ) and ( 10 ) ) , we can derive the general bep expression in terms of the minimum signal distance @xmath20 and the awgn one sided spectral density @xmath101 as .
@xmath102 since is expressed in terms @xmath20 and @xmath101 , it applies to both symmetric and asymmetric pam signals over the awgn channel .
therefore , the bep of the pcsi receiver conditioned on a given value of @xmath10 is @xmath103 , and the average bep over all possible values of @xmath10 is given by @xmath104 this average bep , which is also referred to as the _ genie bound _ , is used as a benchmark when analysing other receivers . specifically ,
when discussing the bep of our receiver , we refer to the average bep over all possible channel states .
from , we see that the average bep is only related to @xmath22 , @xmath101 , @xmath0 and @xmath105 . thus , when the environment condition , i.e. , @xmath105 , the system modulation order @xmath0 and the receiver circuit awgn one - sided psd @xmath101 do not change , using different transmission rates ( different bandwidths ) , to achieve the same error probability
, we need to keep , @xmath106 unchanged . for conventional electrical digital communication systems
, we have @xmath107 which is equivalent to @xmath108 where @xmath100 denotes the electrical - domain energy per bit . from
, we see that when keeping the same level of error probability , @xmath100 is irrelevant to the transmission rate .
this means no matter how fast we transmit data , the energy consumed on each bit does not change , i.e. , to transmit the same amount of data , the total energy consumed is irrelevant to the transmission rate .
however , for optical systems , the situation is different .
the optical - domain energy consumed per bit @xmath109 can be calculated via @xmath110 according to , we have @xmath111 where @xmath112 is defined as the data rate .
we can see that the higher the transmission rate @xmath113 is , the lower the energy consumed on each bit transmission is .
therefore , we can say that , when @xmath22 , @xmath101 , @xmath0 and @xmath105 are unchanged , i.e. , the same level of error probability is retained , to transmit the same amount of data , using a larger data rate ( bandwidth ) is suggested since the total energy consumption is lower . this is because the amplitude of the photo detector output current is proportional to the incident light power @xcite . that means
if we increase the optical power by @xmath114 times , the electrical - domain signal amplitude is increased by @xmath114 times and the electrical - domain signal power is increased by @xmath115 times .
when we use a larger bandwidth , say @xmath116 times of before , to achieve a higher data rate , the noise power , which is the product of the noise power spectral density and the bandwidth , is increased by @xmath116 times . to keep the error probability same ,
the electrical - domain signal power is also required to be increased by @xmath116 times , corresponding to increasing the optical signal power by @xmath117 times . since the transmission rate is increased by @xmath116 times , the required time for transmitting the same amount of data is shortened to @xmath118 of before , and thus the total optical energy consumption is @xmath119 times of before . finally , our conclusion is that using a higher bandwidth is suggested since it saves energy .
it should be emphasized that all the analysis and conclusions in this subsection are based on several basic assumptions : * pin diode is used for photo detection , i.e.
, thermal noise can be regarded as the dominant noise souse and shot noise is negligible * the photo detector will never be saturated by the signal pulse that is with the highest power level * the photo detector can response as fast as the user requires , i.e. , the photo detector bandwidth is no less than the system symbol rate . *
the fso channel is always in a linear regime , where the output power is proportional to the input signal power . without any of the abovementioned assumptions
, the analysis and conclusions may not be true . as discussed in @xcite and @xcite , geometric spread and pointing errors @xmath120 , atmospheric turbulence @xmath121 , and path loss @xmath122 together
determine the overall channel gain @xmath10 .
the channel state @xmath10 is formulated as @xmath123 .
all these three parameters are time - varying for outdoor environments .
the path loss is related to the atmospheric phenomena , such as rain , fog and snow , and the distance between the transmitter and receiver .
therefore , if the distance between the transmitter and the receiver does not chain , @xmath122 changes much slower than @xmath121 and @xmath120 . in @xcite and @xcite , @xmath122 is considered as a deterministic variable while @xmath121 and @xmath120 are considered as random variable . in @xcite
, log - normal distribution is adopted to model @xmath121 for weak turbulence , gamma - gamma distribution for moderate to strong turbulence and the negative exponential distribution for strong turbulence . since in @xcite
, it has been shown that the gamma - gamma distribution can nicely fit the channel fading statistics of all turbulence regimes , in this paper , we only consider @xmath121 is a gamma - gamma distributed random variable , and the pdf of @xmath121 is @xmath124 where @xmath125 is the modified bessel function of the second kind , and @xmath126 and @xmath127 are the variances of the small and large scale eddies , respectively .
pointing error influence on an fso system is discussed in @xcite and @xcite , and we here use the model in @xcite where the pdf of @xmath120 is given as @xmath128 parameter @xmath129 is the fraction of the collected power when no pointing error occurs , and @xmath130 is the ratio between the equivalent beam radius at the receiver and the pointing error displacement standard deviation at the receiver@xcite . without loss of generality
, we can incorporate @xmath122 into @xmath121 which amounts to setting @xmath131 .
then for a turbulent channel with pointing errors , the channel gain is @xmath132 , and by using ( * ? ? ?
* example 13.1.10 ) , its pdf can be derived by @xmath133 full model details can be found in @xcite .
the system parameters of this paper are given as follows : for the weak turbulence channel , @xmath134 , @xmath135 and the corresponding @xmath136 ; for the strong turbulence channel , @xmath137 , @xmath138 and @xmath139 . according to ,
the turbulence with si=0.1244 , which is less than 1 , is in weak irradiance fluctuations regime ; and the turbulence with si=1.3890 , which is larger than 1 , is in moderate - to - strong irradiance fluctuations regime .
the pointing error parameters are chosen to be @xmath140 and @xmath141 . without loss of generality , the photo detector responsivity @xmath9 is assumed to be 1 and the expected channel gain @xmath142 $ ] is set to be 1 .
additionally , we assume the system data rate @xmath113 is on the order of 10 gbps , thus the symbol duration @xmath143 is on the order of @xmath144s and the channel coherence length @xmath29 can be safely regarded as @xmath54 data symbols .
we consider the typical thermal noise , which is -174dbm / hz , passing through a 50@xmath145 receiver circuit .
thus , the value of @xmath17 is @xmath146 , i.e. , @xmath147 . in fig .
[ fg : bep_vs_snr_sss2 ] , we plot the bep versus average receive power curves of our dfb receiver . since the implementation complexity of our dfb receiver is independent of @xmath0 , we show simulation results with up to @xmath148 .
we see that as the value of @xmath76 increases , the bep decreases . to achieve the genie bound ,
the required value of @xmath76 is 12 for the weak turbulence channel and no larger than 16 for the strong turbulence channel . from fig .
[ fg : bep_vs_snr_sss2 ] , we see that if we keep the data rate unchanged and increase @xmath0 to save bandwidth , to achieve the same error probability , we need to increase the transmit power .
this means bandwidth and power are a pair of contradictions .
we can hardly minimize both of them simultaneously , but we can select appropriate values according to practical requirements .
another interesting observation is that if we keep @xmath0 unchanged and use a larger bandwidth to achieve a higher data rate , to achieve the same level error probability , the multiple of the power growth is the square root of that of the data rate growth . specifically , from fig .
[ fg : bep_vs_snr_sss2 ] , we can see that for @xmath149 , if we increase the data rate from 10 gbps to 20 gbps , the corresponding power increment is less than 3db , approximately 1.5 db . to further study the receiver performance with more values of memory lengths , we plot fig .
[ fg : bep_vs_l ] . for the reason of space limit
, we only pick one ( @xmath0 , average receive power , data rate , si ) point here , which is ( @xmath150 , -1 dbm , 40 gbps , si=1.3890 ) .
clearly , as the value of @xmath76 increases , all the bep curve approach the corresponding genie bound . in fig .
[ fg : estimation ] , we plot the estimate of @xmath20 with different memory lengths .
we assume ook modulation and choose @xmath151 .
the numerical results given in fig .
[ fg : estimation ] completely agree with the theoretical analysis given in the previous section .
thus , we have shown that , by both theoretical analysis and simulation , with a higher value of @xmath76 , the estimation of @xmath20 is more accurate .
this enables the bep of our dfb receiver to approach the genie bound .
s ; @xmath150 , -1 dbm , 40 gbps , si=1.3890 . ]
when starting to operate our dfb receiver , @xmath76 pilot symbols are required to obtain an initial value of @xmath152 . unlike some other communication systems that require frequent insertion of pilot symbols to avoid burst errors , in our simulation , no burst errors are observed even with only @xmath76 pilot symbols for initializing and no further frequent insertions .
thus , the pilot - to - data ratio is far smaller than 1 , and we do not consider the power consumed by pilots when calculating the average snr per bit .
since the channel coherence length @xmath29 is very large , we can use the detected data symbols to estimate the unknown channel state instead of using pilot symbols which causes spectral efficiency reduction . in this paper , based on the decision metric of our previously proposed glrt - mlsd receiver ,
we propose a dfb symbol - by - symbol receiver , whose implementation complexity is much lower and is independent of the modulation order .
hence , it is efficient both spectrally and computationally .
we also propose a selective - store strategy , which can help avoid potential channel estimation failures and increase the system memory efficiency .
additionally , we derive a general bep expression for both symmetric and asymmetric m - pam signals , by using which as a benchmark , we have shown that as the number of the detected data symbols used to estimate the channel increases , the bep of our dfb receiver approaches the genie bound .
the authors would like to thank the support by the singapore moe acrf tier 2 grant moe2010-t2 - 1 - 101 . t. song and p .- y .
kam , `` efficient direct detection of @xmath0-pam sequences with implicit csi acquisition for the fso system , '' in _ proc .
globecom workshops ( gc wkshps ) , 2014 _ , dec . 2014 , pp . 475480 .
z. wang , w .- d .
zhong , c. yu , and s. fu , `` performance improvement of on - off - keying free - space optical transmission systems by a co - propagating reference continuous wave light , '' _ optics express _ , vol . 20 , no . 8 , pp . 92849295 , apr .
g. xie , a. dang , and h. guo , `` effects of atmosphere dominated phase fluctuation and intensity scintillation to dpsk system , '' in _ communications ( icc ) , 2011 ieee international conference on _ , 2011 , pp .
t. song and p. y. kam , `` a robust glrt receiver with implicit channel estimation and automatic threshold adjustment for the free space optical channel with im / dd , '' _ j. lightw .
technol _ , vol .
32 , no . 3 , pp .
369383 , feb .
2014 .
m. riediger , r. schober , and l. lampe , `` multiple - symbol detection for photon - counting mimo free - space optical communications , '' _ ieee trans .
wireless commun .
_ , vol . 7 , no . 12 , pp . 5369 5378 , dec
. 2008 .
m. a. al - habash , l. c. andrews , and r. l. phillips , `` mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media , '' _ optical engineering _ , vol .
40 , no . 8 , pp .
15541562 , aug .
d. borah and d. voelz , `` pointing error effects on free - space optical communication links in the presence of atmospheric turbulence , '' _ j. lightw
. technol .
_ , vol . 27 , no . 18 , pp . 3965 3973 , sep[/INST] to detect @xmath0-ary pulse amplitude modulation signals reliably in an fso communication system , the receiver requires accurate knowledge about the instantaneous channel attenuation on the signal . we derive here an optimum
, symbol - by - symbol receiver that jointly estimates the attenuation with the help of past detected data symbols and detects the data symbols accordingly .
few pilot symbols are required , resulting in high spectral efficiency .
detection can be performed with a very low complexity . from both theoretical analysis and simulation ,
we show that as the number of the detected data symbols used for estimating the channel attenuation increases , the bit error probability of our receiver approaches that of detection with perfect channel knowledge . </s> |
Starving koalas secretly culled at Cape Otway, 'overpopulation issues' blamed for ill health
Updated
Almost 700 koalas have been culled in the Cape Otway area of western Victoria because of "overpopulation issues", according to the state's Environment Minister.
The secret cull was done under the previous Liberal government in 2013 and 2014 near the Great Ocean Road.
The koalas were captured and sedated before being put down by wildlife officials.
Environment Minister Lisa Neville called it "a very challenging and complex issue" and said any means to address it must be both "humane and effective".
The Minister said she was seeking advice from experts and a special koala management program would be put in place.
"It is clear it's an overpopulation issue and it is clear that we have had koalas suffer in that Cape Otway area because of ill health and starvation," she said.
"That's just not good enough and that's a terrible way to treat koalas.
"I'm wanting to make sure that we're taking the best action we can in this terrible situation of overpopulation.
"I don't want to see koalas suffer."
Ms Neville promised to be "transparent" with the Victorian community about any action taken to deal with the problem in future.
"Experience suggests that moving these koalas does not work and that can in fact cause even greater suffering," Ms Neville said.
Despite the cull, overpopulation remains a problem in the area.
"[The number] continues to increase and that's why we need to have a look at a koala management strategy to see whether we can reduce that population growth which continues at a very fast pace," she said.
"In this case it is about how we treat and care for koalas which are clearly loved by many Victorians and many people across the world.
"We need to stop their suffering. Our priority must be about treating these koalas humanely."
'The whole of the cape smelled of dead koalas'
Frank Fotinas runs the Bimbi Park Caravan Park at Cape Otway, which promotes camping under koalas.
While they are good for business, Mr Fotinas said the koalas were stripping the trees, leaving acres and acres of dead wood.
"Koalas are great for business but if there's no trees, there's no koalas," he said.
He said the animals were not culled, they were euthanased because they were starving to death and many more died of natural causes.
"A lot more were dying naturally than were euthanased," he said.
"The whole of the cape smelled of dead koalas. It smelled like death.
"You should come and look at the trees. There are hundreds of acres of dead trees."
Mr Fotinas said locals had planted 70,000 banded trees to keep the koalas away and the situation was better than a couple of years ago.
"We just need to constantly remind people about it," he said.
"We need more government intervention. We need DEPI [the Department of Environment and Primary Industries] here."
Topics: animals, states-and-territories, animal-welfare, apollo-bay-3233
First posted ||||| Koalas in Cape Otway are starving due to overpopulation. Photo: Australia Zoo
More than 600 starving koalas were killed in secret culls in the Cape Otway area of western Victoria, it has been revealed.
Wildlife officials did three euthanasia sweeps to kill 686 koalas in 2013 and 2014, in a covert campaign that was designed to avoid any backlash from green groups and the community.
The secret cull was conducted under the previous Liberal government near the Great Ocean Road to address overpopulation issues.
Where the koalas were culled.
The marsupials were starving due to overpopulation in the Cape region, which is said to have the greatest density of koalas in Australia.
Advertisement
The koalas were captured and sedated before being put down.
Koala expert Dr Desley Wisson, from Deakin University, told radio station 3AW the cull was needed.
"Koalas had built up to quite high densities in manna gum areas down at Cape Otway," she said.
"It got to the point where there were no leaves left on the trees and the koalas were literally falling out of trees.
"They were dying of starvation."
Dr Wisson said the koalas had been introduced to the Cape manna gum areas.
"They absolutely adore manna gum ... so they tend to find those manna gum locations and just sit there," she said.
But it was difficult to relocate the koalas.
"It's actually not a very nice thing to move a koala; a lot of them will actually die [from stress] during that process."
Environment Minister Lisa Neville told radio station 3AW no more culls would be done in secret. She would put in place a special koala management program after seeking advice from experts.
"I don't want to see koalas suffer," Ms Neville said.
"I'm making sure the advice comes to me as quickly as we can and we will obviously be very open and transparent with the community.
"It is challenging, it is distressing ... but I think it's absolutely important that we are open with the community."
Frank Fotinas, who runs the Bimbi Park Caravan Park at Cape Otway, told ABC radio the area smelt of dead koalas.
"A lot more were dying naturally than were euthanased," he said.
"The whole of the Cape smelt of dead koalas.
"It smelt like death. You should come and look at the trees. There are hundreds of acres of dead trees." | – Koalas' numbers on one part of Australia are too big for their own good, and some are starving—so officials have quietly been culling their population, Australia's ABC News reports. "We have had koalas suffer in that Cape Otway area because of ill health and starvation" amid overpopulation, says environment minister Lisa Neville. About 700 koalas were secretly killed in 2013 and 2014 under a prior government, ABC reports; the animals were sedated, then euthanized. But the population problem remains. "We need to stop their suffering. Our priority must be about treating these koalas humanely," Neville says, noting that future efforts will be more "transparent." The head of a site that allows camping amid koalas says the animals were destroying hundreds of acres of trees. And "if there's no trees, there's no koalas," he points out. "A lot more were dying naturally than were euthanized," he adds, noting that "the whole of the cape smelled of dead koalas." An expert tells Australian radio station 3AW that koalas "were literally falling out of trees due to starvation." The region is believed to have the highest density of koalas in the country, the Age reports. But moving the animals doesn't seem to be an option: "It's actually not a very nice thing to move a koala; a lot of them will die (from stress) during the move," the expert tells 3AW. (This firefighter went to great lengths to save a koala.) | <s>[INST]Starving koalas secretly culled at Cape Otway, 'overpopulation issues' blamed for ill health
Updated
Almost 700 koalas have been culled in the Cape Otway area of western Victoria because of "overpopulation issues", according to the state's Environment Minister.
The secret cull was done under the previous Liberal government in 2013 and 2014 near the Great Ocean Road.
The koalas were captured and sedated before being put down by wildlife officials.
Environment Minister Lisa Neville called it "a very challenging and complex issue" and said any means to address it must be both "humane and effective".
The Minister said she was seeking advice from experts and a special koala management program would be put in place.
"It is clear it's an overpopulation issue and it is clear that we have had koalas suffer in that Cape Otway area because of ill health and starvation," she said.
"That's just not good enough and that's a terrible way to treat koalas.
"I'm wanting to make sure that we're taking the best action we can in this terrible situation of overpopulation.
"I don't want to see koalas suffer."
Ms Neville promised to be "transparent" with the Victorian community about any action taken to deal with the problem in future.
"Experience suggests that moving these koalas does not work and that can in fact cause even greater suffering," Ms Neville said.
Despite the cull, overpopulation remains a problem in the area.
"[The number] continues to increase and that's why we need to have a look at a koala management strategy to see whether we can reduce that population growth which continues at a very fast pace," she said.
"In this case it is about how we treat and care for koalas which are clearly loved by many Victorians and many people across the world.
"We need to stop their suffering. Our priority must be about treating these koalas humanely."
'The whole of the cape smelled of dead koalas'
Frank Fotinas runs the Bimbi Park Caravan Park at Cape Otway, which promotes camping under koalas.
While they are good for business, Mr Fotinas said the koalas were stripping the trees, leaving acres and acres of dead wood.
"Koalas are great for business but if there's no trees, there's no koalas," he said.
He said the animals were not culled, they were euthanased because they were starving to death and many more died of natural causes.
"A lot more were dying naturally than were euthanased," he said.
"The whole of the cape smelled of dead koalas. It smelled like death.
"You should come and look at the trees. There are hundreds of acres of dead trees."
Mr Fotinas said locals had planted 70,000 banded trees to keep the koalas away and the situation was better than a couple of years ago.
"We just need to constantly remind people about it," he said.
"We need more government intervention. We need DEPI [the Department of Environment and Primary Industries] here."
Topics: animals, states-and-territories, animal-welfare, apollo-bay-3233
First posted ||||| Koalas in Cape Otway are starving due to overpopulation. Photo: Australia Zoo
More than 600 starving koalas were killed in secret culls in the Cape Otway area of western Victoria, it has been revealed.
Wildlife officials did three euthanasia sweeps to kill 686 koalas in 2013 and 2014, in a covert campaign that was designed to avoid any backlash from green groups and the community.
The secret cull was conducted under the previous Liberal government near the Great Ocean Road to address overpopulation issues.
Where the koalas were culled.
The marsupials were starving due to overpopulation in the Cape region, which is said to have the greatest density of koalas in Australia.
Advertisement
The koalas were captured and sedated before being put down.
Koala expert Dr Desley Wisson, from Deakin University, told radio station 3AW the cull was needed.
"Koalas had built up to quite high densities in manna gum areas down at Cape Otway," she said.
"It got to the point where there were no leaves left on the trees and the koalas were literally falling out of trees.
"They were dying of starvation."
Dr Wisson said the koalas had been introduced to the Cape manna gum areas.
"They absolutely adore manna gum ... so they tend to find those manna gum locations and just sit there," she said.
But it was difficult to relocate the koalas.
"It's actually not a very nice thing to move a koala; a lot of them will actually die [from stress] during that process."
Environment Minister Lisa Neville told radio station 3AW no more culls would be done in secret. She would put in place a special koala management program after seeking advice from experts.
"I don't want to see koalas suffer," Ms Neville said.
"I'm making sure the advice comes to me as quickly as we can and we will obviously be very open and transparent with the community.
"It is challenging, it is distressing ... but I think it's absolutely important that we are open with the community."
Frank Fotinas, who runs the Bimbi Park Caravan Park at Cape Otway, told ABC radio the area smelt of dead koalas.
"A lot more were dying naturally than were euthanased," he said.
"The whole of the Cape smelt of dead koalas.
"It smelt like death. You should come and look at the trees. There are hundreds of acres of dead trees."[/INST]– Koalas' numbers on one part of Australia are too big for their own good, and some are starving—so officials have quietly been culling their population, Australia's ABC News reports. "We have had koalas suffer in that Cape Otway area because of ill health and starvation" amid overpopulation, says environment minister Lisa Neville. About 700 koalas were secretly killed in 2013 and 2014 under a prior government, ABC reports; the animals were sedated, then euthanized. But the population problem remains. "We need to stop their suffering. Our priority must be about treating these koalas humanely," Neville says, noting that future efforts will be more "transparent." The head of a site that allows camping amid koalas says the animals were destroying hundreds of acres of trees. And "if there's no trees, there's no koalas," he points out. "A lot more were dying naturally than were euthanized," he adds, noting that "the whole of the cape smelled of dead koalas." An expert tells Australian radio station 3AW that koalas "were literally falling out of trees due to starvation." The region is believed to have the highest density of koalas in the country, the Age reports. But moving the animals doesn't seem to be an option: "It's actually not a very nice thing to move a koala; a lot of them will die (from stress) during the move," the expert tells 3AW. (This firefighter went to great lengths to save a koala.)</s> |
the observation of neutrinoless double-@xmath0 @xmath5 decays would demonstrate the majorana nature of neutrinos @xcite , representing direct evidence for physics beyond the standard model . neutrinoless double-@xmath0 decay is a second - order electroweak process where a nucleus decays through the emission of two electrons , @xmath6 , thereby violating lepton number . the half - life of the isotope decaying through @xmath7 decay is given by @xmath8^{-1 } = g^{0\nu } |m^{0\nu}|^2 \frac{m_{\beta\beta}^2}{m_e^2 } \ ; , \label{eqn : halflife}\ ] ] assuming the exchange of a light majorana neutrino ( mass mechanism ) . here , @xmath9 is the electron mass .
the phase space factors @xmath10 and nuclear matrix elements @xmath11 vary with isotope .
the decay rate is proportional to the square of the effective neutrino mass @xmath1 , which represents a coherent sum over the masses @xmath12 of the neutrino mass eigenstates , @xmath13 weighted by the squares of the corresponding elements @xmath14 of the pontecorvo maki nakagawa sakata ( pmns ) matrix and the majorana phases @xmath15 and @xmath0 .
the seesaw mechanism is the most common model for neutrino mass generation @xcite . here ,
heavy right - handed neutrinos mix with the left - handed neutrinos and generate light majorana masses for the active neutrinos .
in addition to the exchange of these light majorana neutrinos , there are several other potential models @xcite that could contribute to @xmath7 decays , e.g. , left - right symmetric models , @xmath16-parity violating supersymmetry , or models with extra dimensions . observing @xmath7 decays with different isotopes could help to disentangle these mechanisms @xcite .
the search for @xmath7 decays is pursued in a range of experiments that use different isotopes .
experiments where detector material and @xmath7 isotope are identical are constrained in the choice of isotope by the detector technology .
this approach is employed by collaborations such as gerda @xcite , which uses a high - purity @xmath17 detector , exo-200 @xcite and @xcite , which contain enriched @xmath18 , and cuoricino @xcite and cuore-0 @xcite , bolometers made of teo@xmath19 crystals containing @xmath20 .
alternatively , detector and isotope can be separated , which allows experiments such as nemo-3 @xcite to study a variety of isotopes , e.g. , @xmath21 and @xmath22 .
it is therefore important to develop techniques to combine the data taken by different experiments with a range of isotopes .
this allows us to make quantitative comparisons between experiments , to study the consistency of their results , and to obtain combined limits on @xmath1 .
a previous comparison of different experimental results using the published limits on @xmath23 has been performed in ref .
@xcite . in this analysis ,
we simultaneously fit the experimental energy distributions to obtain a combined limit .
such a direct combination of the results for multiple isotopes requires a specific nme calculation to relate the half - lives of the various isotopes before deriving a limit on @xmath1 .
we chose a set of commonly used nme models to perform the combinations , but the procedure is generally applicable to include any nme model .
the combination of the experimental energy distributions is performed for each particular nme model . in principle
, different models could give a better estimate of the nmes for different isotopes , but this case is not considered here , since it would require determining systematic correlations between the different models .
the final limits on @xmath1 are given as a range covering the full set of nme models , following the procedure normally employed by individual experiments .
we take into account theoretical uncertainties on the calculations where they are available . in this article , we present a method based on the published energy distributions from all recent experiments and use it to derive a first combined limit on @xmath1 based on multiple isotopes .
we first demonstrate that we can reproduce the published half - life limits of each individual experiment , before performing the combination using different nme calculations .
we study the consistency of the combined @xmath1 limit with the positive claim of the heidelberg - moscow experiment @xcite .
we also interpret the combined limit on @xmath1 as a constraint on a @xmath4 model with three active and one sterile majorana neutrinos .
limits are calculated using the _ cl_@xmath24 method @xcite , which applies a modified - frequentist approach using a poisson log - likelihood ratio ( llr ) test statistic .
the value of _ cl_@xmath24 is defined as the @xmath3 value of the data under the hypothesis that we observe both signal and background , _
cl_@xmath25 , divided by the @xmath3 value for the background - only hypothesis ( _ cl_@xmath26 ) .
systematic uncertainties are marginalized through gaussian constraints on the priors , with the best fits of these parameters determined by maximizing the likelihood with respect to the data in both the signal - plus - background and background - only hypotheses .
a limit at the @xmath27 confidence level ( cl ) is obtained from the signal strength that produces a value of _ cl_@xmath28 .
the expected limit corresponds to the median of an ensemble of pseudo - experiments generated from the background - only probability distributions , and the @xmath29 standard deviation ranges are derived from the ensemble .
when combining multiple experiments , the limit setting process uses a sum of the experiments individual llrs , assuming no correlations . for a single experiment ,
the signal strength is inversely proportional to the half - life @xmath23 .
when combining multiple experiments , the signal strength is calculated for a common @xmath1 , which is related to @xmath23 using eq .
[ eqn : halflife ] and for a specific nme calculation .
the most stringent published limits on neutrinoless double-@xmath0 decay are currently provided by the cuoricino , cuore , exo-200 , , gerda , and nemo-3 experiments .
we use their most recent published energy distributions , together with the statistical and systematic uncertainties on signal and backgrounds , and the correlations of the systematic uncertainties as quoted by the experiments .
the input distributions are shown in fig .
[ fig : inputs ] with their statistical uncertainties . in total , we combine 250 data points .
the experimental systematic uncertainties are assumed to be uncorrelated between experiments , because the data are taken using completely different experimental approaches .
cuoricino was a bolometric detector comprising 62 teo@xmath19 crystals , which were operated between 2003 and 2008 , for a total exposure of @xmath30 kg@xmath31y @xcite . using this exposure and the average signal efficiency of @xmath32
, we obtain a total expected number of @xmath33 signal decays for a half - life of @xmath34 years .
the energy distribution for the signal published in fig . 9 of ref .
@xcite normalized to this decay rate is used as the input distribution for the limit setting .
we use an uncertainty for the signal normalization of @xmath35 and an energy scale uncertainty of @xmath36 kev .
a normalization uncertainty of @xmath37 is applied for the constant background , and the @xmath38 background , which is centred at an energy of @xmath39 kev , has a normalization uncertainty of @xmath40 .
these background uncertainties are the exposure - weighted statistical uncertainties taken from table 4 of ref .
@xcite .
the cuore experiment has also published results from a first phase , cuore-0 , which utilizes a single tower with @xmath41 teo@xmath19 crystals .
the results correspond to an exposure of @xmath42 kg@xmath31y for the isotope @xmath20 .
we use the data published in fig . 3 of ref .
@xcite and the reported signal efficiency of @xmath43 .
the signal shape is taken from ref .
@xcite , parametrized by a gaussian function with width of @xmath44 kev .
the statistical uncertainty on the background normalization is @xmath45 , whereas the effect of other systematic uncertainties is negligible .
the exo-200 detector contains a liquid xenon time projection chamber that has been in operation since 2011 @xcite .
a total of 200 kg of xenon is used , with @xmath18 enriched to @xmath46 .
we use the energy distribution of the single - site ( ss ) decays published by the exo-200 collaboration in fig .
4(a ) of ref .
@xcite for an exposure of 100 kg@xmath31y , since the sensitivity of ss topologies to @xmath7 decays is significantly higher than for multi - site ( ms ) topologies .
we apply a signal normalization uncertainty of 8.6% with an energy scale uncertainty of 0.2% .
the background normalization uncertainty is 10.9% .
we also apply an overall normalization uncertainty of 9.6% , correlated between signal and background distributions , which is derived from the ratio of ss to ms topologies .
the detector is filled with 13 tons of liquid scintillator , which is loaded with enriched @xmath18 @xcite .
we use fig .
1(a ) of ref .
@xcite , published after a total exposure @xmath47 kg@xmath31y with a background normalization uncertainty of @xmath48 and a signal normalization uncertainty of @xmath49 .
the gerda collaboration uses high - purity germanium calorimeters enriched in @xmath17 @xcite .
we use the dataset obtained between 2011 and 2013 @xcite , with an exposure of 21.6 kg@xmath31y .
the energy distribution is taken from fig . 1 of ref .
@xcite after pulse shape discrimination .
we apply a 9% uncertainty on the signal normalization and a 20% uncertainty on the constant background normalization .
the nemo-3 collaboration took data from 2003 to 2011 with a tracker - calorimeter detector measuring seven @xmath7 candidate isotopes @xcite .
since the @xmath21 measurements are the most sensitive due to the larger isotope mass , we focus on this isotope .
the input distribution is the data shown in fig . 2 of ref .
@xcite , which corresponds to an exposure of @xmath50 kg@xmath31y .
the signal normalization uncertainty is @xmath51 , and the normalization uncertainty are @xmath52 for the two - neutrino background and @xmath53 for the other backgrounds .
.the published limits on @xmath54 for each experiment are compared to the calculated observed and expected limits .
the @xmath55 range around the expected limit and the @xmath56_cl_@xmath26 value of the data are also shown . [ cols="<,^,^,^,^,^ " , ] in table [ tab : combis ] , we show the combined limits on @xmath1 for each nme model .
we provide the observed and expected limits for each combination and the improvements in observed limit and sensitivity over the result obtained by the best individual experiment . as shown in fig .
[ fig : nmeall ] , the most sensitive experiments change for the different models . the combined results are compared to the result obtained by the heidelberg - moscow ( hm ) experiment in fig . [
fig : all ] , where the error bands represent the uncertainties of the hm half - life measurement of @xmath57 y for @xmath17 @xcite .
the @xmath3 values , testing the consistency between the result obtained by the hm experiment using @xmath17 and the combined upper limits , are also given in table [ tab : combis ] .
they are calculated taking into account the experimental uncertainties .
the @xmath3 values differ significantly between different nme models , and any conclusion on the level of consistency between the combination of the latest experimental results and the result obtained with the the @xmath54 reported by the hm group depends strongly on the chosen nme model .
the @xmath3 values range from @xmath58 ( about @xmath59 standard deviations ) for the gcm model to @xmath60 for the ( r)qrpa models .
the @xmath3 value for the gerda result and this hm measurement is @xmath61 , independent of nme model since the experiments both use the isotope @xmath17 . as a function of the lightest neutrino mass @xmath62 .
the width of the horizontal band represents the range of limits obtained with the different nme models .
the neutrino oscillation parameters are taken from ref .
@xcite , using the best fit values .
the inner band for the nh and ih fits shows the full range associated with the unknown majorana phases and the outer band the additional effect of the @xmath59-standard deviation experimental uncertainties on the oscillation parameters .
the limit on @xmath62 derived from the planck data is also shown.,scaledwidth=48.0% ] the best published limit on @xmath1 by @xcite is obtained by combining their data with the earlier exo-200 result @xcite . using a similar set of nmes , the mass range
they obtain is @xmath63@xmath64 mev , whereas our observed combined limit in the range @xmath65@xmath66 mev is slightly higher because we use the latest exo-200 data set . in fig .
[ fig : hierarchies ] , we overlay the range of observed combined limits on the allowed effective mass @xmath1 as a function of the lightest neutrino mass @xmath62 , with the bands representing current measurement uncertainties of the neutrino oscillation parameters assuming either the normal hierarchy ( nh ) with @xmath67 or the inverted hierarchy ( ih ) with @xmath68 for the ordering of the neutrino mass eigenstates in the standard three - neutrino framework .
we also show a limit on @xmath62 , which is derived from the limit on the sum of the neutrino masses obtained by the planck collaboration @xcite .
they set a limit of @xmath69 mev at the @xmath70 cl based on the temperature and the polarization of the cosmic microwave background .
we also interpret the combined limit on @xmath1 as a constraint on a single sterile majorana neutrino that mixes with the three active majorana states . in this model ,
the expression for the effective neutrino mass @xmath1 defined in eq .
[ eq - mbb ] is modified to take into account the mixing with the fourth neutrino state : @xmath71 it includes an additional mass term @xmath72 , a majorana phase @xmath73 , and the element @xmath74 of the now extended , @xmath75 mixing matrix , which is related to the sterile neutrino mixing angle @xmath76 through @xmath77 in the parametrization used here . in this model
, the unitarity constraint applies only for the @xmath75 mixing matrix .
however , the central values of the elements @xmath78 do not change significantly when the @xmath79 unitarity constraint is removed from the global fit @xcite .
the unitarity constraint on the @xmath75 mixing matrix will restrict @xmath80 to be @xmath81 .
our ability to probe a certain range of @xmath82 depends on @xmath62 and the majorana phases ( see , e.g. , @xcite ) .
we take the approach of translating the limits on @xmath1 into corresponding limits on the combination @xmath82 under two extreme situations for a given @xmath62 : * the nme model ( nsm ) that predicts the highest ( least stringent ) limit on @xmath1 , together with the phases @xmath83 , and @xmath84 that provide the smallest contribution to @xmath1 . * the nme model ( gcm ) that predicts the lowest ( most stringent ) limit on @xmath1 , together with the phases @xmath85 that provide the largest contribution to @xmath1 .
this first parameter set allows for large contributions from @xmath82 and thus provides the least constraining limit on @xmath82 , whereas the second set allows for only small contributions from @xmath82 and thus yields the most constraining limit on @xmath82 . for different nme models translated into a constraint on the sterile neutrino in the @xmath86 plane in a @xmath4 model .
different values of the majorana phases @xmath87 and of the lightest active neutrino mass @xmath88 in the nh are shown .
the complete region is excluded for @xmath89 mev with the gcm model and vanishing majorana phases .
, scaledwidth=48.0% ] for different nme models translated into a constraint on the sterile neutrino in the @xmath86 plane in a @xmath4 sterile neutrino model .
different values of the majorana phases @xmath87 and of the lightest active neutrino mass @xmath90 in the ih are shown .
the complete region is excluded for @xmath91 mev with the gcm model and vanishing majorana phases.,scaledwidth=48.0% ] in figs .
[ fig : sterile_nh ] and [ fig : sterile_ih ] , we translate the measured combined limit on @xmath1 for the two situations above into a limit in the ( @xmath92 ) plane for a set of different assumptions on @xmath62 . to be consistent with cosmological bounds , we vary @xmath62 between @xmath93 and @xmath94 mev . for any of the @xmath62 values
considered , all other nme model and majorana phase combinations will produce limit curves that lie in between these extremes .
the values of @xmath95 and @xmath14 @xmath96 are taken from a recent global fit @xcite . including the three - standard deviation uncertainties on these fit values has negligible effect on the results .
the central value of @xmath97 and @xmath98 ev@xmath99 from a global fit @xcite of the oscillation parameters in a @xmath4 sterile neutrino model including reactor , gallium , solar neutrino , and lsnd / karmen @xmath100 disappearance data , all of which are directly sensitive to @xmath72 and @xmath101 , is also shown in figs .
[ fig : sterile_nh ] and [ fig : sterile_ih ] .
the limit from the @xmath7 combined fit is currently close to the ( 3 + 1 ) global best fit value only in the more constraining scenarios calculated using the gcm model and with @xmath102 mev and favorable majorana phases .
our results are consistent with previous analyses ( see , e.g. , @xcite ) that investigate @xmath1 regions allowed by global fits to oscillation experiments under a ( 3 + 1 ) hypothesis . assuming the sterile neutrino is a majorana particle , neutrinoless double-@xmath0 decay
can therefore independently constrain the existence of a sterile neutrino under those extreme assumptions . for a more detailed discussion on constraints to ( 3 + 1 ) sterile neutrino models from neutrinoless double @xmath0 decay and projected implications for next - generation experiments , see ref . @xcite
we have performed the first combination of the latest data sets from experiments searching for neutrinoless double-@xmath0 decay using multiple isotopes . using the _ cl_@xmath103 method
, we set a limit on the effective neutrino mass @xmath1 in the range @xmath2 mev , depending on nme model . combining the data from multiple isotopes and experiments
significantly increases the sensitivity over using the single - best experiment only , corresponding to an increase by a factor of @xmath104 in exposure .
we compare these limits with the claimed observation of the heidelberg - moscow experiment and obtain @xmath3 values that differ significantly depending on the nme calculations chosen , ranging from @xmath58 for the gcm model to @xmath105 for the ( r)qrpa model . using the uncertainties and the full correlation matrix provided by
the ( r)qrpa model changes the limit on @xmath1 by @xmath106 mev compared to using no nme uncertainties .
we also translate the combined limit on @xmath1 into a constraint on a light sterile majorana neutrino in a @xmath4 model .
this translated limit is nme and @xmath62 and majorana phase dependent .
we want to thank fedor imkovic and sean freeman for useful discussions about the nuclear matrix elements . 00 w. h. furry , phys . rev . *
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the combined limits on @xmath1 range between @xmath2 mev , where the spread is due to different model calculations of nuclear matrix elements ( nmes ) .
the statistical consistency ( @xmath3 values ) between this result and the signal observation claimed by the heidelberg - moscow experiment is derived .
the limits on @xmath1 are also evaluated in a @xmath4 sterile neutrino model , assuming all neutrinos are majorana particles . | <s>[INST]the observation of neutrinoless double-@xmath0 @xmath5 decays would demonstrate the majorana nature of neutrinos @xcite , representing direct evidence for physics beyond the standard model . neutrinoless double-@xmath0 decay is a second - order electroweak process where a nucleus decays through the emission of two electrons , @xmath6 , thereby violating lepton number . the half - life of the isotope decaying through @xmath7 decay is given by @xmath8^{-1 } = g^{0\nu } |m^{0\nu}|^2 \frac{m_{\beta\beta}^2}{m_e^2 } \ ; , \label{eqn : halflife}\ ] ] assuming the exchange of a light majorana neutrino ( mass mechanism ) . here , @xmath9 is the electron mass .
the phase space factors @xmath10 and nuclear matrix elements @xmath11 vary with isotope .
the decay rate is proportional to the square of the effective neutrino mass @xmath1 , which represents a coherent sum over the masses @xmath12 of the neutrino mass eigenstates , @xmath13 weighted by the squares of the corresponding elements @xmath14 of the pontecorvo maki nakagawa sakata ( pmns ) matrix and the majorana phases @xmath15 and @xmath0 .
the seesaw mechanism is the most common model for neutrino mass generation @xcite . here ,
heavy right - handed neutrinos mix with the left - handed neutrinos and generate light majorana masses for the active neutrinos .
in addition to the exchange of these light majorana neutrinos , there are several other potential models @xcite that could contribute to @xmath7 decays , e.g. , left - right symmetric models , @xmath16-parity violating supersymmetry , or models with extra dimensions . observing @xmath7 decays with different isotopes could help to disentangle these mechanisms @xcite .
the search for @xmath7 decays is pursued in a range of experiments that use different isotopes .
experiments where detector material and @xmath7 isotope are identical are constrained in the choice of isotope by the detector technology .
this approach is employed by collaborations such as gerda @xcite , which uses a high - purity @xmath17 detector , exo-200 @xcite and @xcite , which contain enriched @xmath18 , and cuoricino @xcite and cuore-0 @xcite , bolometers made of teo@xmath19 crystals containing @xmath20 .
alternatively , detector and isotope can be separated , which allows experiments such as nemo-3 @xcite to study a variety of isotopes , e.g. , @xmath21 and @xmath22 .
it is therefore important to develop techniques to combine the data taken by different experiments with a range of isotopes .
this allows us to make quantitative comparisons between experiments , to study the consistency of their results , and to obtain combined limits on @xmath1 .
a previous comparison of different experimental results using the published limits on @xmath23 has been performed in ref .
@xcite . in this analysis ,
we simultaneously fit the experimental energy distributions to obtain a combined limit .
such a direct combination of the results for multiple isotopes requires a specific nme calculation to relate the half - lives of the various isotopes before deriving a limit on @xmath1 .
we chose a set of commonly used nme models to perform the combinations , but the procedure is generally applicable to include any nme model .
the combination of the experimental energy distributions is performed for each particular nme model . in principle
, different models could give a better estimate of the nmes for different isotopes , but this case is not considered here , since it would require determining systematic correlations between the different models .
the final limits on @xmath1 are given as a range covering the full set of nme models , following the procedure normally employed by individual experiments .
we take into account theoretical uncertainties on the calculations where they are available . in this article , we present a method based on the published energy distributions from all recent experiments and use it to derive a first combined limit on @xmath1 based on multiple isotopes .
we first demonstrate that we can reproduce the published half - life limits of each individual experiment , before performing the combination using different nme calculations .
we study the consistency of the combined @xmath1 limit with the positive claim of the heidelberg - moscow experiment @xcite .
we also interpret the combined limit on @xmath1 as a constraint on a @xmath4 model with three active and one sterile majorana neutrinos .
limits are calculated using the _ cl_@xmath24 method @xcite , which applies a modified - frequentist approach using a poisson log - likelihood ratio ( llr ) test statistic .
the value of _ cl_@xmath24 is defined as the @xmath3 value of the data under the hypothesis that we observe both signal and background , _
cl_@xmath25 , divided by the @xmath3 value for the background - only hypothesis ( _ cl_@xmath26 ) .
systematic uncertainties are marginalized through gaussian constraints on the priors , with the best fits of these parameters determined by maximizing the likelihood with respect to the data in both the signal - plus - background and background - only hypotheses .
a limit at the @xmath27 confidence level ( cl ) is obtained from the signal strength that produces a value of _ cl_@xmath28 .
the expected limit corresponds to the median of an ensemble of pseudo - experiments generated from the background - only probability distributions , and the @xmath29 standard deviation ranges are derived from the ensemble .
when combining multiple experiments , the limit setting process uses a sum of the experiments individual llrs , assuming no correlations . for a single experiment ,
the signal strength is inversely proportional to the half - life @xmath23 .
when combining multiple experiments , the signal strength is calculated for a common @xmath1 , which is related to @xmath23 using eq .
[ eqn : halflife ] and for a specific nme calculation .
the most stringent published limits on neutrinoless double-@xmath0 decay are currently provided by the cuoricino , cuore , exo-200 , , gerda , and nemo-3 experiments .
we use their most recent published energy distributions , together with the statistical and systematic uncertainties on signal and backgrounds , and the correlations of the systematic uncertainties as quoted by the experiments .
the input distributions are shown in fig .
[ fig : inputs ] with their statistical uncertainties . in total , we combine 250 data points .
the experimental systematic uncertainties are assumed to be uncorrelated between experiments , because the data are taken using completely different experimental approaches .
cuoricino was a bolometric detector comprising 62 teo@xmath19 crystals , which were operated between 2003 and 2008 , for a total exposure of @xmath30 kg@xmath31y @xcite . using this exposure and the average signal efficiency of @xmath32
, we obtain a total expected number of @xmath33 signal decays for a half - life of @xmath34 years .
the energy distribution for the signal published in fig . 9 of ref .
@xcite normalized to this decay rate is used as the input distribution for the limit setting .
we use an uncertainty for the signal normalization of @xmath35 and an energy scale uncertainty of @xmath36 kev .
a normalization uncertainty of @xmath37 is applied for the constant background , and the @xmath38 background , which is centred at an energy of @xmath39 kev , has a normalization uncertainty of @xmath40 .
these background uncertainties are the exposure - weighted statistical uncertainties taken from table 4 of ref .
@xcite .
the cuore experiment has also published results from a first phase , cuore-0 , which utilizes a single tower with @xmath41 teo@xmath19 crystals .
the results correspond to an exposure of @xmath42 kg@xmath31y for the isotope @xmath20 .
we use the data published in fig . 3 of ref .
@xcite and the reported signal efficiency of @xmath43 .
the signal shape is taken from ref .
@xcite , parametrized by a gaussian function with width of @xmath44 kev .
the statistical uncertainty on the background normalization is @xmath45 , whereas the effect of other systematic uncertainties is negligible .
the exo-200 detector contains a liquid xenon time projection chamber that has been in operation since 2011 @xcite .
a total of 200 kg of xenon is used , with @xmath18 enriched to @xmath46 .
we use the energy distribution of the single - site ( ss ) decays published by the exo-200 collaboration in fig .
4(a ) of ref .
@xcite for an exposure of 100 kg@xmath31y , since the sensitivity of ss topologies to @xmath7 decays is significantly higher than for multi - site ( ms ) topologies .
we apply a signal normalization uncertainty of 8.6% with an energy scale uncertainty of 0.2% .
the background normalization uncertainty is 10.9% .
we also apply an overall normalization uncertainty of 9.6% , correlated between signal and background distributions , which is derived from the ratio of ss to ms topologies .
the detector is filled with 13 tons of liquid scintillator , which is loaded with enriched @xmath18 @xcite .
we use fig .
1(a ) of ref .
@xcite , published after a total exposure @xmath47 kg@xmath31y with a background normalization uncertainty of @xmath48 and a signal normalization uncertainty of @xmath49 .
the gerda collaboration uses high - purity germanium calorimeters enriched in @xmath17 @xcite .
we use the dataset obtained between 2011 and 2013 @xcite , with an exposure of 21.6 kg@xmath31y .
the energy distribution is taken from fig . 1 of ref .
@xcite after pulse shape discrimination .
we apply a 9% uncertainty on the signal normalization and a 20% uncertainty on the constant background normalization .
the nemo-3 collaboration took data from 2003 to 2011 with a tracker - calorimeter detector measuring seven @xmath7 candidate isotopes @xcite .
since the @xmath21 measurements are the most sensitive due to the larger isotope mass , we focus on this isotope .
the input distribution is the data shown in fig . 2 of ref .
@xcite , which corresponds to an exposure of @xmath50 kg@xmath31y .
the signal normalization uncertainty is @xmath51 , and the normalization uncertainty are @xmath52 for the two - neutrino background and @xmath53 for the other backgrounds .
.the published limits on @xmath54 for each experiment are compared to the calculated observed and expected limits .
the @xmath55 range around the expected limit and the @xmath56_cl_@xmath26 value of the data are also shown . [ cols="<,^,^,^,^,^ " , ] in table [ tab : combis ] , we show the combined limits on @xmath1 for each nme model .
we provide the observed and expected limits for each combination and the improvements in observed limit and sensitivity over the result obtained by the best individual experiment . as shown in fig .
[ fig : nmeall ] , the most sensitive experiments change for the different models . the combined results are compared to the result obtained by the heidelberg - moscow ( hm ) experiment in fig . [
fig : all ] , where the error bands represent the uncertainties of the hm half - life measurement of @xmath57 y for @xmath17 @xcite .
the @xmath3 values , testing the consistency between the result obtained by the hm experiment using @xmath17 and the combined upper limits , are also given in table [ tab : combis ] .
they are calculated taking into account the experimental uncertainties .
the @xmath3 values differ significantly between different nme models , and any conclusion on the level of consistency between the combination of the latest experimental results and the result obtained with the the @xmath54 reported by the hm group depends strongly on the chosen nme model .
the @xmath3 values range from @xmath58 ( about @xmath59 standard deviations ) for the gcm model to @xmath60 for the ( r)qrpa models .
the @xmath3 value for the gerda result and this hm measurement is @xmath61 , independent of nme model since the experiments both use the isotope @xmath17 . as a function of the lightest neutrino mass @xmath62 .
the width of the horizontal band represents the range of limits obtained with the different nme models .
the neutrino oscillation parameters are taken from ref .
@xcite , using the best fit values .
the inner band for the nh and ih fits shows the full range associated with the unknown majorana phases and the outer band the additional effect of the @xmath59-standard deviation experimental uncertainties on the oscillation parameters .
the limit on @xmath62 derived from the planck data is also shown.,scaledwidth=48.0% ] the best published limit on @xmath1 by @xcite is obtained by combining their data with the earlier exo-200 result @xcite . using a similar set of nmes , the mass range
they obtain is @xmath63@xmath64 mev , whereas our observed combined limit in the range @xmath65@xmath66 mev is slightly higher because we use the latest exo-200 data set . in fig .
[ fig : hierarchies ] , we overlay the range of observed combined limits on the allowed effective mass @xmath1 as a function of the lightest neutrino mass @xmath62 , with the bands representing current measurement uncertainties of the neutrino oscillation parameters assuming either the normal hierarchy ( nh ) with @xmath67 or the inverted hierarchy ( ih ) with @xmath68 for the ordering of the neutrino mass eigenstates in the standard three - neutrino framework .
we also show a limit on @xmath62 , which is derived from the limit on the sum of the neutrino masses obtained by the planck collaboration @xcite .
they set a limit of @xmath69 mev at the @xmath70 cl based on the temperature and the polarization of the cosmic microwave background .
we also interpret the combined limit on @xmath1 as a constraint on a single sterile majorana neutrino that mixes with the three active majorana states . in this model ,
the expression for the effective neutrino mass @xmath1 defined in eq .
[ eq - mbb ] is modified to take into account the mixing with the fourth neutrino state : @xmath71 it includes an additional mass term @xmath72 , a majorana phase @xmath73 , and the element @xmath74 of the now extended , @xmath75 mixing matrix , which is related to the sterile neutrino mixing angle @xmath76 through @xmath77 in the parametrization used here . in this model
, the unitarity constraint applies only for the @xmath75 mixing matrix .
however , the central values of the elements @xmath78 do not change significantly when the @xmath79 unitarity constraint is removed from the global fit @xcite .
the unitarity constraint on the @xmath75 mixing matrix will restrict @xmath80 to be @xmath81 .
our ability to probe a certain range of @xmath82 depends on @xmath62 and the majorana phases ( see , e.g. , @xcite ) .
we take the approach of translating the limits on @xmath1 into corresponding limits on the combination @xmath82 under two extreme situations for a given @xmath62 : * the nme model ( nsm ) that predicts the highest ( least stringent ) limit on @xmath1 , together with the phases @xmath83 , and @xmath84 that provide the smallest contribution to @xmath1 . * the nme model ( gcm ) that predicts the lowest ( most stringent ) limit on @xmath1 , together with the phases @xmath85 that provide the largest contribution to @xmath1 .
this first parameter set allows for large contributions from @xmath82 and thus provides the least constraining limit on @xmath82 , whereas the second set allows for only small contributions from @xmath82 and thus yields the most constraining limit on @xmath82 . for different nme models translated into a constraint on the sterile neutrino in the @xmath86 plane in a @xmath4 model .
different values of the majorana phases @xmath87 and of the lightest active neutrino mass @xmath88 in the nh are shown .
the complete region is excluded for @xmath89 mev with the gcm model and vanishing majorana phases .
, scaledwidth=48.0% ] for different nme models translated into a constraint on the sterile neutrino in the @xmath86 plane in a @xmath4 sterile neutrino model .
different values of the majorana phases @xmath87 and of the lightest active neutrino mass @xmath90 in the ih are shown .
the complete region is excluded for @xmath91 mev with the gcm model and vanishing majorana phases.,scaledwidth=48.0% ] in figs .
[ fig : sterile_nh ] and [ fig : sterile_ih ] , we translate the measured combined limit on @xmath1 for the two situations above into a limit in the ( @xmath92 ) plane for a set of different assumptions on @xmath62 . to be consistent with cosmological bounds , we vary @xmath62 between @xmath93 and @xmath94 mev . for any of the @xmath62 values
considered , all other nme model and majorana phase combinations will produce limit curves that lie in between these extremes .
the values of @xmath95 and @xmath14 @xmath96 are taken from a recent global fit @xcite . including the three - standard deviation uncertainties on these fit values has negligible effect on the results .
the central value of @xmath97 and @xmath98 ev@xmath99 from a global fit @xcite of the oscillation parameters in a @xmath4 sterile neutrino model including reactor , gallium , solar neutrino , and lsnd / karmen @xmath100 disappearance data , all of which are directly sensitive to @xmath72 and @xmath101 , is also shown in figs .
[ fig : sterile_nh ] and [ fig : sterile_ih ] .
the limit from the @xmath7 combined fit is currently close to the ( 3 + 1 ) global best fit value only in the more constraining scenarios calculated using the gcm model and with @xmath102 mev and favorable majorana phases .
our results are consistent with previous analyses ( see , e.g. , @xcite ) that investigate @xmath1 regions allowed by global fits to oscillation experiments under a ( 3 + 1 ) hypothesis . assuming the sterile neutrino is a majorana particle , neutrinoless double-@xmath0 decay
can therefore independently constrain the existence of a sterile neutrino under those extreme assumptions . for a more detailed discussion on constraints to ( 3 + 1 ) sterile neutrino models from neutrinoless double @xmath0 decay and projected implications for next - generation experiments , see ref . @xcite
we have performed the first combination of the latest data sets from experiments searching for neutrinoless double-@xmath0 decay using multiple isotopes . using the _ cl_@xmath103 method
, we set a limit on the effective neutrino mass @xmath1 in the range @xmath2 mev , depending on nme model . combining the data from multiple isotopes and experiments
significantly increases the sensitivity over using the single - best experiment only , corresponding to an increase by a factor of @xmath104 in exposure .
we compare these limits with the claimed observation of the heidelberg - moscow experiment and obtain @xmath3 values that differ significantly depending on the nme calculations chosen , ranging from @xmath58 for the gcm model to @xmath105 for the ( r)qrpa model . using the uncertainties and the full correlation matrix provided by
the ( r)qrpa model changes the limit on @xmath1 by @xmath106 mev compared to using no nme uncertainties .
we also translate the combined limit on @xmath1 into a constraint on a light sterile majorana neutrino in a @xmath4 model .
this translated limit is nme and @xmath62 and majorana phase dependent .
we want to thank fedor imkovic and sean freeman for useful discussions about the nuclear matrix elements . 00 w. h. furry , phys . rev . *
56 * , 1184 ( 1939 ) . for a recent review ,
bilenky and c. giunti , mod .
a * 27 * , 1230015 ( 2012 ) .
f. f. deppisch , m. hirsch , and h. ps , j. phys .
g * 39 * , 124007 ( 2012 ) .
r. arnold _
( supernemo collaboration ) , eur .
j. c * 70 * , 927 ( 2010 ) .
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d * 86 * , 113014 ( 2012 ) ; c. giunti , m. laveder , y. f. li , and h. w. long , phys . rev .
d * 87 * , 013004 ( 2013 ) ; a. abada , v. de romeri , and a. m. teixeira , j. high energy phys . * 09 * , 074 ( 2014 ) . c. giunti , e. m. zavanin , arxiv:1505.00978 [ hep - ph ] .[/INST] we present a framework to combine data from the latest neutrinoless double-@xmath0 decay experiments for multiple isotopes and derive a limit on the effective neutrino mass @xmath1 using the experimental energy distributions .
the combined limits on @xmath1 range between @xmath2 mev , where the spread is due to different model calculations of nuclear matrix elements ( nmes ) .
the statistical consistency ( @xmath3 values ) between this result and the signal observation claimed by the heidelberg - moscow experiment is derived .
the limits on @xmath1 are also evaluated in a @xmath4 sterile neutrino model , assuming all neutrinos are majorana particles . </s> |
3-hydroxy-3-methylglutaryl coenzyme a reductase inhibitors ( hmg - coa reductase inhibitors ; statins ) were introduced in clinical practice in 1976 .
statins have drastically changed not only the treatment regimen for hypercholesterolemia but also the treatment strategy for preventing cardiovascular disease .
then , nearly 25 million people received statin therapy worldwide . however , there were limited data regarding racial differences in response to statins .
in addition , mechanisms regarding racial differences are not sufficiently elucidated . in this review ,
several large - scale clinical trials have demonstrated the safety and efficacy of statins in reducing cardiovascular events .
the cholesterol treatment trialists collaboration conducted a meta - analysis of five randomized trials of statins that compared more intensive ( higher dose or more powerful statin ) and less intensive ( lower dose or less powerful statin ) regimens in 39 612 patients with coronary artery disease ( cad ) .
intensive statin treatment was associated with a greater reduction in major vascular events compared with less intensive therapy and a 1 mmol / l ( 39 mg / dl ) decrease in low density lipoprotein cholesterol ( ldl - c ) was associated with a reduction in all - cause mortality , cardiac events , and coronary events by 19 , 21 , and 23% , respectively .
all of these data have updated the clinical guidelines of the european society of cardiology , the american college of cardiology / american heart association , the japanese cardiology society , and the japan atherosclerosis society . however , there is a wide variation in inter - individual or inter - racial differences in response to statins .
in particular , asians and westerners are reported to have different responses to statin from each other .
a lower dose of statins has demonstrated similar relative risk reduction of cardiovascular events to a higher dose of statins in western patients .
in fact , the maximum dose of atorvastatin in clinical practice was 40 mg per day in japan , while the dose is 80 mg per day in the united states .
the maximum dose of available statins in japanese and westerners is shown in table 1 .
discovery ( the direct statin comparison of ldl - c values : an evaluation of rosuvastatin therapy ) programs consisted of a series of trials incorporating 14,000 patients from several countries , which investigated the impact of rosuvastatin on cardiovascular risk reduction . also , clinical outcomes in a number of different populations worldwide and differences in lipid responses to rosuvastatin and atorvastatin between chinese and caucasian were examined .
this study compared the percentage change in ldl - c in response to rosuvastatin or atorvastatin in patients with type iia or iib hypercholesterolemia between chinese and caucasian , which was performed using the following studies : discovery - hong kong , dicovery - asia , dicovery - alpha , dicovery - netherlands , dicovery - penta , dicovery - uk , dicovery - triple country , and other databases .
the ldl - c reduction with rosuvastatin ( 10 mg ) in chinese patients was significantly greater than in westerners ( 52.8% versus 40.9 to 49.7% ) while no significant difference was observed in the ldl - c response to atorvastatin ( 10 mg ) .
a meta - analysis reported that the dose - response relationship between statin dose and ldl - c reduction by rosuvastatin and atorvastatin was similar in western and asian populations , whereas a three to four - fold greater dosage of statins was administered to the western vs the asian population . in the report , a > 40% reduction in ldl - c required atorvastatin 80 mg or rosuvastatin 40 mg in the western population , whereas the dose of atorvastatin or rosuvastatin required to achieve the same result in asians was 18.9 mg or 14.1 mg , respectively . additionally , the required duration of statin administration for lipid - lowering was significantly longer in the western vs the asian population . in concrete terms ,
the duration over which reduction in ldl - c was exhibited by rosuvastatin was 24.0 and 10.3 months in westerners and asians , respectively .
similarly , the duration was 22.0 and 7.8 months for reduction in ldl - c by atorvastatin in westerners and asians , respectively ( table 2 ) .
yang et al . examined the dose - response of rosuvastatin to ldl - c reduction in their meta - analysis including 36 randomized trials .
there was no significant difference in the dose - response relationship for ldl - c reduction by rosuvastatin between westerners and asians .
for atorvastatin , no difference was also observed in pharmacokinetics of the drug between asians and caucasians . a paucity of data regarding the difference in the dose - response relationship between asians and westerners for other statins has been reported .
for simvastatin , ldl - c reduction by simvastatin of 5 mg daily was 26.0% in the japan lipid intervention trial .
the magnitude of the reduction was similar to the results of other simvastatin studies using higher doses ( 2040 mg daily ) conducted in western countries .
for pitavastatin , the pharmacokinetics and dose - response relationship in ldl - c reduction were not different between japanese and caucasian in an open - label , single - dose , two - way crossover pharmacokinetic study , resulting in the recommended dose by the regulatory authorities being similar between the two countries . in summary ,
the differences in response to statins between asians and westerners were observed for all statins except for pitavastatin .
it was speculated that the differences in the ldl - c response to rosuvastatin between chinese and caucasian was yielded by the different pharmacokinetics .
pharmacokinetics is the study of the time course of drug absorption , distribution , metabolism , and excretion . in clinical practice ,
pharmacokinetics is applied to achieve both a safe and effective therapeutic range of drugs in an individual .
a population pharmacokinetic analysis revealed no clinically relevant differences in pharmacokinetics among caucasian , hispanic , and african american or afro
caribbean groups , while other pharmacokinetic studies of rosuvastatin have demonstrated an approximate two - fold elevation in median exposure ( maximum plasma concentration and the area under the plasma concentration curve ) in asian populations compared with westerners . in both populations , rosuvastatin showed dose - dependent reductions in ldl - c .
yang and colleagues also examined racial differences between asian and western populations in rosuvastatin pharmacodynamics in which an indirect comparison was performed .
pharmacodynamics assesses the relationship between the drug concentration at the site of action and the resulting effect quantitatively , which includes both therapeutic and adverse effects .
the pharmacodynamics was examined by assessing a relationship between the dose of rosuvastatin and ldl - c reduction , which showed no significant difference between westerners and asians . based on these data , the differences in response to statins between westerners and asians
detailed mechanisms of the differences in response to statins between asians and westerners are not fully elucidated . to date , several studies have reported that genetic factors were related to differences in reactions to statin and statin - related side effects , which could potentially explain the racial differences between asians and westerners . a genome - wide study in patients treated with
simvastatin found a significant association between single - nucleotide polymorphisms ( snps ) located within the slco1b1 gene on chromosome 12 and muscular side effects of statins .
slco1b1 encodes an organic anion transporting polypeptide 1b1 ( oatp1b1 ) that is expressed on the basolateral membrane of hepatocytes and can facilitate hepatic uptake of certain clinically relevant drugs such as statins except for fluvastatin .
slco1b1 polymorphisms included two snps ( 388a > g , 521t > g ) and four haplotypes ( slco1b1 * 1a , slco1b1 * 1b , sloco1b1 * 5 , and slco1b1 * 15 ) . slco1b1 * 1a is a wild type , slco1b1 * 1b has one snp ( 388a > g ) , slco1b1 * 5 has the other snp and slco1b1 * 15 has both snps .
the transport activity on hepatic cells was upregulated in people with slco1b1 * 1b , while the activity was downregulated in people with slco1b1 * 5 . in people with slco1b1
the frequency of the four important haplotypes was different among different races ( table 3 ) , which could affect racial differences in response to statin .
major genetic determinants of rosuvastatin pharmacokinetics is the 421c > a polymorphism in the drug efflux transporter atp - binding cassette g2 gene ( abcg2 ) .
subjects with the variant allele have plasma rosuvastatin concentration twice as high as those with the wild - type genotype .
the abcg2 polymorphism is more common in east asians than in westerners , which might contribute to the difference in pharmacokinetics and lipid response to rosuvastatin between the two ethnic groups .
a large - scale genetic analysis among 148 snps within 10 genes participating in cholesterol biosynthesis , cholesterol transport , and statin metabolism was conducted .
this analysis assessed lipid reductions in response to pravastatin therapy in 1536 individuals ( caucasian : 88.7% , african american : 6.5% , hispanic : 2.9% , asian : 1.2% , and others : 0.7% ) in which two snps ( snp 12 and snp 29 ) in the gene coding for hmg - coa reductase were significantly associated with efficacy of pravastatin in ldl - c . in individuals with a minor allele of each snp ,
pravastatin reduced total cholesterol by 22% ( absolute difference : 9.2 mg / dl ) compared with those without the snps .
ldl - c was also reduced by 19% ( absolute difference : 6.4 mg / dl ) .
the association between the snps and the lipid - lowering effect of pravastatin was observed after adjusting for the other 33 snps evaluated in the hmg - coa reductase gene as well as for 148 snps in 10 genes evaluated in the study . in addition , the association between snp 29 and the lipid - lowering effect of pravastatin was more profound in westerners compared with the other ethnic groups .
candidate genes by which statins influence ldl - c reduction are shown in table 4 .
genetic effects , not only on efficacy but also on adverse effects of statin , have been previously reported . in the study of the effectiveness of additional reductions in cholesterol and homocysteine ( search ) and in the heart protection study , rs4363657 c and rs4149056 c alleles in slco1b1 had markedly elevated risks of myopathy , which was also found in the statin response examined by genetic hap markers ( strength ) trial .
in the strength trial , carriers of 2 alleles and 1 allele of the rs4149056 had a 2.6- and 1.4-fold higher incidence of adverse effects by simvastatin , while the ldl - c - lowering effect of simvastatin was similar between carriers and non - carriers .
in the subjects treated with atorvastatin and pravastatin , no statistically significant difference was observed in the incidence of adverse effects between those with at least 1 allele and those without . in the search trial ,
participants with rs4363657c and rs4149056 alleles had a 4-fold higher risk of severe myopathy and a 17-fold higher risk when comparing the participants with and without both alleles .
for patients treated with pravastatin , no excess risk was observed in carriers of rs4149056 . in the justification for the use of statins in prevention : an intervention trial evaluating rosuvastatin ( jupiter ) ,
the effect of rs4363657c and rs4149056c in slco1b1 on clinically reported myalgia was assessed . in the rosuvastatin - treated group ,
the rate of myalgia was 4.1 events per 100 person - years , which was comparable with the rate in the placebo group . among those on rosuvastatin
, there were no differences in the rate of myalgia in subjects with each allele compared with those with neither allele .
the hazard ratio for myalgia of the subjects with an rs4363657c or rs4149056c allele compared with those without neither allele was 0.95 ( 95% confidence interval ( ci ) 0.791.14 ) and 0.95 ( 95% ci 0.791.15 ) , respectively . taken together , these lines of evidence indicate that the effect of the rs4363657c and rs4149056c alleles on the risk of myalgia was different between populations treated with rosuvastatin and simvastatin .
carriers of this polymorphism would be expected to have reduced hepatic uptake of statins , resulting in higher circulating statin concentrations and an increased risk of myopathy .
it is possible that increased circulating statin levels as a result of the sclo1b1 polymorphism are less toxic to muscle cells for hydrophilic agents , such as rosuvastatin and pravastatin , compared with more hydrophobic statins such as simvastatin .
in this text , the differences in statin response between asians and westerners and genetic influences on the differences were described . however , genetic effects on statin response are still controversial . in addition , the lipid - lowering effect of statins involved several processes to exhibit lipid - lowering , which include absorption of the drug , transportation to hepatic cells , inhibition of hmg - coa reductase , nuclear translocation of srebp-2 , increased synthesis of ldl receptor , and endocytosis of ldl - c by the ldl receptor .
because each process is affected to some extent by different genetic factors , known genetic variants per se could not fully explain inter - individual or inter - racial differences in response to statins .
therefore , future research is needed to clarify which gene polymorphisms are related to the processes that act to exhibit lipid - lowering effects and to what extent the genetic factors affect the response to statins .
in addition , we should recognize that not only genetic factors but also non - genetic factors , such as body surface area , dietary style , and adherence to drugs play important roles in different responses to statins between different races .
racial differences exist in the response to statins between asians and westerners through different pharmacokinetics , which is partially explained by genetic factors .
future research is required to elucidate to some extent the gene factors that are associated with racial differences in statin response .
h.d . has received speakers ' bureau / honoraria from msd , astrazeneca , kowa pharmaceutical , sanofi - aventis , glaxosmithkline , shionogi , daiichi - sankyo , takeda pharmaceutical , mitsubishi tanabe pharma , pfizer , and astellas pharma and research funds from takeda pharmaceutical , bristol - myers squibb , nippon boehringer ingelheim , astellas pharma , novartis pharma , msd , sanofi - aventis , otsuka pharmaceutical , dainippon sumitomo pharma , pfizer , kowa pharmaceutical , shionogi , astrazeneca , teijin , and morinaga milk industry .
k.m . has received speakers ' bureau / honoraria from msd , astrazeneca , kowa pharmaceutical , sanofi - aventis , shionogi , daiichi - sankyo , takeda pharmaceutical , pfizer , astellas pharma , and novartis pharma . | statin treatment to reduce low - density lipoprotein cholesterol ( ldl - c ) is associated with the prevention of cardiovascular events in western patients .
similar results have been reported in studies conducted in japan .
however , the dose of statins and the degree of ldl - c reduction achieved with statins are different between asian and western patients . in addition , there are limited data regarding racial differences in response to statins . in this review ,
racial differences between asians and westerners in response to statins are described . | <s>[INST]3-hydroxy-3-methylglutaryl coenzyme a reductase inhibitors ( hmg - coa reductase inhibitors ; statins ) were introduced in clinical practice in 1976 .
statins have drastically changed not only the treatment regimen for hypercholesterolemia but also the treatment strategy for preventing cardiovascular disease .
then , nearly 25 million people received statin therapy worldwide . however , there were limited data regarding racial differences in response to statins .
in addition , mechanisms regarding racial differences are not sufficiently elucidated . in this review ,
several large - scale clinical trials have demonstrated the safety and efficacy of statins in reducing cardiovascular events .
the cholesterol treatment trialists collaboration conducted a meta - analysis of five randomized trials of statins that compared more intensive ( higher dose or more powerful statin ) and less intensive ( lower dose or less powerful statin ) regimens in 39 612 patients with coronary artery disease ( cad ) .
intensive statin treatment was associated with a greater reduction in major vascular events compared with less intensive therapy and a 1 mmol / l ( 39 mg / dl ) decrease in low density lipoprotein cholesterol ( ldl - c ) was associated with a reduction in all - cause mortality , cardiac events , and coronary events by 19 , 21 , and 23% , respectively .
all of these data have updated the clinical guidelines of the european society of cardiology , the american college of cardiology / american heart association , the japanese cardiology society , and the japan atherosclerosis society . however , there is a wide variation in inter - individual or inter - racial differences in response to statins .
in particular , asians and westerners are reported to have different responses to statin from each other .
a lower dose of statins has demonstrated similar relative risk reduction of cardiovascular events to a higher dose of statins in western patients .
in fact , the maximum dose of atorvastatin in clinical practice was 40 mg per day in japan , while the dose is 80 mg per day in the united states .
the maximum dose of available statins in japanese and westerners is shown in table 1 .
discovery ( the direct statin comparison of ldl - c values : an evaluation of rosuvastatin therapy ) programs consisted of a series of trials incorporating 14,000 patients from several countries , which investigated the impact of rosuvastatin on cardiovascular risk reduction . also , clinical outcomes in a number of different populations worldwide and differences in lipid responses to rosuvastatin and atorvastatin between chinese and caucasian were examined .
this study compared the percentage change in ldl - c in response to rosuvastatin or atorvastatin in patients with type iia or iib hypercholesterolemia between chinese and caucasian , which was performed using the following studies : discovery - hong kong , dicovery - asia , dicovery - alpha , dicovery - netherlands , dicovery - penta , dicovery - uk , dicovery - triple country , and other databases .
the ldl - c reduction with rosuvastatin ( 10 mg ) in chinese patients was significantly greater than in westerners ( 52.8% versus 40.9 to 49.7% ) while no significant difference was observed in the ldl - c response to atorvastatin ( 10 mg ) .
a meta - analysis reported that the dose - response relationship between statin dose and ldl - c reduction by rosuvastatin and atorvastatin was similar in western and asian populations , whereas a three to four - fold greater dosage of statins was administered to the western vs the asian population . in the report , a > 40% reduction in ldl - c required atorvastatin 80 mg or rosuvastatin 40 mg in the western population , whereas the dose of atorvastatin or rosuvastatin required to achieve the same result in asians was 18.9 mg or 14.1 mg , respectively . additionally , the required duration of statin administration for lipid - lowering was significantly longer in the western vs the asian population . in concrete terms ,
the duration over which reduction in ldl - c was exhibited by rosuvastatin was 24.0 and 10.3 months in westerners and asians , respectively .
similarly , the duration was 22.0 and 7.8 months for reduction in ldl - c by atorvastatin in westerners and asians , respectively ( table 2 ) .
yang et al . examined the dose - response of rosuvastatin to ldl - c reduction in their meta - analysis including 36 randomized trials .
there was no significant difference in the dose - response relationship for ldl - c reduction by rosuvastatin between westerners and asians .
for atorvastatin , no difference was also observed in pharmacokinetics of the drug between asians and caucasians . a paucity of data regarding the difference in the dose - response relationship between asians and westerners for other statins has been reported .
for simvastatin , ldl - c reduction by simvastatin of 5 mg daily was 26.0% in the japan lipid intervention trial .
the magnitude of the reduction was similar to the results of other simvastatin studies using higher doses ( 2040 mg daily ) conducted in western countries .
for pitavastatin , the pharmacokinetics and dose - response relationship in ldl - c reduction were not different between japanese and caucasian in an open - label , single - dose , two - way crossover pharmacokinetic study , resulting in the recommended dose by the regulatory authorities being similar between the two countries . in summary ,
the differences in response to statins between asians and westerners were observed for all statins except for pitavastatin .
it was speculated that the differences in the ldl - c response to rosuvastatin between chinese and caucasian was yielded by the different pharmacokinetics .
pharmacokinetics is the study of the time course of drug absorption , distribution , metabolism , and excretion . in clinical practice ,
pharmacokinetics is applied to achieve both a safe and effective therapeutic range of drugs in an individual .
a population pharmacokinetic analysis revealed no clinically relevant differences in pharmacokinetics among caucasian , hispanic , and african american or afro
caribbean groups , while other pharmacokinetic studies of rosuvastatin have demonstrated an approximate two - fold elevation in median exposure ( maximum plasma concentration and the area under the plasma concentration curve ) in asian populations compared with westerners . in both populations , rosuvastatin showed dose - dependent reductions in ldl - c .
yang and colleagues also examined racial differences between asian and western populations in rosuvastatin pharmacodynamics in which an indirect comparison was performed .
pharmacodynamics assesses the relationship between the drug concentration at the site of action and the resulting effect quantitatively , which includes both therapeutic and adverse effects .
the pharmacodynamics was examined by assessing a relationship between the dose of rosuvastatin and ldl - c reduction , which showed no significant difference between westerners and asians . based on these data , the differences in response to statins between westerners and asians
detailed mechanisms of the differences in response to statins between asians and westerners are not fully elucidated . to date , several studies have reported that genetic factors were related to differences in reactions to statin and statin - related side effects , which could potentially explain the racial differences between asians and westerners . a genome - wide study in patients treated with
simvastatin found a significant association between single - nucleotide polymorphisms ( snps ) located within the slco1b1 gene on chromosome 12 and muscular side effects of statins .
slco1b1 encodes an organic anion transporting polypeptide 1b1 ( oatp1b1 ) that is expressed on the basolateral membrane of hepatocytes and can facilitate hepatic uptake of certain clinically relevant drugs such as statins except for fluvastatin .
slco1b1 polymorphisms included two snps ( 388a > g , 521t > g ) and four haplotypes ( slco1b1 * 1a , slco1b1 * 1b , sloco1b1 * 5 , and slco1b1 * 15 ) . slco1b1 * 1a is a wild type , slco1b1 * 1b has one snp ( 388a > g ) , slco1b1 * 5 has the other snp and slco1b1 * 15 has both snps .
the transport activity on hepatic cells was upregulated in people with slco1b1 * 1b , while the activity was downregulated in people with slco1b1 * 5 . in people with slco1b1
the frequency of the four important haplotypes was different among different races ( table 3 ) , which could affect racial differences in response to statin .
major genetic determinants of rosuvastatin pharmacokinetics is the 421c > a polymorphism in the drug efflux transporter atp - binding cassette g2 gene ( abcg2 ) .
subjects with the variant allele have plasma rosuvastatin concentration twice as high as those with the wild - type genotype .
the abcg2 polymorphism is more common in east asians than in westerners , which might contribute to the difference in pharmacokinetics and lipid response to rosuvastatin between the two ethnic groups .
a large - scale genetic analysis among 148 snps within 10 genes participating in cholesterol biosynthesis , cholesterol transport , and statin metabolism was conducted .
this analysis assessed lipid reductions in response to pravastatin therapy in 1536 individuals ( caucasian : 88.7% , african american : 6.5% , hispanic : 2.9% , asian : 1.2% , and others : 0.7% ) in which two snps ( snp 12 and snp 29 ) in the gene coding for hmg - coa reductase were significantly associated with efficacy of pravastatin in ldl - c . in individuals with a minor allele of each snp ,
pravastatin reduced total cholesterol by 22% ( absolute difference : 9.2 mg / dl ) compared with those without the snps .
ldl - c was also reduced by 19% ( absolute difference : 6.4 mg / dl ) .
the association between the snps and the lipid - lowering effect of pravastatin was observed after adjusting for the other 33 snps evaluated in the hmg - coa reductase gene as well as for 148 snps in 10 genes evaluated in the study . in addition , the association between snp 29 and the lipid - lowering effect of pravastatin was more profound in westerners compared with the other ethnic groups .
candidate genes by which statins influence ldl - c reduction are shown in table 4 .
genetic effects , not only on efficacy but also on adverse effects of statin , have been previously reported . in the study of the effectiveness of additional reductions in cholesterol and homocysteine ( search ) and in the heart protection study , rs4363657 c and rs4149056 c alleles in slco1b1 had markedly elevated risks of myopathy , which was also found in the statin response examined by genetic hap markers ( strength ) trial .
in the strength trial , carriers of 2 alleles and 1 allele of the rs4149056 had a 2.6- and 1.4-fold higher incidence of adverse effects by simvastatin , while the ldl - c - lowering effect of simvastatin was similar between carriers and non - carriers .
in the subjects treated with atorvastatin and pravastatin , no statistically significant difference was observed in the incidence of adverse effects between those with at least 1 allele and those without . in the search trial ,
participants with rs4363657c and rs4149056 alleles had a 4-fold higher risk of severe myopathy and a 17-fold higher risk when comparing the participants with and without both alleles .
for patients treated with pravastatin , no excess risk was observed in carriers of rs4149056 . in the justification for the use of statins in prevention : an intervention trial evaluating rosuvastatin ( jupiter ) ,
the effect of rs4363657c and rs4149056c in slco1b1 on clinically reported myalgia was assessed . in the rosuvastatin - treated group ,
the rate of myalgia was 4.1 events per 100 person - years , which was comparable with the rate in the placebo group . among those on rosuvastatin
, there were no differences in the rate of myalgia in subjects with each allele compared with those with neither allele .
the hazard ratio for myalgia of the subjects with an rs4363657c or rs4149056c allele compared with those without neither allele was 0.95 ( 95% confidence interval ( ci ) 0.791.14 ) and 0.95 ( 95% ci 0.791.15 ) , respectively . taken together , these lines of evidence indicate that the effect of the rs4363657c and rs4149056c alleles on the risk of myalgia was different between populations treated with rosuvastatin and simvastatin .
carriers of this polymorphism would be expected to have reduced hepatic uptake of statins , resulting in higher circulating statin concentrations and an increased risk of myopathy .
it is possible that increased circulating statin levels as a result of the sclo1b1 polymorphism are less toxic to muscle cells for hydrophilic agents , such as rosuvastatin and pravastatin , compared with more hydrophobic statins such as simvastatin .
in this text , the differences in statin response between asians and westerners and genetic influences on the differences were described . however , genetic effects on statin response are still controversial . in addition , the lipid - lowering effect of statins involved several processes to exhibit lipid - lowering , which include absorption of the drug , transportation to hepatic cells , inhibition of hmg - coa reductase , nuclear translocation of srebp-2 , increased synthesis of ldl receptor , and endocytosis of ldl - c by the ldl receptor .
because each process is affected to some extent by different genetic factors , known genetic variants per se could not fully explain inter - individual or inter - racial differences in response to statins .
therefore , future research is needed to clarify which gene polymorphisms are related to the processes that act to exhibit lipid - lowering effects and to what extent the genetic factors affect the response to statins .
in addition , we should recognize that not only genetic factors but also non - genetic factors , such as body surface area , dietary style , and adherence to drugs play important roles in different responses to statins between different races .
racial differences exist in the response to statins between asians and westerners through different pharmacokinetics , which is partially explained by genetic factors .
future research is required to elucidate to some extent the gene factors that are associated with racial differences in statin response .
h.d . has received speakers ' bureau / honoraria from msd , astrazeneca , kowa pharmaceutical , sanofi - aventis , glaxosmithkline , shionogi , daiichi - sankyo , takeda pharmaceutical , mitsubishi tanabe pharma , pfizer , and astellas pharma and research funds from takeda pharmaceutical , bristol - myers squibb , nippon boehringer ingelheim , astellas pharma , novartis pharma , msd , sanofi - aventis , otsuka pharmaceutical , dainippon sumitomo pharma , pfizer , kowa pharmaceutical , shionogi , astrazeneca , teijin , and morinaga milk industry .
k.m . has received speakers ' bureau / honoraria from msd , astrazeneca , kowa pharmaceutical , sanofi - aventis , shionogi , daiichi - sankyo , takeda pharmaceutical , pfizer , astellas pharma , and novartis pharma .[/INST]statin treatment to reduce low - density lipoprotein cholesterol ( ldl - c ) is associated with the prevention of cardiovascular events in western patients .
similar results have been reported in studies conducted in japan .
however , the dose of statins and the degree of ldl - c reduction achieved with statins are different between asian and western patients . in addition , there are limited data regarding racial differences in response to statins . in this review ,
racial differences between asians and westerners in response to statins are described .</s> |
some of the most relevant properties of the universe have been established through astronomical data associated to light curves of distant supernova ia @xcite , the temperature anisotropies in the cosmic microwave background radiation @xcite and the matter power spectrum of large scale structures @xcite .
such observations give a strong evidence that the geometry of the universe is flat and that our universe is undertaking an accelerated expansion at the present epoch .
this acceleration is attributed to a dominant dark energy component , whose most popular candidate is the cosmological constant , @xmath0 .
the present days dominance of dark energy make us wonder if this component may affect the formation and stability of large astrophysical structures , whose physics is basically newtonian .
this is in fact an old question put forward already by einstein @xcite and pursued by many other authors @xcite and @xcite . in general , the problem is rooted in the question whether the expansion of the universe , which in the newtonian sense could be understood as a repulsive force , affects local astrophysical properties of large objects .
the answer is certainly affirmative if part of the terms responsible for the universe expansion survives the newtonian limit of the einstein equations .
this is indeed the case of @xmath0 which is part of the einstein tensor .
in fact , as explained in the main text below , all the effects of the universe expansion can be taken into account , regardless of the model , by generalizing the newtonian limit .
this approach allow us to calculate the impact of a given cosmological model on astrophysical structures .
although , there are several candidates to dark energy which have their own cosmological signature , e.g. @xcite and @xcite , in this paper we will investigate the @xmath0cdm model only .
such consideration is in fact not restrictive and our results will be common to most dark energy models . at astrophysical scales and within the newtonian limit one does not expect to find important differences among the different dark energy models .
this , however should not be interpreted as if @xmath0 has no effect at smaller astrophysical scales .
in fact , the effects of a cosmological constant on the equilibrium and stability of astrophysical structures is not negligible , and can be of relevance to describe features of astrophysical systems such as globular clusters , galaxy clusters or even galaxies @xcite .
motivated by this , we investigate the effects of a dark energy component on the newtonian limit of einstein gravity and its consequences at astrophysical scales . in this article
we investigate how the cosmological constant changes certain aspects of astrophysical hydrostatic equilibrium . in particular
we search for specific imprints which are unique to the existence of a dark energy fluid .
for instance , the instability of previously viable astrophysical models when @xmath0 is included .
we explore such possibility using spherical configurations described by a polytropic equation of state ( e.o.s ) @xmath1 .
the polytropic equation of state derives its importance from its success and consistency , and it is widely used in determining the properties of gravitational structures ranging from stars @xcite to galaxies @xcite .
it leads to an acceptable description of the behavior of astrophysical objects in accordance with observations and numerical simulations @xcite .
the description of such configurations can be verified in the general relativistic framework @xcite and applications of these models to the dark energy problem have in fact been explored @xcite . the effect of a positive cosmological constant can be best visualized as a repulsive non local force acting on the matter distribution .
it is clear that this extra force will result into a minimum density ( either central or average ) which is possible for the distribution to be in equilibrium .
this minimum density is a crucial crossing point : below this value no matter can be in equilibrium , above this value low density objects exist @xcite .
both effects are novel features due to @xmath0
. we will demonstrate such inequalities , which are generalizations of corresponding inequalities found in @xcite and @xcite , for every polytropic index @xmath2 .
however , the most drastic effect can be found in the limiting case of the polytropic equation of state , i.e , the isothermal sphere where the polytropic index @xmath2 goes to infinity .
this case captures , as far as the effects of @xmath0 are concerned , many features also for higher , but finite @xmath2 . the model of the isothermal sphere is often used to model galaxies and galactic clusters @xcite and used in describing effects of gravitational lensing @xcite .
herein lies the importance of the model . regarding the isothermal sphere
we will show that @xmath0 renders the model unacceptable on general grounds .
this essentially means that the model does not even have an appealing asymptotic behavior for large radii and any attempt to definite a physically acceptable radius has its severe drawbacks . the positive cosmological constant offers , however , yet another unique opportunity , namely the possible existence of young low density virialized objects , understood as configurations that have reached virial equilibrium just at the vacuum dominated epoch ( in contrast to the structures forming during the matter dominated era , where the criteria for virialization is roughly @xmath3 ) .
this low density hydrostatic / virialized objects can be explained again due to @xmath0 which now partly plays the role of the outward pressure .
the applicability of fluid models , virial theorem and hydrostatic equilibrium to large astrophysical bodies has been discussed many times in the literature . for a small survey on this topic
we refer the reader to @xcite where one can also find the relevant references .
it is interesting to notice that dark matter halos represent a constant density background which , in the newtonian limit , objects embedded in them feel the analog to a negative cosmological constant .
the equilibrium analysis for such configurations has been performed in @xcite .
a negative @xmath0 will just enhance the attractive gravity effect , whereas a positive one opposes this attraction . as a result
the case @xmath4 reveals different physical concepts as discussed in this paper .
the article is organized as follows . in the next section
we introduce the equations relevant for astrophysical systems as a result of the weak field limit and the non - relativistic limit of einstein field equations taking into account a cosmological constant .
there we derive such limit taking into account the background expansion independently of the dark energy model . in section 3
we derive the equations governing polytropic configurations , the equilibrium conditions and stability criteria . in section 4
we describe the isothermal sphere and investigate its applicability in the presence of @xmath0 . in section 5
we explore some examples of astrophysical configurations where the cosmological constant may play a relevant role .
in particular , we probe into low density objects , fermion ( neutrino ) stars and boson stars .
finally we perform an important comparison between polytropic configurations with @xmath0 and parameterized density of dark matter halos .
we end with conclusions .
we use units @xmath5 except in section 5.4 where we restore @xmath6 and use natural units @xmath7 .
the dynamics of the isotropic and homogeneous cosmological background is determined by the evolution of the ( dimensionless ) scale factor given through the friedman - robertson - walker line element as solution of einstein field equations , @xmath8 , \hspace{0.5cm}\left[\frac{\dot{a}(t)}{a(t)}\right]^{2}=h(t)^{2}=\frac{8}{3}\pi\rho(t)-\frac{k}{a^{2}(t)},\ ] ] corresponding to the raychaudhury equation and friedman equation , respectively .
the total energy density @xmath9 is a contribution from a matter component - baryonic plus dark matter - ( @xmath10 ) , radiation ( @xmath11 ) and a dark energy component ( @xmath12 with @xmath13 ) .
the function @xmath14 is given as @xmath15 where the term @xmath16 represents the equation of state for the dark energy component .
the case @xmath17 corresponds to the cosmological constant @xmath18 .
the effects of the background on virialized structures can be explored through the newtonian limit of field equations from which one can derive a modified poisson s equation ( see e.g. @xcite ) . recalling
that pressure is also a source for gravity , the gravitational potential produced by an overdensity is given by @xmath19 where @xmath20 and @xmath21 . where @xmath22 is the local overdensity with respect to the background density @xmath9 .
notice that equation ( [ o ] ) reduces to the usual poisson equation , @xmath23 , when non relativistic matter dominates the universe , and @xmath24 .
however , at present times , when dark energy dominates , the pressure is non - negligible and @xmath25 might even be non zero , such as in the case of quintessence models @xcite . in this work , however , we will focus in the case of an homogeneous dark energy component where @xmath26 . with this in mind , one can then write the modified poisson equation as @xmath27 note that this equation allows one to probe local effects of different dark energy models through the term @xmath28 given in eq.([fri ] ) . since we will be investigating the configuration and stability of astrophysical objects nowadays ,
when dark energy dominates , it is more instructive to write the above equations in terms of an effective vacuum density i.e. @xmath29 where by using ( [ fri ] ) @xmath30 has been defined as @xmath31{\rho_{\rm vac}},\ ] ] which reduces to @xmath32 for @xmath17 and negligible contribution from the cold dark matter component with respect to the over - density @xmath22 . with @xmath33 being the solution associated to the pure gravitational interaction , the full solution for the potential
can be simply written as @xmath34 which defines the newton - hooke space - time for a scale factor close to the present time ( vacuum dominated epoch ) , @xmath17 and @xmath35 @xcite . for a @xmath0cdm universe with @xmath36 and @xmath37
we get @xmath38 : that is , the positive density of matter which has an attractive effect opposing the repulsive one of @xmath0 reduces effectively the strength of the external force in ( [ pois ] ) .
note that , although in the text we will use the notation @xmath39 which would be vaild in the case of a newton - hook space time , it must be understood that we can replace @xmath32 by @xmath40 for a @xmath0cdm background .
given the potential @xmath41 , we can write the euler s equation for a self - gravitating configuration as @xmath42 , where @xmath43 is the ( statistical ) mean velocity and @xmath9 is the total energy density in the system .
we can go beyond euler s equation and write down the tensor virial equation which reduces to its scalar version for spherical configurations .
the ( scalar ) virial equation with the background contribution reads as @xcite @xmath44 where @xmath45 is the gravitational potential energy defined by @xmath46 and @xmath47 is the contribution of ordered motions to the kinetic energy . also , @xmath48 is the moment of inertia about the center of the configuration and @xmath49 is the trace of the dispersion tensor .
the full description of a self gravitating configuration is completed with an equation for mass conservation , energy conservation and an equation of state @xmath50 .
if we assume equilibrium via @xmath51 , we obtain the known virial theorem @xcite @xmath52 ) , which is valid in the case when we define the boundary of the configuration where @xmath53 . with @xmath54 given in ( [ rhoeff ] )
, one must be aware that an equilibrium configuration is at the most a dynamical one .
this is to say that the external repulsive force in ( [ rhoeff ] ) is time dependent through the inclusion of the background expansion and so are the terms in ( [ virialeq ] ) .
this leads to a violation of energy conservation , which also occurs in the virialization process @xcite ) .
traced over cosmological times , this implies that if we insist on the second derivative of the inertial tensor to be zero , then the internal properties of the object like angular velocity or the internal mean velocity of the components will change with time .
even if in the simplest case , one can assume that the objects shape and its density remain constant .
hence , equilibrium here can be thought of as represented by long time averages in which case the second derivative also vanishes , not because of constant volume and density , but because of stability @xcite .
the expressions derived in the last section , especially ( [ pois ] ) and ( [ virial ] ) can be used for testing dark energy models on configurations in a dynamical state of equilibrium . however , in these cases , one should point out that , in this approach there is no energy conservation within the overdensity : dark energy flows in and out of the overdensity .
such feature is a consequence of the assumption that dark energy does not cluster at small scales ( homogeneity of dark energy ) .
this is in fact the most common assumption in the literature@xcite , with a few exceptions investigated in @xcite . in this paper
, we will concentrate on the possible effects of a background dominated by a dark energy component represented by the cosmological constant at late times ( @xmath551 ) .
it implies that the total density involved in the definitions of the integral quantities appearing in the virial equation can be approximated to @xmath56 . in that case
the poisson equation reduces to the form @xmath57 .
as mentioned before , the symbol @xmath32 has no multiplicative factors in the case of a newton - hooke space time , while for a @xmath0cdm model it must be understood as @xmath58 .
as the reader will see , the most relevant quantities derived here come in forms of ratio of a characterizing density and @xmath32 , and hence the extra factor appearing in the @xmath0cdm can be re - introduced in the characterizing density . for general consideration of equilibrium in the spherical case see @xcite and @xcite , while the quasi spherical collapse with cosmological constant has been discussed in @xcite .
we can determine the relevant features of astrophysical systems by solving the dynamical equations describing a self gravitating configuration ( euler s equation , poisson s equation , continuity equations ) . in order to achieve this goal
we must first know the potential @xmath59 to be able to calculate the gravitational potential energy . to obtain @xmath59
, one must supply the density profile and solve poisson s equation . in certain cases ,
the potential is given and we therefore can solve for the density profile in a simple way . here
we face the situation where no information on the potential ( aside from its boundary conditions ) is available and we also do not have an apriori information about the density profile ( see for instance @xcite for related examples ) . in order to determine both , the potential and the density profile , a complete description of astrophysical systems required .
this means we need to know an equation of state @xmath60 ( here we change notation and we call @xmath9 the proper density of the system ) .
the equation of state can take several forms and the most widely used one is the so - called _ polytropic equation of state _ , expressed as @xmath61 where @xmath62 is the polytropic index and @xmath63 is a parameter that depends on the polytropic index , central density , the mass and the radius of the system .
the exponent @xmath62 is defined as @xmath64 and is associated with processes with constant ( non - zero ) specific heat @xmath65 .
it reduces to the adiabatic exponent if @xmath66 . the polytropic equation of state was introduced to model fully convective configurations . from a statistical point of view , eq .
( [ poly ] ) represents a collisionless system whose distribution function can be written in the form @xmath67 , with @xmath68 being the relative energy and @xmath69 being the relative potential ( where @xmath70 is a constant chosen such that @xmath71)@xcite . in astrophysical contexts , the polytropic equation of state is widely used to describe astrophysical systems such as the sun , compact objects , galaxies and galaxy clusters @xcite .
we now derive the well known lane - emden equation .
we start from poisson equation and euler equation for spherically symmetric configurations , written as @xmath72 le equation for different @xmath73 and different index @xmath2 ranging from @xmath74 ( red , short - dashed line ) , @xmath75 ( blue , long - dashed line ) and @xmath76 ( green , dot short - dashed line).,width=453 ] this set of equations together with eq .
( [ poly ] ) can be integrated in order to solve for the density in terms of the potential as @xmath77^{\frac{1}{\gamma-1}},\ ] ] where @xmath78 is the central density . in view of eq .
( [ new1 ] ) in conjunction with eq .
( [ yyy1 ] ) it is clear that @xmath32 will have the effect to increase the value of @xmath79 .
therefore the boundary of the configuration will be located in a greater @xmath80 as compared to the case @xmath81 . in order to determine the behavior of the density profile , we again combine eq([poly+pois ] ) and eq.([poly ] ) in order to eliminate the potential @xmath82 .
we obtain @xmath83 where we defined the function @xmath84 we can rewrite eq ( [ arbigeo2 ] ) by introducing the variable @xmath85 defined by @xmath86 , where @xmath87 is the central density .
we also introduce the variable @xmath88 where @xmath89 is a length scale .
eq.([arbigeo2 ] ) is finally written as @xcite @xmath90 this is the @xmath0-lane - emden equation ( @xmath91 ) .
note that for constant density , we recover @xmath92 as the first non trivial solution of @xmath91 equation .
this is consistent with the results from virial theorem for constant density spherical objects which tell us that @xmath93 @xcite .
note that using eq .
( [ new1 ] ) we can write the solution @xmath94 with the explicit contribution of @xmath32 as @xmath95 so that for a given @xmath96 smaller than the radius we will obtain @xmath97 as already pointed out before . then the differential equation ( [ le ] ) must be solved with the initial conditions @xmath98 , satisfied by ( [ new2 ] ) .
numerical solutions were obtained for the first time in @xcite .
the solutions presented in fig .
[ lanea ] are given in terms of the ratio @xmath99 for @xmath100 and @xmath76 .
this choice of variables are useful also since @xmath32 sets a fundamental scale of density ( the choice @xmath101 will be explored for the isothermal sphere , where figure [ lanea ] will be helpful for discussions ) .
the radius of a polytropic configuration is determined as the value of @xmath96 when the density of matter with the e.o.s ( [ poly ] ) vanishes .
this happens at a radius located at @xmath102 note that equation ( [ le ] ) yields a transcendental equation to determine @xmath103 .
also one notes from fig .
[ lanea ] that not all values of @xmath104 yield allowed configurations in the sense that we can not find a value of @xmath103 such that @xmath105 .
this might not be surprising since for @xmath76 and @xmath106 we find the situation where the asymptotic behavior is @xmath107 as @xmath108 ( we consider this still as an acceptable behavior ) .
there is , however , one crucial difference when we switch on a non - zero @xmath0 . for @xmath109 not only we can not reach a definite radius but the derivative of the density changes sign and
hence becomes non - physical .
the situation for the cases @xmath110 is somewhat similar to the extreme case of @xmath111 ( isothermal sphere ) . clearly , these features are responsible of the last term in eq.([new2 ] ) , which for high values of @xmath112 may become dominant over the remaining ( gravitational ) terms
. we will discuss this case in section four where we will attempt another definition of a finite radius with the constraint @xmath113 .
for now it is sufficient to mention that , as expected , the radius of the allowed configurations are larger than the corresponding radius when @xmath106
. in this section we will derive the equilibrium conditions for polytropic configurations in the presence of a positive cosmological constant .
we will use the results of last section in order to write down the virial theorem .
the total mass of the configuration can be determined as usual with @xmath114 together with eq.([le ] ) .
one then has a relation between the mass , the radius and the central density : @xmath115 where @xmath116 note that we have introduced the cosmological constant in the equation for the radius , leading to the appearance of the astrophysical length scale @xmath117 ( with @xmath118mpc @xmath119 mpc for the concordance values @xmath120 and @xmath121 ) .
this scale has been already found in the context of schwarzschild - de sitter metric where it is the maximum allowed radius for bound orbits . at the same time it is
the scale of the maximum radius for a self gravitating spherical and homogeneous configuration in the presence of a positive @xmath0 @xcite .
this also let us relate the mean density of the configuration with its central density and/or cosmological parameters as @xmath122 .
similarly we can determine the other relevant quantities appearing in the equations for the energy and the scalar virial theorem ( [ virial ] ) .
for the traces of the moment of inertia tensor and the dispersion tensor @xmath123 we can write @xmath124 where the functions @xmath125 have been defined as @xmath126 using ( [ radius3 ] ) .
these functions are numerically determined in the sequence @xmath127 , such that for a given mass we obtain the radius as @xmath128 .
let us consider the virial theorem ( [ virial ] ) for a polytropic configuration .
the gravitational potential energy @xmath45 can be obtained following the same arguments shown in @xcite .
the method consist in integrating euler s equation and solve for @xmath33 , then using eq.([maw ] ) one obtains @xmath45 .
the final result is written as @xmath129 to show the behavior of @xmath45 with respect to the index @xmath2 , we can solve the the virial theorem ( [ virial ] ) for @xmath123 and replace it in eq.([poliwc ] ) .
we obtain @xmath130\frac{m^{2}}{r}.\ ] ] this expression shows the typical behavior of a @xmath76 polytrope ( even if @xmath131 ) : the configuration has an infinite potential energy , due to the fact that the matter is distributed in a infinite volume . the energy of the configuration in terms of the polytropic index can be easily obtained by using ( [ virial ] ) , ( [ poliwc ] ) and ( [ poliwd ] ) @xmath132.\ ] ] one is tempted to use @xmath133 as the condition to be fulfilled for a gravitationally bounded system . for @xmath81
we recover the condition @xmath134 ( @xmath135 ) for gravitationally bounded configurations in equilibrium . on the other hand , for @xmath136 this condition might not be completely true due to the following reasoning : the two - body effective potential in the presence of a positive cosmological constant does not go asymptotically to zero for large distances , which is to say that @xmath133 is not stringent enough to guarantee a bound system .
therefore , we rather rely on the numerical solutions from which , for every @xmath2 , we infer the value of @xmath137 such that @xmath138 this gives us the lowest possible central density in terms of @xmath39 . the behavior of the @xmath139 , the functions @xmath140 , the solution @xmath141 and the values of @xmath142 are shown in fig [ tablelane2 ] .
note that this inequality can be understood as a generalization of the equilibrium condition @xmath143 , which , when applied for a spherical homogeneous configurations yields @xmath144 with @xmath145 constant @xcite . , @xmath146 , the functions @xmath147 , and @xmath148 .
equilibrium configurations are reached for @xmath149 ( for a @xmath0cdm cosmoolgy one has to rewrite @xmath150).,width=340 ] note that , at @xmath76 the radius of the configuration becomes undefined , as well as the energy .
a @xmath76 polytrope is highly concentrated at the center @xcite .
no criteria can be written since even for @xmath81 there is not a finite radius .
but it is this high concentration at the center and a smooth asymptotic behavior which makes this case still a viable phenomenological model if @xmath0 is zero . on the contrary for non - zero , positive @xmath0
the solutions start oscillating around @xmath151 which makes the definition of the radius more problematic . for @xmath152
the polytropic e.o.s describes an ideal gas ( isothermal sphere ) . since in this limit
the expressions derived before are not well definite , this case will be explored in more detail in the next section . in spite of the mathematical differences , the isothermal sphere bears many similarities to the cases @xmath110 and
our conclusions regarding the definition of a radius in the @xmath111 case equally apply to finite @xmath2 bigger than @xmath153 . and different polytropic index in a modified newton - hook space time with a dark energy equation of state @xmath154 ( black , dots ) and @xmath155 ( red , short dash ) .
compare with fig.[lanea],width=453 ] in the last section we have explored the effects of a dark energy - dominated background with the equation of state @xmath17 .
other dark energy models are often used with @xmath156 and @xmath154 or even @xmath157 , in the so - called phantom regime , or even a time dependent dark energy model ( quintessence ) . a simple generalization to such models
can be easily done by making the following replacement in our equations @xmath158 where @xmath159 , and where the function @xmath14 is defined in eq.([fa ] ) .
note that for this generalization to be coherent with the derivation of @xmath0le in ( [ le ] ) , one needs to consider that the equation of state is close to @xmath160 , so that there is almost no time - dependence , and the energy density for dark energy is almost constant .
this is indeed the case for most popular candidates of dark energy specially at low redshifts @xmath161 .
also , notice once again , that we are still assuming an homogeneous dark energy component which flows freely to and from the overdensity .
hence , violating energy conservation inside it . clearly , other models of dark energy will posses dynamical properties that the cosmological constant does not have .
for instance , we could allow some fraction of dark energy to take part in the collapse and virialization @xcite , which would lead to the presence of self and cross interaction terms for dark energy and the ( polytropic like ) matter in euler equation , which at the end modifies the lane emden equation . with this simplistic approach
, we see that the effects with a general equation of state are smaller than those associated to the cosmological constant .
in particular , the equation of state @xmath156 displays a null effects since it implies @xmath162 ( note that this equation of state can also resemble the curvature term in evolution equation for the background ) . on the other hand , phantom models of dark energy , which are associated to equations of state @xmath157@xcite ,
have quite a strong effect . in fig . [ laneph ]
we show numerical solutions of lane - emden equations for a background dominated with dark energy with @xmath154 and a phantom dark energy with @xmath155 , with @xmath163 .
these curves are to be compared with those at fig.[lanea ] .
clearly equations of state with @xmath164 will generate larger radius than the case described in the main text .
furthermore , the asymptotic behavior of the ratio between the density and @xmath32 is @xmath165 .
stability criteria for polytropic configurations can be derived from the virial equation . using equations ( [ piner ] ) , ( [ pintener ] ) and ( [ poliwc ] ) we can write the virial theorem ( [ virial ] ) in terms of the radius @xmath80 and the mass @xmath166 : @xmath167 where we have assumed that the only contribution to the kinetic energy comes from the pressure in the form of @xmath168 .
note that for @xmath81 and finite mass , one obtains @xmath169 while for @xmath136 we would obtain a cubic equation for the radius . instead of solving for the virial radius , we solve for the mass as a function of central density with the help of eq ( [ radius3 ] ) . we have @xmath170^{\frac{3}{2}}.\ ] ]
the explicit dependence of the mass with respect to the central density splits into two parts : on one hand it has the same form as the usual case with @xmath106 , that is , @xmath171 ; on the other hand the function @xmath172 has a complicated dependence on the central density because of the term @xmath173 . with the help of ( [ radius3 ] ) and ( [ fmas2aa ] ) we can write a mass - radius relation and the radius - central density relation @xmath174 following the stability theorem ( see for instance in @xcite )
, the stability criteria can be determined from the variations of the mass in equilibrium with respect to the central density .
we derive from eq .
( [ fmas2aaa ] ) : @xmath175\rho_{\rm c}^{\frac{3}{2}(\gamma-\frac{4}{3})}.\ ] ] stability ( instability ) stands for @xmath176 ( @xmath177 ) .
this yields a critical value of the polytropic exponent @xmath178 when @xmath179 given by @xmath180 in the sense that polytropic configurations are stable under small radial perturbations if @xmath181 .
it is clear that the second term in ( [ slope2 ] ) also depends on the polytropic index and therefore this equation is essentially a transcendental expression for @xmath178 .
it is worth mentioning that by including the corrections due to general relativity , the critical value for @xmath178 is also modified as @xmath182 @xcite and hence for compact objects the correction to the critical polytropic index is stronger from the effects of general relativity than from the effects of the background .
this is as we would expect it .
stability of relativistic configurations with non - zero cosmological constant has been explored in @xcite .
going back to equation ( [ fmas2aa ] ) , we can write the mass of the configuration as @xmath183 , where @xmath184 is the mass when @xmath106 and @xmath185 is the enhancement factor
. both quantities can be calculated to give @xmath186^{\frac{3}{2}},\ ] ] where @xmath187 are numerical factors ( tabulated in table 1 ) that can be determined in a straightforward way .
similarly , by using eq ( [ radius3 ] ) , the radius can be written as @xmath188 , where @xmath189^{\frac{1}{2}}.\ ] ] in table [ tablelane2a ] we show the values of the enhancement factors @xmath190 and @xmath191 for different values of @xmath173 and different polytropic index @xmath2 .
we also show the values of the critical ratio @xmath139 which separates the configurations with definite ratio such that a zero @xmath103 exist provided that @xmath192 .
we will show some examples where the enhancement factors may be relevant in section 5 .
.numerical values for the enhancement factors @xmath193 ) ( values for @xmath194 have been taken from @xcite ) .
the symbol @xmath195 indicates a non defined radius . [ cols="^,^,^,^",options="header " , ]
in this section we will probe into the possibilities of exotic , low density configurations .
the global interest in such structures is twofold .
first , the cosmological constant will affect the properties of low density objects .
secondly , @xmath0 plays effectively the role of an external , repulsive force .
hence a relevant issue that arises in this context is to see whether the vacuum energy density can partly _
replace _ the pressure which essentially is encoded in the parameter @xmath63 ( @xmath196 ) . by the word _
replace _ we mean that we want to explore the possibility of a finite radius as long as the pressure effects are small in the presence of @xmath32 . as mentioned above the effect of a positive cosmological constant on matter
is best understood as an external repulsive force . in previous sections
we have probed into one extreme which describes the situation where a relatively low density object is pulled apart by this force ( to an extent that we concluded that the isothermal sphere is not a viable model in the presence of @xmath0 ) . limiting
conditions when this happens were derived . on the other hand , approaching with our parameters these limiting conditions , but remaining still on the side of equilibrium , means that relatively low density objects can be still in equilibrium thanks to the positive cosmological constant . the best way to investigate low density structures is to to use the lowest possible central density . as explained in section 3 , for every @xmath2 there
exist a @xmath142 such that @xmath197 which defines the lowest central density .
certainly , a question of interest is to see what such objects would look like .
we start with the parameters of the configuration .
the radius at the critical value @xmath139 is given by eq.([radius3 ] ) after taking the limit @xmath198 ( see ( [ an ] ) ) .
it is given by @xmath199 from fig .
[ lanecrit ] we can see that the product @xmath200 changes a little round the value @xmath201 as we change the index @xmath2 , so that these polytropic configurations will have roughly the same radius ( for a given mass ) .
this implies that such configurations have approximately the same average density @xmath202 .
that is , such configurations have a mean density of the order of the of the critical density of the universe .
given such a density we would , at the first glance , suspect that the object described by this density can not be in equilibrium .
however , our result follows strictly from hydrostatic equilibrium and therefore there is no doubt that such object can theoretically exist .
furthermore , @xmath203 satisfies the inequalities derived in @xcite and @xcite from virial equations and buchdahl inequalities which guarantee that the object is in equilibrium ( @xmath204 ) .
interestingly , the central density for such objects has to be much higher than @xmath203 as , e.g. , for @xmath74 we have @xmath205 and therefore @xmath206 .
, now the functions @xmath140 being evaluated at the value @xmath207 solution of eq.([virtras]).,width=340 ] note that these values have been given from the solution of the lane - emden equation , which is a consequence of dynamical equations reduced to describe our system in a steady state .
however , we have not tried to solve explicitly quantities from the virial theorem .
this makes sense as for dark matter halos ( dmh ) the parametrized density profiles go often only asymptotically to zero and the radius of dmh is defined as a virial radius where the density is approximately two hundred times over the critical one .
therefore , an analysis using virial equations seems to be adequate here . for constant density eq.([vpol ] ) can be expressed as a cubic equation @xcite for the radius at which the virial theorem is satisfied ( let us ignore for these analysis any surface terms coming from the tensor virial equation ) . however , if the density is not constant , this expression becomes a transcendental equation for the dimensionless radius @xmath208 .
this equation is @xmath209},\ ] ] understanding the functions @xmath140 now as integrals up to the value @xmath207 .
once we fix @xmath139 for a given index @xmath2 , we use as a first guess for the iteration process the value @xmath210 . in fig
[ lanecrit ] we show the behavior of the functions @xmath140 and the solutions of eq.([virtras ] ) . for these values , eq .
( [ rque ] ) gives for @xmath74 a radius @xmath211 which can be compared with the radius - mass relation derived in the top - hat sphericall collapse @xcite @xmath212 where @xmath213 is the dimensionless hubble parameter and @xmath214 is the redshift of virialization .
the resulting average density is then of the order of the value predicted by the top - hat sphericall model : @xmath215 note with the help of eq.([a ] ) and ( [ rque ] ) that the mass can be written as proportional to the parameter @xmath216 ( introduced in the polytropic equation of state eq.([poly ] ) ) .
therefore @xmath217 is equivalent to choosing a small pressure and , at the same time , a small mass which , in case of a relatively small radius , amounts to a diluted configuration with small density and pressure . without @xmath0
such configurations would be hardly in equilibrium .
hence , for the configuration which has the extension of pc , eq.([xxx14 ] ) , with one solar mass we conclude that the equilibrium is not fully due to the pressure , but partially maintained also by @xmath0 .
this is possible , as @xmath0 exerts an outwardly directed non local force on the body .
other mean densities , also independent of @xmath166 are for @xmath218 and @xmath75 , respectively : @xmath219 the first value is close to @xmath220 and therefore also to @xmath39 .
certainly , if in this example we choose a small mass , equivalent to choosing a negligible pressure , part of the equilibrium is maintained by the repulsive force of @xmath0 .
in @xcite we found a simple solution of the hydrostatic equation which has a constant density of the order of @xmath39 .
the above is a non - constant and non - trivial generalization of this solution .
the neutrino stars which we will discuss in the subsequent subsection are modeled in close analogy to white dwarfs .
therefore it makes sense to recall some part of the physics of white dwarfs . in addition
we can contrast the example of white dwarfs to the low density cases affected by @xmath0 . in the limit where the thermal energy @xmath221 of a ( newtonian ) white dwarf is much smaller than the energy at rest of the electrons ( @xmath222 ,
these configurations can be treated as polytropic configuration with @xmath74 .
this is the ultra - relativistic limit where the mass of electrons is much smaller than fermi s momentum @xmath223 . in the opposite case
we obtain a polytrope or configuration with @xmath224 .
@xcite . in both cases ,
the parameter @xmath225 from the polytropic equation of state is given as @xmath226 where @xmath227 is the nucleon mass , @xmath228 is the electron mass and @xmath229 is the number of nucleons per electron . using the newtonian limit with cosmological constant , we can derive the mass and radius of these configurations in equilibrium . in the first case , for @xmath74 the mass
is written using ( [ fmas2aa ] ) as @xmath230 which corresponds approximately to the chandrasekhar s limit ( strictly speaking a configuration would have the critical mass , i.e , the chandrasekhar s limit , if its polytropic index @xmath62 is such that @xmath231 ) .
for this situation one has @xmath232 and @xmath233 . on the other hand , for @xmath224 one
obtains @xmath234 and the radius is given by @xmath235 where @xmath236 is the mean density of the sun .
since for these configurations the ratio @xmath173 is much smaller than @xmath237 we see from fig .
[ tablelane2 ] that the effects of @xmath0 are almost negligible .
the critical value of the ratio @xmath173 gives for @xmath74 the inequality @xmath238 and for @xmath224 the same limit reads @xmath239 .
central densities of white dwarfs are of the order of @xmath240 which corresponds to a deviation of nearly thirty orders of magnitude of @xmath39 .
an interesting possibility is to determine the effects of @xmath241 on configurations formed by light fermions .
such configurations can be used , for instance , to model galactic halos @xcite .
while discussing the phenomenological interest of fermion stars below , we intend to describe such a halo .
clearly , these kind of systems will maintain equilibrium by counterbalancing gravity with the degeneracy pressure as in a white dwarf .
for stable configurations ,
i.e , @xmath224 , one must replace the mass of the electron and nucleon by the mass of the considered fermion and set @xmath242 in ( [ kn ] ) and ( [ fmas2aa ] ) .
we then get for the mass and the radius : @xmath243 on the other hand , for @xmath74 one has @xmath244 the cases represent , among other , possible cosmological configurations when the fermion mass if of the order of ev , for instance , massive neutrinos . and @xmath224 .
the masses range from @xmath245 ev up to @xmath246 ev.,width=377 ] in figure [ tablelane244 ] some representative values for the choice @xmath247 ev up to @xmath248 ev are given .
obviously in the case @xmath218 the values for the mass and radius are sensitive to the choice of @xmath249 .
indeed , the dependence on the fermion mass is much stronger than on the central density .
it is justified to speculate that a relative low density objects , affected by @xmath0 , might exist .
if then , as in an example we choose @xmath250 ev and @xmath251 then the mass comes out as @xmath252 solar masses with a radius of the order of magnitude of half mpc which might indeed be the dark matter halo of a galaxy ( or at least part of the halo ) . as pointed out before
, such configurations must have a central density greater than @xmath253 in order to be in equilibrium . from table [ tablelane2a ]
we see that the effect on a configuration with @xmath254 is represented in an increase in the mass by @xmath255 with respect to @xmath256 and an increment of @xmath257 in the radius .
then the conclusion would be that @xmath0 affects such a dark matter halo .
this is to be taken with some caution as the fermions in such a configuration would be essentially non - relativistic .
note also that it is not clear if neutrinos make up a large fraction of the halo , however , we can also speculate about a low density clustering around luminous matter . of course , allowing larger central density might change the picture .
however , the emerging scenario would not necessarily be a viable phenomenological model .
for instance , changing the value of @xmath249 from ev to kev ( mev ) would reduce the mass by twelve ( twenty four ) orders of magnitude which is definitely too small to be of interest . we could counterbalance this by increasing the central density by twenty four ( forty eight ! ) orders of magnitude . such a countermeasure would , however , result in a reduction of the radius by eight ( sixteen ! ) orders of magnitude , again a too small length scale to be of importance for dark matter halos . in other words ,
the example with a fermion mass of the order of one ev and low central density is certainly of some phenomenological interest .
the case @xmath74 is similarly stringent .
a neutrino mass of @xmath258 ev gives a mass for the entire object of the order of ten to the eighteen solar masses which is too large .
a fermion mass of several kev would be suitable for a galaxy halo ( a mass of the order me v and higher would give a too small total mass ) . with a relative low central density as before ( see figure [ tablelane244 ] ) we then obtain the right order of magnitude for the halo .
but then we will have to live with the fact that such halo reaches up to the next large galaxy .
briefly , we touch upon the other possible application of fermions stars which have been discussed as candidates for the central object in our galaxy . if we allow the extension of this object to be @xmath259 au and the mass roughly @xmath260 million solar masses , then the fermion mass would come out as @xmath261 ev for @xmath218 ( @xmath262 ev for @xmath74 ) and the central density as @xmath263 ( @xmath264 for @xmath74 ) .
we end the section by putting forward a speculative question in connection with boson stars .
the latter are general relativistic geons and can be treated exactly only in general relativistic framework i.e. these kind of configurations are based on the interaction of a massive scalar field and gravitation which leads to gravitational bounded systems .
these objects have been also widely discussed as candidates for dark matter @xcite . on the other hand ,
variational methods in the connection with the thomas - fermi equations give relatively good results even without invoking the whole general relativistic formalism . by including @xmath0 we essentially introduce into the theory a new scale ,
say in this case a length scale @xmath265 . the basic parameters of dimension length in a theory with a boson mass @xmath266 and a total mass @xmath267 where @xmath268 is the number of bosons are ( for a better distinction of the different length scales , we restore in this subsection the value of @xmath6 ) @xmath269 the resulting radius of the object s extension can be a combination of these scales i.e. @xmath270 and similar combination of higher order . which one of the combination gets chosen , depends on the details of the model . in a close analogy to @xcite
we can examine this taking into account the presence of a positive cosmological constant by considering the energy of such configuration as a two variable function of the mass and the radius @xmath271 @xmath272 the first term corresponds to the total kinetic energy written as @xmath273 and taking @xmath274 .
the second term is the gravitational potential energy and the third term corresponds to the contribution of the background ( see eq .
( [ virialeq ] ) ) . by treating mass and radius as independent variables ( we think this this is the right procedure since the radius will depend on the external force due to @xmath32 ) , we extremize the energy leading to the following values of mass and radius : @xmath275 such values would lead to a mean density of the order of @xmath276 i.e. an extremely low density configuration .
the mass given in the last expression is the so - called kaup limit @xcite . of course
, this relative simple treatment does not guarantee that the full , general relativistic treatment , will give the same results .
therefore we consider it as a conjecture .
however , it is also obvious from the the discussion above that low density boson stars are a real possibility worth pursuing with more rigor ( we intend to do so in the near future ) .
it is of some importance to see whether our results from the examination of polytropic hydrostatic equilibrium or from the virial equations can be applied to dark matter configurations .
n - body simulations based in a @xmath0cdm model of the universe show that the density profile of virialized dark matter halos ( dmh ) can be described by a profile of the form @xcite @xmath277 where @xmath278 is the characteristic radius ( the logarithmic slope is @xmath279 ) , @xmath280 and the index @xmath281 characterizes the slope of the profile in the central regions of the halo .
the mass of the configuration enclosed in the virial radius @xmath282 is given as @xmath283 such that one can write @xmath284 , where @xmath285 is the concentration parameter , @xmath286 is the ratio between the mean density at the time of virialization and the critical density of the universe ( @xmath287 in the top - hat model for a flat einstein - desitter universe , while @xmath288 in the @xmath0cdm cosmological model @xcite ) and @xmath289 .
this _ universal profile _ has been widely used in modeling dmh in galaxy clusters , and the comparison of these models with a stellar polytropic - like profile -without the explicit contribution from the cosmological constant in the lane - emden equation- can be found in @xcite .
some differences can be described between the @xmath0le and the nfw profiles .
first , on fundamental grounds , it is clear that the nfw profile does not satisfy the le equation ; a basic reason for this is that dark matter is assumed to be collisionless and is only affected by gravity .
however , the fact that the real nature of dark matter is still an unsolved issue leaves an open door through which one can introduce interaction between dark matter particles leading to a different equation of state ( see for instance @xcite ) . on functional forms
, one sees that at the central region the difference is abrupt , since the lane - emden equation has a flat density profile at @xmath290 , while the nfw profile has a cuspy profile of the form @xmath291 .
it has been widely discussed how such cuspy profile is inconsistent with data showing central regions of clusters with homogeneous cores ( see discussion at the end of this section ) .
such small slope in the inner regions can be reproduced by the _
universal profile _ for the case @xmath292 , and for the profile derived from the @xmath0le equation ( which is just a consequence of initial conditions , and hence , its independent of @xmath0 ) . in this case , the effects of the cosmological constant can be reduced to explore the outer regions of the halos and compare , for instance , the slope of the profiles and the virial radius predicted by each one .
le equation for different masses and different index @xmath2 ranging from @xmath74(blue , dots ) , @xmath75 ( red , short - dashed line ) , @xmath293 ( green , long - dashed line ) and @xmath294 ( magenta , dot short - dashed line ) , in the limiting case @xmath295 .
the solution from le equation is written for the critical value of the parameter @xmath139 , shown in table [ tablelane2 ] .
the vertial black line represents the virial radius from the nfw profile .
the vertical colored lines represent the virial radius @xmath296 for the different polytropic indices.,width=453 ] but for the radius given by the condition @xmath105.,width=453 ] the density profiles predicted by the @xmath0le equation and the nfw profile ( for @xmath297 ) are presented in fig.[compav ] for the virial radius given by @xmath207 and in fig.[compac ] for the radius given by @xmath103 , both with @xmath295 . also , the behavior of the radius for different values of mass and polytropic indices are given in fig [ raddd ] ( with @xmath298 kpc and @xmath299 mpc @xmath300 kpc @xcite ) .
( blus , solid line ) for four different values of @xmath2.,width=453 ] we see that the virial radius given by the @xmath0le equation is surprisingly close to the virial radius given by the nfw profile for @xmath74 in the range of masses shown in fig [ raddd ] , and as pointed in eq.([contrast ] ) , this value yields for this model @xmath301 .
however , as can be seen from the plots , the @xmath0le density profile is almost flat until the virial radius . on the other hand ,
the @xmath292 profile allow us to parameterize it as @xmath302 , where the concentration parameter @xmath65 can be written as @xmath303 .
compared with the and @xmath74 @xmath0le profile , with its corresponding @xmath139 , for different masses.,width=453 ] for @xmath294,width=453 ] in fig.[comp1 ] and [ comp4 ] we have compared both profiles with the corresponding @xmath139 for polytropic index @xmath74 and @xmath294 . for the first case
we see that the virial radius are of the same order of magnitude than the one predicted by the nfw profile . for @xmath294 , these quantities differ by one order of magnitude . in all cases ,
the slope of the nfw profiles changes faster than the @xmath0le profile , which implies that the polytropic configurations enclosed by @xmath282 display almost a constant density . the comparison we made above between the polytropic configuration and the nfw profiles shows that up to the cuspy behaviour the polytropic results agree with nfw for the polytropic index @xmath74 .
it is worth pointing out here that it is exactly this cuspy behaviour which seems to be at odds with observational facts @xcite .
our result for @xmath74 is then a good candidate to describe dmh .
indeed , the undesired feature of the cuspy behaviour led at least some groups to model the dmh as a polytropic configuration @xcite . sometimes it is claimed that a polytropic model is favoured over the results from n - body simulation @xcite .
however , the oscillatory behavior of the @xmath74 solutions of the @xmath0le represents a disadvantage when compared with the nfw profiles , although the region of physical interest ( below the virial radius ) is well represented by the solutions of @xmath0le .
in this paper we have explored the effects of a positive cosmological constant on the equilibrium and stability of astrophysical configurations with a polytropic equation of state .
we have found that the radius of these kind of configurations is affected in the sense that not all polytropic indices yield configurations with definite radius even in the asymptotic sense . among other ,
the widely used isothermal sphere model becomes a non - viable model in the presence of @xmath0 unless we are ready to introduce an arbitrary cut - off which renders the model unappealing .
indeed , in this particular case we have tried different definitions of a finite radius with the result that none of them seems to be justified , either from the phenomenological or from the theoretical point of view .
this is then an interesting global result : @xmath0 not only affects quantitatively certain properties of large , low - density astrophysical structures , but it also excludes certain commonly used models regardless what density we use . for polytropic indexes @xmath304 and for _ certain values
_ of the central density we can not find a well definite radius .
these _ certain values _ are encoded in a generalization of the equilibrium condition found for spherical configurations ( i.e , @xmath305 ) written now as @xmath149 .
we obtain @xmath306 , @xmath307 , @xmath308 , @xmath309 .
these values set a minimal central density for a given polytropic index @xmath2 .
we have discussed such minimal density configurations and determined their average density which strongly depend on @xmath2 .
interestingly , the radius of such configurations has a connection to the length scale which appears in the schwarzschild- de sitter as the maximally possible radius for bound orbits @xcite .
in this framework we found also a solution of very low , non - constant density .
indeed , the limiting value of the central density in the above equations is a crucial point . below this value
no matter can be in equilibrium .
however , above this value low density objects can still exist .
both effects are due to @xmath0 : in the first case the external repulsive force is too strong for the matter to be in equilibrium , in the second case this force can counterbalance the attractive newtonian gravity effects ( even if the pressure is small ) .
other examples of low density configuration which we examined in some detail are neutrino stars with mass of the order @xmath310 ev and @xmath310 kev .
in there we found that a nowadays dominating cosmological constant affects both the mass as well as the radius of such exotic objects .
such effect could change those physical quantities several orders of magnitude .
the magnitude of such effects , however , depend on the fermionic masses and on the assumption that the fermions in such a configuration would be essentially non - relativistic .
finally , we made a conjecture regarding boson stars , and used variational methods in connection with the thomas - fermi equations which could give relatively good results even without invoking the whole general relativistic formalism , we then found extremely low density configurations for such astrophysical objects .
notice however , that this conjecture relied purely on arguments based on scales and in fact needs a full general relativistic investigation to confirm the results here obtained .
we have compared polytropic configurations with dark matter density profiles from n - body simulations .
surprisingly , we find a reasonable agreement between both approaches for the polytropic index @xmath74 and restricting ourselves to the virial radius .
our model does not have the the undesired features of the cuspy behaviour of the nfw profiles .
the importance of the astrophysical properties and configurations found in this article is that they are specific features to the existence of a dark energy component .
hence , such configurations ( e.g , low density configurations ) or properties , if ever found in nature would imply a strong evidence for the presence of a dark energy component .
such observations would be a completely independent , and so complementary , of other cosmological probes of dark energy such as supernova ia or the cmbr .
we acknowledge stefanie phleps for her comments on the manuscript .
dfm acknowledge support from the a. humboldt foundation .
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. phys . * 06 * , 008 ( 2006 ) | we explore the effects of a positive cosmological constant on astrophysical and cosmological configurations described by a polytropic equation of state .
we derive the conditions for equilibrium and stability of such configurations and consider some astrophysical examples where our analysis may be relevant .
we show that in the presence of the cosmological constant the isothermal sphere is not a viable astrophysical model since the density in this model does not go asymptotically to zero .
the cosmological constant implies that , for polytropic index smaller than five , the central density has to exceed a certain minimal value in terms of the vacuum density in order to guarantee the existence of a finite size object .
we examine such configurations together with effects of @xmath0 in other exotic possibilities , such as neutrino and boson stars , and we compare our results to n - body simulations . the astrophysical properties and configurations found in this article are specific features resulting from the existence of a dark energy component . hence
, if found in nature would be an independent probe of a cosmological constant , complementary to other observations .
[ firstpage ] cosmology theory dark energy
structure formation | <s>[INST]some of the most relevant properties of the universe have been established through astronomical data associated to light curves of distant supernova ia @xcite , the temperature anisotropies in the cosmic microwave background radiation @xcite and the matter power spectrum of large scale structures @xcite .
such observations give a strong evidence that the geometry of the universe is flat and that our universe is undertaking an accelerated expansion at the present epoch .
this acceleration is attributed to a dominant dark energy component , whose most popular candidate is the cosmological constant , @xmath0 .
the present days dominance of dark energy make us wonder if this component may affect the formation and stability of large astrophysical structures , whose physics is basically newtonian .
this is in fact an old question put forward already by einstein @xcite and pursued by many other authors @xcite and @xcite . in general , the problem is rooted in the question whether the expansion of the universe , which in the newtonian sense could be understood as a repulsive force , affects local astrophysical properties of large objects .
the answer is certainly affirmative if part of the terms responsible for the universe expansion survives the newtonian limit of the einstein equations .
this is indeed the case of @xmath0 which is part of the einstein tensor .
in fact , as explained in the main text below , all the effects of the universe expansion can be taken into account , regardless of the model , by generalizing the newtonian limit .
this approach allow us to calculate the impact of a given cosmological model on astrophysical structures .
although , there are several candidates to dark energy which have their own cosmological signature , e.g. @xcite and @xcite , in this paper we will investigate the @xmath0cdm model only .
such consideration is in fact not restrictive and our results will be common to most dark energy models . at astrophysical scales and within the newtonian limit one does not expect to find important differences among the different dark energy models .
this , however should not be interpreted as if @xmath0 has no effect at smaller astrophysical scales .
in fact , the effects of a cosmological constant on the equilibrium and stability of astrophysical structures is not negligible , and can be of relevance to describe features of astrophysical systems such as globular clusters , galaxy clusters or even galaxies @xcite .
motivated by this , we investigate the effects of a dark energy component on the newtonian limit of einstein gravity and its consequences at astrophysical scales . in this article
we investigate how the cosmological constant changes certain aspects of astrophysical hydrostatic equilibrium . in particular
we search for specific imprints which are unique to the existence of a dark energy fluid .
for instance , the instability of previously viable astrophysical models when @xmath0 is included .
we explore such possibility using spherical configurations described by a polytropic equation of state ( e.o.s ) @xmath1 .
the polytropic equation of state derives its importance from its success and consistency , and it is widely used in determining the properties of gravitational structures ranging from stars @xcite to galaxies @xcite .
it leads to an acceptable description of the behavior of astrophysical objects in accordance with observations and numerical simulations @xcite .
the description of such configurations can be verified in the general relativistic framework @xcite and applications of these models to the dark energy problem have in fact been explored @xcite . the effect of a positive cosmological constant can be best visualized as a repulsive non local force acting on the matter distribution .
it is clear that this extra force will result into a minimum density ( either central or average ) which is possible for the distribution to be in equilibrium .
this minimum density is a crucial crossing point : below this value no matter can be in equilibrium , above this value low density objects exist @xcite .
both effects are novel features due to @xmath0
. we will demonstrate such inequalities , which are generalizations of corresponding inequalities found in @xcite and @xcite , for every polytropic index @xmath2 .
however , the most drastic effect can be found in the limiting case of the polytropic equation of state , i.e , the isothermal sphere where the polytropic index @xmath2 goes to infinity .
this case captures , as far as the effects of @xmath0 are concerned , many features also for higher , but finite @xmath2 . the model of the isothermal sphere is often used to model galaxies and galactic clusters @xcite and used in describing effects of gravitational lensing @xcite .
herein lies the importance of the model . regarding the isothermal sphere
we will show that @xmath0 renders the model unacceptable on general grounds .
this essentially means that the model does not even have an appealing asymptotic behavior for large radii and any attempt to definite a physically acceptable radius has its severe drawbacks . the positive cosmological constant offers , however , yet another unique opportunity , namely the possible existence of young low density virialized objects , understood as configurations that have reached virial equilibrium just at the vacuum dominated epoch ( in contrast to the structures forming during the matter dominated era , where the criteria for virialization is roughly @xmath3 ) .
this low density hydrostatic / virialized objects can be explained again due to @xmath0 which now partly plays the role of the outward pressure .
the applicability of fluid models , virial theorem and hydrostatic equilibrium to large astrophysical bodies has been discussed many times in the literature . for a small survey on this topic
we refer the reader to @xcite where one can also find the relevant references .
it is interesting to notice that dark matter halos represent a constant density background which , in the newtonian limit , objects embedded in them feel the analog to a negative cosmological constant .
the equilibrium analysis for such configurations has been performed in @xcite .
a negative @xmath0 will just enhance the attractive gravity effect , whereas a positive one opposes this attraction . as a result
the case @xmath4 reveals different physical concepts as discussed in this paper .
the article is organized as follows . in the next section
we introduce the equations relevant for astrophysical systems as a result of the weak field limit and the non - relativistic limit of einstein field equations taking into account a cosmological constant .
there we derive such limit taking into account the background expansion independently of the dark energy model . in section 3
we derive the equations governing polytropic configurations , the equilibrium conditions and stability criteria . in section 4
we describe the isothermal sphere and investigate its applicability in the presence of @xmath0 . in section 5
we explore some examples of astrophysical configurations where the cosmological constant may play a relevant role .
in particular , we probe into low density objects , fermion ( neutrino ) stars and boson stars .
finally we perform an important comparison between polytropic configurations with @xmath0 and parameterized density of dark matter halos .
we end with conclusions .
we use units @xmath5 except in section 5.4 where we restore @xmath6 and use natural units @xmath7 .
the dynamics of the isotropic and homogeneous cosmological background is determined by the evolution of the ( dimensionless ) scale factor given through the friedman - robertson - walker line element as solution of einstein field equations , @xmath8 , \hspace{0.5cm}\left[\frac{\dot{a}(t)}{a(t)}\right]^{2}=h(t)^{2}=\frac{8}{3}\pi\rho(t)-\frac{k}{a^{2}(t)},\ ] ] corresponding to the raychaudhury equation and friedman equation , respectively .
the total energy density @xmath9 is a contribution from a matter component - baryonic plus dark matter - ( @xmath10 ) , radiation ( @xmath11 ) and a dark energy component ( @xmath12 with @xmath13 ) .
the function @xmath14 is given as @xmath15 where the term @xmath16 represents the equation of state for the dark energy component .
the case @xmath17 corresponds to the cosmological constant @xmath18 .
the effects of the background on virialized structures can be explored through the newtonian limit of field equations from which one can derive a modified poisson s equation ( see e.g. @xcite ) . recalling
that pressure is also a source for gravity , the gravitational potential produced by an overdensity is given by @xmath19 where @xmath20 and @xmath21 . where @xmath22 is the local overdensity with respect to the background density @xmath9 .
notice that equation ( [ o ] ) reduces to the usual poisson equation , @xmath23 , when non relativistic matter dominates the universe , and @xmath24 .
however , at present times , when dark energy dominates , the pressure is non - negligible and @xmath25 might even be non zero , such as in the case of quintessence models @xcite . in this work , however , we will focus in the case of an homogeneous dark energy component where @xmath26 . with this in mind , one can then write the modified poisson equation as @xmath27 note that this equation allows one to probe local effects of different dark energy models through the term @xmath28 given in eq.([fri ] ) . since we will be investigating the configuration and stability of astrophysical objects nowadays ,
when dark energy dominates , it is more instructive to write the above equations in terms of an effective vacuum density i.e. @xmath29 where by using ( [ fri ] ) @xmath30 has been defined as @xmath31{\rho_{\rm vac}},\ ] ] which reduces to @xmath32 for @xmath17 and negligible contribution from the cold dark matter component with respect to the over - density @xmath22 . with @xmath33 being the solution associated to the pure gravitational interaction , the full solution for the potential
can be simply written as @xmath34 which defines the newton - hooke space - time for a scale factor close to the present time ( vacuum dominated epoch ) , @xmath17 and @xmath35 @xcite . for a @xmath0cdm universe with @xmath36 and @xmath37
we get @xmath38 : that is , the positive density of matter which has an attractive effect opposing the repulsive one of @xmath0 reduces effectively the strength of the external force in ( [ pois ] ) .
note that , although in the text we will use the notation @xmath39 which would be vaild in the case of a newton - hook space time , it must be understood that we can replace @xmath32 by @xmath40 for a @xmath0cdm background .
given the potential @xmath41 , we can write the euler s equation for a self - gravitating configuration as @xmath42 , where @xmath43 is the ( statistical ) mean velocity and @xmath9 is the total energy density in the system .
we can go beyond euler s equation and write down the tensor virial equation which reduces to its scalar version for spherical configurations .
the ( scalar ) virial equation with the background contribution reads as @xcite @xmath44 where @xmath45 is the gravitational potential energy defined by @xmath46 and @xmath47 is the contribution of ordered motions to the kinetic energy . also , @xmath48 is the moment of inertia about the center of the configuration and @xmath49 is the trace of the dispersion tensor .
the full description of a self gravitating configuration is completed with an equation for mass conservation , energy conservation and an equation of state @xmath50 .
if we assume equilibrium via @xmath51 , we obtain the known virial theorem @xcite @xmath52 ) , which is valid in the case when we define the boundary of the configuration where @xmath53 . with @xmath54 given in ( [ rhoeff ] )
, one must be aware that an equilibrium configuration is at the most a dynamical one .
this is to say that the external repulsive force in ( [ rhoeff ] ) is time dependent through the inclusion of the background expansion and so are the terms in ( [ virialeq ] ) .
this leads to a violation of energy conservation , which also occurs in the virialization process @xcite ) .
traced over cosmological times , this implies that if we insist on the second derivative of the inertial tensor to be zero , then the internal properties of the object like angular velocity or the internal mean velocity of the components will change with time .
even if in the simplest case , one can assume that the objects shape and its density remain constant .
hence , equilibrium here can be thought of as represented by long time averages in which case the second derivative also vanishes , not because of constant volume and density , but because of stability @xcite .
the expressions derived in the last section , especially ( [ pois ] ) and ( [ virial ] ) can be used for testing dark energy models on configurations in a dynamical state of equilibrium . however , in these cases , one should point out that , in this approach there is no energy conservation within the overdensity : dark energy flows in and out of the overdensity .
such feature is a consequence of the assumption that dark energy does not cluster at small scales ( homogeneity of dark energy ) .
this is in fact the most common assumption in the literature@xcite , with a few exceptions investigated in @xcite . in this paper
, we will concentrate on the possible effects of a background dominated by a dark energy component represented by the cosmological constant at late times ( @xmath551 ) .
it implies that the total density involved in the definitions of the integral quantities appearing in the virial equation can be approximated to @xmath56 . in that case
the poisson equation reduces to the form @xmath57 .
as mentioned before , the symbol @xmath32 has no multiplicative factors in the case of a newton - hooke space time , while for a @xmath0cdm model it must be understood as @xmath58 .
as the reader will see , the most relevant quantities derived here come in forms of ratio of a characterizing density and @xmath32 , and hence the extra factor appearing in the @xmath0cdm can be re - introduced in the characterizing density . for general consideration of equilibrium in the spherical case see @xcite and @xcite , while the quasi spherical collapse with cosmological constant has been discussed in @xcite .
we can determine the relevant features of astrophysical systems by solving the dynamical equations describing a self gravitating configuration ( euler s equation , poisson s equation , continuity equations ) . in order to achieve this goal
we must first know the potential @xmath59 to be able to calculate the gravitational potential energy . to obtain @xmath59
, one must supply the density profile and solve poisson s equation . in certain cases ,
the potential is given and we therefore can solve for the density profile in a simple way . here
we face the situation where no information on the potential ( aside from its boundary conditions ) is available and we also do not have an apriori information about the density profile ( see for instance @xcite for related examples ) . in order to determine both , the potential and the density profile , a complete description of astrophysical systems required .
this means we need to know an equation of state @xmath60 ( here we change notation and we call @xmath9 the proper density of the system ) .
the equation of state can take several forms and the most widely used one is the so - called _ polytropic equation of state _ , expressed as @xmath61 where @xmath62 is the polytropic index and @xmath63 is a parameter that depends on the polytropic index , central density , the mass and the radius of the system .
the exponent @xmath62 is defined as @xmath64 and is associated with processes with constant ( non - zero ) specific heat @xmath65 .
it reduces to the adiabatic exponent if @xmath66 . the polytropic equation of state was introduced to model fully convective configurations . from a statistical point of view , eq .
( [ poly ] ) represents a collisionless system whose distribution function can be written in the form @xmath67 , with @xmath68 being the relative energy and @xmath69 being the relative potential ( where @xmath70 is a constant chosen such that @xmath71)@xcite . in astrophysical contexts , the polytropic equation of state is widely used to describe astrophysical systems such as the sun , compact objects , galaxies and galaxy clusters @xcite .
we now derive the well known lane - emden equation .
we start from poisson equation and euler equation for spherically symmetric configurations , written as @xmath72 le equation for different @xmath73 and different index @xmath2 ranging from @xmath74 ( red , short - dashed line ) , @xmath75 ( blue , long - dashed line ) and @xmath76 ( green , dot short - dashed line).,width=453 ] this set of equations together with eq .
( [ poly ] ) can be integrated in order to solve for the density in terms of the potential as @xmath77^{\frac{1}{\gamma-1}},\ ] ] where @xmath78 is the central density . in view of eq .
( [ new1 ] ) in conjunction with eq .
( [ yyy1 ] ) it is clear that @xmath32 will have the effect to increase the value of @xmath79 .
therefore the boundary of the configuration will be located in a greater @xmath80 as compared to the case @xmath81 . in order to determine the behavior of the density profile , we again combine eq([poly+pois ] ) and eq.([poly ] ) in order to eliminate the potential @xmath82 .
we obtain @xmath83 where we defined the function @xmath84 we can rewrite eq ( [ arbigeo2 ] ) by introducing the variable @xmath85 defined by @xmath86 , where @xmath87 is the central density .
we also introduce the variable @xmath88 where @xmath89 is a length scale .
eq.([arbigeo2 ] ) is finally written as @xcite @xmath90 this is the @xmath0-lane - emden equation ( @xmath91 ) .
note that for constant density , we recover @xmath92 as the first non trivial solution of @xmath91 equation .
this is consistent with the results from virial theorem for constant density spherical objects which tell us that @xmath93 @xcite .
note that using eq .
( [ new1 ] ) we can write the solution @xmath94 with the explicit contribution of @xmath32 as @xmath95 so that for a given @xmath96 smaller than the radius we will obtain @xmath97 as already pointed out before . then the differential equation ( [ le ] ) must be solved with the initial conditions @xmath98 , satisfied by ( [ new2 ] ) .
numerical solutions were obtained for the first time in @xcite .
the solutions presented in fig .
[ lanea ] are given in terms of the ratio @xmath99 for @xmath100 and @xmath76 .
this choice of variables are useful also since @xmath32 sets a fundamental scale of density ( the choice @xmath101 will be explored for the isothermal sphere , where figure [ lanea ] will be helpful for discussions ) .
the radius of a polytropic configuration is determined as the value of @xmath96 when the density of matter with the e.o.s ( [ poly ] ) vanishes .
this happens at a radius located at @xmath102 note that equation ( [ le ] ) yields a transcendental equation to determine @xmath103 .
also one notes from fig .
[ lanea ] that not all values of @xmath104 yield allowed configurations in the sense that we can not find a value of @xmath103 such that @xmath105 .
this might not be surprising since for @xmath76 and @xmath106 we find the situation where the asymptotic behavior is @xmath107 as @xmath108 ( we consider this still as an acceptable behavior ) .
there is , however , one crucial difference when we switch on a non - zero @xmath0 . for @xmath109 not only we can not reach a definite radius but the derivative of the density changes sign and
hence becomes non - physical .
the situation for the cases @xmath110 is somewhat similar to the extreme case of @xmath111 ( isothermal sphere ) . clearly , these features are responsible of the last term in eq.([new2 ] ) , which for high values of @xmath112 may become dominant over the remaining ( gravitational ) terms
. we will discuss this case in section four where we will attempt another definition of a finite radius with the constraint @xmath113 .
for now it is sufficient to mention that , as expected , the radius of the allowed configurations are larger than the corresponding radius when @xmath106
. in this section we will derive the equilibrium conditions for polytropic configurations in the presence of a positive cosmological constant .
we will use the results of last section in order to write down the virial theorem .
the total mass of the configuration can be determined as usual with @xmath114 together with eq.([le ] ) .
one then has a relation between the mass , the radius and the central density : @xmath115 where @xmath116 note that we have introduced the cosmological constant in the equation for the radius , leading to the appearance of the astrophysical length scale @xmath117 ( with @xmath118mpc @xmath119 mpc for the concordance values @xmath120 and @xmath121 ) .
this scale has been already found in the context of schwarzschild - de sitter metric where it is the maximum allowed radius for bound orbits . at the same time it is
the scale of the maximum radius for a self gravitating spherical and homogeneous configuration in the presence of a positive @xmath0 @xcite .
this also let us relate the mean density of the configuration with its central density and/or cosmological parameters as @xmath122 .
similarly we can determine the other relevant quantities appearing in the equations for the energy and the scalar virial theorem ( [ virial ] ) .
for the traces of the moment of inertia tensor and the dispersion tensor @xmath123 we can write @xmath124 where the functions @xmath125 have been defined as @xmath126 using ( [ radius3 ] ) .
these functions are numerically determined in the sequence @xmath127 , such that for a given mass we obtain the radius as @xmath128 .
let us consider the virial theorem ( [ virial ] ) for a polytropic configuration .
the gravitational potential energy @xmath45 can be obtained following the same arguments shown in @xcite .
the method consist in integrating euler s equation and solve for @xmath33 , then using eq.([maw ] ) one obtains @xmath45 .
the final result is written as @xmath129 to show the behavior of @xmath45 with respect to the index @xmath2 , we can solve the the virial theorem ( [ virial ] ) for @xmath123 and replace it in eq.([poliwc ] ) .
we obtain @xmath130\frac{m^{2}}{r}.\ ] ] this expression shows the typical behavior of a @xmath76 polytrope ( even if @xmath131 ) : the configuration has an infinite potential energy , due to the fact that the matter is distributed in a infinite volume . the energy of the configuration in terms of the polytropic index can be easily obtained by using ( [ virial ] ) , ( [ poliwc ] ) and ( [ poliwd ] ) @xmath132.\ ] ] one is tempted to use @xmath133 as the condition to be fulfilled for a gravitationally bounded system . for @xmath81
we recover the condition @xmath134 ( @xmath135 ) for gravitationally bounded configurations in equilibrium . on the other hand , for @xmath136 this condition might not be completely true due to the following reasoning : the two - body effective potential in the presence of a positive cosmological constant does not go asymptotically to zero for large distances , which is to say that @xmath133 is not stringent enough to guarantee a bound system .
therefore , we rather rely on the numerical solutions from which , for every @xmath2 , we infer the value of @xmath137 such that @xmath138 this gives us the lowest possible central density in terms of @xmath39 . the behavior of the @xmath139 , the functions @xmath140 , the solution @xmath141 and the values of @xmath142 are shown in fig [ tablelane2 ] .
note that this inequality can be understood as a generalization of the equilibrium condition @xmath143 , which , when applied for a spherical homogeneous configurations yields @xmath144 with @xmath145 constant @xcite . , @xmath146 , the functions @xmath147 , and @xmath148 .
equilibrium configurations are reached for @xmath149 ( for a @xmath0cdm cosmoolgy one has to rewrite @xmath150).,width=340 ] note that , at @xmath76 the radius of the configuration becomes undefined , as well as the energy .
a @xmath76 polytrope is highly concentrated at the center @xcite .
no criteria can be written since even for @xmath81 there is not a finite radius .
but it is this high concentration at the center and a smooth asymptotic behavior which makes this case still a viable phenomenological model if @xmath0 is zero . on the contrary for non - zero , positive @xmath0
the solutions start oscillating around @xmath151 which makes the definition of the radius more problematic . for @xmath152
the polytropic e.o.s describes an ideal gas ( isothermal sphere ) . since in this limit
the expressions derived before are not well definite , this case will be explored in more detail in the next section . in spite of the mathematical differences , the isothermal sphere bears many similarities to the cases @xmath110 and
our conclusions regarding the definition of a radius in the @xmath111 case equally apply to finite @xmath2 bigger than @xmath153 . and different polytropic index in a modified newton - hook space time with a dark energy equation of state @xmath154 ( black , dots ) and @xmath155 ( red , short dash ) .
compare with fig.[lanea],width=453 ] in the last section we have explored the effects of a dark energy - dominated background with the equation of state @xmath17 .
other dark energy models are often used with @xmath156 and @xmath154 or even @xmath157 , in the so - called phantom regime , or even a time dependent dark energy model ( quintessence ) . a simple generalization to such models
can be easily done by making the following replacement in our equations @xmath158 where @xmath159 , and where the function @xmath14 is defined in eq.([fa ] ) .
note that for this generalization to be coherent with the derivation of @xmath0le in ( [ le ] ) , one needs to consider that the equation of state is close to @xmath160 , so that there is almost no time - dependence , and the energy density for dark energy is almost constant .
this is indeed the case for most popular candidates of dark energy specially at low redshifts @xmath161 .
also , notice once again , that we are still assuming an homogeneous dark energy component which flows freely to and from the overdensity .
hence , violating energy conservation inside it . clearly , other models of dark energy will posses dynamical properties that the cosmological constant does not have .
for instance , we could allow some fraction of dark energy to take part in the collapse and virialization @xcite , which would lead to the presence of self and cross interaction terms for dark energy and the ( polytropic like ) matter in euler equation , which at the end modifies the lane emden equation . with this simplistic approach
, we see that the effects with a general equation of state are smaller than those associated to the cosmological constant .
in particular , the equation of state @xmath156 displays a null effects since it implies @xmath162 ( note that this equation of state can also resemble the curvature term in evolution equation for the background ) . on the other hand , phantom models of dark energy , which are associated to equations of state @xmath157@xcite ,
have quite a strong effect . in fig . [ laneph ]
we show numerical solutions of lane - emden equations for a background dominated with dark energy with @xmath154 and a phantom dark energy with @xmath155 , with @xmath163 .
these curves are to be compared with those at fig.[lanea ] .
clearly equations of state with @xmath164 will generate larger radius than the case described in the main text .
furthermore , the asymptotic behavior of the ratio between the density and @xmath32 is @xmath165 .
stability criteria for polytropic configurations can be derived from the virial equation . using equations ( [ piner ] ) , ( [ pintener ] ) and ( [ poliwc ] ) we can write the virial theorem ( [ virial ] ) in terms of the radius @xmath80 and the mass @xmath166 : @xmath167 where we have assumed that the only contribution to the kinetic energy comes from the pressure in the form of @xmath168 .
note that for @xmath81 and finite mass , one obtains @xmath169 while for @xmath136 we would obtain a cubic equation for the radius . instead of solving for the virial radius , we solve for the mass as a function of central density with the help of eq ( [ radius3 ] ) . we have @xmath170^{\frac{3}{2}}.\ ] ]
the explicit dependence of the mass with respect to the central density splits into two parts : on one hand it has the same form as the usual case with @xmath106 , that is , @xmath171 ; on the other hand the function @xmath172 has a complicated dependence on the central density because of the term @xmath173 . with the help of ( [ radius3 ] ) and ( [ fmas2aa ] ) we can write a mass - radius relation and the radius - central density relation @xmath174 following the stability theorem ( see for instance in @xcite )
, the stability criteria can be determined from the variations of the mass in equilibrium with respect to the central density .
we derive from eq .
( [ fmas2aaa ] ) : @xmath175\rho_{\rm c}^{\frac{3}{2}(\gamma-\frac{4}{3})}.\ ] ] stability ( instability ) stands for @xmath176 ( @xmath177 ) .
this yields a critical value of the polytropic exponent @xmath178 when @xmath179 given by @xmath180 in the sense that polytropic configurations are stable under small radial perturbations if @xmath181 .
it is clear that the second term in ( [ slope2 ] ) also depends on the polytropic index and therefore this equation is essentially a transcendental expression for @xmath178 .
it is worth mentioning that by including the corrections due to general relativity , the critical value for @xmath178 is also modified as @xmath182 @xcite and hence for compact objects the correction to the critical polytropic index is stronger from the effects of general relativity than from the effects of the background .
this is as we would expect it .
stability of relativistic configurations with non - zero cosmological constant has been explored in @xcite .
going back to equation ( [ fmas2aa ] ) , we can write the mass of the configuration as @xmath183 , where @xmath184 is the mass when @xmath106 and @xmath185 is the enhancement factor
. both quantities can be calculated to give @xmath186^{\frac{3}{2}},\ ] ] where @xmath187 are numerical factors ( tabulated in table 1 ) that can be determined in a straightforward way .
similarly , by using eq ( [ radius3 ] ) , the radius can be written as @xmath188 , where @xmath189^{\frac{1}{2}}.\ ] ] in table [ tablelane2a ] we show the values of the enhancement factors @xmath190 and @xmath191 for different values of @xmath173 and different polytropic index @xmath2 .
we also show the values of the critical ratio @xmath139 which separates the configurations with definite ratio such that a zero @xmath103 exist provided that @xmath192 .
we will show some examples where the enhancement factors may be relevant in section 5 .
.numerical values for the enhancement factors @xmath193 ) ( values for @xmath194 have been taken from @xcite ) .
the symbol @xmath195 indicates a non defined radius . [ cols="^,^,^,^",options="header " , ]
in this section we will probe into the possibilities of exotic , low density configurations .
the global interest in such structures is twofold .
first , the cosmological constant will affect the properties of low density objects .
secondly , @xmath0 plays effectively the role of an external , repulsive force .
hence a relevant issue that arises in this context is to see whether the vacuum energy density can partly _
replace _ the pressure which essentially is encoded in the parameter @xmath63 ( @xmath196 ) . by the word _
replace _ we mean that we want to explore the possibility of a finite radius as long as the pressure effects are small in the presence of @xmath32 . as mentioned above the effect of a positive cosmological constant on matter
is best understood as an external repulsive force . in previous sections
we have probed into one extreme which describes the situation where a relatively low density object is pulled apart by this force ( to an extent that we concluded that the isothermal sphere is not a viable model in the presence of @xmath0 ) . limiting
conditions when this happens were derived . on the other hand , approaching with our parameters these limiting conditions , but remaining still on the side of equilibrium , means that relatively low density objects can be still in equilibrium thanks to the positive cosmological constant . the best way to investigate low density structures is to to use the lowest possible central density . as explained in section 3 , for every @xmath2 there
exist a @xmath142 such that @xmath197 which defines the lowest central density .
certainly , a question of interest is to see what such objects would look like .
we start with the parameters of the configuration .
the radius at the critical value @xmath139 is given by eq.([radius3 ] ) after taking the limit @xmath198 ( see ( [ an ] ) ) .
it is given by @xmath199 from fig .
[ lanecrit ] we can see that the product @xmath200 changes a little round the value @xmath201 as we change the index @xmath2 , so that these polytropic configurations will have roughly the same radius ( for a given mass ) .
this implies that such configurations have approximately the same average density @xmath202 .
that is , such configurations have a mean density of the order of the of the critical density of the universe .
given such a density we would , at the first glance , suspect that the object described by this density can not be in equilibrium .
however , our result follows strictly from hydrostatic equilibrium and therefore there is no doubt that such object can theoretically exist .
furthermore , @xmath203 satisfies the inequalities derived in @xcite and @xcite from virial equations and buchdahl inequalities which guarantee that the object is in equilibrium ( @xmath204 ) .
interestingly , the central density for such objects has to be much higher than @xmath203 as , e.g. , for @xmath74 we have @xmath205 and therefore @xmath206 .
, now the functions @xmath140 being evaluated at the value @xmath207 solution of eq.([virtras]).,width=340 ] note that these values have been given from the solution of the lane - emden equation , which is a consequence of dynamical equations reduced to describe our system in a steady state .
however , we have not tried to solve explicitly quantities from the virial theorem .
this makes sense as for dark matter halos ( dmh ) the parametrized density profiles go often only asymptotically to zero and the radius of dmh is defined as a virial radius where the density is approximately two hundred times over the critical one .
therefore , an analysis using virial equations seems to be adequate here . for constant density eq.([vpol ] ) can be expressed as a cubic equation @xcite for the radius at which the virial theorem is satisfied ( let us ignore for these analysis any surface terms coming from the tensor virial equation ) . however , if the density is not constant , this expression becomes a transcendental equation for the dimensionless radius @xmath208 .
this equation is @xmath209},\ ] ] understanding the functions @xmath140 now as integrals up to the value @xmath207 .
once we fix @xmath139 for a given index @xmath2 , we use as a first guess for the iteration process the value @xmath210 . in fig
[ lanecrit ] we show the behavior of the functions @xmath140 and the solutions of eq.([virtras ] ) . for these values , eq .
( [ rque ] ) gives for @xmath74 a radius @xmath211 which can be compared with the radius - mass relation derived in the top - hat sphericall collapse @xcite @xmath212 where @xmath213 is the dimensionless hubble parameter and @xmath214 is the redshift of virialization .
the resulting average density is then of the order of the value predicted by the top - hat sphericall model : @xmath215 note with the help of eq.([a ] ) and ( [ rque ] ) that the mass can be written as proportional to the parameter @xmath216 ( introduced in the polytropic equation of state eq.([poly ] ) ) .
therefore @xmath217 is equivalent to choosing a small pressure and , at the same time , a small mass which , in case of a relatively small radius , amounts to a diluted configuration with small density and pressure . without @xmath0
such configurations would be hardly in equilibrium .
hence , for the configuration which has the extension of pc , eq.([xxx14 ] ) , with one solar mass we conclude that the equilibrium is not fully due to the pressure , but partially maintained also by @xmath0 .
this is possible , as @xmath0 exerts an outwardly directed non local force on the body .
other mean densities , also independent of @xmath166 are for @xmath218 and @xmath75 , respectively : @xmath219 the first value is close to @xmath220 and therefore also to @xmath39 .
certainly , if in this example we choose a small mass , equivalent to choosing a negligible pressure , part of the equilibrium is maintained by the repulsive force of @xmath0 .
in @xcite we found a simple solution of the hydrostatic equation which has a constant density of the order of @xmath39 .
the above is a non - constant and non - trivial generalization of this solution .
the neutrino stars which we will discuss in the subsequent subsection are modeled in close analogy to white dwarfs .
therefore it makes sense to recall some part of the physics of white dwarfs . in addition
we can contrast the example of white dwarfs to the low density cases affected by @xmath0 . in the limit where the thermal energy @xmath221 of a ( newtonian ) white dwarf is much smaller than the energy at rest of the electrons ( @xmath222 ,
these configurations can be treated as polytropic configuration with @xmath74 .
this is the ultra - relativistic limit where the mass of electrons is much smaller than fermi s momentum @xmath223 . in the opposite case
we obtain a polytrope or configuration with @xmath224 .
@xcite . in both cases ,
the parameter @xmath225 from the polytropic equation of state is given as @xmath226 where @xmath227 is the nucleon mass , @xmath228 is the electron mass and @xmath229 is the number of nucleons per electron . using the newtonian limit with cosmological constant , we can derive the mass and radius of these configurations in equilibrium . in the first case , for @xmath74 the mass
is written using ( [ fmas2aa ] ) as @xmath230 which corresponds approximately to the chandrasekhar s limit ( strictly speaking a configuration would have the critical mass , i.e , the chandrasekhar s limit , if its polytropic index @xmath62 is such that @xmath231 ) .
for this situation one has @xmath232 and @xmath233 . on the other hand , for @xmath224 one
obtains @xmath234 and the radius is given by @xmath235 where @xmath236 is the mean density of the sun .
since for these configurations the ratio @xmath173 is much smaller than @xmath237 we see from fig .
[ tablelane2 ] that the effects of @xmath0 are almost negligible .
the critical value of the ratio @xmath173 gives for @xmath74 the inequality @xmath238 and for @xmath224 the same limit reads @xmath239 .
central densities of white dwarfs are of the order of @xmath240 which corresponds to a deviation of nearly thirty orders of magnitude of @xmath39 .
an interesting possibility is to determine the effects of @xmath241 on configurations formed by light fermions .
such configurations can be used , for instance , to model galactic halos @xcite .
while discussing the phenomenological interest of fermion stars below , we intend to describe such a halo .
clearly , these kind of systems will maintain equilibrium by counterbalancing gravity with the degeneracy pressure as in a white dwarf .
for stable configurations ,
i.e , @xmath224 , one must replace the mass of the electron and nucleon by the mass of the considered fermion and set @xmath242 in ( [ kn ] ) and ( [ fmas2aa ] ) .
we then get for the mass and the radius : @xmath243 on the other hand , for @xmath74 one has @xmath244 the cases represent , among other , possible cosmological configurations when the fermion mass if of the order of ev , for instance , massive neutrinos . and @xmath224 .
the masses range from @xmath245 ev up to @xmath246 ev.,width=377 ] in figure [ tablelane244 ] some representative values for the choice @xmath247 ev up to @xmath248 ev are given .
obviously in the case @xmath218 the values for the mass and radius are sensitive to the choice of @xmath249 .
indeed , the dependence on the fermion mass is much stronger than on the central density .
it is justified to speculate that a relative low density objects , affected by @xmath0 , might exist .
if then , as in an example we choose @xmath250 ev and @xmath251 then the mass comes out as @xmath252 solar masses with a radius of the order of magnitude of half mpc which might indeed be the dark matter halo of a galaxy ( or at least part of the halo ) . as pointed out before
, such configurations must have a central density greater than @xmath253 in order to be in equilibrium . from table [ tablelane2a ]
we see that the effect on a configuration with @xmath254 is represented in an increase in the mass by @xmath255 with respect to @xmath256 and an increment of @xmath257 in the radius .
then the conclusion would be that @xmath0 affects such a dark matter halo .
this is to be taken with some caution as the fermions in such a configuration would be essentially non - relativistic .
note also that it is not clear if neutrinos make up a large fraction of the halo , however , we can also speculate about a low density clustering around luminous matter . of course , allowing larger central density might change the picture .
however , the emerging scenario would not necessarily be a viable phenomenological model .
for instance , changing the value of @xmath249 from ev to kev ( mev ) would reduce the mass by twelve ( twenty four ) orders of magnitude which is definitely too small to be of interest . we could counterbalance this by increasing the central density by twenty four ( forty eight ! ) orders of magnitude . such a countermeasure would , however , result in a reduction of the radius by eight ( sixteen ! ) orders of magnitude , again a too small length scale to be of importance for dark matter halos . in other words ,
the example with a fermion mass of the order of one ev and low central density is certainly of some phenomenological interest .
the case @xmath74 is similarly stringent .
a neutrino mass of @xmath258 ev gives a mass for the entire object of the order of ten to the eighteen solar masses which is too large .
a fermion mass of several kev would be suitable for a galaxy halo ( a mass of the order me v and higher would give a too small total mass ) . with a relative low central density as before ( see figure [ tablelane244 ] ) we then obtain the right order of magnitude for the halo .
but then we will have to live with the fact that such halo reaches up to the next large galaxy .
briefly , we touch upon the other possible application of fermions stars which have been discussed as candidates for the central object in our galaxy . if we allow the extension of this object to be @xmath259 au and the mass roughly @xmath260 million solar masses , then the fermion mass would come out as @xmath261 ev for @xmath218 ( @xmath262 ev for @xmath74 ) and the central density as @xmath263 ( @xmath264 for @xmath74 ) .
we end the section by putting forward a speculative question in connection with boson stars .
the latter are general relativistic geons and can be treated exactly only in general relativistic framework i.e. these kind of configurations are based on the interaction of a massive scalar field and gravitation which leads to gravitational bounded systems .
these objects have been also widely discussed as candidates for dark matter @xcite . on the other hand ,
variational methods in the connection with the thomas - fermi equations give relatively good results even without invoking the whole general relativistic formalism . by including @xmath0 we essentially introduce into the theory a new scale ,
say in this case a length scale @xmath265 . the basic parameters of dimension length in a theory with a boson mass @xmath266 and a total mass @xmath267 where @xmath268 is the number of bosons are ( for a better distinction of the different length scales , we restore in this subsection the value of @xmath6 ) @xmath269 the resulting radius of the object s extension can be a combination of these scales i.e. @xmath270 and similar combination of higher order . which one of the combination gets chosen , depends on the details of the model . in a close analogy to @xcite
we can examine this taking into account the presence of a positive cosmological constant by considering the energy of such configuration as a two variable function of the mass and the radius @xmath271 @xmath272 the first term corresponds to the total kinetic energy written as @xmath273 and taking @xmath274 .
the second term is the gravitational potential energy and the third term corresponds to the contribution of the background ( see eq .
( [ virialeq ] ) ) . by treating mass and radius as independent variables ( we think this this is the right procedure since the radius will depend on the external force due to @xmath32 ) , we extremize the energy leading to the following values of mass and radius : @xmath275 such values would lead to a mean density of the order of @xmath276 i.e. an extremely low density configuration .
the mass given in the last expression is the so - called kaup limit @xcite . of course
, this relative simple treatment does not guarantee that the full , general relativistic treatment , will give the same results .
therefore we consider it as a conjecture .
however , it is also obvious from the the discussion above that low density boson stars are a real possibility worth pursuing with more rigor ( we intend to do so in the near future ) .
it is of some importance to see whether our results from the examination of polytropic hydrostatic equilibrium or from the virial equations can be applied to dark matter configurations .
n - body simulations based in a @xmath0cdm model of the universe show that the density profile of virialized dark matter halos ( dmh ) can be described by a profile of the form @xcite @xmath277 where @xmath278 is the characteristic radius ( the logarithmic slope is @xmath279 ) , @xmath280 and the index @xmath281 characterizes the slope of the profile in the central regions of the halo .
the mass of the configuration enclosed in the virial radius @xmath282 is given as @xmath283 such that one can write @xmath284 , where @xmath285 is the concentration parameter , @xmath286 is the ratio between the mean density at the time of virialization and the critical density of the universe ( @xmath287 in the top - hat model for a flat einstein - desitter universe , while @xmath288 in the @xmath0cdm cosmological model @xcite ) and @xmath289 .
this _ universal profile _ has been widely used in modeling dmh in galaxy clusters , and the comparison of these models with a stellar polytropic - like profile -without the explicit contribution from the cosmological constant in the lane - emden equation- can be found in @xcite .
some differences can be described between the @xmath0le and the nfw profiles .
first , on fundamental grounds , it is clear that the nfw profile does not satisfy the le equation ; a basic reason for this is that dark matter is assumed to be collisionless and is only affected by gravity .
however , the fact that the real nature of dark matter is still an unsolved issue leaves an open door through which one can introduce interaction between dark matter particles leading to a different equation of state ( see for instance @xcite ) . on functional forms
, one sees that at the central region the difference is abrupt , since the lane - emden equation has a flat density profile at @xmath290 , while the nfw profile has a cuspy profile of the form @xmath291 .
it has been widely discussed how such cuspy profile is inconsistent with data showing central regions of clusters with homogeneous cores ( see discussion at the end of this section ) .
such small slope in the inner regions can be reproduced by the _
universal profile _ for the case @xmath292 , and for the profile derived from the @xmath0le equation ( which is just a consequence of initial conditions , and hence , its independent of @xmath0 ) . in this case , the effects of the cosmological constant can be reduced to explore the outer regions of the halos and compare , for instance , the slope of the profiles and the virial radius predicted by each one .
le equation for different masses and different index @xmath2 ranging from @xmath74(blue , dots ) , @xmath75 ( red , short - dashed line ) , @xmath293 ( green , long - dashed line ) and @xmath294 ( magenta , dot short - dashed line ) , in the limiting case @xmath295 .
the solution from le equation is written for the critical value of the parameter @xmath139 , shown in table [ tablelane2 ] .
the vertial black line represents the virial radius from the nfw profile .
the vertical colored lines represent the virial radius @xmath296 for the different polytropic indices.,width=453 ] but for the radius given by the condition @xmath105.,width=453 ] the density profiles predicted by the @xmath0le equation and the nfw profile ( for @xmath297 ) are presented in fig.[compav ] for the virial radius given by @xmath207 and in fig.[compac ] for the radius given by @xmath103 , both with @xmath295 . also , the behavior of the radius for different values of mass and polytropic indices are given in fig [ raddd ] ( with @xmath298 kpc and @xmath299 mpc @xmath300 kpc @xcite ) .
( blus , solid line ) for four different values of @xmath2.,width=453 ] we see that the virial radius given by the @xmath0le equation is surprisingly close to the virial radius given by the nfw profile for @xmath74 in the range of masses shown in fig [ raddd ] , and as pointed in eq.([contrast ] ) , this value yields for this model @xmath301 .
however , as can be seen from the plots , the @xmath0le density profile is almost flat until the virial radius . on the other hand ,
the @xmath292 profile allow us to parameterize it as @xmath302 , where the concentration parameter @xmath65 can be written as @xmath303 .
compared with the and @xmath74 @xmath0le profile , with its corresponding @xmath139 , for different masses.,width=453 ] for @xmath294,width=453 ] in fig.[comp1 ] and [ comp4 ] we have compared both profiles with the corresponding @xmath139 for polytropic index @xmath74 and @xmath294 . for the first case
we see that the virial radius are of the same order of magnitude than the one predicted by the nfw profile . for @xmath294 , these quantities differ by one order of magnitude . in all cases ,
the slope of the nfw profiles changes faster than the @xmath0le profile , which implies that the polytropic configurations enclosed by @xmath282 display almost a constant density . the comparison we made above between the polytropic configuration and the nfw profiles shows that up to the cuspy behaviour the polytropic results agree with nfw for the polytropic index @xmath74 .
it is worth pointing out here that it is exactly this cuspy behaviour which seems to be at odds with observational facts @xcite .
our result for @xmath74 is then a good candidate to describe dmh .
indeed , the undesired feature of the cuspy behaviour led at least some groups to model the dmh as a polytropic configuration @xcite . sometimes it is claimed that a polytropic model is favoured over the results from n - body simulation @xcite .
however , the oscillatory behavior of the @xmath74 solutions of the @xmath0le represents a disadvantage when compared with the nfw profiles , although the region of physical interest ( below the virial radius ) is well represented by the solutions of @xmath0le .
in this paper we have explored the effects of a positive cosmological constant on the equilibrium and stability of astrophysical configurations with a polytropic equation of state .
we have found that the radius of these kind of configurations is affected in the sense that not all polytropic indices yield configurations with definite radius even in the asymptotic sense . among other ,
the widely used isothermal sphere model becomes a non - viable model in the presence of @xmath0 unless we are ready to introduce an arbitrary cut - off which renders the model unappealing .
indeed , in this particular case we have tried different definitions of a finite radius with the result that none of them seems to be justified , either from the phenomenological or from the theoretical point of view .
this is then an interesting global result : @xmath0 not only affects quantitatively certain properties of large , low - density astrophysical structures , but it also excludes certain commonly used models regardless what density we use . for polytropic indexes @xmath304 and for _ certain values
_ of the central density we can not find a well definite radius .
these _ certain values _ are encoded in a generalization of the equilibrium condition found for spherical configurations ( i.e , @xmath305 ) written now as @xmath149 .
we obtain @xmath306 , @xmath307 , @xmath308 , @xmath309 .
these values set a minimal central density for a given polytropic index @xmath2 .
we have discussed such minimal density configurations and determined their average density which strongly depend on @xmath2 .
interestingly , the radius of such configurations has a connection to the length scale which appears in the schwarzschild- de sitter as the maximally possible radius for bound orbits @xcite .
in this framework we found also a solution of very low , non - constant density .
indeed , the limiting value of the central density in the above equations is a crucial point . below this value
no matter can be in equilibrium .
however , above this value low density objects can still exist .
both effects are due to @xmath0 : in the first case the external repulsive force is too strong for the matter to be in equilibrium , in the second case this force can counterbalance the attractive newtonian gravity effects ( even if the pressure is small ) .
other examples of low density configuration which we examined in some detail are neutrino stars with mass of the order @xmath310 ev and @xmath310 kev .
in there we found that a nowadays dominating cosmological constant affects both the mass as well as the radius of such exotic objects .
such effect could change those physical quantities several orders of magnitude .
the magnitude of such effects , however , depend on the fermionic masses and on the assumption that the fermions in such a configuration would be essentially non - relativistic .
finally , we made a conjecture regarding boson stars , and used variational methods in connection with the thomas - fermi equations which could give relatively good results even without invoking the whole general relativistic formalism , we then found extremely low density configurations for such astrophysical objects .
notice however , that this conjecture relied purely on arguments based on scales and in fact needs a full general relativistic investigation to confirm the results here obtained .
we have compared polytropic configurations with dark matter density profiles from n - body simulations .
surprisingly , we find a reasonable agreement between both approaches for the polytropic index @xmath74 and restricting ourselves to the virial radius .
our model does not have the the undesired features of the cuspy behaviour of the nfw profiles .
the importance of the astrophysical properties and configurations found in this article is that they are specific features to the existence of a dark energy component .
hence , such configurations ( e.g , low density configurations ) or properties , if ever found in nature would imply a strong evidence for the presence of a dark energy component .
such observations would be a completely independent , and so complementary , of other cosmological probes of dark energy such as supernova ia or the cmbr .
we acknowledge stefanie phleps for her comments on the manuscript .
dfm acknowledge support from the a. humboldt foundation .
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. phys . * 06 * , 008 ( 2006 )[/INST] we explore the effects of a positive cosmological constant on astrophysical and cosmological configurations described by a polytropic equation of state .
we derive the conditions for equilibrium and stability of such configurations and consider some astrophysical examples where our analysis may be relevant .
we show that in the presence of the cosmological constant the isothermal sphere is not a viable astrophysical model since the density in this model does not go asymptotically to zero .
the cosmological constant implies that , for polytropic index smaller than five , the central density has to exceed a certain minimal value in terms of the vacuum density in order to guarantee the existence of a finite size object .
we examine such configurations together with effects of @xmath0 in other exotic possibilities , such as neutrino and boson stars , and we compare our results to n - body simulations . the astrophysical properties and configurations found in this article are specific features resulting from the existence of a dark energy component . hence
, if found in nature would be an independent probe of a cosmological constant , complementary to other observations .
[ firstpage ] cosmology theory dark energy
structure formation </s> |
A TV host and sports broadcaster on Thursday accused Sen. Al Franken Alan (Al) Stuart FrankenGillibrand announces exploratory committee to run for president on Colbert The Hill’s 12:30 Report: Trump AG pick Barr grilled at hearing | Judge rules against census citizenship question | McConnell blocks second House bill to reopen government Overnight Health Care: House Dems launch major drug pricing investigation | Judge blocks Trump contraception rule rollback | Booker tries to shake doubts about pharmaceutical ties ahead of 2020 | FDA to resume high-risk food inspections MORE (D-Minn.) of kissing and groping her without her consent in 2006.
Leeann Tweeden accused Franken of groping her, without her consent, while she was asleep and provided a photo as evidence.
KABC anchor: Senator Al Franken Kissed and Groped Me Without My Consent, And There’s Nothing Funny About It https://t.co/lG4A1ZTUhC pic.twitter.com/EYIzr9ok2s — Meridith McGraw (@meridithmcgraw) November 16, 2017
The incident happened in December 2006, she said, when she and Franken, then a comedian, were on a USO tour to "entertain our troops."
Franken in a statement apologized for his actions.
ADVERTISEMENT
"It wasn’t until I was back in the U.S. and looking through the CD of photos we were given by the photographer that I saw this one," Tweeden wrote about the photo on KABC.
"I felt violated all over again. Embarrassed. Belittled. Humiliated," she wrote. "How dare anyone grab my breasts like this and think it’s funny?"
Tweeden wrote that Franken, who was the headliner on the tour, had written some skits and told her he had a part for her, adding that she "agreed to play along."
"When I saw the script, Franken had written a moment when his character comes at me for a ‘kiss’. I suspected what he was after, but I figured I could turn my head at the last minute, or put my hand over his mouth, to get more laughs from the crowd," she wrote.
"On the day of the show Franken and I were alone backstage going over our lines one last time. He said to me, 'We need to rehearse the kiss.' I laughed and ignored him. Then he said it again. I said something like, ‘Relax Al, this isn’t SNL…we don’t need to rehearse the kiss.’"
She wrote Franken continued to insist and she got "uncomfortable."
"He repeated that actors really need to rehearse everything and that we must practice the kiss. I said ‘OK’ so he would stop badgering me. We did the line leading up to the kiss and then he came at me, put his hand on the back of my head, mashed his lips against mine and aggressively stuck his tongue in my mouth," she wrote.
"I immediately pushed him away with both of my hands against his chest and told him if he ever did that to me again I wouldn’t be so nice about it the next time."
She said she felt disgusted and violated. She added that she didn't tell anyone what happened at the time, but she was "angry."
Tweeden also said she fell asleep while on the plane back to the U.S. She said is wasn't until she saw the photo of Franken groping her that she told her husband what had happened and showed him the photo.
"I wanted to shout my story to the world with a megaphone to anyone who would listen, but even as angry as I was, I was worried about the potential backlash and damage going public might have on my career as a broadcaster," she wrote.
"But that was then, this is now. I’m no longer afraid."
She said she is sharing her story because there may be others.
"I want the days of silence to be over forever," she wrote.
Tweeden also issued a direct statement to Franken.
"Senator Franken, you wrote the script. But there’s nothing funny about sexual assault," she wrote.
"You knew exactly what you were doing. You forcibly kissed me without my consent, grabbed my breasts while I was sleeping and had someone take a photo of you doing it, knowing I would see it later, and be ashamed."
Franken said he does not remember the incident the same way but acknowledged the photo "wasn't" funny.
“I certainly don’t remember the rehearsal for the skit in the same way, but I send my sincerest apologies to Leeann. As to the photo, it was clearly intended to be funny but wasn't. I shouldn't have done it," he said in a statement.
Tweeden's comments come amid increased reports of sexual harassment in the workplace, including on Capitol Hill. Multiple women in Congress have come forward to say they have been victims of sexual harassment, prompting lawmakers to call for reform.
Rep. Jackie Speier (D-Calif.) said Tuesday the House has paid out $15 million in harassment settlements over more than a decade, though a spokesperson later clarified that figure does not only account for sexual harassment claims.
She said at a Tuesday hearing that two current members of Congress, one Republican and one Democrat, have been accused of sexual harassment.
Her comments come after multiple women have accused GOP Senate candidate Roy Moore of sexual misconduct. Moore is facing growing calls from top Republicans to step aside in the Alabama race, though he has indicated he plans to continue running.
This report was updated at 11:07 a.m. | – A radio host and former Playboy playmate says Sen. Al Franken assaulted her—and unlike some women coming forward with similar tales about other high-profile figures, Leeann Tweeden offered proof. In a first-person account at KABC, Tweeden says she was groped in December 2006 when she and the Democratic senator from Minnesota, then a comedian, were on a plane ride home from the Middle East, where they'd entertained troops as part of a USO tour. As she slept, Tweeden says Franken groped her breasts in a moment that was caught on camera. "It wasn't until I was back in the US and looking through the CD of photos we were given by the photographer that I saw this one," Tweeden says of the photo, which shows Franken grinning, his hands on Tweeden's clothed breasts. Earlier in the trip, Tweeden says Franken had also kissed her without her consent as the pair were rehearsing a skit. Franken decided their characters would kiss and "mashed his lips against mine and aggressively stuck his tongue in my mouth," Tweeden writes. "I felt disgusted and violated" and "wanted to shout my story to the world with a megaphone," she continues. "But even as angry as I was, I was worried about the potential backlash and damage going public might have on my career as a broadcaster," Tweeden writes. But "I've decided it's time to tell my story. #MeToo," she tweeted. Franken apologized Thursday but says he remembers the skit rehearsal differently, per the Hill. "As to the photo, it was clearly intended to be funny but wasn't," he says. "I shouldn't have done it." | <s>[INST]A TV host and sports broadcaster on Thursday accused Sen. Al Franken Alan (Al) Stuart FrankenGillibrand announces exploratory committee to run for president on Colbert The Hill’s 12:30 Report: Trump AG pick Barr grilled at hearing | Judge rules against census citizenship question | McConnell blocks second House bill to reopen government Overnight Health Care: House Dems launch major drug pricing investigation | Judge blocks Trump contraception rule rollback | Booker tries to shake doubts about pharmaceutical ties ahead of 2020 | FDA to resume high-risk food inspections MORE (D-Minn.) of kissing and groping her without her consent in 2006.
Leeann Tweeden accused Franken of groping her, without her consent, while she was asleep and provided a photo as evidence.
KABC anchor: Senator Al Franken Kissed and Groped Me Without My Consent, And There’s Nothing Funny About It https://t.co/lG4A1ZTUhC pic.twitter.com/EYIzr9ok2s — Meridith McGraw (@meridithmcgraw) November 16, 2017
The incident happened in December 2006, she said, when she and Franken, then a comedian, were on a USO tour to "entertain our troops."
Franken in a statement apologized for his actions.
ADVERTISEMENT
"It wasn’t until I was back in the U.S. and looking through the CD of photos we were given by the photographer that I saw this one," Tweeden wrote about the photo on KABC.
"I felt violated all over again. Embarrassed. Belittled. Humiliated," she wrote. "How dare anyone grab my breasts like this and think it’s funny?"
Tweeden wrote that Franken, who was the headliner on the tour, had written some skits and told her he had a part for her, adding that she "agreed to play along."
"When I saw the script, Franken had written a moment when his character comes at me for a ‘kiss’. I suspected what he was after, but I figured I could turn my head at the last minute, or put my hand over his mouth, to get more laughs from the crowd," she wrote.
"On the day of the show Franken and I were alone backstage going over our lines one last time. He said to me, 'We need to rehearse the kiss.' I laughed and ignored him. Then he said it again. I said something like, ‘Relax Al, this isn’t SNL…we don’t need to rehearse the kiss.’"
She wrote Franken continued to insist and she got "uncomfortable."
"He repeated that actors really need to rehearse everything and that we must practice the kiss. I said ‘OK’ so he would stop badgering me. We did the line leading up to the kiss and then he came at me, put his hand on the back of my head, mashed his lips against mine and aggressively stuck his tongue in my mouth," she wrote.
"I immediately pushed him away with both of my hands against his chest and told him if he ever did that to me again I wouldn’t be so nice about it the next time."
She said she felt disgusted and violated. She added that she didn't tell anyone what happened at the time, but she was "angry."
Tweeden also said she fell asleep while on the plane back to the U.S. She said is wasn't until she saw the photo of Franken groping her that she told her husband what had happened and showed him the photo.
"I wanted to shout my story to the world with a megaphone to anyone who would listen, but even as angry as I was, I was worried about the potential backlash and damage going public might have on my career as a broadcaster," she wrote.
"But that was then, this is now. I’m no longer afraid."
She said she is sharing her story because there may be others.
"I want the days of silence to be over forever," she wrote.
Tweeden also issued a direct statement to Franken.
"Senator Franken, you wrote the script. But there’s nothing funny about sexual assault," she wrote.
"You knew exactly what you were doing. You forcibly kissed me without my consent, grabbed my breasts while I was sleeping and had someone take a photo of you doing it, knowing I would see it later, and be ashamed."
Franken said he does not remember the incident the same way but acknowledged the photo "wasn't" funny.
“I certainly don’t remember the rehearsal for the skit in the same way, but I send my sincerest apologies to Leeann. As to the photo, it was clearly intended to be funny but wasn't. I shouldn't have done it," he said in a statement.
Tweeden's comments come amid increased reports of sexual harassment in the workplace, including on Capitol Hill. Multiple women in Congress have come forward to say they have been victims of sexual harassment, prompting lawmakers to call for reform.
Rep. Jackie Speier (D-Calif.) said Tuesday the House has paid out $15 million in harassment settlements over more than a decade, though a spokesperson later clarified that figure does not only account for sexual harassment claims.
She said at a Tuesday hearing that two current members of Congress, one Republican and one Democrat, have been accused of sexual harassment.
Her comments come after multiple women have accused GOP Senate candidate Roy Moore of sexual misconduct. Moore is facing growing calls from top Republicans to step aside in the Alabama race, though he has indicated he plans to continue running.
This report was updated at 11:07 a.m.[/INST]– A radio host and former Playboy playmate says Sen. Al Franken assaulted her—and unlike some women coming forward with similar tales about other high-profile figures, Leeann Tweeden offered proof. In a first-person account at KABC, Tweeden says she was groped in December 2006 when she and the Democratic senator from Minnesota, then a comedian, were on a plane ride home from the Middle East, where they'd entertained troops as part of a USO tour. As she slept, Tweeden says Franken groped her breasts in a moment that was caught on camera. "It wasn't until I was back in the US and looking through the CD of photos we were given by the photographer that I saw this one," Tweeden says of the photo, which shows Franken grinning, his hands on Tweeden's clothed breasts. Earlier in the trip, Tweeden says Franken had also kissed her without her consent as the pair were rehearsing a skit. Franken decided their characters would kiss and "mashed his lips against mine and aggressively stuck his tongue in my mouth," Tweeden writes. "I felt disgusted and violated" and "wanted to shout my story to the world with a megaphone," she continues. "But even as angry as I was, I was worried about the potential backlash and damage going public might have on my career as a broadcaster," Tweeden writes. But "I've decided it's time to tell my story. #MeToo," she tweeted. Franken apologized Thursday but says he remembers the skit rehearsal differently, per the Hill. "As to the photo, it was clearly intended to be funny but wasn't," he says. "I shouldn't have done it."</s> |
the use of standard rods distance scales with no evolution in linear size over the lifetime of the universe to carry out geometric tests of cosmological models was first proposed by hoyle ( 1959 ) , but the application of this idea to real data took a long time , specifically because of the difficulty in finding suitable objects or structures for this purpose .
the earliest tests of cosmological models using the observed dependence of the angular size of galaxies or kpc - scale radio sources could not easily define a true metric rod and were subject to unknown evolutionary effects ( e.g. , sandage 1988 ) .
there was uncertainty about whether the observed size - redshift relation in radio galaxies was an indication of an actual evolution in size ( kapahi 1987 ; barthel & miley 1988 ; neeser et al .
1995 ) , or whether it was due to selection effects ( singal 1998 ; nilsson et al .
this was partially addressed in a subsequent study using an enlarged sample of double - lobed quasars at @xmath16 ( buchalter et al .
1998 ) , which showed no change in apparent angular size within the range @xmath17 , consistent with standard cosmology without significant evolution .
separate investigations specifically to study the cosmic deceleration ( or acceleration ) were carried out by gurvits ( 1993 , 1994 ) ( using vlbi visibility data obtained at 13 cm by preston et al .
this analysis also provided estimates of the dependence of the apparent angular size of compact sources on their luminosity and rest - frame frequency .
similar studies were also carried out by kellermann ( 1993 ) and wilkinson et al .
( 1998 ) . within a few years ,
a much enlarged sample of 330 compact radio sources distributed over a broad range of redshifts @xmath18 started to demonstrate that the angular size - redshift relation for compact radio sources is consistent with the predictions of standard friedmann - robertson - walker models without the need to consider evolutionary or selection effects ( gurvits et al .
1999 ) .
other groups carried out their own cosmological tests using powerful radio - lobed radio galaxies , presumed to be reasonable standard yardsticks to determine global cosmological parameters ( daly 1994 , 1995 ) .
the method was applied and discussed by guerra & daly ( 1996 , 1998 ) , guerra ( 1997 ) , and daly , guerra & wan ( 1998 , 2000 ) , who reported that the data at that time strongly favoured a low ( matter ) density universe .
vishwakarma ( 2001 ) and lima & alcaniz ( 2002 ) used the gurvits et al .
( 1999 ) compact radio source angular size versus redshift data to set constraints on cosmological parameters .
this analysis was extended by chen & ratra ( 2003 ) , who used these data to place constraints on cosmological model parameters for a variety of cosmological constant scenarios . and a more focused study using friib radio galaxy redshift - angular size data to derive constraints on the parameters of a spatially - flat cosmology with a dark - energy scalar field was carried out by podariu et al .
( 2003 ) .
more recently , in one of the better known studies using this method , based on the average linear size of galaxies with the same luminosity ( see , e.g. , mcintosh et al . 2005 ; barden et al . 2005 ; trujillo et al .
2006 ; lpez - corredoira 2010 ) , the measurements do not appear to be consistent with an expanding cosmology , unless galaxies have grown in size by a surprisingly large factor six from redshift @xmath19 to @xmath20 .
perhaps the cosmology itself is wrong or , more simply , there is still some ambiguity concerning the use of galactic size as a standard rod . indeed ,
if another more reliable scale could be found , and shown to be consistent with , say , the standard model ( @xmath0cdm ) , the contrast between this result , and the disparity emerging through the use of galaxies , could be useful in affirming the need for stronger evolution in galactic growth than is predicted by current theory .
our focus in this paper will be galaxy clusters , which can also be used as standard rulers under appropriate conditions .
these are the largest gravitationally collapsed structures in the universe , with a hot diffuse plasma ( @xmath21 k ) filling the intergalactic medium . their angular size versus redshift can be measured using a combination of the sunyaev - zeldovich effect ( sze ) and x - ray surface brightness observations .
the sunyaev - zeldovich effect is the result of high - energy electrons distorting the cosmic microwave background radiation ( cmb ) through inverse compton scattering , during which low - energy cmb photons ( on average ) receive an energy boost from the high - energy electrons in the cluster ( sunyaev & zeldovich 1970 , 1972 ) .
the same hot gas emits x - rays primarily via thermal bremsstrahlung . while the sze is a function of the integrated pressure , @xmath22 ( in terms of the electron number density @xmath23 and temperature @xmath24 ) along the line - of - sight , the x - ray emission scales as @xmath25 ( in terms of the cooling function @xmath26 ) .
this different dependence on density , along with a suitable model for the cluster gas , enables a direct distance determination to the galaxy cluster .
this method is independent of the extragalactic distance ladder and provides distances to high - redshift galaxy clusters .
sze / x - ray distances have been previously used to constrain some cosmological parameters and to test the distance duality relationship of metric gravity models ( see , e.g. , de bernardis et al . 2006 ; lima et al .
2010 ; cao & liang 2011 ; holanda et al .
2012 ; chen & ratra 2012 ; liang et al . 2013 ; chen et al .
2013 ) . in this paper
, we will use these data , not to further examine the distance duality relation per se but , rather , to address two related issues .
first , we will use the newer and larger sample of galaxy - cluster angular size versus redshift measurements from bonamante et al .
( 2006 ) to constrain cosmological models .
in particular , we wish to see if the aforementioned tension between galaxy growth and the conventional expansion scenario is supported by the cluster data , or whether the latter confirm the basic theoretical predictions , thus reinforcing the need for a stronger galactic evolution at high redshifts .
second , we wish to use this relatively new probe of the universe s expansion to directly test the @xmath1 universe ( melia 2007 ; melia & shevchuk 2012 ) against the data and to see how its predictions compare with those of @xmath0cdm .
the outline of this paper is as follows . in 2 , we will briefly summarize the galaxy - cluster angular - size sample at our disposal .
we will present theoretical fits to the data in 3 , and constrain the cosmological parameters both in the context of @xmath0cdm and the @xmath1 universe in
we will end with a discussion and conclusion in 5 .
in addition to the luminosity distance , @xmath27 , which is necessary for measurements involving standard candles such as type ia sne , the angular - diameter distance ( add ) , @xmath28 , is also used in astronomy for objects whose diameter ( i.e. , the standard ruler ) is known . the luminosity distance and add can be measured independently using different celestial objects , but they are related via etherington s reciprocity relation : @xmath29 this relation , sometimes referred as the distance - duality ( dd ) relation , is completely general and is valid for all cosmological models based on riemannian geometry .
that is , its validity is independent of einstein s field equations for gravity and the nature of the matter - energy content of the universe .
it requires only that the source and observer be connected via null geodesics in a riemannian spacetime and that the number of photons be conserved .
x - ray observations of the intra - cluster medium , combined with radio observations of the galaxy cluster s sunyaev - zeldovich effect , allow an estimate of the add to be made . recently ,
bonamante et al . ( 2006 ) determined the distance to 38 clusters of galaxies in the redshift range @xmath30 using x - ray data from _ chandra _ and sze data from the owens valley radio observatory and the berkeley - illinois - maryland association interferometric arrays .
the data shown in table 1 are reproduced from the compilation of bonamante et al .
. * table 1 .
* angular diameter distance of galaxy clusters [ 1 ] [ cols="<,<,>",options="header " , ]
the theoretical angular diameter distance @xmath31 is a function of the cluster s redshift _ z _ , and is different for different cosmological models .
both @xmath0cdm and @xmath1 are frw cosmologies , but the latter includes the additional constraint @xmath32 on the overall equation of state .
the densities are often written in terms of today s critical density , @xmath33 , represented as @xmath34 , @xmath35 , and @xmath36 .
@xmath37 is the hubble constant , and @xmath38 is simply @xmath39 when dark energy is assumed to be a cosmological constant . in a flat @xmath0cdm universe with zero spatial curvature ,
the total scaled energy density is @xmath40 .
when dark energy is included with an unknown equation of state , @xmath41 , the most general form of the angular diameter distance is given by the expression @xmath42 where @xmath43 is the speed of light .
in this equation , @xmath44 represents the spatial curvature of the universe appearing as a term proportional to the spatial curvature constant @xmath45 in the friedmann equation .
in addition , sinn is @xmath46 when @xmath47 and @xmath48 when @xmath49 . for a flat universe with @xmath50 ,
the right - hand expression simplifies to the form @xmath51 times the integral . to cover a reasonable representation of the parameter space in @xmath0cdm , we consider the following two models for dark energy , and one without : \1 . @xmath0cdm the standard " model , with a cosmological constant in a flat universe .
the dark - energy equation of state parameter , @xmath52 , is exactly @xmath53 , and @xmath54 ( since radiation is negligible at low redshifts ) .
@xmath55cdm a flat universe with a constant dark - energy equation of state , but with a @xmath52 that is not necessarily equal to @xmath53 . here
@xmath50 , so the free parameters may be chosen from the following : @xmath37 , @xmath56 and @xmath52 .
\3 . for comparison
, we also consider a model with @xmath57 , i.e. , the einstein - de sitter cosmology . in the @xmath1 universe ,
the angular diameter distance is given by the much simpler expression @xmath58 the factor @xmath59 is in fact the gravitational horizon @xmath60 at the present time , so we may also write the angular diameter distance as @xmath61 a detailed account of the differences between @xmath0cdm and @xmath1 is provided in melia & shevchuk ( 2012 ) , melia & maier ( 2013 ) , and wei et al .
( 2013 ) . a more pedagogical description may also be found in melia ( 2012 ) .
an important distinction between these two models is that whereas the @xmath1 universe expands at a constant rate , @xmath0cdm predicts an early phase of deceleration , followed by a current acceleration .
therefore , an examination of the cluster angular size data , spanning the redshift range ( @xmath62 ) within which the transition from deceleration to acceleration is thought to have occurred , could in principle help to distinguish between these two cosmologies .
briefly , the @xmath1 universe is a friedmann - robertson - walker ( frw ) cosmology that has much in common with @xmath0cdm , but includes an additional ingredient motivated by several theoretical and observational arguments ( melia 2007 ; melia & abdelqader 2009 ; melia & shevchuk 2012 ; melia 2013a ) . like @xmath0cdm
, it adopts an equation of state @xmath63 , with @xmath64 and @xmath65 , but goes one step further by specifying that @xmath66 at all times . here
, @xmath67 is the pressure and @xmath68 is the energy density , and subscripts r , m , and de refer to radiation , matter , and dark energy , respectively .
one might come away with the impression that this equation of state can not be consistent with that ( i.e. , @xmath69/\rho$ ] ) in the standard model .
but in fact nature is telling us that if we ignore the constraint @xmath70 and instead proceed to optimize the parameters in @xmath0cdm by fitting the data , the resultant value of @xmath55 averaged over a hubble time is actually @xmath71 within the measurement errors ( melia 2007 ; melia & shevchuk 2012 ) .
in other words , though @xmath72 in @xmath0cdm can not be equal to @xmath71 from one moment to the next , its value averaged over the age of the universe is equal to what it would have been in @xmath1 . in terms of the expansion dynamics , @xmath0cdm must guess the constituents of the universe and their individual equations of state , and then predict the expansion rate as a function of time .
in contrast , @xmath1 acknowledges the fact that no matter what these constituents are , the total energy density in the universe gives rise to a gravitational horizon coincident with the better known hubble radius .
but because this radius is therefore a proper distance , the application of weyl s postulate forces it to always equal @xmath73 .
thus , on every time slice , the energy density @xmath68 must partition itself among its various constituents ( @xmath74 , @xmath75 and @xmath76 ) in such a way as to always adhere to this constraint , which also guarantees that the expansion rate be constant in time . for each model ,
the best - fit is obtained by minimizing the function @xmath77^{2 } } { \sigma^{2}_{\rm tot , \emph{i}}}\ ; , \end{split}\ ] ] where @xmath78 stands for all the cosmological parameters that define the fitted model , @xmath79 is the redshift of the observed galaxy cluster , @xmath80 is the predicted value of the add in the cosmological model under consideration , and @xmath81 is the measured value .
there are three sources of uncertainty in the measurement of @xmath31 : the cluster modeling error @xmath82 , the statistical error @xmath83 , and the systematic error @xmath84 .
the modeling errors are shown in table 1 and the statistical and systematic errors are presented in table 3 of bonamante et al .
( 2006 ) . in our analysis
, we combine these errors in quadrature . thus , the total uncertainty @xmath85 is given by the expression @xmath86 . 0.2 in , for the @xmath1 ( _ dashed _ ) , einstein - de sitter ( _ dotted _ ) , and concordance ( _ solid _ ) models , respectively . ]
though the number of free parameters characterizing @xmath0cdm can be as large as 6 or 7 , depending on the application , here we take the minimalist approach and use the four most essential ones : the hubble constant @xmath6 , the matter energy density @xmath56 , the dark - energy density @xmath38 , and the dark energy equation of state parameter @xmath52 . by comparison ,
the @xmath1 universe has only one free parameter the hubble constant @xmath6 . 0.2 in constraint contours for the flat @xmath0cdm model , using the bonamante et al .
( 2006 ) add data .
the cross indicates the best - fit pair ( @xmath56 , @xmath6)=(0.50 , 73.93 km @xmath87 @xmath5 ) . ] in this section , we optimize the fit for several dark - energy models ( which we call @xmath0cdm and @xmath55cdm ) , one without dark energy ( the einstein - de sitter universe ) , and for the @xmath1 universe .
the outcome for each model is described and discussed in subsequent subsections . in @xmath0cdm ,
the dark - energy equation of state parameter , @xmath88 , is exactly @xmath53 . assuming a flat universe , @xmath89 , there are only two free parameters : @xmath56 and @xmath6 .
type ia sn measurements ( see , e.g. , perlmutter et al . 1998 , 1999 ; schmidt et al .
1998 ; riess et al . 1998 ; garnavich et al . 1998 ) , cmb anisotropy data ( see , e.g. , ratra et al . 1999 ; podariu et al . 2001 ; spergel et al . 2003
; komatsu et al . 2009 , 2011 ;
hinshaw et al . 2013 ) , and baryon acoustic oscillation ( bao ) peak length scale estimates ( see , e.g. , percival et al . 2007 ; gaztaaga et al . 2009
; samushia & ratra 2009 ) , strongly suggest that we live in a spatially flat , dark energy - dominated unverse with concordance parameter values @xmath90 and @xmath91 .
we will first adopt this concordance model , though to improve the fit we keep @xmath6 as a free parameter .
the 38 cluster distances are fit with this theoretical @xmath92 function and the constraints on @xmath6 are shown in figure 1 ( solid curve ) .
for this fit , we obtain @xmath93 km @xmath4 @xmath5 ( @xmath94 confidence interval ) .
the @xmath95 per degree of freedom for the concordance model with an optimized hubble constant is @xmath96 , remembering that all of its parameters , save for @xmath37 , are assumed to have prior values .
if we relax the priors , and allow both @xmath56 and @xmath6 to be free parameters , we obtain best - fit values @xmath97 , @xmath6 ) = ( 0.50 , @xmath98 km @xmath4 @xmath5 ) .
figure 2 shows the @xmath99 constraint contours of the probability in the ( @xmath56 , @xmath6 ) plane .
these contours show that at the @xmath100 level , @xmath101 km @xmath4 @xmath5 , but that @xmath56 is poorly constrained ; only a lower limit of @xmath102 can be set at this confidence level .
the cross indicates the best - fit pair ( @xmath56 , @xmath6 ) = ( 0.50 , 73.9 km @xmath4 @xmath5 ) .
we find that the @xmath95 per degree of freedom is @xmath103 . for the @xmath55cdm model
, @xmath52 is constant but possibly different from @xmath53 . for a flat universe ( @xmath50 )
, there are therefore possibly three free parameters : @xmath56 , @xmath52 , and @xmath6 , though to keep the discussion as simple as possible , we will here treat @xmath56 as fixed at the value @xmath104 , and allow @xmath37 and @xmath52 to vary . 0.2 in constraint contours for the @xmath55cdm model ( @xmath56
is fixed to be 0.3 ) , using the bonamante et al .
( 2006 ) add data .
the cross indicates the best - fit pair ( @xmath52 , @xmath6)= ( @xmath105 , 73.1 km @xmath4 @xmath5 ) . ]
figure 3 shows the constraints using the bonamante et al .
( 2006 ) add data with the dark - energy model .
these contours show that at the @xmath100 level , @xmath106 km @xmath4 @xmath5 , but that @xmath52 is poorly constrained ; only an upper limit of @xmath107 can be set at this confidence level .
the cross indicates the best - fit pair ( @xmath52 , @xmath6 ) = ( @xmath105 , 73.1 km @xmath4 @xmath5 ) with @xmath108 . with the current level of precision
, we see that the cluster add data can be fit very well with this variation of @xmath0cdm , but the optimized parameter @xmath52 is only marginally consistent with that of the concordance model .
we emphasize , however , that the scatter seen in the best - fit diagram ( figure 4 ) is still significant .
future measurements of the add may provide much tighter constraints on the cosmological parameters . for the einstein - de sitter ( e - des ) model with @xmath109 , the only free parameter is @xmath6 .
as shown in figure 1 ( dotted curve ) , the best fit corresponds to @xmath110 km @xmath4 @xmath5 ( @xmath94 confidence interval ) . with @xmath111 degrees of freedom , the reduced @xmath95 for the einstein - de sitter model with an optimized hubble
constant is @xmath112 . 0.2 in universe , with its sole optimized parameter @xmath113 km @xmath4 @xmath5 , and ( _ solid _ ) the standard , flat @xmath0cdm cosmology , with @xmath7 and @xmath8 km @xmath4 @xmath5 .
the reduced @xmath114 ( with 37 degrees of freedom ) for the @xmath1 fit is 0.786 .
the corresponding value for the optimal @xmath0cdm model ( with 36 degrees of freedom ) is @xmath115 .
the squares are from the low - redshift sample of mason et al .
( 2001 ) ; these are not included in the fits , but are shown here to demonstrate consistency with the measurements at lower redshifts . ]
the @xmath1 universe also has only one free parameter , @xmath6 .
the results for the @xmath1 universe are shown in figure 1 ( dashed line ) .
we see here that the best fit corresponds to @xmath3 km @xmath4 @xmath5 ( @xmath94 confidence interval ) . with @xmath111 degrees of freedom ,
the reduced @xmath95 in @xmath1 is @xmath116 . to facilitate a direct comparison between @xmath0cdm and @xmath1 ,
we show in figure 4 the 38 _
chandra_/sze cluster distance measurements , together with the best - fit theoretical curve in the @xmath1 universe ( corresponding to @xmath113 km @xmath4 @xmath5 ) , and similarly for @xmath0cdm ( with @xmath8 km @xmath87 @xmath5 and @xmath7 ) . in this figure
, we also show the angular diameter distances of nearby clusters from mason et al .
these are not included in the fits , but demonstrate that the best - fit curves are in agreement with low - redshift x - ray / sze measurements . strictly based on their @xmath117 values ,
@xmath0cdm and @xmath118 appear to fit the data comparably well .
however , because these models formulate their observables ( such at the angular diameter distance in equations 2 and 3 ) differently , and because they do not have the same number of free parameters , a comparison of the likelihoods for either being closer to the ` true ' model must be based on model selection tools . as we shall see , the results of our analysis in this paper tend to favour @xmath1 over @xmath0cdm , which we now demonstrate quantitatively .
the use of model selection tools in one - on - one cosmological model comparisons has already been discussed extensively in the literature ( see , e.g. , liddle et al . 2006 , liddle 2007 ) .
more recently , the successful application of model selection tools , such as the akaike information criterion ( aic ) , the kullback information criterion ( kic ) , the bayes information criterion ( bic ) , has been reported by shi et al .
( 2012 ) and melia & maier ( 2013 ) . for each fitted model ,
the aic is given by @xmath119 where @xmath120 is the number of free parameters .
if there are two models for the data , @xmath121 and @xmath122 , and they have been separately fitted , the one with the least resulting aic is assessed as the one more likely to be `` true . '' if @xmath123 is associated with model @xmath124 , the unnormalized confidence that @xmath124 is true is the `` akaike weight '' @xmath125 , with likelihood @xmath126 of being closer to the correct model . thus , the difference @xmath127 determines the extent to which @xmath121 is favoured over @xmath122 .
kic takes into account the fact that the probability density functions of the various competing models may not be symmetric .
the unbiased estimator for the symmetrized version ( cavanaugh 1999 , 2004 ) is given by @xmath128 it is very similar to the aic , but strengthens the dependence on the number of free parameters ( from @xmath129 to @xmath130 ) .
the strength of the evidence in kic favouring one model over another is similar to that for aic ; the likelihood is calculated using the same equation ( 7 ) , though with @xmath123 replaced with @xmath131 . the bayes information criterion ( bic )
is an asymptotic ( @xmath132 ) approximation to the outcome of a conventional bayesian inference procedure for deciding between models ( schwarz 1978 ) , defined by @xmath133 where @xmath134 is the number of data points .
it suppresses overfitting very strongly if @xmath134 is large , and has now been used to compare several popular models against @xmath0cdm ( see , e.g. , shi et al .
2012 ) . with the optimized fits we have reported in this paper
, our analysis of the cluster angular - diameter distances shows that the aic does not favour either @xmath1 or the concordance model when we assume prior values for all of its parameters ( except for the hubble constant ) .
the calculated aic likelihoods in this case are @xmath135 for the former , versus @xmath136 for the latter . however , if we relax some of the priors , and allow both @xmath56 and @xmath37 to be optimized in @xmath0cdm , then @xmath1 is favoured over the standard model with a likelihood of @xmath137 versus @xmath138 using aic , @xmath139 versus @xmath140 using kic , and @xmath141 versus @xmath142 using bic
. the ratios would be much greater for variants of @xmath0cdm that contain more free parameters than the basic @xmath0cdm model . since we fixed @xmath56 in the @xmath55cdm model
, there are 2 free parameters when we are fitting the add data in @xmath55cdm . we find that @xmath1 is favoured over @xmath55cdm by a likelihood of @xmath143 versus @xmath144 using these three model selection criteria .
in this paper , we have used the cluster angular - diameter size versus redshift data to compare the predictions of several cosmological models .
we have individually optimized the parameters in each case by minimizing the @xmath95 statistic .
we have found that the current cluster add constraints are not very restrictive for @xmath55cdm , though its optimized parameter values appear to be consistent at the @xmath100 level with those of the concordance model .
a comparison of the @xmath10 for the @xmath1 universe and @xmath0cdm shows that the cluster angular - diameter distance data favour the former over the latter though , on the basis of these @xmath10 values , one would conclude that both provide good fits to the observations .
the @xmath1 universe fits the data with @xmath2 for a hubble constant @xmath113 km @xmath4 @xmath5 , and @xmath6 is the sole parameter in this model . by comparison ,
the optimal flat @xmath0cdm model , which has two free parameters ( including @xmath7 and @xmath8 km @xmath4 @xmath145 ) , fits the angular - size data with a reduced @xmath9 .
however , statistical tools , such as the akaike , kullback and bayes information criteria , tend to favour the @xmath1 universe .
since @xmath0cdm ( with assumed prior values for @xmath45 and @xmath55 ) has one more free parameter than @xmath1 , the latter is preferred over @xmath0cdm with a likelihood of @xmath137 versus @xmath146 using aic , @xmath139 versus @xmath140 using kic , and @xmath141 versus @xmath142 using bic .
the ratios would be greater for the other variants of @xmath0cdm because they each have more free parameters than the basic @xmath0cdm model . since we fixed @xmath56 in the @xmath55cdm model , there are 2 free parameters when we are fitting the add data in @xmath55cdm .
we find that @xmath1 is favoured over @xmath55cdm by a likelihood of @xmath143 versus @xmath144 using these three model selection criteria .
but as we have found in other one - on - one comparisons , fits to the data using @xmath0cdm often come very close to those of @xmath1 , which lends some support to our inference that the standard model functions as an empirical approximation to the latter .
though it lacks the essential ingredient in @xmath1the equation of state @xmath32it nonetheless has enough free parameters one can optimize to produce a comparable fit to the observations .
there is no better example of this than the comparison of curves in figure 4 .
the optimized @xmath0cdm prediction tracks that of the @xmath1 universe almost identically . for this particular data set
, the difference in outcome using model selection tools is therefore almost entirely due to the fact that @xmath1 has fewer parameters than the standard model . with this result
, we can now address the second goal of our paper to provide some evidence in support of , or against , the strong evolution in galaxy size implied by earlier studies assuming @xmath0cdm .
the analysis of the average linear size of galaxies with the same luminosity , though over a range of redshifts ( see , e.g. , mcintosh et al . 2005 ; barden et al .
2005 ; trujillo et al .
2006 ) , had indicated that the standard model is consistent with these data only if these galaxies were @xmath13 times smaller at @xmath19 than at @xmath20 .
lopz - corredoira ( 2010 ) reconsidered this question , pointing out that current ideas invoked to explain this effect probably can not adequately account for all of the deficit of large objects at high redshifts .
for example , the main argument in favour of the evolution in size for a fixed luminosity is that younger galaxies tend to be brighter , and we should expect to see younger galaxies at high redshift .
therefore , for a given luminosity corresponding to some radius at present , galaxies in the past could have produced the same luminosity with a smaller radius .
lopz - corredoira estimates that this effect can contribute a factor @xmath147 difference in size , depending on whether one is looking at elliptical or disk galaxies .
other factors contributing to the evolution in size include mergers , and observational selection effects , such as extinction .
it appears that none of these explanations , on their own , can account for the required overall growth .
however , our use of galaxy clusters in this paper has shown that the cluster add data are quite consistent with both @xmath0cdm and @xmath1 .
thus , the fact that both of these models provide an excellent explanation for the add measurements using clusters casts some doubt on the suggestion that the inferred galaxy - size evolution is due to the adoption of an incorrect cosmology , rather than effects such as those discussed above .
if it turns out that the combination of growth factors together can not account for the factor six difference in size between @xmath19 and @xmath20 , we would conclude that some other astrophysical reasons are responsible , rather than the adoption of an incorrect expansion scenario . in conclusion
, even though the current galaxy - cluster angular size versus redshift data are still somewhat limited by relatively large uncertainties , we have demonstrated that they can nonetheless already be used to carry out meaningful one - on - one comparisons between competing cosmologies .
the add measurements for these structures appear to be consistent with both @xmath0cdm and the @xmath1 universe , suggesting that the inconsistent results obtained with similar work using individual galaxy sizes are probably not an indication of gross deficiencies with the assumed cosmological model .
we acknowledge yun chen for his kind assistance . this work is partially supported by the national basic research program ( 973 " program ) of china ( grants 2014cb845800 and 2013cb834900 ) , the national natural science foundation of china ( grants nos . 11322328 and 11373068 ) , the one - hundred - talents program , the youth innovation promotion association , and the strategic priority research program the emergence of cosmological structures " ( grant no .
xdb09000000 ) of the chinese academy of sciences , and the natural science foundation of jiangsu province . f.m . is grateful to amherst college for its support through a john woodruff simpson lectureship , and to purple mountain observatory in nanjing , china , for its hospitality while this work was being carried out .
this work was partially supported by grant 2012t1j0011 from the chinese academy of sciences visiting professorships for senior international scientists , and grant gdj20120491013 from the chinese state administration of foreign experts affairs .
daly , r. a. , guerra , e. j. & wan , l. , 1998 , in proc .
33d rencontre de moriond , fundamental parameters in cosmology , eds .
tran thanh van , j. , giraud - heraud , y. , bouchet , f. , damour , t. & mellier , y. ( paris : editions frontieres ) , p. 323 | we use measurements of the galaxy - cluster angular size versus redshift to test and compare the standard model ( @xmath0cdm ) and the @xmath1 universe .
we show that the latter fits the data with a reduced @xmath2 for a hubble constant @xmath3 km @xmath4 @xmath5 , and @xmath6 is the sole parameter in this model . by comparison , the optimal flat @xmath0cdm model , with two free parameters ( including @xmath7 and @xmath8 km @xmath4 @xmath5 ) ,
fits the angular - size data with a reduced @xmath9 . on the basis of their @xmath10 values alone
, both models appear to account for the data very well in spite of the fact that the @xmath1 universe expands at a constant rate , while @xmath0cdm does not .
however , because of the different number of free parameters in these models , selection tools , such as the bayes information criterion , favour @xmath1 over @xmath0cdm with a likelihood of @xmath11 versus @xmath12 .
these results impact the question of galaxy growth at large redshifts .
previous work suggested an inconsistency with the underlying cosmological model unless elliptical and disk galaxies grew in size by a surprisingly large factor @xmath13 from @xmath14 to @xmath15 .
the fact that both @xmath0cdm and @xmath1 fit the cluster - size measurements quite well casts some doubt on the suggestion that the unexpected result with individual galaxies may be due to the use of an incorrect expansion scenario , rather than astrophysical causes , such as mergers and/or selection effects .
cosmology : theory , observations , large - scale structure galaxies : clusters : general galaxies : evolution | <s>[INST]the use of standard rods distance scales with no evolution in linear size over the lifetime of the universe to carry out geometric tests of cosmological models was first proposed by hoyle ( 1959 ) , but the application of this idea to real data took a long time , specifically because of the difficulty in finding suitable objects or structures for this purpose .
the earliest tests of cosmological models using the observed dependence of the angular size of galaxies or kpc - scale radio sources could not easily define a true metric rod and were subject to unknown evolutionary effects ( e.g. , sandage 1988 ) .
there was uncertainty about whether the observed size - redshift relation in radio galaxies was an indication of an actual evolution in size ( kapahi 1987 ; barthel & miley 1988 ; neeser et al .
1995 ) , or whether it was due to selection effects ( singal 1998 ; nilsson et al .
this was partially addressed in a subsequent study using an enlarged sample of double - lobed quasars at @xmath16 ( buchalter et al .
1998 ) , which showed no change in apparent angular size within the range @xmath17 , consistent with standard cosmology without significant evolution .
separate investigations specifically to study the cosmic deceleration ( or acceleration ) were carried out by gurvits ( 1993 , 1994 ) ( using vlbi visibility data obtained at 13 cm by preston et al .
this analysis also provided estimates of the dependence of the apparent angular size of compact sources on their luminosity and rest - frame frequency .
similar studies were also carried out by kellermann ( 1993 ) and wilkinson et al .
( 1998 ) . within a few years ,
a much enlarged sample of 330 compact radio sources distributed over a broad range of redshifts @xmath18 started to demonstrate that the angular size - redshift relation for compact radio sources is consistent with the predictions of standard friedmann - robertson - walker models without the need to consider evolutionary or selection effects ( gurvits et al .
1999 ) .
other groups carried out their own cosmological tests using powerful radio - lobed radio galaxies , presumed to be reasonable standard yardsticks to determine global cosmological parameters ( daly 1994 , 1995 ) .
the method was applied and discussed by guerra & daly ( 1996 , 1998 ) , guerra ( 1997 ) , and daly , guerra & wan ( 1998 , 2000 ) , who reported that the data at that time strongly favoured a low ( matter ) density universe .
vishwakarma ( 2001 ) and lima & alcaniz ( 2002 ) used the gurvits et al .
( 1999 ) compact radio source angular size versus redshift data to set constraints on cosmological parameters .
this analysis was extended by chen & ratra ( 2003 ) , who used these data to place constraints on cosmological model parameters for a variety of cosmological constant scenarios . and a more focused study using friib radio galaxy redshift - angular size data to derive constraints on the parameters of a spatially - flat cosmology with a dark - energy scalar field was carried out by podariu et al .
( 2003 ) .
more recently , in one of the better known studies using this method , based on the average linear size of galaxies with the same luminosity ( see , e.g. , mcintosh et al . 2005 ; barden et al . 2005 ; trujillo et al .
2006 ; lpez - corredoira 2010 ) , the measurements do not appear to be consistent with an expanding cosmology , unless galaxies have grown in size by a surprisingly large factor six from redshift @xmath19 to @xmath20 .
perhaps the cosmology itself is wrong or , more simply , there is still some ambiguity concerning the use of galactic size as a standard rod . indeed ,
if another more reliable scale could be found , and shown to be consistent with , say , the standard model ( @xmath0cdm ) , the contrast between this result , and the disparity emerging through the use of galaxies , could be useful in affirming the need for stronger evolution in galactic growth than is predicted by current theory .
our focus in this paper will be galaxy clusters , which can also be used as standard rulers under appropriate conditions .
these are the largest gravitationally collapsed structures in the universe , with a hot diffuse plasma ( @xmath21 k ) filling the intergalactic medium . their angular size versus redshift can be measured using a combination of the sunyaev - zeldovich effect ( sze ) and x - ray surface brightness observations .
the sunyaev - zeldovich effect is the result of high - energy electrons distorting the cosmic microwave background radiation ( cmb ) through inverse compton scattering , during which low - energy cmb photons ( on average ) receive an energy boost from the high - energy electrons in the cluster ( sunyaev & zeldovich 1970 , 1972 ) .
the same hot gas emits x - rays primarily via thermal bremsstrahlung . while the sze is a function of the integrated pressure , @xmath22 ( in terms of the electron number density @xmath23 and temperature @xmath24 ) along the line - of - sight , the x - ray emission scales as @xmath25 ( in terms of the cooling function @xmath26 ) .
this different dependence on density , along with a suitable model for the cluster gas , enables a direct distance determination to the galaxy cluster .
this method is independent of the extragalactic distance ladder and provides distances to high - redshift galaxy clusters .
sze / x - ray distances have been previously used to constrain some cosmological parameters and to test the distance duality relationship of metric gravity models ( see , e.g. , de bernardis et al . 2006 ; lima et al .
2010 ; cao & liang 2011 ; holanda et al .
2012 ; chen & ratra 2012 ; liang et al . 2013 ; chen et al .
2013 ) . in this paper
, we will use these data , not to further examine the distance duality relation per se but , rather , to address two related issues .
first , we will use the newer and larger sample of galaxy - cluster angular size versus redshift measurements from bonamante et al .
( 2006 ) to constrain cosmological models .
in particular , we wish to see if the aforementioned tension between galaxy growth and the conventional expansion scenario is supported by the cluster data , or whether the latter confirm the basic theoretical predictions , thus reinforcing the need for a stronger galactic evolution at high redshifts .
second , we wish to use this relatively new probe of the universe s expansion to directly test the @xmath1 universe ( melia 2007 ; melia & shevchuk 2012 ) against the data and to see how its predictions compare with those of @xmath0cdm .
the outline of this paper is as follows . in 2 , we will briefly summarize the galaxy - cluster angular - size sample at our disposal .
we will present theoretical fits to the data in 3 , and constrain the cosmological parameters both in the context of @xmath0cdm and the @xmath1 universe in
we will end with a discussion and conclusion in 5 .
in addition to the luminosity distance , @xmath27 , which is necessary for measurements involving standard candles such as type ia sne , the angular - diameter distance ( add ) , @xmath28 , is also used in astronomy for objects whose diameter ( i.e. , the standard ruler ) is known . the luminosity distance and add can be measured independently using different celestial objects , but they are related via etherington s reciprocity relation : @xmath29 this relation , sometimes referred as the distance - duality ( dd ) relation , is completely general and is valid for all cosmological models based on riemannian geometry .
that is , its validity is independent of einstein s field equations for gravity and the nature of the matter - energy content of the universe .
it requires only that the source and observer be connected via null geodesics in a riemannian spacetime and that the number of photons be conserved .
x - ray observations of the intra - cluster medium , combined with radio observations of the galaxy cluster s sunyaev - zeldovich effect , allow an estimate of the add to be made . recently ,
bonamante et al . ( 2006 ) determined the distance to 38 clusters of galaxies in the redshift range @xmath30 using x - ray data from _ chandra _ and sze data from the owens valley radio observatory and the berkeley - illinois - maryland association interferometric arrays .
the data shown in table 1 are reproduced from the compilation of bonamante et al .
. * table 1 .
* angular diameter distance of galaxy clusters [ 1 ] [ cols="<,<,>",options="header " , ]
the theoretical angular diameter distance @xmath31 is a function of the cluster s redshift _ z _ , and is different for different cosmological models .
both @xmath0cdm and @xmath1 are frw cosmologies , but the latter includes the additional constraint @xmath32 on the overall equation of state .
the densities are often written in terms of today s critical density , @xmath33 , represented as @xmath34 , @xmath35 , and @xmath36 .
@xmath37 is the hubble constant , and @xmath38 is simply @xmath39 when dark energy is assumed to be a cosmological constant . in a flat @xmath0cdm universe with zero spatial curvature ,
the total scaled energy density is @xmath40 .
when dark energy is included with an unknown equation of state , @xmath41 , the most general form of the angular diameter distance is given by the expression @xmath42 where @xmath43 is the speed of light .
in this equation , @xmath44 represents the spatial curvature of the universe appearing as a term proportional to the spatial curvature constant @xmath45 in the friedmann equation .
in addition , sinn is @xmath46 when @xmath47 and @xmath48 when @xmath49 . for a flat universe with @xmath50 ,
the right - hand expression simplifies to the form @xmath51 times the integral . to cover a reasonable representation of the parameter space in @xmath0cdm , we consider the following two models for dark energy , and one without : \1 . @xmath0cdm the standard " model , with a cosmological constant in a flat universe .
the dark - energy equation of state parameter , @xmath52 , is exactly @xmath53 , and @xmath54 ( since radiation is negligible at low redshifts ) .
@xmath55cdm a flat universe with a constant dark - energy equation of state , but with a @xmath52 that is not necessarily equal to @xmath53 . here
@xmath50 , so the free parameters may be chosen from the following : @xmath37 , @xmath56 and @xmath52 .
\3 . for comparison
, we also consider a model with @xmath57 , i.e. , the einstein - de sitter cosmology . in the @xmath1 universe ,
the angular diameter distance is given by the much simpler expression @xmath58 the factor @xmath59 is in fact the gravitational horizon @xmath60 at the present time , so we may also write the angular diameter distance as @xmath61 a detailed account of the differences between @xmath0cdm and @xmath1 is provided in melia & shevchuk ( 2012 ) , melia & maier ( 2013 ) , and wei et al .
( 2013 ) . a more pedagogical description may also be found in melia ( 2012 ) .
an important distinction between these two models is that whereas the @xmath1 universe expands at a constant rate , @xmath0cdm predicts an early phase of deceleration , followed by a current acceleration .
therefore , an examination of the cluster angular size data , spanning the redshift range ( @xmath62 ) within which the transition from deceleration to acceleration is thought to have occurred , could in principle help to distinguish between these two cosmologies .
briefly , the @xmath1 universe is a friedmann - robertson - walker ( frw ) cosmology that has much in common with @xmath0cdm , but includes an additional ingredient motivated by several theoretical and observational arguments ( melia 2007 ; melia & abdelqader 2009 ; melia & shevchuk 2012 ; melia 2013a ) . like @xmath0cdm
, it adopts an equation of state @xmath63 , with @xmath64 and @xmath65 , but goes one step further by specifying that @xmath66 at all times . here
, @xmath67 is the pressure and @xmath68 is the energy density , and subscripts r , m , and de refer to radiation , matter , and dark energy , respectively .
one might come away with the impression that this equation of state can not be consistent with that ( i.e. , @xmath69/\rho$ ] ) in the standard model .
but in fact nature is telling us that if we ignore the constraint @xmath70 and instead proceed to optimize the parameters in @xmath0cdm by fitting the data , the resultant value of @xmath55 averaged over a hubble time is actually @xmath71 within the measurement errors ( melia 2007 ; melia & shevchuk 2012 ) .
in other words , though @xmath72 in @xmath0cdm can not be equal to @xmath71 from one moment to the next , its value averaged over the age of the universe is equal to what it would have been in @xmath1 . in terms of the expansion dynamics , @xmath0cdm must guess the constituents of the universe and their individual equations of state , and then predict the expansion rate as a function of time .
in contrast , @xmath1 acknowledges the fact that no matter what these constituents are , the total energy density in the universe gives rise to a gravitational horizon coincident with the better known hubble radius .
but because this radius is therefore a proper distance , the application of weyl s postulate forces it to always equal @xmath73 .
thus , on every time slice , the energy density @xmath68 must partition itself among its various constituents ( @xmath74 , @xmath75 and @xmath76 ) in such a way as to always adhere to this constraint , which also guarantees that the expansion rate be constant in time . for each model ,
the best - fit is obtained by minimizing the function @xmath77^{2 } } { \sigma^{2}_{\rm tot , \emph{i}}}\ ; , \end{split}\ ] ] where @xmath78 stands for all the cosmological parameters that define the fitted model , @xmath79 is the redshift of the observed galaxy cluster , @xmath80 is the predicted value of the add in the cosmological model under consideration , and @xmath81 is the measured value .
there are three sources of uncertainty in the measurement of @xmath31 : the cluster modeling error @xmath82 , the statistical error @xmath83 , and the systematic error @xmath84 .
the modeling errors are shown in table 1 and the statistical and systematic errors are presented in table 3 of bonamante et al .
( 2006 ) . in our analysis
, we combine these errors in quadrature . thus , the total uncertainty @xmath85 is given by the expression @xmath86 . 0.2 in , for the @xmath1 ( _ dashed _ ) , einstein - de sitter ( _ dotted _ ) , and concordance ( _ solid _ ) models , respectively . ]
though the number of free parameters characterizing @xmath0cdm can be as large as 6 or 7 , depending on the application , here we take the minimalist approach and use the four most essential ones : the hubble constant @xmath6 , the matter energy density @xmath56 , the dark - energy density @xmath38 , and the dark energy equation of state parameter @xmath52 . by comparison ,
the @xmath1 universe has only one free parameter the hubble constant @xmath6 . 0.2 in constraint contours for the flat @xmath0cdm model , using the bonamante et al .
( 2006 ) add data .
the cross indicates the best - fit pair ( @xmath56 , @xmath6)=(0.50 , 73.93 km @xmath87 @xmath5 ) . ] in this section , we optimize the fit for several dark - energy models ( which we call @xmath0cdm and @xmath55cdm ) , one without dark energy ( the einstein - de sitter universe ) , and for the @xmath1 universe .
the outcome for each model is described and discussed in subsequent subsections . in @xmath0cdm ,
the dark - energy equation of state parameter , @xmath88 , is exactly @xmath53 . assuming a flat universe , @xmath89 , there are only two free parameters : @xmath56 and @xmath6 .
type ia sn measurements ( see , e.g. , perlmutter et al . 1998 , 1999 ; schmidt et al .
1998 ; riess et al . 1998 ; garnavich et al . 1998 ) , cmb anisotropy data ( see , e.g. , ratra et al . 1999 ; podariu et al . 2001 ; spergel et al . 2003
; komatsu et al . 2009 , 2011 ;
hinshaw et al . 2013 ) , and baryon acoustic oscillation ( bao ) peak length scale estimates ( see , e.g. , percival et al . 2007 ; gaztaaga et al . 2009
; samushia & ratra 2009 ) , strongly suggest that we live in a spatially flat , dark energy - dominated unverse with concordance parameter values @xmath90 and @xmath91 .
we will first adopt this concordance model , though to improve the fit we keep @xmath6 as a free parameter .
the 38 cluster distances are fit with this theoretical @xmath92 function and the constraints on @xmath6 are shown in figure 1 ( solid curve ) .
for this fit , we obtain @xmath93 km @xmath4 @xmath5 ( @xmath94 confidence interval ) .
the @xmath95 per degree of freedom for the concordance model with an optimized hubble constant is @xmath96 , remembering that all of its parameters , save for @xmath37 , are assumed to have prior values .
if we relax the priors , and allow both @xmath56 and @xmath6 to be free parameters , we obtain best - fit values @xmath97 , @xmath6 ) = ( 0.50 , @xmath98 km @xmath4 @xmath5 ) .
figure 2 shows the @xmath99 constraint contours of the probability in the ( @xmath56 , @xmath6 ) plane .
these contours show that at the @xmath100 level , @xmath101 km @xmath4 @xmath5 , but that @xmath56 is poorly constrained ; only a lower limit of @xmath102 can be set at this confidence level .
the cross indicates the best - fit pair ( @xmath56 , @xmath6 ) = ( 0.50 , 73.9 km @xmath4 @xmath5 ) .
we find that the @xmath95 per degree of freedom is @xmath103 . for the @xmath55cdm model
, @xmath52 is constant but possibly different from @xmath53 . for a flat universe ( @xmath50 )
, there are therefore possibly three free parameters : @xmath56 , @xmath52 , and @xmath6 , though to keep the discussion as simple as possible , we will here treat @xmath56 as fixed at the value @xmath104 , and allow @xmath37 and @xmath52 to vary . 0.2 in constraint contours for the @xmath55cdm model ( @xmath56
is fixed to be 0.3 ) , using the bonamante et al .
( 2006 ) add data .
the cross indicates the best - fit pair ( @xmath52 , @xmath6)= ( @xmath105 , 73.1 km @xmath4 @xmath5 ) . ]
figure 3 shows the constraints using the bonamante et al .
( 2006 ) add data with the dark - energy model .
these contours show that at the @xmath100 level , @xmath106 km @xmath4 @xmath5 , but that @xmath52 is poorly constrained ; only an upper limit of @xmath107 can be set at this confidence level .
the cross indicates the best - fit pair ( @xmath52 , @xmath6 ) = ( @xmath105 , 73.1 km @xmath4 @xmath5 ) with @xmath108 . with the current level of precision
, we see that the cluster add data can be fit very well with this variation of @xmath0cdm , but the optimized parameter @xmath52 is only marginally consistent with that of the concordance model .
we emphasize , however , that the scatter seen in the best - fit diagram ( figure 4 ) is still significant .
future measurements of the add may provide much tighter constraints on the cosmological parameters . for the einstein - de sitter ( e - des ) model with @xmath109 , the only free parameter is @xmath6 .
as shown in figure 1 ( dotted curve ) , the best fit corresponds to @xmath110 km @xmath4 @xmath5 ( @xmath94 confidence interval ) . with @xmath111 degrees of freedom , the reduced @xmath95 for the einstein - de sitter model with an optimized hubble
constant is @xmath112 . 0.2 in universe , with its sole optimized parameter @xmath113 km @xmath4 @xmath5 , and ( _ solid _ ) the standard , flat @xmath0cdm cosmology , with @xmath7 and @xmath8 km @xmath4 @xmath5 .
the reduced @xmath114 ( with 37 degrees of freedom ) for the @xmath1 fit is 0.786 .
the corresponding value for the optimal @xmath0cdm model ( with 36 degrees of freedom ) is @xmath115 .
the squares are from the low - redshift sample of mason et al .
( 2001 ) ; these are not included in the fits , but are shown here to demonstrate consistency with the measurements at lower redshifts . ]
the @xmath1 universe also has only one free parameter , @xmath6 .
the results for the @xmath1 universe are shown in figure 1 ( dashed line ) .
we see here that the best fit corresponds to @xmath3 km @xmath4 @xmath5 ( @xmath94 confidence interval ) . with @xmath111 degrees of freedom ,
the reduced @xmath95 in @xmath1 is @xmath116 . to facilitate a direct comparison between @xmath0cdm and @xmath1 ,
we show in figure 4 the 38 _
chandra_/sze cluster distance measurements , together with the best - fit theoretical curve in the @xmath1 universe ( corresponding to @xmath113 km @xmath4 @xmath5 ) , and similarly for @xmath0cdm ( with @xmath8 km @xmath87 @xmath5 and @xmath7 ) . in this figure
, we also show the angular diameter distances of nearby clusters from mason et al .
these are not included in the fits , but demonstrate that the best - fit curves are in agreement with low - redshift x - ray / sze measurements . strictly based on their @xmath117 values ,
@xmath0cdm and @xmath118 appear to fit the data comparably well .
however , because these models formulate their observables ( such at the angular diameter distance in equations 2 and 3 ) differently , and because they do not have the same number of free parameters , a comparison of the likelihoods for either being closer to the ` true ' model must be based on model selection tools . as we shall see , the results of our analysis in this paper tend to favour @xmath1 over @xmath0cdm , which we now demonstrate quantitatively .
the use of model selection tools in one - on - one cosmological model comparisons has already been discussed extensively in the literature ( see , e.g. , liddle et al . 2006 , liddle 2007 ) .
more recently , the successful application of model selection tools , such as the akaike information criterion ( aic ) , the kullback information criterion ( kic ) , the bayes information criterion ( bic ) , has been reported by shi et al .
( 2012 ) and melia & maier ( 2013 ) . for each fitted model ,
the aic is given by @xmath119 where @xmath120 is the number of free parameters .
if there are two models for the data , @xmath121 and @xmath122 , and they have been separately fitted , the one with the least resulting aic is assessed as the one more likely to be `` true . '' if @xmath123 is associated with model @xmath124 , the unnormalized confidence that @xmath124 is true is the `` akaike weight '' @xmath125 , with likelihood @xmath126 of being closer to the correct model . thus , the difference @xmath127 determines the extent to which @xmath121 is favoured over @xmath122 .
kic takes into account the fact that the probability density functions of the various competing models may not be symmetric .
the unbiased estimator for the symmetrized version ( cavanaugh 1999 , 2004 ) is given by @xmath128 it is very similar to the aic , but strengthens the dependence on the number of free parameters ( from @xmath129 to @xmath130 ) .
the strength of the evidence in kic favouring one model over another is similar to that for aic ; the likelihood is calculated using the same equation ( 7 ) , though with @xmath123 replaced with @xmath131 . the bayes information criterion ( bic )
is an asymptotic ( @xmath132 ) approximation to the outcome of a conventional bayesian inference procedure for deciding between models ( schwarz 1978 ) , defined by @xmath133 where @xmath134 is the number of data points .
it suppresses overfitting very strongly if @xmath134 is large , and has now been used to compare several popular models against @xmath0cdm ( see , e.g. , shi et al .
2012 ) . with the optimized fits we have reported in this paper
, our analysis of the cluster angular - diameter distances shows that the aic does not favour either @xmath1 or the concordance model when we assume prior values for all of its parameters ( except for the hubble constant ) .
the calculated aic likelihoods in this case are @xmath135 for the former , versus @xmath136 for the latter . however , if we relax some of the priors , and allow both @xmath56 and @xmath37 to be optimized in @xmath0cdm , then @xmath1 is favoured over the standard model with a likelihood of @xmath137 versus @xmath138 using aic , @xmath139 versus @xmath140 using kic , and @xmath141 versus @xmath142 using bic
. the ratios would be much greater for variants of @xmath0cdm that contain more free parameters than the basic @xmath0cdm model . since we fixed @xmath56 in the @xmath55cdm model
, there are 2 free parameters when we are fitting the add data in @xmath55cdm . we find that @xmath1 is favoured over @xmath55cdm by a likelihood of @xmath143 versus @xmath144 using these three model selection criteria .
in this paper , we have used the cluster angular - diameter size versus redshift data to compare the predictions of several cosmological models .
we have individually optimized the parameters in each case by minimizing the @xmath95 statistic .
we have found that the current cluster add constraints are not very restrictive for @xmath55cdm , though its optimized parameter values appear to be consistent at the @xmath100 level with those of the concordance model .
a comparison of the @xmath10 for the @xmath1 universe and @xmath0cdm shows that the cluster angular - diameter distance data favour the former over the latter though , on the basis of these @xmath10 values , one would conclude that both provide good fits to the observations .
the @xmath1 universe fits the data with @xmath2 for a hubble constant @xmath113 km @xmath4 @xmath5 , and @xmath6 is the sole parameter in this model . by comparison ,
the optimal flat @xmath0cdm model , which has two free parameters ( including @xmath7 and @xmath8 km @xmath4 @xmath145 ) , fits the angular - size data with a reduced @xmath9 .
however , statistical tools , such as the akaike , kullback and bayes information criteria , tend to favour the @xmath1 universe .
since @xmath0cdm ( with assumed prior values for @xmath45 and @xmath55 ) has one more free parameter than @xmath1 , the latter is preferred over @xmath0cdm with a likelihood of @xmath137 versus @xmath146 using aic , @xmath139 versus @xmath140 using kic , and @xmath141 versus @xmath142 using bic .
the ratios would be greater for the other variants of @xmath0cdm because they each have more free parameters than the basic @xmath0cdm model . since we fixed @xmath56 in the @xmath55cdm model , there are 2 free parameters when we are fitting the add data in @xmath55cdm .
we find that @xmath1 is favoured over @xmath55cdm by a likelihood of @xmath143 versus @xmath144 using these three model selection criteria .
but as we have found in other one - on - one comparisons , fits to the data using @xmath0cdm often come very close to those of @xmath1 , which lends some support to our inference that the standard model functions as an empirical approximation to the latter .
though it lacks the essential ingredient in @xmath1the equation of state @xmath32it nonetheless has enough free parameters one can optimize to produce a comparable fit to the observations .
there is no better example of this than the comparison of curves in figure 4 .
the optimized @xmath0cdm prediction tracks that of the @xmath1 universe almost identically . for this particular data set
, the difference in outcome using model selection tools is therefore almost entirely due to the fact that @xmath1 has fewer parameters than the standard model . with this result
, we can now address the second goal of our paper to provide some evidence in support of , or against , the strong evolution in galaxy size implied by earlier studies assuming @xmath0cdm .
the analysis of the average linear size of galaxies with the same luminosity , though over a range of redshifts ( see , e.g. , mcintosh et al . 2005 ; barden et al .
2005 ; trujillo et al .
2006 ) , had indicated that the standard model is consistent with these data only if these galaxies were @xmath13 times smaller at @xmath19 than at @xmath20 .
lopz - corredoira ( 2010 ) reconsidered this question , pointing out that current ideas invoked to explain this effect probably can not adequately account for all of the deficit of large objects at high redshifts .
for example , the main argument in favour of the evolution in size for a fixed luminosity is that younger galaxies tend to be brighter , and we should expect to see younger galaxies at high redshift .
therefore , for a given luminosity corresponding to some radius at present , galaxies in the past could have produced the same luminosity with a smaller radius .
lopz - corredoira estimates that this effect can contribute a factor @xmath147 difference in size , depending on whether one is looking at elliptical or disk galaxies .
other factors contributing to the evolution in size include mergers , and observational selection effects , such as extinction .
it appears that none of these explanations , on their own , can account for the required overall growth .
however , our use of galaxy clusters in this paper has shown that the cluster add data are quite consistent with both @xmath0cdm and @xmath1 .
thus , the fact that both of these models provide an excellent explanation for the add measurements using clusters casts some doubt on the suggestion that the inferred galaxy - size evolution is due to the adoption of an incorrect cosmology , rather than effects such as those discussed above .
if it turns out that the combination of growth factors together can not account for the factor six difference in size between @xmath19 and @xmath20 , we would conclude that some other astrophysical reasons are responsible , rather than the adoption of an incorrect expansion scenario . in conclusion
, even though the current galaxy - cluster angular size versus redshift data are still somewhat limited by relatively large uncertainties , we have demonstrated that they can nonetheless already be used to carry out meaningful one - on - one comparisons between competing cosmologies .
the add measurements for these structures appear to be consistent with both @xmath0cdm and the @xmath1 universe , suggesting that the inconsistent results obtained with similar work using individual galaxy sizes are probably not an indication of gross deficiencies with the assumed cosmological model .
we acknowledge yun chen for his kind assistance . this work is partially supported by the national basic research program ( 973 " program ) of china ( grants 2014cb845800 and 2013cb834900 ) , the national natural science foundation of china ( grants nos . 11322328 and 11373068 ) , the one - hundred - talents program , the youth innovation promotion association , and the strategic priority research program the emergence of cosmological structures " ( grant no .
xdb09000000 ) of the chinese academy of sciences , and the natural science foundation of jiangsu province . f.m . is grateful to amherst college for its support through a john woodruff simpson lectureship , and to purple mountain observatory in nanjing , china , for its hospitality while this work was being carried out .
this work was partially supported by grant 2012t1j0011 from the chinese academy of sciences visiting professorships for senior international scientists , and grant gdj20120491013 from the chinese state administration of foreign experts affairs .
daly , r. a. , guerra , e. j. & wan , l. , 1998 , in proc .
33d rencontre de moriond , fundamental parameters in cosmology , eds .
tran thanh van , j. , giraud - heraud , y. , bouchet , f. , damour , t. & mellier , y. ( paris : editions frontieres ) , p. 323[/INST] we use measurements of the galaxy - cluster angular size versus redshift to test and compare the standard model ( @xmath0cdm ) and the @xmath1 universe .
we show that the latter fits the data with a reduced @xmath2 for a hubble constant @xmath3 km @xmath4 @xmath5 , and @xmath6 is the sole parameter in this model . by comparison , the optimal flat @xmath0cdm model , with two free parameters ( including @xmath7 and @xmath8 km @xmath4 @xmath5 ) ,
fits the angular - size data with a reduced @xmath9 . on the basis of their @xmath10 values alone
, both models appear to account for the data very well in spite of the fact that the @xmath1 universe expands at a constant rate , while @xmath0cdm does not .
however , because of the different number of free parameters in these models , selection tools , such as the bayes information criterion , favour @xmath1 over @xmath0cdm with a likelihood of @xmath11 versus @xmath12 .
these results impact the question of galaxy growth at large redshifts .
previous work suggested an inconsistency with the underlying cosmological model unless elliptical and disk galaxies grew in size by a surprisingly large factor @xmath13 from @xmath14 to @xmath15 .
the fact that both @xmath0cdm and @xmath1 fit the cluster - size measurements quite well casts some doubt on the suggestion that the unexpected result with individual galaxies may be due to the use of an incorrect expansion scenario , rather than astrophysical causes , such as mergers and/or selection effects .
cosmology : theory , observations , large - scale structure galaxies : clusters : general galaxies : evolution </s> |
'One lady got 17 stitches': Kangaroos hopped up on carrots are attacking tourists
Updated
They are the cute and cuddly icons of Australia, but kangaroos are viciously attacking people at a popular tourist spot, and an addiction to carrots is to blame.
"There are people getting kicked and scratched at least every day," tourist shuttle bus driver Shane Lewis said.
"One lady got 17 stitches in her face from her eye to her chin."
Every week, thousands of people flock to the unlikely tourist destination of Morisset Hospital in southern Lake Macquarie, where big mobs of kangaroos can always be found on the grassy slopes.
It's less than a two-hour train ride from Sydney and the travel blogs promise "adorable wild kangaroos" that are "tame enough to get close to and take photos with".
But too many tourists are dangling a carrot to get the perfect roo-selfie.
"The kangaroos see at least 2,000 tourists a week and they don't need 2,000 carrots or bananas and bread, chips and biscuits," Mr Lewis said.
"I've even seen some silly people feeding them McDonalds, KFC, corn chips, oats and there are some foods they are very aggressive for."
Mr Lewis has made a business out of shuttling people from the Morisset train station to the kangaroos at the hospital, but wants more done to prevent people feeding them.
He said he did his best to educate people and warn them of the dangers and, over the past eight months, has been collecting photos of injured tourists to help convey the message.
"Once I show them the photos they usually pull their kids away and put their food away when they know what can actually happen," he said.
"There was a guy who got his stomach gashed open and he wasn't even feeding them but … they'd been to McDonalds 10 minutes before, so whether they still had the food smell on them I have no idea, but for some reason the kangaroo took to him."
Carrots as bad as chocolate
According to the experts the kangaroos have most likely lost their fear of people, and have grown hungrier for the unnatural food being delivered to them.
"If they see a carrot and they've been fed a carrot 100 times before by a tourist, then they're going to come up and take that carrot," said Andrew Daly, an animal keeper at the Australian Reptile Park.
"And in doing so they can be quite aggressive. They can kick, they can scratch with their front paws and do quite a bit of damage, especially when they're trying to get those foods that they really like, or could be addicted to."
And if you thought a carrot was healthier for a kangaroo than junk food, think again.
"They're both just as bad in different ways," Mr Daly said.
"To a kangaroo a carrot is really, really high in sugar, so for us it's quite healthy, but for a kangaroo it's like having a chocolate bar.
"They can gorge or overfeed on them very easily."
And the result will not just be a fat and angry kangaroo.
Mr Daly said feeding kangaroos anything other than grass could cause them to develop deadly diseases.
"One in particular is called lumpy jaw and it's where high sugar diets or any food that can be a bit abrasive in the mouth causes cuts and lesions and then a bacteria will get into those cuts," he said.
"From there the disease develops and it's generally fatal."
Better signage, more education
There are signs zip-tied to traffic poles and nailed to trees at the Morisset Hospital issuing a warning to visitors.
"YOU HAVE ENTERED A WILDLIFE SANCTUARY. DO NOT FEED THE KANGAROOS!!".
But the area is largely unpatrolled and the site is unregulated. There aren't even public toilets.
Mr Lewis has called for more signage and has enlisted the help of local Lake Macquarie MP Greg Piper who last night raised the issue in NSW Parliament.
"Despite a number of warning signs placed throughout the area, people still come in droves and they feed the kangaroos processed foods," he told Parliament.
"I was there only last week and saw tourists attempting to feed the roos corn chips."
Mr Piper said he didn't want to see heavy regulation imposed, but suggested erecting better signage in multiple languages and a greater presence of National Parks and Wildlife rangers to inform and educate visitors.
He also dismissed the idea of closing off the area, which has organically grown into Lake Macquarie's biggest tourist drawcard.
"I don't see how you can close off the area, you can try and discourage them, but I don't think that's going to work," Mr Piper said.
"The fact is that the site is open to the public and it's so heavily advertised, it's well known, the genie is out of the bottle … it's something we just have to manage."
Topics: travel-and-tourism, tourism, animal-attacks, animals, newcastle-2300, morisset-2264
First posted ||||| Image copyright Getty Images Image caption Think twice before hugging for a selfie
People have been warned not to feed kangaroos at a tourist spot in Australia following a string of attacks by the animals.
Each week thousands of people visit the grounds of a hospital in Morisset, New South Wales, to see the wild kangaroos.
But some tourists have been kicked, scratched and left with serious cuts by the hungry marsupials, whose favourite snack is carrots.
Local MP Greg Piper says urgent action is needed to educate tourists.
"While kangaroos are cute, they are also capable of inflicting injury," Mr Piper told the BBC.
He says the problem has escalated over the past few years following a jump in the number of visitors.
"Social media has changed everything," Mr Piper says.
Instagram, Facebook and blogs posting advice on where to get the perfect "Roo selfie" travel fast.
Mr Piper believes around 3,000 people are coming each week to Morisset.
"It's a spot where you're guaranteed to see kangaroos, so it's understandable that people come," he says.
"And I don't want to blame the tourists - it's really a matter of educating them better."
Feeding frenzy
The tourists themselves are not the problem, it's the fact many want to feed the animals - and that's a bad idea.
WARNING: Graphic images of injuries below
For one thing it's not good for the kangaroos. They are grazing animals, and being fed by thousands of tourists each week changes their natural behaviour.
They come to expect and eventually demand food. That's when they can become a danger to humans.
"People don't understand they are wild animals and have to be treated as such," warns Mr Piper.
One of the visitors who was attacked was Anita Bielaszka. And like many other tourists she says she was entirely unaware of the potential dangers.
"We didn't know that we shouldn't feed them," she told the BBC. "Everyone does so we thought it's ok to do it.
"One of the big kangaroos attacked me and everyone get scared. People took their kids and ran away."
Ms Bielaszka escaped with a nasty scar on her leg.
But pictures supplied by Mr Piper of some of the injuries from recent months leave little doubt that a kangaroo can do a lot of damage.
Image copyright Shane Lewis
"A male kangaroo can disembowel someone," says Mr Piper. "They don't set out to do it, but that's the nature of how they fight: they kick with their big hind legs."
But people shouldn't be frightened away.
Coming close to them is usually safe - even petting a kangaroo can be OK, provided it approaches first.
But Mr Piper says it's wise to steer clear of the big male kangaroos.
"The males ones are tall and very powerfully built to the top. They basically look like they work out."
Respect the diet
Most importantly, don't feed the kangaroos - and certainly don't feed them processed food.
Even vegetables are not right for the animals, and in Morisset, it's carrots that most tourists seem to be bringing.
What might be seem like a healthy snack for humans is not necessarily a good lunch for a kangaroo.
Carrots are high in sugar and can cause deadly diseases in the animals.
Mr Piper wants better education for tourists, including more signs in multiple languages, to provide for their safety and the health of the kangaroos. ||||| Wild animals lash out at visitors to NSW hospital site after being fed inappropriate food such as carrots, chips and even McDonald’s
A state MP has called for a coordinated government response to a spate of junk food-crazed kangaroo attacks on tourists on the New South Wales central coast.
The attacks have occurred while tourists attempt to feed the native animals inappropriate food such as carrots and corn chips, and even McDonald’s takeaway, tourist operators in the area say.
“There have been a number of reported incidents in which kangaroos have attacked visitors, in one case causing a very deep gash to a man’s stomach,” the local MP, Greg Piper, told NSW parliament on Tuesday.
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“In most cases they have been kicking out, clawing faces and grappling with people, causing lacerations or significant scratching … Recently one attacked a man, who required 17 stitches in his face.”
Advised on travel websites and social media that the grounds of Morisset hospital near Lake Macquarie is a reliable place to see wild kangaroos for free, foreign and domestic tourists have been flocking to the location, which is about 4.5km from the nearest train station.
Facebook Twitter Pinterest A German tourist reveals his injuries after being attacked by a kangaroo outside Morisset hospital. Photograph: Facebook/Kroosn Shuttle Service Pty Ltd
Piper said last week he had visited the site, which is an operational psychiatric hospital, and had seen tourists offering the animals corn chips as well as apples, bananas and processed foods. Kangaroos’ usual diet is grasses.
Michelle Shaw, the nutritionist at Sydney’s Taronga zoo, said feeding the animals could be very harmful. Kangaroos were grazers, with digestive systems similar to cows, and feeding them even fruit or vegetables could cause stomach ulcers and inhibit the digestion of their proper diet, she said.
“Another problem is research has shown animals can become quite addicted to sugar,” she said. “They are going to seek it out regardless of whether it is going to be good for them or not, so they can become quite aggressive.”
Facebook Twitter Pinterest Lewis says he does his best to warn people about the dangers of feeding the wild animals. Photograph: Facebook/Kroosn Shuttle Service Pty Ltd
A local tour bus operator, Shane Lewis, estimates there are up to 2,000 visitors a week – the majority on weekends – seeking selfies with a roo. His company transports about a quarter of them, by his estimation. He said the animals had learned to associate the tourists with food.
“You can rustle a chip packet and they know what’s in there,” he said. “That makes them aggressive.
Kangaroo attacks Melbourne jogger 'like a damn truck' Read more
“The dangers are, you wouldn’t go near a dog when it’s eating its dinner, but people let their children go over, and I’ve seen kangaroos lash out thinking the kids going to take their food when they’re just coming to pat them.”
He said he had been showing tourists photos of injuries caused by the kangaroos to discourage them from feeding the animals.
“We try to scare them into not being naive and thinking they’re cute and cuddly by showing them the photos, what can happen, and not to give them any food,” he said.
Facebook Twitter Pinterest Shane Lewis has called for better signage at Morisset hospital. Photograph: Facebook/Kroosn Shuttle Service Pty Ltd
Lewis said the presence of tourists was generally positive as it tended to make the animals safer but more education was needed. The site’s population of kangaroos have been subject to vehicle attacks and two bow and arrow attacks, according to the Newcastle Herald.
Piper said it was probably impossible to stop tourists coming to the area – “that joey has left the pouch, so to speak”, he said.
But he called on the state’s national parks department and health department, which owns the hospital site, to install appropriate signage in several languages to remind people that feeding the animals was illegal and unsafe. He also suggested tourism infrastructure such as toilets may be necessary.
| – Perhaps this is revenge for a kangaroo's tourist-related death at a zoo in China. Wild kangaroos known to frequent the grounds of a psychiatric hospital near Lake Macquarie on Australia's east coast have been attacking some of the 3,000 tourists who visit each week, drawing warnings from city officials, reports the BBC. "While kangaroos are cute, they are also capable of inflicting injury," says local member of parliament Greg Piper, who describes kangaroos "kicking out, clawing faces and grappling with people, causing lacerations or significant scratching," per the Guardian. One man "required 17 stitches in his face," while another suffered a nasty gash to his stomach, Piper says, though he claims it's the tourists that are the problem. Descending on the Morisset area for the free opportunity for a "roo selfie," they bring snacks ranging from carrots to fast food, and the kangaroos are getting accustomed to those snacks—and aggressive about taking them, Piper says. "It's a spot where you're guaranteed to see kangaroos, so it's understandable that people come," he notes. But little gets in the way of a hungry kangaroo. "I've seen kangaroos lash out thinking the kids [are] going to take their food when they're just coming to pat them," a tour bus operator tells the Guardian. The animals may be suffering, too. Experts warn food other than grass could result in fatal diseases, sugar addiction, stomach ulcers, and other issues related to diet, as well as aggressive behavior, per the Guardian and ABC Australia. Though signs warn that feeding the kangaroos is dangerous, Piper is calling for better signage and education. | <s>[INST]'One lady got 17 stitches': Kangaroos hopped up on carrots are attacking tourists
Updated
They are the cute and cuddly icons of Australia, but kangaroos are viciously attacking people at a popular tourist spot, and an addiction to carrots is to blame.
"There are people getting kicked and scratched at least every day," tourist shuttle bus driver Shane Lewis said.
"One lady got 17 stitches in her face from her eye to her chin."
Every week, thousands of people flock to the unlikely tourist destination of Morisset Hospital in southern Lake Macquarie, where big mobs of kangaroos can always be found on the grassy slopes.
It's less than a two-hour train ride from Sydney and the travel blogs promise "adorable wild kangaroos" that are "tame enough to get close to and take photos with".
But too many tourists are dangling a carrot to get the perfect roo-selfie.
"The kangaroos see at least 2,000 tourists a week and they don't need 2,000 carrots or bananas and bread, chips and biscuits," Mr Lewis said.
"I've even seen some silly people feeding them McDonalds, KFC, corn chips, oats and there are some foods they are very aggressive for."
Mr Lewis has made a business out of shuttling people from the Morisset train station to the kangaroos at the hospital, but wants more done to prevent people feeding them.
He said he did his best to educate people and warn them of the dangers and, over the past eight months, has been collecting photos of injured tourists to help convey the message.
"Once I show them the photos they usually pull their kids away and put their food away when they know what can actually happen," he said.
"There was a guy who got his stomach gashed open and he wasn't even feeding them but … they'd been to McDonalds 10 minutes before, so whether they still had the food smell on them I have no idea, but for some reason the kangaroo took to him."
Carrots as bad as chocolate
According to the experts the kangaroos have most likely lost their fear of people, and have grown hungrier for the unnatural food being delivered to them.
"If they see a carrot and they've been fed a carrot 100 times before by a tourist, then they're going to come up and take that carrot," said Andrew Daly, an animal keeper at the Australian Reptile Park.
"And in doing so they can be quite aggressive. They can kick, they can scratch with their front paws and do quite a bit of damage, especially when they're trying to get those foods that they really like, or could be addicted to."
And if you thought a carrot was healthier for a kangaroo than junk food, think again.
"They're both just as bad in different ways," Mr Daly said.
"To a kangaroo a carrot is really, really high in sugar, so for us it's quite healthy, but for a kangaroo it's like having a chocolate bar.
"They can gorge or overfeed on them very easily."
And the result will not just be a fat and angry kangaroo.
Mr Daly said feeding kangaroos anything other than grass could cause them to develop deadly diseases.
"One in particular is called lumpy jaw and it's where high sugar diets or any food that can be a bit abrasive in the mouth causes cuts and lesions and then a bacteria will get into those cuts," he said.
"From there the disease develops and it's generally fatal."
Better signage, more education
There are signs zip-tied to traffic poles and nailed to trees at the Morisset Hospital issuing a warning to visitors.
"YOU HAVE ENTERED A WILDLIFE SANCTUARY. DO NOT FEED THE KANGAROOS!!".
But the area is largely unpatrolled and the site is unregulated. There aren't even public toilets.
Mr Lewis has called for more signage and has enlisted the help of local Lake Macquarie MP Greg Piper who last night raised the issue in NSW Parliament.
"Despite a number of warning signs placed throughout the area, people still come in droves and they feed the kangaroos processed foods," he told Parliament.
"I was there only last week and saw tourists attempting to feed the roos corn chips."
Mr Piper said he didn't want to see heavy regulation imposed, but suggested erecting better signage in multiple languages and a greater presence of National Parks and Wildlife rangers to inform and educate visitors.
He also dismissed the idea of closing off the area, which has organically grown into Lake Macquarie's biggest tourist drawcard.
"I don't see how you can close off the area, you can try and discourage them, but I don't think that's going to work," Mr Piper said.
"The fact is that the site is open to the public and it's so heavily advertised, it's well known, the genie is out of the bottle … it's something we just have to manage."
Topics: travel-and-tourism, tourism, animal-attacks, animals, newcastle-2300, morisset-2264
First posted ||||| Image copyright Getty Images Image caption Think twice before hugging for a selfie
People have been warned not to feed kangaroos at a tourist spot in Australia following a string of attacks by the animals.
Each week thousands of people visit the grounds of a hospital in Morisset, New South Wales, to see the wild kangaroos.
But some tourists have been kicked, scratched and left with serious cuts by the hungry marsupials, whose favourite snack is carrots.
Local MP Greg Piper says urgent action is needed to educate tourists.
"While kangaroos are cute, they are also capable of inflicting injury," Mr Piper told the BBC.
He says the problem has escalated over the past few years following a jump in the number of visitors.
"Social media has changed everything," Mr Piper says.
Instagram, Facebook and blogs posting advice on where to get the perfect "Roo selfie" travel fast.
Mr Piper believes around 3,000 people are coming each week to Morisset.
"It's a spot where you're guaranteed to see kangaroos, so it's understandable that people come," he says.
"And I don't want to blame the tourists - it's really a matter of educating them better."
Feeding frenzy
The tourists themselves are not the problem, it's the fact many want to feed the animals - and that's a bad idea.
WARNING: Graphic images of injuries below
For one thing it's not good for the kangaroos. They are grazing animals, and being fed by thousands of tourists each week changes their natural behaviour.
They come to expect and eventually demand food. That's when they can become a danger to humans.
"People don't understand they are wild animals and have to be treated as such," warns Mr Piper.
One of the visitors who was attacked was Anita Bielaszka. And like many other tourists she says she was entirely unaware of the potential dangers.
"We didn't know that we shouldn't feed them," she told the BBC. "Everyone does so we thought it's ok to do it.
"One of the big kangaroos attacked me and everyone get scared. People took their kids and ran away."
Ms Bielaszka escaped with a nasty scar on her leg.
But pictures supplied by Mr Piper of some of the injuries from recent months leave little doubt that a kangaroo can do a lot of damage.
Image copyright Shane Lewis
"A male kangaroo can disembowel someone," says Mr Piper. "They don't set out to do it, but that's the nature of how they fight: they kick with their big hind legs."
But people shouldn't be frightened away.
Coming close to them is usually safe - even petting a kangaroo can be OK, provided it approaches first.
But Mr Piper says it's wise to steer clear of the big male kangaroos.
"The males ones are tall and very powerfully built to the top. They basically look like they work out."
Respect the diet
Most importantly, don't feed the kangaroos - and certainly don't feed them processed food.
Even vegetables are not right for the animals, and in Morisset, it's carrots that most tourists seem to be bringing.
What might be seem like a healthy snack for humans is not necessarily a good lunch for a kangaroo.
Carrots are high in sugar and can cause deadly diseases in the animals.
Mr Piper wants better education for tourists, including more signs in multiple languages, to provide for their safety and the health of the kangaroos. ||||| Wild animals lash out at visitors to NSW hospital site after being fed inappropriate food such as carrots, chips and even McDonald’s
A state MP has called for a coordinated government response to a spate of junk food-crazed kangaroo attacks on tourists on the New South Wales central coast.
The attacks have occurred while tourists attempt to feed the native animals inappropriate food such as carrots and corn chips, and even McDonald’s takeaway, tourist operators in the area say.
“There have been a number of reported incidents in which kangaroos have attacked visitors, in one case causing a very deep gash to a man’s stomach,” the local MP, Greg Piper, told NSW parliament on Tuesday.
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“In most cases they have been kicking out, clawing faces and grappling with people, causing lacerations or significant scratching … Recently one attacked a man, who required 17 stitches in his face.”
Advised on travel websites and social media that the grounds of Morisset hospital near Lake Macquarie is a reliable place to see wild kangaroos for free, foreign and domestic tourists have been flocking to the location, which is about 4.5km from the nearest train station.
Facebook Twitter Pinterest A German tourist reveals his injuries after being attacked by a kangaroo outside Morisset hospital. Photograph: Facebook/Kroosn Shuttle Service Pty Ltd
Piper said last week he had visited the site, which is an operational psychiatric hospital, and had seen tourists offering the animals corn chips as well as apples, bananas and processed foods. Kangaroos’ usual diet is grasses.
Michelle Shaw, the nutritionist at Sydney’s Taronga zoo, said feeding the animals could be very harmful. Kangaroos were grazers, with digestive systems similar to cows, and feeding them even fruit or vegetables could cause stomach ulcers and inhibit the digestion of their proper diet, she said.
“Another problem is research has shown animals can become quite addicted to sugar,” she said. “They are going to seek it out regardless of whether it is going to be good for them or not, so they can become quite aggressive.”
Facebook Twitter Pinterest Lewis says he does his best to warn people about the dangers of feeding the wild animals. Photograph: Facebook/Kroosn Shuttle Service Pty Ltd
A local tour bus operator, Shane Lewis, estimates there are up to 2,000 visitors a week – the majority on weekends – seeking selfies with a roo. His company transports about a quarter of them, by his estimation. He said the animals had learned to associate the tourists with food.
“You can rustle a chip packet and they know what’s in there,” he said. “That makes them aggressive.
Kangaroo attacks Melbourne jogger 'like a damn truck' Read more
“The dangers are, you wouldn’t go near a dog when it’s eating its dinner, but people let their children go over, and I’ve seen kangaroos lash out thinking the kids going to take their food when they’re just coming to pat them.”
He said he had been showing tourists photos of injuries caused by the kangaroos to discourage them from feeding the animals.
“We try to scare them into not being naive and thinking they’re cute and cuddly by showing them the photos, what can happen, and not to give them any food,” he said.
Facebook Twitter Pinterest Shane Lewis has called for better signage at Morisset hospital. Photograph: Facebook/Kroosn Shuttle Service Pty Ltd
Lewis said the presence of tourists was generally positive as it tended to make the animals safer but more education was needed. The site’s population of kangaroos have been subject to vehicle attacks and two bow and arrow attacks, according to the Newcastle Herald.
Piper said it was probably impossible to stop tourists coming to the area – “that joey has left the pouch, so to speak”, he said.
But he called on the state’s national parks department and health department, which owns the hospital site, to install appropriate signage in several languages to remind people that feeding the animals was illegal and unsafe. He also suggested tourism infrastructure such as toilets may be necessary.
[/INST]– Perhaps this is revenge for a kangaroo's tourist-related death at a zoo in China. Wild kangaroos known to frequent the grounds of a psychiatric hospital near Lake Macquarie on Australia's east coast have been attacking some of the 3,000 tourists who visit each week, drawing warnings from city officials, reports the BBC. "While kangaroos are cute, they are also capable of inflicting injury," says local member of parliament Greg Piper, who describes kangaroos "kicking out, clawing faces and grappling with people, causing lacerations or significant scratching," per the Guardian. One man "required 17 stitches in his face," while another suffered a nasty gash to his stomach, Piper says, though he claims it's the tourists that are the problem. Descending on the Morisset area for the free opportunity for a "roo selfie," they bring snacks ranging from carrots to fast food, and the kangaroos are getting accustomed to those snacks—and aggressive about taking them, Piper says. "It's a spot where you're guaranteed to see kangaroos, so it's understandable that people come," he notes. But little gets in the way of a hungry kangaroo. "I've seen kangaroos lash out thinking the kids [are] going to take their food when they're just coming to pat them," a tour bus operator tells the Guardian. The animals may be suffering, too. Experts warn food other than grass could result in fatal diseases, sugar addiction, stomach ulcers, and other issues related to diet, as well as aggressive behavior, per the Guardian and ABC Australia. Though signs warn that feeding the kangaroos is dangerous, Piper is calling for better signage and education.</s> |
Source: Thinkstock
50. Iowa
> Increase in Alzheimer’s, 2017-2025: 14.1%
> Pct. of 65+ pop. with Alzheimer’s: 12.8% (7th highest)
> Population 65+: 16.0% (15th highest)
> Pct. of 65+ pop. in good health: 80.4% (4th highest)
> Avg. retirement income: $20,252 (4th lowest)
There will be a significant increase in Alzheimer’s cases in every state. The number of people living with Alzheimer’s disease in Iowa is projected to climb by 14.1% between 2017 and 2025, the smallest increase of all states. The projected growth of each state’s elderly population is one of the best predictors of how fast Alzheimer’s cases will increase. Nearly 13% of the Iowa’s elderly population has the disease. While this is the seventh highest percentage of all states, it is expected to grow by just 20.7%, one of the slowest growths. The Alzheimer’s death rate in Iowa of 42 for every 100,000 people is fifth highest nationwide.
Source: Thinkstock
49. North Dakota
> Increase in Alzheimer’s, 2017-2025: 14.3%
> Pct. of 65+ pop. with Alzheimer’s: 13.0% (5th highest)
> Population 65+: 14.2% (11th lowest)
> Pct. of 65+ pop. in good health: 75.6% (21st lowest)
> Avg. retirement income: $22,776 (22nd lowest)
While the prevalence of Alzheimer’s in North Dakota will climb at a slower rate than in almost all states, a relatively large share of the state population dies from the disease. With nearly 50 deaths per 100,000 people, North Dakota has the second highest mortality rate for deaths associated with Alzheimer’s disease.
Source: Thinkstock
48. Rhode Island
> Increase in Alzheimer’s, 2017-2025: 17.4%
> Pct. of 65+ pop. with Alzheimer’s: 13.5% (the highest)
> Population 65+: 16.1% (13th highest)
> Pct. of 65+ pop. in good health: 78.1% (16th highest)
> Avg. retirement income: $25,966 (16th highest)
An estimated 13.5% of Rhode Island’s elderly population have Alzheimer’s, the highest share of all states. Alzheimer’s disease was the fifth leading cause of death in Rhode Island in 2014.
Living alone in old age can be a sign of social isolation, but also an indication of independence for many older Americans, as well as people with the disease. For individuals living with late-stage Alzheimer’s disease, living alone can be unsafe. About 31% of Rhode Island residents 65 and older live alone, the second highest share of any state.
Source: Thinkstock
47. South Dakota
> Increase in Alzheimer’s, 2017-2025: 17.6%
> Pct. of 65+ pop. with Alzheimer’s: 12.6% (9th highest)
> Population 65+: 15.7% (21st highest)
> Pct. of 65+ pop. in good health: 77.0% (23rd highest)
> Avg. retirement income: $20,765 (5th lowest)
South Dakota had the highest mortality rate from Alzheimer’s disease of any state with 50.9 deaths per 100,000 state residents. The relatively high incidence of the disease among the state’s elderly population largely explains the high mortality rate. States with low projected increases in the incidence of Alzheimer’s disease almost always have low projected growths in the elderly population, but South Dakota is the exception. The state’s 65 and older population is projected to grow by nearly 27% by 2025, versus the national average growth of approximately 25%.
Regardless, like every other state, South Dakota will need more caregivers. Currently there are only 2.2 caregivers in the state for every Alzheimer’s patient, the fifth lowest ratio in the U.S.
Source: Thinkstock
46. New York
> Increase in Alzheimer’s, 2017-2025: 17.9%
> Pct. of 65+ pop. with Alzheimer’s: 13.2% (4th highest)
> Population 65+: 15.0% (22nd lowest)
> Pct. of 65+ pop. in good health: 73.7% (14th lowest)
> Avg. retirement income: $26,249 (15th highest)
New York’s Medicaid costs for those 65 and older with Alzheimer’s are expected to be $4.6 billion in 2017, the most of any state. Despite a slower than average eight-year growth rate in the number of elderly people with the disease, the state’s Alzheimer’s-related Medicaid costs are expected to remain the highest in the nation also in 2025.
The Empire State has more than 1 million caregivers tending to those with Alzheimer’s disease, or about 2.6 for every Alzheimer’s patient. ||||| The number of people with Alzheimer’s disease, a degenerative brain disease and the most common form of dementia, will rise by at least 14% in all 50 states over the next eight years. However, the rate of increase will be higher in some states than others, according to a recent report from the Alzheimer’s Association, placing greater financial stress on health care programs and boosting the need for caregivers.
Alaska is projected to have the biggest increase in Alzheimer’s cases, from 7,100 in 2015 to 11,000 in 2017, or a 54.9% jump. Arizona, Nevada, Vermont, and Utah round out the top five with projected increases of at least 40% each. Iowa is expected to have the lowest increase, from 64,000 to 73,000, or 14.1%.
24/7 reviewed the Alzheimer’s Association “2017 Alzheimer’s Disease Facts and Figures” report to find for each state the projected percentage increase in the number of people with Alzheimer’s over the next eight years. States in the West and Southeast are expected to have the largest percentage increases in the number of people with Alzheimer’s between 2017 and 2025.
Click here to see the states where people will suffer the most from Alzheimer’s.
Click here to see our detailed findings and methodology. | – Iowa is projected to see a 14% increase in Alzheimer's cases in the next eight years. Sound scary? That's nothing. Iowa actually has the lowest projected increase of any state in the country, per 24/7 Wall St, which cites a recent Alzheimer's Association report. The 10 states with the largest projected increases in Americans with Alzheimer's cases from 2017 to 2025: Alaska: 55% Arizona: 54% Nevada: 49% Vermont: 42% Utah: 40% New Mexico: 39.5% South Carolina: 39.5% Florida: 38.5% Wyoming: 38% Idaho: 37.5% Click for the full list. (More on the Alzheimer's "tidal wave" here.) | <s>[INST]Source: Thinkstock
50. Iowa
> Increase in Alzheimer’s, 2017-2025: 14.1%
> Pct. of 65+ pop. with Alzheimer’s: 12.8% (7th highest)
> Population 65+: 16.0% (15th highest)
> Pct. of 65+ pop. in good health: 80.4% (4th highest)
> Avg. retirement income: $20,252 (4th lowest)
There will be a significant increase in Alzheimer’s cases in every state. The number of people living with Alzheimer’s disease in Iowa is projected to climb by 14.1% between 2017 and 2025, the smallest increase of all states. The projected growth of each state’s elderly population is one of the best predictors of how fast Alzheimer’s cases will increase. Nearly 13% of the Iowa’s elderly population has the disease. While this is the seventh highest percentage of all states, it is expected to grow by just 20.7%, one of the slowest growths. The Alzheimer’s death rate in Iowa of 42 for every 100,000 people is fifth highest nationwide.
Source: Thinkstock
49. North Dakota
> Increase in Alzheimer’s, 2017-2025: 14.3%
> Pct. of 65+ pop. with Alzheimer’s: 13.0% (5th highest)
> Population 65+: 14.2% (11th lowest)
> Pct. of 65+ pop. in good health: 75.6% (21st lowest)
> Avg. retirement income: $22,776 (22nd lowest)
While the prevalence of Alzheimer’s in North Dakota will climb at a slower rate than in almost all states, a relatively large share of the state population dies from the disease. With nearly 50 deaths per 100,000 people, North Dakota has the second highest mortality rate for deaths associated with Alzheimer’s disease.
Source: Thinkstock
48. Rhode Island
> Increase in Alzheimer’s, 2017-2025: 17.4%
> Pct. of 65+ pop. with Alzheimer’s: 13.5% (the highest)
> Population 65+: 16.1% (13th highest)
> Pct. of 65+ pop. in good health: 78.1% (16th highest)
> Avg. retirement income: $25,966 (16th highest)
An estimated 13.5% of Rhode Island’s elderly population have Alzheimer’s, the highest share of all states. Alzheimer’s disease was the fifth leading cause of death in Rhode Island in 2014.
Living alone in old age can be a sign of social isolation, but also an indication of independence for many older Americans, as well as people with the disease. For individuals living with late-stage Alzheimer’s disease, living alone can be unsafe. About 31% of Rhode Island residents 65 and older live alone, the second highest share of any state.
Source: Thinkstock
47. South Dakota
> Increase in Alzheimer’s, 2017-2025: 17.6%
> Pct. of 65+ pop. with Alzheimer’s: 12.6% (9th highest)
> Population 65+: 15.7% (21st highest)
> Pct. of 65+ pop. in good health: 77.0% (23rd highest)
> Avg. retirement income: $20,765 (5th lowest)
South Dakota had the highest mortality rate from Alzheimer’s disease of any state with 50.9 deaths per 100,000 state residents. The relatively high incidence of the disease among the state’s elderly population largely explains the high mortality rate. States with low projected increases in the incidence of Alzheimer’s disease almost always have low projected growths in the elderly population, but South Dakota is the exception. The state’s 65 and older population is projected to grow by nearly 27% by 2025, versus the national average growth of approximately 25%.
Regardless, like every other state, South Dakota will need more caregivers. Currently there are only 2.2 caregivers in the state for every Alzheimer’s patient, the fifth lowest ratio in the U.S.
Source: Thinkstock
46. New York
> Increase in Alzheimer’s, 2017-2025: 17.9%
> Pct. of 65+ pop. with Alzheimer’s: 13.2% (4th highest)
> Population 65+: 15.0% (22nd lowest)
> Pct. of 65+ pop. in good health: 73.7% (14th lowest)
> Avg. retirement income: $26,249 (15th highest)
New York’s Medicaid costs for those 65 and older with Alzheimer’s are expected to be $4.6 billion in 2017, the most of any state. Despite a slower than average eight-year growth rate in the number of elderly people with the disease, the state’s Alzheimer’s-related Medicaid costs are expected to remain the highest in the nation also in 2025.
The Empire State has more than 1 million caregivers tending to those with Alzheimer’s disease, or about 2.6 for every Alzheimer’s patient. ||||| The number of people with Alzheimer’s disease, a degenerative brain disease and the most common form of dementia, will rise by at least 14% in all 50 states over the next eight years. However, the rate of increase will be higher in some states than others, according to a recent report from the Alzheimer’s Association, placing greater financial stress on health care programs and boosting the need for caregivers.
Alaska is projected to have the biggest increase in Alzheimer’s cases, from 7,100 in 2015 to 11,000 in 2017, or a 54.9% jump. Arizona, Nevada, Vermont, and Utah round out the top five with projected increases of at least 40% each. Iowa is expected to have the lowest increase, from 64,000 to 73,000, or 14.1%.
24/7 reviewed the Alzheimer’s Association “2017 Alzheimer’s Disease Facts and Figures” report to find for each state the projected percentage increase in the number of people with Alzheimer’s over the next eight years. States in the West and Southeast are expected to have the largest percentage increases in the number of people with Alzheimer’s between 2017 and 2025.
Click here to see the states where people will suffer the most from Alzheimer’s.
Click here to see our detailed findings and methodology.[/INST]– Iowa is projected to see a 14% increase in Alzheimer's cases in the next eight years. Sound scary? That's nothing. Iowa actually has the lowest projected increase of any state in the country, per 24/7 Wall St, which cites a recent Alzheimer's Association report. The 10 states with the largest projected increases in Americans with Alzheimer's cases from 2017 to 2025: Alaska: 55% Arizona: 54% Nevada: 49% Vermont: 42% Utah: 40% New Mexico: 39.5% South Carolina: 39.5% Florida: 38.5% Wyoming: 38% Idaho: 37.5% Click for the full list. (More on the Alzheimer's "tidal wave" here.)</s> |
the detection and characterization of extrasolar planets has grown dramatically as a field since the first detection in 1992 @xcite .
the most successful detection techniques thus far are radial velocity and transit detection . using ground and space based surveys ( harps , kepler , corot , etc ) ,
these indirect techniques have discovered over 800 planets ( exoplanet.eu ) as well as thousands more planet candidates .
the direct detection of planets provides a unique opportunity to study exoplanets in the context of their formation and evolution .
it complements the underlying semi - major axis exoplanet distribution from rv surveys ( from 100 au down to a few aus ) and enables the characterization of the planet itself with an examination of its emergent flux as a function of wavelength .
the detection of the planets hr8799 bcde @xcite , fomalhaut b @xcite , @xmath2 pic b @xcite , 2mass1207 @xcite , 1rxs j1609 - 2105 b @xcite , hd 95086 b @xcite , koi-94 @xcite as well as discoveries of protoplanetary candidates lkca 15 b @xcite and hd100546 b @xcite , demonstrate the potential breakthroughs of the technique .
however , thus far , most dedicated high contrast imaging surveys have yielded null - results ( e.g. @xcite,@xcite , @xcite , @xcite,@xcite ) .
these null results are due to the lack of contrast at small orbital separations , where most planets are expected to be found . since planets are concluded to be rare at large orbital separations ( @xcite , @xcite ) , high contrast imaging must probe close to the parent star to detect a planet .
high contrast imaging is limited by the diffraction limit , set by the telescope optics , which determines the minimum angular separation achievable under ideal conditions .
since planets are low mass , cold , and red compared to their parent star ( @xcite,@xcite ) , the contrast ratio of their magnitudes is an additional constraint on their detectability .
new instruments and techniques have been developed to combat these constraints at the acquisition and image processing stage .
coronagraphs have been developed to reduce the light scattered in the telescope optics from diffraction during acquisition , but at a cost of throughput and angular resolution @xcite .
coronagraphic optics allow us to probe smaller inner working angles , but are limited by the stellar `` speckles '' which can dominate the flux from a planet @xcite . by turning off the telescope derotator on an alt - az telescope ,
the planet is able to `` rotate '' around the star , while the stellar psf stays relatively stable and the speckles vary randomly in time .
this technique is used in angular differential imaging ( adi , @xcite ) .
it takes advantage of this rotation to identify and subtract ( in post - processing ) the contribution from the stellar psf and speckles .
there are a number of image processing techniques aimed at modelling and subtracting the stellar psf from every image , allowing the sky fixed planet signal to shine through .
loci @xcite is an extension of adi , which models the local stellar psf structure in every image .
principal component analysis ( pca ) ( @xcite , @xcite , @xcite ) models how the psf varies in time by identifying the main linear components of the variation .
application of these image processing techniques has been demonstrated to increase the limiting magnitude achievable by up to a factor of 5 ( @xcite , @xcite ) . in this work
, we present a detailed study of loci and pca image processing techniques in order to optimize the signal - to - noise of a planet at small angular separations with the app coronagraph ( @xcite,@xcite ) .
we compare our results to the previous result of @xcite .
the fomalhaut dataset that is used in the following analyses are a deep but typical observing sequence and will act as an example for the rest of our surveys .
data were obtained of the star fomalhaut at the vlt / ut4 with naco ( @xcite , @xcite ) in july and august 2011 ( 087.c-0701(b ) ) and were analyzed and published in @xcite .
fomalhaut was used as the natural guide star with the visible band wavefront sensor .
the l27 camera on naco was used with the nb4.05 filter ( @xmath3 = 4.051@xmath0 m and @xmath4 = 0.02@xmath0 m ) and the apodizing phase plate coronagraph ( app , @xcite , @xcite ) to provide additional diffraction suppression .
we used pupil tracking mode to perform adi @xcite .
the psf core is intentionally saturated to increase the signal from any potential companions .
the app provides diffraction supression over a 180@xmath5 wedge on one side of the target ( ) .
additional observations are required with a different position angle to cover the full 360@xmath5 around the star . for these observations
, we have three different datasets with different position angles ensuring full pa coverage around the target star .
each dataset has a large amount of field rotation : 119@xmath5 , 117@xmath5 , 120@xmath5 .
data were acquired in cube mode .
each data cube contains 200 frames , each with an integration time of 0.23 seconds .
approximately 70 cubes were obtained for each hemisphere dataset , totalling in an integration time of 160 minutes .
a three point dither pattern was used to allow subtraction of the sky background and detector systematics as detailed in @xcite .
unsaturated short exposure data with the neutral density filter were also taken for photometry .
data cubes at each dither position were pairwise subtracted to remove the sky background and detector systematics .
the cubes were shifted to move the core psf into the middle of a square image and bad frames ( open loop and poor ao ) were discarded ( 5% of hemisphere 1 , 16% of hemisphere 2 , and 7% of hemisphere 3 ) .
the three different app position angle datasets were processed separately .
each hemisphere dataset has its own corresponding unsaturated data for photometry .
fake planets are subsequently used to determine the limiting contrast after image processing .
the unsaturated fomalhaut data is used to add a fake planet in each saturated frame .
one fake planet is added at a time , between @xmath6 and @xmath7 in steps of @xmath8 and delta magnitudes in steps of 1 mag from dm= 7 to 13 . due to the asymmetric nature of the app psf , it is also necessary to determine the signal - to - noise of a planet at different position angles . for our analysis
we placed a planet on opposite sides of the star ( pa=45@xmath5 and 225@xmath5 relative to the sky ) to take into account the asymmetric psf of the app .
these two pa orientations ensure that the planet is on the dark side of the app in at least two of the hemispheres at once .
the mean of the limiting contrast at each pa is stored .
the final science frames are processed with several different algorithms to recover the fake planet signal .
all of the algorithms take advantage of the fake planet s rotation in the sky around the star to model and subtract the stellar psf from each image ( adi , @xcite ) . before each algorithm
is applied , the innermost region is masked out ( r@xmath9 ) where the star has saturated the image and no planet could be detected .
the method of modelling the stellar psf differs between the algorithms , detailed in the following subsections .
one metric for detectability of planets is signal - to - noise ( s / n ) .
it is a measure of the detectability of a point source , assuming the noise is gaussian and decorrelated between diffraction limited elements at that radius .
the equation below is similar to those in the literature , describing local signal - to - noise : @xmath10 where @xmath11 is the sum of the planet flux in an aperture with radius @xmath12 pixels and @xmath13 is the root mean square of the pixels in a 180@xmath5 , 6 pixel wide arc at the same radius , surrounding the star .
the equation above assumes statistically independent pixels , which in the case of speckle noise limited regimes is typically not be the case . for the sake of consistency with other papers in the literature , we use one of the most common definitions of s / n calculation to facilitate comparison with other methods .
this is a widely acknowledged issue in this research field , so while the s / n quoted may be off by a scaling factor , the conclusions in this paper do not rely on the absolute scaling as we are comparing analysis techniques .
coadding the frames in a data cube is a common practice but the best number of frames to coadd has not yet been thoroughly studied .
we experimented with different numbers of coadded frames using fake planets .
we ran the data through our pca pipeline ( detailed in [ sec : pca ] ) with different numbers of frames coadded ( ) . for example , 100 frames coadded means that twice as many images are passed to our pipeline as in the 200 coadded frames case .
shows four s / n curves for planets injected a different angular separations , each with a s / n of approximately 10 .
the curves are offset from 10 for clarity .
coadding 200 or less frames yields a higher s / n .
however , the s / n varies by less than a factor of 2 over all coadds , making this a relatively small effect . for the following analysis
, we keep the coadds fixed at 200 frames , which yields s / n as good as less coadds , but is computationally much faster .
this corresponds to @xmath1470 coadded images in each hemisphere which are passed to our pipeline .
since there is little field rotation between individual frames in a data cube , the smearing effect within a cube is negligible .
locally optimized combination of images ( loci ) @xcite is a widely used planet detection algorithm which spatially models the stellar psf to remove speckles .
an image is divided into rings , which are subdivided into wedges .
an optimal , linear combination of images subtracts speckles within that region .
the least squares fit succeeds at minimizing speckles , but also reduces the planet flux through the subtraction for small angular separations .
each hemisphere dataset is processed with loci independently and the final three hemisphere sky aligned cubes are collapsed . since we are using the app , we only perform loci on the `` dark side '' of the image frames .
this 180@xmath5 d shaped region ( inner=@xmath15 , outer=@xmath16 ) is the only part of each frame that is coadded in the final image .
@xcite analysis of these data used the loci algorithm .
monte carlo simulations exploring loci parameters ensured that this is the best sensitivity loci could produce . principal component analysis ( pca )
is a mathematical technique that relies on the assumption that every image in a stack can be represented as a linear combination of its principal orthogonal components , selecting structures that are present in most of the images .
its recent application to high contrast exoplanet imaging @xcite has been shown to be very effective .
unlike loci @xcite which models the local stellar psf structure , pca models the global psf structure .
the full stack of images with sky rotation is used for pca . however , since we are using the app , only the `` dark side '' of each image is used in the fit .
the s / n from a fake planet is lower if we include the `` bright side '' .
we follow the description of pca outlined in @xcite for the following analysis .
the number of pcs used determines how well the stellar psf is fit .
the first few components are the most stable , have less noise , and contain the most common structure in all the images . for our default analysis
, we used 20 pcs to model the stellar psf .
pca is run on each hemisphere dataset independently , as the pcs are correlated with time .
the final de - rotated frames are coadded into one final image covering the full 360@xmath5 around the star .
the following subsections discuss self - subtraction due to the pca algorithm as well as a series of modifications we performed on pca to optimize the detection of a planet at small @xmath3/d .
self - subtraction due the loci algorithm has been well documented by previous authors @xcite , but its impact on pca is not yet well studied .
the loci algorithm requires that the frames nearest in time to the current frame are not considered in the least squares fit , thus limiting the self - subtraction of a potential planet .
however , this frame rejection technique does not completely account for flux loss from a planet . for our pca analysis
, we draw a distinction between two types of modes : detection and characterization .
characterization mode requires fully accounting for flux loss of the planet as a function of number of pcs as we map between the measured flux and the calibrated estimate of `` true '' flux .
however , in detection mode , since we only care about our ability to separate the planet signal from the background noise , the main issue is the flux loss relative to the separation of the background noise . in this paper , we address simply the detection mode
. shows three plots with the flux ratio and s / n vs the number of pcs it was processed with .
the top figure is for a planet injected at @xmath7 , middle is at @xmath17 and bottom is at @xmath18 .
the `` flux ratio '' is the ratio of the injected planet flux to the pca processed flux in a 4 pixel aperture . for each angular separation , the @xmath19 contrast which yields a s / n of approximately 10
is plotted .
this figure demonstrates that the pca method is more efficient at capturing the patterns associated with the background fluctuations of the field than capturing information associated with the planet translation .
this differential effect means that in detection mode , it is acceptable for the flux ratio to decrease as long as the noise is decreasing as or more rapidly .
* frame rejection + for our pca code detailed above , all the frames are used in the fit and none are rejected .
this was done under the assumption that self - subtraction of the planet happens less rapidly than the noise subtraction when using pca . as discussed in section [ sec : self_sub ] , while we are in `` detection mode '' , the important factor to consider is the s / n rather than planet flux . to test this
, we used only a subset of the frames to determine the pcs .
the frames nearest in time to the frame being fitted were rejected .
these are frames where a potential planet would overlap by 0.5 fwhm or more . the number of frames to reject depends on the separation of the planet from the star .
the total rotation of the planet is limited by the amount of sky rotation achieved during each dataset .
a planet very far from its parent star would appear to rotate faster between frames , thus less frames need to be rejected .
this test allows us to compare the s / n of a fake planet processed with standard pca and `` 0.5 fwhm rejection '' , where we mimic the routine in loci to reject the frames closest in time . *
radius limited + next , we modified the pca basis set by only using the image out to a certain radius . the outer radius ( @xmath20 ) passed to the pca code determines the amount of information provided to the svd algorithm .
extra information does not necessarily provide a better fit .
our previous applications of pca kept @xmath20 fixed .
the information passed to the svd algorithm should be directly related to the stellar psf .
we modified our pca code to vary @xmath20 based on the location of the fake planet .
the new @xmath20 is 1 @xmath3/d greater than the radius of the fake planet ( see ) , thus performing pca on a smaller region .
this experiment was performed to test how significant the stellar psf fit was affected by radii greater than the planet location . *
number of pcs + the main parameter which can be manipulated in pca is the number of pcs used in the svd fit . the first principal value ( the highest singular value in the diagonal matrix ) is the `` variance '' of the image stack from the mean , in the direction of the first pc .
the same is true about the second principal value and so on .
+ shows the pca coefficient values in descending order for one of our datasets .
the first few pca coefficient values are significantly greater than the later values , implying that those pcs contain the most dominant features . increasing
the number of pcs in the stellar psf fit can help bring out the planet signal by removing structure , however it also can add noise . determining the optimal number of pcs for a certain stellar psf fit is an essential but expensive task
. the optimal number of pcs depends on the time variability of complex speckles . + for each dataset and fake planet angular separation , pca was run with different numbers of pcs ranging from 5 to 60 , in increments of 5 .
shows the results of each image processing method detailed in section [ sec : pca ] .
each technique was run with varying planet contrasts at a given radius .
we extrapolated between planet contrasts to determine contrast that yields a s / n of 7 . for the method with varying pcs detailed in section [ sec : pca_mod ] , we noted which number of pcs yielded the highest s / n at which radius .
these are the numbers listed on the yellow curve in .
our standard pca technique yields a better contrast curve than loci for our coronagraphic data .
our modifications to pca , in some cases , yield better sensitivity .
unlike the loci algorithm , rejecting the frames nearest in time ( detailed in section [ sec : pca_mod ] ) yields a worse contrast curve than our standard pca .
this is likely due to the noise being more correlated in frames closer in time , thus providing important information to the svd algorithm and increasing the s / n of the planet .
we did not reject any frames in our final data analysis approach .
limiting the outer radius passed to the svd algorithm yielded a slightly better contrast ratio than standard pca from @xmath17 to @xmath21 .
however , this contrast increase is not significant and is only beneficial because it is less computationally expensive .
our standard pca contrast curve was generated with 20 pcs . by varying the number of pcs we can increase the s / n from a companion .
our pc - varying result yields a consistently more sensitive contrast curve then all the other methods .
we gain between 0.5 and 1 magnitude contrast over our loci analysis from @xmath6 to @xmath7 . from we see that the number of pcs which yield the highest s / n for a planet varies based on its angular separation .
is a 3-d surface plot showing how the number of pcs at each radius affects the contrast at 7@xmath13 for a planet at a fixed pa .
fake planets were added between 2 and 20 pcs in smaller steps to emphasize the structure .
this figure demonstrates that at small angular separations ( @xmath22 @xmath23 ) , the s / n is sensitive to the number of pcs chosen .
this is the region where the diffraction and speckles due to the star are more significant than the unstructured noise from thermal emission and the sky background .
for example , at @xmath6 choosing a small number of pcs yields an 8 magnitude gain in sensitivity than a large number of pcs .
increasing the number of pcs quickly leads to nearly complete self - subtraction .
this can be seen in as a contrast of nearly zero .
as we move to larger radii the optimal number of pcs remains in the 5 - 20 pc range . beyond @xmath23 where the number of pcs shows no significant preference below 45 pcs .
our pca re - analysis of these data improves sensitivity at small inner working angles , from @xmath6 to @xmath24 , in some cases by 1 magnitude ( see blue and yellow curves , ) .
we convert the best 7@xmath13 detection contrast curve to an upper mass limit for planets using the @xcite and @xcite atmospheric models ( ) assuming an age of 440 myr @xcite .
we confirm the non - detection of companions with a model - dependent upper mass limit of 13 - 18 m@xmath1 from 4 - 10 au .
our new upper mass limit is based on our more robust 7@xmath13 detection limit .
the 1 magnitude increase in the contrast ratio at @xmath17 translates to an increased sensitivity of @xmath25 7 @xmath26 .
the increase in sensitivity allows us to probe planetary masses ( @xmath2215 m@xmath1 ) at small angular separations .
we have shown that the number of pcs which yield the highest signal - to - noise depends on the planet s distance from the parent star ( yellow line , ) . at small angular separations
( @xmath22 @xmath23 ) , the s / n is sensitive to the number of pcs chosen ( ) .
this is the limit where the diffraction from the central star is equal to or less significant than the background noise .
we add gaussian white noise to our data to test if this turnover point changes for a fainter target . increasing the sky background noise
makes fomalhaut 1.5 magnitudes fainter , while keeping the telescope conditions and strehl identical .
this is the ideal way to test how fainter targets will behave .
fake planets are once again injected and the best number of pcs at each angular separation is noted .
changing the number of pcs used at each angular separation is still the best method for detecting companions . as expected , the regime of large numbers of pcs at small separations results in low contrast , which then improves down to a plateau at smaller pcs and larger radii .
the turnover point remains near @xmath23 , beyond which the diffraction from the star is no longer significant and the optimal number of pcs is less clear . beyond this separation
, the background noise dominates the svd fit and thus does not help subtract the stellar psf .
we re - analyze our fomalhaut app / naco / nb4.05 data using pca and compare it with the loci algorithm .
pca yields a more sensitive contrast curve than the loci algorithm at small inner working angles .
we tested several modifications to pca and gain up to 1 mag of contrast over our loci analysis from @xmath6 to @xmath7 .
the most effective parameter which optimized pca was varying the number of principal components .
the number of principal components chosen is sensitive for planets at small inner working angles .
the detection limit of a planet at small radii can vary by several magnitudes .
careful attention should be paid to determining the number of principal components used at radii where the speckles are more significant than the unstructured noise of thermal emission and the sky background . running pca for a range of principal components at each angular separation and generating a 3-d surface is a useful way to visualize the optimal number of principal components needed to pull out a faint planet signal .
futher analysis is needed in other wavelengths , as differing strehl ratios may affect the turnover point where the stellar diffraction is less significant than the background noise .
these results have direct application for current and future planet imaging campaigns , which will likely use a combination of pca , loci , and other image processing techniques . , m. a. , quanz , s. p. , meyer , m. r. , et al .
2010 , in society of photo - optical instrumentation engineers ( spie ) conference series , vol . 7735 , society of photo - optical instrumentation engineers ( spie ) conference series , r. , hartung , m. , brandner , w. , et al .
2003 , in society of photo - optical instrumentation engineers ( spie ) conference series , vol .
4841 , society of photo - optical instrumentation engineers ( spie ) conference series , ed . m. iye & a. f. m. moorwood , 944952 , c. , macintosh , b. , & vran , j .- p .
2010 , in society of photo - optical instrumentation engineers ( spie ) conference series , vol .
7736 , society of photo - optical instrumentation engineers ( spie ) conference series , g. , lacombe , f. , puget , p. , et al .
2003 , in society of photo - optical instrumentation engineers ( spie ) conference series , vol . 4839 , society of photo - optical instrumentation engineers ( spie ) conference series , ed .
p. l. wizinowich & d. bonaccini , 140149 | we present the results of a study to optimize the principal component analysis ( pca ) algorithm for planet detection , a new algorithm complementing adi and loci for increasing the contrast achievable next to a bright star .
the stellar psf is constructed by removing linear combinations of principal components , allowing the flux from an extrasolar planet to shine through .
the number of principal components used determines how well the stellar psf is globally modelled . using more principal components may decrease the number of speckles in the final image , but also increases the background noise . we apply pca to fomalhaut vlt naco images acquired at 4.05 @xmath0 m with an apodized phase plate
we do not detect any companions , with a model dependent upper mass limit of 13 - 18 m@xmath1 from 4 - 10 au .
pca achieves greater sensitivity than the loci algorithm for the fomalhaut coronagraphic data by up to 1 magnitude .
we make several adaptations to the pca code and determine which of these prove the most effective at maximizing the signal - to - noise from a planet very close to its parent star .
we demonstrate that optimizing the number of principal components used in pca proves most effective for pulling out a planet signal . | <s>[INST]the detection and characterization of extrasolar planets has grown dramatically as a field since the first detection in 1992 @xcite .
the most successful detection techniques thus far are radial velocity and transit detection . using ground and space based surveys ( harps , kepler , corot , etc ) ,
these indirect techniques have discovered over 800 planets ( exoplanet.eu ) as well as thousands more planet candidates .
the direct detection of planets provides a unique opportunity to study exoplanets in the context of their formation and evolution .
it complements the underlying semi - major axis exoplanet distribution from rv surveys ( from 100 au down to a few aus ) and enables the characterization of the planet itself with an examination of its emergent flux as a function of wavelength .
the detection of the planets hr8799 bcde @xcite , fomalhaut b @xcite , @xmath2 pic b @xcite , 2mass1207 @xcite , 1rxs j1609 - 2105 b @xcite , hd 95086 b @xcite , koi-94 @xcite as well as discoveries of protoplanetary candidates lkca 15 b @xcite and hd100546 b @xcite , demonstrate the potential breakthroughs of the technique .
however , thus far , most dedicated high contrast imaging surveys have yielded null - results ( e.g. @xcite,@xcite , @xcite , @xcite,@xcite ) .
these null results are due to the lack of contrast at small orbital separations , where most planets are expected to be found . since planets are concluded to be rare at large orbital separations ( @xcite , @xcite ) , high contrast imaging must probe close to the parent star to detect a planet .
high contrast imaging is limited by the diffraction limit , set by the telescope optics , which determines the minimum angular separation achievable under ideal conditions .
since planets are low mass , cold , and red compared to their parent star ( @xcite,@xcite ) , the contrast ratio of their magnitudes is an additional constraint on their detectability .
new instruments and techniques have been developed to combat these constraints at the acquisition and image processing stage .
coronagraphs have been developed to reduce the light scattered in the telescope optics from diffraction during acquisition , but at a cost of throughput and angular resolution @xcite .
coronagraphic optics allow us to probe smaller inner working angles , but are limited by the stellar `` speckles '' which can dominate the flux from a planet @xcite . by turning off the telescope derotator on an alt - az telescope ,
the planet is able to `` rotate '' around the star , while the stellar psf stays relatively stable and the speckles vary randomly in time .
this technique is used in angular differential imaging ( adi , @xcite ) .
it takes advantage of this rotation to identify and subtract ( in post - processing ) the contribution from the stellar psf and speckles .
there are a number of image processing techniques aimed at modelling and subtracting the stellar psf from every image , allowing the sky fixed planet signal to shine through .
loci @xcite is an extension of adi , which models the local stellar psf structure in every image .
principal component analysis ( pca ) ( @xcite , @xcite , @xcite ) models how the psf varies in time by identifying the main linear components of the variation .
application of these image processing techniques has been demonstrated to increase the limiting magnitude achievable by up to a factor of 5 ( @xcite , @xcite ) . in this work
, we present a detailed study of loci and pca image processing techniques in order to optimize the signal - to - noise of a planet at small angular separations with the app coronagraph ( @xcite,@xcite ) .
we compare our results to the previous result of @xcite .
the fomalhaut dataset that is used in the following analyses are a deep but typical observing sequence and will act as an example for the rest of our surveys .
data were obtained of the star fomalhaut at the vlt / ut4 with naco ( @xcite , @xcite ) in july and august 2011 ( 087.c-0701(b ) ) and were analyzed and published in @xcite .
fomalhaut was used as the natural guide star with the visible band wavefront sensor .
the l27 camera on naco was used with the nb4.05 filter ( @xmath3 = 4.051@xmath0 m and @xmath4 = 0.02@xmath0 m ) and the apodizing phase plate coronagraph ( app , @xcite , @xcite ) to provide additional diffraction suppression .
we used pupil tracking mode to perform adi @xcite .
the psf core is intentionally saturated to increase the signal from any potential companions .
the app provides diffraction supression over a 180@xmath5 wedge on one side of the target ( ) .
additional observations are required with a different position angle to cover the full 360@xmath5 around the star . for these observations
, we have three different datasets with different position angles ensuring full pa coverage around the target star .
each dataset has a large amount of field rotation : 119@xmath5 , 117@xmath5 , 120@xmath5 .
data were acquired in cube mode .
each data cube contains 200 frames , each with an integration time of 0.23 seconds .
approximately 70 cubes were obtained for each hemisphere dataset , totalling in an integration time of 160 minutes .
a three point dither pattern was used to allow subtraction of the sky background and detector systematics as detailed in @xcite .
unsaturated short exposure data with the neutral density filter were also taken for photometry .
data cubes at each dither position were pairwise subtracted to remove the sky background and detector systematics .
the cubes were shifted to move the core psf into the middle of a square image and bad frames ( open loop and poor ao ) were discarded ( 5% of hemisphere 1 , 16% of hemisphere 2 , and 7% of hemisphere 3 ) .
the three different app position angle datasets were processed separately .
each hemisphere dataset has its own corresponding unsaturated data for photometry .
fake planets are subsequently used to determine the limiting contrast after image processing .
the unsaturated fomalhaut data is used to add a fake planet in each saturated frame .
one fake planet is added at a time , between @xmath6 and @xmath7 in steps of @xmath8 and delta magnitudes in steps of 1 mag from dm= 7 to 13 . due to the asymmetric nature of the app psf , it is also necessary to determine the signal - to - noise of a planet at different position angles . for our analysis
we placed a planet on opposite sides of the star ( pa=45@xmath5 and 225@xmath5 relative to the sky ) to take into account the asymmetric psf of the app .
these two pa orientations ensure that the planet is on the dark side of the app in at least two of the hemispheres at once .
the mean of the limiting contrast at each pa is stored .
the final science frames are processed with several different algorithms to recover the fake planet signal .
all of the algorithms take advantage of the fake planet s rotation in the sky around the star to model and subtract the stellar psf from each image ( adi , @xcite ) . before each algorithm
is applied , the innermost region is masked out ( r@xmath9 ) where the star has saturated the image and no planet could be detected .
the method of modelling the stellar psf differs between the algorithms , detailed in the following subsections .
one metric for detectability of planets is signal - to - noise ( s / n ) .
it is a measure of the detectability of a point source , assuming the noise is gaussian and decorrelated between diffraction limited elements at that radius .
the equation below is similar to those in the literature , describing local signal - to - noise : @xmath10 where @xmath11 is the sum of the planet flux in an aperture with radius @xmath12 pixels and @xmath13 is the root mean square of the pixels in a 180@xmath5 , 6 pixel wide arc at the same radius , surrounding the star .
the equation above assumes statistically independent pixels , which in the case of speckle noise limited regimes is typically not be the case . for the sake of consistency with other papers in the literature , we use one of the most common definitions of s / n calculation to facilitate comparison with other methods .
this is a widely acknowledged issue in this research field , so while the s / n quoted may be off by a scaling factor , the conclusions in this paper do not rely on the absolute scaling as we are comparing analysis techniques .
coadding the frames in a data cube is a common practice but the best number of frames to coadd has not yet been thoroughly studied .
we experimented with different numbers of coadded frames using fake planets .
we ran the data through our pca pipeline ( detailed in [ sec : pca ] ) with different numbers of frames coadded ( ) . for example , 100 frames coadded means that twice as many images are passed to our pipeline as in the 200 coadded frames case .
shows four s / n curves for planets injected a different angular separations , each with a s / n of approximately 10 .
the curves are offset from 10 for clarity .
coadding 200 or less frames yields a higher s / n .
however , the s / n varies by less than a factor of 2 over all coadds , making this a relatively small effect . for the following analysis
, we keep the coadds fixed at 200 frames , which yields s / n as good as less coadds , but is computationally much faster .
this corresponds to @xmath1470 coadded images in each hemisphere which are passed to our pipeline .
since there is little field rotation between individual frames in a data cube , the smearing effect within a cube is negligible .
locally optimized combination of images ( loci ) @xcite is a widely used planet detection algorithm which spatially models the stellar psf to remove speckles .
an image is divided into rings , which are subdivided into wedges .
an optimal , linear combination of images subtracts speckles within that region .
the least squares fit succeeds at minimizing speckles , but also reduces the planet flux through the subtraction for small angular separations .
each hemisphere dataset is processed with loci independently and the final three hemisphere sky aligned cubes are collapsed . since we are using the app , we only perform loci on the `` dark side '' of the image frames .
this 180@xmath5 d shaped region ( inner=@xmath15 , outer=@xmath16 ) is the only part of each frame that is coadded in the final image .
@xcite analysis of these data used the loci algorithm .
monte carlo simulations exploring loci parameters ensured that this is the best sensitivity loci could produce . principal component analysis ( pca )
is a mathematical technique that relies on the assumption that every image in a stack can be represented as a linear combination of its principal orthogonal components , selecting structures that are present in most of the images .
its recent application to high contrast exoplanet imaging @xcite has been shown to be very effective .
unlike loci @xcite which models the local stellar psf structure , pca models the global psf structure .
the full stack of images with sky rotation is used for pca . however , since we are using the app , only the `` dark side '' of each image is used in the fit .
the s / n from a fake planet is lower if we include the `` bright side '' .
we follow the description of pca outlined in @xcite for the following analysis .
the number of pcs used determines how well the stellar psf is fit .
the first few components are the most stable , have less noise , and contain the most common structure in all the images . for our default analysis
, we used 20 pcs to model the stellar psf .
pca is run on each hemisphere dataset independently , as the pcs are correlated with time .
the final de - rotated frames are coadded into one final image covering the full 360@xmath5 around the star .
the following subsections discuss self - subtraction due to the pca algorithm as well as a series of modifications we performed on pca to optimize the detection of a planet at small @xmath3/d .
self - subtraction due the loci algorithm has been well documented by previous authors @xcite , but its impact on pca is not yet well studied .
the loci algorithm requires that the frames nearest in time to the current frame are not considered in the least squares fit , thus limiting the self - subtraction of a potential planet .
however , this frame rejection technique does not completely account for flux loss from a planet . for our pca analysis
, we draw a distinction between two types of modes : detection and characterization .
characterization mode requires fully accounting for flux loss of the planet as a function of number of pcs as we map between the measured flux and the calibrated estimate of `` true '' flux .
however , in detection mode , since we only care about our ability to separate the planet signal from the background noise , the main issue is the flux loss relative to the separation of the background noise . in this paper , we address simply the detection mode
. shows three plots with the flux ratio and s / n vs the number of pcs it was processed with .
the top figure is for a planet injected at @xmath7 , middle is at @xmath17 and bottom is at @xmath18 .
the `` flux ratio '' is the ratio of the injected planet flux to the pca processed flux in a 4 pixel aperture . for each angular separation , the @xmath19 contrast which yields a s / n of approximately 10
is plotted .
this figure demonstrates that the pca method is more efficient at capturing the patterns associated with the background fluctuations of the field than capturing information associated with the planet translation .
this differential effect means that in detection mode , it is acceptable for the flux ratio to decrease as long as the noise is decreasing as or more rapidly .
* frame rejection + for our pca code detailed above , all the frames are used in the fit and none are rejected .
this was done under the assumption that self - subtraction of the planet happens less rapidly than the noise subtraction when using pca . as discussed in section [ sec : self_sub ] , while we are in `` detection mode '' , the important factor to consider is the s / n rather than planet flux . to test this
, we used only a subset of the frames to determine the pcs .
the frames nearest in time to the frame being fitted were rejected .
these are frames where a potential planet would overlap by 0.5 fwhm or more . the number of frames to reject depends on the separation of the planet from the star .
the total rotation of the planet is limited by the amount of sky rotation achieved during each dataset .
a planet very far from its parent star would appear to rotate faster between frames , thus less frames need to be rejected .
this test allows us to compare the s / n of a fake planet processed with standard pca and `` 0.5 fwhm rejection '' , where we mimic the routine in loci to reject the frames closest in time . *
radius limited + next , we modified the pca basis set by only using the image out to a certain radius . the outer radius ( @xmath20 ) passed to the pca code determines the amount of information provided to the svd algorithm .
extra information does not necessarily provide a better fit .
our previous applications of pca kept @xmath20 fixed .
the information passed to the svd algorithm should be directly related to the stellar psf .
we modified our pca code to vary @xmath20 based on the location of the fake planet .
the new @xmath20 is 1 @xmath3/d greater than the radius of the fake planet ( see ) , thus performing pca on a smaller region .
this experiment was performed to test how significant the stellar psf fit was affected by radii greater than the planet location . *
number of pcs + the main parameter which can be manipulated in pca is the number of pcs used in the svd fit . the first principal value ( the highest singular value in the diagonal matrix ) is the `` variance '' of the image stack from the mean , in the direction of the first pc .
the same is true about the second principal value and so on .
+ shows the pca coefficient values in descending order for one of our datasets .
the first few pca coefficient values are significantly greater than the later values , implying that those pcs contain the most dominant features . increasing
the number of pcs in the stellar psf fit can help bring out the planet signal by removing structure , however it also can add noise . determining the optimal number of pcs for a certain stellar psf fit is an essential but expensive task
. the optimal number of pcs depends on the time variability of complex speckles . + for each dataset and fake planet angular separation , pca was run with different numbers of pcs ranging from 5 to 60 , in increments of 5 .
shows the results of each image processing method detailed in section [ sec : pca ] .
each technique was run with varying planet contrasts at a given radius .
we extrapolated between planet contrasts to determine contrast that yields a s / n of 7 . for the method with varying pcs detailed in section [ sec : pca_mod ] , we noted which number of pcs yielded the highest s / n at which radius .
these are the numbers listed on the yellow curve in .
our standard pca technique yields a better contrast curve than loci for our coronagraphic data .
our modifications to pca , in some cases , yield better sensitivity .
unlike the loci algorithm , rejecting the frames nearest in time ( detailed in section [ sec : pca_mod ] ) yields a worse contrast curve than our standard pca .
this is likely due to the noise being more correlated in frames closer in time , thus providing important information to the svd algorithm and increasing the s / n of the planet .
we did not reject any frames in our final data analysis approach .
limiting the outer radius passed to the svd algorithm yielded a slightly better contrast ratio than standard pca from @xmath17 to @xmath21 .
however , this contrast increase is not significant and is only beneficial because it is less computationally expensive .
our standard pca contrast curve was generated with 20 pcs . by varying the number of pcs we can increase the s / n from a companion .
our pc - varying result yields a consistently more sensitive contrast curve then all the other methods .
we gain between 0.5 and 1 magnitude contrast over our loci analysis from @xmath6 to @xmath7 . from we see that the number of pcs which yield the highest s / n for a planet varies based on its angular separation .
is a 3-d surface plot showing how the number of pcs at each radius affects the contrast at 7@xmath13 for a planet at a fixed pa .
fake planets were added between 2 and 20 pcs in smaller steps to emphasize the structure .
this figure demonstrates that at small angular separations ( @xmath22 @xmath23 ) , the s / n is sensitive to the number of pcs chosen .
this is the region where the diffraction and speckles due to the star are more significant than the unstructured noise from thermal emission and the sky background .
for example , at @xmath6 choosing a small number of pcs yields an 8 magnitude gain in sensitivity than a large number of pcs .
increasing the number of pcs quickly leads to nearly complete self - subtraction .
this can be seen in as a contrast of nearly zero .
as we move to larger radii the optimal number of pcs remains in the 5 - 20 pc range . beyond @xmath23 where the number of pcs shows no significant preference below 45 pcs .
our pca re - analysis of these data improves sensitivity at small inner working angles , from @xmath6 to @xmath24 , in some cases by 1 magnitude ( see blue and yellow curves , ) .
we convert the best 7@xmath13 detection contrast curve to an upper mass limit for planets using the @xcite and @xcite atmospheric models ( ) assuming an age of 440 myr @xcite .
we confirm the non - detection of companions with a model - dependent upper mass limit of 13 - 18 m@xmath1 from 4 - 10 au .
our new upper mass limit is based on our more robust 7@xmath13 detection limit .
the 1 magnitude increase in the contrast ratio at @xmath17 translates to an increased sensitivity of @xmath25 7 @xmath26 .
the increase in sensitivity allows us to probe planetary masses ( @xmath2215 m@xmath1 ) at small angular separations .
we have shown that the number of pcs which yield the highest signal - to - noise depends on the planet s distance from the parent star ( yellow line , ) . at small angular separations
( @xmath22 @xmath23 ) , the s / n is sensitive to the number of pcs chosen ( ) .
this is the limit where the diffraction from the central star is equal to or less significant than the background noise .
we add gaussian white noise to our data to test if this turnover point changes for a fainter target . increasing the sky background noise
makes fomalhaut 1.5 magnitudes fainter , while keeping the telescope conditions and strehl identical .
this is the ideal way to test how fainter targets will behave .
fake planets are once again injected and the best number of pcs at each angular separation is noted .
changing the number of pcs used at each angular separation is still the best method for detecting companions . as expected , the regime of large numbers of pcs at small separations results in low contrast , which then improves down to a plateau at smaller pcs and larger radii .
the turnover point remains near @xmath23 , beyond which the diffraction from the star is no longer significant and the optimal number of pcs is less clear . beyond this separation
, the background noise dominates the svd fit and thus does not help subtract the stellar psf .
we re - analyze our fomalhaut app / naco / nb4.05 data using pca and compare it with the loci algorithm .
pca yields a more sensitive contrast curve than the loci algorithm at small inner working angles .
we tested several modifications to pca and gain up to 1 mag of contrast over our loci analysis from @xmath6 to @xmath7 .
the most effective parameter which optimized pca was varying the number of principal components .
the number of principal components chosen is sensitive for planets at small inner working angles .
the detection limit of a planet at small radii can vary by several magnitudes .
careful attention should be paid to determining the number of principal components used at radii where the speckles are more significant than the unstructured noise of thermal emission and the sky background . running pca for a range of principal components at each angular separation and generating a 3-d surface is a useful way to visualize the optimal number of principal components needed to pull out a faint planet signal .
futher analysis is needed in other wavelengths , as differing strehl ratios may affect the turnover point where the stellar diffraction is less significant than the background noise .
these results have direct application for current and future planet imaging campaigns , which will likely use a combination of pca , loci , and other image processing techniques . , m. a. , quanz , s. p. , meyer , m. r. , et al .
2010 , in society of photo - optical instrumentation engineers ( spie ) conference series , vol . 7735 , society of photo - optical instrumentation engineers ( spie ) conference series , r. , hartung , m. , brandner , w. , et al .
2003 , in society of photo - optical instrumentation engineers ( spie ) conference series , vol .
4841 , society of photo - optical instrumentation engineers ( spie ) conference series , ed . m. iye & a. f. m. moorwood , 944952 , c. , macintosh , b. , & vran , j .- p .
2010 , in society of photo - optical instrumentation engineers ( spie ) conference series , vol .
7736 , society of photo - optical instrumentation engineers ( spie ) conference series , g. , lacombe , f. , puget , p. , et al .
2003 , in society of photo - optical instrumentation engineers ( spie ) conference series , vol . 4839 , society of photo - optical instrumentation engineers ( spie ) conference series , ed .
p. l. wizinowich & d. bonaccini , 140149[/INST] we present the results of a study to optimize the principal component analysis ( pca ) algorithm for planet detection , a new algorithm complementing adi and loci for increasing the contrast achievable next to a bright star .
the stellar psf is constructed by removing linear combinations of principal components , allowing the flux from an extrasolar planet to shine through .
the number of principal components used determines how well the stellar psf is globally modelled . using more principal components may decrease the number of speckles in the final image , but also increases the background noise . we apply pca to fomalhaut vlt naco images acquired at 4.05 @xmath0 m with an apodized phase plate
we do not detect any companions , with a model dependent upper mass limit of 13 - 18 m@xmath1 from 4 - 10 au .
pca achieves greater sensitivity than the loci algorithm for the fomalhaut coronagraphic data by up to 1 magnitude .
we make several adaptations to the pca code and determine which of these prove the most effective at maximizing the signal - to - noise from a planet very close to its parent star .
we demonstrate that optimizing the number of principal components used in pca proves most effective for pulling out a planet signal . </s> |
PHOENIX (AP) — She wasn't necessarily popping champagne Thursday, but conservationist Jennifer Pitt was certainly celebrating the arrival of water from the Colorado River into the Sea of Cortez.
It was a monumental moment for conservationists, who said that water hasn't flowed regularly from the Colorado River to the sea in more than 50 years. It temporarily reached the sea twice in the 1980s and last in 1993.
"The pulse flow meeting the sea marks completion of a journey that the Colorado River has not made in a long time, and I take it as a sign of hope not only for our efforts to restore the Colorado River Delta, but also rivers and watersheds everywhere in the world where climate change promises an uncertain future," said Pitt, director of the Environmental Defense Fund's Colorado River Project.
"I think, once again, it is sort of overwhelming, and I think it sheds light on a sort of global interest in the Colorado River completing that journey again," Pitt said.
The water reached the sea on Thursday afternoon. It traveled nearly 100 miles from a previously barren delta at the Morelos Dam just south of where California, Arizona and Mexico meet. It was a result of a bi-national agreement that came together after years of negotiations.
Enough water to supply over 200,000 homes for a year was released on March 23 in an effort to revive trees, wildlife and aquatic life that have perished since the delta dried up decades ago.
Conservationists say it'll be years before they see the environmental effects of the water streaming through, but residents in the town of San Luis Rio Colorado in the Mexican state of Sonora have been frolicking in the water and gathering at the river ever since the flow started.
It's a feat that the water released in March has continued to flow, said Sally Spener, a spokeswoman for the International Boundary and Water Commission.
Spener has said that the success of the project will inform future collaborations between the U.S. and Mexico.
"It's been very exciting for all of us to track the pulse flow as it has moved downstream to parts of the Colorado River channel that have been dry for years. To say that we reconnected the river with the sea is especially gratifying," said Edward Drusina, U.S. Commissioner of the International Boundary and Water Commission. ||||| After coursing through its delta for nearly eight weeks, the fresh waters of the Colorado River have touched the high tides of the salty sea.
It is the first time in sixteen years that the Colorado River, which flows 1,450 miles (2,334 kilometers) from its headwaters in the Rocky Mountains of Colorado to the Sea of Cortez (Gulf of California) in northwestern Mexico, will have reached its final, natural destination.
This reunion between river and sea is due to an agreement between Mexico and the United States, known as Minute 319, to advance the restoration of the Colorado Delta by releasing a pulse flow and sustaining base flows in a five-year experiment.
The pulse flow, which began on March 23, is now nearing its end. Scientists had not planned on the river reaching its estuary as part of this grand experiment. But that it has, is a wonderful bonus.
This confluence of the river and the high tides signals that “improving estuarine conditions in this upper part of the estuary is possible if restoration efforts continue in the future,” Francisco Zamora, director of the Colorado River Delta Legacy Program at the Sonoran Institute, wrote to me in an email. Zamora took the photos featured in this post on Thursday, May 15, from a low-flying plane operated by LightHawk.
If rivers are born with a destiny, it is to reach the sea. They carry sediment, nutrients and freshwater from the land to the coastal zones, helping sustain the productivity and abundance of marine environments.
Deltas and estuaries – where rivers and seas connect – are some of the most biologically rich ecosystems on the planet.
Before the big dams and diversions of the 20th century, the Colorado’s nutrient-rich freshwater mixed with the Upper Gulf’s salty tides to create the perfect water chemistry and nursery grounds for Gulf corvina, totoaba, brown and blue shrimp, and other fisheries of great commercial and cultural importance to the region and to the indigenous Cucapá.
But over recent decades, a combination of over-fishing and lack of freshwater in-flow has caused fish populations in the Upper Gulf to plummet.
Since the completion of Glen Canyon Dam in 1963, the Colorado has connected with the sea only a few times – mostly during El Niño weather events that brought unusually large amounts of snow and rain to the Colorado Rockies and the upper watershed. The last time the Colorado reached the sea was in 1998.
The estuary is now part of a protected biosphere reserve and no-fishing zone, an attempt to give fish – as well as the highly endangered vaquita, the world’s smallest porpoise – a chance to revive their numbers.
The pulse flow, which was designed to mimic the Colorado’s natural spring flood, is an experiment of historic political and ecological significance: it is the first time the United States and Mexico have made a conscious decision to give some water back to the river to revive the health and habitats of its delta.
One of the planet’s great desert aquatic ecosystems, the delta once boasted some 2 million acres of lush wetlands teeming with birds and wildlife.
Over the past eight weeks, the pulse flow has brought needed water to active delta restoration sites, where conservation groups have planted hundreds of thousands of cottonwoods, willows and mesquite to begin re-establishing habitats for hundreds of species of birds and wildlife.
Timed to coincide with the germination of these native trees, the pulse is also helping new habitats emerge spontaneously along the river.
On the heels of the pulse flow, the Colorado River Delta Water Trust will provide sustaining base flows made possible by purchasing voluntary leases of water from delta farmers.
[Change the Course – a partnership of the National Geographic Society, Bonneville Environmental Foundation, and Participant Media – has partnered with the Delta Water Trust to help provide these crucial base flows.]
Compared with the natural, pre-dam flow of the river through its delta, the volume of water restored through Minute 319 is small – less than 1 percent of the river’s historic flow. But that flow is being strategically timed and directed to produce the highest ecological benefit possible. Teams of scientists are monitoring the effects on the hydrology, vegetation, birds and other ecological features of the delta, so that future flow releases can be even more effective.
The pulse flow experiment did not specifically plan on the river reaching the sea.
But against the odds, at least a small volume of the Colorado River has fulfilled its destiny – and made it home.
Sandra Postel is director of the Global Water Policy Project, Freshwater Fellow of the National Geographic Society, and author of several books and numerous articles on global water issues. She is co-creator of Change the Course, the national freshwater conservation and restoration campaign being piloted in the Colorado River Basin. | – The Colorado River has been reunited with an old friend—the sea. Thanks to an agreement between the US and Mexico, water from the river has reached the Sea of Cortez in northwestern Mexico for the first time since either 1998 (according to National Geographic) or 1993 (according to AP). Either way, it's been a long time, and conservationists hope last week's milestone becomes a regular occurrence. The water was released in March from the Morelos Dam near the US-Mexico border, and it took about 8 weeks to complete the journey to the sea. The idea is to restore life to the Colorado River delta, which has pretty much dried up since the advent of the big-dam era. In fact, the experiment is the first time water from the river has been diverted solely for environmental purposes, reports Arizona Public Media. While the initial "pulse flow" is now shut off, smaller amounts of water will be released to the delta over the next few years, and conservationists think it can revive the dormant habitat. (They've been busy planting trees, timed to germinate with the water's release.) "It is sort of overwhelming, and I think it sheds light on a sort of global interest in the Colorado River completing that journey again," says Jennifer Pitt of the Environmental Defense Fund's Colorado River Project. (In other water-related news, scientists have found an underwater "graveyard.") | <s>[INST]PHOENIX (AP) — She wasn't necessarily popping champagne Thursday, but conservationist Jennifer Pitt was certainly celebrating the arrival of water from the Colorado River into the Sea of Cortez.
It was a monumental moment for conservationists, who said that water hasn't flowed regularly from the Colorado River to the sea in more than 50 years. It temporarily reached the sea twice in the 1980s and last in 1993.
"The pulse flow meeting the sea marks completion of a journey that the Colorado River has not made in a long time, and I take it as a sign of hope not only for our efforts to restore the Colorado River Delta, but also rivers and watersheds everywhere in the world where climate change promises an uncertain future," said Pitt, director of the Environmental Defense Fund's Colorado River Project.
"I think, once again, it is sort of overwhelming, and I think it sheds light on a sort of global interest in the Colorado River completing that journey again," Pitt said.
The water reached the sea on Thursday afternoon. It traveled nearly 100 miles from a previously barren delta at the Morelos Dam just south of where California, Arizona and Mexico meet. It was a result of a bi-national agreement that came together after years of negotiations.
Enough water to supply over 200,000 homes for a year was released on March 23 in an effort to revive trees, wildlife and aquatic life that have perished since the delta dried up decades ago.
Conservationists say it'll be years before they see the environmental effects of the water streaming through, but residents in the town of San Luis Rio Colorado in the Mexican state of Sonora have been frolicking in the water and gathering at the river ever since the flow started.
It's a feat that the water released in March has continued to flow, said Sally Spener, a spokeswoman for the International Boundary and Water Commission.
Spener has said that the success of the project will inform future collaborations between the U.S. and Mexico.
"It's been very exciting for all of us to track the pulse flow as it has moved downstream to parts of the Colorado River channel that have been dry for years. To say that we reconnected the river with the sea is especially gratifying," said Edward Drusina, U.S. Commissioner of the International Boundary and Water Commission. ||||| After coursing through its delta for nearly eight weeks, the fresh waters of the Colorado River have touched the high tides of the salty sea.
It is the first time in sixteen years that the Colorado River, which flows 1,450 miles (2,334 kilometers) from its headwaters in the Rocky Mountains of Colorado to the Sea of Cortez (Gulf of California) in northwestern Mexico, will have reached its final, natural destination.
This reunion between river and sea is due to an agreement between Mexico and the United States, known as Minute 319, to advance the restoration of the Colorado Delta by releasing a pulse flow and sustaining base flows in a five-year experiment.
The pulse flow, which began on March 23, is now nearing its end. Scientists had not planned on the river reaching its estuary as part of this grand experiment. But that it has, is a wonderful bonus.
This confluence of the river and the high tides signals that “improving estuarine conditions in this upper part of the estuary is possible if restoration efforts continue in the future,” Francisco Zamora, director of the Colorado River Delta Legacy Program at the Sonoran Institute, wrote to me in an email. Zamora took the photos featured in this post on Thursday, May 15, from a low-flying plane operated by LightHawk.
If rivers are born with a destiny, it is to reach the sea. They carry sediment, nutrients and freshwater from the land to the coastal zones, helping sustain the productivity and abundance of marine environments.
Deltas and estuaries – where rivers and seas connect – are some of the most biologically rich ecosystems on the planet.
Before the big dams and diversions of the 20th century, the Colorado’s nutrient-rich freshwater mixed with the Upper Gulf’s salty tides to create the perfect water chemistry and nursery grounds for Gulf corvina, totoaba, brown and blue shrimp, and other fisheries of great commercial and cultural importance to the region and to the indigenous Cucapá.
But over recent decades, a combination of over-fishing and lack of freshwater in-flow has caused fish populations in the Upper Gulf to plummet.
Since the completion of Glen Canyon Dam in 1963, the Colorado has connected with the sea only a few times – mostly during El Niño weather events that brought unusually large amounts of snow and rain to the Colorado Rockies and the upper watershed. The last time the Colorado reached the sea was in 1998.
The estuary is now part of a protected biosphere reserve and no-fishing zone, an attempt to give fish – as well as the highly endangered vaquita, the world’s smallest porpoise – a chance to revive their numbers.
The pulse flow, which was designed to mimic the Colorado’s natural spring flood, is an experiment of historic political and ecological significance: it is the first time the United States and Mexico have made a conscious decision to give some water back to the river to revive the health and habitats of its delta.
One of the planet’s great desert aquatic ecosystems, the delta once boasted some 2 million acres of lush wetlands teeming with birds and wildlife.
Over the past eight weeks, the pulse flow has brought needed water to active delta restoration sites, where conservation groups have planted hundreds of thousands of cottonwoods, willows and mesquite to begin re-establishing habitats for hundreds of species of birds and wildlife.
Timed to coincide with the germination of these native trees, the pulse is also helping new habitats emerge spontaneously along the river.
On the heels of the pulse flow, the Colorado River Delta Water Trust will provide sustaining base flows made possible by purchasing voluntary leases of water from delta farmers.
[Change the Course – a partnership of the National Geographic Society, Bonneville Environmental Foundation, and Participant Media – has partnered with the Delta Water Trust to help provide these crucial base flows.]
Compared with the natural, pre-dam flow of the river through its delta, the volume of water restored through Minute 319 is small – less than 1 percent of the river’s historic flow. But that flow is being strategically timed and directed to produce the highest ecological benefit possible. Teams of scientists are monitoring the effects on the hydrology, vegetation, birds and other ecological features of the delta, so that future flow releases can be even more effective.
The pulse flow experiment did not specifically plan on the river reaching the sea.
But against the odds, at least a small volume of the Colorado River has fulfilled its destiny – and made it home.
Sandra Postel is director of the Global Water Policy Project, Freshwater Fellow of the National Geographic Society, and author of several books and numerous articles on global water issues. She is co-creator of Change the Course, the national freshwater conservation and restoration campaign being piloted in the Colorado River Basin.[/INST]– The Colorado River has been reunited with an old friend—the sea. Thanks to an agreement between the US and Mexico, water from the river has reached the Sea of Cortez in northwestern Mexico for the first time since either 1998 (according to National Geographic) or 1993 (according to AP). Either way, it's been a long time, and conservationists hope last week's milestone becomes a regular occurrence. The water was released in March from the Morelos Dam near the US-Mexico border, and it took about 8 weeks to complete the journey to the sea. The idea is to restore life to the Colorado River delta, which has pretty much dried up since the advent of the big-dam era. In fact, the experiment is the first time water from the river has been diverted solely for environmental purposes, reports Arizona Public Media. While the initial "pulse flow" is now shut off, smaller amounts of water will be released to the delta over the next few years, and conservationists think it can revive the dormant habitat. (They've been busy planting trees, timed to germinate with the water's release.) "It is sort of overwhelming, and I think it sheds light on a sort of global interest in the Colorado River completing that journey again," says Jennifer Pitt of the Environmental Defense Fund's Colorado River Project. (In other water-related news, scientists have found an underwater "graveyard.")</s> |
a 17-year - old white male presented to dermatological consultation with some asymptomatic , slightly elevated , erythematous papules covered by yellowish scales in the scalp vertex and temporal regions of two years duration and small indurated ulcers with elevated borders at the perineum for six months ( figure 1 ) .
he complained of urinary frequency ( up to 20 times / day ) and excessive thirst ( up to five liters of water / day ) which were previously diagnosed as manifestations of primary polydipsia .
there was a delay in the development of secondary sexual characteristics and a hearing loss in the right ear secondary to a medium otitis five years before the present consultation .
actually , his height was 1.70 m , being at the 25 percentile according to the cdc 2000 growth chart ( height versus age percentile graphic ) .
in addition to the skin lesions , physical exam showed slight bilateral gynecomastia , absence of terminal hairs in the beard area , axillae and pubis , as well as underdevelopment of testicles and penis ( figure 2 ) . there were no lymph node or visceral enlargements .
one scalp lesion and another one from the perineum were biopsied and both revealed a dense cellular infiltrate made up of mononuclear cells with conspicuous eosinophilic cytoplasm and large cleaved vesicular nucleus , some of them with shapes resembling the form of a kidney or of a coffee bean .
the infiltrate was disposed in the superficial and middle dermis , assumed a band - like array and formed a sheet of cells in some areas .
in other foci , in which neoplastic cells were sparser , numerous intermingling eosinophils were present ( figure 3 ) .
the surface of the perineal lesion was ulcerated , while in the lesion of the scalp some neoplastic cells were present between the keratocytes of an otherwise preserved epidermis .
the diagnosis of langerhans cell histiocytosis ( lch ) was made based on morphologic criteria and confirmed by positivity of abnormal langerhans cells by anti - cd1a and anti - s100 immunostains and negativity for anti - cd68 .
he had mild anemia , normal basic biochemistry tests , negative serologic tests for syphilis and negative mycological tests of the lesions ( direct exam and culture ) .
the setting of hypogonadotropic hypogonadism was defined by blood dosage of lh ( 0.10 mui / ml , normal range of 0.8 7,6 ) , fsh ( 0.53 mui / ml , normal range of 0.711.1 ) , total testosterone ( 27.0 ng / dl , normal range : 241827 ) and free testosterone ( 0.50 pg / dl , normal range of 120550 ) and hyperprolactenemia by the high blood level of prolactin ( 32.6 ng / ml , normal range of 4.621.4 ) .
diabetes insipidus was confirmed by water restriction test , in which the patient was unable to concentrate the urine , in spite of an increase of concentration of blood sodium from 139149 meq / l and development of arterial hypotension .
all these parameters were reversed after administration of anti - diuretic hormone analog , which the patient continues to take .
an insulin - induced hypoglycemia provocative test demonstrated gh deficiency , but cortisol secretion was preserved .
magnetic resonance imaging of the sella turcica showed thickening of the pituitary stalk and size reduction of the pituitary , suggesting infiltration of the neurohypophysis by the abnormal langerhans cells .
there was no indication at the mri of other pathologic process that could explain the endocrinologic disturbances .
the final diagnosis was of lch with involvement of the skin , the pituitary stalk ( diabetes insipidus and hyperprolactenemia ) , and the anterior pituitary ( hypogonadotropic hypogonadism and gh deficiency ) .
the patient was treated with a chemotherapy regimen consisting of an induction phase with prednisone 40 mg / m / day every day for four weeks with withdrawal for two additional weeks and vinblastin 6mg / m iv bolus once a week in the first six weeks .
the consolidation phase lasted six months with five days of prednisone 40 mg / m / day and one application of vinblastin 6 mg / m iv bolus every three weeks .
the patient experienced complete remission ( figure 13 ) , and after the end of chemotherapy his puberty was induced by hormonal replacement therapy .
some months later , there was recurrence of lesions in the scalp confirmed on histopathologic grounds , which were successfully treated with topical corticosteroid and nitrogen mustard .
lch is a considerably rare disease with 4.14.6 cases for each million children and is regarded as an idiopathic monoclonal proliferation of abnormal langerhans cells . whether it is an inflammatory condition or a true neoplasm has been a matter of debate .
those cells may infiltrate and affect any organ , such as skin , pituitary , bones , lungs , brain and lymph nodes , liver , spleen , or hematopoietic system .
lch presents with a broad spectrum of manifestations , varying from solitary lesions to disseminated , multisystem , life - threatening disease .
previous to the unifying concept advanced by jaffe and lichtenstein in 1944 , some clinical syndromes had been independently described and later named eponymously .
letterer - siwe disease usually occurs in children under one year of age , has a poor prognosis and manifests itself as fever and skin rash , hepatomegaly , splenomegaly , pulmonary symptoms and anemia .
hand - schuller - christian disease usually affects children older than three years old and is defined by the triad of exophthalmos , diabetes insipidus and skull defect .
eosinophilic granuloma refers to a single bone lesion in older children , teenagers or adults with symptoms of pain , swelling and , eventually , pathologic fracture , but with a very good prognosis .
however , many cases do not fit exactly in any of these late descriptions , which have more historical importance than clinical usage and , currently , cases have been classified into two major categories :
single - system lch , subdivided further into unifocal ( single lesion on bone , skin or lymph node ) or multifocal ( multiple lesions on bone or multiple lymph nodes ) andmulti - system lch , when disease affects two or more different organs , with subdivision into low - risk or high - risk groups depending on the absence or presence of involvement of liver , lungs , spleen or hematopoietic system .
single - system lch , subdivided further into unifocal ( single lesion on bone , skin or lymph node ) or multifocal ( multiple lesions on bone or multiple lymph nodes ) and multi - system lch , when disease affects two or more different organs , with subdivision into low - risk or high - risk groups depending on the absence or presence of involvement of liver , lungs , spleen or hematopoietic system .
typically , the cutaneous lesions consist of small translucent , skin - colored , yellowish , red , or even purpuric scaly papules , usually located on the trunk and scalp .
nodular lesions are particularly present in mucous membranes and may become crusted and ulcerated . a presumptive diagnosis is based mainly on the recognition of the abnormal langerhans cells in the dermis and , eventually , permeating the epidermis and epithelial structure of the anexa
. these cells are morphologically distinctive by virtue of their single large , vesicular , opened - chromatin , cleaved nucleus , with shapes resembling the silhouette of a kidney or a coffee bean and their abundant eosinophilic to amphophilic cytoplasm .
the infiltrate composed of langerhans cells may vary from dense to sparse and might have many intermingling inflammatory cells , particularly eosinophils .
a definitive unequivocal diagnosis requires demonstration through electron microscopy of intracytoplasmatic birbeck bodies or immunostaining of the cells by anti - cd1a and anti - s100 antibodies , with negativity for anti - cd68 [ 5 , 8 ] .
the evaluation of the extent of the disease and the therapy of choice in each case involves a multidisciplinary team of clinicians / pediatricians , dermatologists , pathologists , hematologists , endocrinologists , radiologists and orthopedists .
the therapeutic approach to lch depends upon the number and extent of the lesions , number of organs affected , age of the patient , presence of involvement of liver , lungs , spleen or hematopoietic system and of any organ dysfunction . in most patients with limited cutaneous disease ,
an expectant management usually is enough , but topical steroids can be used too in selected cases .
isolated skin lesions may be surgically excised , while more extensive skin disease might be managed with psoralen - uva phototherapy , photodynamic therapy or topical nitrogen mustard [ 6,1114 ] .
localized bone lesions are managed with curettage , for diagnostic and therapeutic proposes , intralesional steroids , or low - dose radiation . for multi - organ disease , especially the high - risk group ,
prednisone alone or prednisone plus chemotherapeutic drugs , vincristine or etoposide being the most widely used , have been advocated by histiocytosis society protocols .
there is still much controversy about the ideal approach in these cases , and study groups around the world are being conducted to clarify it . | a 17-year - old male presented for dermatologic consultation with slightly elevated reddish papules covered by yellowish scales in the scalp for the last two years and reddish and indurated ulcers in the perineum lasting six months .
additional complaints included polyuria , polydipsia , delay in the development of secondary sexual characteristics and hearing loss of the right ear secondary to a medium otitis .
lesions from scalp and perineum were sampled for histopathologic examination and revealed a dense cellular infiltrate made up of mononuclear cells with conspicuous eosinophilic cytoplasm and large cleaved vesicular nucleus , some of them with shapes resembling the format of a kidney and others reminiscent of coffee beans .
numerous intermingling eosinophils were present .
the diagnosis of langerhans cell histiocytosis was then rendered and confirmed by positive immunostaining of neo - plastic cells for anti - cd1a and anti - s100 protein antibodies .
the work - up revealed diabetes insipidus , hypogonadotropic hypogonadism , hiperprolactenemia , growing - hormone deficiency and thickness of the pituitary stalk .
the patient was treated with prednisone and vinblastin based chemotherapy regimen for six months with complete remission , but presented recurrence of some lesions in the scalp , which were handled with topical mustard and corticosteroids .
after chemotherapy , the endocrinologic disturbances were corrected with hormonal replacement therapy .
the patient is currently in good health with a follow - up of five years . | <s>[INST]a 17-year - old white male presented to dermatological consultation with some asymptomatic , slightly elevated , erythematous papules covered by yellowish scales in the scalp vertex and temporal regions of two years duration and small indurated ulcers with elevated borders at the perineum for six months ( figure 1 ) .
he complained of urinary frequency ( up to 20 times / day ) and excessive thirst ( up to five liters of water / day ) which were previously diagnosed as manifestations of primary polydipsia .
there was a delay in the development of secondary sexual characteristics and a hearing loss in the right ear secondary to a medium otitis five years before the present consultation .
actually , his height was 1.70 m , being at the 25 percentile according to the cdc 2000 growth chart ( height versus age percentile graphic ) .
in addition to the skin lesions , physical exam showed slight bilateral gynecomastia , absence of terminal hairs in the beard area , axillae and pubis , as well as underdevelopment of testicles and penis ( figure 2 ) . there were no lymph node or visceral enlargements .
one scalp lesion and another one from the perineum were biopsied and both revealed a dense cellular infiltrate made up of mononuclear cells with conspicuous eosinophilic cytoplasm and large cleaved vesicular nucleus , some of them with shapes resembling the form of a kidney or of a coffee bean .
the infiltrate was disposed in the superficial and middle dermis , assumed a band - like array and formed a sheet of cells in some areas .
in other foci , in which neoplastic cells were sparser , numerous intermingling eosinophils were present ( figure 3 ) .
the surface of the perineal lesion was ulcerated , while in the lesion of the scalp some neoplastic cells were present between the keratocytes of an otherwise preserved epidermis .
the diagnosis of langerhans cell histiocytosis ( lch ) was made based on morphologic criteria and confirmed by positivity of abnormal langerhans cells by anti - cd1a and anti - s100 immunostains and negativity for anti - cd68 .
he had mild anemia , normal basic biochemistry tests , negative serologic tests for syphilis and negative mycological tests of the lesions ( direct exam and culture ) .
the setting of hypogonadotropic hypogonadism was defined by blood dosage of lh ( 0.10 mui / ml , normal range of 0.8 7,6 ) , fsh ( 0.53 mui / ml , normal range of 0.711.1 ) , total testosterone ( 27.0 ng / dl , normal range : 241827 ) and free testosterone ( 0.50 pg / dl , normal range of 120550 ) and hyperprolactenemia by the high blood level of prolactin ( 32.6 ng / ml , normal range of 4.621.4 ) .
diabetes insipidus was confirmed by water restriction test , in which the patient was unable to concentrate the urine , in spite of an increase of concentration of blood sodium from 139149 meq / l and development of arterial hypotension .
all these parameters were reversed after administration of anti - diuretic hormone analog , which the patient continues to take .
an insulin - induced hypoglycemia provocative test demonstrated gh deficiency , but cortisol secretion was preserved .
magnetic resonance imaging of the sella turcica showed thickening of the pituitary stalk and size reduction of the pituitary , suggesting infiltration of the neurohypophysis by the abnormal langerhans cells .
there was no indication at the mri of other pathologic process that could explain the endocrinologic disturbances .
the final diagnosis was of lch with involvement of the skin , the pituitary stalk ( diabetes insipidus and hyperprolactenemia ) , and the anterior pituitary ( hypogonadotropic hypogonadism and gh deficiency ) .
the patient was treated with a chemotherapy regimen consisting of an induction phase with prednisone 40 mg / m / day every day for four weeks with withdrawal for two additional weeks and vinblastin 6mg / m iv bolus once a week in the first six weeks .
the consolidation phase lasted six months with five days of prednisone 40 mg / m / day and one application of vinblastin 6 mg / m iv bolus every three weeks .
the patient experienced complete remission ( figure 13 ) , and after the end of chemotherapy his puberty was induced by hormonal replacement therapy .
some months later , there was recurrence of lesions in the scalp confirmed on histopathologic grounds , which were successfully treated with topical corticosteroid and nitrogen mustard .
lch is a considerably rare disease with 4.14.6 cases for each million children and is regarded as an idiopathic monoclonal proliferation of abnormal langerhans cells . whether it is an inflammatory condition or a true neoplasm has been a matter of debate .
those cells may infiltrate and affect any organ , such as skin , pituitary , bones , lungs , brain and lymph nodes , liver , spleen , or hematopoietic system .
lch presents with a broad spectrum of manifestations , varying from solitary lesions to disseminated , multisystem , life - threatening disease .
previous to the unifying concept advanced by jaffe and lichtenstein in 1944 , some clinical syndromes had been independently described and later named eponymously .
letterer - siwe disease usually occurs in children under one year of age , has a poor prognosis and manifests itself as fever and skin rash , hepatomegaly , splenomegaly , pulmonary symptoms and anemia .
hand - schuller - christian disease usually affects children older than three years old and is defined by the triad of exophthalmos , diabetes insipidus and skull defect .
eosinophilic granuloma refers to a single bone lesion in older children , teenagers or adults with symptoms of pain , swelling and , eventually , pathologic fracture , but with a very good prognosis .
however , many cases do not fit exactly in any of these late descriptions , which have more historical importance than clinical usage and , currently , cases have been classified into two major categories :
single - system lch , subdivided further into unifocal ( single lesion on bone , skin or lymph node ) or multifocal ( multiple lesions on bone or multiple lymph nodes ) andmulti - system lch , when disease affects two or more different organs , with subdivision into low - risk or high - risk groups depending on the absence or presence of involvement of liver , lungs , spleen or hematopoietic system .
single - system lch , subdivided further into unifocal ( single lesion on bone , skin or lymph node ) or multifocal ( multiple lesions on bone or multiple lymph nodes ) and multi - system lch , when disease affects two or more different organs , with subdivision into low - risk or high - risk groups depending on the absence or presence of involvement of liver , lungs , spleen or hematopoietic system .
typically , the cutaneous lesions consist of small translucent , skin - colored , yellowish , red , or even purpuric scaly papules , usually located on the trunk and scalp .
nodular lesions are particularly present in mucous membranes and may become crusted and ulcerated . a presumptive diagnosis is based mainly on the recognition of the abnormal langerhans cells in the dermis and , eventually , permeating the epidermis and epithelial structure of the anexa
. these cells are morphologically distinctive by virtue of their single large , vesicular , opened - chromatin , cleaved nucleus , with shapes resembling the silhouette of a kidney or a coffee bean and their abundant eosinophilic to amphophilic cytoplasm .
the infiltrate composed of langerhans cells may vary from dense to sparse and might have many intermingling inflammatory cells , particularly eosinophils .
a definitive unequivocal diagnosis requires demonstration through electron microscopy of intracytoplasmatic birbeck bodies or immunostaining of the cells by anti - cd1a and anti - s100 antibodies , with negativity for anti - cd68 [ 5 , 8 ] .
the evaluation of the extent of the disease and the therapy of choice in each case involves a multidisciplinary team of clinicians / pediatricians , dermatologists , pathologists , hematologists , endocrinologists , radiologists and orthopedists .
the therapeutic approach to lch depends upon the number and extent of the lesions , number of organs affected , age of the patient , presence of involvement of liver , lungs , spleen or hematopoietic system and of any organ dysfunction . in most patients with limited cutaneous disease ,
an expectant management usually is enough , but topical steroids can be used too in selected cases .
isolated skin lesions may be surgically excised , while more extensive skin disease might be managed with psoralen - uva phototherapy , photodynamic therapy or topical nitrogen mustard [ 6,1114 ] .
localized bone lesions are managed with curettage , for diagnostic and therapeutic proposes , intralesional steroids , or low - dose radiation . for multi - organ disease , especially the high - risk group ,
prednisone alone or prednisone plus chemotherapeutic drugs , vincristine or etoposide being the most widely used , have been advocated by histiocytosis society protocols .
there is still much controversy about the ideal approach in these cases , and study groups around the world are being conducted to clarify it .[/INST]a 17-year - old male presented for dermatologic consultation with slightly elevated reddish papules covered by yellowish scales in the scalp for the last two years and reddish and indurated ulcers in the perineum lasting six months .
additional complaints included polyuria , polydipsia , delay in the development of secondary sexual characteristics and hearing loss of the right ear secondary to a medium otitis .
lesions from scalp and perineum were sampled for histopathologic examination and revealed a dense cellular infiltrate made up of mononuclear cells with conspicuous eosinophilic cytoplasm and large cleaved vesicular nucleus , some of them with shapes resembling the format of a kidney and others reminiscent of coffee beans .
numerous intermingling eosinophils were present .
the diagnosis of langerhans cell histiocytosis was then rendered and confirmed by positive immunostaining of neo - plastic cells for anti - cd1a and anti - s100 protein antibodies .
the work - up revealed diabetes insipidus , hypogonadotropic hypogonadism , hiperprolactenemia , growing - hormone deficiency and thickness of the pituitary stalk .
the patient was treated with prednisone and vinblastin based chemotherapy regimen for six months with complete remission , but presented recurrence of some lesions in the scalp , which were handled with topical mustard and corticosteroids .
after chemotherapy , the endocrinologic disturbances were corrected with hormonal replacement therapy .
the patient is currently in good health with a follow - up of five years .</s> |
SECTION 1. RECEIPTS OF THE 4.3-CENT FUEL TAX RATE INCREASE DEPOSITED IN
THE HIGHWAY TRUST FUND; ESTABLISHMENT OF INTERCITY
PASSENGER RAIL ACCOUNT.
(a) In General.--Section 9503(f) of the Internal Revenue Code of
1986 (defining Highway Trust Fund financing rate) is amended--
(1) in paragraph (1)(A), by striking ``11.5 cents per
gallon (14 cents per gallon after September 30, 1995)'' and
inserting ``18.3 cents per gallon''; and
(2) in paragraph (1)(B), by striking ``17.5 cents per
gallon (20 cents per gallon after September 30, 1995)'' and
inserting ``24.3 cents per gallon''.
(b) Conforming Amendments.--
(1) Section 9503(f)(2) of such Code is amended--
(A) in subparagraph (B), by striking ``3 cents''
and inserting ``7.3 cents'';
(B) in subparagraph (C), by striking ``zero'' and
inserting ``4.3 cents per gallon'';
(C) in subparagraph (D), by striking ``zero'' and
inserting ``48.54 cents per MCF (determined at standard
temperature and pressure)'';
(D) in subparagraph (E), by striking ``11.5 cents''
and inserting ``15.8 cents''; and
(E) in subparagraph (E), by striking ``17.5 cents''
and inserting ``21.8 cents''.
(2) Section 9503(f)(3)(A) of such Code is amended to read
as follows:
``(A) In general.--If the rate of tax on any fuel
is determined under section 4041(b)(2)(A), 4041(k), or
4081(c), the Highway Trust Fund financing rate is the
rate so determined after September 30, 1997. In the
case of a rate of tax determined under section 4081(c),
the preceding sentence shall be applied by increasing
the rate specified by 0.1 cent.''
(3) Section 9503(f)(3)(C) of such Code is amended to read
as follows:
``(C) Partially exempt methanol or ethanol fuel.--
In the case of a rate of tax determined under section
4041(m), the Highway Trust Fund financing rate is the
rate so determined after September 30, 1995.''
(4) Section 9503(f)(4) of such Code is amended by striking
``zero'' and inserting ``4.3 cents per gallon''.
(c) Establishment of Intercity Passenger Rail Account.--Section
9503 of the Internal Revenue Code of 1986 (relating to Highway Trust
Fund) is amended by adding at the end the following:
``(g) Establishment of Intercity Passenger Rail Account.--
``(1) Creation of account.--There is established in the
Highway Trust Fund a separate account to be known as the
`Intercity Passenger Rail Account', consisting of such amounts
as may be transferred or credited to the Intercity Passenger
Rail Account as provided in this subsection or section 9602(b).
``(2) Transfers to intercity passenger rail account.--
``(A) In general.--The Secretary of the Treasury
shall transfer to the Intercity Passenger Rail Account
the intercity passenger rail portion of the amounts
appropriated to the Highway Trust Fund under subsection
(b) which are attributable to taxes under sections 4041
and 4081 imposed after September 30, 1997, and before
October 1, 2003.
``(B) Intercity passenger rail portion.--For
purposes of subparagraph (A), the term `intercity
passenger rail portion' means an amount determined at
the rate of 0.5 cent for each gallon with respect to
which tax was imposed under section 4041 or 4081.
``(3) Expenditures from account.--
``(A) In general.--Amounts in the Intercity
Passenger Rail Account shall be available without
fiscal year limitation to finance qualified expenses
of--
``(i) the National Railroad Passenger
Corporation, and
``(ii) each non-Amtrak State, to the extent
determined under subparagraph (B).
``(B) Maximum amount of funds to non-amtrak
states.--Each non-Amtrak State shall receive under this
paragraph an amount equal to the lesser of--
``(i) the State's qualified expenses for
the fiscal year, or
``(ii) the product of--
``(I) \1/12\ of 1 percent of the
lesser of--
``(aa) the aggregate
amounts transferred and
credited to the Intercity
Passenger Rail Account under
paragraph (1) for such fiscal
year, or
``(bb) the aggregate
amounts appropriated from the
Intercity Passenger Rail
Account for such fiscal year,
and
``(II) the number of months such
State is a non-Amtrak State in such
fiscal year.
If the amount determined under clause (ii) exceeds the
amount under clause (i) for any fiscal year, the amount
under clause (ii) for the following fiscal year shall
be increased by the amount of such excess.
``(4) Definitions.--For purposes of this subsection--
``(A) Qualified expenses.--The term `qualified
expenses' means expenses incurred, with respect to
obligations made, after September 30, 1997, and before
October 1, 2003--
``(i) for--
``(I) in the case of the National
Railroad Passenger Corporation, the
acquisition of equipment,
rolling stock, and other capital improvements, the upgrading of
maintenance facilities, and the maintenance of existing equipment, in
intercity passenger rail service, and the payment of interest and
principal on obligations incurred for such acquisition, upgrading, and
maintenance, and
``(II) in the case of a non-Amtrak
State, the acquisition of equipment,
rolling stock, and other capital
improvements, the upgrading of
maintenance facilities, and the
maintenance of existing equipment, in
intercity passenger rail or bus
service, and the payment of interest
and principal on obligations incurred
for such acquisition, upgrading, and
maintenance, and
``(ii) certified by the Secretary of
Transportation on October 1 as meeting the
requirements of clause (i) and as qualified for
payment under paragraph (5) for the fiscal year
beginning on such date.
``(B) Non-amtrak state.--The term `non-Amtrak
State' means any State which does not receive intercity
passenger rail service from the National Railroad
Passenger Corporation.
``(5) Contract authority.--Notwithstanding any other
provision of law, the Secretary of Transportation shall certify
expenses as qualified for a fiscal year on October 1 of such
year, in an amount not to exceed the amount of receipts
estimated by the Secretary of the Treasury to be transferred to
the Intercity Passenger Rail Account for such fiscal year. Such
certification shall result in a contractual obligation of the
United States for the payment of such expenses.
``(6) Tax treatment of account expenditures.--With respect
to any payment of qualified expenses from the Intercity
Passenger Rail Account during any taxable year to a taxpayer--
``(A) such payment shall not be included in the
gross income of the taxpayer for such taxable year,
``(B) no deduction shall be allowed to the taxpayer
with respect to any amount paid or incurred which is
attributable to such payment, and
``(C) the basis of any property shall be reduced by
the portion of the cost of such property which is
attributable to such payment.
``(7) Termination.--The Secretary shall determine and
retain, not later than October 1, 2003, the amount in the
Intercity Passenger Rail Account necessary to pay any
outstanding qualified expenses, and shall transfer any amount
not so retained to the Highway Trust Fund.''
(d) Effective Dates.--
(1) Transfer of taxes.--The amendments made by subsections
(a) and (b) apply to fuel removed after September 30, 1997.
(2) Account.--The amendment made by subsection (c) applies
with respect to taxes imposed on and after October 1, 1997. | Amends the Internal Revenue Code to increase the Highway Trust Fund financing rate for gasoline, special motor fuels, and diesel fuel.
Establishes in the Highway Trust Fund the Intercity Passenger Rail Account. Transfers to the Account certain portions of the amounts attributable to taxes imposed between specified dates under provisions relating to gasoline, diesel fuel, special motor fuels, compressed natural gas, methanol and ethanol fuel, and nongasoline noncommercial aviation fuels. Makes amounts in the Account available to finance qualified expenses of the National Railroad Passenger Corporation and each non-Amtrak State. Excludes Account payments from the gross income of payment recipients, disallows a deduction to the recipient, and reduces the basis of any property by the portion attributable to the payment. | <s>[INST]SECTION 1. RECEIPTS OF THE 4.3-CENT FUEL TAX RATE INCREASE DEPOSITED IN
THE HIGHWAY TRUST FUND; ESTABLISHMENT OF INTERCITY
PASSENGER RAIL ACCOUNT.
(a) In General.--Section 9503(f) of the Internal Revenue Code of
1986 (defining Highway Trust Fund financing rate) is amended--
(1) in paragraph (1)(A), by striking ``11.5 cents per
gallon (14 cents per gallon after September 30, 1995)'' and
inserting ``18.3 cents per gallon''; and
(2) in paragraph (1)(B), by striking ``17.5 cents per
gallon (20 cents per gallon after September 30, 1995)'' and
inserting ``24.3 cents per gallon''.
(b) Conforming Amendments.--
(1) Section 9503(f)(2) of such Code is amended--
(A) in subparagraph (B), by striking ``3 cents''
and inserting ``7.3 cents'';
(B) in subparagraph (C), by striking ``zero'' and
inserting ``4.3 cents per gallon'';
(C) in subparagraph (D), by striking ``zero'' and
inserting ``48.54 cents per MCF (determined at standard
temperature and pressure)'';
(D) in subparagraph (E), by striking ``11.5 cents''
and inserting ``15.8 cents''; and
(E) in subparagraph (E), by striking ``17.5 cents''
and inserting ``21.8 cents''.
(2) Section 9503(f)(3)(A) of such Code is amended to read
as follows:
``(A) In general.--If the rate of tax on any fuel
is determined under section 4041(b)(2)(A), 4041(k), or
4081(c), the Highway Trust Fund financing rate is the
rate so determined after September 30, 1997. In the
case of a rate of tax determined under section 4081(c),
the preceding sentence shall be applied by increasing
the rate specified by 0.1 cent.''
(3) Section 9503(f)(3)(C) of such Code is amended to read
as follows:
``(C) Partially exempt methanol or ethanol fuel.--
In the case of a rate of tax determined under section
4041(m), the Highway Trust Fund financing rate is the
rate so determined after September 30, 1995.''
(4) Section 9503(f)(4) of such Code is amended by striking
``zero'' and inserting ``4.3 cents per gallon''.
(c) Establishment of Intercity Passenger Rail Account.--Section
9503 of the Internal Revenue Code of 1986 (relating to Highway Trust
Fund) is amended by adding at the end the following:
``(g) Establishment of Intercity Passenger Rail Account.--
``(1) Creation of account.--There is established in the
Highway Trust Fund a separate account to be known as the
`Intercity Passenger Rail Account', consisting of such amounts
as may be transferred or credited to the Intercity Passenger
Rail Account as provided in this subsection or section 9602(b).
``(2) Transfers to intercity passenger rail account.--
``(A) In general.--The Secretary of the Treasury
shall transfer to the Intercity Passenger Rail Account
the intercity passenger rail portion of the amounts
appropriated to the Highway Trust Fund under subsection
(b) which are attributable to taxes under sections 4041
and 4081 imposed after September 30, 1997, and before
October 1, 2003.
``(B) Intercity passenger rail portion.--For
purposes of subparagraph (A), the term `intercity
passenger rail portion' means an amount determined at
the rate of 0.5 cent for each gallon with respect to
which tax was imposed under section 4041 or 4081.
``(3) Expenditures from account.--
``(A) In general.--Amounts in the Intercity
Passenger Rail Account shall be available without
fiscal year limitation to finance qualified expenses
of--
``(i) the National Railroad Passenger
Corporation, and
``(ii) each non-Amtrak State, to the extent
determined under subparagraph (B).
``(B) Maximum amount of funds to non-amtrak
states.--Each non-Amtrak State shall receive under this
paragraph an amount equal to the lesser of--
``(i) the State's qualified expenses for
the fiscal year, or
``(ii) the product of--
``(I) \1/12\ of 1 percent of the
lesser of--
``(aa) the aggregate
amounts transferred and
credited to the Intercity
Passenger Rail Account under
paragraph (1) for such fiscal
year, or
``(bb) the aggregate
amounts appropriated from the
Intercity Passenger Rail
Account for such fiscal year,
and
``(II) the number of months such
State is a non-Amtrak State in such
fiscal year.
If the amount determined under clause (ii) exceeds the
amount under clause (i) for any fiscal year, the amount
under clause (ii) for the following fiscal year shall
be increased by the amount of such excess.
``(4) Definitions.--For purposes of this subsection--
``(A) Qualified expenses.--The term `qualified
expenses' means expenses incurred, with respect to
obligations made, after September 30, 1997, and before
October 1, 2003--
``(i) for--
``(I) in the case of the National
Railroad Passenger Corporation, the
acquisition of equipment,
rolling stock, and other capital improvements, the upgrading of
maintenance facilities, and the maintenance of existing equipment, in
intercity passenger rail service, and the payment of interest and
principal on obligations incurred for such acquisition, upgrading, and
maintenance, and
``(II) in the case of a non-Amtrak
State, the acquisition of equipment,
rolling stock, and other capital
improvements, the upgrading of
maintenance facilities, and the
maintenance of existing equipment, in
intercity passenger rail or bus
service, and the payment of interest
and principal on obligations incurred
for such acquisition, upgrading, and
maintenance, and
``(ii) certified by the Secretary of
Transportation on October 1 as meeting the
requirements of clause (i) and as qualified for
payment under paragraph (5) for the fiscal year
beginning on such date.
``(B) Non-amtrak state.--The term `non-Amtrak
State' means any State which does not receive intercity
passenger rail service from the National Railroad
Passenger Corporation.
``(5) Contract authority.--Notwithstanding any other
provision of law, the Secretary of Transportation shall certify
expenses as qualified for a fiscal year on October 1 of such
year, in an amount not to exceed the amount of receipts
estimated by the Secretary of the Treasury to be transferred to
the Intercity Passenger Rail Account for such fiscal year. Such
certification shall result in a contractual obligation of the
United States for the payment of such expenses.
``(6) Tax treatment of account expenditures.--With respect
to any payment of qualified expenses from the Intercity
Passenger Rail Account during any taxable year to a taxpayer--
``(A) such payment shall not be included in the
gross income of the taxpayer for such taxable year,
``(B) no deduction shall be allowed to the taxpayer
with respect to any amount paid or incurred which is
attributable to such payment, and
``(C) the basis of any property shall be reduced by
the portion of the cost of such property which is
attributable to such payment.
``(7) Termination.--The Secretary shall determine and
retain, not later than October 1, 2003, the amount in the
Intercity Passenger Rail Account necessary to pay any
outstanding qualified expenses, and shall transfer any amount
not so retained to the Highway Trust Fund.''
(d) Effective Dates.--
(1) Transfer of taxes.--The amendments made by subsections
(a) and (b) apply to fuel removed after September 30, 1997.
(2) Account.--The amendment made by subsection (c) applies
with respect to taxes imposed on and after October 1, 1997.[/INST]Amends the Internal Revenue Code to increase the Highway Trust Fund financing rate for gasoline, special motor fuels, and diesel fuel.
Establishes in the Highway Trust Fund the Intercity Passenger Rail Account. Transfers to the Account certain portions of the amounts attributable to taxes imposed between specified dates under provisions relating to gasoline, diesel fuel, special motor fuels, compressed natural gas, methanol and ethanol fuel, and nongasoline noncommercial aviation fuels. Makes amounts in the Account available to finance qualified expenses of the National Railroad Passenger Corporation and each non-Amtrak State. Excludes Account payments from the gross income of payment recipients, disallows a deduction to the recipient, and reduces the basis of any property by the portion attributable to the payment.</s> |
A 29-year-old Army veteran allegedly killed his mother and rode a tractor through his Simi Valley neighborhood, firing rounds, before police killed him Saturday. Detectives on Sunday were piecing together details about the incident. Jane Yamamoto reports from Simi Valley for NBC4 News at 11 p.m. on Sunday, Aug. 25, 2013. (Published Sunday, Aug. 25, 2013)
A man fatally shot by police after he possibly killed his mother and rode through a neighborhood firing a gun from a tractor was identified on Sunday as a veteran of the U.S. Army.
Ryan Carnan, 29, (pictured) was fatally shot by Simi Valley police officers on Saturday afternoon, officials said.
Wild Standoff Ends with Gunman Dead
Police in Simi Valley are now investigating the background of a man killed by officers after a wild standoff. Detectives believe the man killed his mother, then opened fire on others in her neighborhood while fleeing on a tractor. Jane Yamamoto reports for the NBC4 News at 8 p.m. on Sunday, Aug. 25, 2013. (Published Sunday, Aug. 25, 2013)
The events prompted a bomb-squad callout and the evacuation of homes in the Bridal Path neighborhood of Simi Valley, 30 miles northwest of downtown Los Angeles.
It started with a call to police from the suspect's brother about the killing of their mother, a house fire, the discovery of a woman's body inside the home and calls from residents reporting a man driving through on a tractor firing a gun.
Police Kill Gunman, Find Mother's Body After Standoff
Police fatally shot a gunman who was believed to have killed his own mother and ridden a tractor through a Simi Valley neighborhood, firing his weapon, Saturday night. Jane Yamamoto reports from Simi Valley for NBC4 News at 11 p.m. on Saturday, Aug. 24, 2013. (Published Saturday, Aug. 24, 2013)
He reportedly aimed the gun at residents he encountered on the street.
The identity of the woman and the cause of her death have not been confirmed, police said. But police said they believe it's Carnan's mother - an administrator at Santa Susana High School.
Southern California Police Standoffs
An autopsy was scheduled to be performed on the victim Monday.
Police shot the suspect when "the officers were confronted with a deadly force situation," the Simi Valley Police Department said in a press release.
"Based on the information that was being received by the 911 callers that a subject was actively shooting a firearm in a residential neighborhood, the heroic actions of the officers involved cannot be understated," the press release said.
Residences in the area were evacuated as a precaution as a bomb squad checked the home after the fire was put out.
The officers are home on paid administrative leave pending the outcome of parallel probes into the shooting by the Simi Valley Police Department and the Ventura County District Attorney’s Office.
More Southern California Stories: ||||| advertisement
Grief counselors were expected Monday to arrive at a Southern California high school to help students and staff cope with the death of an employee who was killed allegedly by her son who was fatally shot by police.
Mourners placed flowers outside Santa Susana High School for Sally Carnan, who worked in the attendance office at the Ventura County school.
"We loved her. Everyone loved her," said Cassie Sadowsky, a former student, of the 67-year-old woman affectionately known as "The Attendance Lady."
Carnan's son, Ryan, allegedly killed his mother, set their house on fire, then fired at neighbors and police from a tractor before he was fatally shot by officers on Saturday, authorities said. His mother's body was found inside the home, police said.
Autopsies to reveal details about the deaths were set for Monday.
Carnan, 29, (pictured) had no criminal record with Simi Valley police, officials said. But police were called to the house at least five times, the most recent in 2008.
"Those were mental-health related calls," said Cmdr. Stephanie Shannon, of the Simi Valley Police Department.
A family friend said Ryan Carnan was discharged from the U.S. Army five years ago, around the same time his father died of cancer. Results from an request with the military were not immediately available.
"They 're kinda overcome with everything that's happened," said Brandon Lyman, the family friend.
The incident Saturday started with a call from Ryan Carnan's brother to police, saying Ryan Carnan brother shot their mother, police said.
The call prompted a call to the fire department and a bomb-squad, fearing incendiary devices and the evacuation of homes in the Bridal Path neighborhood of Simi Valley, 30 miles northwest of downtown Los Angeles. Ryan Carnan lived with his mother at a home nearby on Mellow Lane.
He reportedly aimed the gun at residents and police from a tractor, officials said.
Police shot Ryan Carnan when they said they were confronted with a "dangerous and deadly situation."
The officers are home on paid administrative leave pending the outcome of parallel probes into the shooting by the Simi Valley Police Department and the Ventura County District Attorney’s Office.
More Southern California Stories: | – A 29-year-old Army veteran allegedly murdered his mother, set her house on fire, and then fired at residents in Simi Valley, Calif., while driving a tractor before being shot dead by police Saturday, NBC Los Angeles reports. Police were alerted to the situation by Ryan Carnan's brother, who reported their mother had been killed, and by neighborhood residents who spotted a shooter atop a tractor. ABC 7 reports that Carnan allegedly shot at a bicyclist as well as others; police say they shot Carnan after he opened fire on them. Carnan's brother told authorities his brother confessed to shooting and killing their mother, whose body was found inside the burning home, though her cause of death has not been officially verified. No one else was injured. Police aren't sure of Carnan's motive or what led up to the shootings. He had been stationed in Korea at some point, and police had been called to the family home three times over concerns about his mental health, though the last of those calls reportedly occurred five years ago. NBC Los Angeles notes that Sally Carnan was a beloved employee of Santa Susana High School, where she was known as the "Attendance Lady." | <s>[INST]A 29-year-old Army veteran allegedly killed his mother and rode a tractor through his Simi Valley neighborhood, firing rounds, before police killed him Saturday. Detectives on Sunday were piecing together details about the incident. Jane Yamamoto reports from Simi Valley for NBC4 News at 11 p.m. on Sunday, Aug. 25, 2013. (Published Sunday, Aug. 25, 2013)
A man fatally shot by police after he possibly killed his mother and rode through a neighborhood firing a gun from a tractor was identified on Sunday as a veteran of the U.S. Army.
Ryan Carnan, 29, (pictured) was fatally shot by Simi Valley police officers on Saturday afternoon, officials said.
Wild Standoff Ends with Gunman Dead
Police in Simi Valley are now investigating the background of a man killed by officers after a wild standoff. Detectives believe the man killed his mother, then opened fire on others in her neighborhood while fleeing on a tractor. Jane Yamamoto reports for the NBC4 News at 8 p.m. on Sunday, Aug. 25, 2013. (Published Sunday, Aug. 25, 2013)
The events prompted a bomb-squad callout and the evacuation of homes in the Bridal Path neighborhood of Simi Valley, 30 miles northwest of downtown Los Angeles.
It started with a call to police from the suspect's brother about the killing of their mother, a house fire, the discovery of a woman's body inside the home and calls from residents reporting a man driving through on a tractor firing a gun.
Police Kill Gunman, Find Mother's Body After Standoff
Police fatally shot a gunman who was believed to have killed his own mother and ridden a tractor through a Simi Valley neighborhood, firing his weapon, Saturday night. Jane Yamamoto reports from Simi Valley for NBC4 News at 11 p.m. on Saturday, Aug. 24, 2013. (Published Saturday, Aug. 24, 2013)
He reportedly aimed the gun at residents he encountered on the street.
The identity of the woman and the cause of her death have not been confirmed, police said. But police said they believe it's Carnan's mother - an administrator at Santa Susana High School.
Southern California Police Standoffs
An autopsy was scheduled to be performed on the victim Monday.
Police shot the suspect when "the officers were confronted with a deadly force situation," the Simi Valley Police Department said in a press release.
"Based on the information that was being received by the 911 callers that a subject was actively shooting a firearm in a residential neighborhood, the heroic actions of the officers involved cannot be understated," the press release said.
Residences in the area were evacuated as a precaution as a bomb squad checked the home after the fire was put out.
The officers are home on paid administrative leave pending the outcome of parallel probes into the shooting by the Simi Valley Police Department and the Ventura County District Attorney’s Office.
More Southern California Stories: ||||| advertisement
Grief counselors were expected Monday to arrive at a Southern California high school to help students and staff cope with the death of an employee who was killed allegedly by her son who was fatally shot by police.
Mourners placed flowers outside Santa Susana High School for Sally Carnan, who worked in the attendance office at the Ventura County school.
"We loved her. Everyone loved her," said Cassie Sadowsky, a former student, of the 67-year-old woman affectionately known as "The Attendance Lady."
Carnan's son, Ryan, allegedly killed his mother, set their house on fire, then fired at neighbors and police from a tractor before he was fatally shot by officers on Saturday, authorities said. His mother's body was found inside the home, police said.
Autopsies to reveal details about the deaths were set for Monday.
Carnan, 29, (pictured) had no criminal record with Simi Valley police, officials said. But police were called to the house at least five times, the most recent in 2008.
"Those were mental-health related calls," said Cmdr. Stephanie Shannon, of the Simi Valley Police Department.
A family friend said Ryan Carnan was discharged from the U.S. Army five years ago, around the same time his father died of cancer. Results from an request with the military were not immediately available.
"They 're kinda overcome with everything that's happened," said Brandon Lyman, the family friend.
The incident Saturday started with a call from Ryan Carnan's brother to police, saying Ryan Carnan brother shot their mother, police said.
The call prompted a call to the fire department and a bomb-squad, fearing incendiary devices and the evacuation of homes in the Bridal Path neighborhood of Simi Valley, 30 miles northwest of downtown Los Angeles. Ryan Carnan lived with his mother at a home nearby on Mellow Lane.
He reportedly aimed the gun at residents and police from a tractor, officials said.
Police shot Ryan Carnan when they said they were confronted with a "dangerous and deadly situation."
The officers are home on paid administrative leave pending the outcome of parallel probes into the shooting by the Simi Valley Police Department and the Ventura County District Attorney’s Office.
More Southern California Stories:[/INST]– A 29-year-old Army veteran allegedly murdered his mother, set her house on fire, and then fired at residents in Simi Valley, Calif., while driving a tractor before being shot dead by police Saturday, NBC Los Angeles reports. Police were alerted to the situation by Ryan Carnan's brother, who reported their mother had been killed, and by neighborhood residents who spotted a shooter atop a tractor. ABC 7 reports that Carnan allegedly shot at a bicyclist as well as others; police say they shot Carnan after he opened fire on them. Carnan's brother told authorities his brother confessed to shooting and killing their mother, whose body was found inside the burning home, though her cause of death has not been officially verified. No one else was injured. Police aren't sure of Carnan's motive or what led up to the shootings. He had been stationed in Korea at some point, and police had been called to the family home three times over concerns about his mental health, though the last of those calls reportedly occurred five years ago. NBC Los Angeles notes that Sally Carnan was a beloved employee of Santa Susana High School, where she was known as the "Attendance Lady."</s> |
we analyzed ahi signs and symptoms in 90 patients given a diagnosis of ahi during 20072014 .
as part of this confidential hiv testing program , routine , individual donation , hiv nucleic acid amplification testing ( nat ) has been provided to all rapid antibody
negative participants since june 2007 ( samples for nat are obtained at the time of rapid antibody testing ) ( 7,10,11 ) .
ahi was defined as having a negative or indeterminate hiv antibody test result in the presence of detectable hiv-1 rna , corresponding to fiebig stages i ii , with a mean estimated date of infection within the previous 10 days ( 95% ci 714 days ) ( 12 ) .
dates of infection were estimated for all recently infected patients using previously published criteria on the basis of serologic and virologic test results ( 13 ) . at each patient s first visit after documentation of ahi diagnosis ( median 4 days , interquartile range [ iqr ] 36 days after ahi testing ) , we obtained blood samples for cd4 and viral load testing and collected detailed information regarding occurrence , duration , and start and stop dates for 11 signs and symptoms associated with ahi ( 5,14 ) .
in addition , patients who participated during 20072011 were asked if they had sought medical attention for any signs or symptoms .
typical ahi ( i.e. , > 2 signs / symptoms ) was defined according to criteria described by braun et al . ( 14 ) . for statistical analysis ,
, chicago , il , usa ) was used . for analysis on signs or symptoms
compatible with ahi , signs or symptoms that started > 5 days before the estimated date of infection ( i.e. , before the 714 day 95% ci ) were excluded .
the university of california san diego s human research protections program approved the study protocol , consent process , and all study - related procedures .
all 90 participants were male and self - identified as men who have sex with men ( msm ) .
median number of male partners reported for the previous 12 months was 20 ( iqr 1431 ) .
a total of 72 ( 80% ) patients had signs or symptoms associated with ahi that occurred within 2 weeks before undergoing nat ; of these 72 patients , 47 ( 52% of the study population ) had ongoing signs or symptoms , while signs or symptoms had resolved by the time of testing for 25 ( 28% of the study population ) .
twelve ( 13% ) reported signs or symptoms starting after testing , while 6 ( 7% ) reported the absence of signs or symptoms ( table 1 ) .
a total of 66 patients ( 73% of the study population ) reported headache , pharyngitis , or myalgia occurring during the 14 days before ahi testing . * ahi , acute hiv infection ; iqr , interquartile range ; nat , nucleic acid amplification testing ; ns , not significant .
most frequently observed signs or symptoms that occurred during the 14 days before nat or were ongoing at the time of nat were fatigue ( 53 persons , 59% of the study population ) , fever ( 51 , 57% ) , myalgia ( 48 , 53% ) , headache ( 41 , 46% ) , night sweats ( 35 , 39% ) , pharyngitis ( 32 , 36% ) , and gastrointestinal symptoms ( 29 , 32% ) .
overall , 69 patients ( 77% ) reported signs or symptoms that met criteria of compatibility with ahi ( table 2 ) .
onset of signs or symptoms compatible with ahi occurred at a median of 5 days ( iqr 08 , range 4 to 15 days ) after the estimated date of infection . neither viral load nor cd4 count correlated with duration or actual number of signs or symptoms .
* ahi , acute hiv infection ; gi , gastrointestinal ; iqr , interquartile range ; nat , nucleic acid amplification testing ; ns , not significant . defined as having started < 4 days before estimated date of infection or after the estimated date of infection .
data on whether a patient sought medical attention because of signs or symptoms were available for 42 ( 47% ) of 90 patients ; of these , 12 ( 29% ) reported that they sought medical attention because of their signs or symptoms and 30 ( 71% ) did not .
significantly higher viral loads were observed for those who sought medical attention compared with those who did not ( median 6.1 [ iqr 5.76.7 ] log copies / ml vs. 4.7 [ iqr 3.45.5 ] log copies / ml ; p<0.01 ) .
overall , 70 ( 78% ) of the 90 patients fulfilled criteria for having typical ahi and 20 ( 22% ) did not ( of the latter , 14 had only 1 sign or symptom , and 6 were asymptomatic ) .
patients with typical ahi had significantly higher viral loads compared with patients without ( p<0.01 ) . a total of 61 ( 85% ) of 72 patients with signs or symptoms before nat testing fulfilled criteria for having typical ahi .
in addition , 40 ( 85% ) of 47 patients who had ongoing signs or symptoms at the time of ahi testing fulfilled criteria for having typical ahi at that time .
we characterized signs or symptoms relative to the date of ahi diagnosis among persons seeking hiv testing in a program offering universal ahi screening .
two findings are notable : 1 ) 52% of participants reported ongoing signs or symptoms at the time of ahi testing , and 2 ) 80% reported signs or symptoms occurring within 2 weeks before undergoing testing . these findings may have major clinical implications for community - based settings that restrict ahi testing to persons with ongoing signs or symptoms . this practice may be relatively insensitive in settings where msm undergo hiv screening frequently ( 11 ) .
our results show that expansion of ahi screening to include those with signs or symptoms during the 2 weeks before the test may increase the yield of ahi diagnoses by more than half .
although our results may allow for estimation of sensitivity of signs and symptoms for ahi in persons seeking hiv testing , specificity of signs and symptoms remains unknown ( in this study , signs and symptoms were not assessed in those who tested negative , and no control group was available ) .
estimates on frequency of signs and symptoms in hiv - negative persons ( i.e. , specificity ) ranged widely in previous studies .
although in one study a specificity of 65% was estimated for influenza illness like symptoms ( 15 ) , specificities ranging from 38% to 91% for recent symptoms were estimated in another study ( 5 )
. limitations of those studies include the fact that exact time frames for occurrence of signs or symptoms ( e.g. , ongoing at the time of testing or occurring within the last 14 days ) have not been evaluated , which makes comparison of results difficult .
therefore , our results may not be applicable to populations other than msm , although previous studies have reported that clinical features of ahi may not differ by sex and age of patients ( 4 ) . in summary , hiv diagnostic testing strategies that limit ahi testing to patients with ongoing signs or symptoms
in contrast , hiv nat provided for msm who report signs or symptoms during the preceding 2 weeks ( representing 80% of ahi diagnoses ) may increase the yield of ahi diagnoses by more than half . | we analyzed signs and symptoms in 90 patients diagnosed with acute hiv infection in a community - based program that offered universal hiv-1 nucleic acid amplification testing .
forty - seven ( 52% ) patients reported ongoing signs or symptoms at the time of testing .
another 25 ( 28% ) reported signs or symptoms that had occurred during the 14 days before testing . | <s>[INST]we analyzed ahi signs and symptoms in 90 patients given a diagnosis of ahi during 20072014 .
as part of this confidential hiv testing program , routine , individual donation , hiv nucleic acid amplification testing ( nat ) has been provided to all rapid antibody
negative participants since june 2007 ( samples for nat are obtained at the time of rapid antibody testing ) ( 7,10,11 ) .
ahi was defined as having a negative or indeterminate hiv antibody test result in the presence of detectable hiv-1 rna , corresponding to fiebig stages i ii , with a mean estimated date of infection within the previous 10 days ( 95% ci 714 days ) ( 12 ) .
dates of infection were estimated for all recently infected patients using previously published criteria on the basis of serologic and virologic test results ( 13 ) . at each patient s first visit after documentation of ahi diagnosis ( median 4 days , interquartile range [ iqr ] 36 days after ahi testing ) , we obtained blood samples for cd4 and viral load testing and collected detailed information regarding occurrence , duration , and start and stop dates for 11 signs and symptoms associated with ahi ( 5,14 ) .
in addition , patients who participated during 20072011 were asked if they had sought medical attention for any signs or symptoms .
typical ahi ( i.e. , > 2 signs / symptoms ) was defined according to criteria described by braun et al . ( 14 ) . for statistical analysis ,
, chicago , il , usa ) was used . for analysis on signs or symptoms
compatible with ahi , signs or symptoms that started > 5 days before the estimated date of infection ( i.e. , before the 714 day 95% ci ) were excluded .
the university of california san diego s human research protections program approved the study protocol , consent process , and all study - related procedures .
all 90 participants were male and self - identified as men who have sex with men ( msm ) .
median number of male partners reported for the previous 12 months was 20 ( iqr 1431 ) .
a total of 72 ( 80% ) patients had signs or symptoms associated with ahi that occurred within 2 weeks before undergoing nat ; of these 72 patients , 47 ( 52% of the study population ) had ongoing signs or symptoms , while signs or symptoms had resolved by the time of testing for 25 ( 28% of the study population ) .
twelve ( 13% ) reported signs or symptoms starting after testing , while 6 ( 7% ) reported the absence of signs or symptoms ( table 1 ) .
a total of 66 patients ( 73% of the study population ) reported headache , pharyngitis , or myalgia occurring during the 14 days before ahi testing . * ahi , acute hiv infection ; iqr , interquartile range ; nat , nucleic acid amplification testing ; ns , not significant .
most frequently observed signs or symptoms that occurred during the 14 days before nat or were ongoing at the time of nat were fatigue ( 53 persons , 59% of the study population ) , fever ( 51 , 57% ) , myalgia ( 48 , 53% ) , headache ( 41 , 46% ) , night sweats ( 35 , 39% ) , pharyngitis ( 32 , 36% ) , and gastrointestinal symptoms ( 29 , 32% ) .
overall , 69 patients ( 77% ) reported signs or symptoms that met criteria of compatibility with ahi ( table 2 ) .
onset of signs or symptoms compatible with ahi occurred at a median of 5 days ( iqr 08 , range 4 to 15 days ) after the estimated date of infection . neither viral load nor cd4 count correlated with duration or actual number of signs or symptoms .
* ahi , acute hiv infection ; gi , gastrointestinal ; iqr , interquartile range ; nat , nucleic acid amplification testing ; ns , not significant . defined as having started < 4 days before estimated date of infection or after the estimated date of infection .
data on whether a patient sought medical attention because of signs or symptoms were available for 42 ( 47% ) of 90 patients ; of these , 12 ( 29% ) reported that they sought medical attention because of their signs or symptoms and 30 ( 71% ) did not .
significantly higher viral loads were observed for those who sought medical attention compared with those who did not ( median 6.1 [ iqr 5.76.7 ] log copies / ml vs. 4.7 [ iqr 3.45.5 ] log copies / ml ; p<0.01 ) .
overall , 70 ( 78% ) of the 90 patients fulfilled criteria for having typical ahi and 20 ( 22% ) did not ( of the latter , 14 had only 1 sign or symptom , and 6 were asymptomatic ) .
patients with typical ahi had significantly higher viral loads compared with patients without ( p<0.01 ) . a total of 61 ( 85% ) of 72 patients with signs or symptoms before nat testing fulfilled criteria for having typical ahi .
in addition , 40 ( 85% ) of 47 patients who had ongoing signs or symptoms at the time of ahi testing fulfilled criteria for having typical ahi at that time .
we characterized signs or symptoms relative to the date of ahi diagnosis among persons seeking hiv testing in a program offering universal ahi screening .
two findings are notable : 1 ) 52% of participants reported ongoing signs or symptoms at the time of ahi testing , and 2 ) 80% reported signs or symptoms occurring within 2 weeks before undergoing testing . these findings may have major clinical implications for community - based settings that restrict ahi testing to persons with ongoing signs or symptoms . this practice may be relatively insensitive in settings where msm undergo hiv screening frequently ( 11 ) .
our results show that expansion of ahi screening to include those with signs or symptoms during the 2 weeks before the test may increase the yield of ahi diagnoses by more than half .
although our results may allow for estimation of sensitivity of signs and symptoms for ahi in persons seeking hiv testing , specificity of signs and symptoms remains unknown ( in this study , signs and symptoms were not assessed in those who tested negative , and no control group was available ) .
estimates on frequency of signs and symptoms in hiv - negative persons ( i.e. , specificity ) ranged widely in previous studies .
although in one study a specificity of 65% was estimated for influenza illness like symptoms ( 15 ) , specificities ranging from 38% to 91% for recent symptoms were estimated in another study ( 5 )
. limitations of those studies include the fact that exact time frames for occurrence of signs or symptoms ( e.g. , ongoing at the time of testing or occurring within the last 14 days ) have not been evaluated , which makes comparison of results difficult .
therefore , our results may not be applicable to populations other than msm , although previous studies have reported that clinical features of ahi may not differ by sex and age of patients ( 4 ) . in summary , hiv diagnostic testing strategies that limit ahi testing to patients with ongoing signs or symptoms
in contrast , hiv nat provided for msm who report signs or symptoms during the preceding 2 weeks ( representing 80% of ahi diagnoses ) may increase the yield of ahi diagnoses by more than half .[/INST]we analyzed signs and symptoms in 90 patients diagnosed with acute hiv infection in a community - based program that offered universal hiv-1 nucleic acid amplification testing .
forty - seven ( 52% ) patients reported ongoing signs or symptoms at the time of testing .
another 25 ( 28% ) reported signs or symptoms that had occurred during the 14 days before testing .</s> |
in this paper , we consider a simple problem , namely the solution of the scalar wave equation @xmath0 subject to homogeneous initial conditions @xmath1 in the exterior of the unit sphere . here ,
@xmath2 denote the spherical coordinates of a point in @xmath3 with @xmath4 .
standard textbooks on mathematical physics ( such as @xcite ) present exact solutions for the time - harmonic cases governed by the helmholtz equation , but generally fail to discuss the difficulties associated with the fully time - dependent case .
as we shall see , it is a nontrivial matter to develop closed - form solutions , and a surprisingly subtle matter to develop solutions that can be computed without catastrophic cancellation . in this paper
, we restrict our attention to boundary value problems with dirichlet or robin conditions .
we consider the dirichlet problem first , and assume we are given data on the boundary of the unit sphere of the form : @xmath5 it is natural to begin by expanding both @xmath6 and @xmath7 in terms of spherical harmonics .
@xmath8 where @xmath9 @xmath10 is the standard legendre polynomial of degree @xmath11 , and the associated legendre functions @xmath12 are defined by the rodrigues formula @xmath13 we let @xmath14 and @xmath15 denote the laplace transforms of @xmath16 and @xmath17 : @xmath18 @xmath19 it is straightforward @xcite to see that @xmath14 satisfies the linear second order ordinary differential equation ( ode ) @xmath20 \hunm(r , s ) = 0,\ ] ] for which the decaying solution as @xmath21 is the modified spherical hankel function @xmath22 .
it follows that @xmath23 matching boundary data on the unit sphere , we have @xmath24 , and @xmath25 the remaining difficulty is that we have an explicit solution in the laplace transform domain , but we seek the solution in the time domain . for this , we write the right hand side of in a form for which the inverse laplace transform can carried out analytically .
first , from @xcite , we have @xmath26 where @xmath27 ( @xmath28 ) are the simple roots of @xmath29 lying on the open left half of the complex plane .
thus , @xmath30 where the second equality follows from an expansion using partial fractions and the coefficients @xmath31 are given from the residue theorem by the formula : @xmath32 substituting into , we obtain @xmath33 taking the inverse laplace transform of both sides , we have @xmath34 this involves the use of the convolution theorem and the formulas @xmath35 and @xmath36 , where @xmath37 is the heaviside function .
wilcox @xcite studied the solution of the scalar wave equation and derived formula in 1959 . in that short note , wilcox stated that the coefficients @xmath31 given by grew slowly based on the claim that @xmath38 as @xmath39 .
unfortunately , this estimate is incorrect .
in fact , even after multiplication by the exponentially decaying factor @xmath40 , the coefficients @xmath31 ( @xmath28 ) grow exponentially fast as @xmath39 . in the next section , we explain this growth in detail . as a result ,
even though is very convenient for the purpose of theoretical studies , it can not be used for numerical calculation due to catastrophe cancellation in carrying out the summation .
benedict , field and lau @xcite have recently developed algorithms for compressing the kernel , which they call the teleportation kernel , arising in sphere - to - sphere propagation of data both for the standard wave equation as well as wave equations arising in linearized gravitational theories .
for the wave equation their compressed kernels can be used to perform the same function as our solution of the dirichlet problem .
the largest value of @xmath11 considered in @xcite is @xmath41 .
it is as yet unclear if useful compressions for much larger values of @xmath11 can be constructed using their methods .
we first show that the coefficients @xmath31 ( @xmath28 ) defined in grow exponentially as @xmath39 , for fixed large @xmath42 .
indeed , lemma [ lem6.1 ] in section [ sec : num ] shows that the zeros @xmath27 of @xmath29 satisfy the estimates : @xmath43 for all @xmath44 and @xmath45 .
thus when @xmath42 is large , we have @xmath46 where the last line follows from stirling s formula @xmath47 .
we have computed @xmath48 for @xmath49 using , and plotted them in figure [ fig2.1 ] for @xmath50 , clearly exhibiting the exponential growth of @xmath51 .
we also plot @xmath52 as a function of @xmath44 for a fixed value of @xmath11 in fig .
[ fig2.2 ] . _ for increasing values of @xmath11 , with @xmath50 . ,
height=240 ] as a function of @xmath44 , for @xmath53 and @xmath50 .
, height=240 ] from the preceding analysis , it is clear that one can not use as stated , since the desired solution is @xmath54 and catastrophic cancellation will occur in computing @xmath55 from exponentially large intermediate quantities .
fortunately , even though @xmath56 grows exponentially as @xmath11 increases , we can rewrite in the form of a convolution , which involves much more benign growth : @xmath57 where the convolution kernel @xmath58 is defined by the formula @xmath59 if we write @xmath60 then from , we have @xmath61 where @xmath62 is the modified bessel function of the second kind .
the last expression follows from the fact that @xmath63 .
the convolution kernel @xmath64 and its laplace transform @xmath65 are plotted in figs .
[ fig2.3 ] and [ fig2.4 ] , respectively . as a function of @xmath66 for @xmath53 and @xmath50 .
the left - hand plot shows @xmath64 for @xmath67 $ ] , the middle plot shows the same function on @xmath68 $ ] , and the right - hand plot shows the function on @xmath69$].__,height=240 ] of the convolution kernel is plotted on the imaginary axis over the range @xmath70 $ ] for @xmath53 and @xmath50 .
the red ( lower ) curve corresponds to the real part of @xmath65 and the blue ( upper ) curve corresponds to its imaginary part.,height=240 ] the following lemma shows that the convolution kernel grows only quadratically as a function of @xmath11 at @xmath71 .
numerical experiments ( see fig .
[ fig2.3 ] ) suggest that @xmath64 is maximal in magnitude at @xmath71 .
thus , while the sum of exponential expression ( [ eq2.14 ] ) involves catastrophic cancellation , the function @xmath64 is , itself , well - behaved and we may seek an alternative method for the evaluation of the convolution integral .
let @xmath4 .
then @xmath72 by the initial value theorem for the laplace transform , @xmath73 the first equality in follows from . from @xcite ( formula 9.7.2 on page 378 ) , we have the asymptotic expansion @xmath74 where @xmath75 . substituting and into
, we obtain @xmath76 the result now follows from the fact that @xmath77 . despite the fact that @xmath56 grows exponentially with @xmath11 ,
shows that the _ sum of weights _
@xmath31 is only @xmath78 for fixed @xmath42 .
still , however , the formula can not be used in practice because of catastrophic cancellation in the summation @xmath79 thus , we will need a different representation for the convolution operator @xmath80 which is suitable for numerical computation . to obtain a stable formula , we note first that we may rewrite in the form : @xmath81 we then use to express @xmath82 as @xmath83 we can , therefore , compute @xmath84 recursively : @xmath85 and , finally , @xmath86 numerical experiments indicate that the above recursion is stable if the zeros @xmath27 of @xmath29 are arranged in ascending order according to their real parts , i.e. , @xmath87 is closest to the negative real axis and @xmath88 is closest to the imaginary axis .
alternatively , it is easy to show that the functions @xmath89 ( @xmath28 ) are the solutions to the following first order system of ordinary differential equations ( odes ) with zero initial conditions .
@xmath90 where @xmath91 is a column vector of length @xmath11 with the @xmath44th entry being @xmath89 , @xmath92 , @xmath93 are @xmath94 constant matrices defined by the formulas @xmath95 and @xmath96 is a column vector of length @xmath11 whose only nonzero entry is @xmath97 .
the ode system can actually be solved analytically .
that is , one may multiply both sides of by @xmath98 to obtain @xmath99 where @xmath100 .
it is clear that @xmath101 is a constant lower triangular matrix .
one could then diagonalize the system using the eigen - decomposition @xmath102 .
this , however , is numerically unstable since @xmath101 is a highly _ nonnormal _ matrix .
thus , even though the condition number of @xmath101 is not very high ( numerical evidence shows that @xmath103 ) , @xmath104 is extremely ill - conditioned .
in fact , more detailed analysis shows that this approach leads exactly to the formula .
nevertherless , the ode system itself can be solved numerically using standard ode packages , albeit less efficiently than the explicit recursive approach we present in section [ sec : num ] , especially for high precision .
in this section , we consider the robin problem for the scalar wave equation on the unit sphere : @xmath105 with homogeneous initial data @xmath106 and the boundary condition @xmath107 it should be noted that tokita @xcite extended wilcox s analysis of the dirichlet problem to the case of robin boundary conditions of the form @xmath108 , although he assumed that @xmath109 in his discussion .
we are primarily concerned with the case @xmath110 since it arises in the solution of the full maxwell equations @xcite . as in the analysis of the dirichlet problem , we first expand @xmath111 and @xmath112 in terms of spherical harmonics , perform the laplace transform in @xmath66 , match the boundary data and obtain @xmath113 and @xmath114 we turn now to a study the properties of the kernel in , letting @xmath115 and @xmath116 recalling from [ eq2.8 ] that @xmath117 , we have @xmath118 hence , @xmath119 in particular , for @xmath120 , we have @xmath121 obviously , the poles of @xmath122 are simply the zeros of @xmath123 .
those zeros have been characterized by tokita @xcite in the following lemma .
[ lem3.1 ] _ [ adapted from @xcite . ]
_ for @xmath124 , @xmath125 has @xmath126 simple roots denoted by @xmath127 .
all the roots lie in the open left half of the complex plane symmetrically with respect to the real axis .
furthermore , they satisfy the following estimates @xmath128 @xmath129 .
hence , there exists a positive number @xmath130 such that @xmath131 for all @xmath124 and @xmath132 . from the preceding lemma , for @xmath124 we have @xmath133
one could carry out a partial fraction expansion for the right hand side of to obtain @xmath134 where the coefficients @xmath135 are given by the formula @xmath136 this would yield @xmath137 unfortunately , the coefficients @xmath135 ( @xmath138 ) behave as badly as the coefficients @xmath31 defined in for the dirichlet problem .
that is , catastrophic cancellation in makes it ill - suited for numerical computation .
fortunately , as in section [ sec : recurrence ] , we can compute @xmath139 without catastrophic cancellation using the following recurrence ( @xmath140 ) : @xmath141 with @xmath142 we leave the derivation of the recurrence to the reader .
it is possible to write down a system of odes that is equivalent to .
we omit details since the derivation is straightforward and we prefer the recurrence for numerical purposes in any case .
in order to carry out the recurrences or , we first need to compute to compute the zeros of @xmath143 and @xmath144 .
the following lemma provides asymptotic approximations of the zeros of these two functions , which we will use as initial guesses followed by a simple newton iteration . in practice
, we have found that six newton steps are sufficient to achieve double precision accuracy for @xmath145 .
[ lem6.1 ] _
( asymptotic distribution of the zeros of @xmath143 and @xmath144 , adapted from @xcite ) ; see also the appendix . _ 1 .
the zeros of @xmath146 have the following asymptotic expansion @xmath147 uniformly in @xmath44 , where @xmath148 is defined by the formula @xmath149 @xmath150 is the @xmath44th negative zero of the airy function @xmath151 whose asymptotic expansion is given by the formula @xmath152 and @xmath153 is obtained from inverting the equation @xmath154 where the branch is chosen so that @xmath155 is real when @xmath156 is positive imaginary . in other words , @xmath153 lies on the curve whose parametric equation is @xmath157 where @xmath158 $ ] and @xmath159 is the positive root of @xmath160 .
the zeros of @xmath161 have the asymptotic expansion @xmath162 uniformly in @xmath44 , where @xmath163 is defined by the formula @xmath164 and @xmath165 is the @xmath44th negative zero of the first derivative of the airy function @xmath166 whose asymptotic expansion is given by the formula @xmath167 and @xmath168 is defined as in with @xmath155 replaced by @xmath169 .
figure [ fig6.1 ] shows the zeros of @xmath170 , @xmath171 , @xmath172 and @xmath173 . , @xmath171 , @xmath172 and @xmath173 .
the zeros of @xmath29 are marked by red @xmath174 , and the zeros of @xmath123 are marked by blue @xmath175 .
_ , height=288 ] we now present a high - order discretization scheme for computing @xmath84 and @xmath139 .
we will only discuss the computation of @xmath84 in detail , since the treatment of @xmath139 is analogous . recall that the relevant recurrence relations are and .
to proceed , we first introduce the auxillary functions @xmath176 then , becomes @xmath177 it is easy to check that @xmath178 satisfies the recurrence relation @xmath179 thus , we need only consider the calculation of the integral over @xmath180 $ ] . for this , we interpolate @xmath181 by a polynomial of degree @xmath182 with the shifted and scaled legendre nodes as interpolation nodes
. that is , @xmath183 where @xmath184 ( @xmath185 ) are the standard legendre nodes on @xmath186 $ ] and @xmath187 is the @xmath188 entry of the matrix converting function values to the coefficients of a legendre expansion .
substituting into the integral on the right side of and simplifying , we obtain @xmath189 where the coefficients @xmath190 ( @xmath185 ) are given by the formula @xmath191 substituting into , we obtain @xmath192 in order to be able to use , we need to calculate @xmath193 . for this , we can again apply the recurrence and obtain @xmath194 where the coefficients @xmath195 , for @xmath196 , are given by the formula @xmath197 in summary , the algorithm for computing @xmath198 proceeds in two stages : a precomputation stage and a time - marching stage . for spherical harmonic order @xmath11 , time step @xmath199 , and desired order of accuracy @xmath200 , precompute the coefficients needed in the marching scheme for @xmath84 . compute and
store the zeros @xmath27 ( @xmath28 ) of @xmath29 .
compute the legendre nodes @xmath184 ( @xmath185 ) and the @xmath201 matrix @xmath6 which converts function values to the coefficients of the corresponding legendre expansion .
compute the integrals @xmath202 . compute and store the coefficients @xmath203 defined in .
compute the integrals @xmath204 . compute and store the coefficients @xmath205 defined in . compute and
store @xmath206 .
compute and store @xmath207 . given @xmath11 , @xmath42 , @xmath208 , the desired order of accuracy @xmath200 , and the number of desired time steps @xmath209 ,
compute the spherical harmonic mode @xmath84 at @xmath210 defined by .
set @xmath211 .
set @xmath212 .
evaluate the boundary data @xmath213 by computing the spherical harmonic transform of the dirichlet data @xmath7 , and set @xmath214 .
use to compute @xmath215 use to update @xmath216 . set @xmath217 .
compute @xmath218 .
compute @xmath219 . for each spherical harmonic mode , it is easy to see that the precomputation cost is @xmath220 and the marching cost is @xmath221 , where @xmath200 is the desired order of accuracy and @xmath209 is the total number of time steps . thus , if we truncate the spherical harmonic expansion order at @xmath222 , then the precomputation cost is @xmath223 and the marching cost is @xmath224 .
the cost of computing the spherical harmonic transform of the boundary data at all times is @xmath225 and the cost of the inverse spherical harmonic transform at the final time is @xmath226 .
summing all these factors up , we observe that the total computational cost of our algorithm is @xmath224 .
we have implemented the above algorithm in fortran for both the dirichlet and robin problems governed by the scalar wave equation . to test its convergence and stability , we consider the exact solution @xmath227 with @xmath228 , @xmath229 , @xmath230 , @xmath231 , and @xmath232 , @xmath233 , @xmath234 , @xmath235 .
the numerical solution is computed on a sphere of radius @xmath236 at @xmath237 .
tables [ tab8.1]-[tab8.4 ] show the relative @xmath238 error of the numerical solution of the scalar wave equation for varying values of @xmath222 , the order of the spherical expansion and total number of time steps .
note that the solution is oscillatory in both space and time , so that finite difference or finite element methods would have difficulty computing the solution in the far field with high precision because of numerical dispersion errors . in tables
[ tab8.1 ] and [ tab8.3 ] , the order of temporal convolution is @xmath239 and we break the time interval @xmath240 $ ] into @xmath241 equispaced subintervals ( yielding a total of @xmath242 discretization points in time ) . in tables
[ tab8.2 ] and [ tab8.4 ] , we use @xmath243 terms in the spherical harmonic expansions .
these tables show that numerical solution converges spectrally fast to the exact solution .
.relative @xmath238 error of the numerical solution of the dirichlet problem with increasing spherical harmonic expansion order @xmath222 .
@xmath244 is the total number of discretization on the unit sphere .
since the discretization error is usually greater than the truncation error , @xmath245 is chosen to be @xmath246 .
thus @xmath247 .
the total number of discretization points in time is @xmath248 . [
cols="^,^,^,^,^,^,^",options="header " , ] .
the exact solution is of the same form as ( [ uexact ] ) - that is , induced by two sources in the interior of the unit sphere . [ fig8.2],height=192 ] for a true " scattering problem .
dirichlet boundary conditions are generated by two exterior sources placed on the @xmath156-axis , at @xmath249 and @xmath250 .
the left - hand plot shows the value of the boundary data at the north pole of the unit sphere as a function of time , and the right - hand plot shows the solution at the north pole of the outer sphere of radius @xmath236 .
[ fig8.3],height=192 ] for a true " scattering problem .
robin boundary conditions are generated by two exterior sources placed on the @xmath156-axis , at @xmath249 and @xmath250 .
the left - hand plot shows the value of the boundary data at the north pole of the unit sphere as a function of time , and the right - hand plot shows the solution at the north pole of the outer sphere of radius @xmath236 .
[ fig8.4],height=192 ] -plane within the annular region @xmath251 at @xmath252 . with boundary data as in fig .
[ fig8.3 ] .
note that the domain is approximately 50 wavelengths in size .
[ fig8.5],height=192 ]
we have presented an analytic solution for the scalar wave equation in the exterior of a sphere in a form that is numerically tractable and permits high order accuracy even for objects many wavelengths in size . aside from its intrinsic interest in single or multiple scattering from a collection of spheres , our algorithm provides a useful reference solution for any numerical method designed to solve problems of exterior scattering . at the present time , such codes are typically tested by fourier transformation after a long - time simulation and comparison with a set of single frequency solutions computed by separation of variables applied to the helmholtz equation . an exception is the work of sauter and veit @xcite , who make use of a formulation equivalent to that of wilcox to develop a benchmark solution for a time - domain integral equation solver which can be applied to scattering from general geometries .
exponential ill - conditioning is avoided by considering only low - order spherical harmonic expansions .
recently , grote and sim @xcite have also used an approach based on the local exact radiation boundary conditions proposed in @xcite to develop a new hybrid asymptotic / finite difference formalism for multiple scattering in the time domain .
the advantage of the grote - sim method is that spherical harmonic transformations are unnecessary and the evaluation formulas can be localized in angle .
however , they also restrict their attention to low - order expansions , and our preliminary experiments using their formulas indicate a loss of conditioning for @xmath11 large .
( the loss of conditioning presumably also applies to the radiation boundary conditions in @xcite . )
the method developed here should be of immediate use in both contexts as implemented above , our algorithm has @xmath253 complexity .
it is possible , however , to reduce the cost to @xmath254 .
this requires the use of a fast spherical harmonic transform ( see , for example , @xcite and references therein ) . with this fast algorithm ,
the cost of each spherical harmonic transform is reduced from @xmath226 to @xmath255 .
second , we believe that the convolution kernels can be compressed as in @xcite , so that they involve only @xmath256 modes for each @xmath11 for a given precision . we note that compressions for @xmath257 and various radii are reported in @xcite , both for the scalar wave equation considered here ( which they call the flat - space wave equation ) and for wave equations with zerilli and regge - wheeler potentials . in the latter cases ,
compressed kernels are also constructed for smaller values of @xmath11 , as the exact kernels do not have rational transforms .
tabulated coefficients required for implementing the compressed kernels may be found online @xcite .
for the extension of the present approach to the full maxwell equations , see @xcite .
software implementing the algorithm of the present paper will be made available upon request .
an alternative analysis of the instability phenomenon can be carried out using the uniform asymptotic expansions of the bessel functons due to olver @xcite .
we first recall the relationship between @xmath62 and the hankel function , @xmath259 : @xmath260 thus the residues we wish to estimate are given by @xmath261 to approximate these for @xmath262 we use ( see @xcite ) : @xmath263 which hold uniformly in @xmath264 ; thus in particular they hold in @xmath265 where we will be using them . here
@xmath155 is given by ( [ eq6.4 ] ) with the replacement @xmath266 .
i. : : @xmath267 has infinitely many zeros which lie on the negative real axis .
for @xmath44 large the jth zero , @xmath268 , of @xmath267 satisfies ( [ eq6.3 ] ) and the derivative satisfies @xmath269 ii .
: : for @xmath270 the function @xmath267 satisfies the asymptotic formula @xmath271 using ( i. ) we deduce that the poles , @xmath272 , are asymptotically given by ( [ eq6.1 ] ) and approximately lie on the curve @xmath273 where @xmath274 is defined in ( [ eq6.5 ] ) .
this is the curve for which @xmath275 is real and negative . to evaluate the residues we must calculate using ( [ ash]),([asdh ] ) @xmath276 where we have introduced @xmath277 obviously the scaling @xmath278 moves @xmath279 off the curve where the argument of the airy function is real and negative . thus using ( [ aiasy ] ) and ( [ eq6.4 ] ) we deduce that the asymptotic formula for @xmath258 contains an exponential term @xmath280 \nonumber\end{aligned}\ ] ] where @xmath281 here we have introduced @xmath282 . finally , we consider the real part of the expression in parentheses on the second line of ( [ resexp ] ) .
in particular we replace @xmath283 by a continuous variable @xmath284 traversing the scaled curve , @xmath274 , containing the approximate zeros .
then the function @xmath285 depends only on @xmath42 and the coordinate describing the curve ; in particular it is independent of @xmath11 and @xmath44 . in fig .
[ resasy2 ] we plot the real part of @xmath285 scaled by @xmath286 for @xmath50 .
this can be compared with fig .
[ fig2.2 ] by scaling both axes by @xmath53 and recognizing the vertical axis as the base ten logarithm .
we then observe good agreement with the numerical results .
the maximum value plotted in figure [ resasy2 ] is approximately @xmath287 , which is the predicted slope of the straight line plotted in fig .
[ fig2.1 ] .
again the agreement is good .
we note that increasing @xmath42 makes the problem somewhat worse ; the scaled maximum real part is approximately @xmath288 for @xmath289 and @xmath290 for @xmath291 . | we derive new , explicit representations for the solution to the scalar wave equation in the exterior of a sphere , subject to either dirichlet or robin boundary conditions .
our formula leads to a stable and high - order numerical scheme that permits the evaluation of the solution at an arbitrary target , without the use of a spatial grid and without numerical dispersion error . in the process , we correct some errors in the analytic literature concerning the asymptotic behavior of the logarithmic derivative of the spherical modified hankel function .
we illustrate the performance of the method with several numerical examples . 65m70 , 78a40 , 78m16 | <s>[INST]in this paper , we consider a simple problem , namely the solution of the scalar wave equation @xmath0 subject to homogeneous initial conditions @xmath1 in the exterior of the unit sphere . here ,
@xmath2 denote the spherical coordinates of a point in @xmath3 with @xmath4 .
standard textbooks on mathematical physics ( such as @xcite ) present exact solutions for the time - harmonic cases governed by the helmholtz equation , but generally fail to discuss the difficulties associated with the fully time - dependent case .
as we shall see , it is a nontrivial matter to develop closed - form solutions , and a surprisingly subtle matter to develop solutions that can be computed without catastrophic cancellation . in this paper
, we restrict our attention to boundary value problems with dirichlet or robin conditions .
we consider the dirichlet problem first , and assume we are given data on the boundary of the unit sphere of the form : @xmath5 it is natural to begin by expanding both @xmath6 and @xmath7 in terms of spherical harmonics .
@xmath8 where @xmath9 @xmath10 is the standard legendre polynomial of degree @xmath11 , and the associated legendre functions @xmath12 are defined by the rodrigues formula @xmath13 we let @xmath14 and @xmath15 denote the laplace transforms of @xmath16 and @xmath17 : @xmath18 @xmath19 it is straightforward @xcite to see that @xmath14 satisfies the linear second order ordinary differential equation ( ode ) @xmath20 \hunm(r , s ) = 0,\ ] ] for which the decaying solution as @xmath21 is the modified spherical hankel function @xmath22 .
it follows that @xmath23 matching boundary data on the unit sphere , we have @xmath24 , and @xmath25 the remaining difficulty is that we have an explicit solution in the laplace transform domain , but we seek the solution in the time domain . for this , we write the right hand side of in a form for which the inverse laplace transform can carried out analytically .
first , from @xcite , we have @xmath26 where @xmath27 ( @xmath28 ) are the simple roots of @xmath29 lying on the open left half of the complex plane .
thus , @xmath30 where the second equality follows from an expansion using partial fractions and the coefficients @xmath31 are given from the residue theorem by the formula : @xmath32 substituting into , we obtain @xmath33 taking the inverse laplace transform of both sides , we have @xmath34 this involves the use of the convolution theorem and the formulas @xmath35 and @xmath36 , where @xmath37 is the heaviside function .
wilcox @xcite studied the solution of the scalar wave equation and derived formula in 1959 . in that short note , wilcox stated that the coefficients @xmath31 given by grew slowly based on the claim that @xmath38 as @xmath39 .
unfortunately , this estimate is incorrect .
in fact , even after multiplication by the exponentially decaying factor @xmath40 , the coefficients @xmath31 ( @xmath28 ) grow exponentially fast as @xmath39 . in the next section , we explain this growth in detail . as a result ,
even though is very convenient for the purpose of theoretical studies , it can not be used for numerical calculation due to catastrophe cancellation in carrying out the summation .
benedict , field and lau @xcite have recently developed algorithms for compressing the kernel , which they call the teleportation kernel , arising in sphere - to - sphere propagation of data both for the standard wave equation as well as wave equations arising in linearized gravitational theories .
for the wave equation their compressed kernels can be used to perform the same function as our solution of the dirichlet problem .
the largest value of @xmath11 considered in @xcite is @xmath41 .
it is as yet unclear if useful compressions for much larger values of @xmath11 can be constructed using their methods .
we first show that the coefficients @xmath31 ( @xmath28 ) defined in grow exponentially as @xmath39 , for fixed large @xmath42 .
indeed , lemma [ lem6.1 ] in section [ sec : num ] shows that the zeros @xmath27 of @xmath29 satisfy the estimates : @xmath43 for all @xmath44 and @xmath45 .
thus when @xmath42 is large , we have @xmath46 where the last line follows from stirling s formula @xmath47 .
we have computed @xmath48 for @xmath49 using , and plotted them in figure [ fig2.1 ] for @xmath50 , clearly exhibiting the exponential growth of @xmath51 .
we also plot @xmath52 as a function of @xmath44 for a fixed value of @xmath11 in fig .
[ fig2.2 ] . _ for increasing values of @xmath11 , with @xmath50 . ,
height=240 ] as a function of @xmath44 , for @xmath53 and @xmath50 .
, height=240 ] from the preceding analysis , it is clear that one can not use as stated , since the desired solution is @xmath54 and catastrophic cancellation will occur in computing @xmath55 from exponentially large intermediate quantities .
fortunately , even though @xmath56 grows exponentially as @xmath11 increases , we can rewrite in the form of a convolution , which involves much more benign growth : @xmath57 where the convolution kernel @xmath58 is defined by the formula @xmath59 if we write @xmath60 then from , we have @xmath61 where @xmath62 is the modified bessel function of the second kind .
the last expression follows from the fact that @xmath63 .
the convolution kernel @xmath64 and its laplace transform @xmath65 are plotted in figs .
[ fig2.3 ] and [ fig2.4 ] , respectively . as a function of @xmath66 for @xmath53 and @xmath50 .
the left - hand plot shows @xmath64 for @xmath67 $ ] , the middle plot shows the same function on @xmath68 $ ] , and the right - hand plot shows the function on @xmath69$].__,height=240 ] of the convolution kernel is plotted on the imaginary axis over the range @xmath70 $ ] for @xmath53 and @xmath50 .
the red ( lower ) curve corresponds to the real part of @xmath65 and the blue ( upper ) curve corresponds to its imaginary part.,height=240 ] the following lemma shows that the convolution kernel grows only quadratically as a function of @xmath11 at @xmath71 .
numerical experiments ( see fig .
[ fig2.3 ] ) suggest that @xmath64 is maximal in magnitude at @xmath71 .
thus , while the sum of exponential expression ( [ eq2.14 ] ) involves catastrophic cancellation , the function @xmath64 is , itself , well - behaved and we may seek an alternative method for the evaluation of the convolution integral .
let @xmath4 .
then @xmath72 by the initial value theorem for the laplace transform , @xmath73 the first equality in follows from . from @xcite ( formula 9.7.2 on page 378 ) , we have the asymptotic expansion @xmath74 where @xmath75 . substituting and into
, we obtain @xmath76 the result now follows from the fact that @xmath77 . despite the fact that @xmath56 grows exponentially with @xmath11 ,
shows that the _ sum of weights _
@xmath31 is only @xmath78 for fixed @xmath42 .
still , however , the formula can not be used in practice because of catastrophic cancellation in the summation @xmath79 thus , we will need a different representation for the convolution operator @xmath80 which is suitable for numerical computation . to obtain a stable formula , we note first that we may rewrite in the form : @xmath81 we then use to express @xmath82 as @xmath83 we can , therefore , compute @xmath84 recursively : @xmath85 and , finally , @xmath86 numerical experiments indicate that the above recursion is stable if the zeros @xmath27 of @xmath29 are arranged in ascending order according to their real parts , i.e. , @xmath87 is closest to the negative real axis and @xmath88 is closest to the imaginary axis .
alternatively , it is easy to show that the functions @xmath89 ( @xmath28 ) are the solutions to the following first order system of ordinary differential equations ( odes ) with zero initial conditions .
@xmath90 where @xmath91 is a column vector of length @xmath11 with the @xmath44th entry being @xmath89 , @xmath92 , @xmath93 are @xmath94 constant matrices defined by the formulas @xmath95 and @xmath96 is a column vector of length @xmath11 whose only nonzero entry is @xmath97 .
the ode system can actually be solved analytically .
that is , one may multiply both sides of by @xmath98 to obtain @xmath99 where @xmath100 .
it is clear that @xmath101 is a constant lower triangular matrix .
one could then diagonalize the system using the eigen - decomposition @xmath102 .
this , however , is numerically unstable since @xmath101 is a highly _ nonnormal _ matrix .
thus , even though the condition number of @xmath101 is not very high ( numerical evidence shows that @xmath103 ) , @xmath104 is extremely ill - conditioned .
in fact , more detailed analysis shows that this approach leads exactly to the formula .
nevertherless , the ode system itself can be solved numerically using standard ode packages , albeit less efficiently than the explicit recursive approach we present in section [ sec : num ] , especially for high precision .
in this section , we consider the robin problem for the scalar wave equation on the unit sphere : @xmath105 with homogeneous initial data @xmath106 and the boundary condition @xmath107 it should be noted that tokita @xcite extended wilcox s analysis of the dirichlet problem to the case of robin boundary conditions of the form @xmath108 , although he assumed that @xmath109 in his discussion .
we are primarily concerned with the case @xmath110 since it arises in the solution of the full maxwell equations @xcite . as in the analysis of the dirichlet problem , we first expand @xmath111 and @xmath112 in terms of spherical harmonics , perform the laplace transform in @xmath66 , match the boundary data and obtain @xmath113 and @xmath114 we turn now to a study the properties of the kernel in , letting @xmath115 and @xmath116 recalling from [ eq2.8 ] that @xmath117 , we have @xmath118 hence , @xmath119 in particular , for @xmath120 , we have @xmath121 obviously , the poles of @xmath122 are simply the zeros of @xmath123 .
those zeros have been characterized by tokita @xcite in the following lemma .
[ lem3.1 ] _ [ adapted from @xcite . ]
_ for @xmath124 , @xmath125 has @xmath126 simple roots denoted by @xmath127 .
all the roots lie in the open left half of the complex plane symmetrically with respect to the real axis .
furthermore , they satisfy the following estimates @xmath128 @xmath129 .
hence , there exists a positive number @xmath130 such that @xmath131 for all @xmath124 and @xmath132 . from the preceding lemma , for @xmath124 we have @xmath133
one could carry out a partial fraction expansion for the right hand side of to obtain @xmath134 where the coefficients @xmath135 are given by the formula @xmath136 this would yield @xmath137 unfortunately , the coefficients @xmath135 ( @xmath138 ) behave as badly as the coefficients @xmath31 defined in for the dirichlet problem .
that is , catastrophic cancellation in makes it ill - suited for numerical computation .
fortunately , as in section [ sec : recurrence ] , we can compute @xmath139 without catastrophic cancellation using the following recurrence ( @xmath140 ) : @xmath141 with @xmath142 we leave the derivation of the recurrence to the reader .
it is possible to write down a system of odes that is equivalent to .
we omit details since the derivation is straightforward and we prefer the recurrence for numerical purposes in any case .
in order to carry out the recurrences or , we first need to compute to compute the zeros of @xmath143 and @xmath144 .
the following lemma provides asymptotic approximations of the zeros of these two functions , which we will use as initial guesses followed by a simple newton iteration . in practice
, we have found that six newton steps are sufficient to achieve double precision accuracy for @xmath145 .
[ lem6.1 ] _
( asymptotic distribution of the zeros of @xmath143 and @xmath144 , adapted from @xcite ) ; see also the appendix . _ 1 .
the zeros of @xmath146 have the following asymptotic expansion @xmath147 uniformly in @xmath44 , where @xmath148 is defined by the formula @xmath149 @xmath150 is the @xmath44th negative zero of the airy function @xmath151 whose asymptotic expansion is given by the formula @xmath152 and @xmath153 is obtained from inverting the equation @xmath154 where the branch is chosen so that @xmath155 is real when @xmath156 is positive imaginary . in other words , @xmath153 lies on the curve whose parametric equation is @xmath157 where @xmath158 $ ] and @xmath159 is the positive root of @xmath160 .
the zeros of @xmath161 have the asymptotic expansion @xmath162 uniformly in @xmath44 , where @xmath163 is defined by the formula @xmath164 and @xmath165 is the @xmath44th negative zero of the first derivative of the airy function @xmath166 whose asymptotic expansion is given by the formula @xmath167 and @xmath168 is defined as in with @xmath155 replaced by @xmath169 .
figure [ fig6.1 ] shows the zeros of @xmath170 , @xmath171 , @xmath172 and @xmath173 . , @xmath171 , @xmath172 and @xmath173 .
the zeros of @xmath29 are marked by red @xmath174 , and the zeros of @xmath123 are marked by blue @xmath175 .
_ , height=288 ] we now present a high - order discretization scheme for computing @xmath84 and @xmath139 .
we will only discuss the computation of @xmath84 in detail , since the treatment of @xmath139 is analogous . recall that the relevant recurrence relations are and .
to proceed , we first introduce the auxillary functions @xmath176 then , becomes @xmath177 it is easy to check that @xmath178 satisfies the recurrence relation @xmath179 thus , we need only consider the calculation of the integral over @xmath180 $ ] . for this , we interpolate @xmath181 by a polynomial of degree @xmath182 with the shifted and scaled legendre nodes as interpolation nodes
. that is , @xmath183 where @xmath184 ( @xmath185 ) are the standard legendre nodes on @xmath186 $ ] and @xmath187 is the @xmath188 entry of the matrix converting function values to the coefficients of a legendre expansion .
substituting into the integral on the right side of and simplifying , we obtain @xmath189 where the coefficients @xmath190 ( @xmath185 ) are given by the formula @xmath191 substituting into , we obtain @xmath192 in order to be able to use , we need to calculate @xmath193 . for this , we can again apply the recurrence and obtain @xmath194 where the coefficients @xmath195 , for @xmath196 , are given by the formula @xmath197 in summary , the algorithm for computing @xmath198 proceeds in two stages : a precomputation stage and a time - marching stage . for spherical harmonic order @xmath11 , time step @xmath199 , and desired order of accuracy @xmath200 , precompute the coefficients needed in the marching scheme for @xmath84 . compute and
store the zeros @xmath27 ( @xmath28 ) of @xmath29 .
compute the legendre nodes @xmath184 ( @xmath185 ) and the @xmath201 matrix @xmath6 which converts function values to the coefficients of the corresponding legendre expansion .
compute the integrals @xmath202 . compute and store the coefficients @xmath203 defined in .
compute the integrals @xmath204 . compute and store the coefficients @xmath205 defined in . compute and
store @xmath206 .
compute and store @xmath207 . given @xmath11 , @xmath42 , @xmath208 , the desired order of accuracy @xmath200 , and the number of desired time steps @xmath209 ,
compute the spherical harmonic mode @xmath84 at @xmath210 defined by .
set @xmath211 .
set @xmath212 .
evaluate the boundary data @xmath213 by computing the spherical harmonic transform of the dirichlet data @xmath7 , and set @xmath214 .
use to compute @xmath215 use to update @xmath216 . set @xmath217 .
compute @xmath218 .
compute @xmath219 . for each spherical harmonic mode , it is easy to see that the precomputation cost is @xmath220 and the marching cost is @xmath221 , where @xmath200 is the desired order of accuracy and @xmath209 is the total number of time steps . thus , if we truncate the spherical harmonic expansion order at @xmath222 , then the precomputation cost is @xmath223 and the marching cost is @xmath224 .
the cost of computing the spherical harmonic transform of the boundary data at all times is @xmath225 and the cost of the inverse spherical harmonic transform at the final time is @xmath226 .
summing all these factors up , we observe that the total computational cost of our algorithm is @xmath224 .
we have implemented the above algorithm in fortran for both the dirichlet and robin problems governed by the scalar wave equation . to test its convergence and stability , we consider the exact solution @xmath227 with @xmath228 , @xmath229 , @xmath230 , @xmath231 , and @xmath232 , @xmath233 , @xmath234 , @xmath235 .
the numerical solution is computed on a sphere of radius @xmath236 at @xmath237 .
tables [ tab8.1]-[tab8.4 ] show the relative @xmath238 error of the numerical solution of the scalar wave equation for varying values of @xmath222 , the order of the spherical expansion and total number of time steps .
note that the solution is oscillatory in both space and time , so that finite difference or finite element methods would have difficulty computing the solution in the far field with high precision because of numerical dispersion errors . in tables
[ tab8.1 ] and [ tab8.3 ] , the order of temporal convolution is @xmath239 and we break the time interval @xmath240 $ ] into @xmath241 equispaced subintervals ( yielding a total of @xmath242 discretization points in time ) . in tables
[ tab8.2 ] and [ tab8.4 ] , we use @xmath243 terms in the spherical harmonic expansions .
these tables show that numerical solution converges spectrally fast to the exact solution .
.relative @xmath238 error of the numerical solution of the dirichlet problem with increasing spherical harmonic expansion order @xmath222 .
@xmath244 is the total number of discretization on the unit sphere .
since the discretization error is usually greater than the truncation error , @xmath245 is chosen to be @xmath246 .
thus @xmath247 .
the total number of discretization points in time is @xmath248 . [
cols="^,^,^,^,^,^,^",options="header " , ] .
the exact solution is of the same form as ( [ uexact ] ) - that is , induced by two sources in the interior of the unit sphere . [ fig8.2],height=192 ] for a true " scattering problem .
dirichlet boundary conditions are generated by two exterior sources placed on the @xmath156-axis , at @xmath249 and @xmath250 .
the left - hand plot shows the value of the boundary data at the north pole of the unit sphere as a function of time , and the right - hand plot shows the solution at the north pole of the outer sphere of radius @xmath236 .
[ fig8.3],height=192 ] for a true " scattering problem .
robin boundary conditions are generated by two exterior sources placed on the @xmath156-axis , at @xmath249 and @xmath250 .
the left - hand plot shows the value of the boundary data at the north pole of the unit sphere as a function of time , and the right - hand plot shows the solution at the north pole of the outer sphere of radius @xmath236 .
[ fig8.4],height=192 ] -plane within the annular region @xmath251 at @xmath252 . with boundary data as in fig .
[ fig8.3 ] .
note that the domain is approximately 50 wavelengths in size .
[ fig8.5],height=192 ]
we have presented an analytic solution for the scalar wave equation in the exterior of a sphere in a form that is numerically tractable and permits high order accuracy even for objects many wavelengths in size . aside from its intrinsic interest in single or multiple scattering from a collection of spheres , our algorithm provides a useful reference solution for any numerical method designed to solve problems of exterior scattering . at the present time , such codes are typically tested by fourier transformation after a long - time simulation and comparison with a set of single frequency solutions computed by separation of variables applied to the helmholtz equation . an exception is the work of sauter and veit @xcite , who make use of a formulation equivalent to that of wilcox to develop a benchmark solution for a time - domain integral equation solver which can be applied to scattering from general geometries .
exponential ill - conditioning is avoided by considering only low - order spherical harmonic expansions .
recently , grote and sim @xcite have also used an approach based on the local exact radiation boundary conditions proposed in @xcite to develop a new hybrid asymptotic / finite difference formalism for multiple scattering in the time domain .
the advantage of the grote - sim method is that spherical harmonic transformations are unnecessary and the evaluation formulas can be localized in angle .
however , they also restrict their attention to low - order expansions , and our preliminary experiments using their formulas indicate a loss of conditioning for @xmath11 large .
( the loss of conditioning presumably also applies to the radiation boundary conditions in @xcite . )
the method developed here should be of immediate use in both contexts as implemented above , our algorithm has @xmath253 complexity .
it is possible , however , to reduce the cost to @xmath254 .
this requires the use of a fast spherical harmonic transform ( see , for example , @xcite and references therein ) . with this fast algorithm ,
the cost of each spherical harmonic transform is reduced from @xmath226 to @xmath255 .
second , we believe that the convolution kernels can be compressed as in @xcite , so that they involve only @xmath256 modes for each @xmath11 for a given precision . we note that compressions for @xmath257 and various radii are reported in @xcite , both for the scalar wave equation considered here ( which they call the flat - space wave equation ) and for wave equations with zerilli and regge - wheeler potentials . in the latter cases ,
compressed kernels are also constructed for smaller values of @xmath11 , as the exact kernels do not have rational transforms .
tabulated coefficients required for implementing the compressed kernels may be found online @xcite .
for the extension of the present approach to the full maxwell equations , see @xcite .
software implementing the algorithm of the present paper will be made available upon request .
an alternative analysis of the instability phenomenon can be carried out using the uniform asymptotic expansions of the bessel functons due to olver @xcite .
we first recall the relationship between @xmath62 and the hankel function , @xmath259 : @xmath260 thus the residues we wish to estimate are given by @xmath261 to approximate these for @xmath262 we use ( see @xcite ) : @xmath263 which hold uniformly in @xmath264 ; thus in particular they hold in @xmath265 where we will be using them . here
@xmath155 is given by ( [ eq6.4 ] ) with the replacement @xmath266 .
i. : : @xmath267 has infinitely many zeros which lie on the negative real axis .
for @xmath44 large the jth zero , @xmath268 , of @xmath267 satisfies ( [ eq6.3 ] ) and the derivative satisfies @xmath269 ii .
: : for @xmath270 the function @xmath267 satisfies the asymptotic formula @xmath271 using ( i. ) we deduce that the poles , @xmath272 , are asymptotically given by ( [ eq6.1 ] ) and approximately lie on the curve @xmath273 where @xmath274 is defined in ( [ eq6.5 ] ) .
this is the curve for which @xmath275 is real and negative . to evaluate the residues we must calculate using ( [ ash]),([asdh ] ) @xmath276 where we have introduced @xmath277 obviously the scaling @xmath278 moves @xmath279 off the curve where the argument of the airy function is real and negative . thus using ( [ aiasy ] ) and ( [ eq6.4 ] ) we deduce that the asymptotic formula for @xmath258 contains an exponential term @xmath280 \nonumber\end{aligned}\ ] ] where @xmath281 here we have introduced @xmath282 . finally , we consider the real part of the expression in parentheses on the second line of ( [ resexp ] ) .
in particular we replace @xmath283 by a continuous variable @xmath284 traversing the scaled curve , @xmath274 , containing the approximate zeros .
then the function @xmath285 depends only on @xmath42 and the coordinate describing the curve ; in particular it is independent of @xmath11 and @xmath44 . in fig .
[ resasy2 ] we plot the real part of @xmath285 scaled by @xmath286 for @xmath50 .
this can be compared with fig .
[ fig2.2 ] by scaling both axes by @xmath53 and recognizing the vertical axis as the base ten logarithm .
we then observe good agreement with the numerical results .
the maximum value plotted in figure [ resasy2 ] is approximately @xmath287 , which is the predicted slope of the straight line plotted in fig .
[ fig2.1 ] .
again the agreement is good .
we note that increasing @xmath42 makes the problem somewhat worse ; the scaled maximum real part is approximately @xmath288 for @xmath289 and @xmath290 for @xmath291 .[/INST] we derive new , explicit representations for the solution to the scalar wave equation in the exterior of a sphere , subject to either dirichlet or robin boundary conditions .
our formula leads to a stable and high - order numerical scheme that permits the evaluation of the solution at an arbitrary target , without the use of a spatial grid and without numerical dispersion error . in the process , we correct some errors in the analytic literature concerning the asymptotic behavior of the logarithmic derivative of the spherical modified hankel function .
we illustrate the performance of the method with several numerical examples . 65m70 , 78a40 , 78m16 </s> |
prior to the genome era , compositional signatures ( 1 ) or sequence alignments ( 2 ) were used to delineate the phylogenetic patterns across organisms .
the availability of entire genome sequences has sparked a further development of methods for phylogenetic reconstructions on a genome - wide scale . following this long tradition in molecular evolution ,
similar methods were expanded to encompass complete genome information , based on either compositional patterns ( 3,4 ) or concatenated alignments of orthologs ( 5,6 ) .
more recently , methods that exploit the entire gene complement of completely sequenced genomes have been developed .
these include phylogenies based on patterns of conservation of gene order ( 7 ) , gene fusion events ( 8) , gene content ( 7,913 ) , protein folds ( 12 ) , and average ortholog similarity ( 14 ) .
only a few of these approaches were successful in resolving difficult cases , such as correctly grouping pathogens having highly reduced genomes with their free - living relatives and clustering proteobacteria into a monophyletic group ( 7,9,14 ) .
in addition , most of the above mentioned methods are ( i ) not scalable to hundreds of species ( e.g. concatenated alignments ) , ( ii ) unable to place correctly species with reduced genomes ( 13 ) and ( iii ) strongly affected by the number and phylogenetic proximity of species ( e.g. gene order ) ( 15 ) .
herein , we define a new composite measure termed genome conservation , which expresses both the conservation of sequence and gene content between two genomes . this value is derived from the sum of alignment scores between all proteins for every pair of organisms .
larger genomes tend to share more genes , irrespective of their phylogenetic distance ( 9 ) .
thus , a higher conservation score can result from a higher number of shared genes , rather than from phylogenetic proximity . to counterbalance this effect
the genome conservation method is naturally adjusted for missing genes and for gene lengths . if a gene is absent in one of the compared genomes , its contribution to the similarity is zero . however ,
if this absence is a direct result of reductive evolution and difference in genome sizes , absence of this gene would be calibrated by the normalization scheme described below .
the gene length is taken into account in the summation of the blast scores : longer genes generate greater alignment scores and thus , would be more important contributors than shorter genes .
thus , the final similarity is based on both gene content and average sequence similarity of genes , with the adjustment for gene length .
to obtain a similarity measure between any pair of genomes , we have compared all proteins using blastp ( 16 ) , with an e - value cut - off of e-10 , and used the bit - score as the measure of similarities between two sequences .
the bit - score has the advantages of being independent of the searched database size .
moreover , it does not calibrate for protein length , thus , longer proteins have a greater impact than shorter ones .
to eliminate noise created by paralogy in the cases when multiple hits were observed , only the best hit was used ( i.e. the most significant sequence similarity ) .
the total number of sequence similarities thus obtained exceeds 25 million pairs for 153 genomes .
we will denote the sum of all best hits between genomes a and b as (a , b ) . the usage of best blastp hits , when compared with orthologs , abolishes the issue of ortholog identification , which is still an unresolved problem for datasets of this size .
however , it results in non - reciprocal genomic similarities , that is (a , b ) (b , a ) . to calculate the conservation between genome a and genome b , we used the minimum of the two values , i.e. min((a , b ) , (b , a ) ) . to normalize for differences in genome sizes , we calculated the genome conservation distance measure d in two ways ( d1 and d2 ) : d1 = 1-s / min((a , a ) , (b , b ) ) , or d2 = ln(s/(2 * (a , a ) * (b , b)/(((a , a ) ) + ( (b , b ) ) ) ) ) .
d1 ( 9 ) and d2 ( 7 ) correspond to strategies for the transformation and normalization of self - similarity and adjustment for genome sizes , proposed previously .
the tree discussed in the text was produced using d2 , for consistency with gene content trees , reported to be optimal with this normalization ( 7 ) .
gene content trees were generated as described elsewhere ( 7 ) , using identical data as for the genome conservation tree .
average ortholog similarity was computed as the pairwise score divided by the smallest number of hits between the genomes , divided by 1000 as a scaling factor , or (a , b)/(min(n(a , b ) , n(b , a ) ) * 1000 ) , where n(a , b ) is the number of hits between genomes a and b. these values were also normalized between 0 and 100 , for comparison with other measures ( figure 2 ) .
the values of pairwise distances were used to construct a distance matrix ; trees were calculated using quicktree ( 17 ) .
bootstrap values were generated by resampling the pool of alignment scores between pairs of genomes for 1000 times .
this procedure was not applied to the gene content tree , as it requires a jack knife approach rather than genuine bootstrapping ( 7 ) . in order to evaluate the conservation within taxonomic units
, we computed an average of the conservation values , while eliminating taxonomic over - representation . within each species , we averaged the pairwise conservation values of its strains . for higher taxonomic ranks ( e.g. genus , family ) , the conservation between each pair of its sub - ranking taxa was averaged , thereby avoiding bias of unequal taxonomic sampling of sequenced species .
ideally , a species distance metric should enable the reliable inference of phylogeny across variable evolutionary time scales and taxonomic ranges . to assess the performance of genome conservation
, we used standard neighbor - joining procedures ( 17,18 ) and produced a phylogenetic tree for 153 species with known genomes ( 19 ) . the obtained tree ( supplement 1 ) clusters all the major clades consistently with current taxonomic knowledge ( 20 ) and is similar to the gene content - based tree ( 7,9 ) , with a number of important exceptions , described below .
overall , compared to gene content phylogeny ( 7 ) , a previously proposed and widely accepted method for whole - genome - based phylogenetic reconstruction , genome conservation produces significantly improved results ( supplement 2 ) . in the genome conservation tree , the alpha- , gamma- , delta- and epsilon proteobacteria form highly supported clades and consistently form a monophyletic proteobacterial clade ( figure 1a ) .
beta proteobacteria form a clade inside gamma proteobacteria , and there are two inconsistencies with the accepted taxonomy . first , aquifex aeolicus is placed within proteobacteria .
second , the pseudomonas clade and nitrosomonas europaea seem to be flipped with respect to each other . both are coupled to tree nodes with low bootstrap values ( 686 and 585 out of 1000 , respectively ) . in comparison , the gene content method fails to produce a plausible phylogenetic reconstruction of proteobacteria ( figure 1b ) , or other taxa ( supplement 2 ) .
furthermore , the average ortholog similarity approach generates a plausible scenario for evolution of proteobacteria in the shallow branches of the tree , but fails to group both delta and epsilon subdivisions with other proteobacteria , defining them as separate deeply branching groups ( data not shown ) .
the recognition of abundance of horizontal gene transfer ( hgt ) among archaea and bacteria led to the questioning whether a reliable bacterial phylogeny can possibly be reconstructed ( 22 ) .
yet , the overall agreement of whole - genome based methods , such as genome conservation , average pairwise sequence similarity , gene content and 16s rrna phylogenies clearly demonstrates the existence of a consistent bacterial phylogeny ( 23 ) . in comparative genomics , it is crucial to accurately measure the evolutionary distance between organisms .
levels of conservation of 16s rrna sequence may not be sufficient to estimate the evolutionary distance and guarantee species identity , especially in the case of recently divergent organisms ( 24 ) .
presently , species distances are often estimated in millions of years of divergence ( 2527 ) . however , the time of divergence estimated from the
molecular clock is extremely imprecise ( 28 ) and only organisms with fossil records can be dated with some accuracy ( 29 ) .
another popular form of estimating evolutionary distance is measuring the number of neutral substitutions per site .
this technique is appropriate for higher eukaryotes or closely related bacteria ; however , saturation in mutations hinders reliable estimations for highly divergent bacterial species ( 30 ) .
we propose the use of pairwise genome conservation metric as a stable whole - genome based evolutionary measurement to assess conservation between organisms .
a pictorial representation of the genome conservation matrix across all presently sequenced organisms readily demonstrates the ability of this species distance metric to define evolutionary relationships at variable taxonomic ranges , from strain variants up to the three domains of life ( figure 2a ; the complete set of values is available as supplement 3 ) .
we have compared the similarity matrices derived from the three principal genome - based phylogeny methods , namely genome conservation , gene content and average ortholog similarity . all matrices evidently contain a strong phylogenetic signal , represented both by the diagonal ( self - hits ) and various groupings of related taxa ( figure 2 ) .
all matrices are also able to clearly separate the three domains of life and delineate closely related groups .
these similarity matrices are transformed to distance matrices for the construction of phylogenetic trees ( see materials and methods ) , which produce different results .
massive gene loss in some intracellular parasites , such as buchnera and wolbachia , creates an effect where these species share their entire gene content with multiple , distantly related lineages .
the similarity estimated from gene content , normalized by the size of the minimal genome , fails to accurately estimate species distances ( figure 2b ) .
the genome conservation approach also suffers from the same effect , however on a significantly lower level ( figure 2a ) .
finally , average ortholog similarity ( figure 2c ) is independent of genome size , and thus resistant to the problem of drastically reduced genome sizes .
however , it is evident that genome conservation allows the detection of phylogenetic groupings at variable taxonomy ranges , from stains up to entire domains of life ( figure 2a ) .
despite the fact that some of these patterns are also present in the gene content and average ortholog similarity matrices ( figure 2b and c , respectively ) , their resolution is less pronounced , reflected by a blurred distribution of color - encoded similarity across taxa .
having demonstrated that the genome conservation metric reflects meaningful evolutionary relationships , we subsequently explored its ability to resolve long - standing arguments in defining the concept of bacterial taxa ( 31 ) . using genome conservation as a measure of evolutionary divergence
, we investigated how the levels of taxonomical classification in bacteria correspond to evolutionary distances ( figure 3 ) .
overall , there is a clear decrease in genome conservation at the higher taxonomic ranks .
however , the definition of some taxonomic units is not precise , and the ranges of genome conservation for various ranks often overlap ( figure 3 ) .
the other two measures , namely , gene content and average ortholog similarity , also exhibit a gradual reduction across increasing taxonomic distances , yet within a narrower value range , which renders them less effective in detecting taxonomic ranks ( data not shown ) .
it is worth noting that in all cases , the ranks of genus and family are the least well - defined , according to any genomic similarity measure . in particular , we found that the broadest distribution of genome conservation scores is observed within the genus rank .
for example , mycobacterium tuberculosis and m.bovis are 96% similar whereas mycoplasma gallisepticum , m.pneumoniae and m.penetrans are only 16% similar .
another example of questionable classification involves prochlorococcus marinus strains mit9313 and med4 , which present a challenging case for rrna - based taxonomy .
these two strains are 97% similar in their 16s rrna sequence ( 32 ) , while representing distinct genetic populations , with a 2-fold difference in genome size and content ( 33 ) , as well as specific phenotypic properties .
genome conservation between these strains is only 49% , which is more typical for distances between genera within a family , rather than strains within a species .
the genome conservation measurement of classification provides a possibility of a precise and quantitative definition of each taxonomic unit and a guide for future taxonomic classification . in summary ,
the genome conservation method uses a genomic perspective of gene content and couples it with sequence divergence at the whole - genome level . despite the limitation that an entire genome is required in order to place a species in its taxonomic context ,
this approach can delineate poorly resolved taxa and potentially be coupled with local rrna - based phylogenies . however , with the new approaches to whole - genome sequencing in environmental genomics ( 34 ) , the genome conservation approach can provide an unambiguous and consistent classification system for the newly discovered species .
the proposed species distance metric provides a clear measure based on sequence divergence for use in comparative genomics and taxonomy .
part of the complete tree of life containing the proteobacteria generated by genome conservation ( a ) and gene content ( b ) methods .
classes are color - coded , and the spirochaetum leptospira interrogans and deeply branching aquifex aeolicus are shown in black .
trees were generated using d2 normalization as described in materials and methods ; the complete tree is available in supplement 1 .
similarity matrices across all completely sequenced organisms , derived from genome conservation ( a ) , gene content ( b ) and average ortholog similarity ( c ) .
genome conservation and gene content were computed using d1 normalization ( see materials and methods ) .
species are ordered consistently across the different matrices , sorted according to their position on the genome conservation tree ( supplement 1 ) , and major clades are indicated in ( a ) .
the conservation levels in percentages are color - coded , and the values for individual pairwise scores for genome conservation are available ( supplement 3 ) .
it is evident that there are three fields of values , seen as lighter blue sub - matrices representing eukarya , archaea and bacteria , from top left to bottom right in ( a ) .
highly similar groups are evident , for instance escherichia coli strains ( red or yellow ) and enterobacteria ( green ) , both within -proteobacteria . for
see text for discussion , genome conservation computed using d1 normalization ( see materials and methods ) . | species evolutionary relationships have traditionally been defined by sequence similarities of phylogenetic marker molecules , recently followed by whole - genome phylogenies based on gene order , average ortholog similarity or gene content . here
, we introduce genome conservation a novel metric of evolutionary distances between species that simultaneously takes into account , both gene content and sequence similarity at the whole - genome level .
genome conservation represents a robust distance measure , as demonstrated by accurate phylogenetic reconstructions .
the genome conservation matrix for all presently sequenced organisms exhibits a remarkable ability to define evolutionary relationships across all taxonomic ranges .
an assessment of taxonomic ranks with genome conservation shows that certain ranks are inadequately described and raises the possibility for a more precise and quantitative taxonomy in the future .
all phylogenetic reconstructions are available at the genome phylogeny server : < > . | <s>[INST]prior to the genome era , compositional signatures ( 1 ) or sequence alignments ( 2 ) were used to delineate the phylogenetic patterns across organisms .
the availability of entire genome sequences has sparked a further development of methods for phylogenetic reconstructions on a genome - wide scale . following this long tradition in molecular evolution ,
similar methods were expanded to encompass complete genome information , based on either compositional patterns ( 3,4 ) or concatenated alignments of orthologs ( 5,6 ) .
more recently , methods that exploit the entire gene complement of completely sequenced genomes have been developed .
these include phylogenies based on patterns of conservation of gene order ( 7 ) , gene fusion events ( 8) , gene content ( 7,913 ) , protein folds ( 12 ) , and average ortholog similarity ( 14 ) .
only a few of these approaches were successful in resolving difficult cases , such as correctly grouping pathogens having highly reduced genomes with their free - living relatives and clustering proteobacteria into a monophyletic group ( 7,9,14 ) .
in addition , most of the above mentioned methods are ( i ) not scalable to hundreds of species ( e.g. concatenated alignments ) , ( ii ) unable to place correctly species with reduced genomes ( 13 ) and ( iii ) strongly affected by the number and phylogenetic proximity of species ( e.g. gene order ) ( 15 ) .
herein , we define a new composite measure termed genome conservation , which expresses both the conservation of sequence and gene content between two genomes . this value is derived from the sum of alignment scores between all proteins for every pair of organisms .
larger genomes tend to share more genes , irrespective of their phylogenetic distance ( 9 ) .
thus , a higher conservation score can result from a higher number of shared genes , rather than from phylogenetic proximity . to counterbalance this effect
the genome conservation method is naturally adjusted for missing genes and for gene lengths . if a gene is absent in one of the compared genomes , its contribution to the similarity is zero . however ,
if this absence is a direct result of reductive evolution and difference in genome sizes , absence of this gene would be calibrated by the normalization scheme described below .
the gene length is taken into account in the summation of the blast scores : longer genes generate greater alignment scores and thus , would be more important contributors than shorter genes .
thus , the final similarity is based on both gene content and average sequence similarity of genes , with the adjustment for gene length .
to obtain a similarity measure between any pair of genomes , we have compared all proteins using blastp ( 16 ) , with an e - value cut - off of e-10 , and used the bit - score as the measure of similarities between two sequences .
the bit - score has the advantages of being independent of the searched database size .
moreover , it does not calibrate for protein length , thus , longer proteins have a greater impact than shorter ones .
to eliminate noise created by paralogy in the cases when multiple hits were observed , only the best hit was used ( i.e. the most significant sequence similarity ) .
the total number of sequence similarities thus obtained exceeds 25 million pairs for 153 genomes .
we will denote the sum of all best hits between genomes a and b as (a , b ) . the usage of best blastp hits , when compared with orthologs , abolishes the issue of ortholog identification , which is still an unresolved problem for datasets of this size .
however , it results in non - reciprocal genomic similarities , that is (a , b ) (b , a ) . to calculate the conservation between genome a and genome b , we used the minimum of the two values , i.e. min((a , b ) , (b , a ) ) . to normalize for differences in genome sizes , we calculated the genome conservation distance measure d in two ways ( d1 and d2 ) : d1 = 1-s / min((a , a ) , (b , b ) ) , or d2 = ln(s/(2 * (a , a ) * (b , b)/(((a , a ) ) + ( (b , b ) ) ) ) ) .
d1 ( 9 ) and d2 ( 7 ) correspond to strategies for the transformation and normalization of self - similarity and adjustment for genome sizes , proposed previously .
the tree discussed in the text was produced using d2 , for consistency with gene content trees , reported to be optimal with this normalization ( 7 ) .
gene content trees were generated as described elsewhere ( 7 ) , using identical data as for the genome conservation tree .
average ortholog similarity was computed as the pairwise score divided by the smallest number of hits between the genomes , divided by 1000 as a scaling factor , or (a , b)/(min(n(a , b ) , n(b , a ) ) * 1000 ) , where n(a , b ) is the number of hits between genomes a and b. these values were also normalized between 0 and 100 , for comparison with other measures ( figure 2 ) .
the values of pairwise distances were used to construct a distance matrix ; trees were calculated using quicktree ( 17 ) .
bootstrap values were generated by resampling the pool of alignment scores between pairs of genomes for 1000 times .
this procedure was not applied to the gene content tree , as it requires a jack knife approach rather than genuine bootstrapping ( 7 ) . in order to evaluate the conservation within taxonomic units
, we computed an average of the conservation values , while eliminating taxonomic over - representation . within each species , we averaged the pairwise conservation values of its strains . for higher taxonomic ranks ( e.g. genus , family ) , the conservation between each pair of its sub - ranking taxa was averaged , thereby avoiding bias of unequal taxonomic sampling of sequenced species .
ideally , a species distance metric should enable the reliable inference of phylogeny across variable evolutionary time scales and taxonomic ranges . to assess the performance of genome conservation
, we used standard neighbor - joining procedures ( 17,18 ) and produced a phylogenetic tree for 153 species with known genomes ( 19 ) . the obtained tree ( supplement 1 ) clusters all the major clades consistently with current taxonomic knowledge ( 20 ) and is similar to the gene content - based tree ( 7,9 ) , with a number of important exceptions , described below .
overall , compared to gene content phylogeny ( 7 ) , a previously proposed and widely accepted method for whole - genome - based phylogenetic reconstruction , genome conservation produces significantly improved results ( supplement 2 ) . in the genome conservation tree , the alpha- , gamma- , delta- and epsilon proteobacteria form highly supported clades and consistently form a monophyletic proteobacterial clade ( figure 1a ) .
beta proteobacteria form a clade inside gamma proteobacteria , and there are two inconsistencies with the accepted taxonomy . first , aquifex aeolicus is placed within proteobacteria .
second , the pseudomonas clade and nitrosomonas europaea seem to be flipped with respect to each other . both are coupled to tree nodes with low bootstrap values ( 686 and 585 out of 1000 , respectively ) . in comparison , the gene content method fails to produce a plausible phylogenetic reconstruction of proteobacteria ( figure 1b ) , or other taxa ( supplement 2 ) .
furthermore , the average ortholog similarity approach generates a plausible scenario for evolution of proteobacteria in the shallow branches of the tree , but fails to group both delta and epsilon subdivisions with other proteobacteria , defining them as separate deeply branching groups ( data not shown ) .
the recognition of abundance of horizontal gene transfer ( hgt ) among archaea and bacteria led to the questioning whether a reliable bacterial phylogeny can possibly be reconstructed ( 22 ) .
yet , the overall agreement of whole - genome based methods , such as genome conservation , average pairwise sequence similarity , gene content and 16s rrna phylogenies clearly demonstrates the existence of a consistent bacterial phylogeny ( 23 ) . in comparative genomics , it is crucial to accurately measure the evolutionary distance between organisms .
levels of conservation of 16s rrna sequence may not be sufficient to estimate the evolutionary distance and guarantee species identity , especially in the case of recently divergent organisms ( 24 ) .
presently , species distances are often estimated in millions of years of divergence ( 2527 ) . however , the time of divergence estimated from the
molecular clock is extremely imprecise ( 28 ) and only organisms with fossil records can be dated with some accuracy ( 29 ) .
another popular form of estimating evolutionary distance is measuring the number of neutral substitutions per site .
this technique is appropriate for higher eukaryotes or closely related bacteria ; however , saturation in mutations hinders reliable estimations for highly divergent bacterial species ( 30 ) .
we propose the use of pairwise genome conservation metric as a stable whole - genome based evolutionary measurement to assess conservation between organisms .
a pictorial representation of the genome conservation matrix across all presently sequenced organisms readily demonstrates the ability of this species distance metric to define evolutionary relationships at variable taxonomic ranges , from strain variants up to the three domains of life ( figure 2a ; the complete set of values is available as supplement 3 ) .
we have compared the similarity matrices derived from the three principal genome - based phylogeny methods , namely genome conservation , gene content and average ortholog similarity . all matrices evidently contain a strong phylogenetic signal , represented both by the diagonal ( self - hits ) and various groupings of related taxa ( figure 2 ) .
all matrices are also able to clearly separate the three domains of life and delineate closely related groups .
these similarity matrices are transformed to distance matrices for the construction of phylogenetic trees ( see materials and methods ) , which produce different results .
massive gene loss in some intracellular parasites , such as buchnera and wolbachia , creates an effect where these species share their entire gene content with multiple , distantly related lineages .
the similarity estimated from gene content , normalized by the size of the minimal genome , fails to accurately estimate species distances ( figure 2b ) .
the genome conservation approach also suffers from the same effect , however on a significantly lower level ( figure 2a ) .
finally , average ortholog similarity ( figure 2c ) is independent of genome size , and thus resistant to the problem of drastically reduced genome sizes .
however , it is evident that genome conservation allows the detection of phylogenetic groupings at variable taxonomy ranges , from stains up to entire domains of life ( figure 2a ) .
despite the fact that some of these patterns are also present in the gene content and average ortholog similarity matrices ( figure 2b and c , respectively ) , their resolution is less pronounced , reflected by a blurred distribution of color - encoded similarity across taxa .
having demonstrated that the genome conservation metric reflects meaningful evolutionary relationships , we subsequently explored its ability to resolve long - standing arguments in defining the concept of bacterial taxa ( 31 ) . using genome conservation as a measure of evolutionary divergence
, we investigated how the levels of taxonomical classification in bacteria correspond to evolutionary distances ( figure 3 ) .
overall , there is a clear decrease in genome conservation at the higher taxonomic ranks .
however , the definition of some taxonomic units is not precise , and the ranges of genome conservation for various ranks often overlap ( figure 3 ) .
the other two measures , namely , gene content and average ortholog similarity , also exhibit a gradual reduction across increasing taxonomic distances , yet within a narrower value range , which renders them less effective in detecting taxonomic ranks ( data not shown ) .
it is worth noting that in all cases , the ranks of genus and family are the least well - defined , according to any genomic similarity measure . in particular , we found that the broadest distribution of genome conservation scores is observed within the genus rank .
for example , mycobacterium tuberculosis and m.bovis are 96% similar whereas mycoplasma gallisepticum , m.pneumoniae and m.penetrans are only 16% similar .
another example of questionable classification involves prochlorococcus marinus strains mit9313 and med4 , which present a challenging case for rrna - based taxonomy .
these two strains are 97% similar in their 16s rrna sequence ( 32 ) , while representing distinct genetic populations , with a 2-fold difference in genome size and content ( 33 ) , as well as specific phenotypic properties .
genome conservation between these strains is only 49% , which is more typical for distances between genera within a family , rather than strains within a species .
the genome conservation measurement of classification provides a possibility of a precise and quantitative definition of each taxonomic unit and a guide for future taxonomic classification . in summary ,
the genome conservation method uses a genomic perspective of gene content and couples it with sequence divergence at the whole - genome level . despite the limitation that an entire genome is required in order to place a species in its taxonomic context ,
this approach can delineate poorly resolved taxa and potentially be coupled with local rrna - based phylogenies . however , with the new approaches to whole - genome sequencing in environmental genomics ( 34 ) , the genome conservation approach can provide an unambiguous and consistent classification system for the newly discovered species .
the proposed species distance metric provides a clear measure based on sequence divergence for use in comparative genomics and taxonomy .
part of the complete tree of life containing the proteobacteria generated by genome conservation ( a ) and gene content ( b ) methods .
classes are color - coded , and the spirochaetum leptospira interrogans and deeply branching aquifex aeolicus are shown in black .
trees were generated using d2 normalization as described in materials and methods ; the complete tree is available in supplement 1 .
similarity matrices across all completely sequenced organisms , derived from genome conservation ( a ) , gene content ( b ) and average ortholog similarity ( c ) .
genome conservation and gene content were computed using d1 normalization ( see materials and methods ) .
species are ordered consistently across the different matrices , sorted according to their position on the genome conservation tree ( supplement 1 ) , and major clades are indicated in ( a ) .
the conservation levels in percentages are color - coded , and the values for individual pairwise scores for genome conservation are available ( supplement 3 ) .
it is evident that there are three fields of values , seen as lighter blue sub - matrices representing eukarya , archaea and bacteria , from top left to bottom right in ( a ) .
highly similar groups are evident , for instance escherichia coli strains ( red or yellow ) and enterobacteria ( green ) , both within -proteobacteria . for
see text for discussion , genome conservation computed using d1 normalization ( see materials and methods ) .[/INST]species evolutionary relationships have traditionally been defined by sequence similarities of phylogenetic marker molecules , recently followed by whole - genome phylogenies based on gene order , average ortholog similarity or gene content . here
, we introduce genome conservation a novel metric of evolutionary distances between species that simultaneously takes into account , both gene content and sequence similarity at the whole - genome level .
genome conservation represents a robust distance measure , as demonstrated by accurate phylogenetic reconstructions .
the genome conservation matrix for all presently sequenced organisms exhibits a remarkable ability to define evolutionary relationships across all taxonomic ranges .
an assessment of taxonomic ranks with genome conservation shows that certain ranks are inadequately described and raises the possibility for a more precise and quantitative taxonomy in the future .
all phylogenetic reconstructions are available at the genome phylogeny server : < > .</s> |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``FDA Renewing Efficiency From Outside
Reviewer Management Act of 2011''.
SEC. 2. PERSONS ACCREDITED TO REVIEW REPORTS UNDER 510(K) AND MAKE
RECOMMENDATIONS FOR INITIAL CLASSIFICATION.
(a) Time Period for Review of Recommendations of Accredited
Persons.--Section 523(a) of the Federal Food, Drug, and Cosmetic Act
(21 U.S.C. 360m(a)) is amended--
(1) in paragraph (1), by striking ``reviewing reports'' and
inserting ``reviewing and making recommendations to the
Secretary regarding reports''; and
(2) in paragraph (2), by amending subparagraph (B) to read
as follows:
``(B) Time period for review.--Not later than 30
days after the date on which the Secretary is notified
under subparagraph (A) by an accredited person with
respect to a recommendation regarding a report
submitted under section 510(k) or an initial
classification of a device, the Secretary shall make a
determination with respect to the recommendation. If
the Secretary fails to make such a determination by the
end of such 30-day period, the recommendation is deemed
to be accepted by the Secretary.''.
(b) Access to Device Information.--Paragraph (2) of section 523(a)
of the Federal Food, Drug, and Cosmetic Act (21 U.S.C. 360m(a)) is
amended by adding at the end the following:
``(D) Access to device information.--Subject to
section 301(j), for the purpose of providing accredited
persons with additional information to review reports
submitted under section 510(k) and make recommendations
regarding the initial classification of devices, the
Secretary shall regularly publish--
``(i) detailed decision summaries for each
clearance of a device under section 510(k),
classification of a device under section 513,
approval of an application for a device under
section 515, or grant of an exemption for a
device under section 520(m), occurring after
the date of the enactment of this subparagraph;
and
``(ii) total product life cycles
information for devices.''.
(c) Types of Devices To Be Reviewed.--Paragraph (3) of section
523(a) of the Federal Food, Drug, and Cosmetic Act (21 U.S.C. 360m(a))
is amended to read as follows:
``(3) Certain devices.--
``(A) In general.--An accredited person may be used
to perform a review regarding any report submitted
under section 510(k) except that an accredited person--
``(i) may not be used to perform a review
of a class III device; and
``(ii) may be used to perform a review of a
class II device which is intended to be
permanently implantable or life sustaining or
supporting only if a notification is submitted
under subparagraph (B).
``(B) Notification of intent to perform a review.--
Before performing a review of a report submitted under
section 510(k) for a class II device which is intended
to be permanently implantable or life sustaining or
supporting, an accredited person shall submit to the
Secretary a notification of the person's intent to
perform the review. If the Secretary does not object
within 60 days after receipt of such a notification,
the Secretary is deemed to allow the accredited person
to perform such review. If the Secretary objects to
performance of the review by the accredited person, the
Secretary shall specify in writing the basis for the
objection, including any reasons why the accredited
person is not capable of performing the review in a
manner which provides a reasonable assurance of the
safety and effectiveness of the device for its intended
purpose.''.
(d) Accreditation.--Section 523(b) of the Federal Food, Drug, and
Cosmetic Act (21 U.S.C. 360m(b)) is amended--
(1) in paragraph (2)--
(A) in the heading of subparagraph (C), by
inserting ``and training'' after ``auditing'';
(B) in subparagraph (C)--
(i) in clause (i), by striking ``and'' at
the end;
(ii) by redesignating clause (ii) as clause
(iii); and
(iii) by inserting after clause (i) the
following:
``(ii) provide for the initial training and
periodic updating of training of such person;
and''; and
(C) by adding at the end the following:
``(E) Periodic reaccreditation.--
``(i) Period.--Subject to suspension or
withdrawal under subparagraph (B), any
accreditation under this section shall be valid
for a period of 3 years after its issuance.
``(ii) Response to reaccreditation
request.--Upon the submission of a request by
an accredited person to be reaccredited under
this section, the Secretary shall approve or
deny such request not later than 60 days after
receipt of the request.
``(iii) Criteria.--Not later than 120 days
after the date of the enactment of this
subparagraph, the Secretary shall establish and
publish in the Federal Register criteria to
reaccredit or deny reaccreditation to persons
under this section. The reaccreditation of
persons under this section shall specify the
particular activities under subsection (a) for
which such persons are accredited.'';
(2) in paragraph (3)--
(A) in subparagraph (A), by inserting ``a sole
practitioner or'' after ``may not be'';
(B) in subparagraph (B), by striking ``such a
manufacturer, supplier, or vendor'' and inserting ``a
manufacturer, supplier, or vendor of devices of the
type for which such person is accredited''; and
(C) in subparagraph (D), by striking ``devices''
and inserting ``devices of the type for which such
person is accredited'';
(3) by striking paragraph (4) (relating to selection of
accredited persons); and
(4) by redesignating paragraph (5) as paragraph (4).
(e) Duration of Authority.--Section 523(c) of the Federal Food,
Drug, and Cosmetic Act (21 U.S.C. 360m(c)) is amended by striking
``October 1, 2012'' and inserting ``October 1, 2017''.
(f) Report.--Section 523(d) of the Federal Food, Drug, and Cosmetic
Act (21 U.S.C. 360m(d)) is amended by striking ``January 10, 2007'' and
inserting ``January 15, 2015''.
SEC. 3. PERSONS ACCREDITED TO CONDUCT INSPECTIONS.
Section 704(g)(11) of the Federal Food, Drug, and Cosmetic Act (21
U.S.C. 374(g)(11)) is amended by striking ``October 1, 2012'' and
inserting ``October 1, 2017''. | FDA Renewing Efficiency From Outside Reviewer Management Act of 2011 - Amends the Federal Food, Drug, and Cosmetic Act to revise and extend through October 1, 2017, provisions authorizing accredited persons to provide classification reports for a medical device and to inspect class II device or class III device facilities.
Deems a recommendation of an accredited person as to the classification of a medical device to be accepted by the Secretary of Health and Human Services (HHS) if the Secretary fails to make a determination with respect to the recommendation within 30 days.
Requires the Secretary to regularly publish: (1) detailed decision summaries for each clearance of a device, classification of a device, approval of an application of a device, or grant of exemption for a device occurring after the enactment of this Act; and (2) total product life cycles information for devices.
Expands the devices for which an accredited person may perform a review to include: (1) a class II device for which clinical data is required in the report, and (2) a class II device which is intended to be permanently implantable or life sustaining or supporting only if notification is provided to the Secretary before such a review. Deems the review permissible if the Secretary does not object within 60 days.
Requires the Secretary to provide for the initial training and periodic updating of training of accredited persons.
Makes accreditation valid for three years. Sets forth provisions regarding reaccreditation.
Prohibits an accredited person from being a sole practitioner. Provides that the prohibitions against an accredited person being owned or controlled by a manufacturer, supplier, or vendor of devices or engaging in the design, manufacture, promotion, or sale of devices shall apply only if the devices are of the same type for which the person is accredited. | <s>[INST]SECTION 1. SHORT TITLE.
This Act may be cited as the ``FDA Renewing Efficiency From Outside
Reviewer Management Act of 2011''.
SEC. 2. PERSONS ACCREDITED TO REVIEW REPORTS UNDER 510(K) AND MAKE
RECOMMENDATIONS FOR INITIAL CLASSIFICATION.
(a) Time Period for Review of Recommendations of Accredited
Persons.--Section 523(a) of the Federal Food, Drug, and Cosmetic Act
(21 U.S.C. 360m(a)) is amended--
(1) in paragraph (1), by striking ``reviewing reports'' and
inserting ``reviewing and making recommendations to the
Secretary regarding reports''; and
(2) in paragraph (2), by amending subparagraph (B) to read
as follows:
``(B) Time period for review.--Not later than 30
days after the date on which the Secretary is notified
under subparagraph (A) by an accredited person with
respect to a recommendation regarding a report
submitted under section 510(k) or an initial
classification of a device, the Secretary shall make a
determination with respect to the recommendation. If
the Secretary fails to make such a determination by the
end of such 30-day period, the recommendation is deemed
to be accepted by the Secretary.''.
(b) Access to Device Information.--Paragraph (2) of section 523(a)
of the Federal Food, Drug, and Cosmetic Act (21 U.S.C. 360m(a)) is
amended by adding at the end the following:
``(D) Access to device information.--Subject to
section 301(j), for the purpose of providing accredited
persons with additional information to review reports
submitted under section 510(k) and make recommendations
regarding the initial classification of devices, the
Secretary shall regularly publish--
``(i) detailed decision summaries for each
clearance of a device under section 510(k),
classification of a device under section 513,
approval of an application for a device under
section 515, or grant of an exemption for a
device under section 520(m), occurring after
the date of the enactment of this subparagraph;
and
``(ii) total product life cycles
information for devices.''.
(c) Types of Devices To Be Reviewed.--Paragraph (3) of section
523(a) of the Federal Food, Drug, and Cosmetic Act (21 U.S.C. 360m(a))
is amended to read as follows:
``(3) Certain devices.--
``(A) In general.--An accredited person may be used
to perform a review regarding any report submitted
under section 510(k) except that an accredited person--
``(i) may not be used to perform a review
of a class III device; and
``(ii) may be used to perform a review of a
class II device which is intended to be
permanently implantable or life sustaining or
supporting only if a notification is submitted
under subparagraph (B).
``(B) Notification of intent to perform a review.--
Before performing a review of a report submitted under
section 510(k) for a class II device which is intended
to be permanently implantable or life sustaining or
supporting, an accredited person shall submit to the
Secretary a notification of the person's intent to
perform the review. If the Secretary does not object
within 60 days after receipt of such a notification,
the Secretary is deemed to allow the accredited person
to perform such review. If the Secretary objects to
performance of the review by the accredited person, the
Secretary shall specify in writing the basis for the
objection, including any reasons why the accredited
person is not capable of performing the review in a
manner which provides a reasonable assurance of the
safety and effectiveness of the device for its intended
purpose.''.
(d) Accreditation.--Section 523(b) of the Federal Food, Drug, and
Cosmetic Act (21 U.S.C. 360m(b)) is amended--
(1) in paragraph (2)--
(A) in the heading of subparagraph (C), by
inserting ``and training'' after ``auditing'';
(B) in subparagraph (C)--
(i) in clause (i), by striking ``and'' at
the end;
(ii) by redesignating clause (ii) as clause
(iii); and
(iii) by inserting after clause (i) the
following:
``(ii) provide for the initial training and
periodic updating of training of such person;
and''; and
(C) by adding at the end the following:
``(E) Periodic reaccreditation.--
``(i) Period.--Subject to suspension or
withdrawal under subparagraph (B), any
accreditation under this section shall be valid
for a period of 3 years after its issuance.
``(ii) Response to reaccreditation
request.--Upon the submission of a request by
an accredited person to be reaccredited under
this section, the Secretary shall approve or
deny such request not later than 60 days after
receipt of the request.
``(iii) Criteria.--Not later than 120 days
after the date of the enactment of this
subparagraph, the Secretary shall establish and
publish in the Federal Register criteria to
reaccredit or deny reaccreditation to persons
under this section. The reaccreditation of
persons under this section shall specify the
particular activities under subsection (a) for
which such persons are accredited.'';
(2) in paragraph (3)--
(A) in subparagraph (A), by inserting ``a sole
practitioner or'' after ``may not be'';
(B) in subparagraph (B), by striking ``such a
manufacturer, supplier, or vendor'' and inserting ``a
manufacturer, supplier, or vendor of devices of the
type for which such person is accredited''; and
(C) in subparagraph (D), by striking ``devices''
and inserting ``devices of the type for which such
person is accredited'';
(3) by striking paragraph (4) (relating to selection of
accredited persons); and
(4) by redesignating paragraph (5) as paragraph (4).
(e) Duration of Authority.--Section 523(c) of the Federal Food,
Drug, and Cosmetic Act (21 U.S.C. 360m(c)) is amended by striking
``October 1, 2012'' and inserting ``October 1, 2017''.
(f) Report.--Section 523(d) of the Federal Food, Drug, and Cosmetic
Act (21 U.S.C. 360m(d)) is amended by striking ``January 10, 2007'' and
inserting ``January 15, 2015''.
SEC. 3. PERSONS ACCREDITED TO CONDUCT INSPECTIONS.
Section 704(g)(11) of the Federal Food, Drug, and Cosmetic Act (21
U.S.C. 374(g)(11)) is amended by striking ``October 1, 2012'' and
inserting ``October 1, 2017''.[/INST]FDA Renewing Efficiency From Outside Reviewer Management Act of 2011 - Amends the Federal Food, Drug, and Cosmetic Act to revise and extend through October 1, 2017, provisions authorizing accredited persons to provide classification reports for a medical device and to inspect class II device or class III device facilities.
Deems a recommendation of an accredited person as to the classification of a medical device to be accepted by the Secretary of Health and Human Services (HHS) if the Secretary fails to make a determination with respect to the recommendation within 30 days.
Requires the Secretary to regularly publish: (1) detailed decision summaries for each clearance of a device, classification of a device, approval of an application of a device, or grant of exemption for a device occurring after the enactment of this Act; and (2) total product life cycles information for devices.
Expands the devices for which an accredited person may perform a review to include: (1) a class II device for which clinical data is required in the report, and (2) a class II device which is intended to be permanently implantable or life sustaining or supporting only if notification is provided to the Secretary before such a review. Deems the review permissible if the Secretary does not object within 60 days.
Requires the Secretary to provide for the initial training and periodic updating of training of accredited persons.
Makes accreditation valid for three years. Sets forth provisions regarding reaccreditation.
Prohibits an accredited person from being a sole practitioner. Provides that the prohibitions against an accredited person being owned or controlled by a manufacturer, supplier, or vendor of devices or engaging in the design, manufacture, promotion, or sale of devices shall apply only if the devices are of the same type for which the person is accredited.</s> |
hard x - ray observations are the most efficient way of tracing emission due to accretion mechanisms , such in active galactic nuclei ( agn ) . hard x - ray selection is less affected by strong biases present at other wavelengths .
for example , a column of a few times @xmath6 @xmath5 has negligible effect in the 5 - 10 kev band , while it reduces by @xmath7 times nuclear emission below 2 kev .
soft x - ray surveys ( e.g. hasinger et al .
1998 , schmidt et al .
1998 ) are also often contaminated by non nuclear components , like emission from binaries and/or from optically thin plasmas in star - formation regions surrounding the nucleus .
optical and uv color selection is biased against objects with even modest extinction or an intrinsically ` red ' emission spectrum ( see e.g. vignali et al .
sensitive hard x - ray surveys are therefore powerful tools to select large samples of agn less biased against absorption and extinction .
our approach consists in taking advantage of the large field of view and good sensitivity of the bepposax mecs instrument ( boella et al .
1997a , b ) to survey tens to hundreds of square degrees at fluxes @xmath8 ( fiore et al .
2000a ) , and using higher sensitivity xmm - newton and chandra observations to extend the survey down to @xmath9 on several deg@xmath0 ( at this flux the majority of the hard xrb is resolved in sources ) .
the results on the optical identification of a sample of faint chandra sources discovered over the first 0.14 deg@xmath0 have been published by fiore et al .
( 2000b ) .
this approach is complementary to deep pencil beam surveys ( @xmath10 deg@xmath0 , see e.g. mushotzky et al .
2000 , hornschemeier et al .
2000 ) , and we cover a different portion of the redshift luminosity plane . our purpose is to study cosmic source populations at fluxes where a reasonably large fraction of the hard xrb is resolved ( 20 - 30% at the bepposax flux limit ) , but where the x - ray flux is high enough to provide x - ray spectral information in higher sensitivity follow - up observations .
this would allow the determination of the distribution of absorbing columns in the sources making the hard xrb , providing strong constraints on agn synthesis models for the xrb .
furthermore , large area surveys allow the search for previously ` rare ' agn , like ` red ' quasars or other minority agn populations ( kim & elvis 1999 ) and quantify their fractional contribution to the agn family .
finally , at our x - ray flux limits the optical counterparts are bright enough to allow relatively high quality optical spectroscopy , useful to investigate the physics of the sources .
the high energy large area survey ( hellas ) has been performed in the 4.5 - 10 kev band because : a ) this is the band closest to the maximum of the xrb energy density which is reachable with the current imaging x - ray telescopes , and b ) the bepposax mecs point spread function ( psf ) greatly improves with energy , providing a 95 % error radius of 1@xmath11 in the hard band ( fiore et al .
2000a ) , allowing optical identification of the x - ray sources .
about 80 deg@xmath0 of sky have been surveyed so far using 142 bepposax mecs fielda at @xmath12 deg .
( fields centered on bright extended sources and bright galactic sources were excluded from the survey , as well as fields close to lmc , smc and m33 . )
a robust detection algorithm has been used in coadded mecs1+mecs2+mecs3 ( or mecs2+mecs3 for observations performed after the failure of the mecs1 unit ) 4.5 - 10 kev images .
the method consists in first convolving the x - ray image with a wavelet function , to smooth the image and increase contrast , and then in running a standard slide - cell detection method on the smoothed image , to locate count excesses above the local background .
the statistics of each candidate detection is then accurately studied and the final net counts are estimated from the original ( un - smoothed ) image to preserve poisson statistics .
the background is calculated using source - free boxes near the source region .
the detection has been run several time for each field , changing the size of the wavelet function , to a ) take into account the variation of the mecs psf with the offaxis angle , and b ) to detect efficiently sources with variable extension .
the quality of the detection has always been checked interactively .
we used a probability threshold of 99.94 % ( about 3.5 @xmath13 ) .
sources detected in regions of radius 4 , 6 or 8 arcmin around targets ( depending on the target brightness ) have been excluded from the sample , which includes a total of 147 sources down to a 5 - 10 kev flux of @xmath14 .
count rates were converted to fluxes using a fixed conversion factor equal to 7.8@xmath15 ( 5 - 10 kev flux ) per one `` 3 mecs count '' ( 4.5 - 10 kev ) .
this factor is appropriate for a power law spectrum with @xmath16 , but due to the narrow band it is not strongly sensitive to the spectral shape : for @xmath17 and 0.8 it is 8.1 and 7.6 @xmath15 respectively .
the skycoverage varies from @xmath18 deg@xmath0 at @xmath19 to 6.6 , 50 and 84 deg@xmath0 at fluxes of @xmath20 and @xmath21 respectively . after correcting for this skycoverage
we find 16.9@xmath223.0(6.4 ) sources deg@xmath23 at @xmath24 ( fiore et al .
2000a , comastri et al . 2000 ) .
first quoted errors are the @xmath25 statistical confidence interval .
errors in brackets include systematic uncertainties , due to the lack of knowledge of the real spectrum of the faint sources .
this logn - logs corresponds to a resolved fraction of the 5 - 10 xrb equal to 20 - 30 % , depending on the xrb normalization ( comastri this meeting , vecchi et al .
the observed number counts are consistent , within the errors , with the extrapolations from the bepposax ( giommi et al 2000 ) and asca ( cagnoni et al .
1998 , ueda et al .
1999 , della ceca et al .
1999 ) 2 - 10 kev number counts , assuming an average power law spectrum with @xmath26 .
to study the spectral variety of the hellas sources we have calculated for each source the softness ratio ( s - h)/(s+h ) , s=1.3 - 4.5 kev , h=4.5 - 10 kev .
figure 1 plots ( s - h)/(s+h ) as a function of source total 5 - 10 kev flux .
sources under or close to the berillium strongback supporting the mecs window have been excluded from this analysis , because their observed softness may be systematically lower than real .
the number of the remaining sources in the sample is 126 .
many of the hellas sources have a low ( s - h)/(s+h ) , indicating a hard spectrum .
assuming @xmath16 , we find that 36(5 ) of the 126 sources have 1.3 - 4.5 kev count rates lower than that expected at confidence level @xmath27 .
large absorbing columns densities are likely responsible for the hard spectrum of these sources .
a deficit of very hard sources at fluxes @xmath28 is also evident in figure 1 .
this can be due to both an astrophysical and a technical reason .
the first is a redshift effect : the observed softness ratio of sources with similar intrinsic absorbing column density increases with the redshift , as the observed cut - off energy moves toward lower energies .
the second is the mecs reduced sensitivity to hard sources , due to the rapid increase of the vignetting of the telescopes with the energy and with the off - axis angle . to quantify the latter effect we have computed loci of equal 4.5 - 10 kev count rate for a given flux , shown by dashed lines in figure 1 .
the strong curvature of these lines toward low values of ( s - h)/(s+h ) indicate that a large part of the deficit of faint hard sources is probably due to this effect .
the curves are bent toward high flux values at high ( s - h)/(s+h ) too , because the mecs sensitivity is reduced for very soft sources by the berillium window , which absorbs most photons below @xmath29 kev .
the 4.5 - 10 kev sensitivity is maximum for an unabsorbed power law spectrum of @xmath30 .
correlations of the hellas source catalog with catalogs of cosmic sources provide 26 coincidences ( 7 radio - loud agn , 13 radio - quiet agn , 6 clusters of galaxies ) , suggesting that most of the hellas sources are agn .
optical spectroscopic follow - ups have been performed on about 45 hellas error - boxes , providing 36 new identifications ( fiore et al .
1999 , la franca et al .
2000 in preparation ) .
the radio - quiet agn sample includes : \i ) 28 broad line blue continuum quasars \ii ) 2 broad line ` red ' continuum quasars \iii ) 14 type 1.8 - 1.9 - 2 agn \iv ) 5 sources have optical spectra typical of liners of starburst galaxies ( all have strong [ oii ] emission ) .
[ lines ] .*mean ( s - h)/(s+h ) and b r of hellas radio - quiet agn * [ cols="<,^,^,^,^",options="header " , ] @xmath31 the number of chance coincidences in 45 error boxes is @xmath32 for broad line quasar and @xmath33 for narrow line agn ( including in this category strong [ oii ] emission line galaxies like liners and starburst galaxies ) .
@xmath31 at least 5 of the narrow emission line agn lie in small groups and/or in interacting couples .
@xmath31 about 1/3 of the error - boxes studied in detail contains no ` reasonable ' ( in terms of x - ray to optical ratio of known classes of sources ) counterpart to the x - ray source down to r=20.5 @xmath31 optical spectroscopy indicates a wide variety of spectra , with a large fraction of `` intermediate '' objects ( type 1.8 - 1.9 agn , ` red ' quasars ) .
figure 2a ) plots the luminosity of the identified hellas sources as a function of their redshift .
we have identifications of broad line quasars up to z=2.76 and luminosity of @xmath34 erg s@xmath35 , and of narrow line agn up to z=0.4 and luminosity of @xmath36 erg s@xmath35 .
figure 2b ) plots the ( s - h)/(s+h ) of the identified sources as a function of their b
note as the broad line agn are relatively well separated from the narrow line agn in the diagram , although the scatter in both b r and ( s - h)/(s+h ) is large for both class of agn ( also see table 1 ) . both ( s - h)/(s+h ) and b
r of broad line agn are different ( at the @xmath37 level ) from that of narrow line agn , which , on average , have a lower ( s - h)/(s+h ) , and are therefore likely to be more x - ray absorbed , and an higher b
r , and are therefore subjected to a greater extinction .
( s - h)/(s+h ) is plotted as a function of the redshift in figure 3 for the 53 identified sources detected far from the berillium strongback supporting the mecs window .
the dotted lines represent the expectation of unabsorbed power law with @xmath17 and 0.8 .
the dashed lines represent the expectations of a power law absorbed by columns of @xmath38 , @xmath39 and @xmath40 @xmath5 respectively , in the source frame .
note that the softness ratios of constant column density models strongly increases with the redshift .
most of the narrow line agn have ( s - h)/(s+h ) inconsistent with that expected from a power law model with @xmath17 .
absorbing columns , of the order of @xmath4 @xmath5 , are most likely implied .
note also that some of the broad line agn have ( s - h)/(s+h ) inconsistent with that expected for a @xmath41 power law , in particular at high redshift .
the ( s - h)/(s+h ) of the 24 broad line agns is marginally anticorrelated with z ( spearman rank correlation coefficent of -0.364 for 22 degrees of freedom , corresponding to a probability of 92% ) . the number of sources is not large enough to reach a definite conclusion , but it is interesting to note that this correlation goes in the opposite direction than expected .
in fact , the ratio of the optical depth in the optical band , due to dust extinction , to that in the x - ray band , due to photoelectric absorption , should scale as @xmath42 .
highly x - ray obscured broad line blue continuum quasar can exist only if their dust to gas ratio or their dust composition strongly differs from the galactic one ( also see maiolino , this meeting ) .
similar results have been recently found in asca samples by akiyama et al .
( 1999 ) and della ceca et al .
( this meeting ) .
xmm - newton and chandra follow - up observation may easily confirm or disregard a significant absorbing column in these high z broad line quasars .
figure 4 shows the hard x - ray ( 5 - 10 kev ) to optical ( r band ) flux ratio as a function of the x - ray flux for the identified hellas sources and a sample of relatively bright , nearby agn observed by bepposax ( seyfert 1 galaxies , seyfert 2 galaxies , pg quasars with z@xmath430.4 ) . the x - ray to optical ratio of the hellas sources is similar to that of the x - ray brightest objects in the local universe ( with the exception of x - ray selected blazars , like the hbl , which have higher x - ray to optical ratio , but also a relatively strong radio emission ) . while supporting the robustness of our identifications
, this suggests that roughly one third of the hard x - ray background is due to sources similar to local seyferts and quasars .
photometric infrared and optical observations of 10 hellas sources have been carried out using the telescopio nazionale galileo ( tng ; maiolino et al .
the sample includes 4 broad line ` blue ' quasars , 2 broad line ` red ' quasars , 3 type 1.9 agn and 1 liner .
the b , r and j photometry of the 2 ` red ' quasars and the 4 narrow line galaxies is dominated by the emission from the host galaxy .
agn contribution is observed in the k band , especially in the 2 ` red ' quasar .
this means that many , if not most of the objects making the hard x - ray background can not be distinguished from normal galaxies using optical and near - ir photometry .
in fact only the 4 broad line blue quasar would have passed the color criterion of the pg catalog , thus indicating that a large fraction of the accretion power in the universe may actually have been missed in optical color survey such as the bqs ( u b@xmath44 ) .
multicolor photometry techniques based on galaxy templates ( e.g. giallongo et al . 1998 ) may be efficiently used to assess the redshift of the hard x - ray selected sources .
this will be more and more important when large samples of faint x - ray sources will be available from chandra and xmm observations , and optical spectroscopic identification of all of them will not be feasible .
nearly all the 147 hellas sources have been observed in either the nvss and first surveys or by our collaboration using atca . in particular , we observed with atca 20 sources obtaining 8 5@xmath13 detections ( 40 % of the sample ) at a 5 ghz flux limit of 0.5 mjy .
this fraction is higher than in radio follow - ups of einstein and rosat x - ray surveys ( ciliegi et al . 2000 in preparation ) .
this is mainly due to the lower radio - to - x - ray flux limit ratio in our survey .
a similar fraction of radio detections was found by akiyama et al .
( 2000 ) in their correlation of the asca large sky survey sources with the first catalog , which have a radio - to - x - ray flux limit ratio similar to ours .
figure 4b ) shows the radio - to - optical broad band spectral index as a function of the x - ray - to - optical index ( arrows identify sources without a r@xmath4320 counterpart in the small radio error box ) .
note that many of the hellas detections have @xmath45 and @xmath46 consistent with that of radio quiet agn .
a large area , hard x - ray survey performed with bepposax has found a population of faint obscured agn . the x - ray data , complemented by optical , near - ir and radio follow - ups , indicate that the majority of these sources are `` intermediate '' agn i.e. type 1.8 - 1.9 agn , ` red ' quasars , obscured in x - ray by columns of the order of @xmath4 @xmath5 , but showing a wide dispersion in optical extinction .
the sample of identified hellas agn contains higher redshift analogs of nearby seyfert galaxies and quasars .
furthermore , we find marginal evidence for a population of x - ray obscured quasars at z@xmath47 showing broad lines in their optical spectra .
we thank the bepposax sdc , soc and occ teams for the successful operation of the satellite and preliminary data reduction and screening .
this research has been partly supported by asi ars/99/75 contract and murst cofin-98 - 032 contract . | the bepposax 4.5 - 10 kev high energy large area survey has covered about 80 deg@xmath0 of sky down to a flux of @xmath1 . optical spectroscopic identification of @xmath2half of the sources in the sample ( 62 ) shows that many ( @xmath3 ) are highly obscured agn , in line with the predictions of agn synthesis models for the hard x - ray background ( xrb , see e.g. comastri et al .
1995 ) .
the x - ray data , complemented by optical , near - ir and radio follow - up , indicate that the majority of these agn are `` intermediate '' objects , i.e. type 1.8 - 1.9 agn,`red ' quasars , and even a few broad line , blue continuum quasar , obscured in x - rays by columns of the order of @xmath4 @xmath5 , but showing a wide dispersion in optical extinction .
the optical and near - ir photometry of the obscured objects are dominated by galaxy starlight , indicating that a sizeable fraction of the accretion power in the universe may actually have been missed in optical color surveys .
this also implies that multicolor photometry techniques may be efficiently used to assess the redshift of the hard x - ray selected sources . | <s>[INST]hard x - ray observations are the most efficient way of tracing emission due to accretion mechanisms , such in active galactic nuclei ( agn ) . hard x - ray selection is less affected by strong biases present at other wavelengths .
for example , a column of a few times @xmath6 @xmath5 has negligible effect in the 5 - 10 kev band , while it reduces by @xmath7 times nuclear emission below 2 kev .
soft x - ray surveys ( e.g. hasinger et al .
1998 , schmidt et al .
1998 ) are also often contaminated by non nuclear components , like emission from binaries and/or from optically thin plasmas in star - formation regions surrounding the nucleus .
optical and uv color selection is biased against objects with even modest extinction or an intrinsically ` red ' emission spectrum ( see e.g. vignali et al .
sensitive hard x - ray surveys are therefore powerful tools to select large samples of agn less biased against absorption and extinction .
our approach consists in taking advantage of the large field of view and good sensitivity of the bepposax mecs instrument ( boella et al .
1997a , b ) to survey tens to hundreds of square degrees at fluxes @xmath8 ( fiore et al .
2000a ) , and using higher sensitivity xmm - newton and chandra observations to extend the survey down to @xmath9 on several deg@xmath0 ( at this flux the majority of the hard xrb is resolved in sources ) .
the results on the optical identification of a sample of faint chandra sources discovered over the first 0.14 deg@xmath0 have been published by fiore et al .
( 2000b ) .
this approach is complementary to deep pencil beam surveys ( @xmath10 deg@xmath0 , see e.g. mushotzky et al .
2000 , hornschemeier et al .
2000 ) , and we cover a different portion of the redshift luminosity plane . our purpose is to study cosmic source populations at fluxes where a reasonably large fraction of the hard xrb is resolved ( 20 - 30% at the bepposax flux limit ) , but where the x - ray flux is high enough to provide x - ray spectral information in higher sensitivity follow - up observations .
this would allow the determination of the distribution of absorbing columns in the sources making the hard xrb , providing strong constraints on agn synthesis models for the xrb .
furthermore , large area surveys allow the search for previously ` rare ' agn , like ` red ' quasars or other minority agn populations ( kim & elvis 1999 ) and quantify their fractional contribution to the agn family .
finally , at our x - ray flux limits the optical counterparts are bright enough to allow relatively high quality optical spectroscopy , useful to investigate the physics of the sources .
the high energy large area survey ( hellas ) has been performed in the 4.5 - 10 kev band because : a ) this is the band closest to the maximum of the xrb energy density which is reachable with the current imaging x - ray telescopes , and b ) the bepposax mecs point spread function ( psf ) greatly improves with energy , providing a 95 % error radius of 1@xmath11 in the hard band ( fiore et al .
2000a ) , allowing optical identification of the x - ray sources .
about 80 deg@xmath0 of sky have been surveyed so far using 142 bepposax mecs fielda at @xmath12 deg .
( fields centered on bright extended sources and bright galactic sources were excluded from the survey , as well as fields close to lmc , smc and m33 . )
a robust detection algorithm has been used in coadded mecs1+mecs2+mecs3 ( or mecs2+mecs3 for observations performed after the failure of the mecs1 unit ) 4.5 - 10 kev images .
the method consists in first convolving the x - ray image with a wavelet function , to smooth the image and increase contrast , and then in running a standard slide - cell detection method on the smoothed image , to locate count excesses above the local background .
the statistics of each candidate detection is then accurately studied and the final net counts are estimated from the original ( un - smoothed ) image to preserve poisson statistics .
the background is calculated using source - free boxes near the source region .
the detection has been run several time for each field , changing the size of the wavelet function , to a ) take into account the variation of the mecs psf with the offaxis angle , and b ) to detect efficiently sources with variable extension .
the quality of the detection has always been checked interactively .
we used a probability threshold of 99.94 % ( about 3.5 @xmath13 ) .
sources detected in regions of radius 4 , 6 or 8 arcmin around targets ( depending on the target brightness ) have been excluded from the sample , which includes a total of 147 sources down to a 5 - 10 kev flux of @xmath14 .
count rates were converted to fluxes using a fixed conversion factor equal to 7.8@xmath15 ( 5 - 10 kev flux ) per one `` 3 mecs count '' ( 4.5 - 10 kev ) .
this factor is appropriate for a power law spectrum with @xmath16 , but due to the narrow band it is not strongly sensitive to the spectral shape : for @xmath17 and 0.8 it is 8.1 and 7.6 @xmath15 respectively .
the skycoverage varies from @xmath18 deg@xmath0 at @xmath19 to 6.6 , 50 and 84 deg@xmath0 at fluxes of @xmath20 and @xmath21 respectively . after correcting for this skycoverage
we find 16.9@xmath223.0(6.4 ) sources deg@xmath23 at @xmath24 ( fiore et al .
2000a , comastri et al . 2000 ) .
first quoted errors are the @xmath25 statistical confidence interval .
errors in brackets include systematic uncertainties , due to the lack of knowledge of the real spectrum of the faint sources .
this logn - logs corresponds to a resolved fraction of the 5 - 10 xrb equal to 20 - 30 % , depending on the xrb normalization ( comastri this meeting , vecchi et al .
the observed number counts are consistent , within the errors , with the extrapolations from the bepposax ( giommi et al 2000 ) and asca ( cagnoni et al .
1998 , ueda et al .
1999 , della ceca et al .
1999 ) 2 - 10 kev number counts , assuming an average power law spectrum with @xmath26 .
to study the spectral variety of the hellas sources we have calculated for each source the softness ratio ( s - h)/(s+h ) , s=1.3 - 4.5 kev , h=4.5 - 10 kev .
figure 1 plots ( s - h)/(s+h ) as a function of source total 5 - 10 kev flux .
sources under or close to the berillium strongback supporting the mecs window have been excluded from this analysis , because their observed softness may be systematically lower than real .
the number of the remaining sources in the sample is 126 .
many of the hellas sources have a low ( s - h)/(s+h ) , indicating a hard spectrum .
assuming @xmath16 , we find that 36(5 ) of the 126 sources have 1.3 - 4.5 kev count rates lower than that expected at confidence level @xmath27 .
large absorbing columns densities are likely responsible for the hard spectrum of these sources .
a deficit of very hard sources at fluxes @xmath28 is also evident in figure 1 .
this can be due to both an astrophysical and a technical reason .
the first is a redshift effect : the observed softness ratio of sources with similar intrinsic absorbing column density increases with the redshift , as the observed cut - off energy moves toward lower energies .
the second is the mecs reduced sensitivity to hard sources , due to the rapid increase of the vignetting of the telescopes with the energy and with the off - axis angle . to quantify the latter effect we have computed loci of equal 4.5 - 10 kev count rate for a given flux , shown by dashed lines in figure 1 .
the strong curvature of these lines toward low values of ( s - h)/(s+h ) indicate that a large part of the deficit of faint hard sources is probably due to this effect .
the curves are bent toward high flux values at high ( s - h)/(s+h ) too , because the mecs sensitivity is reduced for very soft sources by the berillium window , which absorbs most photons below @xmath29 kev .
the 4.5 - 10 kev sensitivity is maximum for an unabsorbed power law spectrum of @xmath30 .
correlations of the hellas source catalog with catalogs of cosmic sources provide 26 coincidences ( 7 radio - loud agn , 13 radio - quiet agn , 6 clusters of galaxies ) , suggesting that most of the hellas sources are agn .
optical spectroscopic follow - ups have been performed on about 45 hellas error - boxes , providing 36 new identifications ( fiore et al .
1999 , la franca et al .
2000 in preparation ) .
the radio - quiet agn sample includes : \i ) 28 broad line blue continuum quasars \ii ) 2 broad line ` red ' continuum quasars \iii ) 14 type 1.8 - 1.9 - 2 agn \iv ) 5 sources have optical spectra typical of liners of starburst galaxies ( all have strong [ oii ] emission ) .
[ lines ] .*mean ( s - h)/(s+h ) and b r of hellas radio - quiet agn * [ cols="<,^,^,^,^",options="header " , ] @xmath31 the number of chance coincidences in 45 error boxes is @xmath32 for broad line quasar and @xmath33 for narrow line agn ( including in this category strong [ oii ] emission line galaxies like liners and starburst galaxies ) .
@xmath31 at least 5 of the narrow emission line agn lie in small groups and/or in interacting couples .
@xmath31 about 1/3 of the error - boxes studied in detail contains no ` reasonable ' ( in terms of x - ray to optical ratio of known classes of sources ) counterpart to the x - ray source down to r=20.5 @xmath31 optical spectroscopy indicates a wide variety of spectra , with a large fraction of `` intermediate '' objects ( type 1.8 - 1.9 agn , ` red ' quasars ) .
figure 2a ) plots the luminosity of the identified hellas sources as a function of their redshift .
we have identifications of broad line quasars up to z=2.76 and luminosity of @xmath34 erg s@xmath35 , and of narrow line agn up to z=0.4 and luminosity of @xmath36 erg s@xmath35 .
figure 2b ) plots the ( s - h)/(s+h ) of the identified sources as a function of their b
note as the broad line agn are relatively well separated from the narrow line agn in the diagram , although the scatter in both b r and ( s - h)/(s+h ) is large for both class of agn ( also see table 1 ) . both ( s - h)/(s+h ) and b
r of broad line agn are different ( at the @xmath37 level ) from that of narrow line agn , which , on average , have a lower ( s - h)/(s+h ) , and are therefore likely to be more x - ray absorbed , and an higher b
r , and are therefore subjected to a greater extinction .
( s - h)/(s+h ) is plotted as a function of the redshift in figure 3 for the 53 identified sources detected far from the berillium strongback supporting the mecs window .
the dotted lines represent the expectation of unabsorbed power law with @xmath17 and 0.8 .
the dashed lines represent the expectations of a power law absorbed by columns of @xmath38 , @xmath39 and @xmath40 @xmath5 respectively , in the source frame .
note that the softness ratios of constant column density models strongly increases with the redshift .
most of the narrow line agn have ( s - h)/(s+h ) inconsistent with that expected from a power law model with @xmath17 .
absorbing columns , of the order of @xmath4 @xmath5 , are most likely implied .
note also that some of the broad line agn have ( s - h)/(s+h ) inconsistent with that expected for a @xmath41 power law , in particular at high redshift .
the ( s - h)/(s+h ) of the 24 broad line agns is marginally anticorrelated with z ( spearman rank correlation coefficent of -0.364 for 22 degrees of freedom , corresponding to a probability of 92% ) . the number of sources is not large enough to reach a definite conclusion , but it is interesting to note that this correlation goes in the opposite direction than expected .
in fact , the ratio of the optical depth in the optical band , due to dust extinction , to that in the x - ray band , due to photoelectric absorption , should scale as @xmath42 .
highly x - ray obscured broad line blue continuum quasar can exist only if their dust to gas ratio or their dust composition strongly differs from the galactic one ( also see maiolino , this meeting ) .
similar results have been recently found in asca samples by akiyama et al .
( 1999 ) and della ceca et al .
( this meeting ) .
xmm - newton and chandra follow - up observation may easily confirm or disregard a significant absorbing column in these high z broad line quasars .
figure 4 shows the hard x - ray ( 5 - 10 kev ) to optical ( r band ) flux ratio as a function of the x - ray flux for the identified hellas sources and a sample of relatively bright , nearby agn observed by bepposax ( seyfert 1 galaxies , seyfert 2 galaxies , pg quasars with z@xmath430.4 ) . the x - ray to optical ratio of the hellas sources is similar to that of the x - ray brightest objects in the local universe ( with the exception of x - ray selected blazars , like the hbl , which have higher x - ray to optical ratio , but also a relatively strong radio emission ) . while supporting the robustness of our identifications
, this suggests that roughly one third of the hard x - ray background is due to sources similar to local seyferts and quasars .
photometric infrared and optical observations of 10 hellas sources have been carried out using the telescopio nazionale galileo ( tng ; maiolino et al .
the sample includes 4 broad line ` blue ' quasars , 2 broad line ` red ' quasars , 3 type 1.9 agn and 1 liner .
the b , r and j photometry of the 2 ` red ' quasars and the 4 narrow line galaxies is dominated by the emission from the host galaxy .
agn contribution is observed in the k band , especially in the 2 ` red ' quasar .
this means that many , if not most of the objects making the hard x - ray background can not be distinguished from normal galaxies using optical and near - ir photometry .
in fact only the 4 broad line blue quasar would have passed the color criterion of the pg catalog , thus indicating that a large fraction of the accretion power in the universe may actually have been missed in optical color survey such as the bqs ( u b@xmath44 ) .
multicolor photometry techniques based on galaxy templates ( e.g. giallongo et al . 1998 ) may be efficiently used to assess the redshift of the hard x - ray selected sources .
this will be more and more important when large samples of faint x - ray sources will be available from chandra and xmm observations , and optical spectroscopic identification of all of them will not be feasible .
nearly all the 147 hellas sources have been observed in either the nvss and first surveys or by our collaboration using atca . in particular , we observed with atca 20 sources obtaining 8 5@xmath13 detections ( 40 % of the sample ) at a 5 ghz flux limit of 0.5 mjy .
this fraction is higher than in radio follow - ups of einstein and rosat x - ray surveys ( ciliegi et al . 2000 in preparation ) .
this is mainly due to the lower radio - to - x - ray flux limit ratio in our survey .
a similar fraction of radio detections was found by akiyama et al .
( 2000 ) in their correlation of the asca large sky survey sources with the first catalog , which have a radio - to - x - ray flux limit ratio similar to ours .
figure 4b ) shows the radio - to - optical broad band spectral index as a function of the x - ray - to - optical index ( arrows identify sources without a r@xmath4320 counterpart in the small radio error box ) .
note that many of the hellas detections have @xmath45 and @xmath46 consistent with that of radio quiet agn .
a large area , hard x - ray survey performed with bepposax has found a population of faint obscured agn . the x - ray data , complemented by optical , near - ir and radio follow - ups , indicate that the majority of these sources are `` intermediate '' agn i.e. type 1.8 - 1.9 agn , ` red ' quasars , obscured in x - ray by columns of the order of @xmath4 @xmath5 , but showing a wide dispersion in optical extinction .
the sample of identified hellas agn contains higher redshift analogs of nearby seyfert galaxies and quasars .
furthermore , we find marginal evidence for a population of x - ray obscured quasars at z@xmath47 showing broad lines in their optical spectra .
we thank the bepposax sdc , soc and occ teams for the successful operation of the satellite and preliminary data reduction and screening .
this research has been partly supported by asi ars/99/75 contract and murst cofin-98 - 032 contract .[/INST] the bepposax 4.5 - 10 kev high energy large area survey has covered about 80 deg@xmath0 of sky down to a flux of @xmath1 . optical spectroscopic identification of @xmath2half of the sources in the sample ( 62 ) shows that many ( @xmath3 ) are highly obscured agn , in line with the predictions of agn synthesis models for the hard x - ray background ( xrb , see e.g. comastri et al .
1995 ) .
the x - ray data , complemented by optical , near - ir and radio follow - up , indicate that the majority of these agn are `` intermediate '' objects , i.e. type 1.8 - 1.9 agn,`red ' quasars , and even a few broad line , blue continuum quasar , obscured in x - rays by columns of the order of @xmath4 @xmath5 , but showing a wide dispersion in optical extinction .
the optical and near - ir photometry of the obscured objects are dominated by galaxy starlight , indicating that a sizeable fraction of the accretion power in the universe may actually have been missed in optical color surveys .
this also implies that multicolor photometry techniques may be efficiently used to assess the redshift of the hard x - ray selected sources . </s> |
the piperaceae is a huge family of plants , which has been extensively used for traditional medicine . in thailand ,
the ethanol extract of stem showed larvicidal effect and the methanol extract exhibited inhibitory activity on acetylcholinesterase enzyme .
p. chaba or p. longum linn . or long pepper has various thai local names such as di - pli , prik - hang , dipli - chueak . in thai traditional systems of medicine ,
the dried mature unripe fruits of this plant find wide application as carminative , element tonic , antidiarrheal , expectorant and oxytocic for postlabor .
the fruit extract of p. chaba has been shown to exhibit various activities including anti - inflammation [ 57 ] , hepatoprotection , cytotoxicity and antitumor , chemoprevention , antiangiogenesis , immunomodulation , and adipogenesis .
the purpose of this study was to evaluate anti - inflammatory , analgesic , and antipyretic activities of ethanol extract from stem of p. interruptum and fruit of p. chaba in animal models .
stem of p. interruptum ( pi ) was collected from phupan , sakhonnakhon and fruit of p. chaba ( pc ) from khaosaming , chanthaburi , thailand .
the certifications of plant materials were carried out at the herbarium of department of forestry , bangkok , whereas the herbarium vouchers have been kept at the herbarium of southern center of thai medicinal plant at faculty of pharmaceutical science , prince of songkhla university , songkhla , thailand .
skp 146160901 and skp 146160301 are voucher numbers of p. interruptum and p. chaba , respectively .
next , they were cut into small pieces and dried at 50c , powdered , and extracted following a similar procedure of thai traditional practice . dried ground plant material ( 1 kg )
was macerated with 95% ethanol for 3 days , filtered and concentrated to dryness under pressure .
the percentage yields of pi and pc extracts were calculated as 2.47 and 10.89 , respectively .
male sprague - dawley rats weighing 4060 , 100120 , and 200250 g as well as male icr mice weighting 3040 g were obtained from national laboratory animal center , nakorn pathom , thailand .
they were kept in a room maintained under environmental conditions of 25 1c and 12 h dark - light cycle .
rats were kept in the experimental facility for 1 week to allow them to be acclimated prior to dosing .
the animal ethics committee of faculty of medicine , thammasat university , pathumthani , thailand , approved all experimental protocols ( no . 0002/2008 ) .
male rats weighing 4060 g were used for topical application of epp 1 mg/20 l / ear to induce edema on the inner and outer surface of both ears .
the test substances were applied in the same manner in a volume of 20 l prior to applying the irritants .
control group received acetone ( 20 l / ear ) , and the reference group received 1 mg/20 l / ear of phenylbutazone in acetone .
the test group received pi or pc extract at the dose of 1 mg/20 l / ear .
the thickness of each ear was measured with a digital vernier caliper before and at 15 , 30 , 60 , and 120 min after edema induction .
male rats weighing 100120 g were divided into five groups of six rats each .
the test groups were received pi or pc extract ( 300 , 600 , 1,200 mg / kg ) , aspirin ( 300 mg / kg ) , and 5% tween80 ( control ) .
a volume of 0.05 ml of 1% carrageenan in sterile normal saline solution ( nss ) was injected intradermally into the plantar side of the right hind paw of rat .
the edema volumes were determined using a plethysmometer ( model 7140 , ugo basile , italy ) before and 1 , 3 , and 5 h after carrageenan injection .
two sterilized cotton pellets ( 20 1 mg ) were implanted subcutaneously ; one on each side of the abdomen under thiopental anesthesia .
the pi or pc extract ( 1,200 mg / kg ) , aspirin ( 300 mg / kg ) , and prednisolone ( 5 mg / kg ) were orally administered once daily in a dosage regimen for 7 days , whereas the control group received 5% tween only . on the 8th day after implantation
, rats were anaesthetized with thiopental sodium ( 50 mg / kg , intraperitoneally ) . both cotton pellets and thymus were dissected , dried at 60c for 18 h and their dry weight determined .
change in body weight from the beginning and the end of experiment was also recorded . the transudative and granuloma weights were calculated as well as percent granuloma inhibition of the test drugs .
male icr mice weighing 3040 g were divided into six groups of six animals each .
aspirin ( 300 mg / kg ) and morphine ( 10 mg / kg ) were used as a reference group .
pi and pc extract were administered at the doses of 300 , 600 , and 1,200 mg / kg . the formalin test consists of two distinctive phases . for the early phase assessment , test substances
were orally administered to male icr mice 1 h , whereas morphine was injected intraperitoneally 30 min before the formalin injection .
twenty l of 1% formalin in nss was injected subcutaneously into the left dorsal hind paw .
time mice spent on licking of the injected hind paw was determined between 05 min after the formalin injection . in the late phase
, formalin was injected after oral administration of test substances for 40 min , or morphine injection for 10 min .
next , the licking time was determined between 20 and 30 min after the formalin injection . before inducing pyrexia ,
the initial rectal temperature of male rats weighing 200250 g was recorded using a twelve - channel electric thermometer ( letica , model tmp 812 rs , panlab s.l . , spain ) .
next , hyperthermia was induced by subcutaneous injection of 1 ml/100 g body weight of 25% yeast in nss .
then , those animals which show a rise in rectal temperature of more than 1c were orally administered with test substances ; pi and pc extracts were ( 300 , 600 , 1,200 mg / kg ) , aspirin ( 300 mg / kg ) , and 5% tween80 ( control group ) .
the rectal temperature of animals was recorded every 30 min for 2 h following the treatment .
statistical significance was determined by one - way analysis of variance ( anova ) and post hoc least - significant difference ( lsd ) test using spss software ( version 11.0 ) .
the epp - induced rat ear edema is suitably a common model for screening and estimating anti - inflammatory activity of test substances .
topical application of epp on rat ears produced a marked edema formation as shown in figure 1 .
pi and pc extract at the dose of 1 mg / ear significantly inhibited the ear edema formation . as a positive control , phenylbutazone ( 1 mg / ear ) exhibited significant inhibitory activity on the ear edema formation at all determination times .
next , we used the carrageenan - induced paw edema model to further confirm the activities of the extracts .
as depicted in figure 2 , pi extract , at doses of 300 , 600 , and 1,200 mg / kg reduced the paw edema at 1 , 3 , and 5 h after carrageenan injection .
similarly , pc extract , at doses of 1,200 mg / kg significantly reduced the paw edema at 3 and 5 h after carrageenan injection . the positive control aspirin ( 300 mg / kg ) markedly produced significant inhibitory effect of the paw edema at all assessment times . the cotton pellet - induced granuloma formation in rats
was further conducted to determine whether the extracts are able to inhibit the chronic inflammation .
the positive control group treated with prednisolone ( 5 mg / kg , p.o . ) , daily for 7 days elicited a noticeable inhibition on transudation and granuloma formation ( table 1 ) .
in contrast , aspirin ( 300 mg / kg ) did not reduce both parameters .
pi extract at the dose of 1,200 mg / kg decreased transudative weight , whereas pc extract reduced both transudative and granuloma weights .
in addition , pi and pc extracts , similar to prednisolone , significantly decreased the body weight gain and thymus weight of animals while aspirin did not affect those parameters ( table 2 ) .
the formalin test is an applicable and reliable model of nociception . as shown in figure 3 , all doses of pi and pc extracts , aspirin , and morphine
significantly , the pi extract had a much smaller effect in the early phase than the other treatments . in the antipyretic study , pi extract at doses of 300 , 600 , 1,200 mg / kg and aspirin significantly decreased the rectal temperature of hyperthermia rats at all recorded times ( figure 4(a ) ) .
likewise , pc extract at the doses of 600 and 1,200 mg / kg significantly reduced the rectal temperature of rats as shown in figure 4(b ) .
. possesses anti - inflammatory , analgesic , and antipyretic activities in animal models . during the acute phase of inflammation , key inflammatory mediators including histamine , serotonin , bradykinin , and prostaglandin
are released in order to promote vasodilatation and vascular permeability as well as edema . in the present study , pi and
this result suggested that pi and pc extracts possessed anti - inflammatory activity by blocking the inflammatory mediators of the acute phase of inflammation .
the carrageenan - induced paw edema is considered as a model of the acute phase of inflammation which is widely used for discovery and investigation of anti - inflammatory drug .
especially , this model is known to be sensitive to cyclooxygenase inhibitors and has been used to evaluate the effect of nsaids , which involves the inhibition of pgs synthesis .
the initial phase is caused by the release of histamine , serotonin , and bradykinin and followed by the release of prostaglandins ( pgs ) at the 3rd hour and lasts for about 6 hour after carrageenan injection .
the final phase appears to be most interesting in which the maximal vascular response occurs with the leukocyte migration to the inflamed area . in the present study ,
the significant inhibitory effect of both extracts on carrageenan - induced paw edema at the 3rd hour suggests that the underlying mechanism of action of pi and pc extracts may involve blocking of the pgs synthesis and/or the other inflammatory mediators .
cotton pellet - induced granulation is commonly used to assess the transudative and proliferative components of chronic inflammation .
the subcutaneous implantation of cotton pellet in rat has been divided into at least three response phases , transudative phase , exudative phase , and proliferative phase .
the transudative phase is defined as the increase in wet weight of the pellet that occurs during first 3 hour .
an exudative phase is defined as plasma leaking from bloodstream around the granuloma that occurs between 3 and 72 hour after the implantation of pellet .
the proliferative phase is measured as the increase in dry weight of the granuloma that occurs between 3 and 6 days after the implantation .
in addition , the implanted material induces a host inflammatory response and modulates the release of inflammatory mediators which finally lead to tissue proliferation and granular formation [ 2224 ] .
nsaids such as aspirin elicit a slight inhibition , whereas steroidal anti - inflammation drugs strongly inhibit both transudative and proliferative phase of inflammation . in this study ,
similar to prednisolone , pi and pc extract showed similar effects on both transudative and proliferative phases and reduced the body weight gain as well as the thymus weight .
the results obtained suggest a mechanism of anti - inflammatory activity of pi and pc extract as steroidal - like effect .
the response pattern has two distinct periods of intensive licking activity , an early response ( 05 min after injection ) and a late response ( 2030 min after injection ) .
the early phase is due to direct effect of formalin on nociceptors ( noninflammatory pain ) .
the late phase response is development of an inflammatory response and release of analgesic mediators , which reflect inflammatory pain .
experimental results have indicated that substance p and bradykinin participate in the early phase , whereas histamine , serotonin , bradykinin , and pgs are involved in the late phase .
our study showed analgesic activity of pi and pc extracts on both phases of the formalin test suggesting both direct analgesic effects on the nociceptor and an inhibition of inflammatory pain .
thus , their mode of action possibly involves the synthesis and/or release of pgs and/or other pain mediators .
fever is provoked by many exogenous substances in animal models , including bacterial endotoxins and microbe infection .
exogenous pyrogen induces the production of pro - inflammatory cytokines , such as interleukin-1 ( il-1 ) , il-6 , interferon- ( ifn- ) , and tumor necrosis factor- ( tnf- ) , which enter hypothalamic circulation and stimulate the release of local prostaglandins ( pgs ) , thereby resetting the hypothalamic thermal setpoint . like aspirin ,
both pi and pc extract showed antipyretic activity which is likely due to inhibition of the synthesis and/or release of local pge2 into the preoptic area of anterior hypothalamus [ 26 , 27 ] .
the results obtained suggest their mechanism of action similar to nsaids as well as steroid - like effect .
nonetheless , the precise mechanism and the bioactive principles responsible for these actions remain to be elucidated . | piper interruptum opiz . and
piper chaba linn .
are herbaceous plants in the piperaceae family .
the ethanol extract of p. interruptum and p. chaba inhibited ethyl phenylpropiolate - induced ear edema and carrageenan - induced hind paw edema in rats . both extracts reduced transudative and granuloma weights as well as body weight gain and thymus weight of the chronic inflammatory model using cotton pellet - induced granuloma formation in rats .
moreover , both extracts exhibited analgesic activity on both early phase and late phase of formalin test in mice and also showed antipyretic activity on yeast - induced hyperthermia in rats . | <s>[INST]the piperaceae is a huge family of plants , which has been extensively used for traditional medicine . in thailand ,
the ethanol extract of stem showed larvicidal effect and the methanol extract exhibited inhibitory activity on acetylcholinesterase enzyme .
p. chaba or p. longum linn . or long pepper has various thai local names such as di - pli , prik - hang , dipli - chueak . in thai traditional systems of medicine ,
the dried mature unripe fruits of this plant find wide application as carminative , element tonic , antidiarrheal , expectorant and oxytocic for postlabor .
the fruit extract of p. chaba has been shown to exhibit various activities including anti - inflammation [ 57 ] , hepatoprotection , cytotoxicity and antitumor , chemoprevention , antiangiogenesis , immunomodulation , and adipogenesis .
the purpose of this study was to evaluate anti - inflammatory , analgesic , and antipyretic activities of ethanol extract from stem of p. interruptum and fruit of p. chaba in animal models .
stem of p. interruptum ( pi ) was collected from phupan , sakhonnakhon and fruit of p. chaba ( pc ) from khaosaming , chanthaburi , thailand .
the certifications of plant materials were carried out at the herbarium of department of forestry , bangkok , whereas the herbarium vouchers have been kept at the herbarium of southern center of thai medicinal plant at faculty of pharmaceutical science , prince of songkhla university , songkhla , thailand .
skp 146160901 and skp 146160301 are voucher numbers of p. interruptum and p. chaba , respectively .
next , they were cut into small pieces and dried at 50c , powdered , and extracted following a similar procedure of thai traditional practice . dried ground plant material ( 1 kg )
was macerated with 95% ethanol for 3 days , filtered and concentrated to dryness under pressure .
the percentage yields of pi and pc extracts were calculated as 2.47 and 10.89 , respectively .
male sprague - dawley rats weighing 4060 , 100120 , and 200250 g as well as male icr mice weighting 3040 g were obtained from national laboratory animal center , nakorn pathom , thailand .
they were kept in a room maintained under environmental conditions of 25 1c and 12 h dark - light cycle .
rats were kept in the experimental facility for 1 week to allow them to be acclimated prior to dosing .
the animal ethics committee of faculty of medicine , thammasat university , pathumthani , thailand , approved all experimental protocols ( no . 0002/2008 ) .
male rats weighing 4060 g were used for topical application of epp 1 mg/20 l / ear to induce edema on the inner and outer surface of both ears .
the test substances were applied in the same manner in a volume of 20 l prior to applying the irritants .
control group received acetone ( 20 l / ear ) , and the reference group received 1 mg/20 l / ear of phenylbutazone in acetone .
the test group received pi or pc extract at the dose of 1 mg/20 l / ear .
the thickness of each ear was measured with a digital vernier caliper before and at 15 , 30 , 60 , and 120 min after edema induction .
male rats weighing 100120 g were divided into five groups of six rats each .
the test groups were received pi or pc extract ( 300 , 600 , 1,200 mg / kg ) , aspirin ( 300 mg / kg ) , and 5% tween80 ( control ) .
a volume of 0.05 ml of 1% carrageenan in sterile normal saline solution ( nss ) was injected intradermally into the plantar side of the right hind paw of rat .
the edema volumes were determined using a plethysmometer ( model 7140 , ugo basile , italy ) before and 1 , 3 , and 5 h after carrageenan injection .
two sterilized cotton pellets ( 20 1 mg ) were implanted subcutaneously ; one on each side of the abdomen under thiopental anesthesia .
the pi or pc extract ( 1,200 mg / kg ) , aspirin ( 300 mg / kg ) , and prednisolone ( 5 mg / kg ) were orally administered once daily in a dosage regimen for 7 days , whereas the control group received 5% tween only . on the 8th day after implantation
, rats were anaesthetized with thiopental sodium ( 50 mg / kg , intraperitoneally ) . both cotton pellets and thymus were dissected , dried at 60c for 18 h and their dry weight determined .
change in body weight from the beginning and the end of experiment was also recorded . the transudative and granuloma weights were calculated as well as percent granuloma inhibition of the test drugs .
male icr mice weighing 3040 g were divided into six groups of six animals each .
aspirin ( 300 mg / kg ) and morphine ( 10 mg / kg ) were used as a reference group .
pi and pc extract were administered at the doses of 300 , 600 , and 1,200 mg / kg . the formalin test consists of two distinctive phases . for the early phase assessment , test substances
were orally administered to male icr mice 1 h , whereas morphine was injected intraperitoneally 30 min before the formalin injection .
twenty l of 1% formalin in nss was injected subcutaneously into the left dorsal hind paw .
time mice spent on licking of the injected hind paw was determined between 05 min after the formalin injection . in the late phase
, formalin was injected after oral administration of test substances for 40 min , or morphine injection for 10 min .
next , the licking time was determined between 20 and 30 min after the formalin injection . before inducing pyrexia ,
the initial rectal temperature of male rats weighing 200250 g was recorded using a twelve - channel electric thermometer ( letica , model tmp 812 rs , panlab s.l . , spain ) .
next , hyperthermia was induced by subcutaneous injection of 1 ml/100 g body weight of 25% yeast in nss .
then , those animals which show a rise in rectal temperature of more than 1c were orally administered with test substances ; pi and pc extracts were ( 300 , 600 , 1,200 mg / kg ) , aspirin ( 300 mg / kg ) , and 5% tween80 ( control group ) .
the rectal temperature of animals was recorded every 30 min for 2 h following the treatment .
statistical significance was determined by one - way analysis of variance ( anova ) and post hoc least - significant difference ( lsd ) test using spss software ( version 11.0 ) .
the epp - induced rat ear edema is suitably a common model for screening and estimating anti - inflammatory activity of test substances .
topical application of epp on rat ears produced a marked edema formation as shown in figure 1 .
pi and pc extract at the dose of 1 mg / ear significantly inhibited the ear edema formation . as a positive control , phenylbutazone ( 1 mg / ear ) exhibited significant inhibitory activity on the ear edema formation at all determination times .
next , we used the carrageenan - induced paw edema model to further confirm the activities of the extracts .
as depicted in figure 2 , pi extract , at doses of 300 , 600 , and 1,200 mg / kg reduced the paw edema at 1 , 3 , and 5 h after carrageenan injection .
similarly , pc extract , at doses of 1,200 mg / kg significantly reduced the paw edema at 3 and 5 h after carrageenan injection . the positive control aspirin ( 300 mg / kg ) markedly produced significant inhibitory effect of the paw edema at all assessment times . the cotton pellet - induced granuloma formation in rats
was further conducted to determine whether the extracts are able to inhibit the chronic inflammation .
the positive control group treated with prednisolone ( 5 mg / kg , p.o . ) , daily for 7 days elicited a noticeable inhibition on transudation and granuloma formation ( table 1 ) .
in contrast , aspirin ( 300 mg / kg ) did not reduce both parameters .
pi extract at the dose of 1,200 mg / kg decreased transudative weight , whereas pc extract reduced both transudative and granuloma weights .
in addition , pi and pc extracts , similar to prednisolone , significantly decreased the body weight gain and thymus weight of animals while aspirin did not affect those parameters ( table 2 ) .
the formalin test is an applicable and reliable model of nociception . as shown in figure 3 , all doses of pi and pc extracts , aspirin , and morphine
significantly , the pi extract had a much smaller effect in the early phase than the other treatments . in the antipyretic study , pi extract at doses of 300 , 600 , 1,200 mg / kg and aspirin significantly decreased the rectal temperature of hyperthermia rats at all recorded times ( figure 4(a ) ) .
likewise , pc extract at the doses of 600 and 1,200 mg / kg significantly reduced the rectal temperature of rats as shown in figure 4(b ) .
. possesses anti - inflammatory , analgesic , and antipyretic activities in animal models . during the acute phase of inflammation , key inflammatory mediators including histamine , serotonin , bradykinin , and prostaglandin
are released in order to promote vasodilatation and vascular permeability as well as edema . in the present study , pi and
this result suggested that pi and pc extracts possessed anti - inflammatory activity by blocking the inflammatory mediators of the acute phase of inflammation .
the carrageenan - induced paw edema is considered as a model of the acute phase of inflammation which is widely used for discovery and investigation of anti - inflammatory drug .
especially , this model is known to be sensitive to cyclooxygenase inhibitors and has been used to evaluate the effect of nsaids , which involves the inhibition of pgs synthesis .
the initial phase is caused by the release of histamine , serotonin , and bradykinin and followed by the release of prostaglandins ( pgs ) at the 3rd hour and lasts for about 6 hour after carrageenan injection .
the final phase appears to be most interesting in which the maximal vascular response occurs with the leukocyte migration to the inflamed area . in the present study ,
the significant inhibitory effect of both extracts on carrageenan - induced paw edema at the 3rd hour suggests that the underlying mechanism of action of pi and pc extracts may involve blocking of the pgs synthesis and/or the other inflammatory mediators .
cotton pellet - induced granulation is commonly used to assess the transudative and proliferative components of chronic inflammation .
the subcutaneous implantation of cotton pellet in rat has been divided into at least three response phases , transudative phase , exudative phase , and proliferative phase .
the transudative phase is defined as the increase in wet weight of the pellet that occurs during first 3 hour .
an exudative phase is defined as plasma leaking from bloodstream around the granuloma that occurs between 3 and 72 hour after the implantation of pellet .
the proliferative phase is measured as the increase in dry weight of the granuloma that occurs between 3 and 6 days after the implantation .
in addition , the implanted material induces a host inflammatory response and modulates the release of inflammatory mediators which finally lead to tissue proliferation and granular formation [ 2224 ] .
nsaids such as aspirin elicit a slight inhibition , whereas steroidal anti - inflammation drugs strongly inhibit both transudative and proliferative phase of inflammation . in this study ,
similar to prednisolone , pi and pc extract showed similar effects on both transudative and proliferative phases and reduced the body weight gain as well as the thymus weight .
the results obtained suggest a mechanism of anti - inflammatory activity of pi and pc extract as steroidal - like effect .
the response pattern has two distinct periods of intensive licking activity , an early response ( 05 min after injection ) and a late response ( 2030 min after injection ) .
the early phase is due to direct effect of formalin on nociceptors ( noninflammatory pain ) .
the late phase response is development of an inflammatory response and release of analgesic mediators , which reflect inflammatory pain .
experimental results have indicated that substance p and bradykinin participate in the early phase , whereas histamine , serotonin , bradykinin , and pgs are involved in the late phase .
our study showed analgesic activity of pi and pc extracts on both phases of the formalin test suggesting both direct analgesic effects on the nociceptor and an inhibition of inflammatory pain .
thus , their mode of action possibly involves the synthesis and/or release of pgs and/or other pain mediators .
fever is provoked by many exogenous substances in animal models , including bacterial endotoxins and microbe infection .
exogenous pyrogen induces the production of pro - inflammatory cytokines , such as interleukin-1 ( il-1 ) , il-6 , interferon- ( ifn- ) , and tumor necrosis factor- ( tnf- ) , which enter hypothalamic circulation and stimulate the release of local prostaglandins ( pgs ) , thereby resetting the hypothalamic thermal setpoint . like aspirin ,
both pi and pc extract showed antipyretic activity which is likely due to inhibition of the synthesis and/or release of local pge2 into the preoptic area of anterior hypothalamus [ 26 , 27 ] .
the results obtained suggest their mechanism of action similar to nsaids as well as steroid - like effect .
nonetheless , the precise mechanism and the bioactive principles responsible for these actions remain to be elucidated .[/INST]piper interruptum opiz . and
piper chaba linn .
are herbaceous plants in the piperaceae family .
the ethanol extract of p. interruptum and p. chaba inhibited ethyl phenylpropiolate - induced ear edema and carrageenan - induced hind paw edema in rats . both extracts reduced transudative and granuloma weights as well as body weight gain and thymus weight of the chronic inflammatory model using cotton pellet - induced granuloma formation in rats .
moreover , both extracts exhibited analgesic activity on both early phase and late phase of formalin test in mice and also showed antipyretic activity on yeast - induced hyperthermia in rats .</s> |
overwhelming observational evidence ( cf .
references in @xcite ) suggests that large - scale mixing processes took place in sn 1987a and transported newly synthesized @xmath2 from its creation site near the collapsed core all the way out to the hydrogen envelope .
spectroscopic studies of sn 1987f , sn 1988a , sn 1993j ( * ? ? ?
* and references therein ) and sn 1995v @xcite indicate that such mixing is probably generic in core collapse supernovae .
indeed , artificial mixing of the radioactive ejecta within the ( helium ) envelope is indispensable in order to reproduce the light curves and spectra of type ib explosions using one - dimensional ( 1d ) hydrodynamic models ( @xcite ; @xcite , and references therein ) .
these findings have instigated theoretical work on multidimensional supernova models focusing either on the role of convective instabilities in the delayed , neutrino - driven explosion mechanism within about the first second of evolution ( @xcite ; @xcite ; @xcite ; @xcite ; @xcite ) , or on the growth of rayleigh - taylor instabilitites during the late evolutionary stages ( @xcite ; @xcite ; @xcite ; @xcite ; @xcite ) .
however , multidimensional simulations which follow the evolution of the supernova shock from its revival due to neutrino heating , until its emergence from the stellar surface have not yet been performed . in this _ letter _ , we report on preliminary results of high - resolution two - dimensional ( 2d ) computations which for the first time cover the neutrino - driven initiation of the explosion , the accompanying convection and nucleosynthesis as well as the rayleigh - taylor mixing within the first @xmath3 seconds of evolution .
we split our simulation into two stages . the early evolution ( @xmath4s )
is followed with a version of the herakles code ( t. plewa & e. mller , in preparation ) which solves the multidimensional hydrodynamic equations using the direct eulerian version of the piecewise parabolic method @xcite augmented by the consistent multifluid advection scheme of @xcite in order to guarantee exact conservation of nuclear species .
we have added the input physics described in @xcite ( henceforth jm96 ) with the following modifications .
general relativistic corrections are made to the gravitational potential following @xcite .
a 14-isotope network is incorporated in order to compute the explosive nucleosynthesis .
it includes the 13 @xmath5-nuclei from @xmath6 to @xmath2 and a representative tracer nucleus which is used to monitor the distribution of the neutrino - heated , neutron - rich material and to replace the @xmath2 production when @xmath7 drops below @xmath8 ( cf .
our initial data are taken from the 15@xmath0 progenitor model of @xcite which was collapsed by @xcite .
the model is mapped to a 2d grid consisting of 400 radial zones ( @xmath9 cm ) , and 180 angular zones ( @xmath10 ; cf .
jm96 for details ) .
a random initial seed perturbation is added to the velocity field with a modulus of @xmath11 of the ( radial ) velocity of the post - collapse model .
the computations begin 20ms after core bounce and are continued until 885ms when the explosion energy has saturated at @xmath12erg ( this value has still to be corrected for the binding energy of the outer envelope )
. we will henceforth refer to this calculation as our `` explosion model '' .
the subsequent shock propagation through the stellar envelope and the growth of rayleigh - taylor instabilities is followed with the amra adaptive mesh refinement ( amr ) code ( t. plewa & e. mller , in preparation ) .
neutrino physics and gravity are not included in the amr calculations .
both do not influence the propagation of the shock during late evolutionary stages .
however , gravity is important for determining the amount of fallback , a problem which is outside the scope of the present study .
the equation of state takes into account contributions from photons , non - degenerate electrons , @xmath13-pairs , @xmath14 , and the nuclei included in the reaction network .
the amr calculations are started with the inner and outer boundaries located at @xmath15 cm ( i.e. inside the hot bubble containing the neutrino - driven wind ) and @xmath16 cm , respectively .
no further seed perturbations are added .
our maximum resolution is equivalent to that of a uniform grid of @xmath17 zones .
we do not include the entire star but expand the radial extent of the grid by a factor of 2 to 4 whenever the supernova shock is approaching the outer grid boundary , which is moved from its initial value out to @xmath18 cm at @xmath19s . reflecting
boundary conditions are used at @xmath20 and @xmath21 and free outflow is allowed across the inner and outer radial boundaries .
the general features of our explosion model are comparable to the models of jm96 .
the most important difference is caused by our use of general relativistic corrections to the gravitational potential . since the shock has to overcome a deeper potential well than in the newtonian case , the luminosities ( which are prescribed at the inner boundary ) required to obtain a certain final explosion energy
are roughly 20% higher than those of jm96 .
in particular , we have adopted the following set of parameters : @xmath22 ( cf .
the neutrino spectra and the temporal decay of the luminosity are the same as in jm96 . for the chosen neutrino luminosities the shock starts to move out of the iron core almost immediately .
convection between shock and gain radius sets in @xmath23ms after the start of the simulation in form of rising blobs of heated , deleptonized material ( with @xmath24 ) separated by narrow downflows with @xmath25 .
the shock reaches the fe / si interface at @xmath26 cm after @xmath27ms . at this time
the shocked material is still in nuclear statistical equilibrium and is composed mainly of @xmath5-particles and nucleons .
when the temperature right behind the shock drops below @xmath28k , @xmath2 starts to form in a narrow shell . during the ongoing expansion and cooling , nickel is also synthesized in the convective region
however , this synthesis proceeds exclusively in the narrow downflows which separate the rising bubbles and have a sufficiently high electron fraction @xmath7 .
the convective anisotropies therefore lead to a highly inhomogeneous nickel distribution ( fig .
[ fig : hotb ] ) .
freezeout of complete silicon burning occurs at @xmath29ms , and convection ceases at @xmath30ms , at which time the flow pattern becomes frozen in .
subsequently , the entire post - shock region expands nearly uniformly .
the post - shock temperature drops below @xmath31k at @xmath32ms , when the shock is about to cross the si / o interface .
thus , our model shows only moderate oxygen burning ( due to a non - vanishing oxygen abundance in the silicon shell ) , and negligible neon and carbon burning .
this is caused by the specific structure of the progenitor model of @xcite and may change when different ( e.g. more massive ) progenitors are used . in total ,
@xmath33 of @xmath2 are produced , while @xmath34 of material are synthesized at conditions with @xmath35 and end up as neutron - rich nuclei .
[ fig : hotb ] shows the @xmath2 distribution at @xmath36ms . the density ratio between the dense regions which contain the nickel and the low - density , deleptonized material in the bubbles deeper inside is @xmath37 .
during the next seconds the shock detaches from the formerly convective shell that carries the products of explosive nucleosynthesis and crosses the c+o / he - interface , initially accelerating and subsequently decelerating due to the varying density gradient .
twenty seconds after core bounce this unsteady propagation speed of the shock has led to a strong compression of the metal - containing shell . at the inner boundary of the shell pressure waves
have steepened into a reverse shock .
rayleigh - taylor instabilities start to grow at the ni+si / o- and c+o / he - interfaces and are fully developed and interact with each other at @xmath38s .
nickel and silicon are dragged upward into the helium shell in rising mushrooms on angular scales from @xmath39 to about @xmath40 , whereas helium is mixed inward in bubbles .
oxygen and carbon , located in intermediate layers of the progenitor , are swept outward as well as inward in rising and sinking flows . at @xmath41s
the densities and radial velocities between the dense mushrooms and clumps and the ambient medium differ by factors up to 5 and 1.3 , respectively . as fig .
[ fig : amra ] shows , the fastest mushrooms have already propagated out to more than half the radius of the he core .
the excessive outflows along the symmetry axis in fig .
[ fig : amra ] are a numerical artifact caused by the singularity of the polar axis in spherical coordinates . in order not to introduce large errors , only an angular wedge with @xmath42
was used in all the analyses .
the remarkable efficiency of the mixing is clearly visible from fig .
[ fig : mixing ] where the original onion - shell structure of the progenitor s metal core has disappeared after 300s .
we observe large composition gradients between different regions of a mushroom and also between different mushrooms .
some of them contain @xmath2 mass fractions of more than 70% whereas others have only nickel admixtures of 20% or less but show high concentrations of silicon and oxygen .
composition contrasts of at least this magnitude have recently been observed in different filaments of the cas a supernova remnant by @xcite .
we find that also more than @xmath43 of matter consisting of neutron - rich nuclei are mixed into the @xmath2 and @xmath44 clumps .
the reverse shock substantially decelerates the bulk of the nickel from @xmath45km / s at @xmath46ms to 3200 4500km / s at @xmath38s , at which time the maximum velocities @xmath47 have dropped to 5800km / s . after another 50s ,
however , the clumps start to move essentially ballistically through the helium core and only a slight drop of @xmath47 from @xmath48 km / s at @xmath49s to @xmath50km / s at @xmath19s occurs , when most of the @xmath2 has velocities below @xmath51km / s ( fig.[fig : nickelv ] ) .
we have recently accomplished to follow the subsequent evolution of our model up to 16000s after core bounce .
similar to the situation at the c+o / he interface , the supernova shock leaves behind a dense ( rayleigh - taylor unstable ) shell at the he / h interface . while the entire shell is rapidly slowed down , a second reverse shock forms at its inner boundary ( fig .
[ fig : amra ] ) .
our high - resolution simulations reveal a potentially severe problem for the mixing of heavy elements into the hydrogen envelope of type ii supernovae like sn 1987a .
we find that the fast nickel containing clumps , after having penetrated through this reverse shock , dissipate a large fraction of their kinetic energy in bow shocks created by their supersonic motion through the shell medium .
this leads to their deceleration to @xmath52 km / s in our calculations , a negative effect on the clump propagation which has not been discussed previously .
a detailed analysis of this result will be subject of a forthcoming publication .
our calculations provide a _ natural _ explanation for the mixing of @xmath2 into the helium layer , which is required to reproduce the light curves of type ib supernovae @xcite . in this sense
they justify the rather large seed perturbations ( @xmath53 ) which were imposed by @xcite on the radial velocity given from spherically symmetric models of exploding helium cores at about 10@xmath54s after shock formation .
in addition , they may have interesting implications for the modeling of type ib spectra ( woosley , private communication ; compare fig .
[ fig : mixing ] of this work with fig . 7 in @xcite ) .
our simulations suggest that ballistically moving , metal - rich clumps with velocities up to more than @xmath55km / s are ejected during the explosion of type ib ( and ic ) supernovae . in case of type ii supernovae
, however , the dense shell left behind by the shock passing the boundary between helium core and hydrogen envelope , causes a substantial deceleration of the clumps .
the high iron velocities observed in sn 1987a , for example , can therefore not be accounted for by our models .
this problem would be reduced if the density profile at the he / h interface were smoother , leading to less strong variations of the shock velocity .
could this direct to a possible common envelope phase or merger history of the progenitor star ( @xcite ; @xcite ) ? alternatively , the high iron velocities in sn 1987a could require additional energy input from ni decay @xcite or could imply a large global anisotropy of the explosion , e.g. associated with jets emerging from the collapse of a rapidly rotating stellar core @xcite . though final conclusions require three - dimensional calculations , our simulations indicate that all computations of rayleigh - taylor mixing in type ii supernovae carried out so far ( including the case of sn 1987a ; @xcite ) have been started from overly simplified initial conditions since they have neglected clump formation within the first minutes of the explosion .
the mixing of nucleosynthesis products as seen in our models poses another potential problem .
a significant fraction ( @xmath43 of a total of @xmath56 ) of the neutron - rich nuclei which are synthesized in regions with @xmath57 is dragged outward by the nickel containing mushrooms and clumps .
at least this amount will most likely be ejected in the explosion .
a detailed analysis of the nuclear composition is necessary to tell whether this is in conflict with limits from galactic chemical evolution models , which allow for at most @xmath11@xmath58 of neutron - rich nuclei to be ejected per supernova event ( e.g. , @xcite ; @xcite ) .
later fallback will not solve this potential problem : how could it disentangle the clumpy nickel ejecta from their undesirable pollution ?
a better knowledge of the luminosities and spectra of electron neutrinos and antineutrinos emitted from the nascent neutron star is therefore needed to perform more reliable calculations of the neutronization of the neutrino - heated ejecta . during the computations we became aware of oscillations with angle in parts of the postshock flow ( figs .
[ fig : hotb ] and [ fig : amra ] ) .
these are caused by the `` odd - even decoupling '' phenomenon associated with grid - aligned shocks @xcite . as a consequence ,
the maximum nickel velocities , @xmath47 , obtained in our amr calculations have probably been overestimated by @xmath59 because the growth of some of the mushrooms was influenced by the perturbations induced by this numerical defect .
the main results of our study , however , are not affected .
we note that a large number of supernova calculations performed with codes based either on the direct eulerian ( cf . figs . 22 and 24 in @xcite , fig . 20 in jm96 ) , or the lagrangean with remap formulation of the ppm scheme @xcite seem to be affected by this numerical flaw .
we defer a detailed analysis of this problem to a forthcoming publication .
we thank s. woosley for profiles of the progenitor star and s. bruenn for his post - bounce core model .
we acknowledge support by p. ciecielag and r. walder concerning visualization and by the crew of the rechenzentrum garching where the simulations were performed on the nec sx-4b and cray j916 computers .
tp was supported by grant 2.p03d.004.13 from the polish committee for scientific research , htj by dfg grant sfb-375 fr astro - teilchenphysik . | high - resolution two - dimensional simulations were performed for the first five minutes of the evolution of a core collapse supernova explosion in a 15@xmath0 blue supergiant progenitor .
the computations start shortly after bounce and include neutrino - matter interactions by using a light - bulb approximation for the neutrinos , and a treatment of the nucleosynthesis due to explosive silicon and oxygen burning .
we find that newly formed iron - group elements are distributed throughout the inner half of the helium core by rayleigh - taylor instabilities at the ni+si / o and c+o / he interfaces , seeded by convective overturn during the early stages of the explosion . fast moving nickel mushrooms with velocities up to @xmath1km /
s are observed .
this offers a natural explanation for the mixing required in light curve and spectral synthesis studies of type ib explosions .
a continuation of the calculations to later times , however , indicates that the iron velocities observed in sn 1987a can not be reproduced because of a strong deceleration of the clumps in the dense shell left behind by the shock at the he / h interface . | <s>[INST]overwhelming observational evidence ( cf .
references in @xcite ) suggests that large - scale mixing processes took place in sn 1987a and transported newly synthesized @xmath2 from its creation site near the collapsed core all the way out to the hydrogen envelope .
spectroscopic studies of sn 1987f , sn 1988a , sn 1993j ( * ? ? ?
* and references therein ) and sn 1995v @xcite indicate that such mixing is probably generic in core collapse supernovae .
indeed , artificial mixing of the radioactive ejecta within the ( helium ) envelope is indispensable in order to reproduce the light curves and spectra of type ib explosions using one - dimensional ( 1d ) hydrodynamic models ( @xcite ; @xcite , and references therein ) .
these findings have instigated theoretical work on multidimensional supernova models focusing either on the role of convective instabilities in the delayed , neutrino - driven explosion mechanism within about the first second of evolution ( @xcite ; @xcite ; @xcite ; @xcite ; @xcite ) , or on the growth of rayleigh - taylor instabilitites during the late evolutionary stages ( @xcite ; @xcite ; @xcite ; @xcite ; @xcite ) .
however , multidimensional simulations which follow the evolution of the supernova shock from its revival due to neutrino heating , until its emergence from the stellar surface have not yet been performed . in this _ letter _ , we report on preliminary results of high - resolution two - dimensional ( 2d ) computations which for the first time cover the neutrino - driven initiation of the explosion , the accompanying convection and nucleosynthesis as well as the rayleigh - taylor mixing within the first @xmath3 seconds of evolution .
we split our simulation into two stages . the early evolution ( @xmath4s )
is followed with a version of the herakles code ( t. plewa & e. mller , in preparation ) which solves the multidimensional hydrodynamic equations using the direct eulerian version of the piecewise parabolic method @xcite augmented by the consistent multifluid advection scheme of @xcite in order to guarantee exact conservation of nuclear species .
we have added the input physics described in @xcite ( henceforth jm96 ) with the following modifications .
general relativistic corrections are made to the gravitational potential following @xcite .
a 14-isotope network is incorporated in order to compute the explosive nucleosynthesis .
it includes the 13 @xmath5-nuclei from @xmath6 to @xmath2 and a representative tracer nucleus which is used to monitor the distribution of the neutrino - heated , neutron - rich material and to replace the @xmath2 production when @xmath7 drops below @xmath8 ( cf .
our initial data are taken from the 15@xmath0 progenitor model of @xcite which was collapsed by @xcite .
the model is mapped to a 2d grid consisting of 400 radial zones ( @xmath9 cm ) , and 180 angular zones ( @xmath10 ; cf .
jm96 for details ) .
a random initial seed perturbation is added to the velocity field with a modulus of @xmath11 of the ( radial ) velocity of the post - collapse model .
the computations begin 20ms after core bounce and are continued until 885ms when the explosion energy has saturated at @xmath12erg ( this value has still to be corrected for the binding energy of the outer envelope )
. we will henceforth refer to this calculation as our `` explosion model '' .
the subsequent shock propagation through the stellar envelope and the growth of rayleigh - taylor instabilities is followed with the amra adaptive mesh refinement ( amr ) code ( t. plewa & e. mller , in preparation ) .
neutrino physics and gravity are not included in the amr calculations .
both do not influence the propagation of the shock during late evolutionary stages .
however , gravity is important for determining the amount of fallback , a problem which is outside the scope of the present study .
the equation of state takes into account contributions from photons , non - degenerate electrons , @xmath13-pairs , @xmath14 , and the nuclei included in the reaction network .
the amr calculations are started with the inner and outer boundaries located at @xmath15 cm ( i.e. inside the hot bubble containing the neutrino - driven wind ) and @xmath16 cm , respectively .
no further seed perturbations are added .
our maximum resolution is equivalent to that of a uniform grid of @xmath17 zones .
we do not include the entire star but expand the radial extent of the grid by a factor of 2 to 4 whenever the supernova shock is approaching the outer grid boundary , which is moved from its initial value out to @xmath18 cm at @xmath19s . reflecting
boundary conditions are used at @xmath20 and @xmath21 and free outflow is allowed across the inner and outer radial boundaries .
the general features of our explosion model are comparable to the models of jm96 .
the most important difference is caused by our use of general relativistic corrections to the gravitational potential . since the shock has to overcome a deeper potential well than in the newtonian case , the luminosities ( which are prescribed at the inner boundary ) required to obtain a certain final explosion energy
are roughly 20% higher than those of jm96 .
in particular , we have adopted the following set of parameters : @xmath22 ( cf .
the neutrino spectra and the temporal decay of the luminosity are the same as in jm96 . for the chosen neutrino luminosities the shock starts to move out of the iron core almost immediately .
convection between shock and gain radius sets in @xmath23ms after the start of the simulation in form of rising blobs of heated , deleptonized material ( with @xmath24 ) separated by narrow downflows with @xmath25 .
the shock reaches the fe / si interface at @xmath26 cm after @xmath27ms . at this time
the shocked material is still in nuclear statistical equilibrium and is composed mainly of @xmath5-particles and nucleons .
when the temperature right behind the shock drops below @xmath28k , @xmath2 starts to form in a narrow shell . during the ongoing expansion and cooling , nickel is also synthesized in the convective region
however , this synthesis proceeds exclusively in the narrow downflows which separate the rising bubbles and have a sufficiently high electron fraction @xmath7 .
the convective anisotropies therefore lead to a highly inhomogeneous nickel distribution ( fig .
[ fig : hotb ] ) .
freezeout of complete silicon burning occurs at @xmath29ms , and convection ceases at @xmath30ms , at which time the flow pattern becomes frozen in .
subsequently , the entire post - shock region expands nearly uniformly .
the post - shock temperature drops below @xmath31k at @xmath32ms , when the shock is about to cross the si / o interface .
thus , our model shows only moderate oxygen burning ( due to a non - vanishing oxygen abundance in the silicon shell ) , and negligible neon and carbon burning .
this is caused by the specific structure of the progenitor model of @xcite and may change when different ( e.g. more massive ) progenitors are used . in total ,
@xmath33 of @xmath2 are produced , while @xmath34 of material are synthesized at conditions with @xmath35 and end up as neutron - rich nuclei .
[ fig : hotb ] shows the @xmath2 distribution at @xmath36ms . the density ratio between the dense regions which contain the nickel and the low - density , deleptonized material in the bubbles deeper inside is @xmath37 .
during the next seconds the shock detaches from the formerly convective shell that carries the products of explosive nucleosynthesis and crosses the c+o / he - interface , initially accelerating and subsequently decelerating due to the varying density gradient .
twenty seconds after core bounce this unsteady propagation speed of the shock has led to a strong compression of the metal - containing shell . at the inner boundary of the shell pressure waves
have steepened into a reverse shock .
rayleigh - taylor instabilities start to grow at the ni+si / o- and c+o / he - interfaces and are fully developed and interact with each other at @xmath38s .
nickel and silicon are dragged upward into the helium shell in rising mushrooms on angular scales from @xmath39 to about @xmath40 , whereas helium is mixed inward in bubbles .
oxygen and carbon , located in intermediate layers of the progenitor , are swept outward as well as inward in rising and sinking flows . at @xmath41s
the densities and radial velocities between the dense mushrooms and clumps and the ambient medium differ by factors up to 5 and 1.3 , respectively . as fig .
[ fig : amra ] shows , the fastest mushrooms have already propagated out to more than half the radius of the he core .
the excessive outflows along the symmetry axis in fig .
[ fig : amra ] are a numerical artifact caused by the singularity of the polar axis in spherical coordinates . in order not to introduce large errors , only an angular wedge with @xmath42
was used in all the analyses .
the remarkable efficiency of the mixing is clearly visible from fig .
[ fig : mixing ] where the original onion - shell structure of the progenitor s metal core has disappeared after 300s .
we observe large composition gradients between different regions of a mushroom and also between different mushrooms .
some of them contain @xmath2 mass fractions of more than 70% whereas others have only nickel admixtures of 20% or less but show high concentrations of silicon and oxygen .
composition contrasts of at least this magnitude have recently been observed in different filaments of the cas a supernova remnant by @xcite .
we find that also more than @xmath43 of matter consisting of neutron - rich nuclei are mixed into the @xmath2 and @xmath44 clumps .
the reverse shock substantially decelerates the bulk of the nickel from @xmath45km / s at @xmath46ms to 3200 4500km / s at @xmath38s , at which time the maximum velocities @xmath47 have dropped to 5800km / s . after another 50s ,
however , the clumps start to move essentially ballistically through the helium core and only a slight drop of @xmath47 from @xmath48 km / s at @xmath49s to @xmath50km / s at @xmath19s occurs , when most of the @xmath2 has velocities below @xmath51km / s ( fig.[fig : nickelv ] ) .
we have recently accomplished to follow the subsequent evolution of our model up to 16000s after core bounce .
similar to the situation at the c+o / he interface , the supernova shock leaves behind a dense ( rayleigh - taylor unstable ) shell at the he / h interface . while the entire shell is rapidly slowed down , a second reverse shock forms at its inner boundary ( fig .
[ fig : amra ] ) .
our high - resolution simulations reveal a potentially severe problem for the mixing of heavy elements into the hydrogen envelope of type ii supernovae like sn 1987a .
we find that the fast nickel containing clumps , after having penetrated through this reverse shock , dissipate a large fraction of their kinetic energy in bow shocks created by their supersonic motion through the shell medium .
this leads to their deceleration to @xmath52 km / s in our calculations , a negative effect on the clump propagation which has not been discussed previously .
a detailed analysis of this result will be subject of a forthcoming publication .
our calculations provide a _ natural _ explanation for the mixing of @xmath2 into the helium layer , which is required to reproduce the light curves of type ib supernovae @xcite . in this sense
they justify the rather large seed perturbations ( @xmath53 ) which were imposed by @xcite on the radial velocity given from spherically symmetric models of exploding helium cores at about 10@xmath54s after shock formation .
in addition , they may have interesting implications for the modeling of type ib spectra ( woosley , private communication ; compare fig .
[ fig : mixing ] of this work with fig . 7 in @xcite ) .
our simulations suggest that ballistically moving , metal - rich clumps with velocities up to more than @xmath55km / s are ejected during the explosion of type ib ( and ic ) supernovae . in case of type ii supernovae
, however , the dense shell left behind by the shock passing the boundary between helium core and hydrogen envelope , causes a substantial deceleration of the clumps .
the high iron velocities observed in sn 1987a , for example , can therefore not be accounted for by our models .
this problem would be reduced if the density profile at the he / h interface were smoother , leading to less strong variations of the shock velocity .
could this direct to a possible common envelope phase or merger history of the progenitor star ( @xcite ; @xcite ) ? alternatively , the high iron velocities in sn 1987a could require additional energy input from ni decay @xcite or could imply a large global anisotropy of the explosion , e.g. associated with jets emerging from the collapse of a rapidly rotating stellar core @xcite . though final conclusions require three - dimensional calculations , our simulations indicate that all computations of rayleigh - taylor mixing in type ii supernovae carried out so far ( including the case of sn 1987a ; @xcite ) have been started from overly simplified initial conditions since they have neglected clump formation within the first minutes of the explosion .
the mixing of nucleosynthesis products as seen in our models poses another potential problem .
a significant fraction ( @xmath43 of a total of @xmath56 ) of the neutron - rich nuclei which are synthesized in regions with @xmath57 is dragged outward by the nickel containing mushrooms and clumps .
at least this amount will most likely be ejected in the explosion .
a detailed analysis of the nuclear composition is necessary to tell whether this is in conflict with limits from galactic chemical evolution models , which allow for at most @xmath11@xmath58 of neutron - rich nuclei to be ejected per supernova event ( e.g. , @xcite ; @xcite ) .
later fallback will not solve this potential problem : how could it disentangle the clumpy nickel ejecta from their undesirable pollution ?
a better knowledge of the luminosities and spectra of electron neutrinos and antineutrinos emitted from the nascent neutron star is therefore needed to perform more reliable calculations of the neutronization of the neutrino - heated ejecta . during the computations we became aware of oscillations with angle in parts of the postshock flow ( figs .
[ fig : hotb ] and [ fig : amra ] ) .
these are caused by the `` odd - even decoupling '' phenomenon associated with grid - aligned shocks @xcite . as a consequence ,
the maximum nickel velocities , @xmath47 , obtained in our amr calculations have probably been overestimated by @xmath59 because the growth of some of the mushrooms was influenced by the perturbations induced by this numerical defect .
the main results of our study , however , are not affected .
we note that a large number of supernova calculations performed with codes based either on the direct eulerian ( cf . figs . 22 and 24 in @xcite , fig . 20 in jm96 ) , or the lagrangean with remap formulation of the ppm scheme @xcite seem to be affected by this numerical flaw .
we defer a detailed analysis of this problem to a forthcoming publication .
we thank s. woosley for profiles of the progenitor star and s. bruenn for his post - bounce core model .
we acknowledge support by p. ciecielag and r. walder concerning visualization and by the crew of the rechenzentrum garching where the simulations were performed on the nec sx-4b and cray j916 computers .
tp was supported by grant 2.p03d.004.13 from the polish committee for scientific research , htj by dfg grant sfb-375 fr astro - teilchenphysik .[/INST] high - resolution two - dimensional simulations were performed for the first five minutes of the evolution of a core collapse supernova explosion in a 15@xmath0 blue supergiant progenitor .
the computations start shortly after bounce and include neutrino - matter interactions by using a light - bulb approximation for the neutrinos , and a treatment of the nucleosynthesis due to explosive silicon and oxygen burning .
we find that newly formed iron - group elements are distributed throughout the inner half of the helium core by rayleigh - taylor instabilities at the ni+si / o and c+o / he interfaces , seeded by convective overturn during the early stages of the explosion . fast moving nickel mushrooms with velocities up to @xmath1km /
s are observed .
this offers a natural explanation for the mixing required in light curve and spectral synthesis studies of type ib explosions .
a continuation of the calculations to later times , however , indicates that the iron velocities observed in sn 1987a can not be reproduced because of a strong deceleration of the clumps in the dense shell left behind by the shock at the he / h interface . </s> |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Fiscal Accountability and
Intergovernmental Reform Act'' (``FAIR Act'').
SEC. 2. FINDINGS AND PURPOSE.
(a) Findings.--The Congress finds and declares the following:
(1) Federal legislation and regulatory requirements impose
burdens on State and local resources to implement federally
mandated programs without fully evaluating the costs to State
and local governments associated with compliance with those
requirements and oftentimes without provision of adequate
Federal financial assistance. Such Federal legislative and
regulatory initiatives--
(A) force State and local governments to utilize
scarce public resources to comply with Federal
mandates;
(B) prevent these resources from being available to
meet local needs; and
(C) detract from the ability of State and local
governments to establish local priorities for use of
local public resources.
(2) Federal legislation and regulatory programs can result
in inefficient utilization of economic resources, thereby
reducing the pool of resources available--
(A) to enhance productivity, and increase the
quantity and quality of goods and services produced by
the American economy; and
(B) to enhance international competitiveness.
(3) In implementing Congressional policy, Federal agencies
should, consistent with the requirements of Federal law, seek
to implement statutory requirements, to the maximum extent
feasible, in a manner that minimizes--
(A) the inefficient allocation of economic
resources;
(B) the burden that such requirements impose on use
of local public resources by State and local
governments; and
(C) the adverse economic effects of such
regulations on productivity, economic growth, full
employment, creation of productive jobs, and
international competitiveness of American goods and
services.
(b) Purposes.--The purposes of this Act are to--
(1) assist Congress in consideration of proposed
legislation establishing or revising Federal programs so as to
assure that, to the maximum extent practicable, legislation
enacted by Congress will--
(A) minimize the burden of such legislation on
expenditure of scarce local public resources by State
and local governments;
(B) minimize inefficient allocation of economic
resources; and
(C) reduce the adverse effect of such legislation--
(i) on the ability of State and local
governmental entities to use local public
resources to meet local needs and to establish
local priorities for local public resources;
and
(ii) on allocation of economic resources,
productivity, economic growth, full employment,
creation of productive jobs, and international
competitiveness; and
(2) require Federal agencies to exercise discretionary
authority and to implement statutory requirements in a manner
that, consistent with fulfillment of each agency's mission and
with the requirements of other laws, minimizes the impact
regulations affecting the economy have on--
(A) the ability of State and local governmental
entities to use local public resources to meet local
needs; and
(B) the allocation of economic resources,
productivity, economic growth, full employment,
creation of productive jobs, and international
competitiveness of American goods and services.
TITLE I--LEGISLATIVE REFORM
SEC. 101. REPORTS ON LEGISLATION.
(a) Report Required.--
(1) In general.--Except as provided in paragraph (2), when
a committee of the Senate or House of Representatives reports a
bill or resolution of a public character (not including a
resolution of ratification of a treaty) to its House that
mandates unfunded requirements upon State or local governments
or the private sector, the report accompanying the bill or
resolution shall contain an analysis, prepared after
consultation with the Director of the Congressional Budget
Office, detailing the effect of the new requirements on--
(A) State and local government expenditures
necessary to comply with Federal mandates;
(B) private businesses, including the economic
resources required annually to comply with the
legislation and implementing regulations; and
(C) economic growth and competitiveness.
(2) Exception.--Paragraph (1) shall not apply to any bill
with respect to which the Director of the Congressional Budget
Office certifies in writing to the chairman of the committee
reporting the legislation that the estimated costs to State and
local governments and the private sector of implementation of
such legislation during the first 3 years will not exceed
$50,000,000 in the aggregate and during the first 5 years will
not exceed $100,000,000 in the aggregate.
(b) Duties and Functions of Congressional Budget Office.--The
Director of the Congressional Budget Office shall prepare for each bill
or resolution of a public character reported by any committee of the
House of Representatives or of the Senate, an economic analysis of the
effects of the bill or resolution, satisfying the requirements of
subsection (a). The analysis prepared by the Director of the
Congressional Budget Office shall be included in the report
accompanying such bill or resolution.
(c) Legislation Subject to Point of Order.--A bill or resolution is
subject to a point of order against consideration of the bill or
resolution by the House of Representatives or the Senate (as the case
may be) if the bill or resolution is reported for consideration by the
House of Representatives or the Senate unaccompanied by the analysis
required by this section.
SEC. 102. EXERCISE OF RULEMAKING POWERS.
The provisions of this title are enacted by the Congress--
(1) as an exercise of the rulemaking power of the House of
Representatives and the Senate, respectively, and as such they
shall be considered as part of the rules of each House,
respectively, and such rules shall supersede other rules only
to the extent that they are inconsistent therewith; and
(2) with full recognition of the constitutional right of
either House to change such rules (so far as relating to such
House) at any time, in the same manner, and to the same extent
as in the case of any other rule of such House.
SEC. 103. EFFECTIVE DATE.
This title shall apply to any bill or resolution introduced in the
House of Representatives or the Senate after the date of enactment of
this Act.
TITLE II--FEDERAL INTERGOVERNMENTAL RELATIONS
SEC. 201. INTERGOVERNMENTAL AND ECONOMIC IMPACT ASSESSMENT.
(a) Requirement.--When an agency publishes a general notice of
proposed rulemaking for any proposed rule, the notice of proposed
rulemaking shall be accompanied by an Intergovernmental and Economic
Impact Assessment. Such Assessment shall be published in the Federal
Register at the time of the publication of the general notice of
proposed rulemaking for the rule.
(b) Content.--Each Intergovernmental and Economic Impact Assessment
required under this section shall contain--
(1) a description of the reasons why action by the agency
is being considered;
(2) a succinct statement of the objective of, and legal
basis for, the proposed rule;
(3) a good-faith estimate, based on data readily available
to the agency, of the effect the proposed rule will have on the
expenditure of State or local public resources by State and
local governments; and
(4) a good-faith estimate, based on data readily available
to the agency, or a description of the effect the proposed rule
will have on--
(A) the allocation of economic resources; and
(B) productivity, economic growth, full employment,
creation of productive jobs, and international
competitiveness of American goods and services.
SEC. 202. INTERGOVERNMENTAL AND ECONOMIC IMPACT STATEMENT.
(a) Requirement.--When an agency promulgates a final rule, the
agency shall prepare an Intergovernmental and Economic Impact
Statement. The Intergovernmental and Economic Impact Statement shall
contain--
(1) a succinct statement of the need for, and the
objectives of, such rule;
(2) a summary of the issues raised by the public comments
in response to the publication by the agency of the
Intergovernmental and Economic Impact Assessment prepared for
the rule, a summary of the agency's evaluation of such issues,
and a statement of any changes made in the proposed rule as a
result of such comments;
(3) a good-faith estimate, based on information readily
available to the agency, of the effect the rule will have on
the expenditure of State or local public resources by State and
local governments; and
(4) a good-faith estimate, based on information readily
available to the agency, or a description of the effect the
rule will have on productivity, economic growth, full
employment, creation of productive jobs, and international
competitiveness of American goods and services.
(b) Availability.--The agency shall make copies of each
Intergovernmental and Economic Impact Statement available to members of
the public, and shall publish in the Federal Register at the time of
publication of any final rule, a statement describing how the public
may obtain copies of such Statement.
SEC. 203. EFFECT ON OTHER LAWS.
The requirements of this title shall not alter in any manner the
substantive standards otherwise applicable to the implementation by an
agency of statutory requirements or to the exercise by an agency of
authority delegated by law.
SEC. 204. EFFECTIVE DATE.
This title shall apply to any rule proposed and any final rule
promulgated by any agency after the date of the enactment of this Act.
SEC. 205. DEFINITION.
In this title, the term ``agency'' has the meaning stated in
section 551(1) of title 5, United States Code. | TABLE OF CONTENTS:
Title I: Legislative Reform
Title II: Federal Intergovernmental Relations
Fiscal Accountability and Intergovernmental Reform Act (FAIR Act) -
Title I: Legislative Reform
- Provides that, with certain exceptions, whenever a committee of either House reports a bill or resolution of a public character (excluding resolutions of ratification of a treaty) to its House mandating unfunded requirements upon State or local governments or the private sector, the report accompanying that bill or resolution shall analyze the effect of the new requirements on: (1) State and local government expenditures necessary to comply with Federal mandates; (2) private businesses; and (3) economic growth and competitiveness. Requires the Congressional Budget Office to prepare such economic analyses.
Title II: Federal Intergovernmental Relations
- Provides that, whenever an agency publishes a general notice of proposed rulemaking or promulgates a final rule, the agency shall prepare and make available for public comment an Intergovernmental and Economic Impact Assessment. Specifies the contents of such an assessment. | <s>[INST]SECTION 1. SHORT TITLE.
This Act may be cited as the ``Fiscal Accountability and
Intergovernmental Reform Act'' (``FAIR Act'').
SEC. 2. FINDINGS AND PURPOSE.
(a) Findings.--The Congress finds and declares the following:
(1) Federal legislation and regulatory requirements impose
burdens on State and local resources to implement federally
mandated programs without fully evaluating the costs to State
and local governments associated with compliance with those
requirements and oftentimes without provision of adequate
Federal financial assistance. Such Federal legislative and
regulatory initiatives--
(A) force State and local governments to utilize
scarce public resources to comply with Federal
mandates;
(B) prevent these resources from being available to
meet local needs; and
(C) detract from the ability of State and local
governments to establish local priorities for use of
local public resources.
(2) Federal legislation and regulatory programs can result
in inefficient utilization of economic resources, thereby
reducing the pool of resources available--
(A) to enhance productivity, and increase the
quantity and quality of goods and services produced by
the American economy; and
(B) to enhance international competitiveness.
(3) In implementing Congressional policy, Federal agencies
should, consistent with the requirements of Federal law, seek
to implement statutory requirements, to the maximum extent
feasible, in a manner that minimizes--
(A) the inefficient allocation of economic
resources;
(B) the burden that such requirements impose on use
of local public resources by State and local
governments; and
(C) the adverse economic effects of such
regulations on productivity, economic growth, full
employment, creation of productive jobs, and
international competitiveness of American goods and
services.
(b) Purposes.--The purposes of this Act are to--
(1) assist Congress in consideration of proposed
legislation establishing or revising Federal programs so as to
assure that, to the maximum extent practicable, legislation
enacted by Congress will--
(A) minimize the burden of such legislation on
expenditure of scarce local public resources by State
and local governments;
(B) minimize inefficient allocation of economic
resources; and
(C) reduce the adverse effect of such legislation--
(i) on the ability of State and local
governmental entities to use local public
resources to meet local needs and to establish
local priorities for local public resources;
and
(ii) on allocation of economic resources,
productivity, economic growth, full employment,
creation of productive jobs, and international
competitiveness; and
(2) require Federal agencies to exercise discretionary
authority and to implement statutory requirements in a manner
that, consistent with fulfillment of each agency's mission and
with the requirements of other laws, minimizes the impact
regulations affecting the economy have on--
(A) the ability of State and local governmental
entities to use local public resources to meet local
needs; and
(B) the allocation of economic resources,
productivity, economic growth, full employment,
creation of productive jobs, and international
competitiveness of American goods and services.
TITLE I--LEGISLATIVE REFORM
SEC. 101. REPORTS ON LEGISLATION.
(a) Report Required.--
(1) In general.--Except as provided in paragraph (2), when
a committee of the Senate or House of Representatives reports a
bill or resolution of a public character (not including a
resolution of ratification of a treaty) to its House that
mandates unfunded requirements upon State or local governments
or the private sector, the report accompanying the bill or
resolution shall contain an analysis, prepared after
consultation with the Director of the Congressional Budget
Office, detailing the effect of the new requirements on--
(A) State and local government expenditures
necessary to comply with Federal mandates;
(B) private businesses, including the economic
resources required annually to comply with the
legislation and implementing regulations; and
(C) economic growth and competitiveness.
(2) Exception.--Paragraph (1) shall not apply to any bill
with respect to which the Director of the Congressional Budget
Office certifies in writing to the chairman of the committee
reporting the legislation that the estimated costs to State and
local governments and the private sector of implementation of
such legislation during the first 3 years will not exceed
$50,000,000 in the aggregate and during the first 5 years will
not exceed $100,000,000 in the aggregate.
(b) Duties and Functions of Congressional Budget Office.--The
Director of the Congressional Budget Office shall prepare for each bill
or resolution of a public character reported by any committee of the
House of Representatives or of the Senate, an economic analysis of the
effects of the bill or resolution, satisfying the requirements of
subsection (a). The analysis prepared by the Director of the
Congressional Budget Office shall be included in the report
accompanying such bill or resolution.
(c) Legislation Subject to Point of Order.--A bill or resolution is
subject to a point of order against consideration of the bill or
resolution by the House of Representatives or the Senate (as the case
may be) if the bill or resolution is reported for consideration by the
House of Representatives or the Senate unaccompanied by the analysis
required by this section.
SEC. 102. EXERCISE OF RULEMAKING POWERS.
The provisions of this title are enacted by the Congress--
(1) as an exercise of the rulemaking power of the House of
Representatives and the Senate, respectively, and as such they
shall be considered as part of the rules of each House,
respectively, and such rules shall supersede other rules only
to the extent that they are inconsistent therewith; and
(2) with full recognition of the constitutional right of
either House to change such rules (so far as relating to such
House) at any time, in the same manner, and to the same extent
as in the case of any other rule of such House.
SEC. 103. EFFECTIVE DATE.
This title shall apply to any bill or resolution introduced in the
House of Representatives or the Senate after the date of enactment of
this Act.
TITLE II--FEDERAL INTERGOVERNMENTAL RELATIONS
SEC. 201. INTERGOVERNMENTAL AND ECONOMIC IMPACT ASSESSMENT.
(a) Requirement.--When an agency publishes a general notice of
proposed rulemaking for any proposed rule, the notice of proposed
rulemaking shall be accompanied by an Intergovernmental and Economic
Impact Assessment. Such Assessment shall be published in the Federal
Register at the time of the publication of the general notice of
proposed rulemaking for the rule.
(b) Content.--Each Intergovernmental and Economic Impact Assessment
required under this section shall contain--
(1) a description of the reasons why action by the agency
is being considered;
(2) a succinct statement of the objective of, and legal
basis for, the proposed rule;
(3) a good-faith estimate, based on data readily available
to the agency, of the effect the proposed rule will have on the
expenditure of State or local public resources by State and
local governments; and
(4) a good-faith estimate, based on data readily available
to the agency, or a description of the effect the proposed rule
will have on--
(A) the allocation of economic resources; and
(B) productivity, economic growth, full employment,
creation of productive jobs, and international
competitiveness of American goods and services.
SEC. 202. INTERGOVERNMENTAL AND ECONOMIC IMPACT STATEMENT.
(a) Requirement.--When an agency promulgates a final rule, the
agency shall prepare an Intergovernmental and Economic Impact
Statement. The Intergovernmental and Economic Impact Statement shall
contain--
(1) a succinct statement of the need for, and the
objectives of, such rule;
(2) a summary of the issues raised by the public comments
in response to the publication by the agency of the
Intergovernmental and Economic Impact Assessment prepared for
the rule, a summary of the agency's evaluation of such issues,
and a statement of any changes made in the proposed rule as a
result of such comments;
(3) a good-faith estimate, based on information readily
available to the agency, of the effect the rule will have on
the expenditure of State or local public resources by State and
local governments; and
(4) a good-faith estimate, based on information readily
available to the agency, or a description of the effect the
rule will have on productivity, economic growth, full
employment, creation of productive jobs, and international
competitiveness of American goods and services.
(b) Availability.--The agency shall make copies of each
Intergovernmental and Economic Impact Statement available to members of
the public, and shall publish in the Federal Register at the time of
publication of any final rule, a statement describing how the public
may obtain copies of such Statement.
SEC. 203. EFFECT ON OTHER LAWS.
The requirements of this title shall not alter in any manner the
substantive standards otherwise applicable to the implementation by an
agency of statutory requirements or to the exercise by an agency of
authority delegated by law.
SEC. 204. EFFECTIVE DATE.
This title shall apply to any rule proposed and any final rule
promulgated by any agency after the date of the enactment of this Act.
SEC. 205. DEFINITION.
In this title, the term ``agency'' has the meaning stated in
section 551(1) of title 5, United States Code.[/INST]TABLE OF CONTENTS:
Title I: Legislative Reform
Title II: Federal Intergovernmental Relations
Fiscal Accountability and Intergovernmental Reform Act (FAIR Act) -
Title I: Legislative Reform
- Provides that, with certain exceptions, whenever a committee of either House reports a bill or resolution of a public character (excluding resolutions of ratification of a treaty) to its House mandating unfunded requirements upon State or local governments or the private sector, the report accompanying that bill or resolution shall analyze the effect of the new requirements on: (1) State and local government expenditures necessary to comply with Federal mandates; (2) private businesses; and (3) economic growth and competitiveness. Requires the Congressional Budget Office to prepare such economic analyses.
Title II: Federal Intergovernmental Relations
- Provides that, whenever an agency publishes a general notice of proposed rulemaking or promulgates a final rule, the agency shall prepare and make available for public comment an Intergovernmental and Economic Impact Assessment. Specifies the contents of such an assessment.</s> |
Alcohol
Key facts 1
Worldwide, 3.3 million deaths every year result from harmful use of alcohol, 2 this represent 5.9 % of all deaths.
this represent 5.9 % of all deaths. The harmful use of alcohol is a causal factor in more than 200 disease and injury conditions.
Overall 5.1 % of the global burden of disease and injury is attributable to alcohol, as measured in disability- adjusted life years (DALYs). 3
Alcohol consumption causes death and disability relatively early in life. In the age group 20 – 39 years approximately 25 % of the total deaths are alcohol-attributable.
There is a causal relationship between harmful use of alcohol and a range of mental and behavioural disorders, other noncommunicable conditions as well as injuries.
The latest causal relationships have been established between harmful drinking and incidence of infectious diseases such as tuberculosis as well as the course of HIV/AIDS.
Beyond health consequences, the harmful use of alcohol brings significant social and economic losses to individuals and society at large.
Alcohol is a psychoactive substance with dependence-producing properties that has been widely used in many cultures for centuries. The harmful use of alcohol causes a large disease, social and economic burden in societies.
Alcohol impacts people and societies in many ways and it is determined by the volume of alcohol consumed, the pattern of drinking, and, on rare occasions, the quality of alcohol consumed. In 2012, about 3.3 million deaths, or 5.9 % of all global deaths, were attributable to alcohol consumption.
The harmful use of alcohol can also result in harm to other people, such as family members, friends, co-workers and strangers. Moreover, the harmful use of alcohol results in a significant health, social and economic burden on society at large.
Alcohol consumption is a causal factor in more than 200 disease and injury conditions. Drinking alcohol is associated with a risk of developing health problems such as mental and behavioural disorders, including alcohol dependence, major noncommunicable diseases such as liver cirrhosis, some cancers and cardiovascular diseases, as well as injuries resulting from violence and road clashes and collisions.
A significant proportion of the disease burden attributable to alcohol consumption arises from unintentional and intentional injuries, including those due to road traffic crashes, violence, and suicides, and fatal alcohol-related injuries tend to occur in relatively younger age groups.
The latest causal relationships are those between harmful drinking and incidence of infectious diseases such as tuberculosis as well as the course of HIV/AIDS. Alcohol consumption by an expectant mother may cause fetal alcohol syndrome and pre-term birth complications.
Factors affecting alcohol consumption and alcohol-related harm
A variety of factors have been identified at the individual and the societal level, which affect the levels and patterns of alcohol consumption and the magnitude of alcohol-related problems in populations.
Environmental factors include economic development, culture, availability of alcohol, and the comprehensiveness and levels of implementation and enforcement of alcohol policies. For a given level or pattern of drinking, vulnerabilities within a society are likely to have similar differential effects as those between societies. Although there is no single risk factor that is dominant, the more vulnerabilities a person has, the more likely the person is to develop alcohol-related problems as a result of alcohol consumption.
Conceptual causal model of alcohol consumption and health outcomes
The impact of alcohol consumption on chronic and acute health outcomes in populations is largely determined by 2 separate but related dimensions of drinking:
the total volume of alcohol consumed, and
the pattern of drinking.
The context of drinking plays an important role in occurrence of alcohol-related harm, particularly associated with health effects of alcohol intoxication, and, on rare occasions, also the quality of alcohol consumed. Alcohol consumption can have an impact not only on the incidence of diseases, injuries and other health conditions, but also on the course of disorders and their outcomes in individuals.
There are gender differences in alcohol-related mortality, morbidity, as well as levels and patterns of alcohol consumption. The percentage of alcohol-attributable deaths among men amount to 7.6 % of all global deaths compared to 4.0 % of all deaths among women. Total alcohol per capita consumption in 2010 among male and female drinkers worldwide was on average 21.2 litres for males and 8.9 litres of pure alcohol for females.
Ways to reduce the burden from harmful use of alcohol
The health, safety and socioeconomic problems attributable to alcohol can be effectively reduced and requires actions on the levels, patterns and contexts of alcohol consumption and the wider social determinants of health.
Countries have a responsibility for formulating, implementing, monitoring and evaluating public policies to reduce the harmful use of alcohol. Substantial scientific knowledge exists for policy-makers on the effectiveness and cost–effectiveness of the following strategies:
regulating the marketing of alcoholic beverages (in particular to younger people);
regulating and restricting availability of alcohol;
enacting appropriate drink-driving policies;
reducing demand through taxation and pricing mechanisms;
raising awareness of public health problems caused by harmful use of alcohol and ensuring support for effective alcohol policies;
providing accessible and affordable treatment for people with alcohol-use disorders; and
implementing screening and brief interventions programmes for hazardous and harmful drinking in health services.
WHO response
WHO aims to reduce the health burden caused by the harmful use of alcohol and, thereby, to save lives, prevent injuries and diseases and improve the well-being of individuals, communities and society at large.
WHO emphasizes the development, implementation and evaluation of cost-effective interventions for harmful use of alcohol as well as creating, compiling and disseminating scientific information on alcohol use and dependence, and related health and social consequences.
In 2010, the World Health Assembly approved a resolution endorsing a global strategy to reduce the harmful use of alcohol. The resolution urges countries to strengthen national responses to public health problems caused by the harmful use of alcohol.
The global strategy to reduce the harmful use of alcohol represents a collective commitment by WHO Member States to reduce the global burden of disease caused by harmful use of alcohol. The strategy includes evidence-based policies and interventions that can protect health and save lives if adopted, implemented and enforced. The strategy also contains a set of principles to guide the development and implementation of policies; it sets priority areas for global action, recommends target areas for national action and gives a strong mandate to WHO to strengthen action at all levels.
The policy options and interventions available for national action can be grouped into 10 recommended target areas, which are mutually supportive and complementary. The 10 areas are:
leadership, awareness and commitment
health services’ response
community action
drink–driving policies and countermeasures
availability of alcohol
marketing of alcoholic beverages
pricing policies
reducing the negative consequences of drinking and alcohol intoxication
reducing the public health impact of illicit alcohol and informally produced alcohol
monitoring and surveillance.
The Global Information System on Alcohol and Health (GISAH) has been developed by WHO to dynamically present data on levels and patterns of alcohol consumption, alcohol-attributable health and social consequences and policy responses at all levels.
Successful implementation of the strategy will require action by countries, effective global governance and appropriate engagement of all relevant stakeholders. By effectively working together, the negative health and social consequences of alcohol can be reduced.
Footnotes ||||| 21 September 2018 – Geneva. More than 3 million people died as a result of harmful use of alcohol in 2016, according a report released by the World Health Organization (WHO) today. This represents 1 in 20 deaths. More than three quarters of these deaths were among men. Overall, the harmful use of alcohol causes more than 5% of the global disease burden.
“Far too many people, their families and communities suffer the consequences of the harmful use of alcohol through violence, injuries, mental health problems and diseases like cancer and stroke,” said Dr Tedros Adhanom Ghebreyesus, Director-General of WHO. “It’s time to step up action to prevent this serious threat to the development of healthy societies.” | – The World Health Organization today released a new report on alcohol, and it's full of pretty dour stats. Among the most eye-grabbing ones, per the WHO and the AFP: Alcohol kills 3.3 million people worldwide each year. That's more than AIDS, tuberculosis, and violence—combined. That's equal to 5.9% of all deaths across the planet, or more than one in 20. "This actually translates into one death every 10 seconds," says a WHO rep. The report encompasses drunk driving, alcohol-induced violence and abuse, and related diseases and disorders ("the harmful use of alcohol is a causal factor in more than 200 disease and injury conditions," per the report). The UN health agency also noted that drinking is on the rise in countries that have typically seen low consumption, like China and India, as incomes rise. As far as consumption, take in this stat: When it's divvied up across every person on the planet over the age of 15, the average annual consumption is 1.6 gallons of pure alcohol. When calculated across only those who drink, the average is 4.5 gallons. The WHO would like to see governments do more "to protect populations from the negative health consequences of alcohol consumption." Among its suggestions: use taxes and price levels to lower demand. | <s>[INST]Alcohol
Key facts 1
Worldwide, 3.3 million deaths every year result from harmful use of alcohol, 2 this represent 5.9 % of all deaths.
this represent 5.9 % of all deaths. The harmful use of alcohol is a causal factor in more than 200 disease and injury conditions.
Overall 5.1 % of the global burden of disease and injury is attributable to alcohol, as measured in disability- adjusted life years (DALYs). 3
Alcohol consumption causes death and disability relatively early in life. In the age group 20 – 39 years approximately 25 % of the total deaths are alcohol-attributable.
There is a causal relationship between harmful use of alcohol and a range of mental and behavioural disorders, other noncommunicable conditions as well as injuries.
The latest causal relationships have been established between harmful drinking and incidence of infectious diseases such as tuberculosis as well as the course of HIV/AIDS.
Beyond health consequences, the harmful use of alcohol brings significant social and economic losses to individuals and society at large.
Alcohol is a psychoactive substance with dependence-producing properties that has been widely used in many cultures for centuries. The harmful use of alcohol causes a large disease, social and economic burden in societies.
Alcohol impacts people and societies in many ways and it is determined by the volume of alcohol consumed, the pattern of drinking, and, on rare occasions, the quality of alcohol consumed. In 2012, about 3.3 million deaths, or 5.9 % of all global deaths, were attributable to alcohol consumption.
The harmful use of alcohol can also result in harm to other people, such as family members, friends, co-workers and strangers. Moreover, the harmful use of alcohol results in a significant health, social and economic burden on society at large.
Alcohol consumption is a causal factor in more than 200 disease and injury conditions. Drinking alcohol is associated with a risk of developing health problems such as mental and behavioural disorders, including alcohol dependence, major noncommunicable diseases such as liver cirrhosis, some cancers and cardiovascular diseases, as well as injuries resulting from violence and road clashes and collisions.
A significant proportion of the disease burden attributable to alcohol consumption arises from unintentional and intentional injuries, including those due to road traffic crashes, violence, and suicides, and fatal alcohol-related injuries tend to occur in relatively younger age groups.
The latest causal relationships are those between harmful drinking and incidence of infectious diseases such as tuberculosis as well as the course of HIV/AIDS. Alcohol consumption by an expectant mother may cause fetal alcohol syndrome and pre-term birth complications.
Factors affecting alcohol consumption and alcohol-related harm
A variety of factors have been identified at the individual and the societal level, which affect the levels and patterns of alcohol consumption and the magnitude of alcohol-related problems in populations.
Environmental factors include economic development, culture, availability of alcohol, and the comprehensiveness and levels of implementation and enforcement of alcohol policies. For a given level or pattern of drinking, vulnerabilities within a society are likely to have similar differential effects as those between societies. Although there is no single risk factor that is dominant, the more vulnerabilities a person has, the more likely the person is to develop alcohol-related problems as a result of alcohol consumption.
Conceptual causal model of alcohol consumption and health outcomes
The impact of alcohol consumption on chronic and acute health outcomes in populations is largely determined by 2 separate but related dimensions of drinking:
the total volume of alcohol consumed, and
the pattern of drinking.
The context of drinking plays an important role in occurrence of alcohol-related harm, particularly associated with health effects of alcohol intoxication, and, on rare occasions, also the quality of alcohol consumed. Alcohol consumption can have an impact not only on the incidence of diseases, injuries and other health conditions, but also on the course of disorders and their outcomes in individuals.
There are gender differences in alcohol-related mortality, morbidity, as well as levels and patterns of alcohol consumption. The percentage of alcohol-attributable deaths among men amount to 7.6 % of all global deaths compared to 4.0 % of all deaths among women. Total alcohol per capita consumption in 2010 among male and female drinkers worldwide was on average 21.2 litres for males and 8.9 litres of pure alcohol for females.
Ways to reduce the burden from harmful use of alcohol
The health, safety and socioeconomic problems attributable to alcohol can be effectively reduced and requires actions on the levels, patterns and contexts of alcohol consumption and the wider social determinants of health.
Countries have a responsibility for formulating, implementing, monitoring and evaluating public policies to reduce the harmful use of alcohol. Substantial scientific knowledge exists for policy-makers on the effectiveness and cost–effectiveness of the following strategies:
regulating the marketing of alcoholic beverages (in particular to younger people);
regulating and restricting availability of alcohol;
enacting appropriate drink-driving policies;
reducing demand through taxation and pricing mechanisms;
raising awareness of public health problems caused by harmful use of alcohol and ensuring support for effective alcohol policies;
providing accessible and affordable treatment for people with alcohol-use disorders; and
implementing screening and brief interventions programmes for hazardous and harmful drinking in health services.
WHO response
WHO aims to reduce the health burden caused by the harmful use of alcohol and, thereby, to save lives, prevent injuries and diseases and improve the well-being of individuals, communities and society at large.
WHO emphasizes the development, implementation and evaluation of cost-effective interventions for harmful use of alcohol as well as creating, compiling and disseminating scientific information on alcohol use and dependence, and related health and social consequences.
In 2010, the World Health Assembly approved a resolution endorsing a global strategy to reduce the harmful use of alcohol. The resolution urges countries to strengthen national responses to public health problems caused by the harmful use of alcohol.
The global strategy to reduce the harmful use of alcohol represents a collective commitment by WHO Member States to reduce the global burden of disease caused by harmful use of alcohol. The strategy includes evidence-based policies and interventions that can protect health and save lives if adopted, implemented and enforced. The strategy also contains a set of principles to guide the development and implementation of policies; it sets priority areas for global action, recommends target areas for national action and gives a strong mandate to WHO to strengthen action at all levels.
The policy options and interventions available for national action can be grouped into 10 recommended target areas, which are mutually supportive and complementary. The 10 areas are:
leadership, awareness and commitment
health services’ response
community action
drink–driving policies and countermeasures
availability of alcohol
marketing of alcoholic beverages
pricing policies
reducing the negative consequences of drinking and alcohol intoxication
reducing the public health impact of illicit alcohol and informally produced alcohol
monitoring and surveillance.
The Global Information System on Alcohol and Health (GISAH) has been developed by WHO to dynamically present data on levels and patterns of alcohol consumption, alcohol-attributable health and social consequences and policy responses at all levels.
Successful implementation of the strategy will require action by countries, effective global governance and appropriate engagement of all relevant stakeholders. By effectively working together, the negative health and social consequences of alcohol can be reduced.
Footnotes ||||| 21 September 2018 – Geneva. More than 3 million people died as a result of harmful use of alcohol in 2016, according a report released by the World Health Organization (WHO) today. This represents 1 in 20 deaths. More than three quarters of these deaths were among men. Overall, the harmful use of alcohol causes more than 5% of the global disease burden.
“Far too many people, their families and communities suffer the consequences of the harmful use of alcohol through violence, injuries, mental health problems and diseases like cancer and stroke,” said Dr Tedros Adhanom Ghebreyesus, Director-General of WHO. “It’s time to step up action to prevent this serious threat to the development of healthy societies.”[/INST]– The World Health Organization today released a new report on alcohol, and it's full of pretty dour stats. Among the most eye-grabbing ones, per the WHO and the AFP: Alcohol kills 3.3 million people worldwide each year. That's more than AIDS, tuberculosis, and violence—combined. That's equal to 5.9% of all deaths across the planet, or more than one in 20. "This actually translates into one death every 10 seconds," says a WHO rep. The report encompasses drunk driving, alcohol-induced violence and abuse, and related diseases and disorders ("the harmful use of alcohol is a causal factor in more than 200 disease and injury conditions," per the report). The UN health agency also noted that drinking is on the rise in countries that have typically seen low consumption, like China and India, as incomes rise. As far as consumption, take in this stat: When it's divvied up across every person on the planet over the age of 15, the average annual consumption is 1.6 gallons of pure alcohol. When calculated across only those who drink, the average is 4.5 gallons. The WHO would like to see governments do more "to protect populations from the negative health consequences of alcohol consumption." Among its suggestions: use taxes and price levels to lower demand.</s> |
CLOSE President-elect Trump scolded media outlets for inaccurate reports of his political adviser's whereabouts. USA TODAY NETWORK
President-elect Donald Trump speaks with reporters in the lobby of Trump Tower in New York. (Photo: Evan Vucci, AP)
President-elect Donald Trump, in a fresh peek at his foreign policy views, says he is open to lifting sanctions against Russia and is not committed to a longstanding agreement with China over Taiwan. Beijing swiftly responded to the latter remark, calling any revision of the longstanding "One China" policy "non-negotiable."
Trump's comments came in an hour-long interview with The Wall Street Journal on Friday in which he said he will keep the sanctions on Russia in place "for a period of time" but is open to lifting them if Moscow cooperates on issues of mutual interest.
While several sanctions were imposed on Russia in 2014 over its annexation of Crimea, the latest measures, as well as the expulsion of 35 Russian diplomats, were imposed by the Obama administration last month in response to evidence Russia hacked Democratic Party officials during the presidential election.
Trump's latest views on Russia comes only days after CNN's report regarding classified documents presented to Obama and Trump during an intelligence briefing last week that contained unsubstantiated and potentially compromising information about the president-elect.
"If you get along and if Russia is really helping us, why would anybody have sanctions if somebody's doing some really great things?" Trump said in the Journal interview. He added, however, he would keep the latest sanctions in place "at least for a period of time."
Trump acknowledged for the first time this week that he accepts Russia was behind the hacking. But he questioned whether officials were leaking information about their meetings with him, warning that would be a “tremendous blot” on their record.
The president-elect also told the Journal he is willing to meet with Russian President Vladimir Putin after he takes office next week. "I understand that they would like to meet, and that's absolutely fine with me," Trump added.
Regarding China, Trump was specifically asked whether he supports the U.S. "One China" policy on Taiwan, which declares the province as part of China. Trump's response: "Everything is under negotiation, including One China." He described it as leverage in any talks with Beijing over trade and currency issues.
The remarks come only weeks after Trump's unprecedented phone conversation with Taiwanese President Tsai Ing-wen shortly after the November election. There has been no communication between the leaders of the United States and Taiwan since 1979.
The latest comments brought a swift and pointed response from China. In a statement Saturday, Lu Kang, spokesman for the Chinese foreign ministry, called the One China policy "non-negotiable" and the "political foundation" of China-U.S. relations.
"To avoid disruption to the sound and steady development of the China-U.S. relations and bilateral cooperation in key areas, we urge relevant parties in the U.S. to fully recognize the high sensitivity of the Taiwan question, approach Taiwan-related issues with prudence and honor the commitment made by all previous U.S. administrations of both parties on adhering to the one-China policy," Kang said.
Trump's comments appear to represent a departure from remarks by his advisers in early December that the phone call to Taiwan's leader did not signify any formal shift in long-standing U.S. relations with Taiwan or China.
In mid-December, An Fengshan, a spokesman for China's policy-making Taiwan Affairs Office, warned of more serious consequences if U.S. shifts positions on the Taiwan issue.
"If this basis is interfered with or damaged, then the healthy, stable development of China-U.S. relations is out of the question, and peace and stability in the Taiwan Strait will be seriously impacted," he added, according to the BBC..
Contributing: The Associated Press
Read or Share this story: http://usat.ly/2jICkyB ||||| NEW YORK—President-elect Donald Trump suggested he would be open to lifting sanctions on Russia and wasn’t committed to a longstanding agreement with China over Taiwan—two signs that he would use any available leverage to realign the U.S.’s relationship with its two biggest global strategic rivals.
In an hourlong interview, Mr. Trump said that, “at least for a period of time,” he would keep intact sanctions against Russia imposed by the Obama administration in late December in response to Moscow’s alleged cyberattacks to influence... | – Donald Trump dropped some big hints about changes to US policy on its biggest world rivals in a Wall Street Journal interview released Friday evening. On Russia, Trump said he is planning to keep the latest American sanctions in place "at least for a period of time," but he will certainly consider dropping them when he decides the time is right. "If you get along and if Russia is really helping us, why would anybody have sanctions if somebody’s doing some really great things?" he wondered. Some US sanctions were imposed after Russia's internationally condemned annexation of Crimea in 2014, USA Today notes, but the latest ones were brought in last month as punishment for election-related hacking. Trump, who said he is "absolutely fine" with meeting Vladimir Putin soon, took a more combative tone on China. He said everything about the US relationship with Beijing is under consideration, including the "One China" policy on Taiwan. He complained about China's currency policies, and about Beijing's reaction to his phone conversation with Taiwan's president. "We sold them $2 billion of military equipment last year. We can sell them $2 billion of the latest and greatest military equipment but we're not allowed to accept a phone call," he said. He did, however, show the Journal the Christmas card he received from China's President Xi Jinping. "I have a beautiful card from the chairman," he said. (Earlier in the week, Trump met with China's second-richest man.) | <s>[INST]CLOSE President-elect Trump scolded media outlets for inaccurate reports of his political adviser's whereabouts. USA TODAY NETWORK
President-elect Donald Trump speaks with reporters in the lobby of Trump Tower in New York. (Photo: Evan Vucci, AP)
President-elect Donald Trump, in a fresh peek at his foreign policy views, says he is open to lifting sanctions against Russia and is not committed to a longstanding agreement with China over Taiwan. Beijing swiftly responded to the latter remark, calling any revision of the longstanding "One China" policy "non-negotiable."
Trump's comments came in an hour-long interview with The Wall Street Journal on Friday in which he said he will keep the sanctions on Russia in place "for a period of time" but is open to lifting them if Moscow cooperates on issues of mutual interest.
While several sanctions were imposed on Russia in 2014 over its annexation of Crimea, the latest measures, as well as the expulsion of 35 Russian diplomats, were imposed by the Obama administration last month in response to evidence Russia hacked Democratic Party officials during the presidential election.
Trump's latest views on Russia comes only days after CNN's report regarding classified documents presented to Obama and Trump during an intelligence briefing last week that contained unsubstantiated and potentially compromising information about the president-elect.
"If you get along and if Russia is really helping us, why would anybody have sanctions if somebody's doing some really great things?" Trump said in the Journal interview. He added, however, he would keep the latest sanctions in place "at least for a period of time."
Trump acknowledged for the first time this week that he accepts Russia was behind the hacking. But he questioned whether officials were leaking information about their meetings with him, warning that would be a “tremendous blot” on their record.
The president-elect also told the Journal he is willing to meet with Russian President Vladimir Putin after he takes office next week. "I understand that they would like to meet, and that's absolutely fine with me," Trump added.
Regarding China, Trump was specifically asked whether he supports the U.S. "One China" policy on Taiwan, which declares the province as part of China. Trump's response: "Everything is under negotiation, including One China." He described it as leverage in any talks with Beijing over trade and currency issues.
The remarks come only weeks after Trump's unprecedented phone conversation with Taiwanese President Tsai Ing-wen shortly after the November election. There has been no communication between the leaders of the United States and Taiwan since 1979.
The latest comments brought a swift and pointed response from China. In a statement Saturday, Lu Kang, spokesman for the Chinese foreign ministry, called the One China policy "non-negotiable" and the "political foundation" of China-U.S. relations.
"To avoid disruption to the sound and steady development of the China-U.S. relations and bilateral cooperation in key areas, we urge relevant parties in the U.S. to fully recognize the high sensitivity of the Taiwan question, approach Taiwan-related issues with prudence and honor the commitment made by all previous U.S. administrations of both parties on adhering to the one-China policy," Kang said.
Trump's comments appear to represent a departure from remarks by his advisers in early December that the phone call to Taiwan's leader did not signify any formal shift in long-standing U.S. relations with Taiwan or China.
In mid-December, An Fengshan, a spokesman for China's policy-making Taiwan Affairs Office, warned of more serious consequences if U.S. shifts positions on the Taiwan issue.
"If this basis is interfered with or damaged, then the healthy, stable development of China-U.S. relations is out of the question, and peace and stability in the Taiwan Strait will be seriously impacted," he added, according to the BBC..
Contributing: The Associated Press
Read or Share this story: http://usat.ly/2jICkyB ||||| NEW YORK—President-elect Donald Trump suggested he would be open to lifting sanctions on Russia and wasn’t committed to a longstanding agreement with China over Taiwan—two signs that he would use any available leverage to realign the U.S.’s relationship with its two biggest global strategic rivals.
In an hourlong interview, Mr. Trump said that, “at least for a period of time,” he would keep intact sanctions against Russia imposed by the Obama administration in late December in response to Moscow’s alleged cyberattacks to influence...[/INST]– Donald Trump dropped some big hints about changes to US policy on its biggest world rivals in a Wall Street Journal interview released Friday evening. On Russia, Trump said he is planning to keep the latest American sanctions in place "at least for a period of time," but he will certainly consider dropping them when he decides the time is right. "If you get along and if Russia is really helping us, why would anybody have sanctions if somebody’s doing some really great things?" he wondered. Some US sanctions were imposed after Russia's internationally condemned annexation of Crimea in 2014, USA Today notes, but the latest ones were brought in last month as punishment for election-related hacking. Trump, who said he is "absolutely fine" with meeting Vladimir Putin soon, took a more combative tone on China. He said everything about the US relationship with Beijing is under consideration, including the "One China" policy on Taiwan. He complained about China's currency policies, and about Beijing's reaction to his phone conversation with Taiwan's president. "We sold them $2 billion of military equipment last year. We can sell them $2 billion of the latest and greatest military equipment but we're not allowed to accept a phone call," he said. He did, however, show the Journal the Christmas card he received from China's President Xi Jinping. "I have a beautiful card from the chairman," he said. (Earlier in the week, Trump met with China's second-richest man.)</s> |
cerebral palsy is a collective term for motor deficits resulting from non - progressive abnormalities in the immature brain occurring in about 2 of every 1000 live births in developed countries .
inflammatory responses in utero and in neonates have been involved in the development of the white matter lesions that cause cerebral palsy [ 26 ] .
infection in utero can cause damaging perturbations in inflammatory responses , and infants who develop an immune response in utero are at higher risk of cerebral lesions .
interleukin ( il)-6 and il-1 levels in umbilical cord plasma , amniotic fluid , and cerebrospinal fluid are elevated in neonates with periventricular leukomalacia - associated lesions , but this is controversial .
inflammation at or shortly after birth is associated with subnormal development in very preterm infants .
perinatal cytokine levels were often reported to predict the risk of cerebral palsy in preterm children [ 1113 ] .
in addition , polymorphisms in tnf- and il-1 have been found to represent a genetic susceptibility to white matter damage and consequently cerebral palsy .
however , a meta - analysis demonstrated that cerebral palsy is associated with a genetic polymorphism in il-6 , but not with tnf- or any other cytokine .
although the precise immune responses involved in the development of cerebral palsy remain to be fully characterized , aberrant inflammatory responses may continue to influence the reconstruction of cerebral function after birth [ 1820 ] .
tnf- has widespread biological functions , activating neutrophils to eliminate pathogenic microorganisms , stimulating mononuclear cells to produce il-1 and il-6 , and activating b lymphocytes to produce antibodies .
tnf- is secreted by astrocytes , microglia , blood - borne macrophages , and vascular endothelial cells in the central nervous system .
tnf- has been reported to cause increased blood - brain barrier permeability , participating in the development of cerebral edema .
although there is evidence suggesting that high levels of tnf- are associated with cerebral palsy [ 911,14,15,20 ] , little is known about age - related and function - related changes in tnf-. in the present study , levels of plasma tnf- in children with cerebral palsy were measured to assess the hypothesis that tnf- levels can act as a marker of both cerebral palsy presence and cerebral palsy severity .
in addition , patients were evaluated after rehabilitation therapy , and the pre - therapy levels of tnf- were compared with their response to therapy .
children with clinically confirmed spastic cerebral palsy were recruited from the department of rehabilitation , the second affiliated hospital of anhui medical university and the provincial children s hospital between december 2012 and august 2013 .
cerebral palsy was diagnosed according to the definition , classification , and diagnostic criteria recommended by the second national children rehabilitation conference & the ninth chinese cerebral palsy children rehabilitation academic conference in chang sha , china in 2009 .
the inclusion criteria were : 1 ) aged 112 years ; and 2 ) stable health .
exclusion criteria were : 1 ) history of epilepsy or fever in the preceding two months ; 2 ) inflammatory response syndrome ; 3 ) diseases that could elevate tnf- levels for other reasons , such as progressive amyotrophy , encephalomyelitis , severe malnutrition , myasthenia gravis , epilepsy , vision / hearing disorders , or other severe pediatric diseases ; or 4 ) other endocrine disorders , metabolic disorders , autoimmune diseases , or genetic diseases .
the enrolled subjects with cerebral palsy were divided into 2 subgroups : those aged 1 to 3 years ( n=27 ) and those aged 4 to 12 years ( n=27 ) .
twenty - eight control subjects free of brain disorders were recruited according to the same inclusion / exclusion criteria and were individually matched based on sex and age to the subjects with cerebral palsy .
the age cut - off point was selected because the blood - brain barrier mature around 3 years of age , preventing plasma inflammatory factors from damaging the brain .
blood samples were provided by all participants and the plasma levels of tnf- were measured .
patient gross motor function and activities of daily living were evaluated before and after six months of individualized physical and speech therapy .
control participant gross motor function and activities of daily living was evaluated over the same period .
the study was approved by the ethics committee of anhui medical university ( k201209 ) , and informed consents were obtained from the children s legal guardians .
participant gross motor function was evaluated by the gross motor function classification system ( gmfcs ) , which is a 5-level clinical classification system describing the gross motor function on the basis of self - initiated movement abilities .
all assessments were administered by the chief physician of the department ( 30 years of clinical experience in diagnosing , evaluating , and treating cerebral palsy ) .
gmfcs motor deficit severity was classified into levels i ( for the highest level of activity ) to v ( for the lowest level of activity ) .
the activities of daily living was assessed at the beginning of the study and again after six months of individualized physical and speech therapy , and the difference in score was recorded .
plasma tnf- levels were measured by elisa ( bms223/4 , bender medsystems gmbh , vienna , austria ) .
continuous data were analyzed by multivariate analysis by non - conditional logistic regression analysis between all subjects with cerebral palsy and controls .
correlation analysis between tnf- levels and motor functions was performed using the spearman correlation analysis .
the correlation between tnf- levels and improvement of activities of daily living was assessed by pearson correlation analysis .
children with clinically confirmed spastic cerebral palsy were recruited from the department of rehabilitation , the second affiliated hospital of anhui medical university and the provincial children s hospital between december 2012 and august 2013 .
cerebral palsy was diagnosed according to the definition , classification , and diagnostic criteria recommended by the second national children rehabilitation conference & the ninth chinese cerebral palsy children rehabilitation academic conference in chang sha , china in 2009 .
the inclusion criteria were : 1 ) aged 112 years ; and 2 ) stable health .
exclusion criteria were : 1 ) history of epilepsy or fever in the preceding two months ; 2 ) inflammatory response syndrome ; 3 ) diseases that could elevate tnf- levels for other reasons , such as progressive amyotrophy , encephalomyelitis , severe malnutrition , myasthenia gravis , epilepsy , vision / hearing disorders , or other severe pediatric diseases ; or 4 ) other endocrine disorders , metabolic disorders , autoimmune diseases , or genetic diseases .
the enrolled subjects with cerebral palsy were divided into 2 subgroups : those aged 1 to 3 years ( n=27 ) and those aged 4 to 12 years ( n=27 ) .
twenty - eight control subjects free of brain disorders were recruited according to the same inclusion / exclusion criteria and were individually matched based on sex and age to the subjects with cerebral palsy .
the age cut - off point was selected because the blood - brain barrier mature around 3 years of age , preventing plasma inflammatory factors from damaging the brain .
blood samples were provided by all participants and the plasma levels of tnf- were measured .
patient gross motor function and activities of daily living were evaluated before and after six months of individualized physical and speech therapy .
control participant gross motor function and activities of daily living was evaluated over the same period .
the study was approved by the ethics committee of anhui medical university ( k201209 ) , and informed consents were obtained from the children s legal guardians .
participant gross motor function was evaluated by the gross motor function classification system ( gmfcs ) , which is a 5-level clinical classification system describing the gross motor function on the basis of self - initiated movement abilities .
all assessments were administered by the chief physician of the department ( 30 years of clinical experience in diagnosing , evaluating , and treating cerebral palsy ) .
gmfcs motor deficit severity was classified into levels i ( for the highest level of activity ) to v ( for the lowest level of activity ) .
the activities of daily living was assessed at the beginning of the study and again after six months of individualized physical and speech therapy , and the difference in score was recorded .
plasma tnf- levels were measured by elisa ( bms223/4 , bender medsystems gmbh , vienna , austria ) .
all statistical analyses were performed using spss 13.0 ( spss inc . , chicago , il , usa ) .
continuous data were analyzed by multivariate analysis by non - conditional logistic regression analysis between all subjects with cerebral palsy and controls .
correlation analysis between tnf- levels and motor functions was performed using the spearman correlation analysis .
the correlation between tnf- levels and improvement of activities of daily living was assessed by pearson correlation analysis .
there was no significant difference in height , body weight , age , and sex between subjects with cerebral palsy and healthy controls ( tables 1 , 2 ) .
the mean plasma tnf- levels of subjects with cerebral palsy ( 21.46.2 pg / ml ) was significantly higher than in controls ( 11.24.1 pg / ml ) ( p<0.001 ) .
this difference was present in both age subgroups ( younger : 25.04.9 pg / ml vs. 11.43.4 pg / ml , p<0.001 ; and older : 17.85.2 pg / ml vs. 11.04.9 pg / ml , p<0.001 ) . while the levels of tnf- in the plasma of both control subgroups were comparable ( p=0.819 ) , younger subjects with cerebral palsy had significantly higher plasma tnf- levels than older subjects with cerebral palsy ( p<0.001 ) ( table 2 ) .
multivariate analysis revealed that although neither age nor sex were significantly correlated with cerebral palsy , plasma levels of tnf- were significantly correlated with cerebral palsy ( or=1.605 , 95%ci 1.3021.979 , p<0.001 ) ( table 3 ) .
there was no correlation between plasma tnf- levels and gmfcs in the entire group of subjects with cerebral palsy .
however , plasma tnf- levels correlated significantly with gmfcs in the subgroups of patients with spastic triplegia or quadriplegia cerebral palsy ( r=0.525 , p=0.038 ) , and spastic diplegia cerebral palsy ( r=0.521 , p=0.001 ) ( table 4 ) . nevertheless , a general trend toward an association in the whole group could be observed .
pre - rehabilitation plasma tnf- levels were also significantly correlated with the improvements in activities of daily living after 6 months of comprehensive rehabilitation in all subjects with cerebral palsy ( r=0.593 , p<0.001 ) ( table 4 ) .
similar results were observed in subjects with spastic triplegia or quadriplegia cerebral palsy ( r=0.839 , p<0.001 ) , and spastic diplegia cerebral palsy ( r=0.796 , p<0.001 ) .
there was no significant difference in height , body weight , age , and sex between subjects with cerebral palsy and healthy controls ( tables 1 , 2 ) .
the mean plasma tnf- levels of subjects with cerebral palsy ( 21.46.2 pg / ml ) was significantly higher than in controls ( 11.24.1 pg / ml ) ( p<0.001 ) .
this difference was present in both age subgroups ( younger : 25.04.9 pg / ml vs. 11.43.4 pg / ml , p<0.001 ; and older : 17.85.2 pg / ml vs. 11.04.9 pg / ml , p<0.001 ) . while the levels of tnf- in the plasma of both control subgroups were comparable ( p=0.819 ) , younger subjects with cerebral palsy had significantly higher plasma tnf- levels than older subjects with cerebral palsy ( p<0.001 ) ( table 2 ) .
multivariate analysis revealed that although neither age nor sex were significantly correlated with cerebral palsy , plasma levels of tnf- were significantly correlated with cerebral palsy ( or=1.605 , 95%ci 1.3021.979 , p<0.001 ) ( table 3 ) .
there was no correlation between plasma tnf- levels and gmfcs in the entire group of subjects with cerebral palsy . however ,
plasma tnf- levels correlated significantly with gmfcs in the subgroups of patients with spastic triplegia or quadriplegia cerebral palsy ( r=0.525 , p=0.038 ) , and spastic diplegia cerebral palsy ( r=0.521 , p=0.001 ) ( table 4 ) . nevertheless , a general trend toward an association in the whole group could be observed .
pre - rehabilitation plasma tnf- levels were also significantly correlated with the improvements in activities of daily living after 6 months of comprehensive rehabilitation in all subjects with cerebral palsy ( r=0.593 , p<0.001 ) ( table 4 ) .
similar results were observed in subjects with spastic triplegia or quadriplegia cerebral palsy ( r=0.839 , p<0.001 ) , and spastic diplegia cerebral palsy ( r=0.796 , p<0.001 ) .
as early as 2007 , dammann et al . proposed that persistent activation or accumulation of inflammatory cytokines may impede the reconstruction of brain function following brain injury , therefore promoting cerebral palsy .
these pathological changes disturb the maturation of oligodendrocytes , limit neuronal regeneration , and impair synapse formation . in this study , we measured the plasma levels of tnf- in 54 children with spastic cerebral palsy , and in 28 age - matched healthy controls , and examined whether the levels of tnf- were associated with the presence of cerebral palsy and the degree of functional disturbance in cerebral palsy .
the plasma levels of tnf- were significantly higher in children with spastic cerebral palsy , and significantly higher in children with cerebral palsy aged 13 than children aged 412 .
these results suggest that immunological abnormalities , while more pronounced before the age of four , may persist in cerebral palsy throughout childhood .
enormous production of inflammatory cytokines including tnf- and il-1 has been previously detected in vulnerable brain regions of premature infants with white matter injury .
high levels of il-1 , il-6 , il-8 , il-9 , and tnf- have also been detected in the perinatal peripheral blood of full - term and preterm subjects with cerebral palsy , but this is controversial . in the present study ,
only children with no history of fever , epilepsy , or inflammatory disorders in the previous two months were enrolled .
children under the age of four with spastic cerebral palsy had higher levels of plasma tnf- compared with older children .
this observation suggests that the inflammatory response may decrease with age , while the symptoms of cerebral palsy do not necessarily improve . additionally ,
higher baseline levels of tnf- might be a marker of more extensive brain damage and of a weaker than average response to this form of therapy . since therapies targeting activated microglia and astrocytes or anti - cytokine treatments may help reduce
the injury of cerebral palsy , therapeutic interventions designed to reduce inflammation may yield beneficial results in children throughout childhood .
recently , alcaraz et al . reported the use of platelet - rich plasma for the treatment of a patient with cerebral palsy , leading to improvements in the cognitive score and motor functions .
however , the exact mechanisms of these approaches require further study . to investigate the relationship between tnf- and cerebral palsy severity ,
although tnf- levels were not associated with gmfcs in the entire sample , tnf- levels were significantly correlated with gmfcs in patients with spastic triplegia and quadriplegia , and with diplegia , supporting the hypothesis that circulating levels of tnf- can reflect the severity of motor dysfunction in some types of spastic cerebral palsy .
inflammation and intrauterine infection have been reported to activate microglia of the central nervous system , changing the function of neurons and glial cells , and causing cytotoxicity , edema , and brain injury in the fetal and neonatal brain .
elevated levels of circulating tnf- found in the present study suggest that this inflammatory process persists throughout childhood .
a variety of different forms of brain injury have been associated with cerebral palsy including cerebellar atrophy , diffuse cortical atrophy , periventricular leukomalacia , thin corpus callosum , and border - zone infarction .
the present study suggests that the severity of illness was correlated to tnf- levels in spastic triplegia and quadriplegia , and in diplegia .
in addition , the follow - up was short . to confirm the capacity of tnf- to represent a marker of disease severity , or
predict outcome of interventions , long - term follow up of a larger sample will be necessary .
in addition , no comprehensive panel of inflammatory biomarkers was assessed . nevertheless , a correlation between tnf- levels and response to rehabilitation was observed .
if this correlation is confirmed , then the hypothesis that pharmaceutical therapies to reduce inflammation in infants diagnosed with cerebral palsy may lessen the symptoms of cerebral palsy may deserve further attention .
nevertheless , previous attempts to intervene with the development of cerebral palsy have not yielded long term benefits , but a better understanding of the aberrant immune response will undoubtedly help to develop potential therapeutic strategies for early treatment of cerebral palsy . finally , the neuroplasticity phenomenon might be involved in the increase if tnf- levels , but further study is necessary to address this issue .
in conclusion , children with cerebral palsy showed higher plasma levels of tnf- than controls .
in addition , pre - treatment tnf- levels were correlated with the improvements after rehabilitation therapy . | backgroundinflammatory responses in utero and in neonates have been involved in the development of white matter lesions .
this study aimed to investigate the role of tumor necrosis factor - alpha ( tnf- ) in spastic cerebral palsy.material/methodsplasma tnf- was measured by elisa in 54 children with spastic cerebral palsy and 28 aged - matched controls .
both groups were split into age subgroups ( 13 vs. 412 ) .
gross motor function and activities of daily living were assessed on enrollment and after 6 months of rehabilitation.resultstnf- was higher in patients with cerebral palsy than in controls in young ( p<0.001 ) and older subjects ( p<0.001 ) .
tnf- levels were comparable in both control subgroups ( p=0.819 ) .
younger patients with cerebral palsy had significantly higher tnf- levels compared with older ones ( p<0.001 ) .
pre - rehabilitation tnf- levels correlated with improvements in activities of daily living after rehabilitation ( p<0.001).conclusionschildren with cerebral palsy showed higher plasma levels of tnf- than controls .
in addition , pre - treatment tnf- levels were correlated with the improvements after rehabilitation therapy . | <s>[INST]cerebral palsy is a collective term for motor deficits resulting from non - progressive abnormalities in the immature brain occurring in about 2 of every 1000 live births in developed countries .
inflammatory responses in utero and in neonates have been involved in the development of the white matter lesions that cause cerebral palsy [ 26 ] .
infection in utero can cause damaging perturbations in inflammatory responses , and infants who develop an immune response in utero are at higher risk of cerebral lesions .
interleukin ( il)-6 and il-1 levels in umbilical cord plasma , amniotic fluid , and cerebrospinal fluid are elevated in neonates with periventricular leukomalacia - associated lesions , but this is controversial .
inflammation at or shortly after birth is associated with subnormal development in very preterm infants .
perinatal cytokine levels were often reported to predict the risk of cerebral palsy in preterm children [ 1113 ] .
in addition , polymorphisms in tnf- and il-1 have been found to represent a genetic susceptibility to white matter damage and consequently cerebral palsy .
however , a meta - analysis demonstrated that cerebral palsy is associated with a genetic polymorphism in il-6 , but not with tnf- or any other cytokine .
although the precise immune responses involved in the development of cerebral palsy remain to be fully characterized , aberrant inflammatory responses may continue to influence the reconstruction of cerebral function after birth [ 1820 ] .
tnf- has widespread biological functions , activating neutrophils to eliminate pathogenic microorganisms , stimulating mononuclear cells to produce il-1 and il-6 , and activating b lymphocytes to produce antibodies .
tnf- is secreted by astrocytes , microglia , blood - borne macrophages , and vascular endothelial cells in the central nervous system .
tnf- has been reported to cause increased blood - brain barrier permeability , participating in the development of cerebral edema .
although there is evidence suggesting that high levels of tnf- are associated with cerebral palsy [ 911,14,15,20 ] , little is known about age - related and function - related changes in tnf-. in the present study , levels of plasma tnf- in children with cerebral palsy were measured to assess the hypothesis that tnf- levels can act as a marker of both cerebral palsy presence and cerebral palsy severity .
in addition , patients were evaluated after rehabilitation therapy , and the pre - therapy levels of tnf- were compared with their response to therapy .
children with clinically confirmed spastic cerebral palsy were recruited from the department of rehabilitation , the second affiliated hospital of anhui medical university and the provincial children s hospital between december 2012 and august 2013 .
cerebral palsy was diagnosed according to the definition , classification , and diagnostic criteria recommended by the second national children rehabilitation conference & the ninth chinese cerebral palsy children rehabilitation academic conference in chang sha , china in 2009 .
the inclusion criteria were : 1 ) aged 112 years ; and 2 ) stable health .
exclusion criteria were : 1 ) history of epilepsy or fever in the preceding two months ; 2 ) inflammatory response syndrome ; 3 ) diseases that could elevate tnf- levels for other reasons , such as progressive amyotrophy , encephalomyelitis , severe malnutrition , myasthenia gravis , epilepsy , vision / hearing disorders , or other severe pediatric diseases ; or 4 ) other endocrine disorders , metabolic disorders , autoimmune diseases , or genetic diseases .
the enrolled subjects with cerebral palsy were divided into 2 subgroups : those aged 1 to 3 years ( n=27 ) and those aged 4 to 12 years ( n=27 ) .
twenty - eight control subjects free of brain disorders were recruited according to the same inclusion / exclusion criteria and were individually matched based on sex and age to the subjects with cerebral palsy .
the age cut - off point was selected because the blood - brain barrier mature around 3 years of age , preventing plasma inflammatory factors from damaging the brain .
blood samples were provided by all participants and the plasma levels of tnf- were measured .
patient gross motor function and activities of daily living were evaluated before and after six months of individualized physical and speech therapy .
control participant gross motor function and activities of daily living was evaluated over the same period .
the study was approved by the ethics committee of anhui medical university ( k201209 ) , and informed consents were obtained from the children s legal guardians .
participant gross motor function was evaluated by the gross motor function classification system ( gmfcs ) , which is a 5-level clinical classification system describing the gross motor function on the basis of self - initiated movement abilities .
all assessments were administered by the chief physician of the department ( 30 years of clinical experience in diagnosing , evaluating , and treating cerebral palsy ) .
gmfcs motor deficit severity was classified into levels i ( for the highest level of activity ) to v ( for the lowest level of activity ) .
the activities of daily living was assessed at the beginning of the study and again after six months of individualized physical and speech therapy , and the difference in score was recorded .
plasma tnf- levels were measured by elisa ( bms223/4 , bender medsystems gmbh , vienna , austria ) .
continuous data were analyzed by multivariate analysis by non - conditional logistic regression analysis between all subjects with cerebral palsy and controls .
correlation analysis between tnf- levels and motor functions was performed using the spearman correlation analysis .
the correlation between tnf- levels and improvement of activities of daily living was assessed by pearson correlation analysis .
children with clinically confirmed spastic cerebral palsy were recruited from the department of rehabilitation , the second affiliated hospital of anhui medical university and the provincial children s hospital between december 2012 and august 2013 .
cerebral palsy was diagnosed according to the definition , classification , and diagnostic criteria recommended by the second national children rehabilitation conference & the ninth chinese cerebral palsy children rehabilitation academic conference in chang sha , china in 2009 .
the inclusion criteria were : 1 ) aged 112 years ; and 2 ) stable health .
exclusion criteria were : 1 ) history of epilepsy or fever in the preceding two months ; 2 ) inflammatory response syndrome ; 3 ) diseases that could elevate tnf- levels for other reasons , such as progressive amyotrophy , encephalomyelitis , severe malnutrition , myasthenia gravis , epilepsy , vision / hearing disorders , or other severe pediatric diseases ; or 4 ) other endocrine disorders , metabolic disorders , autoimmune diseases , or genetic diseases .
the enrolled subjects with cerebral palsy were divided into 2 subgroups : those aged 1 to 3 years ( n=27 ) and those aged 4 to 12 years ( n=27 ) .
twenty - eight control subjects free of brain disorders were recruited according to the same inclusion / exclusion criteria and were individually matched based on sex and age to the subjects with cerebral palsy .
the age cut - off point was selected because the blood - brain barrier mature around 3 years of age , preventing plasma inflammatory factors from damaging the brain .
blood samples were provided by all participants and the plasma levels of tnf- were measured .
patient gross motor function and activities of daily living were evaluated before and after six months of individualized physical and speech therapy .
control participant gross motor function and activities of daily living was evaluated over the same period .
the study was approved by the ethics committee of anhui medical university ( k201209 ) , and informed consents were obtained from the children s legal guardians .
participant gross motor function was evaluated by the gross motor function classification system ( gmfcs ) , which is a 5-level clinical classification system describing the gross motor function on the basis of self - initiated movement abilities .
all assessments were administered by the chief physician of the department ( 30 years of clinical experience in diagnosing , evaluating , and treating cerebral palsy ) .
gmfcs motor deficit severity was classified into levels i ( for the highest level of activity ) to v ( for the lowest level of activity ) .
the activities of daily living was assessed at the beginning of the study and again after six months of individualized physical and speech therapy , and the difference in score was recorded .
plasma tnf- levels were measured by elisa ( bms223/4 , bender medsystems gmbh , vienna , austria ) .
all statistical analyses were performed using spss 13.0 ( spss inc . , chicago , il , usa ) .
continuous data were analyzed by multivariate analysis by non - conditional logistic regression analysis between all subjects with cerebral palsy and controls .
correlation analysis between tnf- levels and motor functions was performed using the spearman correlation analysis .
the correlation between tnf- levels and improvement of activities of daily living was assessed by pearson correlation analysis .
there was no significant difference in height , body weight , age , and sex between subjects with cerebral palsy and healthy controls ( tables 1 , 2 ) .
the mean plasma tnf- levels of subjects with cerebral palsy ( 21.46.2 pg / ml ) was significantly higher than in controls ( 11.24.1 pg / ml ) ( p<0.001 ) .
this difference was present in both age subgroups ( younger : 25.04.9 pg / ml vs. 11.43.4 pg / ml , p<0.001 ; and older : 17.85.2 pg / ml vs. 11.04.9 pg / ml , p<0.001 ) . while the levels of tnf- in the plasma of both control subgroups were comparable ( p=0.819 ) , younger subjects with cerebral palsy had significantly higher plasma tnf- levels than older subjects with cerebral palsy ( p<0.001 ) ( table 2 ) .
multivariate analysis revealed that although neither age nor sex were significantly correlated with cerebral palsy , plasma levels of tnf- were significantly correlated with cerebral palsy ( or=1.605 , 95%ci 1.3021.979 , p<0.001 ) ( table 3 ) .
there was no correlation between plasma tnf- levels and gmfcs in the entire group of subjects with cerebral palsy .
however , plasma tnf- levels correlated significantly with gmfcs in the subgroups of patients with spastic triplegia or quadriplegia cerebral palsy ( r=0.525 , p=0.038 ) , and spastic diplegia cerebral palsy ( r=0.521 , p=0.001 ) ( table 4 ) . nevertheless , a general trend toward an association in the whole group could be observed .
pre - rehabilitation plasma tnf- levels were also significantly correlated with the improvements in activities of daily living after 6 months of comprehensive rehabilitation in all subjects with cerebral palsy ( r=0.593 , p<0.001 ) ( table 4 ) .
similar results were observed in subjects with spastic triplegia or quadriplegia cerebral palsy ( r=0.839 , p<0.001 ) , and spastic diplegia cerebral palsy ( r=0.796 , p<0.001 ) .
there was no significant difference in height , body weight , age , and sex between subjects with cerebral palsy and healthy controls ( tables 1 , 2 ) .
the mean plasma tnf- levels of subjects with cerebral palsy ( 21.46.2 pg / ml ) was significantly higher than in controls ( 11.24.1 pg / ml ) ( p<0.001 ) .
this difference was present in both age subgroups ( younger : 25.04.9 pg / ml vs. 11.43.4 pg / ml , p<0.001 ; and older : 17.85.2 pg / ml vs. 11.04.9 pg / ml , p<0.001 ) . while the levels of tnf- in the plasma of both control subgroups were comparable ( p=0.819 ) , younger subjects with cerebral palsy had significantly higher plasma tnf- levels than older subjects with cerebral palsy ( p<0.001 ) ( table 2 ) .
multivariate analysis revealed that although neither age nor sex were significantly correlated with cerebral palsy , plasma levels of tnf- were significantly correlated with cerebral palsy ( or=1.605 , 95%ci 1.3021.979 , p<0.001 ) ( table 3 ) .
there was no correlation between plasma tnf- levels and gmfcs in the entire group of subjects with cerebral palsy . however ,
plasma tnf- levels correlated significantly with gmfcs in the subgroups of patients with spastic triplegia or quadriplegia cerebral palsy ( r=0.525 , p=0.038 ) , and spastic diplegia cerebral palsy ( r=0.521 , p=0.001 ) ( table 4 ) . nevertheless , a general trend toward an association in the whole group could be observed .
pre - rehabilitation plasma tnf- levels were also significantly correlated with the improvements in activities of daily living after 6 months of comprehensive rehabilitation in all subjects with cerebral palsy ( r=0.593 , p<0.001 ) ( table 4 ) .
similar results were observed in subjects with spastic triplegia or quadriplegia cerebral palsy ( r=0.839 , p<0.001 ) , and spastic diplegia cerebral palsy ( r=0.796 , p<0.001 ) .
as early as 2007 , dammann et al . proposed that persistent activation or accumulation of inflammatory cytokines may impede the reconstruction of brain function following brain injury , therefore promoting cerebral palsy .
these pathological changes disturb the maturation of oligodendrocytes , limit neuronal regeneration , and impair synapse formation . in this study , we measured the plasma levels of tnf- in 54 children with spastic cerebral palsy , and in 28 age - matched healthy controls , and examined whether the levels of tnf- were associated with the presence of cerebral palsy and the degree of functional disturbance in cerebral palsy .
the plasma levels of tnf- were significantly higher in children with spastic cerebral palsy , and significantly higher in children with cerebral palsy aged 13 than children aged 412 .
these results suggest that immunological abnormalities , while more pronounced before the age of four , may persist in cerebral palsy throughout childhood .
enormous production of inflammatory cytokines including tnf- and il-1 has been previously detected in vulnerable brain regions of premature infants with white matter injury .
high levels of il-1 , il-6 , il-8 , il-9 , and tnf- have also been detected in the perinatal peripheral blood of full - term and preterm subjects with cerebral palsy , but this is controversial . in the present study ,
only children with no history of fever , epilepsy , or inflammatory disorders in the previous two months were enrolled .
children under the age of four with spastic cerebral palsy had higher levels of plasma tnf- compared with older children .
this observation suggests that the inflammatory response may decrease with age , while the symptoms of cerebral palsy do not necessarily improve . additionally ,
higher baseline levels of tnf- might be a marker of more extensive brain damage and of a weaker than average response to this form of therapy . since therapies targeting activated microglia and astrocytes or anti - cytokine treatments may help reduce
the injury of cerebral palsy , therapeutic interventions designed to reduce inflammation may yield beneficial results in children throughout childhood .
recently , alcaraz et al . reported the use of platelet - rich plasma for the treatment of a patient with cerebral palsy , leading to improvements in the cognitive score and motor functions .
however , the exact mechanisms of these approaches require further study . to investigate the relationship between tnf- and cerebral palsy severity ,
although tnf- levels were not associated with gmfcs in the entire sample , tnf- levels were significantly correlated with gmfcs in patients with spastic triplegia and quadriplegia , and with diplegia , supporting the hypothesis that circulating levels of tnf- can reflect the severity of motor dysfunction in some types of spastic cerebral palsy .
inflammation and intrauterine infection have been reported to activate microglia of the central nervous system , changing the function of neurons and glial cells , and causing cytotoxicity , edema , and brain injury in the fetal and neonatal brain .
elevated levels of circulating tnf- found in the present study suggest that this inflammatory process persists throughout childhood .
a variety of different forms of brain injury have been associated with cerebral palsy including cerebellar atrophy , diffuse cortical atrophy , periventricular leukomalacia , thin corpus callosum , and border - zone infarction .
the present study suggests that the severity of illness was correlated to tnf- levels in spastic triplegia and quadriplegia , and in diplegia .
in addition , the follow - up was short . to confirm the capacity of tnf- to represent a marker of disease severity , or
predict outcome of interventions , long - term follow up of a larger sample will be necessary .
in addition , no comprehensive panel of inflammatory biomarkers was assessed . nevertheless , a correlation between tnf- levels and response to rehabilitation was observed .
if this correlation is confirmed , then the hypothesis that pharmaceutical therapies to reduce inflammation in infants diagnosed with cerebral palsy may lessen the symptoms of cerebral palsy may deserve further attention .
nevertheless , previous attempts to intervene with the development of cerebral palsy have not yielded long term benefits , but a better understanding of the aberrant immune response will undoubtedly help to develop potential therapeutic strategies for early treatment of cerebral palsy . finally , the neuroplasticity phenomenon might be involved in the increase if tnf- levels , but further study is necessary to address this issue .
in conclusion , children with cerebral palsy showed higher plasma levels of tnf- than controls .
in addition , pre - treatment tnf- levels were correlated with the improvements after rehabilitation therapy .[/INST]backgroundinflammatory responses in utero and in neonates have been involved in the development of white matter lesions .
this study aimed to investigate the role of tumor necrosis factor - alpha ( tnf- ) in spastic cerebral palsy.material/methodsplasma tnf- was measured by elisa in 54 children with spastic cerebral palsy and 28 aged - matched controls .
both groups were split into age subgroups ( 13 vs. 412 ) .
gross motor function and activities of daily living were assessed on enrollment and after 6 months of rehabilitation.resultstnf- was higher in patients with cerebral palsy than in controls in young ( p<0.001 ) and older subjects ( p<0.001 ) .
tnf- levels were comparable in both control subgroups ( p=0.819 ) .
younger patients with cerebral palsy had significantly higher tnf- levels compared with older ones ( p<0.001 ) .
pre - rehabilitation tnf- levels correlated with improvements in activities of daily living after rehabilitation ( p<0.001).conclusionschildren with cerebral palsy showed higher plasma levels of tnf- than controls .
in addition , pre - treatment tnf- levels were correlated with the improvements after rehabilitation therapy .</s> |
clusters of galaxies are thought to grow into larger systems through complex interactions between smaller systems .
signatures of merging events include temperature and density inhomogeneities and bulk motions in the intracluster medium ( icm ) .
numerical simulations predict simplified bulk motions with a substantial fraction of virial velocity ( @xmath41000 km s@xmath3 ) , lasting several gyr after each merging event ( e.g. , @xcite ; @xcite ) .
measurements of the icm temperature and velocity structure , therefore , provide crucial information for understanding the evolution of clusters .
velocity measurements of bulk motion and turbulence are essential for mass estimation and cosmological studies .
if icm has a significant bulk velocity compared to its thermal velocity , the associated non - thermal pressure would threaten the assumption of hydrostatic equilibrium in deriving the total gravitational mass in a cluster .
for example , factors of 23 discrepancies between the x - ray and lensing mass estimates in some objects ( e.g. , @xcite ; @xcite ) could be partly due to this effect .
@xcite discovered a significant bulk motion in abell 2256 , which is a well known merging cluster .
@xcite performed a fourier analysis of xmm - newton data of the coma cluster , which revealed the presence of a scale - invariant pressure fluctuation ranging between 29 and 64 kpc , and @xmath410% of the total pressure in turbulent form .
however , in relaxed clusters , significant bulk motions and turbulence have not been detected .
on the basis of asca and chandra data , @xcite claimed a large velocity gradient of @xmath42400 km s@xmath3 in the centaurus cluster , which is a relaxed cluster with a cool core .
however , @xcite found a negative result of @xmath5 km s@xmath3 on the basis of suzaku observations of the centaurus cluster .
@xcite also searched for possible bulk motions in the awm 7 cluster with suzaku , and observed no significant bulk motions .
the upper limit of gas velocity was @xmath6 2000 km s@xmath3 .
@xcite do not detect the variation of the redshift of the icm in the ophiuchus cluster , and the upper limit of the velocity difference is 3000 km s@xmath3 .
@xcite studied the icm flow in abell 2319 with suzaku , and detected no velocity differences within the observed region . using spectra with a reflection grating spectrometer ( rgs ) onboard xmm - newton ,
@xcite provided upper limits on turbulence velocities in cluster core regions : at least 15 sources had less than 20% of the thermal energy density in turbulence .
the coma cluster ( @xmath7 ) , also known as abell 1656 , is one of the most studied clusters @xcite and has been observed at all wavelengths from radio to hard x - ray bands .
however , the physical state , particularly the dynamical state , of the coma cluster has not been completely understood .
measurements of the velocity dispersion and distribution of galaxies belonging to the coma cluster constrain the dynamical history of the coma cluster .
@xcite found that two central galaxies , ngc 4889 and ngc 4874 have a significant difference in velocity , which is evidence of a recent merger .
@xcite argued that ngc 4874 was the original dominant galaxy of the main cluster , and that ngc 4889 belonged to a subgroup , that recently merged with the main cluster .
a substructure associated with the galaxy , ngc 4839 , located 40@xmath0 south - west of the cluster core , was found by @xcite and @xcite .
the existence of this subcluster was confirmed by @xcite .
the thermal x - ray emission of the coma cluster has been observed with several x - ray satellites .
@xcite constructed an x - ray map of the coma cluster using rosat all - sky - survey data and determined the x - ray surface brightness profile of the cluster out to a radius of roughly 100@xmath0 .
the temperature maps of clusters provide knowledge about the history of past subcluster mergers . on the basis of asca observations , @xcite and @xcite found that icm is not isothermal .
@xcite used xmm - newton to study the temperature structure in the central region of the coma cluster .
the projected temperature distribution around ngc 4889 and ngc 4874 is remarkably homogeneous , which suggests that the core is mostly in a relaxed state . except at the center ,
the temperature decreases slightly with radius .
a cool filament of an x - ray emission in the direction of the galaxy ngc 4911 , which is located in the south - east of the cluster center , was detected with chandra @xcite and xmm @xcite .
rosat observed a substructure around the ngc 4839 subgroup @xcite , and a hot region in the direction of ngc 4839 was observed by @xcite . by xmm - newton observations
, @xcite found compelling evidence for the subgroup around ngc 4839 was on its first infall into the coma cluster , but it had not passed its core yet .
this interpretation is different from that of @xcite , who suggested that the ngc 4839 group was moving out of the cluster after having already passed through the coma cluster .
non - thermal electrons , observed via diffused radio synchrotron emission , have been detected in more than 50 clusters , and all of them are undergoing mergers ( e.g. , @xcite ; @xcite ) .
the coma cluster also has a cluster - wide synchrotron radio halo , emitted by relativistic electrons due to merging @xcite .
recent non - thermal detections have been claimed by @xcite with rxte and by @xcite with bepposax , although the latter detection is controversial @xcite
. long observations ( @xmath41 ms ) by integral have imaged extended diffuse hard x - ray emission from the coma cluster , although it was found to be completely consistent with thermal emission @xcite .
using the temperature map of icm obtained with the pn detector onboard xmm - newton , @xcite analyzed data obtained from the suzaku hard x - ray detector ( hxd ) @xcite and derived the strongest upper limit of non - thermal emission .
this paper reports results from six suzaku observations of the coma cluster out to 60@xmath0 , @xmath81.5 mpc , conducted using the x - ray imaging spectrometer ( xis ) @xcite onboard suzaku @xcite . owing to its lower background level , suzaku has better sensitivity to the iron k@xmath1 lines than previous satellites .
in addition , the accurate calibration of xis allows us to measure the velocity of icm precisely .
we used the hubble constant , @xmath9 km s@xmath3 mpc@xmath3 .
the distance to the coma cluster is @xmath10 mpc , and @xmath11 corresponds to 28.9 kpc .
we used the abundance ratio by @xcite , in which the solar fe abundance relative to h is 2.95@xmath1210@xmath13 .
errors are quoted at a 90% confidence level for a single parameter .
the remainder of this paper is organized as follows : we present the observations in section 2 and describe the data analysis in section 3 .
we describe the results of spectral fittings and temperature structure in subsection 4.1 , bulk motions in subsection 4.5 , and the fe abundance in subsection 4.6 . in section 5 ,
we discuss the results , and in section 6 , we summarize the findings .
cccccccc field name & target name & sequence & observation & ra & dec & exposure & distance from the + & & number & date & ( deg ) & ( deg ) & ( ks ) & x - ray peak + center & coma radio halo & 801097010 & 2006 - 05 - 31 & 194.9267 & 27.9061 & 150 & + offset & coma cluster offset & 801044010 & 2006 - 05 - 30 & 194.6939 & 27.9466 & 79 & + offset & coma 11 & 802082010 & 2007 - 06 - 19 & 194.6305 & 28.3939 & 53 & + offset & coma bkg2 & 802084010 & 2007 - 06 - 21 & 194.3428 & 28.1403 & 30 & + offset & coma 45 & 802047010 & 2007 - 12 - 02 & 194.2558 & 27.5714 & 30 & + offset & coma 60 & 802048010 & 2007 - 12 - 04 & 194.0251 & 27.4252 & 35 & + offset & coma bkg & 802083010 & 2007 - 06 - 21 & 198.7472 & 31.6480 & 30 & + ( 80 mm , 60mm)figure1_a.eps ( 80 mm , 60mm)figure1_b.eps suzaku carried out six observations in the coma cluster .
the details of the observations are summarized in table [ tab : ob ] .
two central observations were carried out in may 2006 , during the suzaku phase - i period .
the first observation , `` coma radio halo '' , has a pointing that is @xmath14 offset from the x - ray peak of the coma cluster , which has coordinates ( ra , dec ) = ( 194.9367 , 27.9472 ) in degrees .
the second observation , `` coma cluster offset '' , was located @xmath15 west offset from the first observation .
the other observations , in the @xmath16 and @xmath17 north west offset regions and @xmath18 and @xmath19 south west offset regions , were carried out in 2007 , during the suzaku phase - ii period . to eliminate background emissions , archival suzaku data with a 5 degree offset from the coma cluster , observed in june 2007
was also used , and is shown in table [ tab : ob ] .
xis was operated in its normal mode during observations .
the xis instrument consists of four sets of x - ray ccd ( xis0 , 1 , 2 , and 3 ) .
xis1 is a back - illuminated ( bi ) sensor , while xis0 , 2 , and 3 are front - illuminated ( fi ) sensors .
xis2 was not used during the four offset observations beyond 30@xmath0 from the x - ray peak .
figure [ fig : image ] shows a 0.54.0 kev image of xis0 .
we performed data reduction using heasoft version 6.6.3 .
xis event lists created by the rev 2.0 pipeline processing were filtered using the following additional criteria : the geomagnetic cut - off rigidity ( cor2 ) @xmath20 6 gv , and elevation angle from the earth limb @xmath21 .
the data formats of 5x5 and 3x3 editing modes were added .
the exposure times after the data selection are shown in table [ tab : ob ] .
to study the temperature structure and search for possible bulk motions of icm in the coma cluster on the scale of a few arcminutes , we divided the 18@xmath22 square xis field of view ( fov ) of the center and 14@xmath0 offset regions into @xmath23 and @xmath24 cells , respectively , as shown in figure [ fig : image ] .
each region in the center and @xmath15 offset regions subtends @xmath12 ( 117@xmath25 kpc ) , and 9@xmath26 ( 234@xmath27 kpc ) , respectively .
regions around calibration sources were excluded .
luminous point sources in which the flux limit corresponds to @xmath4 10@xmath28 counts s@xmath3 in the 2.010.0 kev energy range were also excluded as circular regions with a radius of 1@xmath0 . at most 10 point sources
were excluded for each of the observed regions .
we extracted spectra from the whole xis fov for regions more than @xmath29 from the x - ray peak . the non x - ray background ( nxb )
was subtracted from each spectrum using a database of night earth observations with the same detector area and cor distribution @xcite .
we included the degradation of energy resolution due to radiation damage in the redistribution matrix file ( rmf ) generated by the xisrmfgen ftools task .
we also created an ancillary response file ( arf ) using the xissimarfgen ftools task @xcite .
a decrease in the low - energy transmission of the xis optical blocking filter ( obf ) was also included in arf . to generate arf files for the center and 14@xmath0 offset regions , we used a @xmath30-model profile for the simulated surface brightness profile in @xcite .
for @xmath16 , @xmath17 , @xmath18 , @xmath19 , and 5 degree offset regions , we generated arfs assuming a uniformly extended emission from an encircled region with a 20@xmath0 radius , because the gradient of surface brightness within each fov is small .
we used the xspec_v11.3.2ag package for spectral analysis .
we have investigated the temperature structure , bulk motions , and iron abundance distribution of the coma cluster . we fitted the spectra with a thermal plasma model ( apec : @xcite ) to obtain the temperature , redshift and fe abundance of icm .
a detailed spectral analysis is presented in subsection [ subsec : single ] .
we used three gaussian models to obtain the temperature using the normalization ratio of k@xmath1 lines of h - like and he - like fe , and redshift using the shift of line centroid energy , which is presented in subsection [ subsec : ratios ] .
( 80 mm , 60mm)figure2.eps cccccccc & & & + @xmath31 & normalization & temperature & normalization & temperature & normalization & + & & ( kev ) & @xmath32 & ( kev ) & @xmath33 & @xmath2/d.o.f & @xmath2/d.o.f + @xmath34 & @xmath35 & 0.07 ( fixed ) & @xmath36 & @xmath37 & @xmath38 & 188/141 & 223/154 + first , we fitted the spectra in the 5@xmath39 offset region to determine the local x - ray background .
as shown in @xcite , the background emission of suzaku xis can be fitted with a three component model : two thermal plasma models ( apec : @xcite ) for the local hot bubble ( lhb ) and the milky way halo ( mwh ) , and a power - law model for the extragalactic cosmic x - ray background ( cxb ) .
mwh and cxb components were convolved with an absorption in the galaxy .
we , therefore , fitted the spectra simultaneously in the 0.58.0 kev energy range for xis fis and the 0.358.0 kev energy range for xis bi using the following model formula : @xmath40-@xmath41 .
we assumed a zero redshift and a solar abundance for lhb and mwh components .
the temperature of lhb was fixed at 0.07 kev @xcite , while the temperature of mwh was variable .
the column density of the galactic neutral hydrogen was fixed at 1.0@xmath42 @xmath43 @xcite . to avoid systematic uncertainties in the background , we ignored the 1.401.55 kev energy range , where a relatively large uncertainty exists because of an instrument al line @xcite , and energies above 8 kev .
we also excluded the narrow energy band between 1.82 and 1.84 kev in the fits because of incomplete responses around the si edge .
results of the spectral fit are shown in figure [ fig : bkgfit ] and the resultant parameters of the fit are shown in table [ tab : bkgtable ] .
the derived photon index and normalization of the cxb component agree with @xcite and @xcite .
the derived temperature and normalizations of the two thermal models are consistent with those obtained from xmm and suzaku observations @xcite .
we generated the simulated spectra of the x - ray background including lhb , mwh , and cxb emissions derived from the resultant parameters of the fits in the 5@xmath39 offset region .
we used the simulated spectra as the background to fit the spectra for icm of the coma cluster .
figure [ fig : bgd ] shows the comparison between the xis0 spectra of the 60@xmath0 offset region of the coma cluster and backgrounds . above 7 kev
, nxb dominates the observed spectra of the 60@xmath0 offset region .
we also show the background - subtracted spectrum of the 60@xmath0 offset region of the coma cluster in figure [ fig : bgd ] ( blue ) .
the x - ray background spectra are well reproduced .
( 80 mm , 60mm)figure3.eps we fitted the xis spectra in each region of the coma cluster using a single temperature model ( apec ) with the galactic absorption , @xmath44 . each spectral bin contained 50 or more counts .
we fitted the spectra in two energy bands : 1.08.0 and 5.08.0 kev . to avoid systematic uncertainties in the background , we ignored energies higher than 8 kev .
we also excluded the narrow energy band between 1.82 and 1.84 kev in the fits because of incomplete responses around the si edge .
temperature , redshift and normalization of the single temperature model were free parameters , and @xmath44 was fixed to the galactic value , @xmath45 , in the direction of the coma cluster .
abundances of he , c , n , and al were fixed to be a solar .
we divided the other metals into three groups : o , ne and mg ; si , s , ar and ca ; and fe and ni , and allowed them to vary .
the resultant parameters are summarized in table [ tab:1 - 8vapecresults ] , and a sample of the spectra is shown in figure [ fig : spec ] . since our data have very high statistics , especially in the central region , there remain residual structures around the si edge structure .
these residuals are probably caused by systematic uncertainties in the response matrix because the bi and fi detectors gave different residuals .
therefore , to avoid systematic uncertainties in all regions , we excluded the energy range of 1.72.3 kev and fitted the spectra again .
the derived temperatures hardly changed , although the reduced @xmath2 decreased by 20% .
the resultant @xmath2 are summarized in table [ tab:1 - 8vapecresults ] .
to constrain the temperature structure , we fitted the spectra of the center and offset regions with a two - temperature ( apec ) model in the energy range of 1.08.0 kev , ignoring the energy range of 1.72.3 kev .
the @xmath46 are improved slightly by less than a few percent .
the derived temperatures of one component are similar to those derived from the single - temperature model fits , and those of the other component are either above 10 kev or below 2 kev . to obtain more detailed constraints for the lower and higher temperature components , we fitted the spectra with a three - temperature ( apec ) model in the energy range of 1.08.0 kev , excluding the 1.72.3 kev energy range to avoid uncertainties in the response matrix . in this model , the lowest , middle and highest temperatures
are restricted to below 6 kev , within 6.010.0 kev , and above 10.0 kev , respectively .
the resultant @xmath46 values are shown in table [ tab:1 - 8vapecresults ] . to derive the fe abundance and velocity of the bulk - motion from fe - k lines
, we fitted the spectra of each region with the single - temperature apec model in an energy range of 5.08.0 kev .
the results are shown in table [ tab:1 - 8vapecresults ] . to precisely determine the bulk velocity of icm , the accuracy of photon energy measurements is crucial .
some sensors have large uncertainties in the determination of the line centroid energy .
thus , we averaged the spectrum over fov in ( i ) all detectors , and ( ii ) all detectors except for different mn k@xmath1 line centroid energies to check the spectral shape and measured redshift in the center and ngc 4839 regions ( 44@xmath0 offset region ) .
cccccccccc & & & gaussians + region & @xmath47 & @xmath46/d.o.f .
& @xmath46/d.o.f . & @xmath46/d.o.f . & @xmath46/d.o.f . & fe & redshift & @xmath46/d.o.f .
& @xmath47 from line + & [ kev ] & ( 1 t ) & ( 1 t ) & ( 2 t ) & ( 3 t ) & [ solar ] & [ @xmath48 & & ratio [ kev ] + center & & & & & & & & & + @xmath49 & @xmath50 & @xmath51 & @xmath52 & @xmath53 & @xmath54 & @xmath55 & @xmath56 & @xmath57 & @xmath58 + @xmath59 & @xmath60 & @xmath61 & @xmath62 & @xmath63 & @xmath64 & @xmath65 & @xmath66 & @xmath67 & @xmath68 + @xmath69 & @xmath70 & @xmath71 & @xmath72 & @xmath73 & @xmath74 & @xmath75 & @xmath76 & @xmath77 & @xmath78 + @xmath79 & @xmath80 & @xmath81 & @xmath82 & @xmath83 & @xmath84 & @xmath85 & @xmath86 & @xmath87 & @xmath88 + @xmath89 & @xmath90 & @xmath91 & @xmath92 & @xmath93 & @xmath94 & @xmath95 & @xmath96 & @xmath97 & @xmath98 + @xmath99 & @xmath100 & @xmath101 & @xmath102 & @xmath103 & @xmath104 & @xmath105 & @xmath106 & @xmath107 & @xmath108 + @xmath109 & @xmath110 & @xmath111 & @xmath112 & @xmath113 & @xmath114 & @xmath115 & @xmath116 & @xmath117 & @xmath118 + @xmath119 & @xmath120 & @xmath121 & @xmath122 & @xmath123 & @xmath124 & @xmath125 & @xmath126 & @xmath127 & @xmath128 + @xmath129 & @xmath130 & @xmath131 & @xmath112 & @xmath132 & @xmath133 & @xmath134 & @xmath135 & @xmath136 & @xmath137 + @xmath138 & @xmath139 & @xmath140 & @xmath141 & @xmath142 & @xmath143 & @xmath144 & @xmath145 & @xmath146 & @xmath147 + @xmath148 & @xmath149 & @xmath150 & @xmath151 & @xmath123 & @xmath152 & @xmath153 & @xmath154 & @xmath155 & @xmath156 + @xmath157 & @xmath158 & @xmath159 & @xmath160 & @xmath161 & @xmath162 & @xmath163 & @xmath164 & @xmath165 & @xmath166 + @xmath167 & @xmath168 & @xmath169 & @xmath170 & @xmath171 & @xmath172 & @xmath173 & @xmath174 & @xmath175 & @xmath176 + @xmath177 & @xmath178 & @xmath179 & @xmath180 & @xmath181 & @xmath182 & @xmath183 & @xmath184 & @xmath185 & @xmath186 + offset & & & & & & & & & + @xmath187 & @xmath188 & @xmath189 & @xmath190 & @xmath191 & @xmath192 & @xmath193 & @xmath194 & @xmath97 & @xmath195 + @xmath196 & @xmath197 & @xmath198 & @xmath199 & @xmath200 & @xmath201 & @xmath202 & @xmath203 & @xmath204 & @xmath205 + @xmath206 & @xmath207 & @xmath208 & @xmath209 & @xmath210 & @xmath211 & @xmath212 & @xmath213 & @xmath214 & @xmath215 + @xmath216 & @xmath217 & @xmath218 & @xmath219 & @xmath220 & @xmath221 & @xmath222 & @xmath223 & @xmath224 & @xmath225 + offset & @xmath226 & @xmath227 & @xmath228 & @xmath229 & @xmath230 & @xmath231 & @xmath232 & @xmath233 & @xmath234 + offset & @xmath235 & @xmath236 & @xmath237 & @xmath238 & @xmath239 & @xmath240 & @xmath241 & @xmath242 & @xmath243 + offset & @xmath244 & @xmath245 & @xmath246 & @xmath247 & @xmath248 & @xmath249 & @xmath250 & @xmath251 & @xmath252 + offset & @xmath253 & @xmath254 & @xmath255 & @xmath256 & @xmath257 & @xmath258 & @xmath259 & @xmath260 & @xmath261 + ( 80 mm , 60mm)figure4a.eps ( 80 mm , 60mm)figure4b.eps ( 80 mm , 60mm)figure4c.eps ( 80 mm , 60mm)figure4d.eps ( 80 mm , 60mm)figure4e.eps ( 80 mm , 60mm)figure4f.eps to derive the icm temperature from the normalization ratio of k@xmath1 lines of h - like and he - like fe , and the possible bulk motions of icm from the central energy of the lines , we fitted the spectra in the energy range of 5.08.0 kev with a sum of bremsstrahlung and three gaussian components , which correspond to k@xmath1 lines of he - like and h - like fe , and a mixture of the k@xmath1 line of he - like ni and the k@xmath30 line of he - like fe . the temperature and normalization of the bremsstrahlung component , and the central energy and normalizations of the gaussian components were free parameters , while the line width of gaussian models was fixed at 0 .
the best - fit spectra are shown in figure [ fig : bremss_spec ] .
( 80 mm , 60mm)figure5a.eps ( 80 mm , 60mm)figure5b.eps ( 80 mm , 60mm)figure5c.eps ( 80 mm , 60mm)figure5d.eps ( 80 mm , 60mm)figure5e.eps ( 80 mm , 60mm)figure5f.eps
( 80mm,60mm)figure6a.eps ( 80mm,60mm)figure6b.eps figure [ fig : kt_apec ] shows a radial profile and map of the derived temperatures from the spectral fits with the single temperature ( apec ) model in the energy range of 1.08.0 kev .
the radial temperature profile of the coma cluster is relatively flat within @xmath4500 kpc , which corresponds to the 14@xmath0 offset region , and decreases with the radius to the outer region .
while the regions observed with suzaku are limited , the resultant temperature profile is similar to that derived from xmm - newton observations , which cover nearly the entire coma cluster out to @xmath41200 kpc @xcite .
excluding the south - east quadrant ( cell numbers : 2,3,6 , and 7 ) , and the 14@xmath0 offset region , temperatures of cells in the center region have a flat distribution within a small range between @xmath48 kev and @xmath49 kev . within 300 kpc from the x - ray peak in the center region ,
the weighted mean temperature with statistical errors of the 16 cells is 8.34@xmath2620.19 kev .
the south - east quadrant ( cell numbers : 2,3,6 , and 7 ) in the center region has a slightly cooler temperature : the weighted average with statistical errors of the four cells is 7.39@xmath2620.11 kev .
this value is close to that of 5.07.0 kev in the cool temperature region observed by xmm - newton , which would be a counterpart of the south - east quadrant region @xcite .
on the other hand , the north - west quadrant in the center region ( cell numbers : 8,13 , and 14 ) and the nearby area of the 14@xmath0 offset region ( cell numbers : 17,18 ) have slightly higher temperatures of @xmath49 kev .
the 34@xmath0 offset region located to the north - west of the 14@xmath0 offset region , also has a relatively high temperature of @xmath489 kev .
this direction corresponds to the hot spot , @xmath263 kev in @xcite with asca , and @xmath2640.4 kev in @xcite with xmm - newton .
recent integral observations have shown a surface brightness excess relative to xmm observations , which is well - represented by the extended hot thermal emission with @xmath265 kev @xcite .
the temperature in the 30@xmath0 offset region is around @xmath467 kev , and is clearly cooler than temperatures in the inner region .
this value is consistent with the previous results in @xcite , and @xcite .
the 44@xmath0 and 60@xmath0 offset regions include the ngc 4839 subcluster , and temperatures decreases with radius to 5.31@xmath2620.20 kev and 3.74@xmath2620.13 kev , respectively .
these values are cooler than those in @xcite with asca , but are consistent with those in @xcite and @xcite with xmm - newton .
temperatures of the core and tail of ngc 4839 with xmm - newton , which is located in the 44@xmath0 offset region with suzaku , are @xmath266 kev and @xmath267 kev , respectively @xcite .
the temperature of the main body of the subcluster is @xmath268 kev @xcite .
suzaku provided more significant temperatures than previous measurements in these regions . in summary ,
the temperature distribution observed with suzaku is fairly consistent with the previous results observed with asca , xmm and integral .
in addition , we note that statistical and systematic errors with suzaku are much smaller than those in previous results .
( 80mm,60mm)figure7a.eps ( 80mm,60mm)figure7b.eps as shown in figure [ fig : spec ] , the spectra in the energy range of 1.08.0 kev are well - represented by the single - temperature model . except for discrepancies between fi and bi detectors around the si - edge ,
there are no systematic residuals .
figure [ fig:3tchi ] shows a comparison of the resultant @xmath2 fitted with single and three temperature ( apec ) models in the energy range of 1.08.0 kev , excluding the 1.72.3 kev energy range .
a more statistically rigorous approach would be to apply the f - test to compare single - temperature and three temperature models .
the f - test indicates that the three - temperature model is significantly better than the single - temperature model in regions 1 , 5 , 6 , 7 , 9 , 10 , and 11 of the center region and 17 of the 14@xmath0 offset region , and better in regions 2 , and 14 of the center region , and 16 , and 19 of the 14@xmath0 offset region , 30@xmath0 offset region , 44@xmath0 offset region , and 60@xmath0 offset region .
the largest f statistic value is 11.4 in cell number 7 of the center region , and the least f statistic value is 0.238 in cell number 8 of the center region .
however , the single - temperature model fit still represents the spectra fairly well .
( 80mm,60mm)figure8a.eps ( 80mm,60mm)figure8b.eps the spectra accumulated over each region may contain multi temperature components , although the single temperature ( apec ) model represented those spectra well . because the ratio of he - like and h - like fe k@xmath1 lines strongly depends on the plasma temperature , comparisons of temperatures derived from the line ratio and spectral fits with the thermal model are useful for understanding the temperature structure of icm .
figure [ fig : kt_ratio ] shows the ratios of the resultant normalizations of the fe k@xmath1 lines , plotted versus the temperature derived from the spectral fits with the single temperature ( apec ) model in the energy range of 1.08.0 kev . to convert line ratios to plasma temperature , we generated mock spectra assuming the single temperature apec or mekal @xcite plasma code models , convolved with xis energy resolution .
we then fitted the mock spectra with a sum of a bremsstrahlung and three gaussian models .
the theoretical line ratios from apec and mekal plasma codes are also plotted in figure [ fig : kt_ratio ] .
the derived line ratios agreed with these theoretical line ratios of the apec plasma code assuming the single temperature model , while the mekal model gave a line ratio value several % lower at a given temperature . assuming a single temperature plasma , we converted the observed line ratios to plasma temperatures using the theoretical relation for the apec model .
results are shown in table [ tab:1 - 8vapecresults ] and figure [ fig : kt_ratio ] . as shown in figure [ fig : kt_ratio ] , line temperatures agreed with those derived from the spectral fits very well .
( 80 mm , 60mm)figure9a.eps ( 80 mm , 60mm)figure9b.eps @xcite claimed a significant temperature difference of icm at the edge of the radio halo on the basis of xmm - newton observations : the temperature at the inner edge of the radio halo is 6.8@xmath2620.6 kev , while the temperature at the outer edge of the radio halo is 16.3@xmath2622.9 kev .
to examine this temperature difference , we extracted spectra from counterpart regions in the 34@xmath0 offset region , which are represented by two red boxes in figure [ fig : fino ] , and fitted the spectra with the single temperature ( apec ) model .
as shown in figure [ fig : fino ] , there are no significant temperature differences for each box in the 34@xmath0 offset region .
we then divided fov of the 34@xmath0 offset region into 2@xmath269 cells as shown in figure [ fig : fino ] , and fitted the spectra with the single temperature ( apec ) model .
the derived temperatures are also consistent with each other .
to constrain the line - of - sight gas motion using the he - like fe - k@xmath1 line , precise calibration of the xis energy scale is crucial .
because the six data sets used in the present analysis have three different observation epochs ( may 2006 , june 2009 and december 2009 ) , it is necessary to check the energy scale for each observation .
in addition , the energy gain may vary from place to place on the same ccd chip owing to the charge transfer inefficiency .
we thus estimate the xis calibration uncertainty in the following two ways : ( i ) measurements of the calibration source energy and ( ii ) comparisons of redshift values derived from four or three sets of xis .
\(i ) the fiducial absolute energy scale can be examined by measuring the centroid energy of the mn k@xmath1 line from built - in calibration sources , which illuminate two corners of each xis chip .
the spectra accumulated from the calibration source regions were fitted to the power - law model for continuum and two gaussian functions for the mn k@xmath1 line at 5.894 kev and mn k@xmath30 line at 6.490 kev . because the mn k@xmath30 line has an intrinsically complex line shape and
is contaminated by the cluster iron emission , only the mn k@xmath1 line is used for the calibration .
figures [ fig : cal ] and [ fig : cal_result ] show the result of spectral fitting and the mn k@xmath1 line centroid energy , respectively .
as shown in the left panel of figure [ fig : cal_result ] , measured line energies for the center or 14@xmath0 offset regions are systematically lower than the mn k@xmath1 line energy by 7.3 ev if they are averaged over four sensors and two detector segments in each pointing . for xis3 ,
centroid energies are lower than those of the other three chips , however , we confirmed that the spectral analysis of the redshift measurement with and without xis3 gave statistically consistent results ( see section [ sec : resultred ] for more details ) .
we then estimate the @xmath270 systematic uncertainty on the energy scale to be @xmath271 ev .
this is justified also from the fact that if we calculate the @xmath2 value using the measured mn k@xmath1 line centroid @xmath272 and the @xmath270 statistical error @xmath273 in the xis - i detector , and the mn k@xmath1 line energy in literature @xmath274 .
@xmath2 is defined as @xmath275e@xmath276 . with @xmath271
ev , @xmath2 becomes less than 10 for 7 degrees of freedom , which means the probability of @xmath2 exceeding @xmath2 versus the number of degrees of freedom becomes less than 10% : the number of bins is 8 for four sensors and two detector segments , and @xmath277 can be regarded as being consistent with @xmath274 when we consider @xmath271 ev . in the same manner ,
the systematic errors are obtained as @xmath278 ev , @xmath59 ev , @xmath109 ev , @xmath89 ev for @xmath16 , 34@xmath0 , @xmath18 , and @xmath19 offset regions , respectively .
therefore , for the safety s sake , we assign 7 ev for the 1@xmath279 ( 68% confidence level ) gain uncertainty .
\(ii ) though calibration sources provide information on the absolute energy scale at the corners of ccd chips , the gain may be dependent on position .
this intrachip variation can be effectively studied by comparing line energies of the same sky regions ( which correspond to different detector regions ) on four or three xis sensors ( see also section 3.1 in @xcite ) . to examine this issue , we divided the center region into 16 cells , and fitted the @xmath280 model in the energy range of 5.08.0 kev for each xis sensor .
we then estimate the 1@xmath279 systematic error with a reference to obtained redshift , calculating as @xmath281 for each pair of xis sensors , where @xmath282 is the measured line centroid for the xis - i detector in each region , @xmath283 is the mean of the line centroid for all xis - i detectors in each region , and @xmath284 is the @xmath270 statistical error in the xis - i detector . with @xmath28511
ev , @xmath46 becomes less than 17 for 11 degrees of freedom , which means the probability of @xmath46 exceeding @xmath46 versus the number of degrees of freedom becomes less than 10% : the number of bins is 12 for the spectral regions except for the calibration source region in the center region .
@xmath284 is @xmath4 10 ev , which is larger than the gain uncertainty : thus , we ignored @xmath284 to avoid underestimating the systematic error .
because @xmath284 is ignored in these estimates , the obtained value is an upper limit for intrachip variation within a 68% confidence level . in summary ,
the intrachip variation is an upper limit and is larger than the gain uncertainty .
thus , we concluded from ( i ) and ( ii ) that the 1@xmath279 systematic error within a 68% confidence level is 11 ev . the systematic error is then 18 ev , which corresponds to 818 km s@xmath3 in the line of sight velocity , when we quote a 90@xmath286 confidence level .
( 80mm,60mm)figure10a.eps ( 80mm,60mm)figure10b.eps ( 80mm,60mm)figure11a.eps ( 80mm,60mm)figure11b.eps ( 80 mm , 60mm)figure12a.eps ( 80 mm , 60mm)figure12b.eps as mentioned in subsection [
subsec : single ] and [ subsec : ratios ] , the line - of - sight velocity of icm or redshift can be evaluated using two different spectral models : the apec model or the bremsstrahlung with three gaussian lines .
it is then useful to compare these results and see if there is any systematic uncertainty in the redshift measurement due to spectral modeling . in the apec model , the temperature dependence of the fe k@xmath1 line energy
is already implemented in the plasma code , which in turn evokes a parameter coupling between the temperature and line energy ( or redshift ) . on the other hand , in the bremsstrahlung@xmath287gaussian model
, the line centroid should be determined almost independently of the continuum temperature , although its temperature dependence has to be corrected later .
we did this correction by deriving the rest - frame fe k@xmath1 centroid energy as a function of temperature on the basis of spectral simulations , assuming the apec model and xis energy responses . in figure
[ fig : redshift ] , the comparison of redshift measured by the two different models is shown for all analysis regions defined in figure [ fig : image ] . because there consistency between the two within their statistical errors ,
we conclude that either method robustly determines the icm redshift for the present observations .
therefore , we will show results of the fits with the apec model because the uncertainties with apec are smaller .
the obtained redshifts from the spectral fits with the single temperature ( apec ) model in the energy range of 5.08.0 kev are shown in figure [ fig : redshift ] , where the icm velocity in the line of sight is also calculated as @xmath288 .
the resultant redshifts are consistent with the optical redshift in @xcite from the ned data base , within statistical and systematic errors , which corresponds to @xmath2620.0027 in the redshift
. the direct measurements of the central energy of the k@xmath1 line of he - like fe also give almost the same redshifts derived from the spectral fits with the single temperature ( apec ) model . to quantitatively derive the redshift , we calculated the mean redshift of the icm in all pointings to be @xmath289 .
this is slightly lower than the optical redshift , @xmath290 from the ned database , but within 90@xmath286 error .
as shown in table [ tab:1 - 8vapecresults ] , in the center and 14@xmath0 offset regions , the derived highest and lowest redshift are @xmath291 for cell numbers 5 and 8 of the center region , and @xmath292 for cell number 2 of the center region . based on these redshift measurements ,
the derived icm bulk velocities are @xmath293 km s@xmath3 , and @xmath294 km s@xmath3 . including systematic errors of @xmath295 km s@xmath3 with 90@xmath286 confidence level ( section [ subsec : cal ] ) , there is no significant difference .
we estimate the 90@xmath286 upper limit on the velocity gradient to be @xmath296 km s@xmath3 .
if we further add systematic and statistical errors in the quadrature , the upper limit of the gas velocity within the 90@xmath286 confidence level becomes @xmath297 @xmath298 2200 km s@xmath3 . for simplicity , assuming that the gas is rigidly rotating at a typical circular velocity of @xmath299 , then @xmath300 km s@xmath3 , which does not exceed the sound velocity of the coma cluster , which is 1500 km s@xmath3 for a temperature of 8 kev .
the average redshift in the center region is as follows : @xmath301 in the north - west region ( cell numbers 8 , 9 , 12 , and 13 ) , @xmath302 in the south - west region ( cell numbers 10 , 11 , 14 , and 15 ) , @xmath303 in the north - east region ( cell numbers 0 , 1 , 4 , and 5 ) , and @xmath304 in the south - east region ( cell numbers 2 , 3 , 6 , and 7 ) .
we also show the averaged redshift over fov in the upper panel in table [ tab : redshift ] .
these results are consistent with each other in the center region , and with the observed redshifts in the 14@xmath0 offset region within statistical and systematic errors .
the difference in the icm velocity between the center and 30@xmath0 offset regions is derived as @xmath305 km s@xmath3 , and the difference between the center and 34@xmath0 offset regions is @xmath306 km s@xmath3 .
these are also consistent with each other .
components of the velocity in the plane of the sky are not measured .
if we assume that three components are similar , then the limit on the radial velocity translates into a limit of @xmath307 500 km s@xmath3 , which does not exceed the speed of sound and is consistent with systematic errors .
therefore , there were no significant velocity variations on the 10@xmath0 scale within central regions ( center and 14@xmath0 , 30@xmath0 , and 34@xmath0 offset regions ) from our analysis . in the ngc 4839 subcluster region ( 44@xmath0 offset region ) , the observed redshift is 0.0269@xmath2620.0033 , which corresponds to 1140@xmath308 km s@xmath3 as the icm bulk velocity without systematic errors .
there also seems to be no significant difference between the core of the coma cluster and the ngc 4839 subcluster within the 90% confidence level . as mentioned in subsection [ subsec : cal ]
, some sensors have large uncertainties in the determination of the line centroid energy . on xis3 in the center region , the mn k@xmath1 line centroid energy of segment a was different from others .
similarly , the segment d of xis1 in the ngc 4839 region was also different .
we averaged the spectrum over fov in ( i ) all detectors , and ( ii ) all detectors except those with different mn k@xmath1 line centroid energies to check the spectral shape and measured redshift in the center and ngc 4839 regions ( 44@xmath0 offset region ) .
the results are shown in the lower section in table [ tab : redshift ] .
for the center region , the derived redshifts were fairly consistent including xis3 or not .
on the other hand , for the ngc 4839 subcluster region , the resultant redshift changed slightly from 0.0268 to 0.0287 , although this was also consistent within statistical and systematic errors .
as shown in figure [ fig : cal_result ] , the peak of the he - like fe - k@xmath1 line of xis1 is more shifted than that of the other two sensors .
the measured redshifts in the 44@xmath0 offset region were 0.0271@xmath2620.0023 , 0.0303@xmath2620.0051 , and 0.0255@xmath2620.0027 for xis0 , 1 , and 3 , respectively .
because the measured redshift of the averaged spectra between xis0 and 3 was consistent with the redshift from simultaneous spectral fits , the value 0.0269 would be plausible . in conclusion
, there was no significant difference in the icm velocity between the core of the coma cluster and the ngc 4839 subcluster within 90% confidence .
ccccc field & x - ray ( @xmath309 ) & optical ( @xmath309 ) & x - ray ( @xmath310 ) & optical ( @xmath310 ) + & & & km s@xmath3 & km s@xmath3 + all pointings & 0.0227@xmath2620.0005 & 0.02307 & 6810@xmath262150 & 6917 + center & 0.0227@xmath2620.0005 & 0.02286 & 6810@xmath262150 & 6853 + 14@xmath0 offset & 0.0230@xmath2620.001 & 0.02286 & 6900@xmath262300 & 6853 + center and 14@xmath0 offset & 0.0227@xmath2620.0005 & 0.02286 & 6810@xmath262150 & 6853 + ngc 4839 & 0.0269@xmath2620.0033 & 0.02448 & 8070@xmath262990 & 7339 + center ( xis0123 ) & 0.0226@xmath2620.0005 & 0.02286 & 6775@xmath262150 & 6853 + center ( xis012 ) & 0.0226@xmath2620.0005 & 0.02286 & 6775@xmath262150 & 6853 + ngc 4839 ( xis013 ) & 0.0287@xmath2620.0033 & 0.02448 & 8604@xmath262990 & 7339 + ngc 4839 ( xis03 ) & 0.0268@xmath2620.0033 & 0.02448 & 8034@xmath262990 & 7339 + + [ tab : redshift ] ( 80 mm , 60mm)figure13a.eps ( 80 mm , 60mm)figure13b.eps to measure the abundance using the strong fe
k lines , we employed the results of spectral fitting in the 5.08.0 kev energy range for the fe abundance .
because of the good statistics , the spectra in the lower energy band primarily determine the fitted temperatures .
although the spectra are well fitted with a single - temperature model , a small discrepancy between the model and data around the fe - k line can yield a large systematic uncertainty in the derived fe abundances . within the 34@xmath0 region ,
temperatures and abundances derived from the spectral fitting in the 5.08.0 kev energy range agree well with those from 1.08.0 kev energy ranges within 5% . in the 44@xmath0 and 60@xmath0 offset regions , the fe abundances from the 5.08.0 kev energy range are smaller than those from the 1.08.0 kev range by @xmath40.1 solar .
@xmath46 values for the limited energy range of 5.08.0 kev from the former fitting are 10% smaller than those from the latter , although the single - temperature model reproduces the observed spectra at 1.08.0 kev well .
therefore , we adopted the fe abundance derived from the spectral fitting in the 5.08.0 kev energy range .
figure [ fig : fe ] shows a radial profile and map of the fe abundance of icm with the single temperature ( apec ) model in the 5.08.0 kev energy range . within 30@xmath0 from the x - ray peak , fe abundances are almost constant at @xmath40.4 solar .
the derived fe abundances are 0.41@xmath2620.01 solar in the center region , and 0.38@xmath2620.02 solar in the 14@xmath0 offset region .
the fe abundances in the 30@xmath0 and 34@xmath0 offset regions are slightly lower , @xmath40.3 solar , although it has larger uncertainties .
these values agree with recent xmm results @xcite within 1.2 mpc .
the fe abundance in the ngc 4839 subcluster region is comparable to that in the central region , and higher than that in the 30@xmath0 and 34@xmath0 offset regions .
the average value in the subcluster region is 0.33@xmath2620.09 solar .
this value is also consistent with that in @xcite , although the error bars in their results are much larger than those in our results .
x - ray observations of clusters of galaxies can play a major role in determining cosmological parameters , because of the importance of measuring gravitational mass .
the ratio of he - like k@xmath1 to h - like k@xmath1 lines of fe is a very steep function of temperature , and has a different temperature dependence from that of the continuum .
the continuum emission is affected by the systematic uncertainties in the response and non - thermal emission , while the line ratio does not .
thus , by comparing the fitted temperatures between these two methods , the effects of the systematic uncertainty in the response and/or of the non - thermal emission is increased . using the apec plasma code
, the temperatures derived from the spectral fitting of the 1.08.0 kev energy range and the line ratio of fe agree within a few percent when we averaged all regions .
the systematic uncertainties in temperatures from the line ratio are in the level of the systematic difference between those from apec and mekal , which is about 3% .
the consistency of observed temperatures from the continuum and those from line ratios supports the accuracy of suzaku measurements of plasma temperature .
in contrast , systematic differences of @xmath4 10% in the cluster temperature among chandra , pn , and mos were reported in relatively high temperature clusters ( @xcite ) . even using the same instrument , the derived temperatures changed systematically by @xmath311% between calibrations @xcite .
a systematic uncertainty of several percent in response matrices of a detector can also cause systematic uncertainties in the temperature structure .
@xcite found that the temperature structures of icm in the coma cluster derived from multi - temperature fits with pn and mos spectra were different , although the two detectors gave consistent temperatures within several percent .
when they allowed higher temperature components over 10 kev in hot clusters including the coma cluster , using mos data , fe abundances from the he - like line increased by several tens of percent , owing to artificial detection of a hot component , while those derived by pn were unchanged .
however , with suzaku , we found that the single - temperature model fits the spectra of the coma cluster very well , and we do not need temperature components above 10 kev or below 2 kev to fit the spectra .
the multi - temperature components observed by xmm were not needed . in the outer regions of clusters at low surface brightness
, uncertainties in the background of chandra and xmm also lead to systematic uncertainties in icm temperatures .
some analyses found that icm temperatures decreased outward by half at 0.6@xmath312 ( e.g. , @xcite ; @xcite ) , while others found flatter profiles ( e.g. , @xcite ) .
systematic uncertainties in the derived temperatures due to uncertainties in the background with suzaku observations are much smaller , because suzaku xis has a much lower and more stable background . also , previous xmm and chandra results of temperatures in the outer regions have statistical errors more than 20% , while those of suzaku have errors less than 10% .
we need precise measurements of icm temperatures to search for a non - thermal hard component as an excess of the thermal component . on the basis of the icm temperature map derived with xmm - pn
, @xcite found that the suzaku hxd - pin spectrum was described with the thermal emission from icm , and there was no significant evidence of excess hard emission .
the temperatures of the coma cluster derived from suzaku - xis are consistent within error bars with those from the pn detector : the weighted average of temperatures with statistical errors within the center field is close to that derived with xmm - pn within a few percent .
the temperatures of offset fields are consistent with those from xmm - pn within error bars .
thus , our results support the non - detection of non - thermal hard emissions by @xcite @xcite reported the existence of hot gas at @xmath313 kev in rx j1347.5 - 1145 .
they concluded that the gas properties can be explained by a fairly recent ( within the last 0.5 gyr ) collision of two massive ( 5@xmath1210@xmath314 m@xmath315 ) clusters with bullet - like high velocity ( @xmath316 km s@xmath3 ) .
in contrast , @xcite found that there was no extremely high temperature gas in the coma cluster in the hxd - pin spectrum up to 70 kev .
on the basis of the consistency of derived temperatures from the continuum and the line ratio and the results from the spectral analysis of hxd - pin , we conclude that the amount of very high temperature gas is rather small . from the spatial variation of the derived temperatures ,
there is no region with extremely hot temperature : the derived temperatures range from 7.0 to 9.0 kev within the center , 14@xmath0 offset , and @xmath17 offset regions .
the coma cluster has a cluster - wide synchrotron radio halo .
if the electrons in the cluster were accelerated by a very strong shock that occurred owing to a recent merger , we might expect the cluster to contain more very hot gas , although it is difficult to make this argument quantitative . in any case , in the coma cluster , relativistic electrons producing the radio halo were apparently generated without producing a large amount of very hot gas .
an example of a process which might do this is the turbulent re - acceleration model ( e.g. , @xcite ) . within the center and offset regions the spatial variation of derived temperatures
is relatively small , from 7 kev to 9 kev .
there are no extremely hot and cool regions .
we did not detect any temperature jump corresponding to a shock in the offset regions . within each region for the spectral analysis , the single - temperature model fit the spectrum .
therefore , in the center of the coma cluster , icm is in a nearly relaxed state .
although the variation was small , there was some asymmetric temperature structure , like a hot region northwest of the center .
if the cluster had been an isolated system collapsing from self - gravity , the temperature structures would be symmetric .
the observed asymmetry in the temperature distribution indicates that external effects or interactions , such as merging , have occurred .
numerical simulations of the evolution of the cluster ( e.g. , @xcite ; @xcite ) show that nonaxisymmetric structures in the temperature distribution are erased several gyr after each merger .
the presence of asymmetric temperature structures suggest that the central region of the coma cluster has experienced a merger , and the lack of hard component shows that its core have relaxed in the last several gyr .
the observed cool region in the southeast of the center region coincides with the filamentary structure originating near ngc 4911 and ngc 4921 @xcite .
@xcite reported that the temperature of this cold area ranges from 5 to 7 kev .
this region mostly contain the stripped subcluster gas , which is thought to be relatively cool in the initial state .
the numerical simulations ( e.g. , @xcite ) suggest that the gas would maintain its temperature for several gyr .
@xcite showed that even a single subcluster collision with supersonic velocity creates both hot and cool regions in the main cluster .
although heating due to collisions occurs , cooling would also occur through the adiabatic expansion of the stripped gas .
the measurements of bulk motions in icm are also important to derive the gravitational mass of clusters of galaxies .
we constrained the upper limit of icm bulk motions in the center and offset regions on the scale of 117 kpc ( ) and 234 kpc ( 9@xmath0 ) , respectively , which correspond to the scales of regions for spectral accumulation ( see section [ sec : obs ] and subsection [ sec : resultred ] ) .
the upper limit of gas bulk motions is @xmath297 @xmath298 1100 km s@xmath3 .
as summarized in table [ tab : redshift ] , considering the systematic error of 18 ev , or 818 km s@xmath3 with a 90@xmath286 confidence level ( section [ subsec : cal ] ) , there are no significant bulk motions in the center and offset fields .
compared with the sound velocity of the coma cluster , @xmath317 km s@xmath3 for a temperature of @xmath47 = 8 kev , the bulk - motion in the central region of the coma cluster does not exceed the sound velocity .
our results do not conflict with the discovery of pressure fluctuations in the center of the coma cluster by @xcite which indicates that at least 10% of the icm pressure is in turbulent form .
we have not constrained the turbulence , and the scale of the fluctuation ranges between 29 kpc and 64 kpc , which is smaller than our scale of spectral analysis .
the velocity difference between the main cluster and the ngc 4839 subcluster from optical observations is 486 km s@xmath3 .
although the best - fit line - of - sight velocity of the subcluster is higher than that of the main cluster by @xmath4 1000 km s@xmath3 , the difference is comparable to statistical and systematic errors . because the temperature of the region is about 5 kev ,
the sound velocity is @xmath4 1150 km s@xmath3 . considering the error bars ,
we conclude that the relative line - of - sight gas velocity in the ngc 4839 subgroup region does not greatly exceed the sound velocity .
numerical simulations indicate that a major merger between clusters raises the temperature of icm and induces a bulk velocity of the order of 1000 km s@xmath3 ( e.g. , @xcite ; @xcite ) . in the late phase of mergers , turbulent motions develop in a simulation by @xcite .
the non - detection of bulk - motions in icm of the coma cluster also indicates that the central region of the cluster is in a somewhat relaxed state .
if so , the non - thermal electrons relevant to the radio halo of the coma cluster may have been accelerated by the intracluster turbulence rather than shocks . in conclusion
, the line - of - sight gas velocity of the coma cluster in the observed region does not greatly exceed the sound velocity , and the central region of the coma cluster is in a nearly relaxed state .
this means that the assumption of hydrostatic equilibrium is approximately valid in calculating the cluster mass of the coma cluster .
the fe abundance is nearly constant at @xmath4 0.4 solar within a clustocentric radius of 0.5 mpc , and beyond that distance it decreases with the radius to 0.20.3 solar .
this profile is consistent with those measured by xmm ( @xcite ; @xcite ) .
suzaku has a lower level of background , and a slightly better energy resolution : therefore , systematic uncertainties in fe abundance are considered to be smaller .
differences in abundance profiles of icm in central regions of clusters with and without cool cores have been reported ( @xcite , @xcite , @xcite ) .
@xcite showed an abundance difference between the two type of clusters within 0.1@xmath312 , while at 0.10.3@xmath312 , the average values of fe abundances are both @xmath4 0.40.5 solar , and are consistent with each other .
the coma cluster is thought to have experienced a major merger in the recent past and subsequently , the central region came to a somewhat relaxed state . during a cluster merger ,
the mixing of icm could destroy any central fe peak .
in the first stage of merging , the fe peak and cool core remain intact as observed in some ongoing merging clusters ( @xcite ; @xcite ) .
for example , abell 2256 , an ongoing merging cluster , has an abundance gradient in the direction opposite of the merging direction owing to the remixing of the gas .
numerical simulation also support this scenario .
@xcite performed hydrodynamical simulations with two different merger types of clusters : cluster 1 has only small merger events , while cluster 2 undergoes a major merger ( mass ratio 1:3 ) . in cluster 1 ,
the abundance is more than @xmath4 0.4 solar within a radius of 0.1 mpc , and decreases from @xmath4 0.3 solar to @xmath4 0.1 solar with a decrease in radius .
the situation is different in cluster 2 . in the coma cluster ,
the fe abundance is @xmath4 0.4 solar and homogeneous within a radius of 0.5 mpc .
this value of the fe abundance is similar to those at 0.20.3@xmath312 in other clusters as shown in figure [ fig : fe ] .
therefore , tn the coma cluster , the merger have destroyed the cool core , and mixed the icm completely at least within 0.5 mpc .
the coma cluster which was observed with the x - ray imaging spectrometer ( xis ) onboard suzaku , was analyzed by the x - ray satellite in six pointings , centered on the x - ray peak and offset by west , , , , and .
because of its low background , suzaku is the most sensitive x - ray satellite for observing k@xmath1 lines of fe in the intracluster medium . after obtaining accurate measurements of fe lines
, we studied the temperature structure of the intracluster medium , searched for possible bulk - motions , and measured the fe abundance in the cluster .
the spectra of each extracted region were well fitted by the single - temperature apec model , and the two- or three- temperature apec model did not improve @xmath2 .
the temperatures derived from the observed ratios of k@xmath1 lines of h - like and he - like fe agree well with those from spectral fittings with the single - temperature apec model .
because this line ratio is a strong function of plasma temperature , the observed consistency supports the accuracy of temperature measurements with suzaku , and constrains the temperature structure of icm .
the observed values of the central energy of the he - like fe line of the center , , and offset regions are constant within 500 @xmath318 , which corresponds to the calibration error .
because relative bulk velocities in the coma cluster are smaller than the sound velocity of the intracluster medium , 1500 km s @xmath3 , we can verify the derived total mass in a cluster on the basis of the hydrostatic icm equilibrium inside the offset region .
significant bulk velocities were also not found in the offset region , which corresponds to the ngc 4839 subcluster .
the results on the temperature and velocity structure suggest that the core of the coma cluster is in a fairly relaxed state .
this is consistent with models in which the non - thermal electrons relevant to the radio halo are accelerated by the intracluster turbulence rather than large - scale shocks .
this is also consistent with the fact that numerical simulations show that the turbulence motion is developed in the late phase of mergers .
the observed fe abundance of the intracluster medium is almost constant at 0.4 solar inside the offset region , and decreases with radius .
the central abundance is slightly lower than that of other clusters or groups .
this indicates that central regions of the gas were mixed well during the past merger growth of the cluster .
+ _ acknowledgements . _
we wish to thank the referee for his / her suggestions on the paper .
the authors are grateful to all members of suzaku for their contributions in instrument preparation , spacecraft operation , software development , and in - orbit instrumental calibration .
to analyze the data , we used the isas analysis servers provided by isas / c - soda .
n. o. acknowledges support by the ministry of education , culture , sports , science and technology of japan , grant - in - aid for scientific research no .
cls was supported in part by nasa suzaku grants nnx08az99 g , nnx09ah25 g , and nnx09ah74 g . | the coma cluster was observed with an x - ray imaging spectrometer ( xis ) onboard suzaku in six pointings , including the central x - ray peak region , the 14@xmath0 west offset region , 30@xmath0 and 34@xmath0 north - west offset regions , and 44@xmath0 and 60@xmath0 south - west offset regions .
owing to its lower background level , suzaku has better sensitivity to fe k@xmath1 lines than other satellites . using precise fe line measurements , we studied the temperature structure , possible bulk motions , and iron abundance distributions in the intracluster medium ( icm ) .
the observed spectra were well - represented by a single - temperature model , and two- or three- temperature model did not improve @xmath2 substantially .
the temperature , derived from k@xmath1 line ratios of h - like and he - like fe , agree with those derived from the single - temperature model . because the line ratio is a steep function of temperature , the consistency supports the accuracy of temperature measurements conducted with suzaku . within the 34@xmath0 region ,
the redshift derived from the central energy of the he - like fe line is consistent with that from optical observations , within a calibration error of 18 ev or 818 km s@xmath3 in the line of sight .
this value is smaller than the sound velocity of icm , which is 1500 km s@xmath3 .
the central energy of fe lines at the 44@xmath0 offset region around the ngc 4839 subcluster is also consistent with those within the 34@xmath0 region .
these results on the temperature and velocity structure suggest that the core of the cluster is in a relaxed state , and non - thermal electrons relevant to the radio halo are accelerated by intracluster turbulence rather than large - scale shocks .
fe abundance is almost constant at 0.4 solar within the 34@xmath0 region , and decreases with radius .
this value is slightly lower than those of other clusters , which means the gas have been mixed well during a past merger associated with the growth of the cluster . | <s>[INST]clusters of galaxies are thought to grow into larger systems through complex interactions between smaller systems .
signatures of merging events include temperature and density inhomogeneities and bulk motions in the intracluster medium ( icm ) .
numerical simulations predict simplified bulk motions with a substantial fraction of virial velocity ( @xmath41000 km s@xmath3 ) , lasting several gyr after each merging event ( e.g. , @xcite ; @xcite ) .
measurements of the icm temperature and velocity structure , therefore , provide crucial information for understanding the evolution of clusters .
velocity measurements of bulk motion and turbulence are essential for mass estimation and cosmological studies .
if icm has a significant bulk velocity compared to its thermal velocity , the associated non - thermal pressure would threaten the assumption of hydrostatic equilibrium in deriving the total gravitational mass in a cluster .
for example , factors of 23 discrepancies between the x - ray and lensing mass estimates in some objects ( e.g. , @xcite ; @xcite ) could be partly due to this effect .
@xcite discovered a significant bulk motion in abell 2256 , which is a well known merging cluster .
@xcite performed a fourier analysis of xmm - newton data of the coma cluster , which revealed the presence of a scale - invariant pressure fluctuation ranging between 29 and 64 kpc , and @xmath410% of the total pressure in turbulent form .
however , in relaxed clusters , significant bulk motions and turbulence have not been detected .
on the basis of asca and chandra data , @xcite claimed a large velocity gradient of @xmath42400 km s@xmath3 in the centaurus cluster , which is a relaxed cluster with a cool core .
however , @xcite found a negative result of @xmath5 km s@xmath3 on the basis of suzaku observations of the centaurus cluster .
@xcite also searched for possible bulk motions in the awm 7 cluster with suzaku , and observed no significant bulk motions .
the upper limit of gas velocity was @xmath6 2000 km s@xmath3 .
@xcite do not detect the variation of the redshift of the icm in the ophiuchus cluster , and the upper limit of the velocity difference is 3000 km s@xmath3 .
@xcite studied the icm flow in abell 2319 with suzaku , and detected no velocity differences within the observed region . using spectra with a reflection grating spectrometer ( rgs ) onboard xmm - newton ,
@xcite provided upper limits on turbulence velocities in cluster core regions : at least 15 sources had less than 20% of the thermal energy density in turbulence .
the coma cluster ( @xmath7 ) , also known as abell 1656 , is one of the most studied clusters @xcite and has been observed at all wavelengths from radio to hard x - ray bands .
however , the physical state , particularly the dynamical state , of the coma cluster has not been completely understood .
measurements of the velocity dispersion and distribution of galaxies belonging to the coma cluster constrain the dynamical history of the coma cluster .
@xcite found that two central galaxies , ngc 4889 and ngc 4874 have a significant difference in velocity , which is evidence of a recent merger .
@xcite argued that ngc 4874 was the original dominant galaxy of the main cluster , and that ngc 4889 belonged to a subgroup , that recently merged with the main cluster .
a substructure associated with the galaxy , ngc 4839 , located 40@xmath0 south - west of the cluster core , was found by @xcite and @xcite .
the existence of this subcluster was confirmed by @xcite .
the thermal x - ray emission of the coma cluster has been observed with several x - ray satellites .
@xcite constructed an x - ray map of the coma cluster using rosat all - sky - survey data and determined the x - ray surface brightness profile of the cluster out to a radius of roughly 100@xmath0 .
the temperature maps of clusters provide knowledge about the history of past subcluster mergers . on the basis of asca observations , @xcite and @xcite found that icm is not isothermal .
@xcite used xmm - newton to study the temperature structure in the central region of the coma cluster .
the projected temperature distribution around ngc 4889 and ngc 4874 is remarkably homogeneous , which suggests that the core is mostly in a relaxed state . except at the center ,
the temperature decreases slightly with radius .
a cool filament of an x - ray emission in the direction of the galaxy ngc 4911 , which is located in the south - east of the cluster center , was detected with chandra @xcite and xmm @xcite .
rosat observed a substructure around the ngc 4839 subgroup @xcite , and a hot region in the direction of ngc 4839 was observed by @xcite . by xmm - newton observations
, @xcite found compelling evidence for the subgroup around ngc 4839 was on its first infall into the coma cluster , but it had not passed its core yet .
this interpretation is different from that of @xcite , who suggested that the ngc 4839 group was moving out of the cluster after having already passed through the coma cluster .
non - thermal electrons , observed via diffused radio synchrotron emission , have been detected in more than 50 clusters , and all of them are undergoing mergers ( e.g. , @xcite ; @xcite ) .
the coma cluster also has a cluster - wide synchrotron radio halo , emitted by relativistic electrons due to merging @xcite .
recent non - thermal detections have been claimed by @xcite with rxte and by @xcite with bepposax , although the latter detection is controversial @xcite
. long observations ( @xmath41 ms ) by integral have imaged extended diffuse hard x - ray emission from the coma cluster , although it was found to be completely consistent with thermal emission @xcite .
using the temperature map of icm obtained with the pn detector onboard xmm - newton , @xcite analyzed data obtained from the suzaku hard x - ray detector ( hxd ) @xcite and derived the strongest upper limit of non - thermal emission .
this paper reports results from six suzaku observations of the coma cluster out to 60@xmath0 , @xmath81.5 mpc , conducted using the x - ray imaging spectrometer ( xis ) @xcite onboard suzaku @xcite . owing to its lower background level , suzaku has better sensitivity to the iron k@xmath1 lines than previous satellites .
in addition , the accurate calibration of xis allows us to measure the velocity of icm precisely .
we used the hubble constant , @xmath9 km s@xmath3 mpc@xmath3 .
the distance to the coma cluster is @xmath10 mpc , and @xmath11 corresponds to 28.9 kpc .
we used the abundance ratio by @xcite , in which the solar fe abundance relative to h is 2.95@xmath1210@xmath13 .
errors are quoted at a 90% confidence level for a single parameter .
the remainder of this paper is organized as follows : we present the observations in section 2 and describe the data analysis in section 3 .
we describe the results of spectral fittings and temperature structure in subsection 4.1 , bulk motions in subsection 4.5 , and the fe abundance in subsection 4.6 . in section 5 ,
we discuss the results , and in section 6 , we summarize the findings .
cccccccc field name & target name & sequence & observation & ra & dec & exposure & distance from the + & & number & date & ( deg ) & ( deg ) & ( ks ) & x - ray peak + center & coma radio halo & 801097010 & 2006 - 05 - 31 & 194.9267 & 27.9061 & 150 & + offset & coma cluster offset & 801044010 & 2006 - 05 - 30 & 194.6939 & 27.9466 & 79 & + offset & coma 11 & 802082010 & 2007 - 06 - 19 & 194.6305 & 28.3939 & 53 & + offset & coma bkg2 & 802084010 & 2007 - 06 - 21 & 194.3428 & 28.1403 & 30 & + offset & coma 45 & 802047010 & 2007 - 12 - 02 & 194.2558 & 27.5714 & 30 & + offset & coma 60 & 802048010 & 2007 - 12 - 04 & 194.0251 & 27.4252 & 35 & + offset & coma bkg & 802083010 & 2007 - 06 - 21 & 198.7472 & 31.6480 & 30 & + ( 80 mm , 60mm)figure1_a.eps ( 80 mm , 60mm)figure1_b.eps suzaku carried out six observations in the coma cluster .
the details of the observations are summarized in table [ tab : ob ] .
two central observations were carried out in may 2006 , during the suzaku phase - i period .
the first observation , `` coma radio halo '' , has a pointing that is @xmath14 offset from the x - ray peak of the coma cluster , which has coordinates ( ra , dec ) = ( 194.9367 , 27.9472 ) in degrees .
the second observation , `` coma cluster offset '' , was located @xmath15 west offset from the first observation .
the other observations , in the @xmath16 and @xmath17 north west offset regions and @xmath18 and @xmath19 south west offset regions , were carried out in 2007 , during the suzaku phase - ii period . to eliminate background emissions , archival suzaku data with a 5 degree offset from the coma cluster , observed in june 2007
was also used , and is shown in table [ tab : ob ] .
xis was operated in its normal mode during observations .
the xis instrument consists of four sets of x - ray ccd ( xis0 , 1 , 2 , and 3 ) .
xis1 is a back - illuminated ( bi ) sensor , while xis0 , 2 , and 3 are front - illuminated ( fi ) sensors .
xis2 was not used during the four offset observations beyond 30@xmath0 from the x - ray peak .
figure [ fig : image ] shows a 0.54.0 kev image of xis0 .
we performed data reduction using heasoft version 6.6.3 .
xis event lists created by the rev 2.0 pipeline processing were filtered using the following additional criteria : the geomagnetic cut - off rigidity ( cor2 ) @xmath20 6 gv , and elevation angle from the earth limb @xmath21 .
the data formats of 5x5 and 3x3 editing modes were added .
the exposure times after the data selection are shown in table [ tab : ob ] .
to study the temperature structure and search for possible bulk motions of icm in the coma cluster on the scale of a few arcminutes , we divided the 18@xmath22 square xis field of view ( fov ) of the center and 14@xmath0 offset regions into @xmath23 and @xmath24 cells , respectively , as shown in figure [ fig : image ] .
each region in the center and @xmath15 offset regions subtends @xmath12 ( 117@xmath25 kpc ) , and 9@xmath26 ( 234@xmath27 kpc ) , respectively .
regions around calibration sources were excluded .
luminous point sources in which the flux limit corresponds to @xmath4 10@xmath28 counts s@xmath3 in the 2.010.0 kev energy range were also excluded as circular regions with a radius of 1@xmath0 . at most 10 point sources
were excluded for each of the observed regions .
we extracted spectra from the whole xis fov for regions more than @xmath29 from the x - ray peak . the non x - ray background ( nxb )
was subtracted from each spectrum using a database of night earth observations with the same detector area and cor distribution @xcite .
we included the degradation of energy resolution due to radiation damage in the redistribution matrix file ( rmf ) generated by the xisrmfgen ftools task .
we also created an ancillary response file ( arf ) using the xissimarfgen ftools task @xcite .
a decrease in the low - energy transmission of the xis optical blocking filter ( obf ) was also included in arf . to generate arf files for the center and 14@xmath0 offset regions , we used a @xmath30-model profile for the simulated surface brightness profile in @xcite .
for @xmath16 , @xmath17 , @xmath18 , @xmath19 , and 5 degree offset regions , we generated arfs assuming a uniformly extended emission from an encircled region with a 20@xmath0 radius , because the gradient of surface brightness within each fov is small .
we used the xspec_v11.3.2ag package for spectral analysis .
we have investigated the temperature structure , bulk motions , and iron abundance distribution of the coma cluster . we fitted the spectra with a thermal plasma model ( apec : @xcite ) to obtain the temperature , redshift and fe abundance of icm .
a detailed spectral analysis is presented in subsection [ subsec : single ] .
we used three gaussian models to obtain the temperature using the normalization ratio of k@xmath1 lines of h - like and he - like fe , and redshift using the shift of line centroid energy , which is presented in subsection [ subsec : ratios ] .
( 80 mm , 60mm)figure2.eps cccccccc & & & + @xmath31 & normalization & temperature & normalization & temperature & normalization & + & & ( kev ) & @xmath32 & ( kev ) & @xmath33 & @xmath2/d.o.f & @xmath2/d.o.f + @xmath34 & @xmath35 & 0.07 ( fixed ) & @xmath36 & @xmath37 & @xmath38 & 188/141 & 223/154 + first , we fitted the spectra in the 5@xmath39 offset region to determine the local x - ray background .
as shown in @xcite , the background emission of suzaku xis can be fitted with a three component model : two thermal plasma models ( apec : @xcite ) for the local hot bubble ( lhb ) and the milky way halo ( mwh ) , and a power - law model for the extragalactic cosmic x - ray background ( cxb ) .
mwh and cxb components were convolved with an absorption in the galaxy .
we , therefore , fitted the spectra simultaneously in the 0.58.0 kev energy range for xis fis and the 0.358.0 kev energy range for xis bi using the following model formula : @xmath40-@xmath41 .
we assumed a zero redshift and a solar abundance for lhb and mwh components .
the temperature of lhb was fixed at 0.07 kev @xcite , while the temperature of mwh was variable .
the column density of the galactic neutral hydrogen was fixed at 1.0@xmath42 @xmath43 @xcite . to avoid systematic uncertainties in the background , we ignored the 1.401.55 kev energy range , where a relatively large uncertainty exists because of an instrument al line @xcite , and energies above 8 kev .
we also excluded the narrow energy band between 1.82 and 1.84 kev in the fits because of incomplete responses around the si edge .
results of the spectral fit are shown in figure [ fig : bkgfit ] and the resultant parameters of the fit are shown in table [ tab : bkgtable ] .
the derived photon index and normalization of the cxb component agree with @xcite and @xcite .
the derived temperature and normalizations of the two thermal models are consistent with those obtained from xmm and suzaku observations @xcite .
we generated the simulated spectra of the x - ray background including lhb , mwh , and cxb emissions derived from the resultant parameters of the fits in the 5@xmath39 offset region .
we used the simulated spectra as the background to fit the spectra for icm of the coma cluster .
figure [ fig : bgd ] shows the comparison between the xis0 spectra of the 60@xmath0 offset region of the coma cluster and backgrounds . above 7 kev
, nxb dominates the observed spectra of the 60@xmath0 offset region .
we also show the background - subtracted spectrum of the 60@xmath0 offset region of the coma cluster in figure [ fig : bgd ] ( blue ) .
the x - ray background spectra are well reproduced .
( 80 mm , 60mm)figure3.eps we fitted the xis spectra in each region of the coma cluster using a single temperature model ( apec ) with the galactic absorption , @xmath44 . each spectral bin contained 50 or more counts .
we fitted the spectra in two energy bands : 1.08.0 and 5.08.0 kev . to avoid systematic uncertainties in the background , we ignored energies higher than 8 kev .
we also excluded the narrow energy band between 1.82 and 1.84 kev in the fits because of incomplete responses around the si edge .
temperature , redshift and normalization of the single temperature model were free parameters , and @xmath44 was fixed to the galactic value , @xmath45 , in the direction of the coma cluster .
abundances of he , c , n , and al were fixed to be a solar .
we divided the other metals into three groups : o , ne and mg ; si , s , ar and ca ; and fe and ni , and allowed them to vary .
the resultant parameters are summarized in table [ tab:1 - 8vapecresults ] , and a sample of the spectra is shown in figure [ fig : spec ] . since our data have very high statistics , especially in the central region , there remain residual structures around the si edge structure .
these residuals are probably caused by systematic uncertainties in the response matrix because the bi and fi detectors gave different residuals .
therefore , to avoid systematic uncertainties in all regions , we excluded the energy range of 1.72.3 kev and fitted the spectra again .
the derived temperatures hardly changed , although the reduced @xmath2 decreased by 20% .
the resultant @xmath2 are summarized in table [ tab:1 - 8vapecresults ] .
to constrain the temperature structure , we fitted the spectra of the center and offset regions with a two - temperature ( apec ) model in the energy range of 1.08.0 kev , ignoring the energy range of 1.72.3 kev .
the @xmath46 are improved slightly by less than a few percent .
the derived temperatures of one component are similar to those derived from the single - temperature model fits , and those of the other component are either above 10 kev or below 2 kev . to obtain more detailed constraints for the lower and higher temperature components , we fitted the spectra with a three - temperature ( apec ) model in the energy range of 1.08.0 kev , excluding the 1.72.3 kev energy range to avoid uncertainties in the response matrix . in this model , the lowest , middle and highest temperatures
are restricted to below 6 kev , within 6.010.0 kev , and above 10.0 kev , respectively .
the resultant @xmath46 values are shown in table [ tab:1 - 8vapecresults ] . to derive the fe abundance and velocity of the bulk - motion from fe - k lines
, we fitted the spectra of each region with the single - temperature apec model in an energy range of 5.08.0 kev .
the results are shown in table [ tab:1 - 8vapecresults ] . to precisely determine the bulk velocity of icm , the accuracy of photon energy measurements is crucial .
some sensors have large uncertainties in the determination of the line centroid energy .
thus , we averaged the spectrum over fov in ( i ) all detectors , and ( ii ) all detectors except for different mn k@xmath1 line centroid energies to check the spectral shape and measured redshift in the center and ngc 4839 regions ( 44@xmath0 offset region ) .
cccccccccc & & & gaussians + region & @xmath47 & @xmath46/d.o.f .
& @xmath46/d.o.f . & @xmath46/d.o.f . & @xmath46/d.o.f . & fe & redshift & @xmath46/d.o.f .
& @xmath47 from line + & [ kev ] & ( 1 t ) & ( 1 t ) & ( 2 t ) & ( 3 t ) & [ solar ] & [ @xmath48 & & ratio [ kev ] + center & & & & & & & & & + @xmath49 & @xmath50 & @xmath51 & @xmath52 & @xmath53 & @xmath54 & @xmath55 & @xmath56 & @xmath57 & @xmath58 + @xmath59 & @xmath60 & @xmath61 & @xmath62 & @xmath63 & @xmath64 & @xmath65 & @xmath66 & @xmath67 & @xmath68 + @xmath69 & @xmath70 & @xmath71 & @xmath72 & @xmath73 & @xmath74 & @xmath75 & @xmath76 & @xmath77 & @xmath78 + @xmath79 & @xmath80 & @xmath81 & @xmath82 & @xmath83 & @xmath84 & @xmath85 & @xmath86 & @xmath87 & @xmath88 + @xmath89 & @xmath90 & @xmath91 & @xmath92 & @xmath93 & @xmath94 & @xmath95 & @xmath96 & @xmath97 & @xmath98 + @xmath99 & @xmath100 & @xmath101 & @xmath102 & @xmath103 & @xmath104 & @xmath105 & @xmath106 & @xmath107 & @xmath108 + @xmath109 & @xmath110 & @xmath111 & @xmath112 & @xmath113 & @xmath114 & @xmath115 & @xmath116 & @xmath117 & @xmath118 + @xmath119 & @xmath120 & @xmath121 & @xmath122 & @xmath123 & @xmath124 & @xmath125 & @xmath126 & @xmath127 & @xmath128 + @xmath129 & @xmath130 & @xmath131 & @xmath112 & @xmath132 & @xmath133 & @xmath134 & @xmath135 & @xmath136 & @xmath137 + @xmath138 & @xmath139 & @xmath140 & @xmath141 & @xmath142 & @xmath143 & @xmath144 & @xmath145 & @xmath146 & @xmath147 + @xmath148 & @xmath149 & @xmath150 & @xmath151 & @xmath123 & @xmath152 & @xmath153 & @xmath154 & @xmath155 & @xmath156 + @xmath157 & @xmath158 & @xmath159 & @xmath160 & @xmath161 & @xmath162 & @xmath163 & @xmath164 & @xmath165 & @xmath166 + @xmath167 & @xmath168 & @xmath169 & @xmath170 & @xmath171 & @xmath172 & @xmath173 & @xmath174 & @xmath175 & @xmath176 + @xmath177 & @xmath178 & @xmath179 & @xmath180 & @xmath181 & @xmath182 & @xmath183 & @xmath184 & @xmath185 & @xmath186 + offset & & & & & & & & & + @xmath187 & @xmath188 & @xmath189 & @xmath190 & @xmath191 & @xmath192 & @xmath193 & @xmath194 & @xmath97 & @xmath195 + @xmath196 & @xmath197 & @xmath198 & @xmath199 & @xmath200 & @xmath201 & @xmath202 & @xmath203 & @xmath204 & @xmath205 + @xmath206 & @xmath207 & @xmath208 & @xmath209 & @xmath210 & @xmath211 & @xmath212 & @xmath213 & @xmath214 & @xmath215 + @xmath216 & @xmath217 & @xmath218 & @xmath219 & @xmath220 & @xmath221 & @xmath222 & @xmath223 & @xmath224 & @xmath225 + offset & @xmath226 & @xmath227 & @xmath228 & @xmath229 & @xmath230 & @xmath231 & @xmath232 & @xmath233 & @xmath234 + offset & @xmath235 & @xmath236 & @xmath237 & @xmath238 & @xmath239 & @xmath240 & @xmath241 & @xmath242 & @xmath243 + offset & @xmath244 & @xmath245 & @xmath246 & @xmath247 & @xmath248 & @xmath249 & @xmath250 & @xmath251 & @xmath252 + offset & @xmath253 & @xmath254 & @xmath255 & @xmath256 & @xmath257 & @xmath258 & @xmath259 & @xmath260 & @xmath261 + ( 80 mm , 60mm)figure4a.eps ( 80 mm , 60mm)figure4b.eps ( 80 mm , 60mm)figure4c.eps ( 80 mm , 60mm)figure4d.eps ( 80 mm , 60mm)figure4e.eps ( 80 mm , 60mm)figure4f.eps to derive the icm temperature from the normalization ratio of k@xmath1 lines of h - like and he - like fe , and the possible bulk motions of icm from the central energy of the lines , we fitted the spectra in the energy range of 5.08.0 kev with a sum of bremsstrahlung and three gaussian components , which correspond to k@xmath1 lines of he - like and h - like fe , and a mixture of the k@xmath1 line of he - like ni and the k@xmath30 line of he - like fe . the temperature and normalization of the bremsstrahlung component , and the central energy and normalizations of the gaussian components were free parameters , while the line width of gaussian models was fixed at 0 .
the best - fit spectra are shown in figure [ fig : bremss_spec ] .
( 80 mm , 60mm)figure5a.eps ( 80 mm , 60mm)figure5b.eps ( 80 mm , 60mm)figure5c.eps ( 80 mm , 60mm)figure5d.eps ( 80 mm , 60mm)figure5e.eps ( 80 mm , 60mm)figure5f.eps
( 80mm,60mm)figure6a.eps ( 80mm,60mm)figure6b.eps figure [ fig : kt_apec ] shows a radial profile and map of the derived temperatures from the spectral fits with the single temperature ( apec ) model in the energy range of 1.08.0 kev .
the radial temperature profile of the coma cluster is relatively flat within @xmath4500 kpc , which corresponds to the 14@xmath0 offset region , and decreases with the radius to the outer region .
while the regions observed with suzaku are limited , the resultant temperature profile is similar to that derived from xmm - newton observations , which cover nearly the entire coma cluster out to @xmath41200 kpc @xcite .
excluding the south - east quadrant ( cell numbers : 2,3,6 , and 7 ) , and the 14@xmath0 offset region , temperatures of cells in the center region have a flat distribution within a small range between @xmath48 kev and @xmath49 kev . within 300 kpc from the x - ray peak in the center region ,
the weighted mean temperature with statistical errors of the 16 cells is 8.34@xmath2620.19 kev .
the south - east quadrant ( cell numbers : 2,3,6 , and 7 ) in the center region has a slightly cooler temperature : the weighted average with statistical errors of the four cells is 7.39@xmath2620.11 kev .
this value is close to that of 5.07.0 kev in the cool temperature region observed by xmm - newton , which would be a counterpart of the south - east quadrant region @xcite .
on the other hand , the north - west quadrant in the center region ( cell numbers : 8,13 , and 14 ) and the nearby area of the 14@xmath0 offset region ( cell numbers : 17,18 ) have slightly higher temperatures of @xmath49 kev .
the 34@xmath0 offset region located to the north - west of the 14@xmath0 offset region , also has a relatively high temperature of @xmath489 kev .
this direction corresponds to the hot spot , @xmath263 kev in @xcite with asca , and @xmath2640.4 kev in @xcite with xmm - newton .
recent integral observations have shown a surface brightness excess relative to xmm observations , which is well - represented by the extended hot thermal emission with @xmath265 kev @xcite .
the temperature in the 30@xmath0 offset region is around @xmath467 kev , and is clearly cooler than temperatures in the inner region .
this value is consistent with the previous results in @xcite , and @xcite .
the 44@xmath0 and 60@xmath0 offset regions include the ngc 4839 subcluster , and temperatures decreases with radius to 5.31@xmath2620.20 kev and 3.74@xmath2620.13 kev , respectively .
these values are cooler than those in @xcite with asca , but are consistent with those in @xcite and @xcite with xmm - newton .
temperatures of the core and tail of ngc 4839 with xmm - newton , which is located in the 44@xmath0 offset region with suzaku , are @xmath266 kev and @xmath267 kev , respectively @xcite .
the temperature of the main body of the subcluster is @xmath268 kev @xcite .
suzaku provided more significant temperatures than previous measurements in these regions . in summary ,
the temperature distribution observed with suzaku is fairly consistent with the previous results observed with asca , xmm and integral .
in addition , we note that statistical and systematic errors with suzaku are much smaller than those in previous results .
( 80mm,60mm)figure7a.eps ( 80mm,60mm)figure7b.eps as shown in figure [ fig : spec ] , the spectra in the energy range of 1.08.0 kev are well - represented by the single - temperature model . except for discrepancies between fi and bi detectors around the si - edge ,
there are no systematic residuals .
figure [ fig:3tchi ] shows a comparison of the resultant @xmath2 fitted with single and three temperature ( apec ) models in the energy range of 1.08.0 kev , excluding the 1.72.3 kev energy range .
a more statistically rigorous approach would be to apply the f - test to compare single - temperature and three temperature models .
the f - test indicates that the three - temperature model is significantly better than the single - temperature model in regions 1 , 5 , 6 , 7 , 9 , 10 , and 11 of the center region and 17 of the 14@xmath0 offset region , and better in regions 2 , and 14 of the center region , and 16 , and 19 of the 14@xmath0 offset region , 30@xmath0 offset region , 44@xmath0 offset region , and 60@xmath0 offset region .
the largest f statistic value is 11.4 in cell number 7 of the center region , and the least f statistic value is 0.238 in cell number 8 of the center region .
however , the single - temperature model fit still represents the spectra fairly well .
( 80mm,60mm)figure8a.eps ( 80mm,60mm)figure8b.eps the spectra accumulated over each region may contain multi temperature components , although the single temperature ( apec ) model represented those spectra well . because the ratio of he - like and h - like fe k@xmath1 lines strongly depends on the plasma temperature , comparisons of temperatures derived from the line ratio and spectral fits with the thermal model are useful for understanding the temperature structure of icm .
figure [ fig : kt_ratio ] shows the ratios of the resultant normalizations of the fe k@xmath1 lines , plotted versus the temperature derived from the spectral fits with the single temperature ( apec ) model in the energy range of 1.08.0 kev . to convert line ratios to plasma temperature , we generated mock spectra assuming the single temperature apec or mekal @xcite plasma code models , convolved with xis energy resolution .
we then fitted the mock spectra with a sum of a bremsstrahlung and three gaussian models .
the theoretical line ratios from apec and mekal plasma codes are also plotted in figure [ fig : kt_ratio ] .
the derived line ratios agreed with these theoretical line ratios of the apec plasma code assuming the single temperature model , while the mekal model gave a line ratio value several % lower at a given temperature . assuming a single temperature plasma , we converted the observed line ratios to plasma temperatures using the theoretical relation for the apec model .
results are shown in table [ tab:1 - 8vapecresults ] and figure [ fig : kt_ratio ] . as shown in figure [ fig : kt_ratio ] , line temperatures agreed with those derived from the spectral fits very well .
( 80 mm , 60mm)figure9a.eps ( 80 mm , 60mm)figure9b.eps @xcite claimed a significant temperature difference of icm at the edge of the radio halo on the basis of xmm - newton observations : the temperature at the inner edge of the radio halo is 6.8@xmath2620.6 kev , while the temperature at the outer edge of the radio halo is 16.3@xmath2622.9 kev .
to examine this temperature difference , we extracted spectra from counterpart regions in the 34@xmath0 offset region , which are represented by two red boxes in figure [ fig : fino ] , and fitted the spectra with the single temperature ( apec ) model .
as shown in figure [ fig : fino ] , there are no significant temperature differences for each box in the 34@xmath0 offset region .
we then divided fov of the 34@xmath0 offset region into 2@xmath269 cells as shown in figure [ fig : fino ] , and fitted the spectra with the single temperature ( apec ) model .
the derived temperatures are also consistent with each other .
to constrain the line - of - sight gas motion using the he - like fe - k@xmath1 line , precise calibration of the xis energy scale is crucial .
because the six data sets used in the present analysis have three different observation epochs ( may 2006 , june 2009 and december 2009 ) , it is necessary to check the energy scale for each observation .
in addition , the energy gain may vary from place to place on the same ccd chip owing to the charge transfer inefficiency .
we thus estimate the xis calibration uncertainty in the following two ways : ( i ) measurements of the calibration source energy and ( ii ) comparisons of redshift values derived from four or three sets of xis .
\(i ) the fiducial absolute energy scale can be examined by measuring the centroid energy of the mn k@xmath1 line from built - in calibration sources , which illuminate two corners of each xis chip .
the spectra accumulated from the calibration source regions were fitted to the power - law model for continuum and two gaussian functions for the mn k@xmath1 line at 5.894 kev and mn k@xmath30 line at 6.490 kev . because the mn k@xmath30 line has an intrinsically complex line shape and
is contaminated by the cluster iron emission , only the mn k@xmath1 line is used for the calibration .
figures [ fig : cal ] and [ fig : cal_result ] show the result of spectral fitting and the mn k@xmath1 line centroid energy , respectively .
as shown in the left panel of figure [ fig : cal_result ] , measured line energies for the center or 14@xmath0 offset regions are systematically lower than the mn k@xmath1 line energy by 7.3 ev if they are averaged over four sensors and two detector segments in each pointing . for xis3 ,
centroid energies are lower than those of the other three chips , however , we confirmed that the spectral analysis of the redshift measurement with and without xis3 gave statistically consistent results ( see section [ sec : resultred ] for more details ) .
we then estimate the @xmath270 systematic uncertainty on the energy scale to be @xmath271 ev .
this is justified also from the fact that if we calculate the @xmath2 value using the measured mn k@xmath1 line centroid @xmath272 and the @xmath270 statistical error @xmath273 in the xis - i detector , and the mn k@xmath1 line energy in literature @xmath274 .
@xmath2 is defined as @xmath275e@xmath276 . with @xmath271
ev , @xmath2 becomes less than 10 for 7 degrees of freedom , which means the probability of @xmath2 exceeding @xmath2 versus the number of degrees of freedom becomes less than 10% : the number of bins is 8 for four sensors and two detector segments , and @xmath277 can be regarded as being consistent with @xmath274 when we consider @xmath271 ev . in the same manner ,
the systematic errors are obtained as @xmath278 ev , @xmath59 ev , @xmath109 ev , @xmath89 ev for @xmath16 , 34@xmath0 , @xmath18 , and @xmath19 offset regions , respectively .
therefore , for the safety s sake , we assign 7 ev for the 1@xmath279 ( 68% confidence level ) gain uncertainty .
\(ii ) though calibration sources provide information on the absolute energy scale at the corners of ccd chips , the gain may be dependent on position .
this intrachip variation can be effectively studied by comparing line energies of the same sky regions ( which correspond to different detector regions ) on four or three xis sensors ( see also section 3.1 in @xcite ) . to examine this issue , we divided the center region into 16 cells , and fitted the @xmath280 model in the energy range of 5.08.0 kev for each xis sensor .
we then estimate the 1@xmath279 systematic error with a reference to obtained redshift , calculating as @xmath281 for each pair of xis sensors , where @xmath282 is the measured line centroid for the xis - i detector in each region , @xmath283 is the mean of the line centroid for all xis - i detectors in each region , and @xmath284 is the @xmath270 statistical error in the xis - i detector . with @xmath28511
ev , @xmath46 becomes less than 17 for 11 degrees of freedom , which means the probability of @xmath46 exceeding @xmath46 versus the number of degrees of freedom becomes less than 10% : the number of bins is 12 for the spectral regions except for the calibration source region in the center region .
@xmath284 is @xmath4 10 ev , which is larger than the gain uncertainty : thus , we ignored @xmath284 to avoid underestimating the systematic error .
because @xmath284 is ignored in these estimates , the obtained value is an upper limit for intrachip variation within a 68% confidence level . in summary ,
the intrachip variation is an upper limit and is larger than the gain uncertainty .
thus , we concluded from ( i ) and ( ii ) that the 1@xmath279 systematic error within a 68% confidence level is 11 ev . the systematic error is then 18 ev , which corresponds to 818 km s@xmath3 in the line of sight velocity , when we quote a 90@xmath286 confidence level .
( 80mm,60mm)figure10a.eps ( 80mm,60mm)figure10b.eps ( 80mm,60mm)figure11a.eps ( 80mm,60mm)figure11b.eps ( 80 mm , 60mm)figure12a.eps ( 80 mm , 60mm)figure12b.eps as mentioned in subsection [
subsec : single ] and [ subsec : ratios ] , the line - of - sight velocity of icm or redshift can be evaluated using two different spectral models : the apec model or the bremsstrahlung with three gaussian lines .
it is then useful to compare these results and see if there is any systematic uncertainty in the redshift measurement due to spectral modeling . in the apec model , the temperature dependence of the fe k@xmath1 line energy
is already implemented in the plasma code , which in turn evokes a parameter coupling between the temperature and line energy ( or redshift ) . on the other hand , in the bremsstrahlung@xmath287gaussian model
, the line centroid should be determined almost independently of the continuum temperature , although its temperature dependence has to be corrected later .
we did this correction by deriving the rest - frame fe k@xmath1 centroid energy as a function of temperature on the basis of spectral simulations , assuming the apec model and xis energy responses . in figure
[ fig : redshift ] , the comparison of redshift measured by the two different models is shown for all analysis regions defined in figure [ fig : image ] . because there consistency between the two within their statistical errors ,
we conclude that either method robustly determines the icm redshift for the present observations .
therefore , we will show results of the fits with the apec model because the uncertainties with apec are smaller .
the obtained redshifts from the spectral fits with the single temperature ( apec ) model in the energy range of 5.08.0 kev are shown in figure [ fig : redshift ] , where the icm velocity in the line of sight is also calculated as @xmath288 .
the resultant redshifts are consistent with the optical redshift in @xcite from the ned data base , within statistical and systematic errors , which corresponds to @xmath2620.0027 in the redshift
. the direct measurements of the central energy of the k@xmath1 line of he - like fe also give almost the same redshifts derived from the spectral fits with the single temperature ( apec ) model . to quantitatively derive the redshift , we calculated the mean redshift of the icm in all pointings to be @xmath289 .
this is slightly lower than the optical redshift , @xmath290 from the ned database , but within 90@xmath286 error .
as shown in table [ tab:1 - 8vapecresults ] , in the center and 14@xmath0 offset regions , the derived highest and lowest redshift are @xmath291 for cell numbers 5 and 8 of the center region , and @xmath292 for cell number 2 of the center region . based on these redshift measurements ,
the derived icm bulk velocities are @xmath293 km s@xmath3 , and @xmath294 km s@xmath3 . including systematic errors of @xmath295 km s@xmath3 with 90@xmath286 confidence level ( section [ subsec : cal ] ) , there is no significant difference .
we estimate the 90@xmath286 upper limit on the velocity gradient to be @xmath296 km s@xmath3 .
if we further add systematic and statistical errors in the quadrature , the upper limit of the gas velocity within the 90@xmath286 confidence level becomes @xmath297 @xmath298 2200 km s@xmath3 . for simplicity , assuming that the gas is rigidly rotating at a typical circular velocity of @xmath299 , then @xmath300 km s@xmath3 , which does not exceed the sound velocity of the coma cluster , which is 1500 km s@xmath3 for a temperature of 8 kev .
the average redshift in the center region is as follows : @xmath301 in the north - west region ( cell numbers 8 , 9 , 12 , and 13 ) , @xmath302 in the south - west region ( cell numbers 10 , 11 , 14 , and 15 ) , @xmath303 in the north - east region ( cell numbers 0 , 1 , 4 , and 5 ) , and @xmath304 in the south - east region ( cell numbers 2 , 3 , 6 , and 7 ) .
we also show the averaged redshift over fov in the upper panel in table [ tab : redshift ] .
these results are consistent with each other in the center region , and with the observed redshifts in the 14@xmath0 offset region within statistical and systematic errors .
the difference in the icm velocity between the center and 30@xmath0 offset regions is derived as @xmath305 km s@xmath3 , and the difference between the center and 34@xmath0 offset regions is @xmath306 km s@xmath3 .
these are also consistent with each other .
components of the velocity in the plane of the sky are not measured .
if we assume that three components are similar , then the limit on the radial velocity translates into a limit of @xmath307 500 km s@xmath3 , which does not exceed the speed of sound and is consistent with systematic errors .
therefore , there were no significant velocity variations on the 10@xmath0 scale within central regions ( center and 14@xmath0 , 30@xmath0 , and 34@xmath0 offset regions ) from our analysis . in the ngc 4839 subcluster region ( 44@xmath0 offset region ) , the observed redshift is 0.0269@xmath2620.0033 , which corresponds to 1140@xmath308 km s@xmath3 as the icm bulk velocity without systematic errors .
there also seems to be no significant difference between the core of the coma cluster and the ngc 4839 subcluster within the 90% confidence level . as mentioned in subsection [ subsec : cal ]
, some sensors have large uncertainties in the determination of the line centroid energy . on xis3 in the center region , the mn k@xmath1 line centroid energy of segment a was different from others .
similarly , the segment d of xis1 in the ngc 4839 region was also different .
we averaged the spectrum over fov in ( i ) all detectors , and ( ii ) all detectors except those with different mn k@xmath1 line centroid energies to check the spectral shape and measured redshift in the center and ngc 4839 regions ( 44@xmath0 offset region ) .
the results are shown in the lower section in table [ tab : redshift ] .
for the center region , the derived redshifts were fairly consistent including xis3 or not .
on the other hand , for the ngc 4839 subcluster region , the resultant redshift changed slightly from 0.0268 to 0.0287 , although this was also consistent within statistical and systematic errors .
as shown in figure [ fig : cal_result ] , the peak of the he - like fe - k@xmath1 line of xis1 is more shifted than that of the other two sensors .
the measured redshifts in the 44@xmath0 offset region were 0.0271@xmath2620.0023 , 0.0303@xmath2620.0051 , and 0.0255@xmath2620.0027 for xis0 , 1 , and 3 , respectively .
because the measured redshift of the averaged spectra between xis0 and 3 was consistent with the redshift from simultaneous spectral fits , the value 0.0269 would be plausible . in conclusion
, there was no significant difference in the icm velocity between the core of the coma cluster and the ngc 4839 subcluster within 90% confidence .
ccccc field & x - ray ( @xmath309 ) & optical ( @xmath309 ) & x - ray ( @xmath310 ) & optical ( @xmath310 ) + & & & km s@xmath3 & km s@xmath3 + all pointings & 0.0227@xmath2620.0005 & 0.02307 & 6810@xmath262150 & 6917 + center & 0.0227@xmath2620.0005 & 0.02286 & 6810@xmath262150 & 6853 + 14@xmath0 offset & 0.0230@xmath2620.001 & 0.02286 & 6900@xmath262300 & 6853 + center and 14@xmath0 offset & 0.0227@xmath2620.0005 & 0.02286 & 6810@xmath262150 & 6853 + ngc 4839 & 0.0269@xmath2620.0033 & 0.02448 & 8070@xmath262990 & 7339 + center ( xis0123 ) & 0.0226@xmath2620.0005 & 0.02286 & 6775@xmath262150 & 6853 + center ( xis012 ) & 0.0226@xmath2620.0005 & 0.02286 & 6775@xmath262150 & 6853 + ngc 4839 ( xis013 ) & 0.0287@xmath2620.0033 & 0.02448 & 8604@xmath262990 & 7339 + ngc 4839 ( xis03 ) & 0.0268@xmath2620.0033 & 0.02448 & 8034@xmath262990 & 7339 + + [ tab : redshift ] ( 80 mm , 60mm)figure13a.eps ( 80 mm , 60mm)figure13b.eps to measure the abundance using the strong fe
k lines , we employed the results of spectral fitting in the 5.08.0 kev energy range for the fe abundance .
because of the good statistics , the spectra in the lower energy band primarily determine the fitted temperatures .
although the spectra are well fitted with a single - temperature model , a small discrepancy between the model and data around the fe - k line can yield a large systematic uncertainty in the derived fe abundances . within the 34@xmath0 region ,
temperatures and abundances derived from the spectral fitting in the 5.08.0 kev energy range agree well with those from 1.08.0 kev energy ranges within 5% . in the 44@xmath0 and 60@xmath0 offset regions , the fe abundances from the 5.08.0 kev energy range are smaller than those from the 1.08.0 kev range by @xmath40.1 solar .
@xmath46 values for the limited energy range of 5.08.0 kev from the former fitting are 10% smaller than those from the latter , although the single - temperature model reproduces the observed spectra at 1.08.0 kev well .
therefore , we adopted the fe abundance derived from the spectral fitting in the 5.08.0 kev energy range .
figure [ fig : fe ] shows a radial profile and map of the fe abundance of icm with the single temperature ( apec ) model in the 5.08.0 kev energy range . within 30@xmath0 from the x - ray peak , fe abundances are almost constant at @xmath40.4 solar .
the derived fe abundances are 0.41@xmath2620.01 solar in the center region , and 0.38@xmath2620.02 solar in the 14@xmath0 offset region .
the fe abundances in the 30@xmath0 and 34@xmath0 offset regions are slightly lower , @xmath40.3 solar , although it has larger uncertainties .
these values agree with recent xmm results @xcite within 1.2 mpc .
the fe abundance in the ngc 4839 subcluster region is comparable to that in the central region , and higher than that in the 30@xmath0 and 34@xmath0 offset regions .
the average value in the subcluster region is 0.33@xmath2620.09 solar .
this value is also consistent with that in @xcite , although the error bars in their results are much larger than those in our results .
x - ray observations of clusters of galaxies can play a major role in determining cosmological parameters , because of the importance of measuring gravitational mass .
the ratio of he - like k@xmath1 to h - like k@xmath1 lines of fe is a very steep function of temperature , and has a different temperature dependence from that of the continuum .
the continuum emission is affected by the systematic uncertainties in the response and non - thermal emission , while the line ratio does not .
thus , by comparing the fitted temperatures between these two methods , the effects of the systematic uncertainty in the response and/or of the non - thermal emission is increased . using the apec plasma code
, the temperatures derived from the spectral fitting of the 1.08.0 kev energy range and the line ratio of fe agree within a few percent when we averaged all regions .
the systematic uncertainties in temperatures from the line ratio are in the level of the systematic difference between those from apec and mekal , which is about 3% .
the consistency of observed temperatures from the continuum and those from line ratios supports the accuracy of suzaku measurements of plasma temperature .
in contrast , systematic differences of @xmath4 10% in the cluster temperature among chandra , pn , and mos were reported in relatively high temperature clusters ( @xcite ) . even using the same instrument , the derived temperatures changed systematically by @xmath311% between calibrations @xcite .
a systematic uncertainty of several percent in response matrices of a detector can also cause systematic uncertainties in the temperature structure .
@xcite found that the temperature structures of icm in the coma cluster derived from multi - temperature fits with pn and mos spectra were different , although the two detectors gave consistent temperatures within several percent .
when they allowed higher temperature components over 10 kev in hot clusters including the coma cluster , using mos data , fe abundances from the he - like line increased by several tens of percent , owing to artificial detection of a hot component , while those derived by pn were unchanged .
however , with suzaku , we found that the single - temperature model fits the spectra of the coma cluster very well , and we do not need temperature components above 10 kev or below 2 kev to fit the spectra .
the multi - temperature components observed by xmm were not needed . in the outer regions of clusters at low surface brightness
, uncertainties in the background of chandra and xmm also lead to systematic uncertainties in icm temperatures .
some analyses found that icm temperatures decreased outward by half at 0.6@xmath312 ( e.g. , @xcite ; @xcite ) , while others found flatter profiles ( e.g. , @xcite ) .
systematic uncertainties in the derived temperatures due to uncertainties in the background with suzaku observations are much smaller , because suzaku xis has a much lower and more stable background . also , previous xmm and chandra results of temperatures in the outer regions have statistical errors more than 20% , while those of suzaku have errors less than 10% .
we need precise measurements of icm temperatures to search for a non - thermal hard component as an excess of the thermal component . on the basis of the icm temperature map derived with xmm - pn
, @xcite found that the suzaku hxd - pin spectrum was described with the thermal emission from icm , and there was no significant evidence of excess hard emission .
the temperatures of the coma cluster derived from suzaku - xis are consistent within error bars with those from the pn detector : the weighted average of temperatures with statistical errors within the center field is close to that derived with xmm - pn within a few percent .
the temperatures of offset fields are consistent with those from xmm - pn within error bars .
thus , our results support the non - detection of non - thermal hard emissions by @xcite @xcite reported the existence of hot gas at @xmath313 kev in rx j1347.5 - 1145 .
they concluded that the gas properties can be explained by a fairly recent ( within the last 0.5 gyr ) collision of two massive ( 5@xmath1210@xmath314 m@xmath315 ) clusters with bullet - like high velocity ( @xmath316 km s@xmath3 ) .
in contrast , @xcite found that there was no extremely high temperature gas in the coma cluster in the hxd - pin spectrum up to 70 kev .
on the basis of the consistency of derived temperatures from the continuum and the line ratio and the results from the spectral analysis of hxd - pin , we conclude that the amount of very high temperature gas is rather small . from the spatial variation of the derived temperatures ,
there is no region with extremely hot temperature : the derived temperatures range from 7.0 to 9.0 kev within the center , 14@xmath0 offset , and @xmath17 offset regions .
the coma cluster has a cluster - wide synchrotron radio halo .
if the electrons in the cluster were accelerated by a very strong shock that occurred owing to a recent merger , we might expect the cluster to contain more very hot gas , although it is difficult to make this argument quantitative . in any case , in the coma cluster , relativistic electrons producing the radio halo were apparently generated without producing a large amount of very hot gas .
an example of a process which might do this is the turbulent re - acceleration model ( e.g. , @xcite ) . within the center and offset regions the spatial variation of derived temperatures
is relatively small , from 7 kev to 9 kev .
there are no extremely hot and cool regions .
we did not detect any temperature jump corresponding to a shock in the offset regions . within each region for the spectral analysis , the single - temperature model fit the spectrum .
therefore , in the center of the coma cluster , icm is in a nearly relaxed state .
although the variation was small , there was some asymmetric temperature structure , like a hot region northwest of the center .
if the cluster had been an isolated system collapsing from self - gravity , the temperature structures would be symmetric .
the observed asymmetry in the temperature distribution indicates that external effects or interactions , such as merging , have occurred .
numerical simulations of the evolution of the cluster ( e.g. , @xcite ; @xcite ) show that nonaxisymmetric structures in the temperature distribution are erased several gyr after each merger .
the presence of asymmetric temperature structures suggest that the central region of the coma cluster has experienced a merger , and the lack of hard component shows that its core have relaxed in the last several gyr .
the observed cool region in the southeast of the center region coincides with the filamentary structure originating near ngc 4911 and ngc 4921 @xcite .
@xcite reported that the temperature of this cold area ranges from 5 to 7 kev .
this region mostly contain the stripped subcluster gas , which is thought to be relatively cool in the initial state .
the numerical simulations ( e.g. , @xcite ) suggest that the gas would maintain its temperature for several gyr .
@xcite showed that even a single subcluster collision with supersonic velocity creates both hot and cool regions in the main cluster .
although heating due to collisions occurs , cooling would also occur through the adiabatic expansion of the stripped gas .
the measurements of bulk motions in icm are also important to derive the gravitational mass of clusters of galaxies .
we constrained the upper limit of icm bulk motions in the center and offset regions on the scale of 117 kpc ( ) and 234 kpc ( 9@xmath0 ) , respectively , which correspond to the scales of regions for spectral accumulation ( see section [ sec : obs ] and subsection [ sec : resultred ] ) .
the upper limit of gas bulk motions is @xmath297 @xmath298 1100 km s@xmath3 .
as summarized in table [ tab : redshift ] , considering the systematic error of 18 ev , or 818 km s@xmath3 with a 90@xmath286 confidence level ( section [ subsec : cal ] ) , there are no significant bulk motions in the center and offset fields .
compared with the sound velocity of the coma cluster , @xmath317 km s@xmath3 for a temperature of @xmath47 = 8 kev , the bulk - motion in the central region of the coma cluster does not exceed the sound velocity .
our results do not conflict with the discovery of pressure fluctuations in the center of the coma cluster by @xcite which indicates that at least 10% of the icm pressure is in turbulent form .
we have not constrained the turbulence , and the scale of the fluctuation ranges between 29 kpc and 64 kpc , which is smaller than our scale of spectral analysis .
the velocity difference between the main cluster and the ngc 4839 subcluster from optical observations is 486 km s@xmath3 .
although the best - fit line - of - sight velocity of the subcluster is higher than that of the main cluster by @xmath4 1000 km s@xmath3 , the difference is comparable to statistical and systematic errors . because the temperature of the region is about 5 kev ,
the sound velocity is @xmath4 1150 km s@xmath3 . considering the error bars ,
we conclude that the relative line - of - sight gas velocity in the ngc 4839 subgroup region does not greatly exceed the sound velocity .
numerical simulations indicate that a major merger between clusters raises the temperature of icm and induces a bulk velocity of the order of 1000 km s@xmath3 ( e.g. , @xcite ; @xcite ) . in the late phase of mergers , turbulent motions develop in a simulation by @xcite .
the non - detection of bulk - motions in icm of the coma cluster also indicates that the central region of the cluster is in a somewhat relaxed state .
if so , the non - thermal electrons relevant to the radio halo of the coma cluster may have been accelerated by the intracluster turbulence rather than shocks . in conclusion
, the line - of - sight gas velocity of the coma cluster in the observed region does not greatly exceed the sound velocity , and the central region of the coma cluster is in a nearly relaxed state .
this means that the assumption of hydrostatic equilibrium is approximately valid in calculating the cluster mass of the coma cluster .
the fe abundance is nearly constant at @xmath4 0.4 solar within a clustocentric radius of 0.5 mpc , and beyond that distance it decreases with the radius to 0.20.3 solar .
this profile is consistent with those measured by xmm ( @xcite ; @xcite ) .
suzaku has a lower level of background , and a slightly better energy resolution : therefore , systematic uncertainties in fe abundance are considered to be smaller .
differences in abundance profiles of icm in central regions of clusters with and without cool cores have been reported ( @xcite , @xcite , @xcite ) .
@xcite showed an abundance difference between the two type of clusters within 0.1@xmath312 , while at 0.10.3@xmath312 , the average values of fe abundances are both @xmath4 0.40.5 solar , and are consistent with each other .
the coma cluster is thought to have experienced a major merger in the recent past and subsequently , the central region came to a somewhat relaxed state . during a cluster merger ,
the mixing of icm could destroy any central fe peak .
in the first stage of merging , the fe peak and cool core remain intact as observed in some ongoing merging clusters ( @xcite ; @xcite ) .
for example , abell 2256 , an ongoing merging cluster , has an abundance gradient in the direction opposite of the merging direction owing to the remixing of the gas .
numerical simulation also support this scenario .
@xcite performed hydrodynamical simulations with two different merger types of clusters : cluster 1 has only small merger events , while cluster 2 undergoes a major merger ( mass ratio 1:3 ) . in cluster 1 ,
the abundance is more than @xmath4 0.4 solar within a radius of 0.1 mpc , and decreases from @xmath4 0.3 solar to @xmath4 0.1 solar with a decrease in radius .
the situation is different in cluster 2 . in the coma cluster ,
the fe abundance is @xmath4 0.4 solar and homogeneous within a radius of 0.5 mpc .
this value of the fe abundance is similar to those at 0.20.3@xmath312 in other clusters as shown in figure [ fig : fe ] .
therefore , tn the coma cluster , the merger have destroyed the cool core , and mixed the icm completely at least within 0.5 mpc .
the coma cluster which was observed with the x - ray imaging spectrometer ( xis ) onboard suzaku , was analyzed by the x - ray satellite in six pointings , centered on the x - ray peak and offset by west , , , , and .
because of its low background , suzaku is the most sensitive x - ray satellite for observing k@xmath1 lines of fe in the intracluster medium . after obtaining accurate measurements of fe lines
, we studied the temperature structure of the intracluster medium , searched for possible bulk - motions , and measured the fe abundance in the cluster .
the spectra of each extracted region were well fitted by the single - temperature apec model , and the two- or three- temperature apec model did not improve @xmath2 .
the temperatures derived from the observed ratios of k@xmath1 lines of h - like and he - like fe agree well with those from spectral fittings with the single - temperature apec model .
because this line ratio is a strong function of plasma temperature , the observed consistency supports the accuracy of temperature measurements with suzaku , and constrains the temperature structure of icm .
the observed values of the central energy of the he - like fe line of the center , , and offset regions are constant within 500 @xmath318 , which corresponds to the calibration error .
because relative bulk velocities in the coma cluster are smaller than the sound velocity of the intracluster medium , 1500 km s @xmath3 , we can verify the derived total mass in a cluster on the basis of the hydrostatic icm equilibrium inside the offset region .
significant bulk velocities were also not found in the offset region , which corresponds to the ngc 4839 subcluster .
the results on the temperature and velocity structure suggest that the core of the coma cluster is in a fairly relaxed state .
this is consistent with models in which the non - thermal electrons relevant to the radio halo are accelerated by the intracluster turbulence rather than large - scale shocks .
this is also consistent with the fact that numerical simulations show that the turbulence motion is developed in the late phase of mergers .
the observed fe abundance of the intracluster medium is almost constant at 0.4 solar inside the offset region , and decreases with radius .
the central abundance is slightly lower than that of other clusters or groups .
this indicates that central regions of the gas were mixed well during the past merger growth of the cluster .
+ _ acknowledgements . _
we wish to thank the referee for his / her suggestions on the paper .
the authors are grateful to all members of suzaku for their contributions in instrument preparation , spacecraft operation , software development , and in - orbit instrumental calibration .
to analyze the data , we used the isas analysis servers provided by isas / c - soda .
n. o. acknowledges support by the ministry of education , culture , sports , science and technology of japan , grant - in - aid for scientific research no .
cls was supported in part by nasa suzaku grants nnx08az99 g , nnx09ah25 g , and nnx09ah74 g .[/INST] the coma cluster was observed with an x - ray imaging spectrometer ( xis ) onboard suzaku in six pointings , including the central x - ray peak region , the 14@xmath0 west offset region , 30@xmath0 and 34@xmath0 north - west offset regions , and 44@xmath0 and 60@xmath0 south - west offset regions .
owing to its lower background level , suzaku has better sensitivity to fe k@xmath1 lines than other satellites . using precise fe line measurements , we studied the temperature structure , possible bulk motions , and iron abundance distributions in the intracluster medium ( icm ) .
the observed spectra were well - represented by a single - temperature model , and two- or three- temperature model did not improve @xmath2 substantially .
the temperature , derived from k@xmath1 line ratios of h - like and he - like fe , agree with those derived from the single - temperature model . because the line ratio is a steep function of temperature , the consistency supports the accuracy of temperature measurements conducted with suzaku . within the 34@xmath0 region ,
the redshift derived from the central energy of the he - like fe line is consistent with that from optical observations , within a calibration error of 18 ev or 818 km s@xmath3 in the line of sight .
this value is smaller than the sound velocity of icm , which is 1500 km s@xmath3 .
the central energy of fe lines at the 44@xmath0 offset region around the ngc 4839 subcluster is also consistent with those within the 34@xmath0 region .
these results on the temperature and velocity structure suggest that the core of the cluster is in a relaxed state , and non - thermal electrons relevant to the radio halo are accelerated by intracluster turbulence rather than large - scale shocks .
fe abundance is almost constant at 0.4 solar within the 34@xmath0 region , and decreases with radius .
this value is slightly lower than those of other clusters , which means the gas have been mixed well during a past merger associated with the growth of the cluster . </s> |
SECTION 1. MAKING IT ILLEGAL TO OPERATE A MOTOR VEHICLE WITH A DRUG OR
ALCOHOL IN THE BODY OF THE DRIVER AT LAND BORDER PORTS OF
ENTRY.
Section 13(a) of title 18, United States Code, is amended--
(1) by inserting ``(1)'' after ``(a)''; and
(2) by adding at the end the following:
``(2) Whoever with a drug or alcohol in his or her body operates a
motor vehicle at a land border port of entry in a manner that is
punishable, because of the presence of the drug or alcohol, if
committed within the jurisdiction of the State in which that land
border port of entry is located (under the laws of that State in force
at the time of the act) shall be guilty of a like offense and subject
to a like punishment.
``(3) Any individual who operates a motor vehicle at a land border
port of entry is deemed to have given consent to submit to a chemical
or other test of the blood, breath, or urine of the driver by an
officer or employee of the Immigration and Naturalization Service
authorized under section 287(h) of the Immigration and Nationality Act
(8 U.S.C. 1357(h)) for the purpose of determining the presence or
concentration of a drug or alcohol in such blood, breath, or urine.
``(4) If an individual refuses to submit to such a test after being
advised by the officer or employee that the refusal will result in
notification under this paragraph, the Attorney General shall give
notice of the refusal to--
``(A) the State or foreign state that issued the license
permitting the individual to operate a motor vehicle; or
``(B) if the individual has no such license, the State or
foreign state in which the individual is a resident.
``(5) The Attorney General shall give notice of a conviction of an
individual under this section for operation of a motor vehicle at a
land border port of entry with a drug or alcohol in the body of the
individual, to--
``(A) the State or foreign state that issued the license
permitting the individual to operate a motor vehicle; or
``(B) if the individual has no such license, the State or
foreign state in which the individual is a resident.
``(6) For purposes of this subsection, the term `land border port
of entry' means any land border port of entry (as defined in section
287(h)(3) of the Immigration and Nationality Act (8 U.S.C. 1357(h)(3)))
that was not reserved or acquired as provided in section 7 of this
title.''.
SEC. 2. AUTHORIZING OFFICERS AND EMPLOYEES OF THE IMMIGRATION AND
NATURALIZATION SERVICE TO CONDUCT TESTS FOR A DRUG OR
ALCOHOL.
Section 287 of the Immigration and Nationality Act (8 U.S.C. 1357)
is amended by adding at the end the following:
``(h)(1) If an officer or employee of the Service authorized under
regulations prescribed by the Attorney General is inspecting a driver
at a land border port of entry and has reasonable grounds to believe
that, because of alcohol in the body of the driver, operation of a
motor vehicle by the driver is an offense under section 13 of title 18,
United States Code, the officer or employee may require the driver to
submit to a test of the breath of the driver to determine the presence
or concentration of the alcohol.
``(2) If an officer or employee of the Service authorized under
regulations prescribed by the Attorney General arrests a driver under
this section for operation of a motor vehicle in violation of section
13 of title 18, United States Code, because of a drug or alcohol in the
body of the driver, the officer or employee may require the driver to
submit to a chemical or other test to determine the presence or
concentration of the drug or alcohol in the blood, breath, or urine of
the driver.
``(3) For purposes of this subsection:
``(A) The term `driver' means an individual who is
operating a motor vehicle at a land border port of entry.
``(B) The term `land border port of entry' means any
immigration checkpoint operated by the Immigration and
Naturalization Service at a land border between a State (as
that term is used in section 13 of title 18, United States
Code) and a foreign state.''.
SEC. 3. REQUIRING NOTICE AT LAND BORDER PORTS OF ENTRY REGARDING
OPERATION OF A MOTOR VEHICLE AND DRUGS AND ALCOHOL.
(a) In General.--The Immigration and Nationality Act is amended by
inserting after section 294 (8 U.S.C. 1363a) the following:
``notice at land border ports of entry regarding operation of a motor
vehicle and drugs and alcohol
``Sec. 295. At each point where motor vehicles regularly enter a
land border port of entry (as defined in section 287(h)(3)), the
Attorney General shall post a notice that operation of a motor vehicle
with a drug or alcohol in the body of the driver at a land border port
of entry is an offense under Federal law.''.
(b) Clerical Amendment.--The first section of the Immigration and
Nationality Act is amended in the table of contents by inserting after
the item relating to section 294 the following:
``Sec. 295. Notice at land border ports of entry regarding operation of
a motor vehicle and drugs and alcohol.''.
SEC. 4. IMPOUNDMENT OF VEHICLE FOR REFUSAL TO SUBMIT TO TEST FOR DRUG
OR ALCOHOL.
Not more than 180 days after the date of the enactment of this Act,
the Attorney General shall issue regulations authorizing an officer or
employee of the Immigration and Naturalization Service to impound a
vehicle, if the individual who operates the vehicle refuses to submit
to a chemical or other test under section 13(a)(3) of title 18, United
States Code.
SEC. 5. EFFECTIVE DATE.
This Act shall take effect 180 days after the date of the enactment
of this Act. | (Sec. 2) Amends the Immigration and Nationality Act (INA) to authorize an INS officer who: (1) inspects a driver at a land border port of entry and who has reasonable grounds to believe that the driver may be operating a motor vehicle in violation of State laws to require the driver to submit to a breath test to determine the presence or concentration of the alcohol; and (2) arrests a driver for such prohibited operation of a motor vehicle to require the driver to submit to a drug or alcohol test.
(Sec. 3) Amends the INA to require the Attorney General, at each point where motor vehicles regularly enter a land border port of entry, to post a notice that operation of a motor vehicle with a drug or alcohol in the driver's body at a land border port of entry is an offense under Federal law.
(Sec. 4) Directs the Attorney General to issue regulations authorizing an INS officer to impound a vehicle if the individual who operates it refuses to submit to such a test. | <s>[INST]SECTION 1. MAKING IT ILLEGAL TO OPERATE A MOTOR VEHICLE WITH A DRUG OR
ALCOHOL IN THE BODY OF THE DRIVER AT LAND BORDER PORTS OF
ENTRY.
Section 13(a) of title 18, United States Code, is amended--
(1) by inserting ``(1)'' after ``(a)''; and
(2) by adding at the end the following:
``(2) Whoever with a drug or alcohol in his or her body operates a
motor vehicle at a land border port of entry in a manner that is
punishable, because of the presence of the drug or alcohol, if
committed within the jurisdiction of the State in which that land
border port of entry is located (under the laws of that State in force
at the time of the act) shall be guilty of a like offense and subject
to a like punishment.
``(3) Any individual who operates a motor vehicle at a land border
port of entry is deemed to have given consent to submit to a chemical
or other test of the blood, breath, or urine of the driver by an
officer or employee of the Immigration and Naturalization Service
authorized under section 287(h) of the Immigration and Nationality Act
(8 U.S.C. 1357(h)) for the purpose of determining the presence or
concentration of a drug or alcohol in such blood, breath, or urine.
``(4) If an individual refuses to submit to such a test after being
advised by the officer or employee that the refusal will result in
notification under this paragraph, the Attorney General shall give
notice of the refusal to--
``(A) the State or foreign state that issued the license
permitting the individual to operate a motor vehicle; or
``(B) if the individual has no such license, the State or
foreign state in which the individual is a resident.
``(5) The Attorney General shall give notice of a conviction of an
individual under this section for operation of a motor vehicle at a
land border port of entry with a drug or alcohol in the body of the
individual, to--
``(A) the State or foreign state that issued the license
permitting the individual to operate a motor vehicle; or
``(B) if the individual has no such license, the State or
foreign state in which the individual is a resident.
``(6) For purposes of this subsection, the term `land border port
of entry' means any land border port of entry (as defined in section
287(h)(3) of the Immigration and Nationality Act (8 U.S.C. 1357(h)(3)))
that was not reserved or acquired as provided in section 7 of this
title.''.
SEC. 2. AUTHORIZING OFFICERS AND EMPLOYEES OF THE IMMIGRATION AND
NATURALIZATION SERVICE TO CONDUCT TESTS FOR A DRUG OR
ALCOHOL.
Section 287 of the Immigration and Nationality Act (8 U.S.C. 1357)
is amended by adding at the end the following:
``(h)(1) If an officer or employee of the Service authorized under
regulations prescribed by the Attorney General is inspecting a driver
at a land border port of entry and has reasonable grounds to believe
that, because of alcohol in the body of the driver, operation of a
motor vehicle by the driver is an offense under section 13 of title 18,
United States Code, the officer or employee may require the driver to
submit to a test of the breath of the driver to determine the presence
or concentration of the alcohol.
``(2) If an officer or employee of the Service authorized under
regulations prescribed by the Attorney General arrests a driver under
this section for operation of a motor vehicle in violation of section
13 of title 18, United States Code, because of a drug or alcohol in the
body of the driver, the officer or employee may require the driver to
submit to a chemical or other test to determine the presence or
concentration of the drug or alcohol in the blood, breath, or urine of
the driver.
``(3) For purposes of this subsection:
``(A) The term `driver' means an individual who is
operating a motor vehicle at a land border port of entry.
``(B) The term `land border port of entry' means any
immigration checkpoint operated by the Immigration and
Naturalization Service at a land border between a State (as
that term is used in section 13 of title 18, United States
Code) and a foreign state.''.
SEC. 3. REQUIRING NOTICE AT LAND BORDER PORTS OF ENTRY REGARDING
OPERATION OF A MOTOR VEHICLE AND DRUGS AND ALCOHOL.
(a) In General.--The Immigration and Nationality Act is amended by
inserting after section 294 (8 U.S.C. 1363a) the following:
``notice at land border ports of entry regarding operation of a motor
vehicle and drugs and alcohol
``Sec. 295. At each point where motor vehicles regularly enter a
land border port of entry (as defined in section 287(h)(3)), the
Attorney General shall post a notice that operation of a motor vehicle
with a drug or alcohol in the body of the driver at a land border port
of entry is an offense under Federal law.''.
(b) Clerical Amendment.--The first section of the Immigration and
Nationality Act is amended in the table of contents by inserting after
the item relating to section 294 the following:
``Sec. 295. Notice at land border ports of entry regarding operation of
a motor vehicle and drugs and alcohol.''.
SEC. 4. IMPOUNDMENT OF VEHICLE FOR REFUSAL TO SUBMIT TO TEST FOR DRUG
OR ALCOHOL.
Not more than 180 days after the date of the enactment of this Act,
the Attorney General shall issue regulations authorizing an officer or
employee of the Immigration and Naturalization Service to impound a
vehicle, if the individual who operates the vehicle refuses to submit
to a chemical or other test under section 13(a)(3) of title 18, United
States Code.
SEC. 5. EFFECTIVE DATE.
This Act shall take effect 180 days after the date of the enactment
of this Act.[/INST](Sec. 2) Amends the Immigration and Nationality Act (INA) to authorize an INS officer who: (1) inspects a driver at a land border port of entry and who has reasonable grounds to believe that the driver may be operating a motor vehicle in violation of State laws to require the driver to submit to a breath test to determine the presence or concentration of the alcohol; and (2) arrests a driver for such prohibited operation of a motor vehicle to require the driver to submit to a drug or alcohol test.
(Sec. 3) Amends the INA to require the Attorney General, at each point where motor vehicles regularly enter a land border port of entry, to post a notice that operation of a motor vehicle with a drug or alcohol in the driver's body at a land border port of entry is an offense under Federal law.
(Sec. 4) Directs the Attorney General to issue regulations authorizing an INS officer to impound a vehicle if the individual who operates it refuses to submit to such a test.</s> |
ankle sprain occurs more often in active movements such as walking , running , and jumping .
among lower limb injuries , ligament injuries of the ankle account for more than 50% of the
cases .
furthermore , at least 7% of people with ankle sprain had additional repetitive
symptoms , including re - injuries and functional anomalies1 .
re - injury of ankle sprain triggers chronic ankle instability ( cai ) ,
which acts as a cause for recurrent sprains in 5572% of the cases .
these patients with
re - injuries complained of residual symptoms for 6 to 18 months2 . in this way , many previous studies reported a high recurrence rate
of ankle sprain3 , 4 and attributed the causes of this high recurrence rate to deformed
tissues around the ankle joint , loss of proprioceptive sense5 , and reuse of the ankle joint before complete recovery .
cai refers to the repetition of lateral
ankle joint instability after an initial lateral ankle ligament sprain , with residual
symptoms such as pain , edema , and giving way of the ankle joint6 .
furthermore , the greatest causes of repetitive ankle sprain
were reported to be the muscular weakness of the tibialis anterior and peroneus longus , and
the increased ankle instability due to the hypofunction of the proprioceptive sense7 , 8 . in
addition ,
when the instability of the ankle joint increases , other motion patterns are
required to compensate for the instability , which causes the motion deformations of the hip
joint and trunk , resulting in the side effect of the changed anatomical arrangement9 .
kim eun - kyung10 claimed that rehabilitation exercise treatment programs
such as muscle strengthening , kidney , and proprioceptive sense enhancement exercises are
required to prevent and treat the chronic pain and functional ankle joint instability after
ankle joint sprain .
a rehabilitation exercise through 4-week balance training has been also
reported to elicit significant changes in the lower leg rotation and hindfoot angle11 .
odriscoll et al.12 reported that functional rehabilitation exercises for 6
weeks , including muscle - strengthening exercise , balancing exercise , and agility and jump
training caused significant changes in balancing ability and hindfoot angle .
therefore , an
appropriate functional rehabilitation program should be applied to improve chronic ankle
joint instability by reinforcing the muscular function of the ankle joint and enhancing the
proprioceptive sense in patients with chronic ankle sprain .
hence , in this study , an ankle
functional rehabilitation exercise was applied to patients with chronic ankle sprain and its
effects on ankle joint fms result and isokinetic muscular function were examined .
this
presents a new alternative to the functional rehabilitation exercise program for the
prevention and rehabilitation of ankle sprain for patients with chronic ankle sprain .
the subjects of this study were 16 patients with chronic ankle pain and chronic ankle
sprain whose chronic cai had been diagnosed by medical examination , simple radiological
examination , computed tomography , and magnetic resonance imaging .
they were randomized to
the ankle functional rehabilitation exercise group ( afreg ; n=8 ) and control group ( cong ;
n=8 ) .
for the physical characteristics of the subjects , the mean age , height , and weight of
the afreg were 20.8 0.5 years , 174.6 7.1 cm , and 69.6 9.03 kg .
those of the cong were
20.7 1.1 years , 174.1 6.5 cm , and 66.2 7.6 kg . after receiving an explanation of the
intent and purpose of this study
the
two groups had no problem in homogeneity because they had no significant intergroup
differences in physical characteristics .
the ankle functional rehabilitation exercise
program mainly consisted of a proprioceptive sense exercise program , which was performed in
a total of 12 times , 6 times per week for 2 weeks , with an exercise time of 60 minutes .
the
ankle functional rehabilitation exercise program used the exercise tools for proprioceptive
sense exercise , jumper ( togu , germany ) and togu ( togu , germany ) . in detail , the exercise
items were ( 1 ) balance squat and ( 2 ) supine pelvic lift , performed while standing on the
jumper , and ( 3 ) lunge and ( 4 ) dorsi and plantar flexion , performed by weight bearing while
standing on the togu .
the exercise time was maintained at 30 seconds per set , during which
isometric training was performed .
for the fms related to ankle joint , deep squat , hurdle
step , and in - line lunge tests were performed in relation to the ankle joint functional
movement in 7 patterns by using the fms test kit ( usa ) , which is a functional motion
inspection measurement system . for the ankle joint isokinetic muscular function inspection ,
the peak torque ( nm ) at the angular speed of 240 was measured by using cybex humac norm
( ankle joint system , usa ) .
the measured data were analyzed by using the spss 21.0
statistical program for windows .
a paired - test was conducted for comparison of the groups
between before and after the application .
all of the subjects understood the purpose of this study and provided written informed
consent prior to their participation in accordance with the ethical standards of the
declaration of helsinki .
in the ankle joint fms , the afreg showed significant improvements in all the fms items
after application ( p<0.05 ) , and the cong did not show any significant changes after the
application ( table 1table 1.the comparison of ankle joint of fms in the each group ( unit : nm)groupmuscle strengthpre ( mean sd)post ( mean sd)afregdst*1.6 0.52.5 0.5hst*1.8 0.32.7 0.4ilt*2.0 0.02.8 0.3congdst1.7 0.41.7 0.4hst1.8 0.32.1 0.9ilt2.0 0.02.3 0.5*p<0.05 ; afreg : ankle functional rehabilitation exercise group ; cong : control
group ; dst : deep squat test ; hst : hurdle step test ; ilt : in - line lunge test ) . * p<0.05 ; afreg : ankle functional rehabilitation exercise group ; cong : control
group ; dst : deep squat test ; hst : hurdle step test ; ilt : in - line lunge test for changes in the ankle joint isokinetic muscular functions , the afreg showed significant
improvements in every item after application ( p<0.05 ) , whereas cong did not show any
significant changes after application ( table
2table 2.the comparison of ankle joint of peak torque in the each group ( unit : nm)groupmuscle strengthpre ( mean sd)post ( mean sd)afregadfr*27.2 6.934.7 12.4adfl*25.5 7.033.7 9.7apfr*41.6 14.464.6 9.8apfl*40.1 13.859.2 13.0congadfr31.0 10.628.1 7.0adfl28.7 10.129.1 8.1apfr38.6 11.350.8 19.0apfl42.7 10.752.5 21.6*p<0.05 ; afre : ankle functional rehabilitation exercise group ; cong : control
group ; adfr : ankle dorsi flexion right ; adfl : ankle dorsi flexion left ; apfr : ankle
plantar flexion right ; apfl : ankle planter flexion left ) . * p<0.05 ; afre : ankle functional rehabilitation exercise group ; cong : control
group ; adfr : ankle dorsi flexion right ; adfl : ankle dorsi flexion left ; apfr : ankle
plantar flexion right ; apfl : ankle planter flexion left
the cai generates structural changes of the soft tissues around the ankle due to repetitive
ankle sprains and causes dysfunction in the stability of ankle neuromuscular control and in
musculoskeletal stability13 . among the
problems in patients with chronic ankle sprain
furthermore , scott15 reported that
functional rehabilitation exercise more effectively reduced pain and edema than surgery and
fixation .
another previous study also reported that functional rehabilitation exercise
through the training of proprioceptive sense decreased the re - injury rate of the ankle16 . recently , active research is being
conducted to present the directions of functional rehabilitation exercise , and studies on
the evaluation of functional rehabilitation exercise are being conducted as well17 .
this study was conducted to demonstrate that chronic ankle sprain is caused by chronic
dysfunction and instability of the ankle joint , and the muscular function and stability of
the ankle joint were improved through the application of ankle functional rehabilitation
exercise .
the afreg showed significant improvements in all items of the fms and ankle joint
isokinetic muscular function after application ( p<0.05 ) , whereas the cong showed no
significant changes after application .
the fms ( functional movement screen ) is known to be
useful for evaluating asymmetries of the body and defects in functional exercise motions
based on the basic motions of the proprioceptive sensory receptor , stability , and mobility ,
which are the motion patterns of the body18 , 19 .
thus , it was used as a measurement item
in this study . in this study , by using this fms evaluation method , the functional defects of the ankle
were chosen as the measurement items before and after exercise . furthermore , the isokinetic
measuring instrument is an effective tool for evaluating muscular function because it can
produce the maximum muscular force according to the resistance within the predefined range
of motion of the joint .
hence , in this
study , an isokinetic instrument was used to measure the effects of the functional
rehabilitation exercise program on the improvement of muscular functions .
functional rehabilitation exercise is an integrated form of training for muscular strength ,
agility , proprioceptive sense , and special exercise functions and refers to various patterns
of exercise programs .
it has been shown to effectively decrease pain and dysfunction .
furthermore , it has the effect of protecting tissues from many physical burdens applied
during physical activities by increasing the reaction speed of surrounding muscles and nerve
tissues , restoring stability , and reinforcing muscles21 .
in addition , an 8-week functional rehabilitation program , including proprioceptive
exercise , helped the stabilization of the unstable ankle joint by improving postural sway
and isokinetic muscular function ( isokinetic strength)22 .
an ankle joint balance improvement exercise program was effective
in the rehabilitation and prevention of chronic ankle instability and sprain , and the
control of proprioceptive ability protected the body from injuries11 .
in the application of rehabilitation exercise program for resolving functional ankle
instability , the combined application of muscle strengthening and proprioceptive exercises
was more effective than muscle strengthening exercise alone22 . besides , because ankle instability is caused by the combination of
the lack of proprioceptive sense and eversion muscle weakening , rehabilitation programs must
focus on the improvement of the proprioceptive sense and muscular strength23 .
furthermore , both improved proprioceptive
sensibility and the functional capabilities of the surrounding muscles of the ankle joints ,
thereby providing a coping mechanism for the unexpected inversion of ankle joints24 . therefore ,
the ankle functional rehabilitation program applied in this study was mainly
composed of the exercise of proprioceptive sense in order to achieve the stability of the
affected site by recovering the motion control ability while reinforcing the muscular
strength of the patients with chronic ankle sprain .
the improvement was achieved as a result
of the improved muscular functions of the muscles comprising the ankle joint and the
improved integrated system of the muscles and nerves that support balance and enables the
exhibition of stable forces through the integration of the proprioceptive receptor and
motion sensory nerves by the muscles around the trunk , pelvis , and abdomen .
consequently , the application of ankle functional rehabilitation exercise in patients with
chronic ankle sprain in this study will present a new alternative solution as an effective
rehabilitation program for the reinforcement of ankle joint fms and isokinetic muscular
function . | [ purpose ] this study was conducted to investigate the effects of ankle functional
rehabilitation exercise on ankle joint functional movement screen results and isokinetic
muscular function in patients with chronic ankle sprain patients .
[ subjects and methods ]
in this study , 16 patients with chronic ankle sprain were randomized to an ankle
functional rehabilitation exercise group ( n=8 ) and a control group ( n=8 ) .
the ankle
functional rehabilitation exercise centered on a proprioceptive sense exercise program ,
which was applied 12 times for 2 weeks . to verify changes after the application ,
ankle
joint functional movement screen scores and isokinetic muscular function were measured and
analyzed . [ results ]
the ankle functional rehabilitation exercise group showed significant
improvements in all items of the ankle joint functional movement screen and in isokinetic
muscular function after the exercise , whereas the control group showed no difference after
the application .
[ conclusion ] the ankle functional rehabilitation exercise program can be
effectively applied in patients with chronic ankle sprain for the improvement of ankle
joint functional movement screen score and isokinetic muscular function . | <s>[INST]ankle sprain occurs more often in active movements such as walking , running , and jumping .
among lower limb injuries , ligament injuries of the ankle account for more than 50% of the
cases .
furthermore , at least 7% of people with ankle sprain had additional repetitive
symptoms , including re - injuries and functional anomalies1 .
re - injury of ankle sprain triggers chronic ankle instability ( cai ) ,
which acts as a cause for recurrent sprains in 5572% of the cases .
these patients with
re - injuries complained of residual symptoms for 6 to 18 months2 . in this way , many previous studies reported a high recurrence rate
of ankle sprain3 , 4 and attributed the causes of this high recurrence rate to deformed
tissues around the ankle joint , loss of proprioceptive sense5 , and reuse of the ankle joint before complete recovery .
cai refers to the repetition of lateral
ankle joint instability after an initial lateral ankle ligament sprain , with residual
symptoms such as pain , edema , and giving way of the ankle joint6 .
furthermore , the greatest causes of repetitive ankle sprain
were reported to be the muscular weakness of the tibialis anterior and peroneus longus , and
the increased ankle instability due to the hypofunction of the proprioceptive sense7 , 8 . in
addition ,
when the instability of the ankle joint increases , other motion patterns are
required to compensate for the instability , which causes the motion deformations of the hip
joint and trunk , resulting in the side effect of the changed anatomical arrangement9 .
kim eun - kyung10 claimed that rehabilitation exercise treatment programs
such as muscle strengthening , kidney , and proprioceptive sense enhancement exercises are
required to prevent and treat the chronic pain and functional ankle joint instability after
ankle joint sprain .
a rehabilitation exercise through 4-week balance training has been also
reported to elicit significant changes in the lower leg rotation and hindfoot angle11 .
odriscoll et al.12 reported that functional rehabilitation exercises for 6
weeks , including muscle - strengthening exercise , balancing exercise , and agility and jump
training caused significant changes in balancing ability and hindfoot angle .
therefore , an
appropriate functional rehabilitation program should be applied to improve chronic ankle
joint instability by reinforcing the muscular function of the ankle joint and enhancing the
proprioceptive sense in patients with chronic ankle sprain .
hence , in this study , an ankle
functional rehabilitation exercise was applied to patients with chronic ankle sprain and its
effects on ankle joint fms result and isokinetic muscular function were examined .
this
presents a new alternative to the functional rehabilitation exercise program for the
prevention and rehabilitation of ankle sprain for patients with chronic ankle sprain .
the subjects of this study were 16 patients with chronic ankle pain and chronic ankle
sprain whose chronic cai had been diagnosed by medical examination , simple radiological
examination , computed tomography , and magnetic resonance imaging .
they were randomized to
the ankle functional rehabilitation exercise group ( afreg ; n=8 ) and control group ( cong ;
n=8 ) .
for the physical characteristics of the subjects , the mean age , height , and weight of
the afreg were 20.8 0.5 years , 174.6 7.1 cm , and 69.6 9.03 kg .
those of the cong were
20.7 1.1 years , 174.1 6.5 cm , and 66.2 7.6 kg . after receiving an explanation of the
intent and purpose of this study
the
two groups had no problem in homogeneity because they had no significant intergroup
differences in physical characteristics .
the ankle functional rehabilitation exercise
program mainly consisted of a proprioceptive sense exercise program , which was performed in
a total of 12 times , 6 times per week for 2 weeks , with an exercise time of 60 minutes .
the
ankle functional rehabilitation exercise program used the exercise tools for proprioceptive
sense exercise , jumper ( togu , germany ) and togu ( togu , germany ) . in detail , the exercise
items were ( 1 ) balance squat and ( 2 ) supine pelvic lift , performed while standing on the
jumper , and ( 3 ) lunge and ( 4 ) dorsi and plantar flexion , performed by weight bearing while
standing on the togu .
the exercise time was maintained at 30 seconds per set , during which
isometric training was performed .
for the fms related to ankle joint , deep squat , hurdle
step , and in - line lunge tests were performed in relation to the ankle joint functional
movement in 7 patterns by using the fms test kit ( usa ) , which is a functional motion
inspection measurement system . for the ankle joint isokinetic muscular function inspection ,
the peak torque ( nm ) at the angular speed of 240 was measured by using cybex humac norm
( ankle joint system , usa ) .
the measured data were analyzed by using the spss 21.0
statistical program for windows .
a paired - test was conducted for comparison of the groups
between before and after the application .
all of the subjects understood the purpose of this study and provided written informed
consent prior to their participation in accordance with the ethical standards of the
declaration of helsinki .
in the ankle joint fms , the afreg showed significant improvements in all the fms items
after application ( p<0.05 ) , and the cong did not show any significant changes after the
application ( table 1table 1.the comparison of ankle joint of fms in the each group ( unit : nm)groupmuscle strengthpre ( mean sd)post ( mean sd)afregdst*1.6 0.52.5 0.5hst*1.8 0.32.7 0.4ilt*2.0 0.02.8 0.3congdst1.7 0.41.7 0.4hst1.8 0.32.1 0.9ilt2.0 0.02.3 0.5*p<0.05 ; afreg : ankle functional rehabilitation exercise group ; cong : control
group ; dst : deep squat test ; hst : hurdle step test ; ilt : in - line lunge test ) . * p<0.05 ; afreg : ankle functional rehabilitation exercise group ; cong : control
group ; dst : deep squat test ; hst : hurdle step test ; ilt : in - line lunge test for changes in the ankle joint isokinetic muscular functions , the afreg showed significant
improvements in every item after application ( p<0.05 ) , whereas cong did not show any
significant changes after application ( table
2table 2.the comparison of ankle joint of peak torque in the each group ( unit : nm)groupmuscle strengthpre ( mean sd)post ( mean sd)afregadfr*27.2 6.934.7 12.4adfl*25.5 7.033.7 9.7apfr*41.6 14.464.6 9.8apfl*40.1 13.859.2 13.0congadfr31.0 10.628.1 7.0adfl28.7 10.129.1 8.1apfr38.6 11.350.8 19.0apfl42.7 10.752.5 21.6*p<0.05 ; afre : ankle functional rehabilitation exercise group ; cong : control
group ; adfr : ankle dorsi flexion right ; adfl : ankle dorsi flexion left ; apfr : ankle
plantar flexion right ; apfl : ankle planter flexion left ) . * p<0.05 ; afre : ankle functional rehabilitation exercise group ; cong : control
group ; adfr : ankle dorsi flexion right ; adfl : ankle dorsi flexion left ; apfr : ankle
plantar flexion right ; apfl : ankle planter flexion left
the cai generates structural changes of the soft tissues around the ankle due to repetitive
ankle sprains and causes dysfunction in the stability of ankle neuromuscular control and in
musculoskeletal stability13 . among the
problems in patients with chronic ankle sprain
furthermore , scott15 reported that
functional rehabilitation exercise more effectively reduced pain and edema than surgery and
fixation .
another previous study also reported that functional rehabilitation exercise
through the training of proprioceptive sense decreased the re - injury rate of the ankle16 . recently , active research is being
conducted to present the directions of functional rehabilitation exercise , and studies on
the evaluation of functional rehabilitation exercise are being conducted as well17 .
this study was conducted to demonstrate that chronic ankle sprain is caused by chronic
dysfunction and instability of the ankle joint , and the muscular function and stability of
the ankle joint were improved through the application of ankle functional rehabilitation
exercise .
the afreg showed significant improvements in all items of the fms and ankle joint
isokinetic muscular function after application ( p<0.05 ) , whereas the cong showed no
significant changes after application .
the fms ( functional movement screen ) is known to be
useful for evaluating asymmetries of the body and defects in functional exercise motions
based on the basic motions of the proprioceptive sensory receptor , stability , and mobility ,
which are the motion patterns of the body18 , 19 .
thus , it was used as a measurement item
in this study . in this study , by using this fms evaluation method , the functional defects of the ankle
were chosen as the measurement items before and after exercise . furthermore , the isokinetic
measuring instrument is an effective tool for evaluating muscular function because it can
produce the maximum muscular force according to the resistance within the predefined range
of motion of the joint .
hence , in this
study , an isokinetic instrument was used to measure the effects of the functional
rehabilitation exercise program on the improvement of muscular functions .
functional rehabilitation exercise is an integrated form of training for muscular strength ,
agility , proprioceptive sense , and special exercise functions and refers to various patterns
of exercise programs .
it has been shown to effectively decrease pain and dysfunction .
furthermore , it has the effect of protecting tissues from many physical burdens applied
during physical activities by increasing the reaction speed of surrounding muscles and nerve
tissues , restoring stability , and reinforcing muscles21 .
in addition , an 8-week functional rehabilitation program , including proprioceptive
exercise , helped the stabilization of the unstable ankle joint by improving postural sway
and isokinetic muscular function ( isokinetic strength)22 .
an ankle joint balance improvement exercise program was effective
in the rehabilitation and prevention of chronic ankle instability and sprain , and the
control of proprioceptive ability protected the body from injuries11 .
in the application of rehabilitation exercise program for resolving functional ankle
instability , the combined application of muscle strengthening and proprioceptive exercises
was more effective than muscle strengthening exercise alone22 . besides , because ankle instability is caused by the combination of
the lack of proprioceptive sense and eversion muscle weakening , rehabilitation programs must
focus on the improvement of the proprioceptive sense and muscular strength23 .
furthermore , both improved proprioceptive
sensibility and the functional capabilities of the surrounding muscles of the ankle joints ,
thereby providing a coping mechanism for the unexpected inversion of ankle joints24 . therefore ,
the ankle functional rehabilitation program applied in this study was mainly
composed of the exercise of proprioceptive sense in order to achieve the stability of the
affected site by recovering the motion control ability while reinforcing the muscular
strength of the patients with chronic ankle sprain .
the improvement was achieved as a result
of the improved muscular functions of the muscles comprising the ankle joint and the
improved integrated system of the muscles and nerves that support balance and enables the
exhibition of stable forces through the integration of the proprioceptive receptor and
motion sensory nerves by the muscles around the trunk , pelvis , and abdomen .
consequently , the application of ankle functional rehabilitation exercise in patients with
chronic ankle sprain in this study will present a new alternative solution as an effective
rehabilitation program for the reinforcement of ankle joint fms and isokinetic muscular
function .[/INST][ purpose ] this study was conducted to investigate the effects of ankle functional
rehabilitation exercise on ankle joint functional movement screen results and isokinetic
muscular function in patients with chronic ankle sprain patients .
[ subjects and methods ]
in this study , 16 patients with chronic ankle sprain were randomized to an ankle
functional rehabilitation exercise group ( n=8 ) and a control group ( n=8 ) .
the ankle
functional rehabilitation exercise centered on a proprioceptive sense exercise program ,
which was applied 12 times for 2 weeks . to verify changes after the application ,
ankle
joint functional movement screen scores and isokinetic muscular function were measured and
analyzed . [ results ]
the ankle functional rehabilitation exercise group showed significant
improvements in all items of the ankle joint functional movement screen and in isokinetic
muscular function after the exercise , whereas the control group showed no difference after
the application .
[ conclusion ] the ankle functional rehabilitation exercise program can be
effectively applied in patients with chronic ankle sprain for the improvement of ankle
joint functional movement screen score and isokinetic muscular function .</s> |
Author, commentator, civil rights activist and Princeton University professor Cornel West has been arrested while protesting on the steps of the Supreme Court about corporate influence in politics.
A Supreme Court spokeswoman says 19 people were arrested Sunday afternoon after they refused to leave the grounds of the court.
Ann Wilcox, an attorney and legal adviser to the protesters, says West was among those arrested. West attended the dedication of the Martin Luther King Jr. Memorial on the National Mall before joining the October 2011 Stop the Machine protest in Washington's Freedom Plaza.
The protest is marking 10 years since the start of the war in Afghanistan and has an anti-war and anti-corporate greed message.
West is a well-known left-leaning academic whose books include "Race Matters" and "Democracy Matters." ||||| West, a former Harvard University professor now teaching at Princeton University , took part Sunday in the dedication of the monument to the Rev. Martin Luther King Jr. , an event that was delayed from August because of Hurricane Irene . He then, according to media reports, moved on to a protest at the home of the high court.A well-known commentator on civil rights issues, West recently got into a TV spat with presidential candidate Herman Cain , telling Cain to "get off the symbolic crack pipe."In Washington, the anti-corporate protest movement is known as Occupy D.C.Kathy Arberg, a spokeswoman for the court, said Sunday evening that "19 people with Occupy D.C. were arrested at the court this afternoon by Supreme Court police and charged" under federal law. She did not divulge the name of West or any other protester arrested.Global protests over the weekend led to the arrests of more than 250 people in the United States and worldwide. | – Activist Princeton University professor and well-known commentator Cornel West was one of 19 people arrested on the steps of the Supreme Court yesterday afternoon while protesting the influence of corporate money in politics, reports AP. The group was busted when they refused to leave the grounds, according to a spokeswoman for the Supreme Court. West had attended the dedication ceremony for the Martin Luther King Jr. Memorial prior to joining protests against the Afghanistan war and corporate greed. The Supreme Court last year blocked limits on corporate campaign contributions. West recently blasted presidential Herman Cain on TV, telling him to "get off the symbolic crack pipe," notes the Los Angeles Times. | <s>[INST]Author, commentator, civil rights activist and Princeton University professor Cornel West has been arrested while protesting on the steps of the Supreme Court about corporate influence in politics.
A Supreme Court spokeswoman says 19 people were arrested Sunday afternoon after they refused to leave the grounds of the court.
Ann Wilcox, an attorney and legal adviser to the protesters, says West was among those arrested. West attended the dedication of the Martin Luther King Jr. Memorial on the National Mall before joining the October 2011 Stop the Machine protest in Washington's Freedom Plaza.
The protest is marking 10 years since the start of the war in Afghanistan and has an anti-war and anti-corporate greed message.
West is a well-known left-leaning academic whose books include "Race Matters" and "Democracy Matters." ||||| West, a former Harvard University professor now teaching at Princeton University , took part Sunday in the dedication of the monument to the Rev. Martin Luther King Jr. , an event that was delayed from August because of Hurricane Irene . He then, according to media reports, moved on to a protest at the home of the high court.A well-known commentator on civil rights issues, West recently got into a TV spat with presidential candidate Herman Cain , telling Cain to "get off the symbolic crack pipe."In Washington, the anti-corporate protest movement is known as Occupy D.C.Kathy Arberg, a spokeswoman for the court, said Sunday evening that "19 people with Occupy D.C. were arrested at the court this afternoon by Supreme Court police and charged" under federal law. She did not divulge the name of West or any other protester arrested.Global protests over the weekend led to the arrests of more than 250 people in the United States and worldwide.[/INST]– Activist Princeton University professor and well-known commentator Cornel West was one of 19 people arrested on the steps of the Supreme Court yesterday afternoon while protesting the influence of corporate money in politics, reports AP. The group was busted when they refused to leave the grounds, according to a spokeswoman for the Supreme Court. West had attended the dedication ceremony for the Martin Luther King Jr. Memorial prior to joining protests against the Afghanistan war and corporate greed. The Supreme Court last year blocked limits on corporate campaign contributions. West recently blasted presidential Herman Cain on TV, telling him to "get off the symbolic crack pipe," notes the Los Angeles Times.</s> |
Giant squid filmed in Pacific depths: Japan scientists
TOKYO — Scientists and broadcasters said Monday they have captured footage of an elusive giant squid roaming the depths of the Pacific Ocean, showing it in its natural habitat for the first time ever.
Japan's National Science Museum succeeded in filming the deep-sea creature at a depth of more than half a kilometre (a third of a mile) after teaming up with Japanese public broadcaster NHK and the US Discovery Channel.
The massive invertebrate is the stuff of legend, with sightings of a huge ocean-dwelling beast reported by sailors for centuries.
The creature is thought to be the genesis of the Nordic legend of Kraken, a sea monster believed to have attacked ships in waters off Scandinavia over the last millennium.
Modern-day scientists on their own Moby Dick-style search used a submersible to descend to the dark and cold depths of the northern Pacific Ocean, where at around 630 metres (2,066 feet) they managed to film a three-metre specimen.
After around 100 missions, during which they spent 400 hours in the cramped submarine, the three-man crew tracked the creature from a spot some 15 kilometres (nine miles) east of Chichi island in the north Pacific.
Museum researcher Tsunemi Kubodera said they followed the enormous mollusc to a depth of 900 metres as it swam into the ocean abyss.
NHK showed footage of the silver-coloured creature, which had huge black eyes, as it swam against the current, holding a bait squid in its arms.
For Kubodera it was the culmination of a lengthy quest for the beast.
"It was shining and so beautiful," Kubodera told AFP. "I was so thrilled when I saw it first hand, but I was confident we would because we rigorously researched the areas we might find it, based on past data."
Kubodera said the creature had its two longest arms missing, and estimated it would have been eight metres long if it had been whole. He gave no explanation for its missing arms.
He said it was the first video footage of a live giant squid in its natural habitat -- the depths of the sea where there is little oxygen and the weight of the water above exerts enormous pressure.
Kubodera, a squid specialist, also filmed what he says was the first live video footage of a giant squid in 2006, but only from his boat after it was hooked and brought up to the surface.
"Researchers around the world have tried to film giant squid in their natural habitats, but all attempts were in vain before," Kubodera said.
"With this footage we hope to discover more about the life of the species," he said, adding that he planned to publish his findings soon.
Kubodera said the two successful sightings of the squid -- in 2012 and 2006 -- were both in the same area, some 1,000 kilometres south of Tokyo, suggesting it could be a major habitat for the species.
The giant squid, "Architeuthis" to scientists, is sometimes described as one of the last mysteries of the ocean, being part of a world so hostile to humans that it has been little explored.
Researchers say Architeuthis eats other types of squid and grenadier, a species of fish that lives in the deep ocean. They say it can grow to be longer than 10 metres.
NHK said it and the Discovery Channel are scheduled to air special documentaries on the find later this month.
Copyright © 2013 AFP. All rights reserved. More » ||||| The giant squid has been captured on video in its natural habitat for the first time ever.
This long-sought after footage — considered by many to be the Holy Grail of natural history filmmaking — will be revealed by Discovery Channel and NHK in January 2013.
With razor-toothed suckers and eyes the size of dinner plates, tales of this creature have been around since ancient times. The Norse legend of the sea monster the Kraken, and the Scylla from Greek mythology, might have derived from the elusive giant squid.
This massive predator has always been shrouded in secrecy, and every attempt to capture a live giant squid on camera in its natural habitat has failed. Until now.
Mankind finally confronts the greatest mystery of the deep as the first-ever footage of a live giant squid in its natural habitat is revealed in Discovery Channel’s Monster Squid: The Giant Is Real, which premieres on Sunday, January 27, 2013 at 10/9c as the season finale of Curiosity. NHK will air their special on the first-ever footage of the giant squid in early January 2013.
QUIZ: Take the Giant Squid Quiz
“When Discovery does natural history it sets the bar high, and this ground breaking project features the very first-ever footage of a live giant squid in its natural habitat. Our crew came face-to-face with the giant squid, and it’s the ideal season finale for our Curiosity series that stirs the imagination of our audience, bravely asking questions and fearlessly seeking answers. This latest production, four years in the making, is a world-first achievement for television, and I’m excited to share it,” said Eileen O’Neill, Group President of Discovery and TLC Networks.
VIDEO: Discovery News Report from Aug. 18, 2010 | – Discovery is about to release the Kraken: Until now, the giant squid had never been caught on video in its natural habitat. But Japan's National Science Museum has managed to capture the footage, and it's headed for the small screen on the country's public television. Then, on Jan. 27, the Discovery Channel will unveil the video of the creature "with razor-toothed suckers and eyes the size of dinner plates." That's not totally an exaggeration. The giant squid is believed to have inspired centuries of legends among sailors. The squid in question is about 10 feet long—though scientists say it would have been 26 feet long had it not been missing two arms—and was taped some 2,000 feet underwater in the north Pacific. It took experts some 400 hours squeezed into a submersible to get the footage, AFP reports. "It was shining and so beautiful," says a researcher of the silvery, black-eyed squid. "I was so thrilled when I saw it firsthand." | <s>[INST]Giant squid filmed in Pacific depths: Japan scientists
TOKYO — Scientists and broadcasters said Monday they have captured footage of an elusive giant squid roaming the depths of the Pacific Ocean, showing it in its natural habitat for the first time ever.
Japan's National Science Museum succeeded in filming the deep-sea creature at a depth of more than half a kilometre (a third of a mile) after teaming up with Japanese public broadcaster NHK and the US Discovery Channel.
The massive invertebrate is the stuff of legend, with sightings of a huge ocean-dwelling beast reported by sailors for centuries.
The creature is thought to be the genesis of the Nordic legend of Kraken, a sea monster believed to have attacked ships in waters off Scandinavia over the last millennium.
Modern-day scientists on their own Moby Dick-style search used a submersible to descend to the dark and cold depths of the northern Pacific Ocean, where at around 630 metres (2,066 feet) they managed to film a three-metre specimen.
After around 100 missions, during which they spent 400 hours in the cramped submarine, the three-man crew tracked the creature from a spot some 15 kilometres (nine miles) east of Chichi island in the north Pacific.
Museum researcher Tsunemi Kubodera said they followed the enormous mollusc to a depth of 900 metres as it swam into the ocean abyss.
NHK showed footage of the silver-coloured creature, which had huge black eyes, as it swam against the current, holding a bait squid in its arms.
For Kubodera it was the culmination of a lengthy quest for the beast.
"It was shining and so beautiful," Kubodera told AFP. "I was so thrilled when I saw it first hand, but I was confident we would because we rigorously researched the areas we might find it, based on past data."
Kubodera said the creature had its two longest arms missing, and estimated it would have been eight metres long if it had been whole. He gave no explanation for its missing arms.
He said it was the first video footage of a live giant squid in its natural habitat -- the depths of the sea where there is little oxygen and the weight of the water above exerts enormous pressure.
Kubodera, a squid specialist, also filmed what he says was the first live video footage of a giant squid in 2006, but only from his boat after it was hooked and brought up to the surface.
"Researchers around the world have tried to film giant squid in their natural habitats, but all attempts were in vain before," Kubodera said.
"With this footage we hope to discover more about the life of the species," he said, adding that he planned to publish his findings soon.
Kubodera said the two successful sightings of the squid -- in 2012 and 2006 -- were both in the same area, some 1,000 kilometres south of Tokyo, suggesting it could be a major habitat for the species.
The giant squid, "Architeuthis" to scientists, is sometimes described as one of the last mysteries of the ocean, being part of a world so hostile to humans that it has been little explored.
Researchers say Architeuthis eats other types of squid and grenadier, a species of fish that lives in the deep ocean. They say it can grow to be longer than 10 metres.
NHK said it and the Discovery Channel are scheduled to air special documentaries on the find later this month.
Copyright © 2013 AFP. All rights reserved. More » ||||| The giant squid has been captured on video in its natural habitat for the first time ever.
This long-sought after footage — considered by many to be the Holy Grail of natural history filmmaking — will be revealed by Discovery Channel and NHK in January 2013.
With razor-toothed suckers and eyes the size of dinner plates, tales of this creature have been around since ancient times. The Norse legend of the sea monster the Kraken, and the Scylla from Greek mythology, might have derived from the elusive giant squid.
This massive predator has always been shrouded in secrecy, and every attempt to capture a live giant squid on camera in its natural habitat has failed. Until now.
Mankind finally confronts the greatest mystery of the deep as the first-ever footage of a live giant squid in its natural habitat is revealed in Discovery Channel’s Monster Squid: The Giant Is Real, which premieres on Sunday, January 27, 2013 at 10/9c as the season finale of Curiosity. NHK will air their special on the first-ever footage of the giant squid in early January 2013.
QUIZ: Take the Giant Squid Quiz
“When Discovery does natural history it sets the bar high, and this ground breaking project features the very first-ever footage of a live giant squid in its natural habitat. Our crew came face-to-face with the giant squid, and it’s the ideal season finale for our Curiosity series that stirs the imagination of our audience, bravely asking questions and fearlessly seeking answers. This latest production, four years in the making, is a world-first achievement for television, and I’m excited to share it,” said Eileen O’Neill, Group President of Discovery and TLC Networks.
VIDEO: Discovery News Report from Aug. 18, 2010[/INST]– Discovery is about to release the Kraken: Until now, the giant squid had never been caught on video in its natural habitat. But Japan's National Science Museum has managed to capture the footage, and it's headed for the small screen on the country's public television. Then, on Jan. 27, the Discovery Channel will unveil the video of the creature "with razor-toothed suckers and eyes the size of dinner plates." That's not totally an exaggeration. The giant squid is believed to have inspired centuries of legends among sailors. The squid in question is about 10 feet long—though scientists say it would have been 26 feet long had it not been missing two arms—and was taped some 2,000 feet underwater in the north Pacific. It took experts some 400 hours squeezed into a submersible to get the footage, AFP reports. "It was shining and so beautiful," says a researcher of the silvery, black-eyed squid. "I was so thrilled when I saw it firsthand."</s> |
recently , information on the excited states of light unstable nuclei has increased rapidly @xcite . in the excited states of
light unstable nuclei , an exotic molecular structure of light unstable nuclei is one of the attractive subjects in experimental and theoretical research .
for example , molecular structure has been suggested to appear in neutron - rich nuclei , such as @xmath4be and @xmath5be @xcite .
w. von oertzen et al .
@xcite proposed a kind of exotic clustering structure with a @xmath6 configuration in the excited states of @xmath0be .
however , there have been few microscopic studies on the excited states of @xmath0be .
needless to say , @xmath3-cluster cores are very important in the ground and excited states of @xmath0be as well as in @xmath7be and @xmath4be .
however , we should not forget the breaking of @xmath3-clusters in @xmath0be because there are many valence neutrons around the @xmath3-clusters .
the experimental data concerning the @xmath8-decay strength are very useful to estimate the breaking of the 2@xmath3 clustering structure in be isotopes , because gamow - teller transitions from li to be are not allowed if the @xmath3-cluster cores in the daughter state of be are completely ideal ones with a simple @xmath9 configuration .
it is very interesting that the recently measured @xmath8-decay strength from @xmath0li to @xmath0be indicates significant breaking of @xmath3-clusters in the excited states of @xmath0be @xcite .
therefore , it is important to also study the breaking of @xmath3-clusters due to the surrounding neutrons as well as the development of clustering in @xmath0be .
we should point out another interesting feature in @xmath0be .
abnormal parity of the ground state in @xmath0be has been known for a long time .
namely , the spin parity of the ground state is @xmath10 , which seems to be inconsistent with the ordinary shell - model picture in which @xmath0be with 7 neutrons may have a @xmath11 state as the ground state .
it has long been a problem why parity inversion occurs in @xmath0be . as possible reasons for this parity inversion , such effects as the halo structure ,
a core deformation , clustering and paring are suggested .
for example , the energy gain of a positive parity state of @xmath0be is discussed in refs @xcite .
however , the ground - state structure has not been sufficiently studied by fully microscopic calculations without such assumptions as the existence of core nuclei .
although the clustering structure must be important in be isotopes , it is difficult for mean - field approaches to describe developed clustering structures . with a theoretical method of antisymmetrized molecular dynamics , dot et al .
have studied the abnormal parity ground state of @xmath0be without assuming cores or the stability of the mean field . however , in their work@xcite , the effects of angular - momentum projections and three - body forces were approximately estimated by perturbative treatments . our aim is to make a systematic research on the structure of the ground and excited states of @xmath0be based on the microscopic calculations .
an important point is that the theoretical approach should be free from such model assumptions as stability of the mean field , and the existence of inert cores or clusters .
first of all , traditional mean - field approaches are not useful to study the developed clustering structure in be isotopes . with cluster models , the clustering structure of the excited states of @xmath7be and @xmath4be has been successfully explained @xcite by assuming 2-@xmath3 cores and surrounding neutrons . since the assumption of 2 @xmath3-cluster cores is not appropriate to discuss the breaking of @xmath3-cores , these cluster models are not sufficient for investigations of @xmath0be with many valence neutrons . in fact , it is difficult to use them to directly calculate the experimental data of the @xmath8-decay strength from @xmath0li . with these models it may not be possible to describe the recently discovered excited state at 8.04 mev with the strong @xmath8 transition strength from @xmath0li .
we have applied a theoretical approach of antisymmetrized molecular dynamics ( amd ) .
the amd method has already proved to be useful for studying the structures of light nuclei @xcite . within this framework
, we do not need such model assumptions as inert cores , clusters , nor axial symmetries , because the basis wave functions of a nuclear system are written by slater determinants where all centers of the gaussian - type spatial part of single - particle wave functions are free parameters . in amd studies of neutron - rich nuclei , we investigated the structures of be isotopes @xcite . in amd calculations ,
many kinds of experimental data for nuclear structure have been reproduced . due to the flexibility of the amd wave function , we have succeeded to describe the structure changes between shell - model - like states and clustering states with an increase in the neutron number . in previous studies @xcite on
be isotopes , the excited states of @xmath0be were not studied in detail because the calculations are based on the variation before a total - angular - momentum projection .
recently , the amd framework has been developed to be an extended version based on variational calculations after a spin - parity projection(vap ) , which has already been confirmed to be powerful for studying the excited states of light nuclei .
the method has been applied to a stable nucleus @xmath5c @xcite , and to unstable nuclei : @xmath4be , @xmath5be and @xmath12be@xcite . in the present work
, the structures of the ground and excited states of @xmath0be were studied by performing vap calculations using the amd method . in the next section ( sec .
[ sec : formulation ] ) , we explain the formulation of amd for a nuclear structure study of the ground and excited states .
the adopted effective interactions are briefly explained in sec .
[ sec : interaction ] . in sec.[sec : results ] , we present the theoretical results concerning the energy levels , @xmath8 decays and @xmath13 transitions compared with the experimental data .
we predict a new rotational band with a well - developed clustering structure which comes from @xmath6 configurations . in sec.[sec : discus ] , the intrinsic structure and behavior of the valence neutrons are discussed .
we also discuss the breaking of @xmath3-clusters which has an important effect on the @xmath8-decay strength . finally , we summarize our work in sec . [
sec : summary ]
in this section , the formulation of amd for a nuclear structure study of the excited states is explained briefly . for more detailed descriptions of the amd framework the reader
is referred to refs .
@xcite an amd wave function of a nucleus with mass number @xmath14 is a slater determinant of gaussian wave packets ; @xmath15,\\ \chi_{\xi_i}= \left(\begin{array}{l } { 1\over 2}+\xi_{i}\\ { 1\over 2}-\xi_{i } \end{array}\right ) , \end{array}\right . \end{aligned}\ ] ] where the @xmath16th single - particle wave function @xmath17 is a product of the spatial wave function @xmath18 , the intrinsic spin function @xmath19 and the isospin function @xmath20 .
the spatial part @xmath18 is presented by a gaussian wave packet whose center is defined by complex parameters @xmath21 , @xmath22 , @xmath23 .
@xmath19 is the intrinsic spin function parameterized by @xmath24 , while @xmath20 is the isospin function which is fixed to be up(proton ) or down(neutron ) in the present calculations .
thus an amd wave function is parameterized by a set of complex parameters @xmath25 .
@xmath26 are the centers of gaussians for spatial parts and the parameters @xmath24 s determine the directions of intrinsic spins of the single particle wave functions .
if we consider a parity eigenstate projected from an amd wave function , the total wave function consists of two slater determinants , @xmath27 where @xmath28 is a parity projection operator . in the case of a total - angular - momentum projection(@xmath29-projection ) , the wave function of a system is represented by the integral of the rotated states , @xmath30 where the function @xmath31 is the well - known wigner s d function and @xmath32 stands for the rotation operator with euler angle @xmath33 . in principal the total wave function
can be a superposition of independent amd wave functions .
for example , a system is written by a superposition of spin - parity projected amd wave functions @xmath34 as follows , @xmath35 expectation values of a given tensor operator @xmath36(rank @xmath37 ) for the total - angular - momentum projected states @xmath38 and @xmath39 are calculated as follows , @xmath40 the three - dimensional integral can be evaluated numerically by taking a finite number of mesh points of the euler angle @xmath33=(@xmath41 ) .
we make variational calculations for a trial wave function to find the state which minimizes the energy of the system ; @xmath42 in the amd framework , the energy variation is performed by a method of frictional cooling , one of the imaginary time methods .
regarding the frictional cooling method , the reader is referred to papers @xcite .
the time development of the parameters @xmath43 of a wave function @xmath44 is simulated by the frictional cooling equations , @xmath45 @xmath46 with arbitrary real numbers @xmath47 and @xmath48 .
it is easily proved that the energy of the system decreases with each time step due to the frictional term:@xmath49 . after sufficient cooling iterations ,
the parameters for the minimum - energy state are obtained . in order to obtain the wave function for a @xmath50 state
, we make the energy variation after a spin - parity projection(vap ) for an amd wave function by using the frictional cooling method explained above .
that is to say we perform the energy variation for the trial function @xmath51 , the spin - parity eigenstate projected from an amd wave function .
first we make variational calculations after only the parity projection but before the spin projection(vbp ) to prepare an initial trial wave function @xmath52 . after obtaining an initial wave function in vbp calculations
we evaluate the expectation values of hamiltonian for the spin - parity - projected states by choosing the body - fixed @xmath53-axis for the @xmath33 rotation to be the approximate principal @xmath54-axis on the intrinsic deformation . then we find an appropriate @xmath55 quantum that gives the minimum diagonal energy of the spin - parity eigenstate @xmath56 where @xmath57 . for each spin parity @xmath50
, we start vap calculations for the normalized energy expectation value @xmath58 with the adopted @xmath55 quantum from the initial state . in general
, the direction of the approximately principal @xmath54-axis is automatically determined in the energy variation because the shape of the intrinsic system can vary freely .
the approximately principal axis can deviate from the @xmath53-axis in the vap procedure with a given @xmath57 .
that is to say that the optimum state @xmath34 obtained after the variation may contain so - called @xmath59-mixing ( @xmath60 ) components .
however , the deviation of @xmath54-axis from the @xmath53-axis is found to be small in many cases .
it means that the obtained states do not contain @xmath59-mixing components so much , and @xmath55 well corresponds to the @xmath59 quantum . concerning the states in the lowest band with each parity , we can obtain appropriate initial wave functions by simple vbp calculations as mentioned above .
for the highly excited states , in order to obtain initial wave functions and appropriate @xmath55 quanta for vap calculations we make vbp calculations with a constraint on amd wave function .
the details of the amd calculation with constraints have been described in refs .
@xcite . in the present calculations ,
we adopt a constraint as the expectation value of the total - oscillator quanta to equal with a given number . after choosing a corresponding @xmath55 quantum , we perform vap calculations from the initial wave function .
when we obtain other local minimum states than the obtained states , we consider them as the states in higher rotational bands .
after the vap calculations for @xmath61 states , the optimum intrinsic states @xmath62 , and @xmath63 are obtained . here
@xmath64 indicates the number of the calculated levels .
we consider that the obtained wave functions approximately represent the intrinsic wave functions of the @xmath61 states .
we determine the final wave functions by superposing the obtained amd wave functions .
that is to say that we determine the coefficients @xmath65 in eq .
[ eqn : superpose ] for each @xmath61 state by diagonalizing the hamiltonian matrix @xmath66 ) and ( @xmath67 ) . in comparison with the experimental data such as the energy levels and the strength @xmath13 transitions , the theoretical values are calculated with the final states after diagonalization .
the adopted interaction for the central force is the case 3 of mv1 force @xcite , which contains a zero - range three - body term:@xmath68 in addition to the two - body interaction:@xmath69 , @xmath70 + v_r \exp\left[-\left(\frac{|{\bf r}_i-{\bf r}_j|}{r_r}\right)^2\right ] \right\rbrace,\\ & v^{(3 ) } = \sum_{i < j < k } v^{(3)}\delta({\bf r}_i-{\bf r}_j ) \delta({\bf r}_i-{\bf r}_k),\end{aligned}\ ] ] where @xmath71 and @xmath72 stand for the spin and isospin exchange operators , respectively . as for the two - body spin - orbit force:@xmath73
, we use the g3rs force @xcite as follows , @xmath74 the coulomb interaction:@xmath75 is approximated by a sum of seven gaussians .
the total interaction v is a sum of these interactions : @xmath76 .
the structures of the excited states of @xmath0be are studied based on the vap calculations in the framework of amd . in this section
we present the theoretical results concerning the energy levels , the @xmath13 transitions , and the @xmath8 transitions , which should be directly compared with the experimental data .
more detailed discussions of the intrinsic structures are given in the next section .
we adopt two sets of the interaction parameters .
one parameter set ( 1 ) is @xmath77 , @xmath78 for majorana , bartlett and heisenberg terms in the central force and @xmath79 mev for the strength of the spin - orbit forces , which have been used in the previous study on the excited states of @xmath4be .
we also try another set ( 2 ) with weaker spin - orbit forces as @xmath80 mev .
other parameters in the case ( 2 ) are same as those in the case ( 1 ) .
the width parameter @xmath81 is chosen to be 0.18 @xmath82 which gives the minimum energy of @xmath0be in a vbp calculation . in vbp calculations
we know that the lowest positive parity band @xmath83consists of @xmath10 , @xmath84,@xmath85,@xmath86 and @xmath87 states , and the lowest negative parity band @xmath88 consists of @xmath11 , @xmath89 , and @xmath90 states
. therefore the @xmath91 states in the lowest bands are obtained by vap calculations for @xmath34 with the corresponding @xmath92 values as @xmath93 , @xmath94 , @xmath95 , @xmath96 , @xmath97 , @xmath98 , @xmath99 , @xmath100 .
we calculate the higher excited states in the second negative parity band by vap calculations with @xmath92= @xmath101 , @xmath102 , @xmath103 , @xmath104 , @xmath105 .
these states are considered to belong to a band with @xmath106 . after obtaining the intrinsic states in this second negative parity band for @xmath107 , the excited @xmath108 and @xmath109 states in @xmath106
are found as local minimums with vap calculations by starting from the intrinsic states obtained for the higher spin states . in order to find the other excited @xmath89 state ,
we make vap calculations for the spin - parity projected amd wave function with the fixed intrinsic spin directions as 3 spin - down protons , one spin - up proton , 4 spin - down and 4 spin - up neutrons .
the obtained wave function for the @xmath89 state is dominated by a component of total - intrinsic spin @xmath110 for protons .
we superpose the wave functions to calculate the final wave functions by diagonalizing hamiltonian and norm matrixes simultaneously .
we should notice that all possible excited states are not exhausted in the present calculations .
in this work we perform vap calculations basically for the rotational states which can be known from vbp calculations with or without constraint .
for the higher excited states we must extend the vap calculations with orthogonal condition to the lower states by superpositions as the previous studies @xcite . above the states shown in the present results , there should exist other excited states which may be obtained with the extended vap calculations .
the theoretical binding energies of @xmath0be are 58.2 mev in the case ( 1 ) and 54.4 mev in the case ( 2 ) , both of which underestimate the experimental value 65.48 mev
. the binding energy can be reproduced by choosing a interaction parameter such as @xmath111 of the majorana term .
however unfortunately it is difficult to reproduce all the features of nuclear structures such as binding energies , energy levels , radii , deformations and so on with one set of interaction parameters . since we study the excited states taking care about the excitation energies and the intrinsic structures , we adopt the case(1 ) interaction which reproduces well the features of the excited states of @xmath4be@xcite except for the binding energy .
with this interaction the spin - parity @xmath10 of the ground state of @xmath0be can be described in the present calculations .
we also use another interaction case ( 2 ) with the weaker spin - orbit forces to be compared .
the improvement of effective interactions is one of the important problems in nuclear studies .
here we comment on the stability of amd wave functions above threshold energies .
since the single particle wave functions are written by gaussians in amd calculations , the relative motion between particles in a system is restricted by a gaussian or a linear combination of gaussians . because of the limitation of the model space , continuum states nor out going waves can not be represented in the present model . even if the energy of a nucleus is above the threshold energies of particle decays , the particles can not necessarily go away in the present framework . in this sense ,
the system is treated in the bound state approximation .
the widths for the particle decays should be discussed carefully by other frameworks such as the method with reduced width amplitude or the complex scaling method beyond the present amd framework .
= 0.4 = 0.45 the energy levels of @xmath0be are shown in fig.[fig : be11spe ] .
there are many low - lying levels in the experimental data .
the abnormal spin parity @xmath10 of the ground state has been known , although the normal spin parity of @xmath0be is @xmath11 in the simple shell - model picture . the calculations with the case(1 )
interaction reproduce the parity inversion between @xmath10 and @xmath11 states . in the theoretical results , the rotational bands @xmath83 and @xmath88 start from the band head @xmath10 and @xmath11 states , respectively .
also in the results with the case(2 ) interaction , the @xmath10 state is lowest in the @xmath83 band , however , it is slightly higher than the negative parity @xmath11 state by 1.4 mev . as a result
, the abnormal parity of the ground state can not be reproduced by the case ( 2 ) interaction which the spin - orbit forces are weaker than those in the case ( 1 ) .
we should not conclude the calculations with the case(1 ) interaction are better than those in the case ( 2 ) , because the neutron halo effect on the energy gain of @xmath10 state is not taken into account in the present calculations .
the details of the reproduction of parity inversion with the case(1 ) interaction are described in the later section . in both results in the case ( 1 ) and the case ( 2 ) , there exist some rotational bands in the low energy region . by classifying the calculated excited states we can obtain three rotational bands @xmath112 , @xmath113 and @xmath114 which are dominated by @xmath115 , @xmath116 and @xmath6 neutron configurations , respectively . in fig.[fig : be11rot ]
, we show the excitation energies of the rotational bands as a function of total spin @xmath117 .
we find a new eccentric band @xmath114 which starts from the second @xmath89 state at about 4 mev .
the excited states in the @xmath114 band are dominated by @xmath6 excited configurations with 2 particles and 3 holes in neutron shells .
the @xmath114 band is constructed by a well - deformed intrinsic state with a developed clustering structure .
the rotational band indicates large moment of inertia and it reaches the high spin states about 20 mev .
the highest spin is @xmath118 in the case ( 1 ) and @xmath119 in the case ( 2 ) . in vap calculations with further high spins
, we can not obtain any stable states since an @xmath3 particle escapes far away in the variational calculations .
it means that the energy of the relative motion between clusters is beyond the classical barrier due to the coulomb and centrifugal forces .
since the barrier hight is very sensitive to the binding energy , we examine the highest spin of the @xmath114 band with another set of the interaction parameters taking care of the binding energy of @xmath0be .
if we change the majorana exchange term of case ( 1 ) to @xmath111 , we can make the system bound as deeply as the experimental binding energy .
then a @xmath120 state is obtained as the highest spin state .
w. von oertzen et al . suggested some candidates for the states belonging to this new negative parity band in the experimental data observed in the 2 neutron transfer reactions , @xmath7be(@xmath121c , @xmath0c)@xmath0be @xcite .
although they suggested a possibility of @xmath122 state , the present results are negative to such a high spin state as @xmath122 in the rotational @xmath114 band , because @xmath120 is the highest spin made from the @xmath123-@xmath124 configurations .
it should be noticed that the present work is the first microscopic calculation which predicts the @xmath106 band with the well - developed clustering structure . since @xmath0be is a loosely bound system , further studies taking account of widths of the excited states are necessary to determine the band terminal .
we find a excited @xmath89 state at about 10 mev ( fig [ fig : be11spe ] ) . in this state ,
the proton structure is quite strange comparing with the other excited states of @xmath0be . in most of the states of @xmath0be
, we find @xmath1 cores as well as other be isotopes : @xmath125be , @xmath7be and @xmath4be .
however , in the @xmath89 state at 10 mev , only one @xmath3-cluster is formed .
the other 2 protons do not form a @xmath3-cluster but couple to be totally @xmath126 with aligned intrinsic spins .
it is analogue with the structure of the first @xmath127 state with the unnatural spin parity in @xmath5c .
we consider that this @xmath89 state must be the newly measured state at 8.04 mev @xcite to which the @xmath8-decay transition from @xmath0li is strong .
although its excitation energy is overestimated in the present calculations , it is easily improved by changing parameters @xmath128 and @xmath129 of the bartlett and heisenberg terms .
for example the parameters @xmath130 , @xmath131 , @xmath132 gives 2 mev lower excitation energy of the @xmath89 state than the one with @xmath133 , @xmath134 , @xmath77 .
here we fit the majorana parameter @xmath64 as to give the same @xmath3-@xmath3 interaction as the case ( 1 ) .
the change of parameters gives no significant effect on the excitation energies of the other states with 2-@xmath3 clusters .
the results indicate that the bartlett and heisenberg terms should be taken into consideration in the detailed study of the energy levels though they have been often omitted in the traditional works on stable nuclei .
data concerning the @xmath8-decay strength are very useful to investigate structures of excited states .
there are many experimental data concerning the @xmath135 and @xmath136 decays into the excited states of @xmath0be .
the strength of the @xmath135 decays from @xmath0li has been measured recently @xcite . for
the @xmath136 decays , the strength of gamov - teller(gt ) transitions has been deduced from the charge exchange reactions @xmath0b@xmath137he)@xmath0be @xcite . in the gt transitions from @xmath0li@xmath138 and @xmath0b@xmath138 , the allowed daughter states are @xmath11 , @xmath89 or @xmath90 states . in table
[ tab : be11beta ] the experimental log@xmath139 values are presented comparing with the theoretical results . in order to calculate the log(@xmath140 ) values of gt transistions into the excited states of @xmath0be we prepare the parent states @xmath0li@xmath138 and @xmath0b@xmath138 by vap calculations in the same framework .
the experimental log(@xmath140 ) values are reproduced well by the theoretical calculations .
it is easily understood that the decays into the excited states in @xmath114 band are weak because these states have the ell - developed clustering structures with dominated @xmath6 components which make the overlap of a gt operator with the parent state of @xmath0b to be small .
on the other hands , we consider that three levels at 0.32 mev , 2.69 mev and 3.96 mev measured in the @xmath136 transitions correspond to the states @xmath141 , @xmath142 and @xmath143 in the @xmath113 band because the experimental data indicate the significant @xmath136 strength as log@xmath139 @xmath144 5.0 , which consistent with the theoretical results .
what is important in the @xmath135 decays from @xmath0li is that the strength is very sensitive to the breaking of 2 @xmath3-cluster cores in @xmath0be .
if the daughter state of @xmath0be poses 2 ideal @xmath3-cluster cores with @xmath9 configurations , the gt transitions from @xmath0li are forbidden completely because of pauli principle . in another word ,
the strength of gt transitions from @xmath0li indicates the degree of the @xmath3-cluster breaking in the daughter states of @xmath0be . from this point of view ,
one of the reasons for the weak @xmath135 transitions as log@xmath139=5.67 to the lowest @xmath11 state at 0.32 mev is the 2@xmath3-cluster structure in @xmath0be(@xmath11 ) .
another reason for the weak @xmath135 transitions has been suggested to be the effect of the halo structure in @xmath0li by t. suzuki et al . @xcite .
the ground state of @xmath0li is known to have the neutron halo structure which originates from @xmath145-orbits .
the mixing of the @xmath145-orbits causes weak @xmath135 transitions to the normal states of @xmath0be . since the halo structure of @xmath0li
can not described in the present amd wave function , the possible halo effects on the @xmath135 decays are not included in the present results .
if we suppose the mixing ratio of @xmath145-orbits in the ground @xmath0li state as to be 50 % , the theoretical log@xmath139 values concerning the @xmath135 decays into @xmath141 , @xmath142 and @xmath143 is expected to be increased by log(2)@xmath146 due to the mixing . even if we add 0.3 of the halo effect by hands to the present log(@xmath140 ) values for @xmath142 and @xmath143 states , the log(@xmath140 ) values in case(1 )
are still smaller than 5.0 , because of the sufficient cluster breaking .
they are consistent with the experimentally measured rather small log@xmath140 values for the decays to @xmath0be(2.7 mev ) and @xmath0be(3.9 mev ) . in another word ,
the experimental data indicates the significant breaking of 2 @xmath3-cluster cores in these states(2.7mev and 3.9mev ) which we consider as the excited states @xmath142 and @xmath143
. in the recent experiments of the measurements of @xmath135 decays , a new excited state at 8.04 mev with strong @xmath135 transitions has been discovered .
the calculated log@xmath139 values for the @xmath89 state of @xmath0be at about 10 mev well corresponds to this newly observed state at 8.04 mev .
the transition is strong because the 2@xmath3-cluster structure disappears completely in this state .
as shown in table [ tab : be11beta ] , the experimental data concerning the strength of @xmath135 decays have been systematically reproduced in the present calculations .
considering the increases of log@xmath140 due to the halo effect of @xmath0li , the theoretical values of log@xmath140 for @xmath135 calculated with the case ( 1 ) interaction well agree to the experimental data .
the reason for the good reproduction is because the significant breaking of 2-@xmath3 clusters in @xmath0be is described in the present calculations .
it is the same reason as the previous studies of @xmath5c in which the experimental data concerning the strength of @xmath135 and @xmath136 decays have been well reproduced .
the quantitative discussion of the 2@xmath3-core breaking will be given in the next section . in table [ tab : be11be2 ] , we show the theoretical @xmath147 values .
it has been proved that amd calculations reproduce well @xmath147 values of light neutron - rich nuclei . as shown in the previous studies @xcite , the experimental @xmath148-moments and @xmath147 values of various nuclei
have been reproduced well by using the bare charges in the amd framework because of the advantage of the amd method which can directly describe proton deformations .
also in the present results , the features of proton - matter deformations in the intrinsic states are reflected in the theoretical @xmath147 values . in the lowest negative parity band @xmath88 , the intrinsic system deforms
because of 2 @xmath3-cluster cores although the development of clustering is smallest comparing with the other bands .
@xmath147 values are larger in the ground @xmath83 band which has the developed clustering structure with a large deformation .
the @xmath147 values are enhanced between the states in the second negative parity band @xmath106 with an extremely large deformation due to the clustering development .
.[tab : be11beta ] log(ft ) values of the @xmath8 transitions .
the theoretical values are obtained from the gamow - teller transition strength .
the experimental data of @xmath8 decays from @xmath0li are taken from ref.@xcite .
log@xmath140 values concerning the gamow - teller transition from @xmath0b are deduced from the charge exchange reactions @xcite . [ cols="^,^,^,^,^ " , ] comparing with the previous amd studies of low - lying states of @xmath0be @xcite , another improvement in the present framework is treating the intrinsic spin functions as variational parameters . in the table[tab : be11vbp ] , the effect of the flexible intrinsic spins are seen in the difference between ( c ) the vap calculations with the fixed intrinsic spins and ( d ) the vap calculations with the variational intrinsic spins .
the treatment of flexible intrinsic spins gives an important effect on the parity inversion of @xmath0be .
it reduces @xmath149 to a 1.1 mev smaller value in ( d ) than that in the calculations ( c ) .
the importance of the flexible intrinsic spins in @xmath150 shell - closure states has been already argued in the studies of @xmath5c @xcite by one of the authors . in the case of @xmath0be , it is natural to consider that the @xmath150 sub - shell effect is one of the reasons for the parity inversion because the @xmath151-orbit sould be raised relatively higher than @xmath152-orbits .
unfortunately , the simple amd method with the fixed intrinsic spins describe the sub - shell effects insufficiently .
this is one of the advantages of the present framework which can describe well both aspects of the clustering and shell effects . regarding the other reasons of parity inversion , sagawa et al .
@xcite and dot et al .
@xcite suggested the paring effects in the neutron @xmath153-shell . in the present framework ,
a part of the paring effects in @xmath153-shell should be included automatically by the spin - parity projections and the superpositions . as mentioned above , the clustering effects , the three - body forces , the @xmath150 sub - shell effects
are included in the present calculations .
the paring effects are expected to be partially contained .
the other effect which should be important for parity inversion is the neutron - halo effect@xcite . according to the study in ref.@xcite , the effect due to the neutron halo structure
is estimated as 0.6 mev reduction of @xmath149 .
however the halo effect is not taken into account in the present calculations .
we think that this halo effect and the residual paring effect are contained effectively in the strength parameter @xmath154 mev of the spin - orbit force which is slightly stronger that the parameter @xmath155 mev adopted in ref.@xcite .
the halo structures should be important only for the loosely bound states with low - spin orbits such as @xmath145-orbits and @xmath153-orbits at most .
the present strong effective spin - orbit force in case(1 ) may artificially reduce too much the theoretical excitation energies of the other states in @xmath112 band except for the @xmath10 state . before concluding the relative position of the energies between @xmath113 and @xmath156 bands we should more detailed researches by taking the remained effects such as the halo structure into consideration .
we studied the structures of the ground and excited states of @xmath0be with vap calculations in the framework of antisymmetrized molecular dynamics .
various kinds of excited states with the clustering structures and also the non - clustering structures were discovered in the theoretical results .
we predicted many excited states .
most of the states belong to three rotational bands : @xmath112 , @xmath113 and @xmath114 , which are dominated by @xmath115 , @xmath116 and @xmath6 configurations , respectively .
it should be pointed out that the formation of 2 @xmath3-cluster cores is seen in many excited states of @xmath0be in the the present resutls in spite of no assumption of the existence of clusters .
the interesting point is that an eccentric rotational band @xmath114 with the mostly developed clustering structure starts from the @xmath157 state at about 4 mev and reaches high spin states .
the experimental data concerning the @xmath136-decay and @xmath135-decay strength were reproduced well .
we also argued that the cluster breaking plays an important role to allow the @xmath8 decays from @xmath0li .
the significant breaking of 2-@xmath3 cores in the states in @xmath113 band has been seen in quantitatively estimating the breaking of clusters .
we discovered a non - clustering state at about 10 mev .
one of the characteristics of this state is the strong @xmath8 decays from @xmath0li , which well corresponds to the new excited states at 8.04 mev found in the @xmath135-decay measurements . by analyzing the single - particle wave functions in the intrinsic states
, it was found that the molecular @xmath158-orbits surrounding 2-@xmath3 cores play important roles in the clustering structures of @xmath0be . in the ground band @xmath112
, one neutron occupies the @xmath158-orbits . in the newly predicted @xmath114 band
is dominated by @xmath6 configurations with two neutrons in the @xmath158-orbit .
when the surrounding neutrons occupy the @xmath158-orbits , the clustering development is enhanced so as to gain their kinetic energy . in another word ,
one of the reasons for the parity inversion and the low - lying @xmath6 states is the energy gain of the @xmath158-orbits with the developed clustering structures .
concerning the mechanism of the parity inversion , we described the importance of molecular neutron orbits in the developed clustering structure and also mentioned about the @xmath150 sub - shell effect . although the spin parity of the ground state is described with a set of interaction parameters case ( 1 ) , we need more detailed researches taking the halo structures of the ground state into account .
the authors would like to thank dr .
n. itagaki and dr .
dot for many discussions .
they are also thankful to professor w. von oertzen for helpful discussions and comments .
the computational calculations of this work are supported by the supercomputer project no.58 , no.70 of high energy accelerator research organization(kek ) , and research center for nuclear physics in osaka university .
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( north - holland , amsterdam , 1975 ) , p.571 . | the structures of the ground and excited states of @xmath0be were studied with a microscopic method of antisymmetrized molecular dynamics .
the theoretical results reproduce the abnormal parity of the ground state and predict various kinds of excited states .
we suggest a new negative - parity band with a well - developed clustering structure which reaches high - spin states . focusing on a @xmath1 clustering structure , we investigated structure of the ground and excited states .
we point out that molecular orbits play important roles for the intruder ground state and the low - lying @xmath2 states .
the features of the breaking of @xmath3 clusters were also studied with the help of data for gamow - teller transitions . | <s>[INST]recently , information on the excited states of light unstable nuclei has increased rapidly @xcite . in the excited states of
light unstable nuclei , an exotic molecular structure of light unstable nuclei is one of the attractive subjects in experimental and theoretical research .
for example , molecular structure has been suggested to appear in neutron - rich nuclei , such as @xmath4be and @xmath5be @xcite .
w. von oertzen et al .
@xcite proposed a kind of exotic clustering structure with a @xmath6 configuration in the excited states of @xmath0be .
however , there have been few microscopic studies on the excited states of @xmath0be .
needless to say , @xmath3-cluster cores are very important in the ground and excited states of @xmath0be as well as in @xmath7be and @xmath4be .
however , we should not forget the breaking of @xmath3-clusters in @xmath0be because there are many valence neutrons around the @xmath3-clusters .
the experimental data concerning the @xmath8-decay strength are very useful to estimate the breaking of the 2@xmath3 clustering structure in be isotopes , because gamow - teller transitions from li to be are not allowed if the @xmath3-cluster cores in the daughter state of be are completely ideal ones with a simple @xmath9 configuration .
it is very interesting that the recently measured @xmath8-decay strength from @xmath0li to @xmath0be indicates significant breaking of @xmath3-clusters in the excited states of @xmath0be @xcite .
therefore , it is important to also study the breaking of @xmath3-clusters due to the surrounding neutrons as well as the development of clustering in @xmath0be .
we should point out another interesting feature in @xmath0be .
abnormal parity of the ground state in @xmath0be has been known for a long time .
namely , the spin parity of the ground state is @xmath10 , which seems to be inconsistent with the ordinary shell - model picture in which @xmath0be with 7 neutrons may have a @xmath11 state as the ground state .
it has long been a problem why parity inversion occurs in @xmath0be . as possible reasons for this parity inversion , such effects as the halo structure ,
a core deformation , clustering and paring are suggested .
for example , the energy gain of a positive parity state of @xmath0be is discussed in refs @xcite .
however , the ground - state structure has not been sufficiently studied by fully microscopic calculations without such assumptions as the existence of core nuclei .
although the clustering structure must be important in be isotopes , it is difficult for mean - field approaches to describe developed clustering structures . with a theoretical method of antisymmetrized molecular dynamics , dot et al .
have studied the abnormal parity ground state of @xmath0be without assuming cores or the stability of the mean field . however , in their work@xcite , the effects of angular - momentum projections and three - body forces were approximately estimated by perturbative treatments . our aim is to make a systematic research on the structure of the ground and excited states of @xmath0be based on the microscopic calculations .
an important point is that the theoretical approach should be free from such model assumptions as stability of the mean field , and the existence of inert cores or clusters .
first of all , traditional mean - field approaches are not useful to study the developed clustering structure in be isotopes . with cluster models , the clustering structure of the excited states of @xmath7be and @xmath4be has been successfully explained @xcite by assuming 2-@xmath3 cores and surrounding neutrons . since the assumption of 2 @xmath3-cluster cores is not appropriate to discuss the breaking of @xmath3-cores , these cluster models are not sufficient for investigations of @xmath0be with many valence neutrons . in fact , it is difficult to use them to directly calculate the experimental data of the @xmath8-decay strength from @xmath0li . with these models it may not be possible to describe the recently discovered excited state at 8.04 mev with the strong @xmath8 transition strength from @xmath0li .
we have applied a theoretical approach of antisymmetrized molecular dynamics ( amd ) .
the amd method has already proved to be useful for studying the structures of light nuclei @xcite . within this framework
, we do not need such model assumptions as inert cores , clusters , nor axial symmetries , because the basis wave functions of a nuclear system are written by slater determinants where all centers of the gaussian - type spatial part of single - particle wave functions are free parameters . in amd studies of neutron - rich nuclei , we investigated the structures of be isotopes @xcite . in amd calculations ,
many kinds of experimental data for nuclear structure have been reproduced . due to the flexibility of the amd wave function , we have succeeded to describe the structure changes between shell - model - like states and clustering states with an increase in the neutron number . in previous studies @xcite on
be isotopes , the excited states of @xmath0be were not studied in detail because the calculations are based on the variation before a total - angular - momentum projection .
recently , the amd framework has been developed to be an extended version based on variational calculations after a spin - parity projection(vap ) , which has already been confirmed to be powerful for studying the excited states of light nuclei .
the method has been applied to a stable nucleus @xmath5c @xcite , and to unstable nuclei : @xmath4be , @xmath5be and @xmath12be@xcite . in the present work
, the structures of the ground and excited states of @xmath0be were studied by performing vap calculations using the amd method . in the next section ( sec .
[ sec : formulation ] ) , we explain the formulation of amd for a nuclear structure study of the ground and excited states .
the adopted effective interactions are briefly explained in sec .
[ sec : interaction ] . in sec.[sec : results ] , we present the theoretical results concerning the energy levels , @xmath8 decays and @xmath13 transitions compared with the experimental data .
we predict a new rotational band with a well - developed clustering structure which comes from @xmath6 configurations . in sec.[sec : discus ] , the intrinsic structure and behavior of the valence neutrons are discussed .
we also discuss the breaking of @xmath3-clusters which has an important effect on the @xmath8-decay strength . finally , we summarize our work in sec . [
sec : summary ]
in this section , the formulation of amd for a nuclear structure study of the excited states is explained briefly . for more detailed descriptions of the amd framework the reader
is referred to refs .
@xcite an amd wave function of a nucleus with mass number @xmath14 is a slater determinant of gaussian wave packets ; @xmath15,\\ \chi_{\xi_i}= \left(\begin{array}{l } { 1\over 2}+\xi_{i}\\ { 1\over 2}-\xi_{i } \end{array}\right ) , \end{array}\right . \end{aligned}\ ] ] where the @xmath16th single - particle wave function @xmath17 is a product of the spatial wave function @xmath18 , the intrinsic spin function @xmath19 and the isospin function @xmath20 .
the spatial part @xmath18 is presented by a gaussian wave packet whose center is defined by complex parameters @xmath21 , @xmath22 , @xmath23 .
@xmath19 is the intrinsic spin function parameterized by @xmath24 , while @xmath20 is the isospin function which is fixed to be up(proton ) or down(neutron ) in the present calculations .
thus an amd wave function is parameterized by a set of complex parameters @xmath25 .
@xmath26 are the centers of gaussians for spatial parts and the parameters @xmath24 s determine the directions of intrinsic spins of the single particle wave functions .
if we consider a parity eigenstate projected from an amd wave function , the total wave function consists of two slater determinants , @xmath27 where @xmath28 is a parity projection operator . in the case of a total - angular - momentum projection(@xmath29-projection ) , the wave function of a system is represented by the integral of the rotated states , @xmath30 where the function @xmath31 is the well - known wigner s d function and @xmath32 stands for the rotation operator with euler angle @xmath33 . in principal the total wave function
can be a superposition of independent amd wave functions .
for example , a system is written by a superposition of spin - parity projected amd wave functions @xmath34 as follows , @xmath35 expectation values of a given tensor operator @xmath36(rank @xmath37 ) for the total - angular - momentum projected states @xmath38 and @xmath39 are calculated as follows , @xmath40 the three - dimensional integral can be evaluated numerically by taking a finite number of mesh points of the euler angle @xmath33=(@xmath41 ) .
we make variational calculations for a trial wave function to find the state which minimizes the energy of the system ; @xmath42 in the amd framework , the energy variation is performed by a method of frictional cooling , one of the imaginary time methods .
regarding the frictional cooling method , the reader is referred to papers @xcite .
the time development of the parameters @xmath43 of a wave function @xmath44 is simulated by the frictional cooling equations , @xmath45 @xmath46 with arbitrary real numbers @xmath47 and @xmath48 .
it is easily proved that the energy of the system decreases with each time step due to the frictional term:@xmath49 . after sufficient cooling iterations ,
the parameters for the minimum - energy state are obtained . in order to obtain the wave function for a @xmath50 state
, we make the energy variation after a spin - parity projection(vap ) for an amd wave function by using the frictional cooling method explained above .
that is to say we perform the energy variation for the trial function @xmath51 , the spin - parity eigenstate projected from an amd wave function .
first we make variational calculations after only the parity projection but before the spin projection(vbp ) to prepare an initial trial wave function @xmath52 . after obtaining an initial wave function in vbp calculations
we evaluate the expectation values of hamiltonian for the spin - parity - projected states by choosing the body - fixed @xmath53-axis for the @xmath33 rotation to be the approximate principal @xmath54-axis on the intrinsic deformation . then we find an appropriate @xmath55 quantum that gives the minimum diagonal energy of the spin - parity eigenstate @xmath56 where @xmath57 . for each spin parity @xmath50
, we start vap calculations for the normalized energy expectation value @xmath58 with the adopted @xmath55 quantum from the initial state . in general
, the direction of the approximately principal @xmath54-axis is automatically determined in the energy variation because the shape of the intrinsic system can vary freely .
the approximately principal axis can deviate from the @xmath53-axis in the vap procedure with a given @xmath57 .
that is to say that the optimum state @xmath34 obtained after the variation may contain so - called @xmath59-mixing ( @xmath60 ) components .
however , the deviation of @xmath54-axis from the @xmath53-axis is found to be small in many cases .
it means that the obtained states do not contain @xmath59-mixing components so much , and @xmath55 well corresponds to the @xmath59 quantum . concerning the states in the lowest band with each parity , we can obtain appropriate initial wave functions by simple vbp calculations as mentioned above .
for the highly excited states , in order to obtain initial wave functions and appropriate @xmath55 quanta for vap calculations we make vbp calculations with a constraint on amd wave function .
the details of the amd calculation with constraints have been described in refs .
@xcite . in the present calculations ,
we adopt a constraint as the expectation value of the total - oscillator quanta to equal with a given number . after choosing a corresponding @xmath55 quantum , we perform vap calculations from the initial wave function .
when we obtain other local minimum states than the obtained states , we consider them as the states in higher rotational bands .
after the vap calculations for @xmath61 states , the optimum intrinsic states @xmath62 , and @xmath63 are obtained . here
@xmath64 indicates the number of the calculated levels .
we consider that the obtained wave functions approximately represent the intrinsic wave functions of the @xmath61 states .
we determine the final wave functions by superposing the obtained amd wave functions .
that is to say that we determine the coefficients @xmath65 in eq .
[ eqn : superpose ] for each @xmath61 state by diagonalizing the hamiltonian matrix @xmath66 ) and ( @xmath67 ) . in comparison with the experimental data such as the energy levels and the strength @xmath13 transitions , the theoretical values are calculated with the final states after diagonalization .
the adopted interaction for the central force is the case 3 of mv1 force @xcite , which contains a zero - range three - body term:@xmath68 in addition to the two - body interaction:@xmath69 , @xmath70 + v_r \exp\left[-\left(\frac{|{\bf r}_i-{\bf r}_j|}{r_r}\right)^2\right ] \right\rbrace,\\ & v^{(3 ) } = \sum_{i < j < k } v^{(3)}\delta({\bf r}_i-{\bf r}_j ) \delta({\bf r}_i-{\bf r}_k),\end{aligned}\ ] ] where @xmath71 and @xmath72 stand for the spin and isospin exchange operators , respectively . as for the two - body spin - orbit force:@xmath73
, we use the g3rs force @xcite as follows , @xmath74 the coulomb interaction:@xmath75 is approximated by a sum of seven gaussians .
the total interaction v is a sum of these interactions : @xmath76 .
the structures of the excited states of @xmath0be are studied based on the vap calculations in the framework of amd . in this section
we present the theoretical results concerning the energy levels , the @xmath13 transitions , and the @xmath8 transitions , which should be directly compared with the experimental data .
more detailed discussions of the intrinsic structures are given in the next section .
we adopt two sets of the interaction parameters .
one parameter set ( 1 ) is @xmath77 , @xmath78 for majorana , bartlett and heisenberg terms in the central force and @xmath79 mev for the strength of the spin - orbit forces , which have been used in the previous study on the excited states of @xmath4be .
we also try another set ( 2 ) with weaker spin - orbit forces as @xmath80 mev .
other parameters in the case ( 2 ) are same as those in the case ( 1 ) .
the width parameter @xmath81 is chosen to be 0.18 @xmath82 which gives the minimum energy of @xmath0be in a vbp calculation . in vbp calculations
we know that the lowest positive parity band @xmath83consists of @xmath10 , @xmath84,@xmath85,@xmath86 and @xmath87 states , and the lowest negative parity band @xmath88 consists of @xmath11 , @xmath89 , and @xmath90 states
. therefore the @xmath91 states in the lowest bands are obtained by vap calculations for @xmath34 with the corresponding @xmath92 values as @xmath93 , @xmath94 , @xmath95 , @xmath96 , @xmath97 , @xmath98 , @xmath99 , @xmath100 .
we calculate the higher excited states in the second negative parity band by vap calculations with @xmath92= @xmath101 , @xmath102 , @xmath103 , @xmath104 , @xmath105 .
these states are considered to belong to a band with @xmath106 . after obtaining the intrinsic states in this second negative parity band for @xmath107 , the excited @xmath108 and @xmath109 states in @xmath106
are found as local minimums with vap calculations by starting from the intrinsic states obtained for the higher spin states . in order to find the other excited @xmath89 state ,
we make vap calculations for the spin - parity projected amd wave function with the fixed intrinsic spin directions as 3 spin - down protons , one spin - up proton , 4 spin - down and 4 spin - up neutrons .
the obtained wave function for the @xmath89 state is dominated by a component of total - intrinsic spin @xmath110 for protons .
we superpose the wave functions to calculate the final wave functions by diagonalizing hamiltonian and norm matrixes simultaneously .
we should notice that all possible excited states are not exhausted in the present calculations .
in this work we perform vap calculations basically for the rotational states which can be known from vbp calculations with or without constraint .
for the higher excited states we must extend the vap calculations with orthogonal condition to the lower states by superpositions as the previous studies @xcite . above the states shown in the present results , there should exist other excited states which may be obtained with the extended vap calculations .
the theoretical binding energies of @xmath0be are 58.2 mev in the case ( 1 ) and 54.4 mev in the case ( 2 ) , both of which underestimate the experimental value 65.48 mev
. the binding energy can be reproduced by choosing a interaction parameter such as @xmath111 of the majorana term .
however unfortunately it is difficult to reproduce all the features of nuclear structures such as binding energies , energy levels , radii , deformations and so on with one set of interaction parameters . since we study the excited states taking care about the excitation energies and the intrinsic structures , we adopt the case(1 ) interaction which reproduces well the features of the excited states of @xmath4be@xcite except for the binding energy .
with this interaction the spin - parity @xmath10 of the ground state of @xmath0be can be described in the present calculations .
we also use another interaction case ( 2 ) with the weaker spin - orbit forces to be compared .
the improvement of effective interactions is one of the important problems in nuclear studies .
here we comment on the stability of amd wave functions above threshold energies .
since the single particle wave functions are written by gaussians in amd calculations , the relative motion between particles in a system is restricted by a gaussian or a linear combination of gaussians . because of the limitation of the model space , continuum states nor out going waves can not be represented in the present model . even if the energy of a nucleus is above the threshold energies of particle decays , the particles can not necessarily go away in the present framework . in this sense ,
the system is treated in the bound state approximation .
the widths for the particle decays should be discussed carefully by other frameworks such as the method with reduced width amplitude or the complex scaling method beyond the present amd framework .
= 0.4 = 0.45 the energy levels of @xmath0be are shown in fig.[fig : be11spe ] .
there are many low - lying levels in the experimental data .
the abnormal spin parity @xmath10 of the ground state has been known , although the normal spin parity of @xmath0be is @xmath11 in the simple shell - model picture . the calculations with the case(1 )
interaction reproduce the parity inversion between @xmath10 and @xmath11 states . in the theoretical results , the rotational bands @xmath83 and @xmath88 start from the band head @xmath10 and @xmath11 states , respectively .
also in the results with the case(2 ) interaction , the @xmath10 state is lowest in the @xmath83 band , however , it is slightly higher than the negative parity @xmath11 state by 1.4 mev . as a result
, the abnormal parity of the ground state can not be reproduced by the case ( 2 ) interaction which the spin - orbit forces are weaker than those in the case ( 1 ) .
we should not conclude the calculations with the case(1 ) interaction are better than those in the case ( 2 ) , because the neutron halo effect on the energy gain of @xmath10 state is not taken into account in the present calculations .
the details of the reproduction of parity inversion with the case(1 ) interaction are described in the later section . in both results in the case ( 1 ) and the case ( 2 ) , there exist some rotational bands in the low energy region . by classifying the calculated excited states we can obtain three rotational bands @xmath112 , @xmath113 and @xmath114 which are dominated by @xmath115 , @xmath116 and @xmath6 neutron configurations , respectively . in fig.[fig : be11rot ]
, we show the excitation energies of the rotational bands as a function of total spin @xmath117 .
we find a new eccentric band @xmath114 which starts from the second @xmath89 state at about 4 mev .
the excited states in the @xmath114 band are dominated by @xmath6 excited configurations with 2 particles and 3 holes in neutron shells .
the @xmath114 band is constructed by a well - deformed intrinsic state with a developed clustering structure .
the rotational band indicates large moment of inertia and it reaches the high spin states about 20 mev .
the highest spin is @xmath118 in the case ( 1 ) and @xmath119 in the case ( 2 ) . in vap calculations with further high spins
, we can not obtain any stable states since an @xmath3 particle escapes far away in the variational calculations .
it means that the energy of the relative motion between clusters is beyond the classical barrier due to the coulomb and centrifugal forces .
since the barrier hight is very sensitive to the binding energy , we examine the highest spin of the @xmath114 band with another set of the interaction parameters taking care of the binding energy of @xmath0be .
if we change the majorana exchange term of case ( 1 ) to @xmath111 , we can make the system bound as deeply as the experimental binding energy .
then a @xmath120 state is obtained as the highest spin state .
w. von oertzen et al . suggested some candidates for the states belonging to this new negative parity band in the experimental data observed in the 2 neutron transfer reactions , @xmath7be(@xmath121c , @xmath0c)@xmath0be @xcite .
although they suggested a possibility of @xmath122 state , the present results are negative to such a high spin state as @xmath122 in the rotational @xmath114 band , because @xmath120 is the highest spin made from the @xmath123-@xmath124 configurations .
it should be noticed that the present work is the first microscopic calculation which predicts the @xmath106 band with the well - developed clustering structure . since @xmath0be is a loosely bound system , further studies taking account of widths of the excited states are necessary to determine the band terminal .
we find a excited @xmath89 state at about 10 mev ( fig [ fig : be11spe ] ) . in this state ,
the proton structure is quite strange comparing with the other excited states of @xmath0be . in most of the states of @xmath0be
, we find @xmath1 cores as well as other be isotopes : @xmath125be , @xmath7be and @xmath4be .
however , in the @xmath89 state at 10 mev , only one @xmath3-cluster is formed .
the other 2 protons do not form a @xmath3-cluster but couple to be totally @xmath126 with aligned intrinsic spins .
it is analogue with the structure of the first @xmath127 state with the unnatural spin parity in @xmath5c .
we consider that this @xmath89 state must be the newly measured state at 8.04 mev @xcite to which the @xmath8-decay transition from @xmath0li is strong .
although its excitation energy is overestimated in the present calculations , it is easily improved by changing parameters @xmath128 and @xmath129 of the bartlett and heisenberg terms .
for example the parameters @xmath130 , @xmath131 , @xmath132 gives 2 mev lower excitation energy of the @xmath89 state than the one with @xmath133 , @xmath134 , @xmath77 .
here we fit the majorana parameter @xmath64 as to give the same @xmath3-@xmath3 interaction as the case ( 1 ) .
the change of parameters gives no significant effect on the excitation energies of the other states with 2-@xmath3 clusters .
the results indicate that the bartlett and heisenberg terms should be taken into consideration in the detailed study of the energy levels though they have been often omitted in the traditional works on stable nuclei .
data concerning the @xmath8-decay strength are very useful to investigate structures of excited states .
there are many experimental data concerning the @xmath135 and @xmath136 decays into the excited states of @xmath0be .
the strength of the @xmath135 decays from @xmath0li has been measured recently @xcite . for
the @xmath136 decays , the strength of gamov - teller(gt ) transitions has been deduced from the charge exchange reactions @xmath0b@xmath137he)@xmath0be @xcite . in the gt transitions from @xmath0li@xmath138 and @xmath0b@xmath138 , the allowed daughter states are @xmath11 , @xmath89 or @xmath90 states . in table
[ tab : be11beta ] the experimental log@xmath139 values are presented comparing with the theoretical results . in order to calculate the log(@xmath140 ) values of gt transistions into the excited states of @xmath0be we prepare the parent states @xmath0li@xmath138 and @xmath0b@xmath138 by vap calculations in the same framework .
the experimental log(@xmath140 ) values are reproduced well by the theoretical calculations .
it is easily understood that the decays into the excited states in @xmath114 band are weak because these states have the ell - developed clustering structures with dominated @xmath6 components which make the overlap of a gt operator with the parent state of @xmath0b to be small .
on the other hands , we consider that three levels at 0.32 mev , 2.69 mev and 3.96 mev measured in the @xmath136 transitions correspond to the states @xmath141 , @xmath142 and @xmath143 in the @xmath113 band because the experimental data indicate the significant @xmath136 strength as log@xmath139 @xmath144 5.0 , which consistent with the theoretical results .
what is important in the @xmath135 decays from @xmath0li is that the strength is very sensitive to the breaking of 2 @xmath3-cluster cores in @xmath0be .
if the daughter state of @xmath0be poses 2 ideal @xmath3-cluster cores with @xmath9 configurations , the gt transitions from @xmath0li are forbidden completely because of pauli principle . in another word ,
the strength of gt transitions from @xmath0li indicates the degree of the @xmath3-cluster breaking in the daughter states of @xmath0be . from this point of view ,
one of the reasons for the weak @xmath135 transitions as log@xmath139=5.67 to the lowest @xmath11 state at 0.32 mev is the 2@xmath3-cluster structure in @xmath0be(@xmath11 ) .
another reason for the weak @xmath135 transitions has been suggested to be the effect of the halo structure in @xmath0li by t. suzuki et al . @xcite .
the ground state of @xmath0li is known to have the neutron halo structure which originates from @xmath145-orbits .
the mixing of the @xmath145-orbits causes weak @xmath135 transitions to the normal states of @xmath0be . since the halo structure of @xmath0li
can not described in the present amd wave function , the possible halo effects on the @xmath135 decays are not included in the present results .
if we suppose the mixing ratio of @xmath145-orbits in the ground @xmath0li state as to be 50 % , the theoretical log@xmath139 values concerning the @xmath135 decays into @xmath141 , @xmath142 and @xmath143 is expected to be increased by log(2)@xmath146 due to the mixing . even if we add 0.3 of the halo effect by hands to the present log(@xmath140 ) values for @xmath142 and @xmath143 states , the log(@xmath140 ) values in case(1 )
are still smaller than 5.0 , because of the sufficient cluster breaking .
they are consistent with the experimentally measured rather small log@xmath140 values for the decays to @xmath0be(2.7 mev ) and @xmath0be(3.9 mev ) . in another word ,
the experimental data indicates the significant breaking of 2 @xmath3-cluster cores in these states(2.7mev and 3.9mev ) which we consider as the excited states @xmath142 and @xmath143
. in the recent experiments of the measurements of @xmath135 decays , a new excited state at 8.04 mev with strong @xmath135 transitions has been discovered .
the calculated log@xmath139 values for the @xmath89 state of @xmath0be at about 10 mev well corresponds to this newly observed state at 8.04 mev .
the transition is strong because the 2@xmath3-cluster structure disappears completely in this state .
as shown in table [ tab : be11beta ] , the experimental data concerning the strength of @xmath135 decays have been systematically reproduced in the present calculations .
considering the increases of log@xmath140 due to the halo effect of @xmath0li , the theoretical values of log@xmath140 for @xmath135 calculated with the case ( 1 ) interaction well agree to the experimental data .
the reason for the good reproduction is because the significant breaking of 2-@xmath3 clusters in @xmath0be is described in the present calculations .
it is the same reason as the previous studies of @xmath5c in which the experimental data concerning the strength of @xmath135 and @xmath136 decays have been well reproduced .
the quantitative discussion of the 2@xmath3-core breaking will be given in the next section . in table [ tab : be11be2 ] , we show the theoretical @xmath147 values .
it has been proved that amd calculations reproduce well @xmath147 values of light neutron - rich nuclei . as shown in the previous studies @xcite , the experimental @xmath148-moments and @xmath147 values of various nuclei
have been reproduced well by using the bare charges in the amd framework because of the advantage of the amd method which can directly describe proton deformations .
also in the present results , the features of proton - matter deformations in the intrinsic states are reflected in the theoretical @xmath147 values . in the lowest negative parity band @xmath88 , the intrinsic system deforms
because of 2 @xmath3-cluster cores although the development of clustering is smallest comparing with the other bands .
@xmath147 values are larger in the ground @xmath83 band which has the developed clustering structure with a large deformation .
the @xmath147 values are enhanced between the states in the second negative parity band @xmath106 with an extremely large deformation due to the clustering development .
.[tab : be11beta ] log(ft ) values of the @xmath8 transitions .
the theoretical values are obtained from the gamow - teller transition strength .
the experimental data of @xmath8 decays from @xmath0li are taken from ref.@xcite .
log@xmath140 values concerning the gamow - teller transition from @xmath0b are deduced from the charge exchange reactions @xcite . [ cols="^,^,^,^,^ " , ] comparing with the previous amd studies of low - lying states of @xmath0be @xcite , another improvement in the present framework is treating the intrinsic spin functions as variational parameters . in the table[tab : be11vbp ] , the effect of the flexible intrinsic spins are seen in the difference between ( c ) the vap calculations with the fixed intrinsic spins and ( d ) the vap calculations with the variational intrinsic spins .
the treatment of flexible intrinsic spins gives an important effect on the parity inversion of @xmath0be .
it reduces @xmath149 to a 1.1 mev smaller value in ( d ) than that in the calculations ( c ) .
the importance of the flexible intrinsic spins in @xmath150 shell - closure states has been already argued in the studies of @xmath5c @xcite by one of the authors . in the case of @xmath0be , it is natural to consider that the @xmath150 sub - shell effect is one of the reasons for the parity inversion because the @xmath151-orbit sould be raised relatively higher than @xmath152-orbits .
unfortunately , the simple amd method with the fixed intrinsic spins describe the sub - shell effects insufficiently .
this is one of the advantages of the present framework which can describe well both aspects of the clustering and shell effects . regarding the other reasons of parity inversion , sagawa et al .
@xcite and dot et al .
@xcite suggested the paring effects in the neutron @xmath153-shell . in the present framework ,
a part of the paring effects in @xmath153-shell should be included automatically by the spin - parity projections and the superpositions . as mentioned above , the clustering effects , the three - body forces , the @xmath150 sub - shell effects
are included in the present calculations .
the paring effects are expected to be partially contained .
the other effect which should be important for parity inversion is the neutron - halo effect@xcite . according to the study in ref.@xcite , the effect due to the neutron halo structure
is estimated as 0.6 mev reduction of @xmath149 .
however the halo effect is not taken into account in the present calculations .
we think that this halo effect and the residual paring effect are contained effectively in the strength parameter @xmath154 mev of the spin - orbit force which is slightly stronger that the parameter @xmath155 mev adopted in ref.@xcite .
the halo structures should be important only for the loosely bound states with low - spin orbits such as @xmath145-orbits and @xmath153-orbits at most .
the present strong effective spin - orbit force in case(1 ) may artificially reduce too much the theoretical excitation energies of the other states in @xmath112 band except for the @xmath10 state . before concluding the relative position of the energies between @xmath113 and @xmath156 bands we should more detailed researches by taking the remained effects such as the halo structure into consideration .
we studied the structures of the ground and excited states of @xmath0be with vap calculations in the framework of antisymmetrized molecular dynamics .
various kinds of excited states with the clustering structures and also the non - clustering structures were discovered in the theoretical results .
we predicted many excited states .
most of the states belong to three rotational bands : @xmath112 , @xmath113 and @xmath114 , which are dominated by @xmath115 , @xmath116 and @xmath6 configurations , respectively .
it should be pointed out that the formation of 2 @xmath3-cluster cores is seen in many excited states of @xmath0be in the the present resutls in spite of no assumption of the existence of clusters .
the interesting point is that an eccentric rotational band @xmath114 with the mostly developed clustering structure starts from the @xmath157 state at about 4 mev and reaches high spin states .
the experimental data concerning the @xmath136-decay and @xmath135-decay strength were reproduced well .
we also argued that the cluster breaking plays an important role to allow the @xmath8 decays from @xmath0li .
the significant breaking of 2-@xmath3 cores in the states in @xmath113 band has been seen in quantitatively estimating the breaking of clusters .
we discovered a non - clustering state at about 10 mev .
one of the characteristics of this state is the strong @xmath8 decays from @xmath0li , which well corresponds to the new excited states at 8.04 mev found in the @xmath135-decay measurements . by analyzing the single - particle wave functions in the intrinsic states
, it was found that the molecular @xmath158-orbits surrounding 2-@xmath3 cores play important roles in the clustering structures of @xmath0be . in the ground band @xmath112
, one neutron occupies the @xmath158-orbits . in the newly predicted @xmath114 band
is dominated by @xmath6 configurations with two neutrons in the @xmath158-orbit .
when the surrounding neutrons occupy the @xmath158-orbits , the clustering development is enhanced so as to gain their kinetic energy . in another word ,
one of the reasons for the parity inversion and the low - lying @xmath6 states is the energy gain of the @xmath158-orbits with the developed clustering structures .
concerning the mechanism of the parity inversion , we described the importance of molecular neutron orbits in the developed clustering structure and also mentioned about the @xmath150 sub - shell effect . although the spin parity of the ground state is described with a set of interaction parameters case ( 1 ) , we need more detailed researches taking the halo structures of the ground state into account .
the authors would like to thank dr .
n. itagaki and dr .
dot for many discussions .
they are also thankful to professor w. von oertzen for helpful discussions and comments .
the computational calculations of this work are supported by the supercomputer project no.58 , no.70 of high energy accelerator research organization(kek ) , and research center for nuclear physics in osaka university .
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( north - holland , amsterdam , 1975 ) , p.571 .[/INST] the structures of the ground and excited states of @xmath0be were studied with a microscopic method of antisymmetrized molecular dynamics .
the theoretical results reproduce the abnormal parity of the ground state and predict various kinds of excited states .
we suggest a new negative - parity band with a well - developed clustering structure which reaches high - spin states . focusing on a @xmath1 clustering structure , we investigated structure of the ground and excited states .
we point out that molecular orbits play important roles for the intruder ground state and the low - lying @xmath2 states .
the features of the breaking of @xmath3 clusters were also studied with the help of data for gamow - teller transitions . </s> |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``E. Clay Shaw, Jr. Missing Children's
Assistance Reauthorization Act of 2013''.
SEC. 2. AMENDMENTS.
(a) Findings.--Section 402 of the Missing Children's Assistance Act
(42 U.S.C. 5771) is amended--
(1) by redesignating paragraphs (3) through (9) as paragraphs
(4) through (10), respectively, and
(2) by inserting after paragraph (2) the following:
``(3) many missing children are runaways;''.
(b) Duties and Functions of Administrator.--Section 404 of the
Missing Children's Assistance Act (42 U.S.C. 5773) is amended--
(1) in subsection (a)--
(A) in paragraph(5)--
(i) by striking ``Representatives, and'' and inserting
``Representatives, the Committee on Education and the
Workforce of the House of Representatives,'', and
(ii) by inserting ``, and the Committee on the
Judiciary of the Senate'' after ``Senate'',
(B) by redesignating paragraphs (4) and (5) as (5) and (6),
respectively, and
(C) by inserting after paragraph (3) the following:
``(4) coordinate with the United States Interagency Council on
Homelessness to ensure that homeless services professionals are
aware of educational resources and assistance provided by the
Center regarding child sexual exploitation;'',
(2) in subsection (b)--
(A) in paragraph (1)--
(i) in subparagraph (C)--
(I) by striking ``and'' after ``governments,'', and
(II) by inserting ``State and local educational
agencies,'' after ``agencies,'',
(ii) in subparagraph (R) by striking ``and'' at the
end,
(iii) in subparagraph (S) by striking the period at the
end and inserting a semicolon, and
(iv) by adding at the end the following:
``(T) provide technical assistance and training to State
and local law enforcement agencies and statewide clearinghouses
to coordinate with State and local educational agencies in
identifying and recovering missing children;
``(U) assist the efforts of law enforcement agencies in
coordinating with child welfare agencies to respond to foster
children missing from the State welfare system; and
``(V) provide technical assistance to law enforcement
agencies and first responders in identifying, locating, and
recovering victims of, and children at risk for, child sex
trafficking.'', and
(B) by amending paragraph (2) to read as follows:
``(2) Limitation.--
``(A) In general.--Notwithstanding any other provision of
law, no Federal funds may be used to pay the compensation of an
individual employed by the Center if such compensation, as
determined at the beginning of each grant year, exceeds 110
percent of the maximum annual salary payable to a member of the
Federal Government's Senior Executive Service (SES) for that
year. The Center may compensate an employee at a higher rate
provided the amount in excess of this limitation is paid with
non-Federal funds.
``(B) Definition of compensation.--For the purpose of this
paragraph, the term `compensation'--
``(i) includes salary, bonuses, periodic payments,
severance pay, the value of a compensatory or paid leave
benefit not excluded by clause (ii), and the fair market
value of any employee perquisite or benefit not excluded by
clause (ii); and
``(ii) excludes any Center expenditure for health,
medical, or life insurance, or disability or retirement
pay, including pensions benefits.'',
(3) in subsection (c)(1)--
(A) by striking ``periodically'' and inserting
``triennially'', and
(B) by striking ``kidnapings'' and inserting
``kidnappings'', and
(4) in subsection (c)(2) by inserting ``, in compliance with
the Family Educational Rights and Privacy Act of 1974 (20 U.S.C.
1232g)'' after ``birth certificates''.
(c) Grants.--Section 405(a) of the Missing Children's Assistance
Act (42 U.S.C. 5775(a)) is amended--
(1) in paragraph (1) by inserting ``schools, school leaders,
teachers, State and local educational agencies, homeless shelters
and service providers,'' after ``children,'', and
(2) in paragraph (3) by inserting ``and schools'' after
``communities''.
SEC. 3. AUTHORIZATION OF APPROPRIATIONS.
Section 407 of the Missing Children's Assistance Act (42 U.S.C.
5777) is amended--
(1) in subsection (a) by striking ``such'' and all that follows
through the period at the end, and inserting ``$40,000,000 for each
of the fiscal years 2014 through 2018, up to $32,200,000 of which
shall be used to carry out section 404(b) for each such fiscal
year.'', and
(2) by striking ``sec. 407'' and inserting ``sec. 408''.
SEC. 4. OVERSIGHT AND ACCOUNTABILITY.
The Missing Children's Assistance Act (42 U.S.C. 5771 et seq.) is
amended by inserting after section 406 the following:
``SEC. 407. OVERSIGHT AND ACCOUNTABILITY.
``All grants awarded by the Department of Justice that are
authorized under this title shall be subject to the following:
``(1) Audit requirement.--For 2 of the fiscal years in the
period of fiscal years 2014 through 2018, the Inspector General of
the Department of Justice shall conduct audits of the recipient of
grants under this title to prevent waste, fraud, and abuse by the
grantee.
``(2) Mandatory exclusion.--If the recipient of grant funds
under this title is found to have an unresolved audit finding, then
that entity shall not be eligible to receive grant funds under this
title during the 2 fiscal years beginning after the 12-month period
described in paragraph (4).
``(3) Repayment of grant funds.--If an entity is awarded grant
funds under this title during the 2-fiscal-year period in which the
entity is barred from receiving grants under paragraph (2), the
Attorney General shall--
``(A) deposit an amount equal to the grant funds that were
improperly awarded to the grantee into the General Fund of the
Treasury; and
``(B) seek to recoup the costs of the repayment to the fund
from the grant recipient that was erroneously awarded grant
funds.
``(4) Defined term.--In this section, the term `unresolved
audit finding' means an audit report finding in the final report of
the Inspector General of the Department of Justice that the grantee
has utilized grant funds for an unauthorized expenditure or
otherwise unallowable cost that is not closed or resolved within a
12-month period beginning on the date when the final audit report
is issued.
``(5) Nonprofit organization requirements.--
``(A) Definition.--For purposes of this section and the
grant programs described in this title, the term `nonprofit',
relating to an entity, means the entity is described in section
501(c)(3) of the Internal Revenue Code of 1986 and is exempt
from taxation under section 501(a) of such Code.
``(B) Prohibition.--The Attorney General shall not award a
grant under any grant program described in this title to a
nonprofit organization that holds money in off-shore accounts
for the purpose of avoiding paying the tax described in section
511(a) of the Internal Revenue Code of 1986.
``(C) Disclosure.--Each nonprofit organization that is
awarded a grant under this title and uses the procedures
prescribed in regulations under section 53.4958-6 of title 26
of the Code of Federal Regulations to create a rebuttable
presumption of reasonableness of the compensation for its
officers, directors, trustees and key employees, shall disclose
to the Attorney General the process for determining such
compensation, including the independent persons involved in
reviewing and approving such compensation, the comparability
data used, and contemporaneous substantiation of the
deliberation and decision. Upon request, the Attorney General
shall make the information available for public inspection.
``(6) Conference expenditures.--
``(A) Limitation.--No amounts authorized to be appropriated
under this title may be used to host or support any expenditure
for conferences that uses more than $20,000 unless the Deputy
Attorney General or the appropriate Assistant Attorney General,
Director, or principal deputy director as the Deputy Attorney
General may designate, provides prior written authorization
that the funds may be expended to host a conference.
``(B) Written approval.--Written approval under
subparagraph (A) shall include a written estimate of all costs
associated with the conference, including the cost of all food
and beverages, audio/visual equipment, honoraria for speakers,
and any entertainment.
``(C) Report.--The Deputy Attorney General shall submit an
annual report to the Committee on the Judiciary of the Senate,
the Committee on the Judiciary of the House of Representatives,
and the Committee on Education and the Workforce of the House
of Representatives on all conference expenditures approved by
operation of this paragraph.
``(7) Prohibition on lobbying activity.--
``(A) In general.--Amounts authorized to be appropriated
under this title may not be utilized by any grant recipient
to--
``(i) lobby any representative of the Department of
Justice regarding the award of any grant funding; or
``(ii) lobby any representative of a Federal, State,
local, or tribal government regarding the award of grant
funding.
``(B) Penalty.--If the Attorney General determines that any
recipient of a grant under this title has violated subparagraph
(A), the Attorney General shall--
``(i) require the grant recipient to repay the grant in
full; and
``(ii) prohibit the grant recipient from receiving
another grant under this title for not less than 5 years.
``(C) Clarification.--For purposes of this paragraph,
submitting an application for a grant under this title shall
not be considered lobbying activity in violation of
subparagraph (A).''.
Speaker of the House of Representatives.
Vice President of the United States and
President of the Senate. | (This measure has not been amended since it passed the House on September 17, 2013. E. Clay Shaw, Jr. Missing Children's Assistance Reauthorization Act of 2013 - (Sec. 2) Amends the Missing Children's Assistance to declare that many missing children are runaways. Requires the Administrator of the Office of Juvenile Justice and Delinquency Prevention of the Department of Justice (DOJ) to send the Office's annual report to the President and Congress specifically to the Committee on Education and the Workforce of the House of Representatives and the Committee on the Judiciary of the Senate. Requires the Administrator also to coordinate with the U.S. Interagency Council on Homelessness to ensure that homeless services professionals are aware of educational resources and assistance provided by the Center regarding child sexual exploitation. Adds to the authorized uses of the annual grant to National Center for Missing and Exploited Children: (1) giving technical assistance and training to state and local law enforcement agencies and statewide clearinghouses to coordinate with state and local educational agencies in identifying and recovering missing children; (2) assisting the efforts of law enforcement agencies in coordinating with child welfare agencies to respond to foster children missing from the state welfare system; and (3) giving technical assistance to law enforcement agencies and first responders in identifying, locating, and recovering victims of, and children at risk for, child sex trafficking. Prohibits the use of federal funds to pay the compensation of any Center employee exceeding 110% of the maximum annual salary payable to a member of the federal government's Senior Executive Service (SES) for that year. Allows the Center to compensate an employee at a higher rate provided the amount exceeding this limitation is paid with non-federal funds. Excludes from the meaning of such compensation any health, medical, or life insurance payments, disability or retirement pay, or pensions benefits. Requires the Administrator to conduct national incidence studies triennially (currently, periodically) to determine for a given year the actual number of children reported missing, the number who are victims of abduction by strangers, the number who are the victims of parental kidnappings, and the number who are recovered each year. Requires that the Administrator's duty to provide to state and local governments, public and private nonprofit agencies, and individuals information to facilitate the lawful use of school records and birth certificates to identify and locate missing children be performed in compliance with the Family Educational Rights and Privacy Act of 1974. Authorizes the Administration to make grants or enter into contracts with the Center and with public agencies or nonprofit private organizations for research, demonstration projects, or service programs designed to: (1) educate schools, school leaders, teachers, state and local educational agencies, homeless shelters, and service providers in ways to prevent the abduction and sexual exploitation of children; and (2) aid schools in the collection of materials useful to parents in assisting others in the identification of missing children. (Sec. 3) Authorizes appropriations for FY2014-FY2018, including specified funds each year for the annual grant to the Center. (Sec. 4) Subjects grant recipients to audits by the DOJ Inspector General for two of the fiscal years between FY2014 and FY2018. Bars eligibility to receive grant funds for two fiscal years for any grant recipient found to have an unresolved audit finding that it has used grant funds for an unauthorized expenditure or otherwise unallowable cost that is not closed or resolved within 12 months after the final audit report is issued. Requires the Attorney General to seek repayment from a debarred grantee of any grant funds awarded during the two-fiscal year debarment. Prohibits the Attorney General from awarding a grant to a nonprofit organization that holds money in off-shore accounts to avoid paying the tax on unrelated business income of charitable and other tax-exempt organizations. Prohibits the use of more than $20,000 of authorized funds to host or support any expenditure for conferences without prior written authorization by the Deputy Attorney General or a specified designee. Prohibits the use of authorized funds by any grant recipient to lobby: (1) any DOJ representative regarding the award of any grant funding; or (2) any representative of a federal, state, local, or tribal government regarding the award of grant funding. Requires any recipient violating this prohibition to repay the grant in full, and denies the recipient eligibility for another grant for five years. | <s>[INST]SECTION 1. SHORT TITLE.
This Act may be cited as the ``E. Clay Shaw, Jr. Missing Children's
Assistance Reauthorization Act of 2013''.
SEC. 2. AMENDMENTS.
(a) Findings.--Section 402 of the Missing Children's Assistance Act
(42 U.S.C. 5771) is amended--
(1) by redesignating paragraphs (3) through (9) as paragraphs
(4) through (10), respectively, and
(2) by inserting after paragraph (2) the following:
``(3) many missing children are runaways;''.
(b) Duties and Functions of Administrator.--Section 404 of the
Missing Children's Assistance Act (42 U.S.C. 5773) is amended--
(1) in subsection (a)--
(A) in paragraph(5)--
(i) by striking ``Representatives, and'' and inserting
``Representatives, the Committee on Education and the
Workforce of the House of Representatives,'', and
(ii) by inserting ``, and the Committee on the
Judiciary of the Senate'' after ``Senate'',
(B) by redesignating paragraphs (4) and (5) as (5) and (6),
respectively, and
(C) by inserting after paragraph (3) the following:
``(4) coordinate with the United States Interagency Council on
Homelessness to ensure that homeless services professionals are
aware of educational resources and assistance provided by the
Center regarding child sexual exploitation;'',
(2) in subsection (b)--
(A) in paragraph (1)--
(i) in subparagraph (C)--
(I) by striking ``and'' after ``governments,'', and
(II) by inserting ``State and local educational
agencies,'' after ``agencies,'',
(ii) in subparagraph (R) by striking ``and'' at the
end,
(iii) in subparagraph (S) by striking the period at the
end and inserting a semicolon, and
(iv) by adding at the end the following:
``(T) provide technical assistance and training to State
and local law enforcement agencies and statewide clearinghouses
to coordinate with State and local educational agencies in
identifying and recovering missing children;
``(U) assist the efforts of law enforcement agencies in
coordinating with child welfare agencies to respond to foster
children missing from the State welfare system; and
``(V) provide technical assistance to law enforcement
agencies and first responders in identifying, locating, and
recovering victims of, and children at risk for, child sex
trafficking.'', and
(B) by amending paragraph (2) to read as follows:
``(2) Limitation.--
``(A) In general.--Notwithstanding any other provision of
law, no Federal funds may be used to pay the compensation of an
individual employed by the Center if such compensation, as
determined at the beginning of each grant year, exceeds 110
percent of the maximum annual salary payable to a member of the
Federal Government's Senior Executive Service (SES) for that
year. The Center may compensate an employee at a higher rate
provided the amount in excess of this limitation is paid with
non-Federal funds.
``(B) Definition of compensation.--For the purpose of this
paragraph, the term `compensation'--
``(i) includes salary, bonuses, periodic payments,
severance pay, the value of a compensatory or paid leave
benefit not excluded by clause (ii), and the fair market
value of any employee perquisite or benefit not excluded by
clause (ii); and
``(ii) excludes any Center expenditure for health,
medical, or life insurance, or disability or retirement
pay, including pensions benefits.'',
(3) in subsection (c)(1)--
(A) by striking ``periodically'' and inserting
``triennially'', and
(B) by striking ``kidnapings'' and inserting
``kidnappings'', and
(4) in subsection (c)(2) by inserting ``, in compliance with
the Family Educational Rights and Privacy Act of 1974 (20 U.S.C.
1232g)'' after ``birth certificates''.
(c) Grants.--Section 405(a) of the Missing Children's Assistance
Act (42 U.S.C. 5775(a)) is amended--
(1) in paragraph (1) by inserting ``schools, school leaders,
teachers, State and local educational agencies, homeless shelters
and service providers,'' after ``children,'', and
(2) in paragraph (3) by inserting ``and schools'' after
``communities''.
SEC. 3. AUTHORIZATION OF APPROPRIATIONS.
Section 407 of the Missing Children's Assistance Act (42 U.S.C.
5777) is amended--
(1) in subsection (a) by striking ``such'' and all that follows
through the period at the end, and inserting ``$40,000,000 for each
of the fiscal years 2014 through 2018, up to $32,200,000 of which
shall be used to carry out section 404(b) for each such fiscal
year.'', and
(2) by striking ``sec. 407'' and inserting ``sec. 408''.
SEC. 4. OVERSIGHT AND ACCOUNTABILITY.
The Missing Children's Assistance Act (42 U.S.C. 5771 et seq.) is
amended by inserting after section 406 the following:
``SEC. 407. OVERSIGHT AND ACCOUNTABILITY.
``All grants awarded by the Department of Justice that are
authorized under this title shall be subject to the following:
``(1) Audit requirement.--For 2 of the fiscal years in the
period of fiscal years 2014 through 2018, the Inspector General of
the Department of Justice shall conduct audits of the recipient of
grants under this title to prevent waste, fraud, and abuse by the
grantee.
``(2) Mandatory exclusion.--If the recipient of grant funds
under this title is found to have an unresolved audit finding, then
that entity shall not be eligible to receive grant funds under this
title during the 2 fiscal years beginning after the 12-month period
described in paragraph (4).
``(3) Repayment of grant funds.--If an entity is awarded grant
funds under this title during the 2-fiscal-year period in which the
entity is barred from receiving grants under paragraph (2), the
Attorney General shall--
``(A) deposit an amount equal to the grant funds that were
improperly awarded to the grantee into the General Fund of the
Treasury; and
``(B) seek to recoup the costs of the repayment to the fund
from the grant recipient that was erroneously awarded grant
funds.
``(4) Defined term.--In this section, the term `unresolved
audit finding' means an audit report finding in the final report of
the Inspector General of the Department of Justice that the grantee
has utilized grant funds for an unauthorized expenditure or
otherwise unallowable cost that is not closed or resolved within a
12-month period beginning on the date when the final audit report
is issued.
``(5) Nonprofit organization requirements.--
``(A) Definition.--For purposes of this section and the
grant programs described in this title, the term `nonprofit',
relating to an entity, means the entity is described in section
501(c)(3) of the Internal Revenue Code of 1986 and is exempt
from taxation under section 501(a) of such Code.
``(B) Prohibition.--The Attorney General shall not award a
grant under any grant program described in this title to a
nonprofit organization that holds money in off-shore accounts
for the purpose of avoiding paying the tax described in section
511(a) of the Internal Revenue Code of 1986.
``(C) Disclosure.--Each nonprofit organization that is
awarded a grant under this title and uses the procedures
prescribed in regulations under section 53.4958-6 of title 26
of the Code of Federal Regulations to create a rebuttable
presumption of reasonableness of the compensation for its
officers, directors, trustees and key employees, shall disclose
to the Attorney General the process for determining such
compensation, including the independent persons involved in
reviewing and approving such compensation, the comparability
data used, and contemporaneous substantiation of the
deliberation and decision. Upon request, the Attorney General
shall make the information available for public inspection.
``(6) Conference expenditures.--
``(A) Limitation.--No amounts authorized to be appropriated
under this title may be used to host or support any expenditure
for conferences that uses more than $20,000 unless the Deputy
Attorney General or the appropriate Assistant Attorney General,
Director, or principal deputy director as the Deputy Attorney
General may designate, provides prior written authorization
that the funds may be expended to host a conference.
``(B) Written approval.--Written approval under
subparagraph (A) shall include a written estimate of all costs
associated with the conference, including the cost of all food
and beverages, audio/visual equipment, honoraria for speakers,
and any entertainment.
``(C) Report.--The Deputy Attorney General shall submit an
annual report to the Committee on the Judiciary of the Senate,
the Committee on the Judiciary of the House of Representatives,
and the Committee on Education and the Workforce of the House
of Representatives on all conference expenditures approved by
operation of this paragraph.
``(7) Prohibition on lobbying activity.--
``(A) In general.--Amounts authorized to be appropriated
under this title may not be utilized by any grant recipient
to--
``(i) lobby any representative of the Department of
Justice regarding the award of any grant funding; or
``(ii) lobby any representative of a Federal, State,
local, or tribal government regarding the award of grant
funding.
``(B) Penalty.--If the Attorney General determines that any
recipient of a grant under this title has violated subparagraph
(A), the Attorney General shall--
``(i) require the grant recipient to repay the grant in
full; and
``(ii) prohibit the grant recipient from receiving
another grant under this title for not less than 5 years.
``(C) Clarification.--For purposes of this paragraph,
submitting an application for a grant under this title shall
not be considered lobbying activity in violation of
subparagraph (A).''.
Speaker of the House of Representatives.
Vice President of the United States and
President of the Senate.[/INST](This measure has not been amended since it passed the House on September 17, 2013. E. Clay Shaw, Jr. Missing Children's Assistance Reauthorization Act of 2013 - (Sec. 2) Amends the Missing Children's Assistance to declare that many missing children are runaways. Requires the Administrator of the Office of Juvenile Justice and Delinquency Prevention of the Department of Justice (DOJ) to send the Office's annual report to the President and Congress specifically to the Committee on Education and the Workforce of the House of Representatives and the Committee on the Judiciary of the Senate. Requires the Administrator also to coordinate with the U.S. Interagency Council on Homelessness to ensure that homeless services professionals are aware of educational resources and assistance provided by the Center regarding child sexual exploitation. Adds to the authorized uses of the annual grant to National Center for Missing and Exploited Children: (1) giving technical assistance and training to state and local law enforcement agencies and statewide clearinghouses to coordinate with state and local educational agencies in identifying and recovering missing children; (2) assisting the efforts of law enforcement agencies in coordinating with child welfare agencies to respond to foster children missing from the state welfare system; and (3) giving technical assistance to law enforcement agencies and first responders in identifying, locating, and recovering victims of, and children at risk for, child sex trafficking. Prohibits the use of federal funds to pay the compensation of any Center employee exceeding 110% of the maximum annual salary payable to a member of the federal government's Senior Executive Service (SES) for that year. Allows the Center to compensate an employee at a higher rate provided the amount exceeding this limitation is paid with non-federal funds. Excludes from the meaning of such compensation any health, medical, or life insurance payments, disability or retirement pay, or pensions benefits. Requires the Administrator to conduct national incidence studies triennially (currently, periodically) to determine for a given year the actual number of children reported missing, the number who are victims of abduction by strangers, the number who are the victims of parental kidnappings, and the number who are recovered each year. Requires that the Administrator's duty to provide to state and local governments, public and private nonprofit agencies, and individuals information to facilitate the lawful use of school records and birth certificates to identify and locate missing children be performed in compliance with the Family Educational Rights and Privacy Act of 1974. Authorizes the Administration to make grants or enter into contracts with the Center and with public agencies or nonprofit private organizations for research, demonstration projects, or service programs designed to: (1) educate schools, school leaders, teachers, state and local educational agencies, homeless shelters, and service providers in ways to prevent the abduction and sexual exploitation of children; and (2) aid schools in the collection of materials useful to parents in assisting others in the identification of missing children. (Sec. 3) Authorizes appropriations for FY2014-FY2018, including specified funds each year for the annual grant to the Center. (Sec. 4) Subjects grant recipients to audits by the DOJ Inspector General for two of the fiscal years between FY2014 and FY2018. Bars eligibility to receive grant funds for two fiscal years for any grant recipient found to have an unresolved audit finding that it has used grant funds for an unauthorized expenditure or otherwise unallowable cost that is not closed or resolved within 12 months after the final audit report is issued. Requires the Attorney General to seek repayment from a debarred grantee of any grant funds awarded during the two-fiscal year debarment. Prohibits the Attorney General from awarding a grant to a nonprofit organization that holds money in off-shore accounts to avoid paying the tax on unrelated business income of charitable and other tax-exempt organizations. Prohibits the use of more than $20,000 of authorized funds to host or support any expenditure for conferences without prior written authorization by the Deputy Attorney General or a specified designee. Prohibits the use of authorized funds by any grant recipient to lobby: (1) any DOJ representative regarding the award of any grant funding; or (2) any representative of a federal, state, local, or tribal government regarding the award of grant funding. Requires any recipient violating this prohibition to repay the grant in full, and denies the recipient eligibility for another grant for five years.</s> |
in the last decade or so , detection of high energy materials ( hems ) for security screening , detection of non exploded ordnance , for demining and pollution check have become an active and important area of research1 - 3 . one main category of the detection of hems include the bulk detection systems wherein x ray or neutron imaging are employed to locate large quantities of explosives4 .
another method involves vapour and particle detection where trace quantities of explosives are detected via molecular signatures4 .
one of the main tools used for such detection is a laser .
laser offers two main advantages in these detections due to their long range propagation of intense energy and high wavelength specificity with regards to atomic / molecular spectroscopy .
present work explores a somewhat new territory of thin film detection using a long known tool of optical pumping5 .
thin film detection of hems have been recently explored elsewhere5 , however in context of physical / absorption property of the thin film . in the present work magnetic property of the hems
is used6 to detect them using the metal thin film magnetometer .
lithium atoms present in the thin film are optically pumped so that they can no more absorb light from the resonant light source .
now in presence of a rf signal , which quantifies the ambient magnetic field , this polarised atomic system is again randomised thus making it reabsorb the resonant light .
this gives a quantified measurement of the magnetic field surrounding the thin film detector .
this is then mapped to the presence of magnetic hems and hence the hems are detected .
one measures the larmor precession frequency @xmath0 of atomic spins in a magnetic field b , given by @xmath1 where the gyro magnetic ratio @xmath2 serves as the conversion factor between the frequency and the field strength .
as equation ( 1 ) suggests , the larmor precession frequency measurement gives a measure of the b field around .
so a measurement of larmor precession frequency gives a measure of the ambient b field which is accomplished by using a rf field .
this when mapped to the hem magnetic field gives the final shape to the hem detector .
first step in making the lithium thin film is to check for the stability of li in various solvents .
we have done the same using uv / visible spectroscopy of lithium in various polar/ non - polar solvents .
this is done in presence/ absence of laser beam irradiating the atomic system .
laser system is a 1064 nm dpss nd - yag laser .
the absorption spectra of irradiated li solutions taken in the quartz cuvette of optical length10 mm were measured with wavelength from 200 to 800 nm using the perkin elmer uv - visible spectrophotometer .
all the reagents and solvents of high pure grade were purchased from sigma , aldrich , merck , alfa - aesar and used without further purifications .
1 mm li solutions using solvents have been prepared .
the saturated solution of pmma was prepared by dissolving the polymer in chloroform for 48 hrs at room temperature and then li was added . lithium system with various solvents is then characterised with regards to the particle size dispersed in the solvents to estimate particle density in the resulting thin film .
this is done using the sem characterisation .
this is important in making sure that lithium particle are indeed uniformly distributed in the solvent and give a good system for performing optical pumping experiments .
another part of the experiment we plan to show optical pumping phenomenon in lithium atomic beam system .
for the same we successfully made a li atomic beam setup using a combination of rotary - turbo - ion pump to go down to ultra - high - vacuum ( uhv ) of 10 - 9 torr of pressure .
figure 3 shows full uhv chambered lithium atomic beam .
the atomic source ( figure 4 ) basically comprises of a thin walled ss tube welded to a two pin feed through with solid li inside which is resistively heated to around 4000c to get enough vapours .
this is achieved by passing around 4 - 5 a of current across the coil . to avoid divergence of the beam
we have put an aperture , a circular cu plate with a 1 mm hole punched at the centre of it .
this gives a narrow li atomic beam with transverse divergence of roughly 1 cm at around 10 cm away from the source .
this was checked by tuning a diode laser at 670 nm to the resonance for the li d lines and seeing the transverse extension of the fluorescence spot through a window .
typical fluorescence signal captured by a ccd camera ( 30 fps thor labs usb camera ) are shown in the figure 5 .
laser used for the purpose is an external cavity diode laser ( ecdl ) at 670 nm tunable from 665 - 675 from toptica photonics with power output of 35 mw .
the @xmath3 of compounds is changed with the solvent and the concentration of solution .
four types of shifts in the @xmath4 values are possible : ( i ) shift of @xmath4 to longer wavelength or less energy is due to the substituent or solvent effect is referred as bathochromic or red shift ( ii ) shift of @xmath4 to shorter wavelength or higher energy is due to the substituent or solvent effect is referred as hypsochromic or blue shift ( iii ) an increase in the absorption intensity called as hyperchromic shift and ( iv ) decrease in the absorption intensity called as hypochromic shift .
the electronic transitions are usually accompanied by a simultaneous change between the vibrational levels .
we found this shift happening in all the solvents .
a typical spectra is shown in figure 6 for acetonitrile and lithium solution .
such spectra were taken for nine polar and non - polar solvents and the shift in cut off wavelength measured ( table 1 ) . except for the case of acetonitrile ( an )
we found the cut off wavelength varying post laser irradiation ( table 1 ) .
this gave us confidence that an can be the perfect solvent with which lithium can be added to form a stable film which will not get affected by laser perturbation and optical pumping can be performed with such combination . to give brief chemical reactivity of an with li
, an reacts with li at room temperature to liberate hydrogen gas in figure 6 , the sharp band at 194 nm moved to the higher wavelength of 190 nm ( i.e. , red shift ) and two new broad bands have appeared at 256 nm and 292 nm .
it is due to the formation of mono - lithium derivatives of acetonitrile and released hydrogen gas on irradiation .
the uv - visible spectrum of the li solution shows cyanide absorption higher than the parent acetonitrile indicating a weakening of the cyanide linkage . [ cols="<,<,^,^,^,^ " , ] the nitriles are known to undergo n @xmath5 @xmath6 transition and n @xmath5 @xmath7 transition of characteristic cut off wavelengths of 194 nm and 300 nm .
the two distinctive bands at 256 nm and 292 nm after irradiation are due to the formation of , an organometallic compound .
the bond is of intermediate character between ionic and covalent bonds .
the various bands of solutions both irradiated and non - irradiated apparently of the characteristic bands of lithium containing compounds : @xmath8 @xmath8 @xmath8 @xmath8 .
further sem characterisation was conducted to ascertain the density of the li particles in the solution with various solvents . analysing the case of an we found that li particles get uniformly distributed in the solvent and give good system to work towards optical pumping of lithium . finally to achieve optical pumping in vapour system we worked on confining the uhv li atomic beam in two directions using laser cooling .
post image analysis results are as shown in the figure below .
in conclusion we can say that we have worked towards making a hem detection system using phenomenon of optical pumping .
we first investigated stability of li in various solvents and found an as the most suitable one to make a stable thin film .
this system we analysed for lithium distribution using sem and found the distribution as uniform . before going for optical pumping on this system we made a uhv li beam at @xmath9 torr pressure wherein beam as confined using laser cooling to achieve optical pumping . as future
work we plan to achieve optical pumping in the thin film system and finally use it for detecting presence of hems .
national fusion program , board of research on fusion science and technology and drdo is greatly acknowledged for the financial assistance for the present work .
j. sarah caygill , frank davis , seamus p.j .
higson : current trends in explosive detection techniques , talanta 88 , 14 - 29(2012 ) .
j. h. van helden , n .
lang , u. macherius , h. zimmermann , and j. ropcke : sensitive trace gas detection with cavity enhanced absorption spectroscopy using a continuous wave external - cavity quantum cascade laser , appl .
103 , 131114(2013 ) .
jeffrey i. steinfeld , jody wormhoudt : explosives detection : a challenge for physical chemistry , annu .
49 , 203?32(1998 ) .
jehuda yinon : field detection and monitoring of explosives , trends in analytical chemistry , 21 , 4 ( 2002 )
. w. happer : optical pumping , rev .
phys , 44 , 169(1972 ) .
allen n. garroway , michael l. buess , joel b. miller , bryan h. suits , andrew d. hibbs , geoffrey a. barrall , robert matthews , and lowell j. burnett : remote sensing by nuclear quadrupole resonance , ieee transaction on geosciences and remote sensing , 39 , 6(2001 ) . | we present our work on high energy material detection based on thin film of lithium using the phenomenon of optical pumping . the lithium atoms present in the thin film
are optically pumped to one of the ground hyperfine energy levels so that they can no more absorb light from the resonant light source . now in presence of a rf signal , which quantifies the ambient magnetic field , this polarised atomic system is again randomised thus making it reabsorb the resonant light .
this gives a quantified measurement of the magnetic field surrounding the thin film detector .
this is then mapped to the presence of magnetic hems and hence the hems are detected .
our approach in this regard starts with verifying the stability of lithium atoms in various solvents so as to get a suitable liquid medium to form a thin film . in this
regard , various uv - visible characterisation spectra are presented to finally approach a stable system for the detection .
we have worked on around 10 polar and non polar solvents to see the stability criteria .
uv - visible probe has been found to be quite effective in addressing issue of hosting lithium atoms by various solvents .
further results on the atomic system size as dispersed in the various solvents are presented .
atomic system size gives us a good quantitative estimate of the density of lithium dispersed system in the thin film .
finally a separate atomic system under ultra - high - vacuum is presented to achieve optical pumping wherein the polarisation and depolarisation of atomic system is seen using a 670 nm diode laser system which is electronically locked using a double window hollow cathode lamp .
these both systems will finally be combined together to give the final form to the detection system . as this
whole system measures relative change in magnetic field due to the presence of hems , it gives a more reliable and accurate detection method compared to the absolute measurement detectors . | <s>[INST]in the last decade or so , detection of high energy materials ( hems ) for security screening , detection of non exploded ordnance , for demining and pollution check have become an active and important area of research1 - 3 . one main category of the detection of hems include the bulk detection systems wherein x ray or neutron imaging are employed to locate large quantities of explosives4 .
another method involves vapour and particle detection where trace quantities of explosives are detected via molecular signatures4 .
one of the main tools used for such detection is a laser .
laser offers two main advantages in these detections due to their long range propagation of intense energy and high wavelength specificity with regards to atomic / molecular spectroscopy .
present work explores a somewhat new territory of thin film detection using a long known tool of optical pumping5 .
thin film detection of hems have been recently explored elsewhere5 , however in context of physical / absorption property of the thin film . in the present work magnetic property of the hems
is used6 to detect them using the metal thin film magnetometer .
lithium atoms present in the thin film are optically pumped so that they can no more absorb light from the resonant light source .
now in presence of a rf signal , which quantifies the ambient magnetic field , this polarised atomic system is again randomised thus making it reabsorb the resonant light .
this gives a quantified measurement of the magnetic field surrounding the thin film detector .
this is then mapped to the presence of magnetic hems and hence the hems are detected .
one measures the larmor precession frequency @xmath0 of atomic spins in a magnetic field b , given by @xmath1 where the gyro magnetic ratio @xmath2 serves as the conversion factor between the frequency and the field strength .
as equation ( 1 ) suggests , the larmor precession frequency measurement gives a measure of the b field around .
so a measurement of larmor precession frequency gives a measure of the ambient b field which is accomplished by using a rf field .
this when mapped to the hem magnetic field gives the final shape to the hem detector .
first step in making the lithium thin film is to check for the stability of li in various solvents .
we have done the same using uv / visible spectroscopy of lithium in various polar/ non - polar solvents .
this is done in presence/ absence of laser beam irradiating the atomic system .
laser system is a 1064 nm dpss nd - yag laser .
the absorption spectra of irradiated li solutions taken in the quartz cuvette of optical length10 mm were measured with wavelength from 200 to 800 nm using the perkin elmer uv - visible spectrophotometer .
all the reagents and solvents of high pure grade were purchased from sigma , aldrich , merck , alfa - aesar and used without further purifications .
1 mm li solutions using solvents have been prepared .
the saturated solution of pmma was prepared by dissolving the polymer in chloroform for 48 hrs at room temperature and then li was added . lithium system with various solvents is then characterised with regards to the particle size dispersed in the solvents to estimate particle density in the resulting thin film .
this is done using the sem characterisation .
this is important in making sure that lithium particle are indeed uniformly distributed in the solvent and give a good system for performing optical pumping experiments .
another part of the experiment we plan to show optical pumping phenomenon in lithium atomic beam system .
for the same we successfully made a li atomic beam setup using a combination of rotary - turbo - ion pump to go down to ultra - high - vacuum ( uhv ) of 10 - 9 torr of pressure .
figure 3 shows full uhv chambered lithium atomic beam .
the atomic source ( figure 4 ) basically comprises of a thin walled ss tube welded to a two pin feed through with solid li inside which is resistively heated to around 4000c to get enough vapours .
this is achieved by passing around 4 - 5 a of current across the coil . to avoid divergence of the beam
we have put an aperture , a circular cu plate with a 1 mm hole punched at the centre of it .
this gives a narrow li atomic beam with transverse divergence of roughly 1 cm at around 10 cm away from the source .
this was checked by tuning a diode laser at 670 nm to the resonance for the li d lines and seeing the transverse extension of the fluorescence spot through a window .
typical fluorescence signal captured by a ccd camera ( 30 fps thor labs usb camera ) are shown in the figure 5 .
laser used for the purpose is an external cavity diode laser ( ecdl ) at 670 nm tunable from 665 - 675 from toptica photonics with power output of 35 mw .
the @xmath3 of compounds is changed with the solvent and the concentration of solution .
four types of shifts in the @xmath4 values are possible : ( i ) shift of @xmath4 to longer wavelength or less energy is due to the substituent or solvent effect is referred as bathochromic or red shift ( ii ) shift of @xmath4 to shorter wavelength or higher energy is due to the substituent or solvent effect is referred as hypsochromic or blue shift ( iii ) an increase in the absorption intensity called as hyperchromic shift and ( iv ) decrease in the absorption intensity called as hypochromic shift .
the electronic transitions are usually accompanied by a simultaneous change between the vibrational levels .
we found this shift happening in all the solvents .
a typical spectra is shown in figure 6 for acetonitrile and lithium solution .
such spectra were taken for nine polar and non - polar solvents and the shift in cut off wavelength measured ( table 1 ) . except for the case of acetonitrile ( an )
we found the cut off wavelength varying post laser irradiation ( table 1 ) .
this gave us confidence that an can be the perfect solvent with which lithium can be added to form a stable film which will not get affected by laser perturbation and optical pumping can be performed with such combination . to give brief chemical reactivity of an with li
, an reacts with li at room temperature to liberate hydrogen gas in figure 6 , the sharp band at 194 nm moved to the higher wavelength of 190 nm ( i.e. , red shift ) and two new broad bands have appeared at 256 nm and 292 nm .
it is due to the formation of mono - lithium derivatives of acetonitrile and released hydrogen gas on irradiation .
the uv - visible spectrum of the li solution shows cyanide absorption higher than the parent acetonitrile indicating a weakening of the cyanide linkage . [ cols="<,<,^,^,^,^ " , ] the nitriles are known to undergo n @xmath5 @xmath6 transition and n @xmath5 @xmath7 transition of characteristic cut off wavelengths of 194 nm and 300 nm .
the two distinctive bands at 256 nm and 292 nm after irradiation are due to the formation of , an organometallic compound .
the bond is of intermediate character between ionic and covalent bonds .
the various bands of solutions both irradiated and non - irradiated apparently of the characteristic bands of lithium containing compounds : @xmath8 @xmath8 @xmath8 @xmath8 .
further sem characterisation was conducted to ascertain the density of the li particles in the solution with various solvents . analysing the case of an we found that li particles get uniformly distributed in the solvent and give good system to work towards optical pumping of lithium . finally to achieve optical pumping in vapour system we worked on confining the uhv li atomic beam in two directions using laser cooling .
post image analysis results are as shown in the figure below .
in conclusion we can say that we have worked towards making a hem detection system using phenomenon of optical pumping .
we first investigated stability of li in various solvents and found an as the most suitable one to make a stable thin film .
this system we analysed for lithium distribution using sem and found the distribution as uniform . before going for optical pumping on this system we made a uhv li beam at @xmath9 torr pressure wherein beam as confined using laser cooling to achieve optical pumping . as future
work we plan to achieve optical pumping in the thin film system and finally use it for detecting presence of hems .
national fusion program , board of research on fusion science and technology and drdo is greatly acknowledged for the financial assistance for the present work .
j. sarah caygill , frank davis , seamus p.j .
higson : current trends in explosive detection techniques , talanta 88 , 14 - 29(2012 ) .
j. h. van helden , n .
lang , u. macherius , h. zimmermann , and j. ropcke : sensitive trace gas detection with cavity enhanced absorption spectroscopy using a continuous wave external - cavity quantum cascade laser , appl .
103 , 131114(2013 ) .
jeffrey i. steinfeld , jody wormhoudt : explosives detection : a challenge for physical chemistry , annu .
49 , 203?32(1998 ) .
jehuda yinon : field detection and monitoring of explosives , trends in analytical chemistry , 21 , 4 ( 2002 )
. w. happer : optical pumping , rev .
phys , 44 , 169(1972 ) .
allen n. garroway , michael l. buess , joel b. miller , bryan h. suits , andrew d. hibbs , geoffrey a. barrall , robert matthews , and lowell j. burnett : remote sensing by nuclear quadrupole resonance , ieee transaction on geosciences and remote sensing , 39 , 6(2001 ) .[/INST] we present our work on high energy material detection based on thin film of lithium using the phenomenon of optical pumping . the lithium atoms present in the thin film
are optically pumped to one of the ground hyperfine energy levels so that they can no more absorb light from the resonant light source . now in presence of a rf signal , which quantifies the ambient magnetic field , this polarised atomic system is again randomised thus making it reabsorb the resonant light .
this gives a quantified measurement of the magnetic field surrounding the thin film detector .
this is then mapped to the presence of magnetic hems and hence the hems are detected .
our approach in this regard starts with verifying the stability of lithium atoms in various solvents so as to get a suitable liquid medium to form a thin film . in this
regard , various uv - visible characterisation spectra are presented to finally approach a stable system for the detection .
we have worked on around 10 polar and non polar solvents to see the stability criteria .
uv - visible probe has been found to be quite effective in addressing issue of hosting lithium atoms by various solvents .
further results on the atomic system size as dispersed in the various solvents are presented .
atomic system size gives us a good quantitative estimate of the density of lithium dispersed system in the thin film .
finally a separate atomic system under ultra - high - vacuum is presented to achieve optical pumping wherein the polarisation and depolarisation of atomic system is seen using a 670 nm diode laser system which is electronically locked using a double window hollow cathode lamp .
these both systems will finally be combined together to give the final form to the detection system . as this
whole system measures relative change in magnetic field due to the presence of hems , it gives a more reliable and accurate detection method compared to the absolute measurement detectors . </s> |
thymomas are lympho epithelial neoplasm characterized by admixture of epithelial cells and mature lymphocytes . in adults , thymoma is the most common primary tumor of the anterior mediastinum , comprising 20 - 30% of all mediastinal masses .
seventy percent of thymomas occur in patients over the age of 40 years , and nearly all thymomas occur over the 20 years of age . clinical presentation may vary ; from asymptomatic mediastinal masses detected on chest radiographs to compressive symptoms like dysphagia , venous congestion or dyspnea .
some tumors are associated with paraneoplastic syndromes like myasthenia gravis , pure red cell aplasia , acquired hypogammaglobulinemia , and connective tissue disorders . in children ,
thymoma is extremely rare in children and adolescents , with less than 50 cases of pediatric thymoma reported in the literature . as a result of this rarity , it is difficult to predict prognosis or formulate treatment guidelines for these patients . in a comprehensive review ,
liang et al . have attempted the same in patients of pediatric thymoma reported over the past 3 decades .
they found that younger ( < 10 years ) and male patients had a worse prognosis .
we report a case of thymoma in an 8-year - old boy with early tumor stage and favorable clinical and histopathological features .
an 8-year - old boy presented to the pediatric clinic with a 3-month history of intermittent cough and occasional pain in the right upper chest .
the chest radiograph revealed a right perihilar shadow with mediastinal widening . computed tomography ( ct ) chest revealed a large , ( maximum diameter 7.2 cm )
lobulated , homogenous soft tissue mass in the anterior mediastinum arising from the right side of the thymus gland .
the mass was overlying the superior vena cava and brachiocephalic vein ; however , the fat planes were maintained .
there was no lymphadenopathy or pleural effusion , and both the lungs were normal [ figure 1 ] .
serum levels of markers for germ cell tumors , that is , -fetoprotein , -human chorionic gonadotropin and lactate dehydrogenase were within the normal range .
image - guided fine - needle aspiration cytology from the lesion showed a lymphoepithelial lesion , suggestive of a thymoma or thymic hyperplasia .
computed tomography chest showing a large , lobulated , homogenous soft tissue anterior mediastinal mass ( marked t ) .
fat planes with the superior vena cava , brachiocephalic vein and pericardium are maintained with a provisional diagnosis of thymoma , the boy underwent a midline sternotomy .
there was a solitary , well - encapsulated , multi septated mass measuring around 7.5 cm 3.5 cm 3 cm arising from the thymus and overlying the superior vena cava and brachiochephalic vein .
the lower part was abutting the pericardium ; however , the lesion could be easily separated from the pericardium and the great vessels .
the patient had an uneventful recovery and was discharged on the seventh postoperative day . on cut - section
microscopy revealed a well - encapsulated tumor arranged in lobules and nests separated by fibrous septa , along with extensive areas of necrosis . in high - power ( 100 ) , an admixture of round to oval epithelial cells devoid of atypia admixed with small lymphocytes in even proportions , could be appreciated [ figure 3 ] .
a final diagnosis of thymoma ( masaoka stage i , who type b2 ) with extensive areas of necrosis was made .
gross images show ( a ) a well - circumscribed mass with intact capsule ( b ) cut - surface shows cystic change with extensive necrosis photomicrograph shows encapsulated tumor with extensive necrosis with few preserved areas ( h and e , 40 ) .
high - power ( inset ) shows admixture of epithelial cells and small lymphocytes ( h and e , 100 )
thymomas and thymic carcinomas are epithelial tumors of the thymus . in children , thymic lesions comprise only 2 - 3% of all mediastinal tumors , with thymomas still rarer ( < 1% ) .
the presenting symptoms may vary widely ; from vague chest discomfort , to florid compressive symptoms like dyspnea and superior vena cava syndrome .
some children may have an incidentally - detected soft tissue mass with calcifications , on chest radiograph .
approximately , 20% of children with thymomas have paraneoplastic syndromes , of which around 70% are myasthenia gravis .
myasthenia gravis is also mostly seen in children with thymoma who are < 10 years of age , and in 70% of patients with the b2 subtype .
all patients with suspected thymoma should have serum antiacetylcholine receptor antibody levels measured before surgery .
contrast - enhanced ct is the imaging modality of choice in the evaluation and staging of thymoma .
the most widely used thymoma classification is the masaoka staging system which is based on the presence of invasion into surrounding organs , completeness of resection , association with myasthenia gravis , tumor size , and involvement of great vessels , to determine postoperative survival .
the who system , based on the morphology of epithelial cells as well as the lymphocyte - to - epithelial cell ratio , was developed in 1999 to include histological features as prognostic factors .
both these systems have been evaluated in large series ; the clinical value of both has been validated .
liang et al . reviewed 32 cases of pediatric thymoma in english literature and found that younger patients ( < 10 years old ) were predominantly male , presented with a more advanced tumor stage ( masaoka stage iii / iv ) , had a less favorable outcome and were more likely to have paraneoplastic syndromes .
the unusual features in our patient were the absence of adverse prognostic factors like local invasion and autoimmune disorders ( myasthenia gravis ) , despite the young age ( < 10 years ) .
extensive necrosis is seldom seen in thymoma with only a few reports mentioning necrosis in adult patients . however , none reported the same in children .
moran et al . studied 25 cases of thymoma with necrosis ; the authors do not consider it an adverse prognostic factor .
this may explain the simultaneous presence of necrosis and other favorable factors in our case .
, treatment protocols have not been clearly defined due to paucity of cases ; however , most authors have favored regimens similar to adult regimens , that is , based on cisplatin , doxorubicin , prednisolone , and cyclophosphamide .
complete resection is also a significant predictor of 5-year survival in masaoka stage i , ii and iii . despite the fact that who type b2 disease has poorer long - term survival ( ~60% )
since our case had all favorable factors and one doubtful factor ( b2 disease ) , we did not prescribe adjuvant treatment .
the patient is , however , on long - term surveillance for recurrence and detection of second malignancies like non - hodgkin lymphoma and soft tissue sarcomas , which are known to occur .
complete surgical excision is the treatment modality of choice . due to its common association with myasthenia gravis , | thymoma represents < 1% of all mediastinal tumors in children .
less than 50 cases of pediatric thymoma are reported in the literature .
thymomas are considered to be highly aggressive in pediatric patients , especially when age is < 10 years .
paraneoplastic syndromes , of which around 70% are myasthenia gravis , correlate with poor prognosis . in this article , we report a case of a thymoma in an 8-year - old boy , who had favorable histopathology ( masaoka stage i , who type b2 ) , despite the presence of young age and necrosis along with absence of myasthenia gravis .
we have also reviewed the available literature on pediatric thymoma . | <s>[INST]thymomas are lympho epithelial neoplasm characterized by admixture of epithelial cells and mature lymphocytes . in adults , thymoma is the most common primary tumor of the anterior mediastinum , comprising 20 - 30% of all mediastinal masses .
seventy percent of thymomas occur in patients over the age of 40 years , and nearly all thymomas occur over the 20 years of age . clinical presentation may vary ; from asymptomatic mediastinal masses detected on chest radiographs to compressive symptoms like dysphagia , venous congestion or dyspnea .
some tumors are associated with paraneoplastic syndromes like myasthenia gravis , pure red cell aplasia , acquired hypogammaglobulinemia , and connective tissue disorders . in children ,
thymoma is extremely rare in children and adolescents , with less than 50 cases of pediatric thymoma reported in the literature . as a result of this rarity , it is difficult to predict prognosis or formulate treatment guidelines for these patients . in a comprehensive review ,
liang et al . have attempted the same in patients of pediatric thymoma reported over the past 3 decades .
they found that younger ( < 10 years ) and male patients had a worse prognosis .
we report a case of thymoma in an 8-year - old boy with early tumor stage and favorable clinical and histopathological features .
an 8-year - old boy presented to the pediatric clinic with a 3-month history of intermittent cough and occasional pain in the right upper chest .
the chest radiograph revealed a right perihilar shadow with mediastinal widening . computed tomography ( ct ) chest revealed a large , ( maximum diameter 7.2 cm )
lobulated , homogenous soft tissue mass in the anterior mediastinum arising from the right side of the thymus gland .
the mass was overlying the superior vena cava and brachiocephalic vein ; however , the fat planes were maintained .
there was no lymphadenopathy or pleural effusion , and both the lungs were normal [ figure 1 ] .
serum levels of markers for germ cell tumors , that is , -fetoprotein , -human chorionic gonadotropin and lactate dehydrogenase were within the normal range .
image - guided fine - needle aspiration cytology from the lesion showed a lymphoepithelial lesion , suggestive of a thymoma or thymic hyperplasia .
computed tomography chest showing a large , lobulated , homogenous soft tissue anterior mediastinal mass ( marked t ) .
fat planes with the superior vena cava , brachiocephalic vein and pericardium are maintained with a provisional diagnosis of thymoma , the boy underwent a midline sternotomy .
there was a solitary , well - encapsulated , multi septated mass measuring around 7.5 cm 3.5 cm 3 cm arising from the thymus and overlying the superior vena cava and brachiochephalic vein .
the lower part was abutting the pericardium ; however , the lesion could be easily separated from the pericardium and the great vessels .
the patient had an uneventful recovery and was discharged on the seventh postoperative day . on cut - section
microscopy revealed a well - encapsulated tumor arranged in lobules and nests separated by fibrous septa , along with extensive areas of necrosis . in high - power ( 100 ) , an admixture of round to oval epithelial cells devoid of atypia admixed with small lymphocytes in even proportions , could be appreciated [ figure 3 ] .
a final diagnosis of thymoma ( masaoka stage i , who type b2 ) with extensive areas of necrosis was made .
gross images show ( a ) a well - circumscribed mass with intact capsule ( b ) cut - surface shows cystic change with extensive necrosis photomicrograph shows encapsulated tumor with extensive necrosis with few preserved areas ( h and e , 40 ) .
high - power ( inset ) shows admixture of epithelial cells and small lymphocytes ( h and e , 100 )
thymomas and thymic carcinomas are epithelial tumors of the thymus . in children , thymic lesions comprise only 2 - 3% of all mediastinal tumors , with thymomas still rarer ( < 1% ) .
the presenting symptoms may vary widely ; from vague chest discomfort , to florid compressive symptoms like dyspnea and superior vena cava syndrome .
some children may have an incidentally - detected soft tissue mass with calcifications , on chest radiograph .
approximately , 20% of children with thymomas have paraneoplastic syndromes , of which around 70% are myasthenia gravis .
myasthenia gravis is also mostly seen in children with thymoma who are < 10 years of age , and in 70% of patients with the b2 subtype .
all patients with suspected thymoma should have serum antiacetylcholine receptor antibody levels measured before surgery .
contrast - enhanced ct is the imaging modality of choice in the evaluation and staging of thymoma .
the most widely used thymoma classification is the masaoka staging system which is based on the presence of invasion into surrounding organs , completeness of resection , association with myasthenia gravis , tumor size , and involvement of great vessels , to determine postoperative survival .
the who system , based on the morphology of epithelial cells as well as the lymphocyte - to - epithelial cell ratio , was developed in 1999 to include histological features as prognostic factors .
both these systems have been evaluated in large series ; the clinical value of both has been validated .
liang et al . reviewed 32 cases of pediatric thymoma in english literature and found that younger patients ( < 10 years old ) were predominantly male , presented with a more advanced tumor stage ( masaoka stage iii / iv ) , had a less favorable outcome and were more likely to have paraneoplastic syndromes .
the unusual features in our patient were the absence of adverse prognostic factors like local invasion and autoimmune disorders ( myasthenia gravis ) , despite the young age ( < 10 years ) .
extensive necrosis is seldom seen in thymoma with only a few reports mentioning necrosis in adult patients . however , none reported the same in children .
moran et al . studied 25 cases of thymoma with necrosis ; the authors do not consider it an adverse prognostic factor .
this may explain the simultaneous presence of necrosis and other favorable factors in our case .
, treatment protocols have not been clearly defined due to paucity of cases ; however , most authors have favored regimens similar to adult regimens , that is , based on cisplatin , doxorubicin , prednisolone , and cyclophosphamide .
complete resection is also a significant predictor of 5-year survival in masaoka stage i , ii and iii . despite the fact that who type b2 disease has poorer long - term survival ( ~60% )
since our case had all favorable factors and one doubtful factor ( b2 disease ) , we did not prescribe adjuvant treatment .
the patient is , however , on long - term surveillance for recurrence and detection of second malignancies like non - hodgkin lymphoma and soft tissue sarcomas , which are known to occur .
complete surgical excision is the treatment modality of choice . due to its common association with myasthenia gravis ,[/INST]thymoma represents < 1% of all mediastinal tumors in children .
less than 50 cases of pediatric thymoma are reported in the literature .
thymomas are considered to be highly aggressive in pediatric patients , especially when age is < 10 years .
paraneoplastic syndromes , of which around 70% are myasthenia gravis , correlate with poor prognosis . in this article , we report a case of a thymoma in an 8-year - old boy , who had favorable histopathology ( masaoka stage i , who type b2 ) , despite the presence of young age and necrosis along with absence of myasthenia gravis .
we have also reviewed the available literature on pediatric thymoma .</s> |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Portfolio Lending and Mortgage
Access Act''.
SEC. 2. MINIMUM STANDARDS FOR RESIDENTIAL MORTGAGE LOANS.
Section 129C(b) of the Truth in Lending Act (15 U.S.C. 1639c(b)) is
amended by adding at the end the following:
``(4) Safe harbor.--
``(A) In general.--A residential mortgage loan
shall be deemed a qualified mortgage loan for purposes
of this subsection if the loan--
``(i) is originated by, and continuously
retained in the portfolio of, a covered
institution;
``(ii) is in compliance with the
limitations with respect to prepayment
penalties described in subsections (c)(1) and
(c)(3);
``(iii) is in compliance with the
requirements related to points and fees under
paragraph (2)(A)(vii);
``(iv) does not have negative amortization
terms or interest-only terms; and
``(v) is a loan for which the covered
institution considers, documents, and verifies
the debt, income, and financial resources of
the consumer in accordance with subparagraph
(C).
``(B) Exception for certain transfers.--
Subparagraph (A) shall not apply to a residential
mortgage loan if the legal title to such residential
mortgage loan is sold, assigned, or otherwise
transferred to another person unless the legal title to
such residential mortgage loan is sold, assigned, or
otherwise transferred--
``(i) to another person by reason of the
bankruptcy or failure of the covered
institution that originated such loan;
``(ii) to an insured depository institution
or insured credit union that has less than
$10,000,000,000 in total consolidated assets on
the date of such sale, assignment, or transfer,
if the loan is retained in portfolio by such
insured depository institution or insured
credit union;
``(iii) pursuant to a merger of the covered
institution that originated such loan with
another person or the acquisition of a the
covered institution that originated such loan
by another person or of another person by a
covered institution, if the loan is retained in
portfolio by the person to whom the loan is
sold, assigned, or otherwise transferred; or
``(iv) to a wholly owned subsidiary of the
covered institution that originated such loan
if the loan is considered to be an asset of
such covered institution for regulatory
accounting purposes.
``(C) Consideration and documentation
requirements.--The consideration and documentation
requirements described in subparagraph (A)(v) shall--
``(i) not be construed to require
compliance with, or documentation in accordance
with, appendix Q to part 1026 of title 12, Code
of Federal Regulations, or any successor
regulation; and
``(ii) be construed to permit multiple
methods of documentation.
``(D) Definitions.--In this paragraph--
``(i) the term `covered institution' means
an insured depository institution or an insured
credit union that, together with its
affiliates, has less than $10,000,000,000 in
total consolidated assets on the date on the
origination of a residential mortgage loan;
``(ii) the term `insured credit union' has
the meaning given the term in section 101 of
the Federal Credit Union Act (12 U.S.C. 1752);
``(iii) the term `insured depository
institution' has the meaning given the term in
section 3 of the Federal Deposit Insurance Act
(12 U.S.C. 1813);
``(iv) the term `interest-only term' means
a term of a residential mortgage loan that
allows one or more of the periodic payments
made under the loan to be applied solely to
accrued interest and not to the principal of
the loan; and
``(v) the term `negative amortization term'
means a term of a residential mortgage loan
under which the payment of periodic payments
will result in an increase in the principal of
the loan.''.
Passed the House of Representatives March 6, 2018.
Attest:
KAREN L. HAAS,
Clerk. | Portfolio Lending and Mortgage Access Act (Sec. 2) This bill amends the Truth in Lending Act to allow a depository institution or credit union with assets below a specified threshold to forgo certain ability-to-pay requirements regarding residential mortgage loans. Specifically, those requirements are waived if a loan: (1) is originated by and continuously retained by the institution, (2) complies with requirements regarding prepayment penalties and points and fees, and (3) does not have negative amortization or interest-only terms. Furthermore, for such requirements to be waived, the institution must consider and verify the debt, income, and financial resources of the consumer. The bill also provides for circumstances in which such requirements shall be waived with respect to a loan that is transferred: (1) by reason of bankruptcy or failure of the originating institution, (2) to a similar institution, (3) in the event of a merger, or (4) to a wholly owned subsidiary of the institution. | <s>[INST]SECTION 1. SHORT TITLE.
This Act may be cited as the ``Portfolio Lending and Mortgage
Access Act''.
SEC. 2. MINIMUM STANDARDS FOR RESIDENTIAL MORTGAGE LOANS.
Section 129C(b) of the Truth in Lending Act (15 U.S.C. 1639c(b)) is
amended by adding at the end the following:
``(4) Safe harbor.--
``(A) In general.--A residential mortgage loan
shall be deemed a qualified mortgage loan for purposes
of this subsection if the loan--
``(i) is originated by, and continuously
retained in the portfolio of, a covered
institution;
``(ii) is in compliance with the
limitations with respect to prepayment
penalties described in subsections (c)(1) and
(c)(3);
``(iii) is in compliance with the
requirements related to points and fees under
paragraph (2)(A)(vii);
``(iv) does not have negative amortization
terms or interest-only terms; and
``(v) is a loan for which the covered
institution considers, documents, and verifies
the debt, income, and financial resources of
the consumer in accordance with subparagraph
(C).
``(B) Exception for certain transfers.--
Subparagraph (A) shall not apply to a residential
mortgage loan if the legal title to such residential
mortgage loan is sold, assigned, or otherwise
transferred to another person unless the legal title to
such residential mortgage loan is sold, assigned, or
otherwise transferred--
``(i) to another person by reason of the
bankruptcy or failure of the covered
institution that originated such loan;
``(ii) to an insured depository institution
or insured credit union that has less than
$10,000,000,000 in total consolidated assets on
the date of such sale, assignment, or transfer,
if the loan is retained in portfolio by such
insured depository institution or insured
credit union;
``(iii) pursuant to a merger of the covered
institution that originated such loan with
another person or the acquisition of a the
covered institution that originated such loan
by another person or of another person by a
covered institution, if the loan is retained in
portfolio by the person to whom the loan is
sold, assigned, or otherwise transferred; or
``(iv) to a wholly owned subsidiary of the
covered institution that originated such loan
if the loan is considered to be an asset of
such covered institution for regulatory
accounting purposes.
``(C) Consideration and documentation
requirements.--The consideration and documentation
requirements described in subparagraph (A)(v) shall--
``(i) not be construed to require
compliance with, or documentation in accordance
with, appendix Q to part 1026 of title 12, Code
of Federal Regulations, or any successor
regulation; and
``(ii) be construed to permit multiple
methods of documentation.
``(D) Definitions.--In this paragraph--
``(i) the term `covered institution' means
an insured depository institution or an insured
credit union that, together with its
affiliates, has less than $10,000,000,000 in
total consolidated assets on the date on the
origination of a residential mortgage loan;
``(ii) the term `insured credit union' has
the meaning given the term in section 101 of
the Federal Credit Union Act (12 U.S.C. 1752);
``(iii) the term `insured depository
institution' has the meaning given the term in
section 3 of the Federal Deposit Insurance Act
(12 U.S.C. 1813);
``(iv) the term `interest-only term' means
a term of a residential mortgage loan that
allows one or more of the periodic payments
made under the loan to be applied solely to
accrued interest and not to the principal of
the loan; and
``(v) the term `negative amortization term'
means a term of a residential mortgage loan
under which the payment of periodic payments
will result in an increase in the principal of
the loan.''.
Passed the House of Representatives March 6, 2018.
Attest:
KAREN L. HAAS,
Clerk.[/INST]Portfolio Lending and Mortgage Access Act (Sec. 2) This bill amends the Truth in Lending Act to allow a depository institution or credit union with assets below a specified threshold to forgo certain ability-to-pay requirements regarding residential mortgage loans. Specifically, those requirements are waived if a loan: (1) is originated by and continuously retained by the institution, (2) complies with requirements regarding prepayment penalties and points and fees, and (3) does not have negative amortization or interest-only terms. Furthermore, for such requirements to be waived, the institution must consider and verify the debt, income, and financial resources of the consumer. The bill also provides for circumstances in which such requirements shall be waived with respect to a loan that is transferred: (1) by reason of bankruptcy or failure of the originating institution, (2) to a similar institution, (3) in the event of a merger, or (4) to a wholly owned subsidiary of the institution. </s> |
"The Daily Show with Trevor Noah" is on the rise, and yes, the Trump Administration has something to do with that. But Comedy Central credits the host for taking a different approach than his competitors.
Donald Trump hasn’t yet gone after “The Daily Show,” and that’s fine by host Trevor Noah.
“I don’t think Trump’s attack is the mark of a good show,” he told IndieWire last month, after taping an episode in his Midtown Manhattan studio. “People always go, ‘He’s attacking ‘SNL.’ Actually, he is attacking Alec Baldwin. That’s what gets to him, the fact that that’s whom he aspires to. That’s a New York guy. That’s the face of fame for him. He has his peers that he wants to be associated with, and everyone else he doesn’t really care about. That’s part of the problem of Donald Trump. He lives in his own world.”
And it turns out, Noah is doing very well without Trump’s seal of disapproval. Just 18 months after Noah took over the Comedy Central franchise from Jon Stewart, “The Daily Show” finished the first quarter of 2017 with its best ratings since the host transition. It is the only daily late-night talk show this year to enjoy year-to-year improvement among both total viewers and adults 18-49.
It’s a solid turnaround for “The Daily Show” and Comedy Central, which took more than a few lumps after losing marquee talents Stewart, Stephen Colbert, John Oliver, and Samantha Bee over the course of a year. (More recently, the network canceled “The Nightly Show with Larry Wilmore” due to low ratings.) Noah also had a bumpy start before even taking over, as several of his old Twitter posts were criticized for being offensive.
Comedy Central
Comedy Central has always stressed that hiring Noah was about recalibrating “The Daily Show” for a new, younger generation, and it is doing particularly well with young viewers, surpassing “The Tonight Show Starring Jimmy Fallon” as the top late-night talk show among millennials under 25, and it’s now the No. 1 late-night talk show with men under 35.
“Our whole orientation was, if we try to replace Jon Stewart with just a younger version of Jon Stewart, it’s a fool’s errand and will never work,” said Comedy Central president Kent Alterman. “Our gut instinct about him is being borne out. I never really had any doubts about [Noah], and we never had doubts that it would take time. No matter how much I said that publicly it didn’t matter, people always thought the obligation was to compare Trevor’s Day 1 to Jon’s last day after 16 years. We always told people that we didn’t hire Trevor for his experience; we hired him for his talent and his brain.”
Noah is the first to credit the Trump Effect for giving “The Daily Show” renewed purpose and vigor.
“We’re in a world where maybe, for a certain amount of people, there was no need for a late-night satirical show in their lives when it was presumed that Hillary Clinton would win,” he said. “[When that didn’t happen], we felt the click in the show. I felt it in myself as a person. You feel that there is a fear and a tension, and when that tension rises, comedy is oftentimes the release.”
READ MORE: ‘Donald Trump’ Promises to Make Late Night Great Again with Comedy Central’s ‘The President Show’
Noah now sees his early days hosting “The Daily Show” during the presidential campaign as training for how to handle the job under a Trump administration. “Before the election and leading up to it, I remember people were like, ‘Why aren’t you more angry? Where’s your rage?’ I said, ‘Why would I be angry? What would my rage stem from? What is my origin story, for me to all of a sudden be this character you think I should be?’
“All I did was read; I learned. In essence, I’ve realized now that I was learning at the same time as Donald Trump was. We were learning about the country at the same time. The only difference is, I feel like I still read my briefings and he doesn’t.”
Noah’s growing knowledge is on display every night on “The Daily Show” set, even in between commercials. One night, he gave the crowd a succinct play-by-play of how House Speaker Paul Ryan had painted the Republicans in a corner by trying to push through Trumpcare so fast (something that later played out the way Noah had predicted). Some of those impromptu chats have wound up on “The Daily Show’s” social media channels, which have seen YouTube and Facebook video viewership grow by 200% over the last year.
Meanwhile, Alterman has heard the criticism that Noah isn’t angry enough on air, but believes it’s a complaint coming mostly from older viewers.
“Our research shows younger people don’t feel that way,” he said. “One thing that sets Trevor apart is he can take these strong positions and really go after whatever targets are out there, but he doesn’t do it in a dogmatic yelling way.”
Early on in the Trump campaign, Noah said he purposely approached it from a neutral perspective. “That’s why very early on, I said, ‘I can see how Trump’s connecting. I can see why I think he won that debate.’ People are like, ‘Are you mad?’ Even as a person who’s just come into it, very quickly you realize that there is an artificial middle that has been created and facts and truth and honesty are almost artifacts of a bygone era.”
(STORY CONTINUES ON NEXT PAGE)
Sign Up: Stay on top of the latest breaking film and TV news! Sign up for our Email Newsletters here. ||||| Stewart’s decision to retire as host of the satirical news show after 16 years has left liberal America in mourning. So why is he leaving just before an election – and what will happen when he steps out from behind the desk?
There was no one moment when Jon Stewart knew it was time for him to leave what he describes as “the most perfect job in the world”; no epiphany, no flashpoint. “Life,” he says, in the lightly self-mocking tone he uses when talking about himself, “doesn’t really work that way, with a finger pointing at you out of the sky, saying, ‘Leave now!’ That only happens when you’re fired, and trust me, I know about that.”
Instead, he describes his decision to quit The Daily Show, the American satirical news programme he has hosted for 16 years, as something closer to the end of a long-term relationship. “It’s not like I thought the show wasn’t working any more, or that I didn’t know how to do it. It was more, ‘Yup, it’s working. But I’m not getting the same satisfaction.’” He slaps his hands on his desk, conclusively.
“These things are cyclical. You have moments of dissatisfaction, and then you come out of it and it’s OK. But the cycles become longer and maybe more entrenched, and that’s when you realise, ‘OK, I’m on the back side of it now.’”
Facebook Twitter Pinterest Stewart announces he is to leave The Daily Show
Stewart and I speak twice in the space of a few months. The first time last October, when he flew from New York to London with his family for the premiere of his directorial debut at the London Film Festival. Rosewater is an engrossing and pacy film that tells the true story of Iranian-born journalist Maziar Bahari, who was arrested and tortured in Iran in 2009, after sending footage of street riots to the BBC.
The second time, we speak soon after Stewart announces his retirement from The Daily Show. He is in his office in New York, preparing to shoot a Friday-night episode, and the difference in his mood is striking. His voice is about an octave lower, and he sounds weary, weighed down.
But talking about his film in London, he is animated to the point of hyperactivity, gleefully pointing out the pretentious decor in the hotel room where we meet (“A photo of a submissive woman with a cigar in her mouth! Just what every room needs!”). He notes, in a tone that is both sincere and satirical, and that will be familiar to fans of The Daily Show, the lavishness of the food: “My compliments to the prop master, because that really is a beautiful tomato and mozzarella salad,” he intones solemnly to a bemused waiter.
It was heartbreaking interviewing Obama... that's what the gig is
Like every TV celebrity, in person, Stewart is both better-looking than you expect and smaller, with his long torso making up most of his 5ft 7in, giving the illusion of height from behind his studio desk. He is dressed casually, and after years of watching him on TV wearing a suit, seeing him in a T-shirt and casual trousers feels almost like catching my father half-undressed.
At 52, Stewart has the bouncy energy of a man half his age and, unlike most in the public eye, has an aversion to compliments. If I tell him I liked something about the film, he will immediately deflect the compliment and insist it was all down to Bahari, or the film’s star Gael García Bernal, or the crew. For all the claims of his detractors that Stewart is the epitome of East Coast elitism, there is more self-deprecating New Jersey grit here than arrogant Manhattan elan.
Much as he might wince to hear it, for the past 16 years Stewart has occupied a place in America’s cultural and political life far greater than the small audience of his cable show would suggest. The Daily Show’s simple format consists of a mix of reports from roving reporters (who have included Steve Carell, Stephen Colbert and John Oliver), monologues delivered by Stewart and an end-of-show interview. Over time, Stewart has evolved from a satirist to a broadcaster celebrated as the voice of US liberalism, the one who will give the definitive progressive take on a story.
Facebook Twitter Pinterest Stewart on the Charlie Hebdo murders
His moving monologue after the Charlie Hebdo killings in January was widely shared; his frequent on-air support of Democrat senator Elizabeth Warren helped her evolve in the eyes of the public from Harvard professor to dream 2016 presidential candidate – particularly among those who find Hillary Clinton too centrist and hawkish. Stewart’s energetic campaigning on behalf of the 9/11 first responders (the emergency services who were first on the scene, many of whom later suffered debilitating illnesses), prompted the New York Times to compare him to Walter Cronkite and Edward R Murrow, the most revered newscasters in American history. It is a delicious irony that in the world of American TV news, one populated by raging egotists and self-aggrandisers, the person who is generally cited as the most influential is Stewart – a man so disinterested in his own celebrity, he often didn’t bother to collect his 18 Emmys, preferring to stay at home with his family.
When George Bush left office in 2008, some worried that Stewart would run out of material. This proved as shortsighted as the hope that Obama would be America’s grand salvation. Stewart, who describes himself as “a leftist”, has always hammered the Democrats with the vigour of a disappointed supporter, and subjected Obama to one of his most damaging interviews during his first term: the president admitted that his 2008 slogan probably should have been “Yes We Can, But...” At the time, Stewart laughed, but today he admits with a shrug, “It was heartbreaking. It’s generally heartbreaking – that’s what the gig is.”
Facebook Twitter Pinterest Stewart gave Barack Obama one of his toughest interviews, suggesting his 2008 election slogan should have been ‘Yes we can, but…’ Photograph: Empics Entertainment
His seemingly effortless interview with Tony Blair in 2008 cut through Blair’s crusader mentality in a mere six minutes, as Stewart calmly rejected Blair’s theory that any kind of military action can keep the west safe. As Blair stammered, huffed and shifted in his seat, Stewart concluded that: “19 people flew into the towers. It seems hard for me to imagine that we could go to war enough, to make the world safe enough, that 19 people wouldn’t want to do harm to us. So it seems like we have to rethink a strategy that is less military-based.” This was Stewart at his best; it’s also fair to say that some of the interviews, generally those with actors and authors, seem like mere puffery, a point with which Stewart agrees (he embraces criticism as eagerly as he deflects compliments).
How often does he really connect with his interviewees? “Have you seen the show? Mostly, I’m not even listening. But I can bullshit anyone for six minutes.”
When we meet in October, I ask if he is thinking of leaving The Daily Show because he seems increasingly, well, bored, making frequent references to the fact he’s been doing the show “for 75, 80, 1,000 years”.
Facebook Twitter Pinterest Tony Blair gets the Jon Stewart treatment on The Daily Show in 2008.
He bats away my question with a joke: “Are you offering me a job?”
Well, I might be able to get you Guardian work experience.
“Aww, I’m too shitty a writer for that.”
But he doesn’t reject the idea entirely (of leaving The Daily Show, that is. I think The Guardian will have to wait): “[If I left the show,] I would do what I’m doing. Whether it’s standup, the show, books or films, I consider all this just different vehicles to continue a conversation about what it means to be a democratic nation, and to have it written into the constitution that all men are created equal – but to live with that for 100 years with slaves. How do those contradictions play themselves out? And how do we honestly assess our failings and move forward with integrity?”
When I catch up with him again, I ask if he knew he’d be leaving when we had that conversation.
“No, no – but some of it had been in the back of my head for quite some time. But you don’t want to make any kind of decision when you’re in the crucible of the process, just like you don’t decide whether you’re going to continue to run marathons in mile 24,” he says.
Facebook Twitter Pinterest Watch a review of Rosewater
He switches to a chewy exaggeration of his native Noo Joi-zy accent, deflating his seriousness with a comedy voice. “You wait until you’re done, you have a nice cup o’ water, you put the blanket on, you sit and then you decide.”
I had assumed that, as well as the metaphorical cup o’ water, he had decided to quit because he had so much fun making Rosewater. But Stewart says not.
“Honestly, it was a combination of the limitations of my brain and a format that is geared towards following an increasingly redundant process, which is our political process. I was just thinking, ‘Are there other ways to skin this cat?’ And, beyond that, it would be nice to be home when my little elves get home from school, occasionally.”
He has a 10-year-old son, Nathan, and a nine-year-old daughter, Maggie; Stewart and his wife, Tracey, have been married for almost as long as he’s been doing the show, after Stewart proposed to her via a crossword puzzle.
If anything, it was the prospect of the upcoming US election that pushed him to leave the show. “I’d covered an election four times, and it didn’t appear that there was going to be anything wildly different about this one,” he says.
Ah, but who could have anticipated the excitement over Hillary Clinton’s deleted emails?
“Anyone could, because that story is absolutely everything that it’s supposed to be about,” he says, with a groan; as a revelation, it managed to be at once depressing and completely unsurprising. “I also felt that, for the show, you don’t want to leave when the cupboard’s bare. So I think it’s a better introduction when you have something providing you with assisted fuel, like a presidential campaign. But really, the value of this show is so much deeper than my contribution,” he says.
If Oprah can leave and the world still spins, I honestly think it will survive me
Stewart likes to credit “the team”, but given that he has always been deeply involved in the script (unusually for a host), writing and rewriting drafts right up to the last minute, the show will be a pretty different beast without him. He has described his successor, the South African comedian Trevor Noah, as “incredibly thoughtful, considerate and funny”, and defended him when it was discovered, to widespread fury, that Noah had in the past tweeted offensive jokes about Jews, overweight women and transgender people.
The furore over Noah’s tweets reflects just how high Stewart has set the bar. There was such an outpouring of grief when he announced he was stepping down, that he mused on air the following day, “Did I die?” Even the normally dispassionate New Yorker magazine claimed, under the headline Jon Stewart, We Need You In 2016, “the last hope for bringing some rationality to the 2016 Presidential field died”. Not since Oprah Winfrey announced her retirement from network television has a US TV host’s departure received such international coverage, but Stewart bridles when I make the Winfrey comparison: “If Oprah can leave and the world still spins, I honestly think it will survive me.”
And it should be noted that not everyone was distraught. Fox News, displaying its mastery of making colour-based accusations about the kettle from its pot-based position, reported that Stewart was “not a force for good” and that his sustained criticisms of the right “had no foothold in the facts”. The Daily Show duly responded with a Vine of Fox News’ best factual distortions.
Stewart’s 2011 interview with Donald Rumsfeld is one of the few he now regrets: ‘I should have pushed, but he’s very adept at deflecting.’ Photograph: Comedy Central
Does he have any regrets? Stewart recounts one big disappointment – an anodyne interview with Donald Rumsfeld in 2011 that failed to claim the former secretary of defence’s scalp. “He just went into the general gobbledegook.” Stewart puts on a pretty good imitation of Rumsfeld: “‘Mnah mnah mnah, well, you have to remember, it was 9/11 mnah mnah.’ I should have pushed, but he’s very adept at deflecting.” He looks genuinely crushed for a moment, then rallies: “That interview with Rumsfeld went shitty, but it’s still just an interview. He’s the one who has to live with the repercussions of what he really did, so there’s nothing that could happen on my show that carries that same level of regret.”
In 2010, Stewart hosted a Rally To Restore Sanity in Washington DC, attracting 215,000 people, who cheered him on as he berated the media, or “the country’s 24-hour politico–pundit-perpetual-panic-‘conflictinator’.” I covered the rally for the Guardian and, as enjoyable as Stewart was, he didn’t look especially comfortable up on the stage, ginning up the people. He agrees that entering politics “is not my bag”: he’d rather make sense of the mess than get into it himself.
He can be brutal about the leftwing media, too (CNN has been a frequent target, for being mediocre and too attached to pointless computer graphics). MSNBC, the liberal 24-hour news network, is, Stewart says, “better” than Fox News, “because it’s not steeped in distortion and ignorance as a virtue. But they’re both relentless and built for 9/11. So, in the absence of such a catastrophic event, they take the nothing and amplify it and make it craziness.”
My biggest objection to Fox News, I say, is not the scaremongering, it’s the way it’s reshaped the Republican party. It will misrepresent social and economic issues, and promote the more extreme elements of the party, politicians such as Sarah Palin and Mike Huckabee, in a way that is hugely detrimental to American politics. (For the record, Rupert Murdoch disagrees, and last year claimed that Fox News “absolutely saved” the Republican party.) “Watching these channels all day is incredibly depressing,” says Stewart. “I live in a constant state of depression. I think of us as turd miners. I put on my helmet, I go and mine turds, hopefully I don’t get turd lung disease.”
With Maziar Bahari, the Iranian-born journalist imprisoned by Tehran for filming the 2009 anti-government protests. Photograph: Rex Features
Now that he is leaving The Daily Show, is there any circumstance in which he would watch Fox News again? He takes a few seconds to ponder the question. “Umm… All right, let’s say that it’s a nuclear winter, and I have been wandering, and there appears to be a flickering light through what appears to be a radioactive cloud and I think that light might be a food source that could help my family. I might glance at it for a moment until I realise, that’s Fox News, and then I shut it off. That’s the circumstance.”
About a week before we met last year, Piers Morgan, who had just lost his nightly interview show on CNN, loudly blamed news anchor Anderson Cooper, whose show ran before Morgan’s, for his low ratings. Stewart shakes his head in wonder at this claim. “That guy may be the biggest – I mean, isn’t there a room underneath the Tower of London where you can just lock him up? He’s upset because he got shit-kicked. Who’s he going to blame – himself? That would mean self-reflection, of which he is incapable.”
We talk a little about what were then mere rumours that phone hacking had taken place at the Daily Mirror while Morgan was its editor. (It has since been alleged in the high court that hacking was carried out “on an industrial scale” during Morgan’s tenure.) “Right, that is a guy who is a bad person, which is fine – bad people are everywhere,” Stewart shrugs. “But where does something like that come from? Is there a secret fountain of doucheyness somewhere?”
Since he asked, I tell Stewart how Morgan and Simon Cowell became friends in the 1990s, after Morgan helped promote the Cowell-produced singing duo Robson & Jerome in the Sun. When Morgan was fired from the Mirror, Cowell returned the favour by casting him as a judge on his talent shows and, in turn, introducing him to an American TV audience.
Stewart’s face is frozen into a parody of Munch’s The Scream, and he is briefly speechless. “Well,” he eventually says, “all I can say is, ‘Damn you Robson and whatever the other guy’s name was.’ Just awful.”
***
Jon Stuart Leibowitz was born in New York and raised in New Jersey, the son of a teacher and a professor of physics. He grew up in the shadow of the Vietnam war and Watergate, events that left him, he has said in the past, “with a healthy scepticism towards official reports”. He jokingly recalls the time his older brother fired him from his first job at Woolworths as one of the defining, “scarring events” of his youth. But his parents’ divorce when he was 11 was clearly more so, prompting him to drop his surname and eventually legally change it to Stewart. He has described his relationship with his father as still “complicated”. “There was a thought of using my mother’s maiden name, but I thought that would be just too big a fuck you to my dad,” he says. “Did I have some problems with my father? Yes. Yet people always view it [changing his surname] through the prism of ethnic identity.”
Stewart with his children, Nathan and Maggie, in 2011. Photograph: Getty Images
So it was a family thing as opposed to a Jewish thing? “Right. So whenever I criticise Israel’s actions it’s [he puts on a Yiddishy accent] ‘He’s changed his name! He’s not a Jew! He hates himself!’ And I’m like, ‘I hate myself for a lot of reasons, but not because I’m Jewish.’”
After college, Stewart performed on the standup circuit in New York, landing his own talkshow on MTV in the 1990s. In 1999, he took over the then little-loved Daily Show on Comedy Central, turning it from hit-and-miss satire to the news- and politics-focused programme it is today. Coming to it at 38, he says, the job was so ideal, “I couldn’t have created one better”.
Since Stewart announced his departure, much has been written about him being the most trusted news source for young Americans. Stewart kiboshes this as “conventional wisdom. In the sea of information that surrounds people of that generation, I’d be truly surprised if their only news comes four days of the week, for a few minutes a night.” He laughs when I describe him as a celebrity (“I’m not Madonna!” he hoots, raising an eyebrow). The only restriction fame has put on his freedom, he says, is “I don’t hang out on the Upper West Side during Sukkot”. Isn’t he being a bit faux modest, I ask, especially when he insists that what he does is comedy and not news? That comes with a certain profile. He thinks about this for a few seconds. “It’s not that I… I mean, it’s satire, so it’s an expression of real feelings. So I don’t mean that in the sense of, ‘I don’t mean this.’ What I mean is, the tools of satire should not be confused with the tools of news. We use hyperbole, but the underlying sentiment has to feel ethically, intentionally correct, otherwise we wouldn’t do it.”
‘Would I watch Fox News? If it was a nuclear winter and it might help my family’
If Stewart ever needed proof that his show has an impact, he got it in pretty much the worst way possible in October 2009, when he discovered that Iranian guards had arrested Maziar Bahari shortly after he gave an interview to The Daily Show in Iran. “And not just Maziar, but everybody we interviewed there had been arrested. So, being American, we thought, ‘This must be all about us!’” he says.
The Daily Show spoke to the prisoners’ families and asked what they could do to help, and the response was unanimous: keep talking about the arrests on the show. So Stewart did. Ironically, the reason The Daily Show had gone to Iran in the first place was to undermine Bush’s description of the region as “the axis of evil”: Stewart wanted America to see a country populated by “people with families who are wonderful”. And although they found those, the project turned out to be, he says, “a very, uh, sobering experience”.
When Bahari was released after 118 days, Stewart learned that his Iranian guards had cited the (completely benign) Daily Show interview he gave as a justification to torture and imprison him. “And that,” he says, with some understatement, “just stunned me.”
At the Rally to Restore Sanity and/or Fear, in 2010. Photograph: Carolyn Kaster/AP
He and Bahari became friends; when Bahari was in the US, they would meet for breakfast in Manhattan, near Stewart’s Tribeca home. Bahari said he hoped someone would make a movie of his book about his experience, Then They Came For Me. Stewart helped Bahari contact screenwriters, only to find that most were already busy, and he started to get, he says, “impatient with the process”. So, over oatmeal in a coffee shop, he and Bahari decided Stewart would write and direct the film himself.
Rosewater focuses primarily on the relationship between Bahari (Gael García Bernal) and one particular jailer, played by Kim Bodnia (Martin in Scandinavian TV thriller The Bridge). The movie wears its liberal heart on its sleeve, but reins in the tub-thumping for the sake of the story. Experts in Iranian relations will no doubt find the depiction of the government a little simplistic, and Stewart, characteristically, agrees.
“Look, it’s a film about Iran made by a New York Jew – it’s going to be reductive for those who are from the region. But hopefully, for an audience that is more western and more accustomed to films like Not Without My Daughter, this will appear to be a relatively nuanced portrayal. I got a whole pantheon of Sally Field references in here,” he grins, tapping his head, a reference to the hysterically anti-Iranian 1991 film.
A more obvious criticism is the lack of Iranian actors: Kim Bodnia, as Rosewater, is Danish and Bernal is Mexican. Stewart, again, concedes the point. “If I was Iranian, I’d probably look at [Bernal] and be like, ‘Really? Those Rs? Come on, man.’ But Maziar was our touchstone, and if he wasn’t bothered by it, I wasn’t bothered by it. My original vision was, ‘Maziar, we’re going to do this in Persian and use real prisoners and it’s going to be only Iranians!’ And he was like, ‘Don’t you want people to see it?’”
He did, but ultimately not that many people did, at least in the US. The film got decent reviews, but made only $3m – it turns out not that many Americans want to see a film about an Iranian prisoner. For once, perhaps, Stewart was just that little bit too progressive, something he has joked about on The Daily Show, mock weeping.
How disappointed was he? “Oh, sure, I would have liked more people to have seen it. But it’s a ridiculous thing to say. We got to prepare this incredible meal and then at the very end say, ‘Aww, I wish more people came.’ I don’t actually feel that way. I always knew the movie wasn’t The Hunger Games. But I hope it finds a little foothold in the UK.”
For the next few months, Stewart will focus on The Daily Show, handing over to Trevor Noah later this year and trying to convince viewers that it will be just fine without him. He has, he says, “a couple of other projects on the burner” – he would like to make more films – and it’s impossible to imagine him in fallow retirement. But it won’t be quite the same for us fans, getting to watch him every night, having him translate the day’s news for us. Stewart would scoff, but, for liberals who care about American politics, his departure from The Daily Show marks the end of an era.
“Honestly,” he says, “the country will survive.” And he’s right, it will. But even as he says it, it sounds, somewhat heartbreakingly, as if he’s already out that door.
• Rosewater is released on 8 May. The Daily Show is on Comedy Central (times vary). ||||| You're awesome!
That's right! Your browser is up-to-date, which means you can use YouTube's latest features. Enjoy! | – Jon Stewart has long said he'd tired of the grind on The Daily Show and that his "dissatisfaction" led to his 2015 departure. But in a recent behind-the-scenes chat with Stewart's replacement, Trevor Noah, and other show staffers, Noah reveals Stewart was facing a stronger emotion than dissatisfaction. Noah says when he found out his boss was leaving, he confronted him to find out why, saying he'd fight for him if he was being forced out. But Stewart confessed he was "tired"—and more. "He said, 'I'm angry all the time,'" Noah says. "'I don't find any of this funny. I do not know how to make it funny right now, and I don't think the host of the show ... deserves a host who does not feel that it is funny.'" Stewart also told Noah to "relish the fact that you can make jokes about these things ... because there will come a day when you are too angry to laugh. But don't rush to get there. You're young and you're fresh." Noah appears to have taken Stewart's advice to heart. In an IndieWire interview last year, he said when people would ask him where his "rage" was, he'd answer: "Why would I be angry? What would my rage stem from?" Instead, he noted, he wants to connect with his audience in a more neutral way. "I am selling you a home and a little space that we can share together to process what is happening in our lives," he said, adding that he prefers to replace "rage" with "an incredulousness." Watch the entire hourlong panel here (the relevant bit starts around 28:30.) | <s>[INST]"The Daily Show with Trevor Noah" is on the rise, and yes, the Trump Administration has something to do with that. But Comedy Central credits the host for taking a different approach than his competitors.
Donald Trump hasn’t yet gone after “The Daily Show,” and that’s fine by host Trevor Noah.
“I don’t think Trump’s attack is the mark of a good show,” he told IndieWire last month, after taping an episode in his Midtown Manhattan studio. “People always go, ‘He’s attacking ‘SNL.’ Actually, he is attacking Alec Baldwin. That’s what gets to him, the fact that that’s whom he aspires to. That’s a New York guy. That’s the face of fame for him. He has his peers that he wants to be associated with, and everyone else he doesn’t really care about. That’s part of the problem of Donald Trump. He lives in his own world.”
And it turns out, Noah is doing very well without Trump’s seal of disapproval. Just 18 months after Noah took over the Comedy Central franchise from Jon Stewart, “The Daily Show” finished the first quarter of 2017 with its best ratings since the host transition. It is the only daily late-night talk show this year to enjoy year-to-year improvement among both total viewers and adults 18-49.
It’s a solid turnaround for “The Daily Show” and Comedy Central, which took more than a few lumps after losing marquee talents Stewart, Stephen Colbert, John Oliver, and Samantha Bee over the course of a year. (More recently, the network canceled “The Nightly Show with Larry Wilmore” due to low ratings.) Noah also had a bumpy start before even taking over, as several of his old Twitter posts were criticized for being offensive.
Comedy Central
Comedy Central has always stressed that hiring Noah was about recalibrating “The Daily Show” for a new, younger generation, and it is doing particularly well with young viewers, surpassing “The Tonight Show Starring Jimmy Fallon” as the top late-night talk show among millennials under 25, and it’s now the No. 1 late-night talk show with men under 35.
“Our whole orientation was, if we try to replace Jon Stewart with just a younger version of Jon Stewart, it’s a fool’s errand and will never work,” said Comedy Central president Kent Alterman. “Our gut instinct about him is being borne out. I never really had any doubts about [Noah], and we never had doubts that it would take time. No matter how much I said that publicly it didn’t matter, people always thought the obligation was to compare Trevor’s Day 1 to Jon’s last day after 16 years. We always told people that we didn’t hire Trevor for his experience; we hired him for his talent and his brain.”
Noah is the first to credit the Trump Effect for giving “The Daily Show” renewed purpose and vigor.
“We’re in a world where maybe, for a certain amount of people, there was no need for a late-night satirical show in their lives when it was presumed that Hillary Clinton would win,” he said. “[When that didn’t happen], we felt the click in the show. I felt it in myself as a person. You feel that there is a fear and a tension, and when that tension rises, comedy is oftentimes the release.”
READ MORE: ‘Donald Trump’ Promises to Make Late Night Great Again with Comedy Central’s ‘The President Show’
Noah now sees his early days hosting “The Daily Show” during the presidential campaign as training for how to handle the job under a Trump administration. “Before the election and leading up to it, I remember people were like, ‘Why aren’t you more angry? Where’s your rage?’ I said, ‘Why would I be angry? What would my rage stem from? What is my origin story, for me to all of a sudden be this character you think I should be?’
“All I did was read; I learned. In essence, I’ve realized now that I was learning at the same time as Donald Trump was. We were learning about the country at the same time. The only difference is, I feel like I still read my briefings and he doesn’t.”
Noah’s growing knowledge is on display every night on “The Daily Show” set, even in between commercials. One night, he gave the crowd a succinct play-by-play of how House Speaker Paul Ryan had painted the Republicans in a corner by trying to push through Trumpcare so fast (something that later played out the way Noah had predicted). Some of those impromptu chats have wound up on “The Daily Show’s” social media channels, which have seen YouTube and Facebook video viewership grow by 200% over the last year.
Meanwhile, Alterman has heard the criticism that Noah isn’t angry enough on air, but believes it’s a complaint coming mostly from older viewers.
“Our research shows younger people don’t feel that way,” he said. “One thing that sets Trevor apart is he can take these strong positions and really go after whatever targets are out there, but he doesn’t do it in a dogmatic yelling way.”
Early on in the Trump campaign, Noah said he purposely approached it from a neutral perspective. “That’s why very early on, I said, ‘I can see how Trump’s connecting. I can see why I think he won that debate.’ People are like, ‘Are you mad?’ Even as a person who’s just come into it, very quickly you realize that there is an artificial middle that has been created and facts and truth and honesty are almost artifacts of a bygone era.”
(STORY CONTINUES ON NEXT PAGE)
Sign Up: Stay on top of the latest breaking film and TV news! Sign up for our Email Newsletters here. ||||| Stewart’s decision to retire as host of the satirical news show after 16 years has left liberal America in mourning. So why is he leaving just before an election – and what will happen when he steps out from behind the desk?
There was no one moment when Jon Stewart knew it was time for him to leave what he describes as “the most perfect job in the world”; no epiphany, no flashpoint. “Life,” he says, in the lightly self-mocking tone he uses when talking about himself, “doesn’t really work that way, with a finger pointing at you out of the sky, saying, ‘Leave now!’ That only happens when you’re fired, and trust me, I know about that.”
Instead, he describes his decision to quit The Daily Show, the American satirical news programme he has hosted for 16 years, as something closer to the end of a long-term relationship. “It’s not like I thought the show wasn’t working any more, or that I didn’t know how to do it. It was more, ‘Yup, it’s working. But I’m not getting the same satisfaction.’” He slaps his hands on his desk, conclusively.
“These things are cyclical. You have moments of dissatisfaction, and then you come out of it and it’s OK. But the cycles become longer and maybe more entrenched, and that’s when you realise, ‘OK, I’m on the back side of it now.’”
Facebook Twitter Pinterest Stewart announces he is to leave The Daily Show
Stewart and I speak twice in the space of a few months. The first time last October, when he flew from New York to London with his family for the premiere of his directorial debut at the London Film Festival. Rosewater is an engrossing and pacy film that tells the true story of Iranian-born journalist Maziar Bahari, who was arrested and tortured in Iran in 2009, after sending footage of street riots to the BBC.
The second time, we speak soon after Stewart announces his retirement from The Daily Show. He is in his office in New York, preparing to shoot a Friday-night episode, and the difference in his mood is striking. His voice is about an octave lower, and he sounds weary, weighed down.
But talking about his film in London, he is animated to the point of hyperactivity, gleefully pointing out the pretentious decor in the hotel room where we meet (“A photo of a submissive woman with a cigar in her mouth! Just what every room needs!”). He notes, in a tone that is both sincere and satirical, and that will be familiar to fans of The Daily Show, the lavishness of the food: “My compliments to the prop master, because that really is a beautiful tomato and mozzarella salad,” he intones solemnly to a bemused waiter.
It was heartbreaking interviewing Obama... that's what the gig is
Like every TV celebrity, in person, Stewart is both better-looking than you expect and smaller, with his long torso making up most of his 5ft 7in, giving the illusion of height from behind his studio desk. He is dressed casually, and after years of watching him on TV wearing a suit, seeing him in a T-shirt and casual trousers feels almost like catching my father half-undressed.
At 52, Stewart has the bouncy energy of a man half his age and, unlike most in the public eye, has an aversion to compliments. If I tell him I liked something about the film, he will immediately deflect the compliment and insist it was all down to Bahari, or the film’s star Gael García Bernal, or the crew. For all the claims of his detractors that Stewart is the epitome of East Coast elitism, there is more self-deprecating New Jersey grit here than arrogant Manhattan elan.
Much as he might wince to hear it, for the past 16 years Stewart has occupied a place in America’s cultural and political life far greater than the small audience of his cable show would suggest. The Daily Show’s simple format consists of a mix of reports from roving reporters (who have included Steve Carell, Stephen Colbert and John Oliver), monologues delivered by Stewart and an end-of-show interview. Over time, Stewart has evolved from a satirist to a broadcaster celebrated as the voice of US liberalism, the one who will give the definitive progressive take on a story.
Facebook Twitter Pinterest Stewart on the Charlie Hebdo murders
His moving monologue after the Charlie Hebdo killings in January was widely shared; his frequent on-air support of Democrat senator Elizabeth Warren helped her evolve in the eyes of the public from Harvard professor to dream 2016 presidential candidate – particularly among those who find Hillary Clinton too centrist and hawkish. Stewart’s energetic campaigning on behalf of the 9/11 first responders (the emergency services who were first on the scene, many of whom later suffered debilitating illnesses), prompted the New York Times to compare him to Walter Cronkite and Edward R Murrow, the most revered newscasters in American history. It is a delicious irony that in the world of American TV news, one populated by raging egotists and self-aggrandisers, the person who is generally cited as the most influential is Stewart – a man so disinterested in his own celebrity, he often didn’t bother to collect his 18 Emmys, preferring to stay at home with his family.
When George Bush left office in 2008, some worried that Stewart would run out of material. This proved as shortsighted as the hope that Obama would be America’s grand salvation. Stewart, who describes himself as “a leftist”, has always hammered the Democrats with the vigour of a disappointed supporter, and subjected Obama to one of his most damaging interviews during his first term: the president admitted that his 2008 slogan probably should have been “Yes We Can, But...” At the time, Stewart laughed, but today he admits with a shrug, “It was heartbreaking. It’s generally heartbreaking – that’s what the gig is.”
Facebook Twitter Pinterest Stewart gave Barack Obama one of his toughest interviews, suggesting his 2008 election slogan should have been ‘Yes we can, but…’ Photograph: Empics Entertainment
His seemingly effortless interview with Tony Blair in 2008 cut through Blair’s crusader mentality in a mere six minutes, as Stewart calmly rejected Blair’s theory that any kind of military action can keep the west safe. As Blair stammered, huffed and shifted in his seat, Stewart concluded that: “19 people flew into the towers. It seems hard for me to imagine that we could go to war enough, to make the world safe enough, that 19 people wouldn’t want to do harm to us. So it seems like we have to rethink a strategy that is less military-based.” This was Stewart at his best; it’s also fair to say that some of the interviews, generally those with actors and authors, seem like mere puffery, a point with which Stewart agrees (he embraces criticism as eagerly as he deflects compliments).
How often does he really connect with his interviewees? “Have you seen the show? Mostly, I’m not even listening. But I can bullshit anyone for six minutes.”
When we meet in October, I ask if he is thinking of leaving The Daily Show because he seems increasingly, well, bored, making frequent references to the fact he’s been doing the show “for 75, 80, 1,000 years”.
Facebook Twitter Pinterest Tony Blair gets the Jon Stewart treatment on The Daily Show in 2008.
He bats away my question with a joke: “Are you offering me a job?”
Well, I might be able to get you Guardian work experience.
“Aww, I’m too shitty a writer for that.”
But he doesn’t reject the idea entirely (of leaving The Daily Show, that is. I think The Guardian will have to wait): “[If I left the show,] I would do what I’m doing. Whether it’s standup, the show, books or films, I consider all this just different vehicles to continue a conversation about what it means to be a democratic nation, and to have it written into the constitution that all men are created equal – but to live with that for 100 years with slaves. How do those contradictions play themselves out? And how do we honestly assess our failings and move forward with integrity?”
When I catch up with him again, I ask if he knew he’d be leaving when we had that conversation.
“No, no – but some of it had been in the back of my head for quite some time. But you don’t want to make any kind of decision when you’re in the crucible of the process, just like you don’t decide whether you’re going to continue to run marathons in mile 24,” he says.
Facebook Twitter Pinterest Watch a review of Rosewater
He switches to a chewy exaggeration of his native Noo Joi-zy accent, deflating his seriousness with a comedy voice. “You wait until you’re done, you have a nice cup o’ water, you put the blanket on, you sit and then you decide.”
I had assumed that, as well as the metaphorical cup o’ water, he had decided to quit because he had so much fun making Rosewater. But Stewart says not.
“Honestly, it was a combination of the limitations of my brain and a format that is geared towards following an increasingly redundant process, which is our political process. I was just thinking, ‘Are there other ways to skin this cat?’ And, beyond that, it would be nice to be home when my little elves get home from school, occasionally.”
He has a 10-year-old son, Nathan, and a nine-year-old daughter, Maggie; Stewart and his wife, Tracey, have been married for almost as long as he’s been doing the show, after Stewart proposed to her via a crossword puzzle.
If anything, it was the prospect of the upcoming US election that pushed him to leave the show. “I’d covered an election four times, and it didn’t appear that there was going to be anything wildly different about this one,” he says.
Ah, but who could have anticipated the excitement over Hillary Clinton’s deleted emails?
“Anyone could, because that story is absolutely everything that it’s supposed to be about,” he says, with a groan; as a revelation, it managed to be at once depressing and completely unsurprising. “I also felt that, for the show, you don’t want to leave when the cupboard’s bare. So I think it’s a better introduction when you have something providing you with assisted fuel, like a presidential campaign. But really, the value of this show is so much deeper than my contribution,” he says.
If Oprah can leave and the world still spins, I honestly think it will survive me
Stewart likes to credit “the team”, but given that he has always been deeply involved in the script (unusually for a host), writing and rewriting drafts right up to the last minute, the show will be a pretty different beast without him. He has described his successor, the South African comedian Trevor Noah, as “incredibly thoughtful, considerate and funny”, and defended him when it was discovered, to widespread fury, that Noah had in the past tweeted offensive jokes about Jews, overweight women and transgender people.
The furore over Noah’s tweets reflects just how high Stewart has set the bar. There was such an outpouring of grief when he announced he was stepping down, that he mused on air the following day, “Did I die?” Even the normally dispassionate New Yorker magazine claimed, under the headline Jon Stewart, We Need You In 2016, “the last hope for bringing some rationality to the 2016 Presidential field died”. Not since Oprah Winfrey announced her retirement from network television has a US TV host’s departure received such international coverage, but Stewart bridles when I make the Winfrey comparison: “If Oprah can leave and the world still spins, I honestly think it will survive me.”
And it should be noted that not everyone was distraught. Fox News, displaying its mastery of making colour-based accusations about the kettle from its pot-based position, reported that Stewart was “not a force for good” and that his sustained criticisms of the right “had no foothold in the facts”. The Daily Show duly responded with a Vine of Fox News’ best factual distortions.
Stewart’s 2011 interview with Donald Rumsfeld is one of the few he now regrets: ‘I should have pushed, but he’s very adept at deflecting.’ Photograph: Comedy Central
Does he have any regrets? Stewart recounts one big disappointment – an anodyne interview with Donald Rumsfeld in 2011 that failed to claim the former secretary of defence’s scalp. “He just went into the general gobbledegook.” Stewart puts on a pretty good imitation of Rumsfeld: “‘Mnah mnah mnah, well, you have to remember, it was 9/11 mnah mnah.’ I should have pushed, but he’s very adept at deflecting.” He looks genuinely crushed for a moment, then rallies: “That interview with Rumsfeld went shitty, but it’s still just an interview. He’s the one who has to live with the repercussions of what he really did, so there’s nothing that could happen on my show that carries that same level of regret.”
In 2010, Stewart hosted a Rally To Restore Sanity in Washington DC, attracting 215,000 people, who cheered him on as he berated the media, or “the country’s 24-hour politico–pundit-perpetual-panic-‘conflictinator’.” I covered the rally for the Guardian and, as enjoyable as Stewart was, he didn’t look especially comfortable up on the stage, ginning up the people. He agrees that entering politics “is not my bag”: he’d rather make sense of the mess than get into it himself.
He can be brutal about the leftwing media, too (CNN has been a frequent target, for being mediocre and too attached to pointless computer graphics). MSNBC, the liberal 24-hour news network, is, Stewart says, “better” than Fox News, “because it’s not steeped in distortion and ignorance as a virtue. But they’re both relentless and built for 9/11. So, in the absence of such a catastrophic event, they take the nothing and amplify it and make it craziness.”
My biggest objection to Fox News, I say, is not the scaremongering, it’s the way it’s reshaped the Republican party. It will misrepresent social and economic issues, and promote the more extreme elements of the party, politicians such as Sarah Palin and Mike Huckabee, in a way that is hugely detrimental to American politics. (For the record, Rupert Murdoch disagrees, and last year claimed that Fox News “absolutely saved” the Republican party.) “Watching these channels all day is incredibly depressing,” says Stewart. “I live in a constant state of depression. I think of us as turd miners. I put on my helmet, I go and mine turds, hopefully I don’t get turd lung disease.”
With Maziar Bahari, the Iranian-born journalist imprisoned by Tehran for filming the 2009 anti-government protests. Photograph: Rex Features
Now that he is leaving The Daily Show, is there any circumstance in which he would watch Fox News again? He takes a few seconds to ponder the question. “Umm… All right, let’s say that it’s a nuclear winter, and I have been wandering, and there appears to be a flickering light through what appears to be a radioactive cloud and I think that light might be a food source that could help my family. I might glance at it for a moment until I realise, that’s Fox News, and then I shut it off. That’s the circumstance.”
About a week before we met last year, Piers Morgan, who had just lost his nightly interview show on CNN, loudly blamed news anchor Anderson Cooper, whose show ran before Morgan’s, for his low ratings. Stewart shakes his head in wonder at this claim. “That guy may be the biggest – I mean, isn’t there a room underneath the Tower of London where you can just lock him up? He’s upset because he got shit-kicked. Who’s he going to blame – himself? That would mean self-reflection, of which he is incapable.”
We talk a little about what were then mere rumours that phone hacking had taken place at the Daily Mirror while Morgan was its editor. (It has since been alleged in the high court that hacking was carried out “on an industrial scale” during Morgan’s tenure.) “Right, that is a guy who is a bad person, which is fine – bad people are everywhere,” Stewart shrugs. “But where does something like that come from? Is there a secret fountain of doucheyness somewhere?”
Since he asked, I tell Stewart how Morgan and Simon Cowell became friends in the 1990s, after Morgan helped promote the Cowell-produced singing duo Robson & Jerome in the Sun. When Morgan was fired from the Mirror, Cowell returned the favour by casting him as a judge on his talent shows and, in turn, introducing him to an American TV audience.
Stewart’s face is frozen into a parody of Munch’s The Scream, and he is briefly speechless. “Well,” he eventually says, “all I can say is, ‘Damn you Robson and whatever the other guy’s name was.’ Just awful.”
***
Jon Stuart Leibowitz was born in New York and raised in New Jersey, the son of a teacher and a professor of physics. He grew up in the shadow of the Vietnam war and Watergate, events that left him, he has said in the past, “with a healthy scepticism towards official reports”. He jokingly recalls the time his older brother fired him from his first job at Woolworths as one of the defining, “scarring events” of his youth. But his parents’ divorce when he was 11 was clearly more so, prompting him to drop his surname and eventually legally change it to Stewart. He has described his relationship with his father as still “complicated”. “There was a thought of using my mother’s maiden name, but I thought that would be just too big a fuck you to my dad,” he says. “Did I have some problems with my father? Yes. Yet people always view it [changing his surname] through the prism of ethnic identity.”
Stewart with his children, Nathan and Maggie, in 2011. Photograph: Getty Images
So it was a family thing as opposed to a Jewish thing? “Right. So whenever I criticise Israel’s actions it’s [he puts on a Yiddishy accent] ‘He’s changed his name! He’s not a Jew! He hates himself!’ And I’m like, ‘I hate myself for a lot of reasons, but not because I’m Jewish.’”
After college, Stewart performed on the standup circuit in New York, landing his own talkshow on MTV in the 1990s. In 1999, he took over the then little-loved Daily Show on Comedy Central, turning it from hit-and-miss satire to the news- and politics-focused programme it is today. Coming to it at 38, he says, the job was so ideal, “I couldn’t have created one better”.
Since Stewart announced his departure, much has been written about him being the most trusted news source for young Americans. Stewart kiboshes this as “conventional wisdom. In the sea of information that surrounds people of that generation, I’d be truly surprised if their only news comes four days of the week, for a few minutes a night.” He laughs when I describe him as a celebrity (“I’m not Madonna!” he hoots, raising an eyebrow). The only restriction fame has put on his freedom, he says, is “I don’t hang out on the Upper West Side during Sukkot”. Isn’t he being a bit faux modest, I ask, especially when he insists that what he does is comedy and not news? That comes with a certain profile. He thinks about this for a few seconds. “It’s not that I… I mean, it’s satire, so it’s an expression of real feelings. So I don’t mean that in the sense of, ‘I don’t mean this.’ What I mean is, the tools of satire should not be confused with the tools of news. We use hyperbole, but the underlying sentiment has to feel ethically, intentionally correct, otherwise we wouldn’t do it.”
‘Would I watch Fox News? If it was a nuclear winter and it might help my family’
If Stewart ever needed proof that his show has an impact, he got it in pretty much the worst way possible in October 2009, when he discovered that Iranian guards had arrested Maziar Bahari shortly after he gave an interview to The Daily Show in Iran. “And not just Maziar, but everybody we interviewed there had been arrested. So, being American, we thought, ‘This must be all about us!’” he says.
The Daily Show spoke to the prisoners’ families and asked what they could do to help, and the response was unanimous: keep talking about the arrests on the show. So Stewart did. Ironically, the reason The Daily Show had gone to Iran in the first place was to undermine Bush’s description of the region as “the axis of evil”: Stewart wanted America to see a country populated by “people with families who are wonderful”. And although they found those, the project turned out to be, he says, “a very, uh, sobering experience”.
When Bahari was released after 118 days, Stewart learned that his Iranian guards had cited the (completely benign) Daily Show interview he gave as a justification to torture and imprison him. “And that,” he says, with some understatement, “just stunned me.”
At the Rally to Restore Sanity and/or Fear, in 2010. Photograph: Carolyn Kaster/AP
He and Bahari became friends; when Bahari was in the US, they would meet for breakfast in Manhattan, near Stewart’s Tribeca home. Bahari said he hoped someone would make a movie of his book about his experience, Then They Came For Me. Stewart helped Bahari contact screenwriters, only to find that most were already busy, and he started to get, he says, “impatient with the process”. So, over oatmeal in a coffee shop, he and Bahari decided Stewart would write and direct the film himself.
Rosewater focuses primarily on the relationship between Bahari (Gael García Bernal) and one particular jailer, played by Kim Bodnia (Martin in Scandinavian TV thriller The Bridge). The movie wears its liberal heart on its sleeve, but reins in the tub-thumping for the sake of the story. Experts in Iranian relations will no doubt find the depiction of the government a little simplistic, and Stewart, characteristically, agrees.
“Look, it’s a film about Iran made by a New York Jew – it’s going to be reductive for those who are from the region. But hopefully, for an audience that is more western and more accustomed to films like Not Without My Daughter, this will appear to be a relatively nuanced portrayal. I got a whole pantheon of Sally Field references in here,” he grins, tapping his head, a reference to the hysterically anti-Iranian 1991 film.
A more obvious criticism is the lack of Iranian actors: Kim Bodnia, as Rosewater, is Danish and Bernal is Mexican. Stewart, again, concedes the point. “If I was Iranian, I’d probably look at [Bernal] and be like, ‘Really? Those Rs? Come on, man.’ But Maziar was our touchstone, and if he wasn’t bothered by it, I wasn’t bothered by it. My original vision was, ‘Maziar, we’re going to do this in Persian and use real prisoners and it’s going to be only Iranians!’ And he was like, ‘Don’t you want people to see it?’”
He did, but ultimately not that many people did, at least in the US. The film got decent reviews, but made only $3m – it turns out not that many Americans want to see a film about an Iranian prisoner. For once, perhaps, Stewart was just that little bit too progressive, something he has joked about on The Daily Show, mock weeping.
How disappointed was he? “Oh, sure, I would have liked more people to have seen it. But it’s a ridiculous thing to say. We got to prepare this incredible meal and then at the very end say, ‘Aww, I wish more people came.’ I don’t actually feel that way. I always knew the movie wasn’t The Hunger Games. But I hope it finds a little foothold in the UK.”
For the next few months, Stewart will focus on The Daily Show, handing over to Trevor Noah later this year and trying to convince viewers that it will be just fine without him. He has, he says, “a couple of other projects on the burner” – he would like to make more films – and it’s impossible to imagine him in fallow retirement. But it won’t be quite the same for us fans, getting to watch him every night, having him translate the day’s news for us. Stewart would scoff, but, for liberals who care about American politics, his departure from The Daily Show marks the end of an era.
“Honestly,” he says, “the country will survive.” And he’s right, it will. But even as he says it, it sounds, somewhat heartbreakingly, as if he’s already out that door.
• Rosewater is released on 8 May. The Daily Show is on Comedy Central (times vary). ||||| You're awesome!
That's right! Your browser is up-to-date, which means you can use YouTube's latest features. Enjoy![/INST]– Jon Stewart has long said he'd tired of the grind on The Daily Show and that his "dissatisfaction" led to his 2015 departure. But in a recent behind-the-scenes chat with Stewart's replacement, Trevor Noah, and other show staffers, Noah reveals Stewart was facing a stronger emotion than dissatisfaction. Noah says when he found out his boss was leaving, he confronted him to find out why, saying he'd fight for him if he was being forced out. But Stewart confessed he was "tired"—and more. "He said, 'I'm angry all the time,'" Noah says. "'I don't find any of this funny. I do not know how to make it funny right now, and I don't think the host of the show ... deserves a host who does not feel that it is funny.'" Stewart also told Noah to "relish the fact that you can make jokes about these things ... because there will come a day when you are too angry to laugh. But don't rush to get there. You're young and you're fresh." Noah appears to have taken Stewart's advice to heart. In an IndieWire interview last year, he said when people would ask him where his "rage" was, he'd answer: "Why would I be angry? What would my rage stem from?" Instead, he noted, he wants to connect with his audience in a more neutral way. "I am selling you a home and a little space that we can share together to process what is happening in our lives," he said, adding that he prefers to replace "rage" with "an incredulousness." Watch the entire hourlong panel here (the relevant bit starts around 28:30.)</s> |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Water Supply Permitting Coordination
Act''.
SEC. 2. DEFINITIONS.
In this Act:
(1) Bureau.--The term ``Bureau'' means the Bureau of
Reclamation.
(2) Cooperating agencies.--The term ``cooperating agency''
means a Federal agency with jurisdiction over a review,
analysis, opinion, statement, permit, license, or other
approval or decision required for a qualifying project under
applicable Federal laws and regulations, or a State agency
subject to section 3(c).
(3) Qualifying projects.--The term ``qualifying projects''
means new surface water storage projects in the States covered
under the Act of June 17, 1902 (32 Stat. 388, chapter 1093),
and Acts supplemental to and amendatory of that Act (43 U.S.C.
371 et seq.) constructed on lands administered by the
Department of the Interior or the Department of Agriculture,
exclusive of any easement, right-of-way, lease, or any private
holding.
(4) Secretary.--The term ``Secretary'' means the Secretary
of the Interior.
SEC. 3. ESTABLISHMENT OF LEAD AGENCY AND COOPERATING AGENCIES.
(a) Establishment of Lead Agency.--The Bureau is established as the
lead agency for purposes of coordinating all reviews, analyses,
opinions, statements, permits, licenses, or other approvals or
decisions required under Federal law to construct qualifying projects.
(b) Identification and Establishment of Cooperating Agencies.--The
Commissioner of the Bureau shall--
(1) identify, as early as practicable upon receipt of an
application for a qualifying project, any Federal agency that
may have jurisdiction over a review, analysis, opinion,
statement, permit, license, approval, or decision required for
a qualifying project under applicable Federal laws and
regulations; and
(2) notify any such agency, within a reasonable timeframe,
that the agency has been designated as a cooperating agency in
regards to the qualifying project unless that agency responds
to the Bureau in writing, within a timeframe set forth by the
Bureau, notifying the Bureau that the agency--
(A) has no jurisdiction or authority with respect
to the qualifying project;
(B) has no expertise or information relevant to the
qualifying project or any review, analysis, opinion,
statement, permit, license, or other approval or
decision associated therewith; or
(C) does not intend to submit comments on the
qualifying project or conduct any review of such a
project or make any decision with respect to such
project in a manner other than in cooperation with the
Bureau.
(c) State Authority.--A State in which a qualifying project is
being considered may choose, consistent with State law--
(1) to participate as a cooperating agency; and
(2) to make subject to the processes of this Act all State
agencies that--
(A) have jurisdiction over the qualifying project;
(B) are required to conduct or issue a review,
analysis, or opinion for the qualifying project; or
(C) are required to make a determination on issuing
a permit, license, or approval for the qualifying
project.
SEC. 4. BUREAU RESPONSIBILITIES.
(a) In General.--The principal responsibilities of the Bureau under
this Act are--
(1) to serve as the point of contact for applicants, State
agencies, Indian tribes, and others regarding proposed
qualifying projects;
(2) to coordinate preparation of unified environmental
documentation that will serve as the basis for all Federal
decisions necessary to authorize the use of Federal lands for
qualifying projects; and
(3) to coordinate all Federal agency reviews necessary for
project development and construction of qualifying projects.
(b) Coordination Process.--The Bureau shall have the following
coordination responsibilities:
(1) Preapplication coordination.--Notify cooperating
agencies of proposed qualifying projects not later than 30 days
after receipt of a proposal and facilitate a preapplication
meeting for prospective applicants, relevant Federal and State
agencies, and Indian tribes--
(A) to explain applicable processes, data
requirements, and applicant submissions necessary to
complete the required Federal agency reviews within the
timeframe established; and
(B) to establish the schedule for the qualifying
project.
(2) Consultation with cooperating agencies.--Consult with
the cooperating agencies throughout the Federal agency review
process, identify and obtain relevant data in a timely manner,
and set necessary deadlines for cooperating agencies.
(3) Schedule.--Work with the qualifying project applicant
and cooperating agencies to establish a project schedule. In
establishing the schedule, the Bureau shall consider, among
other factors--
(A) the responsibilities of cooperating agencies
under applicable laws and regulations;
(B) the resources available to the cooperating
agencies and the non-Federal qualifying project
sponsor, as applicable;
(C) the overall size and complexity of the
qualifying project;
(D) the overall schedule for and cost of the
qualifying project; and
(E) the sensitivity of the natural and historic
resources that may be affected by the qualifying
project.
(4) Environmental compliance.--Prepare a unified
environmental review document for each qualifying project
application, incorporating a single environmental record on
which all cooperating agencies with authority to issue
approvals for a given qualifying project shall base project
approval decisions. Help ensure that cooperating agencies make
necessary decisions, within their respective authorities,
regarding Federal approvals in accordance with the following
timelines:
(A) Not later than 1 year after acceptance of a
completed project application when an environmental
assessment and finding of no significant impact is
determined to be the appropriate level of review under
the National Environmental Policy Act of 1969 (42
U.S.C. 4321 et seq.).
(B) Not later than 1 year and 30 days after the
close of the public comment period for a draft
environmental impact statement under the National
Environmental Policy Act of 1969 (42 U.S.C. 4321 et
seq.), when an environmental impact statement is
required under the same.
(5) Consolidated administrative record.--Maintain a
consolidated administrative record of the information assembled
and used by the cooperating agencies as the basis for agency
decisions.
(6) Project data records.--To the extent practicable and
consistent with Federal law, ensure that all project data is
submitted and maintained in generally accessible electronic
format, compile, and where authorized under existing law, make
available such project data to cooperating agencies, the
qualifying project applicant, and to the public.
(7) Project manager.--Appoint a project manager for each
qualifying project. The project manager shall have authority to
oversee the project and to facilitate the issuance of the
relevant final authorizing documents, and shall be responsible
for ensuring fulfillment of all Bureau responsibilities set
forth in this section and all cooperating agency
responsibilities under section 5.
SEC. 5. COOPERATING AGENCY RESPONSIBILITIES.
(a) Adherence to Bureau Schedule.--
(1) Timeframes.--On notification of an application for a
qualifying project, the head of each cooperating agency shall
submit to the Bureau a timeframe under which the cooperating
agency reasonably will be able to complete the authorizing
responsibilities of the cooperating agency.
(2) Schedule.--
(A) Use of timeframes.--The Bureau shall use the
timeframes submitted under this subsection to establish
the project schedule under section 4.
(B) Adherence.--Each cooperating agency shall
adhere to the project schedule established by the
Bureau under subparagraph (A).
(b) Environmental Record.--The head of each cooperating agency
shall submit to the Bureau all environmental review material produced
or compiled in the course of carrying out activities required under
Federal law, consistent with the project schedule established by the
Bureau under subsection (a)(2).
(c) Data Submission.--To the extent practicable and consistent with
Federal law, the head of each cooperating agency shall submit all
relevant project data to the Bureau in a generally accessible
electronic format, subject to the project schedule established by the
Bureau under subsection (a)(2).
SEC. 6. FUNDING TO PROCESS PERMITS.
(a) In General.--The Secretary, after public notice in accordance
with subchapter II of chapter 5, and chapter 7, of title 5, United
States Code (commonly known as the ``Administrative Procedure Act''),
may accept and expend funds contributed by a non-Federal public entity
to expedite the evaluation of a permit of that entity related to a
qualifying project.
(b) Effect on Permitting.--
(1) In general.--In carrying out this section, the
Secretary shall ensure that the use of funds accepted under
subsection (a) will not substantively or procedurally impact
impartial decisionmaking with respect to permits.
(2) Evaluation of permits.--In carrying out this section,
the Secretary shall ensure that the evaluation of permits
carried out using funds accepted under this section shall--
(A) be reviewed by the Regional Director of the
Bureau of the region in which the qualifying project or
activity is located (or a designee); and
(B) use the same procedures for decisions that
would otherwise be required for the evaluation of
permits for similar projects or activities not carried
out using funds authorized under this section.
(3) Impartial decisionmaking.--In carrying out this
section, the Secretary and the head of each cooperating agency
receiving funds under this section for a qualifying project
shall ensure that the use of the funds accepted under this
section for the qualifying project shall not--
(A) substantively or procedurally impact impartial
decisionmaking with respect to the issuance of permits;
or
(B) diminish, modify, or otherwise affect the
statutory or regulatory authorities of the cooperating
agency.
(c) Limitation on Use of Funds.--None of the funds accepted under
this section shall be used to carry out a review of the evaluation of
permits required under subsection (b)(2)(A).
(d) Public Availability.--The Secretary shall ensure that all final
permit decisions carried out using funds authorized under this section
are made available to the public, including on the Internet. | Water Supply Permitting Coordination Act This bill establishes the Bureau of Reclamation as the lead agency for purposes of coordinating all reviews, permits, licenses, or other approvals or decisions (reviews) required under federal law to construct new surface water storage projects in the states covered under the Reclamation Act on lands administered by the Department of the Interior or the Department of Agriculture, exclusive of any easement, right-of-way, lease, or any private holding (qualifying projects). The Bureau: (1) upon receipt of an application for a qualifying project, shall identify any federal agency that may have jurisdiction over a required review; and (2) shall notify such agency that it has been designated as a cooperating agency unless specified conditions apply. Each cooperating agency must submit to the Bureau: (1) a timeframe for completing the agency's authorizing responsibilities, (2) all environmental review material produced in the course of carrying out activities required under federal law consistent with the project schedule, and (3) all relevant project data. A state in which a qualifying project is being considered may choose to: (1) participate as a cooperating agency; and (2) make subject to the processes of this bill all state agencies that have jurisdiction over the project, are required to conduct or issue a review, or are required to make a determination on issuing a permit, license, or approval for the qualifying project. The principal responsibilities of the Bureau are to: (1) serve as the point of contact for applicants, state agencies, Indian tribes, and others regarding qualifying projects; (2) coordinate preparation of unified environmental documentation that will serve as the basis for all federal decisions necessary to authorize the use of federal lands for qualifying projects; and (3) coordinate all federal agency reviews necessary for the development and construction of qualifying projects. The Department of the Interior, after public notice, may accept and expend funds contributed by a non-federal public entity to expedite the evaluation of a permit of that entity related to a qualifying project. Interior must ensure that all final permit decisions are made available to the public, including on the Internet. | <s>[INST]SECTION 1. SHORT TITLE.
This Act may be cited as the ``Water Supply Permitting Coordination
Act''.
SEC. 2. DEFINITIONS.
In this Act:
(1) Bureau.--The term ``Bureau'' means the Bureau of
Reclamation.
(2) Cooperating agencies.--The term ``cooperating agency''
means a Federal agency with jurisdiction over a review,
analysis, opinion, statement, permit, license, or other
approval or decision required for a qualifying project under
applicable Federal laws and regulations, or a State agency
subject to section 3(c).
(3) Qualifying projects.--The term ``qualifying projects''
means new surface water storage projects in the States covered
under the Act of June 17, 1902 (32 Stat. 388, chapter 1093),
and Acts supplemental to and amendatory of that Act (43 U.S.C.
371 et seq.) constructed on lands administered by the
Department of the Interior or the Department of Agriculture,
exclusive of any easement, right-of-way, lease, or any private
holding.
(4) Secretary.--The term ``Secretary'' means the Secretary
of the Interior.
SEC. 3. ESTABLISHMENT OF LEAD AGENCY AND COOPERATING AGENCIES.
(a) Establishment of Lead Agency.--The Bureau is established as the
lead agency for purposes of coordinating all reviews, analyses,
opinions, statements, permits, licenses, or other approvals or
decisions required under Federal law to construct qualifying projects.
(b) Identification and Establishment of Cooperating Agencies.--The
Commissioner of the Bureau shall--
(1) identify, as early as practicable upon receipt of an
application for a qualifying project, any Federal agency that
may have jurisdiction over a review, analysis, opinion,
statement, permit, license, approval, or decision required for
a qualifying project under applicable Federal laws and
regulations; and
(2) notify any such agency, within a reasonable timeframe,
that the agency has been designated as a cooperating agency in
regards to the qualifying project unless that agency responds
to the Bureau in writing, within a timeframe set forth by the
Bureau, notifying the Bureau that the agency--
(A) has no jurisdiction or authority with respect
to the qualifying project;
(B) has no expertise or information relevant to the
qualifying project or any review, analysis, opinion,
statement, permit, license, or other approval or
decision associated therewith; or
(C) does not intend to submit comments on the
qualifying project or conduct any review of such a
project or make any decision with respect to such
project in a manner other than in cooperation with the
Bureau.
(c) State Authority.--A State in which a qualifying project is
being considered may choose, consistent with State law--
(1) to participate as a cooperating agency; and
(2) to make subject to the processes of this Act all State
agencies that--
(A) have jurisdiction over the qualifying project;
(B) are required to conduct or issue a review,
analysis, or opinion for the qualifying project; or
(C) are required to make a determination on issuing
a permit, license, or approval for the qualifying
project.
SEC. 4. BUREAU RESPONSIBILITIES.
(a) In General.--The principal responsibilities of the Bureau under
this Act are--
(1) to serve as the point of contact for applicants, State
agencies, Indian tribes, and others regarding proposed
qualifying projects;
(2) to coordinate preparation of unified environmental
documentation that will serve as the basis for all Federal
decisions necessary to authorize the use of Federal lands for
qualifying projects; and
(3) to coordinate all Federal agency reviews necessary for
project development and construction of qualifying projects.
(b) Coordination Process.--The Bureau shall have the following
coordination responsibilities:
(1) Preapplication coordination.--Notify cooperating
agencies of proposed qualifying projects not later than 30 days
after receipt of a proposal and facilitate a preapplication
meeting for prospective applicants, relevant Federal and State
agencies, and Indian tribes--
(A) to explain applicable processes, data
requirements, and applicant submissions necessary to
complete the required Federal agency reviews within the
timeframe established; and
(B) to establish the schedule for the qualifying
project.
(2) Consultation with cooperating agencies.--Consult with
the cooperating agencies throughout the Federal agency review
process, identify and obtain relevant data in a timely manner,
and set necessary deadlines for cooperating agencies.
(3) Schedule.--Work with the qualifying project applicant
and cooperating agencies to establish a project schedule. In
establishing the schedule, the Bureau shall consider, among
other factors--
(A) the responsibilities of cooperating agencies
under applicable laws and regulations;
(B) the resources available to the cooperating
agencies and the non-Federal qualifying project
sponsor, as applicable;
(C) the overall size and complexity of the
qualifying project;
(D) the overall schedule for and cost of the
qualifying project; and
(E) the sensitivity of the natural and historic
resources that may be affected by the qualifying
project.
(4) Environmental compliance.--Prepare a unified
environmental review document for each qualifying project
application, incorporating a single environmental record on
which all cooperating agencies with authority to issue
approvals for a given qualifying project shall base project
approval decisions. Help ensure that cooperating agencies make
necessary decisions, within their respective authorities,
regarding Federal approvals in accordance with the following
timelines:
(A) Not later than 1 year after acceptance of a
completed project application when an environmental
assessment and finding of no significant impact is
determined to be the appropriate level of review under
the National Environmental Policy Act of 1969 (42
U.S.C. 4321 et seq.).
(B) Not later than 1 year and 30 days after the
close of the public comment period for a draft
environmental impact statement under the National
Environmental Policy Act of 1969 (42 U.S.C. 4321 et
seq.), when an environmental impact statement is
required under the same.
(5) Consolidated administrative record.--Maintain a
consolidated administrative record of the information assembled
and used by the cooperating agencies as the basis for agency
decisions.
(6) Project data records.--To the extent practicable and
consistent with Federal law, ensure that all project data is
submitted and maintained in generally accessible electronic
format, compile, and where authorized under existing law, make
available such project data to cooperating agencies, the
qualifying project applicant, and to the public.
(7) Project manager.--Appoint a project manager for each
qualifying project. The project manager shall have authority to
oversee the project and to facilitate the issuance of the
relevant final authorizing documents, and shall be responsible
for ensuring fulfillment of all Bureau responsibilities set
forth in this section and all cooperating agency
responsibilities under section 5.
SEC. 5. COOPERATING AGENCY RESPONSIBILITIES.
(a) Adherence to Bureau Schedule.--
(1) Timeframes.--On notification of an application for a
qualifying project, the head of each cooperating agency shall
submit to the Bureau a timeframe under which the cooperating
agency reasonably will be able to complete the authorizing
responsibilities of the cooperating agency.
(2) Schedule.--
(A) Use of timeframes.--The Bureau shall use the
timeframes submitted under this subsection to establish
the project schedule under section 4.
(B) Adherence.--Each cooperating agency shall
adhere to the project schedule established by the
Bureau under subparagraph (A).
(b) Environmental Record.--The head of each cooperating agency
shall submit to the Bureau all environmental review material produced
or compiled in the course of carrying out activities required under
Federal law, consistent with the project schedule established by the
Bureau under subsection (a)(2).
(c) Data Submission.--To the extent practicable and consistent with
Federal law, the head of each cooperating agency shall submit all
relevant project data to the Bureau in a generally accessible
electronic format, subject to the project schedule established by the
Bureau under subsection (a)(2).
SEC. 6. FUNDING TO PROCESS PERMITS.
(a) In General.--The Secretary, after public notice in accordance
with subchapter II of chapter 5, and chapter 7, of title 5, United
States Code (commonly known as the ``Administrative Procedure Act''),
may accept and expend funds contributed by a non-Federal public entity
to expedite the evaluation of a permit of that entity related to a
qualifying project.
(b) Effect on Permitting.--
(1) In general.--In carrying out this section, the
Secretary shall ensure that the use of funds accepted under
subsection (a) will not substantively or procedurally impact
impartial decisionmaking with respect to permits.
(2) Evaluation of permits.--In carrying out this section,
the Secretary shall ensure that the evaluation of permits
carried out using funds accepted under this section shall--
(A) be reviewed by the Regional Director of the
Bureau of the region in which the qualifying project or
activity is located (or a designee); and
(B) use the same procedures for decisions that
would otherwise be required for the evaluation of
permits for similar projects or activities not carried
out using funds authorized under this section.
(3) Impartial decisionmaking.--In carrying out this
section, the Secretary and the head of each cooperating agency
receiving funds under this section for a qualifying project
shall ensure that the use of the funds accepted under this
section for the qualifying project shall not--
(A) substantively or procedurally impact impartial
decisionmaking with respect to the issuance of permits;
or
(B) diminish, modify, or otherwise affect the
statutory or regulatory authorities of the cooperating
agency.
(c) Limitation on Use of Funds.--None of the funds accepted under
this section shall be used to carry out a review of the evaluation of
permits required under subsection (b)(2)(A).
(d) Public Availability.--The Secretary shall ensure that all final
permit decisions carried out using funds authorized under this section
are made available to the public, including on the Internet.[/INST]Water Supply Permitting Coordination Act This bill establishes the Bureau of Reclamation as the lead agency for purposes of coordinating all reviews, permits, licenses, or other approvals or decisions (reviews) required under federal law to construct new surface water storage projects in the states covered under the Reclamation Act on lands administered by the Department of the Interior or the Department of Agriculture, exclusive of any easement, right-of-way, lease, or any private holding (qualifying projects). The Bureau: (1) upon receipt of an application for a qualifying project, shall identify any federal agency that may have jurisdiction over a required review; and (2) shall notify such agency that it has been designated as a cooperating agency unless specified conditions apply. Each cooperating agency must submit to the Bureau: (1) a timeframe for completing the agency's authorizing responsibilities, (2) all environmental review material produced in the course of carrying out activities required under federal law consistent with the project schedule, and (3) all relevant project data. A state in which a qualifying project is being considered may choose to: (1) participate as a cooperating agency; and (2) make subject to the processes of this bill all state agencies that have jurisdiction over the project, are required to conduct or issue a review, or are required to make a determination on issuing a permit, license, or approval for the qualifying project. The principal responsibilities of the Bureau are to: (1) serve as the point of contact for applicants, state agencies, Indian tribes, and others regarding qualifying projects; (2) coordinate preparation of unified environmental documentation that will serve as the basis for all federal decisions necessary to authorize the use of federal lands for qualifying projects; and (3) coordinate all federal agency reviews necessary for the development and construction of qualifying projects. The Department of the Interior, after public notice, may accept and expend funds contributed by a non-federal public entity to expedite the evaluation of a permit of that entity related to a qualifying project. Interior must ensure that all final permit decisions are made available to the public, including on the Internet.</s> |
the provision of hemodialysis for patients with end - stage kidney disease requires a functioning arteriovenous vascular access .
this is achieved through surgical creation of an arteriovenous anastomosis using either native vessels ( arteriovenous fistulae , avfs ) or prosthetic material ( arteriovenous grafts , avgs ) . with repeated use ,
vascular access dysfunction continues to be a major cause of morbidity and mortality and represents a significant proportion of the costs associated with hemodialysis care .
percutaneous transluminal angioplasty is commonly used to treat arteriovenous access stenosis and is established practice in many centers around the world . despite this , lesions treated with balloon angioplasty are prone to restenosis ; at 12 months , approximately half of all avfs require repeated intervention to maintain patency [ 3 , 4 ] .
factors such as increased lesion length , upper arm avfs , and younger avf age have been shown to be associated with patency loss after balloon angioplasty .
specific locations are also more prone to recurrent stenosis , particularly the juxta - anastomosis in radiocephalic avfs and cephalic arch in brachiocephalic avfs . in situations of resistant or recurrent stenosis
early after angioplasty , endovascular stent placement should be considered and may prolong access patency .
the aim of this study was to report our experience using vascular stents ( self - expanding nitinol and polytetrafluoroethylene ( ptfe ) covered stents ) for the treatment of resistant and recurrent stenosis and to determine if there were any predictors of patency after endovascular stent placement .
the human research ethics committee for the cairns hospital and hinterland health service approved the study ( hrec/13/qch/120 - 872 ) .
hemodialysis vascular access and radiology databases were searched to identify all stent placements for vascular access stenosis and to determine long - term patency outcomes .
all patients who underwent stent placement for resistant or recurrent hemodialysis access stenosis ( both avfs and avgs ) between january 2008 and december 2012 at cairns hospital were included .
indications for the placement of self - expandable nitinol stents ( lifestent and e - luminexx ; bard peripheral vascular ) were ( 1 ) recurrent stenosis , defined as restenosis of a previously treated lesion within three months of balloon angioplasty , and ( 2 ) resistant stenosis , defined as greater than 30% stenosis of the treated lesion after ultra - high pressure balloon inflation at recommended burst pressure .
indication for the placement of ptfe covered stents ( fluency plus ; bard peripheral vascular , viabahn ; gore , and advanta ; atrium ) was recurrent stenosis within three months of angioplasty in the cephalic arch or central veins , at the discretion of the operator .
the central veins were defined as the subclavian and innominate veins and superior vena cava .
arteriovenous access was investigated for recurrent stenosis on the basis of the following standardized monitoring and surveillance techniques : decreased or absent thrill , difficult cannulation , prolonged bleeding time after dialysis , development of collateral veins , excessive dynamic venous pressures on three consecutive occasions , decreased arterial blood flow ( fistula blood flow rate < 500 ml / min ; flow - qc ; transonic systems , ithaca , new york ) or decreased blood flow by more than 25% of baseline , or abnormal recirculation measurements ( > 10% ) [ 6 , 8 ] .
location of stent placement was classified according to a seven - zone system modified from previous studies ( figure 1 ) [ 4 , 8 ] : arterial inflow , anastomosis , juxta - anastomosis ( distal 5 cm of cephalic vein adjacent to the arteriovenous anastomosis ) , forearm venous outflow , upper arm venous outflow , cephalic arch ( proximal 5 cm of the cephalic vein ) , and central veins . in the case of brachiobasilic saphenous vein grafts and ptfe grafts ,
vein - vein anastomotic stenosis and vein - graft anastomotic stenosis were grouped with juxta - anastomotic stenosis .
stent placement was performed using standard techniques previously published by our center [ 6 , 8 ] .
imaging from the cannulation site to the right atrium was obtained using intravenous contrast . a vascular sheath and guide wire
intermediate , high pressure and ultra - high pressure balloons were used at recommended burst pressure to treat stenotic lesions .
bare metal self - expandable nitinol stents ( lifestent and e - luminexx ; bard peripheral vascular ) and covered stents ( fluency plus ; bard peripheral vascular , viabahn ; gore , and advanta ; atrium ) were placed according to the manufacturer 's recommended deployment technique . in all instances attempt
was made to achieve equal length of the stent on either side of the lesion and postplacement balloon dilatation was performed .
anatomical success was defined as less than 30% residual stenosis after stent placement and demonstrated continuity of the access circuit on contrast study .
clinical success was defined as the ability to provide uninterrupted hemodialysis at prescribed access flow rates for three consecutive sessions using the same access .
long - term patency was defined in accordance with the society of interventional radiology reporting standards following treatment with stent placement .
postintervention primary patency was defined as the interval after stent placement until repeated percutaneous intervention is required or the development of access thrombosis .
postintervention secondary patency was defined as the interval after stent placement until the access is surgically declotted , revised , or abandoned .
open surgical repair was employed after failed percutaneous salvage of stenosis , thrombosis , or pseudoaneurysm repair .
data were recorded and analyzed using spss ( version 21 ; ibm , armonk , new york ) .
kaplan - meier curves were used to determine poststent primary and secondary patency rates . during follow - up , participants were censored because of death with a functioning access , renal transplantation , switch to peritoneal dialysis , or loss to follow - up .
univariate and multivariate cox regression analysis was performed to determine if there were any predictors of patency after stent placement .
ten variables were analyzed : patient age , gender , indigenous ethnicity , diabetes , history of vascular disease ( stroke , coronary or peripheral artery disease ) , type of stent ( self - expandable nitinol or ptfe covered stents ) , access age ( time from creation to stent placement ) , type ( native fistula or native vein / prosthetic graft ) , lesion location ( upper arm or forearm ) , and antiplatelet therapy .
during the five - year study period , 60 stent procedures were performed in 45 cases of dysfunctional arteriovenous access in 45 patients .
the mean patient age was 57 years and brachiocephalic avfs were the most common type of access ( 64% ) ( table 1 ) .
the majority of patients ( 60% ) were of aboriginal and/or torres strait islander ethnicity . in 51 cases ,
the treated lesion had undergone angioplasty on one previous occasion with recurrence of stenosis within three months . in six cases ,
the treated lesion had been treated with angioplasty on two occasions , although stenosis had recurred beyond three months after the first angioplasty . in three instances a stent
was placed during the index procedure due to resistant stenosis despite ultra - high pressure balloon inflation at the recommended burst pressure .
the location of stent placement according to type of arteriovenous access is presented in table 2 .
juxta - anastomotic stenosis was the most commonly treated area in radiocephalic avfs . in brachiocephalic avfs ,
minor complications included one venous spasm and one access hematoma that did not require specific treatment and extravasation of contrast in another case that settled with balloon tamponade .
one procedure was unsuccessful because of failed percutaneous thrombolysis , and stent placement was abandoned .
mean follow - up was 24.5 months ( range : five days to 4.8 years ) .
one patient was lost to follow - up 30 months after stent placement due to relocation to another hospital .
the mean poststent primary patency was 14 months ( standard deviation 13 months ) and the mean poststent secondary patency was 25 months ( standard deviation 18 months ) .
poststent primary patency at 6 , 12 , and 24 months was 64% , 46% , and 35% , respectively ( figure 2 ) .
poststent secondary patency at 6 , 12 , and 24 months was 95% , 89% , and 85% , respectively ( figure 3 ) .
the mean poststent primary patency for both bare metal and covered stents was 14 months ( standard deviation 14 and 12 months , resp . ) .
the mean poststent secondary patency for bare metal stents was 29 months ( standard deviation 20 months ) .
the mean poststent secondary patency for covered stents was 18 months ( standard deviation 11 months ) .
poststent primary patency rates for each of the seven treated areas are presented in figure 4 .
there was a significant difference in poststent primary patency between the seven treatment areas ( log - rank p = 0.00012 ) .
stent placement used to treat more central lesions above the elbow , especially the upper arm venous outflow , cephalic arch , and central veins , tended to result in poorer outcomes compared to juxta - anastomotic stenosis and forearm venous outflow lesions . during the follow - up period , 25 cases ( 42% )
thirty - five cases ( 58% ) required multiple further interventions ; additional 99 interventions were performed to maintain patency , equating to an average of 2.2 further interventions per patient after the index stent deployment .
five cases required further two interventions , seven cases required further three interventions , two cases required further four interventions , three cases required further five interventions , two cases required further six interventions , and two cases required further seven interventions .
fifty - eight out of 99 ( 59% ) of the additional interventions to maintain patency were related to in - stent or peri - stent restenosis . in multivariate cox regression , upper arm lesions and access age less than one year at stent
insertion were the only factors associated with reduced postintervention primary patency ( adjusted hazards ratio [ hr ] 5.1 , 95% confidence interval [ ci ] 1.517 , p = 0.0084 , and hr 3.5 , 95% ci 1.57.8 , p = 0.0029 , resp . , table 3 ) .
there was no significant association between any of the other tested variables and postintervention primary patency ( table 3 ) .
resistant or recurrent stenosis throughout the access circuit poses challenges in terms of providing optimal hemodialysis treatment . in this study ,
stent placement to treat upper arm lesions and in access less than 12 months of age was associated with increased risk of primary patency loss .
twelve - month poststent primary and secondary patency rates of 46% and 89% , respectively , were achieved , comparable to studies published in the interventional radiology and vascular surgery literature .
certain anatomical regions of the access circuit are particularly prone to the development of resistant or recurrent stenosis .
the vein immediately adjacent to the arteriovenous anastomosis ( commonly referred to as juxta - anastomosis ) is a common site of stenosis due , in part , to injury sustained at the time of swinging the vein to form the anastomosis from the vein 's original anatomical location .
the proximal portion of the cephalic vein ( known as the cephalic arch ) is similarly problematic due to the anatomy / morphology of the vein , presence of valves , and extrinsic compression from the clavipectoral fascia , all of which limit vascular remodeling . in this study ,
more than half of all stents ( 56% ) were at these two discrete locations .
this study found that more central lesions such as those throughout the upper arm venous outflow , cephalic arch , and central veins had poorer patency after treatment with stents compared to juxta - anastomotic lesions ( for all types of access ) and forearm venous outflow lesions ( figure 4 ) .
this reinforces clinical observations that brachiocephalic avfs can be particularly problematic and prone to recurrent stenosis , particularly at the cephalic arch .
this is consistent with one of the largest studies reporting the outcome of 135 stent procedures , which found the mean time to reintervention was significantly longer for forearm avfs compared to upper arm avfs .
this finding was confirmed after adjustment for other risk factors in multivariate cox regression , where stent placement in upper arm lesions was associated with reduced poststent primary patency compared to forearm lesions .
this may be related to high flow rates and possibly reflect the role of hemodynamic stress in the development of neointimal hyperplasia .
our findings are supported by studies of both balloon angioplasty and stent placement that reported that interventions in upper arm access were associated with reduced postintervention primary patency [ 8 , 14 , 15 ] . however ,
this association has not been consistently reported [ 16 , 17 ] and remains to be confirmed in larger prospective studies .
stent placement in arteriovenous access less than 12 months of age was associated with reduced postintervention primary patency .
avfs that develop stenosis in the first six to 12 months after creation are likely to be intrinsically defective ; the early development of stenosis in a previously healthy vein after arteriovenous access formation is a reflection of accelerated neointimal hyperplasia .
it is unsurprising then that restenosis is more likely after stent insertion for these patients who developed problematic stenoses in relatively new avfs .
although antiplatelet therapy has been shown to reduce access thrombosis , we found no association between antiplatelet therapy and poststent patency . whilst antiplatelet therapy has endothelial protective benefits in the arterial system , similar effects in the venous system have yet to be demonstrated
the observational nature of this study precluded our ability to definitively answer the question of which type of stent provides superior patency .
covered stents were only used to treat more proximal lesions such as cephalic arch and central stenosis . on the other hand ,
nitinol stents were used throughout the access circuit . one small randomized trial found that covered stents provided superior patency compared to nitinol stents for the treatment of recurrent cephalic arch stenosis . a recently published randomized trial also found that covered stent placement for cephalic arch stenosis provided both superior access circuit primary patency and target lesion primary patency compared to balloon angioplasty alone .
this builds upon increasing evidence , most notably the flair trial and presented results of revise and renova , that covered stents prolong access circuit patency in graft - vein anastomotic stenosis compared to balloon angioplasty .
the results from this study are likely to reflect the small number of covered stents used and discrepancies in the location of covered stent placement .
this study demonstrated that secondary patency , which reflects continued function of the access , was 85% two years after initial stent placement . in order to provide sustained dialysis using the same access , an average of 2.2 additional interventions per access were required .
of these , approximately 41% were performed for newly developed lesions , slightly less than previously reported in other studies . in most cases , angioplasty was required at the site of stent placement either for in - stent or for peri - stent stenosis .
it is important to note that endothelial injury from repeated balloon angioplasty contributes to the formation of neointimal hyperplasia .
previous studies have demonstrated that repeated angioplasty is associated with increasing cellular proliferation of treated lesions .
aggressive smooth muscle and myofibroblast proliferation due to stent related luminal mismatch causing turbulent flow and altered hemodynamics are important in the pathogenesis of in - stent and peri - stent restenosis [ 2325 ] .
the presence of the stent itself also contributes to the pathogenesis of neointimal hyperplasia by attracting macrophages and inducing the expression of a cascade of proinflammatory cytokines . despite the need for repeated interventions at different intervals ,
there are several potential advantages of using endovascular stents in comparison to open surgical repair .
stent placement avoids the need for hospitalization ; all procedures were performed in a radiology angiographic suite without interruption to patients ' dialysis schedules .
open surgical repair of these lesions is technically complex and highly demanding of patients and is usually only considered once endovascular options are exhausted or ineffective .
demographic changes in dialysis populations mean that more elderly patients with vascular comorbidities are commencing hemodialysis .
it is vitally important to preserve sites for future access creation in these patients with relatively poor peripheral vasculature .
there are some important considerations required prior to stent placement . for juxta - anastomotic stenosis in radiocephalic avfs , surgical revision with formation of a more proximal anastomosis
may be preferred because there is an adequate length of cephalic vein available for cannulation in comparison to upper arm avfs .
juxta - anastomotic stenosis in upper arm access is often located at the elbow flexure crease , which can make stents prone to fractures .
similarly , at the cephalic arch , repeated movement of the upper arm girdle can lead to stent migration , particularly if the stent has not endothelialized , resulting in axillary vein thrombosis and occlusion .
comparison with other percutaneous interventions ( e.g. , drug - eluting and cutting balloon angioplasty ) and surgical repair were beyond the scope of this study . without this comparison
, it was not possible to extrapolate from the data that secondary patency rates observed were directly attributable to stent placement .
it is likely that other confounding factors specific to our center such as a dedicated nurse practitioner vascular access coordinator , access surveillance protocols , and an interventional nephrology led service model influenced the reported outcomes .
the cost - benefit of repeated angioplasties compared to surgical correction is an important consideration that warrants further investigation .
future randomized trials are needed to assess the utility of covered stents to treat recurrent stenosis , particularly at the cephalic arch in patients with brachiocephalic avfs .
this study demonstrated that resistant or recurrent stenosis could be successfully treated by endovascular stent placement , although multiple procedures are required to maintain patency .
stent placement for upper arm lesions and in arteriovenous access less than 12 months of age was associated with reduced postintervention primary patency . | this study aims to report the outcomes of nitinol and polytetrafluoroethylene covered stent placement to treat hemodialysis arteriovenous access stenosis at a single center over a five - year period .
clinical and radiological information was reviewed retrospectively .
poststent primary and secondary patency rates were determined using kaplan - meier analysis .
ten clinical variables were subjected to multivariate cox regression analysis to determine predictors of patency after stent placement . during the study period
60 stents were deployed in 45 patients , with a mean follow - up of 24.5 months .
the clinical and anatomical success rate was 98.3% ( 59/60 ) .
poststent primary patency rates at 6 , 12 , and 24 months were 64% , 46% , and 35% , respectively .
poststent secondary patency rates at 6 , 12 , and 24 months were 95% , 89% , and 85% , respectively .
stent placement for upper arm lesions and in access less than 12 months of age was associated with reduced primary patency ( adjusted hazards ratio [ hr ] 5.1 , p = 0.0084 , and hr 3.5 , p = 0.0029 , resp . )
. resistant or recurrent stenosis can be successfully treated by endovascular stent placement with durable long - term patency , although multiple procedures are often required .
stent placement for upper arm lesions and in arteriovenous access less than 12 months of age was associated with increased risk of patency loss . | <s>[INST]the provision of hemodialysis for patients with end - stage kidney disease requires a functioning arteriovenous vascular access .
this is achieved through surgical creation of an arteriovenous anastomosis using either native vessels ( arteriovenous fistulae , avfs ) or prosthetic material ( arteriovenous grafts , avgs ) . with repeated use ,
vascular access dysfunction continues to be a major cause of morbidity and mortality and represents a significant proportion of the costs associated with hemodialysis care .
percutaneous transluminal angioplasty is commonly used to treat arteriovenous access stenosis and is established practice in many centers around the world . despite this , lesions treated with balloon angioplasty are prone to restenosis ; at 12 months , approximately half of all avfs require repeated intervention to maintain patency [ 3 , 4 ] .
factors such as increased lesion length , upper arm avfs , and younger avf age have been shown to be associated with patency loss after balloon angioplasty .
specific locations are also more prone to recurrent stenosis , particularly the juxta - anastomosis in radiocephalic avfs and cephalic arch in brachiocephalic avfs . in situations of resistant or recurrent stenosis
early after angioplasty , endovascular stent placement should be considered and may prolong access patency .
the aim of this study was to report our experience using vascular stents ( self - expanding nitinol and polytetrafluoroethylene ( ptfe ) covered stents ) for the treatment of resistant and recurrent stenosis and to determine if there were any predictors of patency after endovascular stent placement .
the human research ethics committee for the cairns hospital and hinterland health service approved the study ( hrec/13/qch/120 - 872 ) .
hemodialysis vascular access and radiology databases were searched to identify all stent placements for vascular access stenosis and to determine long - term patency outcomes .
all patients who underwent stent placement for resistant or recurrent hemodialysis access stenosis ( both avfs and avgs ) between january 2008 and december 2012 at cairns hospital were included .
indications for the placement of self - expandable nitinol stents ( lifestent and e - luminexx ; bard peripheral vascular ) were ( 1 ) recurrent stenosis , defined as restenosis of a previously treated lesion within three months of balloon angioplasty , and ( 2 ) resistant stenosis , defined as greater than 30% stenosis of the treated lesion after ultra - high pressure balloon inflation at recommended burst pressure .
indication for the placement of ptfe covered stents ( fluency plus ; bard peripheral vascular , viabahn ; gore , and advanta ; atrium ) was recurrent stenosis within three months of angioplasty in the cephalic arch or central veins , at the discretion of the operator .
the central veins were defined as the subclavian and innominate veins and superior vena cava .
arteriovenous access was investigated for recurrent stenosis on the basis of the following standardized monitoring and surveillance techniques : decreased or absent thrill , difficult cannulation , prolonged bleeding time after dialysis , development of collateral veins , excessive dynamic venous pressures on three consecutive occasions , decreased arterial blood flow ( fistula blood flow rate < 500 ml / min ; flow - qc ; transonic systems , ithaca , new york ) or decreased blood flow by more than 25% of baseline , or abnormal recirculation measurements ( > 10% ) [ 6 , 8 ] .
location of stent placement was classified according to a seven - zone system modified from previous studies ( figure 1 ) [ 4 , 8 ] : arterial inflow , anastomosis , juxta - anastomosis ( distal 5 cm of cephalic vein adjacent to the arteriovenous anastomosis ) , forearm venous outflow , upper arm venous outflow , cephalic arch ( proximal 5 cm of the cephalic vein ) , and central veins . in the case of brachiobasilic saphenous vein grafts and ptfe grafts ,
vein - vein anastomotic stenosis and vein - graft anastomotic stenosis were grouped with juxta - anastomotic stenosis .
stent placement was performed using standard techniques previously published by our center [ 6 , 8 ] .
imaging from the cannulation site to the right atrium was obtained using intravenous contrast . a vascular sheath and guide wire
intermediate , high pressure and ultra - high pressure balloons were used at recommended burst pressure to treat stenotic lesions .
bare metal self - expandable nitinol stents ( lifestent and e - luminexx ; bard peripheral vascular ) and covered stents ( fluency plus ; bard peripheral vascular , viabahn ; gore , and advanta ; atrium ) were placed according to the manufacturer 's recommended deployment technique . in all instances attempt
was made to achieve equal length of the stent on either side of the lesion and postplacement balloon dilatation was performed .
anatomical success was defined as less than 30% residual stenosis after stent placement and demonstrated continuity of the access circuit on contrast study .
clinical success was defined as the ability to provide uninterrupted hemodialysis at prescribed access flow rates for three consecutive sessions using the same access .
long - term patency was defined in accordance with the society of interventional radiology reporting standards following treatment with stent placement .
postintervention primary patency was defined as the interval after stent placement until repeated percutaneous intervention is required or the development of access thrombosis .
postintervention secondary patency was defined as the interval after stent placement until the access is surgically declotted , revised , or abandoned .
open surgical repair was employed after failed percutaneous salvage of stenosis , thrombosis , or pseudoaneurysm repair .
data were recorded and analyzed using spss ( version 21 ; ibm , armonk , new york ) .
kaplan - meier curves were used to determine poststent primary and secondary patency rates . during follow - up , participants were censored because of death with a functioning access , renal transplantation , switch to peritoneal dialysis , or loss to follow - up .
univariate and multivariate cox regression analysis was performed to determine if there were any predictors of patency after stent placement .
ten variables were analyzed : patient age , gender , indigenous ethnicity , diabetes , history of vascular disease ( stroke , coronary or peripheral artery disease ) , type of stent ( self - expandable nitinol or ptfe covered stents ) , access age ( time from creation to stent placement ) , type ( native fistula or native vein / prosthetic graft ) , lesion location ( upper arm or forearm ) , and antiplatelet therapy .
during the five - year study period , 60 stent procedures were performed in 45 cases of dysfunctional arteriovenous access in 45 patients .
the mean patient age was 57 years and brachiocephalic avfs were the most common type of access ( 64% ) ( table 1 ) .
the majority of patients ( 60% ) were of aboriginal and/or torres strait islander ethnicity . in 51 cases ,
the treated lesion had undergone angioplasty on one previous occasion with recurrence of stenosis within three months . in six cases ,
the treated lesion had been treated with angioplasty on two occasions , although stenosis had recurred beyond three months after the first angioplasty . in three instances a stent
was placed during the index procedure due to resistant stenosis despite ultra - high pressure balloon inflation at the recommended burst pressure .
the location of stent placement according to type of arteriovenous access is presented in table 2 .
juxta - anastomotic stenosis was the most commonly treated area in radiocephalic avfs . in brachiocephalic avfs ,
minor complications included one venous spasm and one access hematoma that did not require specific treatment and extravasation of contrast in another case that settled with balloon tamponade .
one procedure was unsuccessful because of failed percutaneous thrombolysis , and stent placement was abandoned .
mean follow - up was 24.5 months ( range : five days to 4.8 years ) .
one patient was lost to follow - up 30 months after stent placement due to relocation to another hospital .
the mean poststent primary patency was 14 months ( standard deviation 13 months ) and the mean poststent secondary patency was 25 months ( standard deviation 18 months ) .
poststent primary patency at 6 , 12 , and 24 months was 64% , 46% , and 35% , respectively ( figure 2 ) .
poststent secondary patency at 6 , 12 , and 24 months was 95% , 89% , and 85% , respectively ( figure 3 ) .
the mean poststent primary patency for both bare metal and covered stents was 14 months ( standard deviation 14 and 12 months , resp . ) .
the mean poststent secondary patency for bare metal stents was 29 months ( standard deviation 20 months ) .
the mean poststent secondary patency for covered stents was 18 months ( standard deviation 11 months ) .
poststent primary patency rates for each of the seven treated areas are presented in figure 4 .
there was a significant difference in poststent primary patency between the seven treatment areas ( log - rank p = 0.00012 ) .
stent placement used to treat more central lesions above the elbow , especially the upper arm venous outflow , cephalic arch , and central veins , tended to result in poorer outcomes compared to juxta - anastomotic stenosis and forearm venous outflow lesions . during the follow - up period , 25 cases ( 42% )
thirty - five cases ( 58% ) required multiple further interventions ; additional 99 interventions were performed to maintain patency , equating to an average of 2.2 further interventions per patient after the index stent deployment .
five cases required further two interventions , seven cases required further three interventions , two cases required further four interventions , three cases required further five interventions , two cases required further six interventions , and two cases required further seven interventions .
fifty - eight out of 99 ( 59% ) of the additional interventions to maintain patency were related to in - stent or peri - stent restenosis . in multivariate cox regression , upper arm lesions and access age less than one year at stent
insertion were the only factors associated with reduced postintervention primary patency ( adjusted hazards ratio [ hr ] 5.1 , 95% confidence interval [ ci ] 1.517 , p = 0.0084 , and hr 3.5 , 95% ci 1.57.8 , p = 0.0029 , resp . , table 3 ) .
there was no significant association between any of the other tested variables and postintervention primary patency ( table 3 ) .
resistant or recurrent stenosis throughout the access circuit poses challenges in terms of providing optimal hemodialysis treatment . in this study ,
stent placement to treat upper arm lesions and in access less than 12 months of age was associated with increased risk of primary patency loss .
twelve - month poststent primary and secondary patency rates of 46% and 89% , respectively , were achieved , comparable to studies published in the interventional radiology and vascular surgery literature .
certain anatomical regions of the access circuit are particularly prone to the development of resistant or recurrent stenosis .
the vein immediately adjacent to the arteriovenous anastomosis ( commonly referred to as juxta - anastomosis ) is a common site of stenosis due , in part , to injury sustained at the time of swinging the vein to form the anastomosis from the vein 's original anatomical location .
the proximal portion of the cephalic vein ( known as the cephalic arch ) is similarly problematic due to the anatomy / morphology of the vein , presence of valves , and extrinsic compression from the clavipectoral fascia , all of which limit vascular remodeling . in this study ,
more than half of all stents ( 56% ) were at these two discrete locations .
this study found that more central lesions such as those throughout the upper arm venous outflow , cephalic arch , and central veins had poorer patency after treatment with stents compared to juxta - anastomotic lesions ( for all types of access ) and forearm venous outflow lesions ( figure 4 ) .
this reinforces clinical observations that brachiocephalic avfs can be particularly problematic and prone to recurrent stenosis , particularly at the cephalic arch .
this is consistent with one of the largest studies reporting the outcome of 135 stent procedures , which found the mean time to reintervention was significantly longer for forearm avfs compared to upper arm avfs .
this finding was confirmed after adjustment for other risk factors in multivariate cox regression , where stent placement in upper arm lesions was associated with reduced poststent primary patency compared to forearm lesions .
this may be related to high flow rates and possibly reflect the role of hemodynamic stress in the development of neointimal hyperplasia .
our findings are supported by studies of both balloon angioplasty and stent placement that reported that interventions in upper arm access were associated with reduced postintervention primary patency [ 8 , 14 , 15 ] . however ,
this association has not been consistently reported [ 16 , 17 ] and remains to be confirmed in larger prospective studies .
stent placement in arteriovenous access less than 12 months of age was associated with reduced postintervention primary patency .
avfs that develop stenosis in the first six to 12 months after creation are likely to be intrinsically defective ; the early development of stenosis in a previously healthy vein after arteriovenous access formation is a reflection of accelerated neointimal hyperplasia .
it is unsurprising then that restenosis is more likely after stent insertion for these patients who developed problematic stenoses in relatively new avfs .
although antiplatelet therapy has been shown to reduce access thrombosis , we found no association between antiplatelet therapy and poststent patency . whilst antiplatelet therapy has endothelial protective benefits in the arterial system , similar effects in the venous system have yet to be demonstrated
the observational nature of this study precluded our ability to definitively answer the question of which type of stent provides superior patency .
covered stents were only used to treat more proximal lesions such as cephalic arch and central stenosis . on the other hand ,
nitinol stents were used throughout the access circuit . one small randomized trial found that covered stents provided superior patency compared to nitinol stents for the treatment of recurrent cephalic arch stenosis . a recently published randomized trial also found that covered stent placement for cephalic arch stenosis provided both superior access circuit primary patency and target lesion primary patency compared to balloon angioplasty alone .
this builds upon increasing evidence , most notably the flair trial and presented results of revise and renova , that covered stents prolong access circuit patency in graft - vein anastomotic stenosis compared to balloon angioplasty .
the results from this study are likely to reflect the small number of covered stents used and discrepancies in the location of covered stent placement .
this study demonstrated that secondary patency , which reflects continued function of the access , was 85% two years after initial stent placement . in order to provide sustained dialysis using the same access , an average of 2.2 additional interventions per access were required .
of these , approximately 41% were performed for newly developed lesions , slightly less than previously reported in other studies . in most cases , angioplasty was required at the site of stent placement either for in - stent or for peri - stent stenosis .
it is important to note that endothelial injury from repeated balloon angioplasty contributes to the formation of neointimal hyperplasia .
previous studies have demonstrated that repeated angioplasty is associated with increasing cellular proliferation of treated lesions .
aggressive smooth muscle and myofibroblast proliferation due to stent related luminal mismatch causing turbulent flow and altered hemodynamics are important in the pathogenesis of in - stent and peri - stent restenosis [ 2325 ] .
the presence of the stent itself also contributes to the pathogenesis of neointimal hyperplasia by attracting macrophages and inducing the expression of a cascade of proinflammatory cytokines . despite the need for repeated interventions at different intervals ,
there are several potential advantages of using endovascular stents in comparison to open surgical repair .
stent placement avoids the need for hospitalization ; all procedures were performed in a radiology angiographic suite without interruption to patients ' dialysis schedules .
open surgical repair of these lesions is technically complex and highly demanding of patients and is usually only considered once endovascular options are exhausted or ineffective .
demographic changes in dialysis populations mean that more elderly patients with vascular comorbidities are commencing hemodialysis .
it is vitally important to preserve sites for future access creation in these patients with relatively poor peripheral vasculature .
there are some important considerations required prior to stent placement . for juxta - anastomotic stenosis in radiocephalic avfs , surgical revision with formation of a more proximal anastomosis
may be preferred because there is an adequate length of cephalic vein available for cannulation in comparison to upper arm avfs .
juxta - anastomotic stenosis in upper arm access is often located at the elbow flexure crease , which can make stents prone to fractures .
similarly , at the cephalic arch , repeated movement of the upper arm girdle can lead to stent migration , particularly if the stent has not endothelialized , resulting in axillary vein thrombosis and occlusion .
comparison with other percutaneous interventions ( e.g. , drug - eluting and cutting balloon angioplasty ) and surgical repair were beyond the scope of this study . without this comparison
, it was not possible to extrapolate from the data that secondary patency rates observed were directly attributable to stent placement .
it is likely that other confounding factors specific to our center such as a dedicated nurse practitioner vascular access coordinator , access surveillance protocols , and an interventional nephrology led service model influenced the reported outcomes .
the cost - benefit of repeated angioplasties compared to surgical correction is an important consideration that warrants further investigation .
future randomized trials are needed to assess the utility of covered stents to treat recurrent stenosis , particularly at the cephalic arch in patients with brachiocephalic avfs .
this study demonstrated that resistant or recurrent stenosis could be successfully treated by endovascular stent placement , although multiple procedures are required to maintain patency .
stent placement for upper arm lesions and in arteriovenous access less than 12 months of age was associated with reduced postintervention primary patency .[/INST]this study aims to report the outcomes of nitinol and polytetrafluoroethylene covered stent placement to treat hemodialysis arteriovenous access stenosis at a single center over a five - year period .
clinical and radiological information was reviewed retrospectively .
poststent primary and secondary patency rates were determined using kaplan - meier analysis .
ten clinical variables were subjected to multivariate cox regression analysis to determine predictors of patency after stent placement . during the study period
60 stents were deployed in 45 patients , with a mean follow - up of 24.5 months .
the clinical and anatomical success rate was 98.3% ( 59/60 ) .
poststent primary patency rates at 6 , 12 , and 24 months were 64% , 46% , and 35% , respectively .
poststent secondary patency rates at 6 , 12 , and 24 months were 95% , 89% , and 85% , respectively .
stent placement for upper arm lesions and in access less than 12 months of age was associated with reduced primary patency ( adjusted hazards ratio [ hr ] 5.1 , p = 0.0084 , and hr 3.5 , p = 0.0029 , resp . )
. resistant or recurrent stenosis can be successfully treated by endovascular stent placement with durable long - term patency , although multiple procedures are often required .
stent placement for upper arm lesions and in arteriovenous access less than 12 months of age was associated with increased risk of patency loss .</s> |
cystic fibrosis ( cf ) is a genetic disease characterized by increased viscosity of the bronchial mucus and impaired mucocilliary clearance which predisposes to microbial colonization and infections of the respiratory tract .
adult patients with cf have a high incidence of fungal colonization ( 42% ) and invasive disease ( 11% ) .
a variety of yeasts and filamentous fungi have been recovered from their respiratory samples , before and after lung transplantation .
are the most common fungal species isolated , responsible of invasive infection after lung transplantation in patients with cf .
recently , invasive pulmonary infections with emerging molds like scedosporium spp . , rasamsonia argillacea or exophiala dermatitidis have been described , associated with fungemia for some of them : scedosporium apiospermum and fusarium solani
.
arthrographis kalrae , an emerging mold is an environmental saprophytic fungus , mainly found in soil and compost . in recent years
, cases of opportunistic infections attributed to this pathogen were described : pulmonary infection , endocarditis , sinusitis , meningitis , keratitis , onychomycosis and mycetoma , affecting both immunocompromised and immunocompetent patients .
our patient , a 19-year - old woman , was diagnosed with cystic fibrosis at the age of 4 months .
she developed an exocrine pancreatic insufficiency , an insulin - dependent diabetes , a moderate chronic renal failure and a severe malnutrition ( bmi 14 ) .
she also presented a permanent bacterial pulmonary colonization with staphylococcus aureus and pseudomonas aeruginosa , treated by aerosols of colistin . from 1998 to 2005
the lung colonization by a. fumigatus became permanent ( positive sputa culture , presence of anti - aspergillus antibodies ) for which a treatment with itraconazole 200 mg / day was initiated , increased up to 500 mg / day due to low serum levels . in march 2012 ,
a. kalrae and various aspergillus species ( a. fumigatus , a. flavus and a. nidulans ) were regularly isolated in sputa cultures .
itraconazole was then stopped and replaced by voriconazole 2200 mg / day , later increased to 2250 mg / day .
the pre - transplant sputum culture found bacteria colonies ( p. aeruginosa , s. aureus ) , one colony of a. terreus , three of a. fumigatus and ten of a. kalrae . on day 1 post - transplant ,
blood cultures , broncho - alveolar lavage ( bal ) and two tracheal aspirations were made .
the patient received a probabilistic antibiotic treatment associating ceftazidime , ciprofloxacin , teicoplanin , aerosols of colistin and voriconazole 2200 mg twice a day . on day 3
, mold colonies were isolated in blood cultures , bal , tracheal aspirations and in a bronchial smear of the explanted lung cultures . on day 4 , molds were identified as a. kalrae , associated with one colony of a. terreus in the bal . given these results , antifungal therapy was modified on day 4 for caspofungin 50 mg / day in combination with liposomal amphotericin b i.v . 3
three colonies of a. kalrae and three colonies of a. fumigatus were found in another bal performed on day 5 post - transplant .
the ct - scans and the chest radiographies performed during this acute episode ( day 0 , 3 and 21 ) were not contributory
. only the first ct - scan showed signs of pulmonary infection of the lingula and lower lobe on day 21 . on day 33 , the liposomal amphotericin b i.v .
was replaced by aerosols of liposomal amphotericin b 3/week , maintained until day 110 post - transplant . despite the negativation of pulmonary samples and the resolution of this acute fungal infection in the following months , the patient died 8 months after her transplantation because of a bacterial septic shock in a context of humoral rejection and a state of severe malnutrition .
after two days of incubation at 35 c on chromogenic medium chromid candida ( biomerieux , france ) for the respiratory samples and on bactec plus aerobic f ( beckton dickinson , france ) at 37 c , there was growth of small yeast - like colonies .
identification was performed based on three methods : a morphological examination , the biochemical characteristics and a mass spectrometry study .
macroscopically , we observed small creamy , beige yeast - like colonies after two days of growth on chromogenic medium chromid candida ( fig .
1 ) . after 7 days of incubation , the colonies became dry and grainy .
the same aspects were observed on sabouraud chloramphenicol ( biorad , france ) and sabouraud chloramphenicol actidione ( biorad , france ) at 37 c and 27 c ( fig .
3 ) . however , growth on sabouraud chloramphenicol medium with actidione was slower ( 5 days for yeast - like colonies ) than without .
a slide culture incubated for 48 h at 27 c on pcb medium ( biorad , france ) showed characteristic hyaline , septate hyphae with one - celled , smooth - walled arthroconidia and irregularly branched hyphae , with dendritic conidiophores ( fig .
the isolate was also inoculated into wells of an i d 32 plate ( biomerieux , france ) .
after 72 h of incubation , the profile code obtained did not correspond to any taxon scored in the manufacturer 's database . in parallel , mass spectrometry was performed using the microflex lt mass spectrometer ( bruker daltonics , france ) , and analyzed using the maldi biotyper software ( version 3.1 with enlarged database version 3.3.1.0 containing 4613 entries ) .
mass spectrometry technique allowed to identify a. kalrae with logscore values > 2.0 ( 2.28 , 2.24 ) , according to the manufacturer 's recommendations .
the identification was confirmed by a dna sequencing ( using the internal transcribed spacer , its1 and its4 ) and comparison of obtained sequences to genbank ( http://www.ncbi.nlm.nih.gov/genbank , accession number for closest hit km588309.1 ) and cbs ( http://www.cbs.knaw.nl , accession number for closest hit cbs 10896_ex24366_12125_its ) databases .
a. kalrae was identified with an e - value of 0 ( genbank ) , an overlap of 100% ( cbs ) and 100% identification concordance .
the blood culture strain mics measured by etest gave the following results : amphotericin b 0.75 mg / ml , flucytosine > 32 mg / ml , voriconazole 0.125 mg / ml , posaconazole 0.50 mg / ml , fluconazole > 32 mg / ml , micafungin 0.012 mg / ml , caspofungin 0.047 mg / ml . the strain was sent to the national reference center , at pasteur institute .
there , the mics values were determined according to the eucast method and gave the following results : amphotericin b 0.125 mg / ml , flucytosin>64 mg / ml , voriconazole 0.125 mg / ml , posaconazole 0.125 mg / ml , fluconazole 64 mg / ml , micafungin 4 mg / ml and caspofungin>4 mg / ml .
arthrographis is a genus containing 5 species : a. kalrae , a. cuboidea , a. lignicola , a. pinicola and a. alba .
a. kalrae is a saprophytic fungus with a worldwide distribution , found in soil and compost . in recent years , clinical cases of invasive infections attributed to this pathogen
currently , one case of infection with arthrographis sp . and 14 cases of infection with a. kalrae have been reported ( table 1 ) : two onychomycosis , , one mycetoma , five keratitis , , , , one of which associated with sinusitis , two knee joint infection , , one endocarditis , two pulmonary infections , , one meningitis and one fungal stroke .
these cases have a worldwide distribution : seven cases in europe , one in china , one in japan , three in usa , one in mexico , one in malaysia and one in australia .
three of the five patients with keratitis were soft contact lens wearers ; the other two and the two patients with the knee joint infections have had an injury contaminated with soil .
the rest of the patients had predisposing infection factors like malnutrition , systemic corticosteroids , radiotherapy , aids , allogeneic hematopoietic stem cell transplant .
diagnoses were always based on phenotypic characteristics and microscopic morphology using de hoog and sigler , and carmichael descriptions . in most cases ,
identification of the species was confirmed by molecular biology techniques ( its , d1/d2 sequencing ) .
no data were available about the most appropriate treatment for this kind of infection . in the previous described cases , when tested the strains were sensitive to azoles , amphotericin b and terbinafin and resistant to flucytosin , but no sensibility results were showed for echinocandins .
the azoles showed high activity ( mean mic 0.46 g / ml ) , amphotericin b very little activity ( mean mic : 2 g / ml ) and echinocandins showed no in vitro activity ( mean mec at 24 h>8 g / ml ) .
these results are different from ours but concordant with those of the national reference center for invasive mycoses and antifungals , which is using the eucast method .
all patients described except the one with onychomycosis were treated with azoles associated or not with amphotericin b. some reported patients also required surgery ( keratitis and knee joint infection ) .
three patients died during their a. kalrae infection , one of them because of the fungus ( patient with fungal stroke ) .
given the fact that our patient developed a septic shock with a fungemia despite a prophylaxis with voriconazole , the choice was made to treat her with caspofungin in combination with liposomal amphotericin b. the clinical response was favorable with this treatment , regardless the resistance to the caspofungin detected by the national reference center . in the case of our patient , the evolution of the fungal infection was favorable with a rapid negativity of blood cultures and respiratory samples .
the combination of caspofungin and liposomal amphotericin b was effective in our patient whose colonization by the fungus could not be eliminated by a long - term treatment with voriconazole .
we therefore describe here the first case , to our knowledge , of an a. kalrae fungemia in a cystic fibrosis patient with an assumed pulmonary portal of entry .
please note that this journal requires full disclosure of all sources of funding and potential conflicts of interest .
the journal also requires a declaration that the author(s ) have obtained written and signed consent to publish the case report from the patient or legal guardian(s ) .
the statements on funding , conflict of interest and consent need to be submitted via our ethical form that can be downloaded from the submission site www.ees.elsevier.com/mmcr .
please note that your manuscript will not be considered for publication until the signed ethical form has been received .
| arthrographis kalrae is a hyalin fungus .
it is a saprophyte of the environment , mainly found in soil and compost . in recent years
, cases of opportunistic infections attributed to this pathogen have been described .
our patient was a 19-year - old woman with cystic fibrosis .
she presented a bacterial and fungal pulmonary colonization with aspergillus fumigatus and arthrographis .
kalrae . after her lung transplantation
, she developed an a. kalrae fungemia , treated with caspofungin 50 mg / day associated to liposomal amphotericin b i.v .
3 mg / kg / day .
the patient died 8 months after her transplantation as the result of a bacterial septic shock . | <s>[INST]cystic fibrosis ( cf ) is a genetic disease characterized by increased viscosity of the bronchial mucus and impaired mucocilliary clearance which predisposes to microbial colonization and infections of the respiratory tract .
adult patients with cf have a high incidence of fungal colonization ( 42% ) and invasive disease ( 11% ) .
a variety of yeasts and filamentous fungi have been recovered from their respiratory samples , before and after lung transplantation .
are the most common fungal species isolated , responsible of invasive infection after lung transplantation in patients with cf .
recently , invasive pulmonary infections with emerging molds like scedosporium spp . , rasamsonia argillacea or exophiala dermatitidis have been described , associated with fungemia for some of them : scedosporium apiospermum and fusarium solani
.
arthrographis kalrae , an emerging mold is an environmental saprophytic fungus , mainly found in soil and compost . in recent years
, cases of opportunistic infections attributed to this pathogen were described : pulmonary infection , endocarditis , sinusitis , meningitis , keratitis , onychomycosis and mycetoma , affecting both immunocompromised and immunocompetent patients .
our patient , a 19-year - old woman , was diagnosed with cystic fibrosis at the age of 4 months .
she developed an exocrine pancreatic insufficiency , an insulin - dependent diabetes , a moderate chronic renal failure and a severe malnutrition ( bmi 14 ) .
she also presented a permanent bacterial pulmonary colonization with staphylococcus aureus and pseudomonas aeruginosa , treated by aerosols of colistin . from 1998 to 2005
the lung colonization by a. fumigatus became permanent ( positive sputa culture , presence of anti - aspergillus antibodies ) for which a treatment with itraconazole 200 mg / day was initiated , increased up to 500 mg / day due to low serum levels . in march 2012 ,
a. kalrae and various aspergillus species ( a. fumigatus , a. flavus and a. nidulans ) were regularly isolated in sputa cultures .
itraconazole was then stopped and replaced by voriconazole 2200 mg / day , later increased to 2250 mg / day .
the pre - transplant sputum culture found bacteria colonies ( p. aeruginosa , s. aureus ) , one colony of a. terreus , three of a. fumigatus and ten of a. kalrae . on day 1 post - transplant ,
blood cultures , broncho - alveolar lavage ( bal ) and two tracheal aspirations were made .
the patient received a probabilistic antibiotic treatment associating ceftazidime , ciprofloxacin , teicoplanin , aerosols of colistin and voriconazole 2200 mg twice a day . on day 3
, mold colonies were isolated in blood cultures , bal , tracheal aspirations and in a bronchial smear of the explanted lung cultures . on day 4 , molds were identified as a. kalrae , associated with one colony of a. terreus in the bal . given these results , antifungal therapy was modified on day 4 for caspofungin 50 mg / day in combination with liposomal amphotericin b i.v . 3
three colonies of a. kalrae and three colonies of a. fumigatus were found in another bal performed on day 5 post - transplant .
the ct - scans and the chest radiographies performed during this acute episode ( day 0 , 3 and 21 ) were not contributory
. only the first ct - scan showed signs of pulmonary infection of the lingula and lower lobe on day 21 . on day 33 , the liposomal amphotericin b i.v .
was replaced by aerosols of liposomal amphotericin b 3/week , maintained until day 110 post - transplant . despite the negativation of pulmonary samples and the resolution of this acute fungal infection in the following months , the patient died 8 months after her transplantation because of a bacterial septic shock in a context of humoral rejection and a state of severe malnutrition .
after two days of incubation at 35 c on chromogenic medium chromid candida ( biomerieux , france ) for the respiratory samples and on bactec plus aerobic f ( beckton dickinson , france ) at 37 c , there was growth of small yeast - like colonies .
identification was performed based on three methods : a morphological examination , the biochemical characteristics and a mass spectrometry study .
macroscopically , we observed small creamy , beige yeast - like colonies after two days of growth on chromogenic medium chromid candida ( fig .
1 ) . after 7 days of incubation , the colonies became dry and grainy .
the same aspects were observed on sabouraud chloramphenicol ( biorad , france ) and sabouraud chloramphenicol actidione ( biorad , france ) at 37 c and 27 c ( fig .
3 ) . however , growth on sabouraud chloramphenicol medium with actidione was slower ( 5 days for yeast - like colonies ) than without .
a slide culture incubated for 48 h at 27 c on pcb medium ( biorad , france ) showed characteristic hyaline , septate hyphae with one - celled , smooth - walled arthroconidia and irregularly branched hyphae , with dendritic conidiophores ( fig .
the isolate was also inoculated into wells of an i d 32 plate ( biomerieux , france ) .
after 72 h of incubation , the profile code obtained did not correspond to any taxon scored in the manufacturer 's database . in parallel , mass spectrometry was performed using the microflex lt mass spectrometer ( bruker daltonics , france ) , and analyzed using the maldi biotyper software ( version 3.1 with enlarged database version 3.3.1.0 containing 4613 entries ) .
mass spectrometry technique allowed to identify a. kalrae with logscore values > 2.0 ( 2.28 , 2.24 ) , according to the manufacturer 's recommendations .
the identification was confirmed by a dna sequencing ( using the internal transcribed spacer , its1 and its4 ) and comparison of obtained sequences to genbank ( http://www.ncbi.nlm.nih.gov/genbank , accession number for closest hit km588309.1 ) and cbs ( http://www.cbs.knaw.nl , accession number for closest hit cbs 10896_ex24366_12125_its ) databases .
a. kalrae was identified with an e - value of 0 ( genbank ) , an overlap of 100% ( cbs ) and 100% identification concordance .
the blood culture strain mics measured by etest gave the following results : amphotericin b 0.75 mg / ml , flucytosine > 32 mg / ml , voriconazole 0.125 mg / ml , posaconazole 0.50 mg / ml , fluconazole > 32 mg / ml , micafungin 0.012 mg / ml , caspofungin 0.047 mg / ml . the strain was sent to the national reference center , at pasteur institute .
there , the mics values were determined according to the eucast method and gave the following results : amphotericin b 0.125 mg / ml , flucytosin>64 mg / ml , voriconazole 0.125 mg / ml , posaconazole 0.125 mg / ml , fluconazole 64 mg / ml , micafungin 4 mg / ml and caspofungin>4 mg / ml .
arthrographis is a genus containing 5 species : a. kalrae , a. cuboidea , a. lignicola , a. pinicola and a. alba .
a. kalrae is a saprophytic fungus with a worldwide distribution , found in soil and compost . in recent years , clinical cases of invasive infections attributed to this pathogen
currently , one case of infection with arthrographis sp . and 14 cases of infection with a. kalrae have been reported ( table 1 ) : two onychomycosis , , one mycetoma , five keratitis , , , , one of which associated with sinusitis , two knee joint infection , , one endocarditis , two pulmonary infections , , one meningitis and one fungal stroke .
these cases have a worldwide distribution : seven cases in europe , one in china , one in japan , three in usa , one in mexico , one in malaysia and one in australia .
three of the five patients with keratitis were soft contact lens wearers ; the other two and the two patients with the knee joint infections have had an injury contaminated with soil .
the rest of the patients had predisposing infection factors like malnutrition , systemic corticosteroids , radiotherapy , aids , allogeneic hematopoietic stem cell transplant .
diagnoses were always based on phenotypic characteristics and microscopic morphology using de hoog and sigler , and carmichael descriptions . in most cases ,
identification of the species was confirmed by molecular biology techniques ( its , d1/d2 sequencing ) .
no data were available about the most appropriate treatment for this kind of infection . in the previous described cases , when tested the strains were sensitive to azoles , amphotericin b and terbinafin and resistant to flucytosin , but no sensibility results were showed for echinocandins .
the azoles showed high activity ( mean mic 0.46 g / ml ) , amphotericin b very little activity ( mean mic : 2 g / ml ) and echinocandins showed no in vitro activity ( mean mec at 24 h>8 g / ml ) .
these results are different from ours but concordant with those of the national reference center for invasive mycoses and antifungals , which is using the eucast method .
all patients described except the one with onychomycosis were treated with azoles associated or not with amphotericin b. some reported patients also required surgery ( keratitis and knee joint infection ) .
three patients died during their a. kalrae infection , one of them because of the fungus ( patient with fungal stroke ) .
given the fact that our patient developed a septic shock with a fungemia despite a prophylaxis with voriconazole , the choice was made to treat her with caspofungin in combination with liposomal amphotericin b. the clinical response was favorable with this treatment , regardless the resistance to the caspofungin detected by the national reference center . in the case of our patient , the evolution of the fungal infection was favorable with a rapid negativity of blood cultures and respiratory samples .
the combination of caspofungin and liposomal amphotericin b was effective in our patient whose colonization by the fungus could not be eliminated by a long - term treatment with voriconazole .
we therefore describe here the first case , to our knowledge , of an a. kalrae fungemia in a cystic fibrosis patient with an assumed pulmonary portal of entry .
please note that this journal requires full disclosure of all sources of funding and potential conflicts of interest .
the journal also requires a declaration that the author(s ) have obtained written and signed consent to publish the case report from the patient or legal guardian(s ) .
the statements on funding , conflict of interest and consent need to be submitted via our ethical form that can be downloaded from the submission site www.ees.elsevier.com/mmcr .
please note that your manuscript will not be considered for publication until the signed ethical form has been received .
[/INST]arthrographis kalrae is a hyalin fungus .
it is a saprophyte of the environment , mainly found in soil and compost . in recent years
, cases of opportunistic infections attributed to this pathogen have been described .
our patient was a 19-year - old woman with cystic fibrosis .
she presented a bacterial and fungal pulmonary colonization with aspergillus fumigatus and arthrographis .
kalrae . after her lung transplantation
, she developed an a. kalrae fungemia , treated with caspofungin 50 mg / day associated to liposomal amphotericin b i.v .
3 mg / kg / day .
the patient died 8 months after her transplantation as the result of a bacterial septic shock .</s> |
attempts to answer even the simplest questions about the behaviour of computer programs are bedevilled by uncomputability .
the concept of asymptotic intrinsic universality introduced here is based upon a bayesian approach to emulation by computer programs of other computer programs .
the method provides a means to quantify their reprogramming capabilities , associating them with a deciding procedure that asymptotically recognizes computation with a confidence value and sets forth a hierarchy of reprogrammability ( see @xcite ) based upon the likelihood of a system being , in one degree or another , close to ( or removed from ) turing universality . in @xcite , a related conjecture concerning other kinds of simply defined programs
was presented , suggesting that all busy beaver turing machines may be capable of universal computation , as they seem to share some of the informational and complex properties of systems known to be capable of universal computational behaviour .
we have recently found that most computer programs can be reprogrammed to emulate an increasing number of other ( different ) computer programs of the same size @xcite under a similar _ block emulation _ transformation or set of compilers of increasing size .
we also previously advanced a conceptual framework for reprogrammability based upon the display of different qualitative output behaviours @xcite and modelled as a type of turing test to determine computational capabilities @xcite .
this has been used in connection with an instance of natural computation in an _ in - silico _ simulation of porphyrin molecules @xcite in the context of spatial computing . here
we advance a bayesian method , namely _
asymptotic intrinsic universality _
, that draws everything together and translates the seminal concept of computation universality to degrees of belief and confidence based upon emulation and reprogrammability capabilities applicable to natural computation .
we test the method with a case study of the set of turing machines defined by the busy beaver functions .
a turing machine consists of a finite alphabet set with symbols @xmath0 and states @xmath1 , with 0 the `` halting state '' .
the turing machine `` runs '' on an one - way unbounded tape and for each pair : the machine s current `` state '' @xmath2 ; and the tape symbol @xmath3 the machine s head is `` reading '' . for each pair @xmath4 there is a corresponding instruction @xmath5 : a state @xmath6 to transition into ( which may be the same as the one it was in ) . if 0 the machine halts ; a unique symbol @xmath7 to write on the tape ( the machine can overwrite a @xmath8 on a @xmath9 , a @xmath9 on a @xmath8 , a @xmath8 on a @xmath8 , and a @xmath9 on a @xmath9 ) , and a direction to move in @xmath10 : @xmath11 ( left ) , @xmath8 ( right ) or @xmath9 ( none , when halting ) . for @xmath12 ,
there are @xmath13 turing machines with @xmath14 states according to this formalism .
the output string is taken from the number of contiguous cells on the tape the head has gone through .
we denote by @xmath15 the set ( or space ) of all @xmath14-state 2-symbol turing machines ( with the halting state not included among the @xmath14 states ) and by @xmath16 a specific turing machine with @xmath14 states and @xmath17 symbols . a _ busy beaver turing machine _
@xcite is a turing machine that , when provided with a blank tape , does a lot of work .
formally , it is an @xmath14-state @xmath17-symbol turing machine started on an initially blank tape that writes a maximum number of 1s or moves the head a maximum number of times upon halting .
an online computer program showing the behaviour of these computer programs can be found in @xcite .
most turing machines never halt , yet busy beavers do halt ( by definition over the empty tape ) .
we know from algorithmic information theory that among those turing machines that do halt , most will halt quickly or will perform very little work , yet by definition busy beavers are those that perform the greatest amount of work . in a recent investigation @xcite
focused on cellular automata ( ca ) , we have also shown that most computer programs are candidates for intrinsic universality , and thus for turing universality .
there are known values for all 2-symbol busy beavers up to 4-state turing machines , and explicit constructions give exact or lower bounds for other state and symbol pairs . if @xmath18 is the number of 1s on the tape of a turing machine @xmath19 upon halting , then : @xmath20 . if @xmath21 is the number of steps that a machine @xmath19 takes upon halting , then @xmath22 .
@xmath23 and @xmath24 are noncomputable functions by reduction to the halting problem . yet values are known for @xmath15 with @xmath25 .
busy beavers are the turing machines that perform more computation among the machines if their same size ( by number of states but more appropriately by program length in bits ) needed .
this follows from rado s definitions and it means that busy beavers have also the greatest logical depth , as defined by bennett @xcite . yet a busy beaver is required to halt .
when running for the longest time or writing the largest number of non - blank symbols , @xmath26 has to be clever enough to make wise use of its resources and an instruction away to halt at the end .
there is thus evidence that these machines are far from trivial and that for several important measures of complexity they are among most complex , if not the most , yet their computational power is unknown and its investigation would represent a way to connect complexity to computational power .
here we undertake first steps with interesting results .
the notion of _ intrinsic _ computational universality used for cellular automata was an adaptation of classical turing - universality @xcite .
_ intrinsic universality _ is stronger than turing - universality @xcite and the concept can be extended and adapted to other computing systems , including computer programs in general .
a computer program of a given size is intrinsically universal if it is able to emulate the output behaviour of any other computer program under a coarse - graining compiler @xcite .
the so - called _ game of life _ is an example of 2-dimensional cellular automaton that is not only turing - universal but also intrinsic universal @xcite .
this means that the game of life does not only compute any computable function but can also emulate the behavior of any other 2d - dimensional cellular automaton ( under rescaling ) .
( emulation / simulation by rescaling / coarse - graining ) : let @xmath27 and @xmath28 be two computer programs
. then @xmath27 emulates / simulates @xmath28 if there exists a rescaling / projection @xmath29 of @xmath27 such that @xmath30 , where @xmath31 and @xmath32 are the computed functions of @xmath27 and @xmath28 .
we consider @xmath29 a compiler to translate @xmath27 into @xmath28 ( see fig .
[ fig_3 ] ) .
the exploration of the computing capabilities of computer programs can then proceed by _ block emulation _ , whereby the scale of space - time diagrams of a computation are found and rescaled / coarse - grained .
illustration of the process of one turing machine emulating another via a block transformation . in this case
( a ) shows a @xmath33 with initial tape @xmath34 after 2 steps . by performing the block transformation of length 3 ( b ) on the initial condition of ( a ) , after 6 steps using the same @xmath33 rule one gets ( c ) .
if the output of every 3rd step is taken and the back transformation ( d ) performed on these outputs , one gets the output ( e ) .
this is identical with the output of @xmath35 with rule number @xmath36 run on the same initial condition as in ( a ) for 2 steps . in other words ,
( e ) is the coarse - grained version of the block transformed @xmath37 ( a ) which in turn produces the same output as @xmath38 of rule number @xmath36 . in this picture
one can not see the compiler directly as it is encoded within the internal states of the @xmath37 .
[ fig_emul_visual ] , width=453 ] the emulations here explored are related to an even stronger form of _ intrinsic universality _ , namely linear - time intrinsic universality @xcite , which implies that all emulations carry only a linear overhead as a result of our brute force exploration of the compiler and rule space .
this is because the coarse - graining emulation is of a block of fixed length and therefore what one can consider a compiler ( another computer program of fixed size ) .
following these ideas , one can try out different possible compilers and see what type of computer programs a specific computer program is able to emulate .
the _ linear _ block transformation was suggested in @xcite .
the exploration of the emulating space of turing machines ( tm ) is more complicated than for cellular automata because the space - time diagram does not contain the head configuration state of the turing machine .
we ran the random tms and the busy beaver turing machines for the number of steps given by @xmath24 .
for example , for @xmath39 states , @xmath40 , given by the busy beaver @xmath41 .
we looked for all transformations which allow a back transformation for block sizes 2 to 4 and only considered ( 2-symbol , 4-state ) and 3-symbol , 2-state ) busy beaver turing machines and a sample of random turing machines of the same size .
flow diagram of emulation of tms.,title="fig:",width=472 ] + to ascertain which tm from the same rule space corresponded to the emulated busy beaver or tm , we adopted the following algorithm : for a @xmath14-state and @xmath17-symbol turing machine ( tm ) , we enumerated all possible block transformations @xmath42 of given block size @xmath14 ( @xmath14-tuples ) , e.g. @xmath43 for a 3-symbol , 2 state tm .
we found a total of @xmath44 possible transformations .
we applied each member of the set of possible transformations to a tm of the corresponding rule space , in this paper that of a busy beaver ( @xmath45 ) or a randomly selected tm given a randomly initialized tape .
we then let the tm evolve for n steps .
then we took every n output line of the tm and performed a back transformation on the output , e.g. @xmath46 . at the same time we drew a tm of the same rule space out of a random sample and let it evolve for @xmath14 steps using the same initial tape .
if the output was a valid output of a tm , we tried to match it with the output of the busy beaver or random tm described above . in order to exclude trivial emulations
, we filtered out all those emulated tms which are just a @xmath14-time repetition of the initial tape .
it is important to note that we are not taking the initial states of the tms into account .
we are just focusing on the output of tms when performing the block transformations .
these facts suggest the following conjectures , which are also relevant to the dynamic behaviour of a set of simply - described machines characterized by universal behaviour . in previous work we explored these conjectures relating to busy beavers with numerical approximations of their sensitivity to initial conditions @xcite and the qualitative behaviour that initial conditions induce over space - time diagrams @xcite . which was similar to work we did on the game of life @xcite
a _ weak _ universal turing machine is a machine that allows its initial tape to be in a non all-`blank ' configuration .
if @xmath26 is weak universal , then it is allowed to start either from a periodic tape configuration or an infinite sequence produced by e.g. a finite automaton . in other words , these are machines that are turing universal not necessarily running on non - empty tapes . [ conjecture ] the busy beaver conjecture(s ) as advanced in @xcite establish(es ) that : ( strong version ) : for all @xmath47 , @xmath26 is turing universal . ( sparse version ) : for some @xmath47 , @xmath26 is turing universal .
( weak version ) : for all @xmath47 , @xmath26 is weak turing universal .
( weakest version ) : for some @xmath47 , @xmath26 is ( weak ) turing universal . here we provide evidence in favour of all conjectures in the form of an increasingly monotonic asymptotic intrinsic universal behaviour .
it is known that among all 2-state 2-symbol turing machines , none can be universal .
@xmath26 , as defined by rado @xcite , is a turing machine with @xmath14 states plus the halting state .
@xmath48 is thus actually @xmath33 , a 3-state 2-symbol machine in which one state is specially reserved for halting only .
if @xmath45 is unary , then it will be assumed to be a 2-symbol turing machine , otherwise it will be denoted by @xmath49 .
typical space - time evolution / behaviour of _ busy beaver turing machines_. the first 6 figures from left to right correspond to busy beaver machines with 2-symbols and 2 to 6 states ( for illustration purposes only those @xmath50 were plotted with a background mesh ) for which the first 3 have exact ( @xmath24 ) runtime values ( 6 , 21 , 107 ) . for the rest
a cutoff value was arbitrarily chosen , so as to provide an optimally effective illustration .
the behaviour of a busy beaver can not be a trivial repetition because it does have to avoid getting into an infinite cycle in order to halt.,title="fig:",width=302 ] typical space - time evolution / behaviour of _ busy beaver turing machines_. the first 6 figures from left to right correspond to busy beaver machines with 2-symbols and 2 to 6 states ( for illustration purposes only those @xmath50 were plotted with a background mesh ) for which the first 3 have exact ( @xmath24 ) runtime values ( 6 , 21 , 107 ) . for the rest a cutoff value was arbitrarily chosen , so as to provide an optimally effective illustration .
the behaviour of a busy beaver can not be a trivial repetition because it does have to avoid getting into an infinite cycle in order to halt.,title="fig:",width=151 ]
we looked into the number of compilers up to a certain size for which a computer program can emulate other computer programs of the same size ( e.g. in number of states for tms , number neighbours for cas , or description bits in general ) .
given all the unknown priors and the uncertainty in the degree of belief , we need a basic function that : is increasingly monotonic .
normalizing by total number of explored compilers should provide a measure for comparison , but the function itself should only count the number of emulations .
@xmath51 when @xmath52 .
evidently any emulation should amount to a non - zero value .
nonlinearly converges to 1 .
we want a function that `` slowly '' converges to a positive value and incorporates a degree of belief weighting the number of emulations found .
because intrinsic universality implies turing universality @xcite , this approach is of relevance in finding the reprogramming capabilities of classical and unconventional computing systems .
asymptotic intrinsic universality curve ( @xmath53 , made continuous for illustration purposes ) is the bayesian approach to the otherwise seminal but abstract concept of computation universality applicable to both abstract and natural / unconventional computation .
for example , we found evidence in favour of a conjecture postulating that busy beaver turing machines are somewhere on the asymptotic universality curve , highly so if the degree of belief according to @xmath54 assigns it a higher confidence every time that such a machine in question is able to emulate some other.,width=340 ] the exact shape of the function has no essential meaning as long as it is concave and complies with the above requirements .
a canonical function is @xmath53 , where @xmath55 is the number of different non - trivial emulations of a system under evaluation and @xmath56 $ ] the degree of belief modifying the rate of convergence , in this case @xmath57 ( see fig .
[ universality ] ) .
we then define the asymptotic intrinsic universality of a computing system @xmath58 as : ( asymptotic intrinsic universality ) : let @xmath58 be a computing machine of fixed size and @xmath59 the number of non - equivalent ( e.g. under coarse - graining ) emulations of other computing systems of the same size that @xmath58 can emulate , then @xmath60 is the function that retrieves a confidence value of reprogrammability based upon the intrinsic universality of @xmath58 according to belief @xmath54 . here
we provide evidence in favour of the busy beaver conjectures by way of the different qualitative behavioural properties they display and their intrinsic universality capabilities . among the intuitions suggesting the truth of one of these conjectures ,
is that it is easier to find a machine capable of halting and performing unbounded computations for a turing machine if the machine already halts after performing a sophisticated calculation , than it is to find a machine showing sophisticated behaviour whose previous characteristic was simply to halt .
this claim can actually be quantified , given that the number of turing machines that halt after @xmath61 for increasing values of @xmath14 decreases exponentially @xcite .
in other words , if a machine capable of halting is chosen by chance , there is an exponentially increasing chance of finding that it will halt sooner rather than later , meaning that most of these machines will behave trivially because they will not have enough time to do anything interesting before halting .
a b + a - d : histograms of the compressed lengths ( @xmath59 axis using compress ) of the space - time diagrams of @xmath26 for @xmath623 to 6 for @xmath63 steps each , showing accumulation of different qualitative behaviours .
e : a right - left compressed behaviour of a busy beaver runnning for @xmath64 . only rows for which the head has moved further to the right or left than ever before are kept , a method suggested in @xcite .
f : function computed by the busy beaver @xmath65 for consecutive initial conditions 1 to 100 in binary.,title="fig:",width=188 ] a - d : histograms of the compressed lengths ( @xmath59 axis using compress ) of the space - time diagrams of @xmath26 for @xmath623 to 6 for @xmath63 steps each , showing accumulation of different qualitative behaviours .
e : a right - left compressed behaviour of a busy beaver runnning for @xmath64 . only rows for which the head has moved further to the right or left than ever before are kept , a method suggested in @xcite .
f : function computed by the busy beaver @xmath65 for consecutive initial conditions 1 to 100 in binary.,title="fig:",width=188 ] + c d + a - d : histograms of the compressed lengths ( @xmath59 axis using compress ) of the space - time diagrams of @xmath26 for @xmath623 to 6 for @xmath63 steps each , showing accumulation of different qualitative behaviours .
e : a right - left compressed behaviour of a busy beaver runnning for @xmath64 .
only rows for which the head has moved further to the right or left than ever before are kept , a method suggested in @xcite .
f : function computed by the busy beaver @xmath65 for consecutive initial conditions 1 to 100 in binary.,title="fig:",width=188 ] a - d : histograms of the compressed lengths ( @xmath59 axis using compress ) of the space - time diagrams of @xmath26 for @xmath623 to 6 for @xmath63 steps each , showing accumulation of different qualitative behaviours .
e : a right - left compressed behaviour of a busy beaver runnning for @xmath64 .
only rows for which the head has moved further to the right or left than ever before are kept , a method suggested in @xcite .
f : function computed by the busy beaver @xmath65 for consecutive initial conditions 1 to 100 in binary.,title="fig:",width=188 ] + e f + a - d : histograms of the compressed lengths ( @xmath59 axis using compress ) of the space - time diagrams of @xmath26 for @xmath623 to 6 for @xmath63 steps each , showing accumulation of different qualitative behaviours .
e : a right - left compressed behaviour of a busy beaver runnning for @xmath64 . only rows for which the head has moved further to the right or left than ever before are kept , a method suggested in @xcite .
f : function computed by the busy beaver @xmath65 for consecutive initial conditions 1 to 100 in binary.,title="fig:",width=170 ] a - d : histograms of the compressed lengths ( @xmath59 axis using compress ) of the space - time diagrams of @xmath26 for @xmath623 to 6 for @xmath63 steps each , showing accumulation of different qualitative behaviours .
e : a right - left compressed behaviour of a busy beaver runnning for @xmath64 . only rows for which the head has moved further to the right or left than ever before are kept , a method suggested in @xcite .
f : function computed by the busy beaver @xmath65 for consecutive initial conditions 1 to 100 in binary.,title="fig:",width=207 ] + left : state diagram after 20 steps ( state 1 is a down - tick , state 2 is an up - tick ) .
right : two runs from different `` random '' initial conditions of length 100 bits showing ( left ) a quick halting ( computation of the identity ) and ( right ) an apparently random movement of the head for another initial condition running on the same 4-state 3-symbol busy beaver turing machine.,title="fig:",width=207 ] left : state diagram after 20 steps ( state 1 is a down - tick , state 2 is an up - tick ) .
right : two runs from different `` random '' initial conditions of length 100 bits showing ( left ) a quick halting ( computation of the identity ) and ( right ) an apparently random movement of the head for another initial condition running on the same 4-state 3-symbol busy beaver turing machine.,title="fig:",width=75 ] left : state diagram after 20 steps ( state 1 is a down - tick , state 2 is an up - tick ) .
right : two runs from different `` random '' initial conditions of length 100 bits showing ( left ) a quick halting ( computation of the identity ) and ( right ) an apparently random movement of the head for another initial condition running on the same 4-state 3-symbol busy beaver turing machine.,title="fig:",width=73 ] fig .
[ mainfig ] provides a summation of the behavioural investigation of busy beaver machines .
histograms show the different qualitative behaviour in bimodal and multimodal discrete distributions .
the multimodality is not an effect of the size of the initial condition that grows smoothly by @xmath66 , nor of the stepwise behaviour of the lossless compression algorithm ( compress based upon deflate ) . if it were an effect of the length of the initial condition , then subfigs .
b - d would look like subfig .
a , which is not the case .
they display genuinely different behaviours ( see fig . [ mainfig2](right ) ) .
the state diagram in fig .
[ mainfig2](left ) suggests how to choose an initial configuration for the machine to enter into an infinite loop ( e.g. connected cycle on the left ) , and therefore how to enter into a never - halting computation , a requirement for ( weak ) turing universality .
[ mainfig2](right ) shows the behaviour of @xmath67 for 2 different initial conditions , one for which it halts ( or `` computes '' the identity ) and another for which the computation goes on in a rather complex head movement fashion .
top : boxplots showing the differences in the emulation power of ( left ) @xmath37 versus a set of randomly selected tms in @xmath68 , and ( right ) @xmath33 versus a set of randomly selected tms in @xmath69 .
the data show how many emulations on average a set of busy beavers of a given rule space and a set of random tms selected from the same rule space can produce for given block sizes .
the data shows a variance for both tm types , since the output of valid block transformations is compared with the output of a tm sample taken from the same rule space .
trivial tms ( c.f .
flow chart in fig [ diagram ] ) are excluded .
each emulation is counted , even if it corresponds to the same tm .
the diamond shapes represent the mean of the data points .
bottom : same plots , but only tm evolutions with different hash values ( from their evolution ) are counted , i.e. only distinct tms are counted , rendering the difference between busy beavers and random turing machines even more prominent.,title="fig:",width=204 ] top : boxplots showing the differences in the emulation power of ( left ) @xmath37 versus a set of randomly selected tms in @xmath68 , and ( right ) @xmath33 versus a set of randomly selected tms in @xmath69 .
the data show how many emulations on average a set of busy beavers of a given rule space and a set of random tms selected from the same rule space can produce for given block sizes .
the data shows a variance for both tm types , since the output of valid block transformations is compared with the output of a tm sample taken from the same rule space .
trivial tms ( c.f . flow chart in fig [ diagram ] ) are excluded .
each emulation is counted , even if it corresponds to the same tm .
the diamond shapes represent the mean of the data points .
bottom : same plots , but only tm evolutions with different hash values ( from their evolution ) are counted , i.e. only distinct tms are counted , rendering the difference between busy beavers and random turing machines even more prominent.,title="fig:",width=249 ] + top : boxplots showing the differences in the emulation power of ( left ) @xmath37 versus a set of randomly selected tms in @xmath68 , and ( right ) @xmath33 versus a set of randomly selected tms in @xmath69 .
the data show how many emulations on average a set of busy beavers of a given rule space and a set of random tms selected from the same rule space can produce for given block sizes .
the data shows a variance for both tm types , since the output of valid block transformations is compared with the output of a tm sample taken from the same rule space .
trivial tms ( c.f .
flow chart in fig [ diagram ] ) are excluded .
each emulation is counted , even if it corresponds to the same tm .
the diamond shapes represent the mean of the data points .
bottom : same plots , but only tm evolutions with different hash values ( from their evolution ) are counted , i.e. only distinct tms are counted , rendering the difference between busy beavers and random turing machines even more prominent.,title="fig:",width=204 ] top : boxplots showing the differences in the emulation power of ( left ) @xmath37 versus a set of randomly selected tms in @xmath68 , and ( right ) @xmath33 versus a set of randomly selected tms in @xmath69 .
the data show how many emulations on average a set of busy beavers of a given rule space and a set of random tms selected from the same rule space can produce for given block sizes .
the data shows a variance for both tm types , since the output of valid block transformations is compared with the output of a tm sample taken from the same rule space .
trivial tms ( c.f .
flow chart in fig [ diagram ] ) are excluded .
each emulation is counted , even if it corresponds to the same tm .
the diamond shapes represent the mean of the data points .
bottom : same plots , but only tm evolutions with different hash values ( from their evolution ) are counted , i.e. only distinct tms are counted , rendering the difference between busy beavers and random turing machines even more prominent.,title="fig:",width=249 ] fig . [ fig_2 ] shows that busy beavers are much more capable of emulating the behaviour of other ( non - trivial ) turing machines than the control case , a sample of random turing machines from the same rule space size ( i.e. all machines are of the same size ) .
this is consonant with theoretical expectations @xcite .
the capacity for universal behaviour implies that a system is capable of being reprogrammed and is therefore reactive to external input .
it is no surprise that universal systems should be capable of responding to their input and doing so succinctly , if the systems in question are efficient universal systems . if the system is incapable of reacting to any input or if the output is predictable ( decidable ) for any input , the system can not be universal .
we have here provided evidence that busy beavers comply with all the requirements for turing universality and must therefore be considered a very interesting non - trivial set of turing machines that are candidates for turing universality .
evidence in favour of the conjectures is based upon the following observations : busy beavers produce space - time diagrams of the highest complexity compared to the space - time diagrams of other rules in the same rule space .
busy beavers show qualitatively different behaviour for different initial conditions ; they can halt and it is not difficult to devise ways to perform non - halting computations based upon infinite loops , especially for non - empty inputs .
the small set of busy beavers investigated emulate a larger number of other ( non - trivial ) turing machines on average compared to random turing machines of the same size .
in other words , we found evidence indicating that @xmath70 , where @xmath71 is a random turing machine in the complement set of the busy beavers @xmath72 , and the confidence level @xmath54 is fixed .
thus the measure of asymptotic intrinsic universality that we defined @xmath73 converges to 1 much faster than @xmath74 .
asymptotic intrinsic universality is strictly stronger than turing universality .
[ fig_2 ] : random tm statistics serve as a control because we know that the set of machines that either quickly halt or never halt are of density measure 1 , and will therefore end up dominating the average emulation with @xmath75 for @xmath76 .
so if we find , as we in fact did , that @xmath77 grows faster than @xmath78 , we would be demonstrating with a high level of confidence that busy beaver turing machines have greater reprogramming capabilities and are candidates for intrinsic universality , and therefore turing universality .
we have brought together several concepts that are relevant and applicable to natural computation where , e.g. , resources are often scarce and computation occurs independently of the substrate , making for concepts that are disembodied , independent not only of specific hardware but of models and formalisms ( e.g. whether one can define a halting configuration ) . on the one hand , there is the use of the concept of intrinsic universality , which our definition of asymptotic universality relies upon .
intrinsic universality as originally formulated for cellular automata does not require a halting configuration .
this makes it applicable to natural computation , because a halting state is an arbitrary choice the option to design a state as a halting one which is meaningless in natural computation .
furthermore , the coarse - graining only takes into consideration the output configuration rather than the state configuration , which is consistent with recent extensions for _ membrane computing _ or p systems @xcite , where a computation with only one possible output can be reached through many different paths , regardless of the internal states transited through en route .
indeed , since we are not looking ` inside ' the tm ( its internal states ) , we are treating it as a black box ( see fig . [ fig_3 ] ) on which we perform an external observer test .
the compiler used to look at the internal states is a behaviourally shallow one .
interestingly , the transformed tm ( in fig .
[ fig_3 ] , a busy beaver ) does lock immediately into the same pattern .
again , one would need to visualize the internal states to see a difference between other emulations producing the same output . on the other hand , in a world where `` emptiness '' or simple / completely regular initial conditions can not be guaranteed , weak universality is more realistic .
the concept of asymptotic universality is based upon and adapted to deal with these situations in the context of natural computation where a system may be a black box but its behaviour can be reinterpreted ( by emulation ) and exploited . of course one difficulty is to identify different behaviours in order to undertake a behavioural comparison , and this is why we have also introduced complexity indices that can serve as tools to quantify the space - time evolutions of systems or their representations .
a limitation of any empirical approach is that of a non - universal system able to emulate an increasing number of non - universal systems may not be universal but an open question is whether there is a threshold n above which a system is universal after simulating n number of other systems .
this is also why the emulation results should be complemented by an analysis of the complexity of the emulations themselves .
while we do know that , for example , finite automata are bounded by the kind of complexity they can produce by the complexity of the set of regular languages , the connection between these qualitative differences and the computational power of the systems in this context is a future subject of further investigation .
the chief advantage of this approach is the amenability to non - formal evidence of the reprogrammability of less conventional systems , where formal proofs of universality are difficult , if not impossible to come by . in other words , while the method does disclose universal systems at the limit , it does not rule out non - universal ones , thus producing possible false positives .
however limited , any false positive is still a reprogrammable system , thereby providing a more natural / pragmatic definition of _ natural universality_. it would not have been possible to anticipate that the behaviour displayed would have been that of busy beavers , despite their complexity for empty inputs . nor could the low emulation capabilities of all other trivial and non - trivial machines in the complement set of the busy beavers @xmath72 have been anticipated , because they are no longer being tested and quantified over the full set of possible initial conditions but over the subset that allow the emulation of other computer programs ( turing machines ) of the same ( growing ) size .
in other words , what we are exploring is the cartesian product @xmath79 of the pairs @xmath80 , where @xmath81 is a computer program ( e.g. a turing machine ) and @xmath82 a compiler that maps @xmath83 onto @xmath84 of size @xmath85 ( in this case the number of states , but in the general the number of bits , i.e. its kolmogorov complexity @xcite ) .
here we explored the reprogrammable space , a subset of the the space of all computer programs for either a specific input or , equivalently ( per turing universality ) , for all inputs .
this also means that most of the machines that either halt almost immediately and therefore do nothing interesting , or else never halt , can actually be effectively reprogrammed , and the results obtained here and in @xcite strongly suggest that they may even be candidates for intrinsic universality ( i.e. the ability to emulate any other computer program under a coarse - graining compiler ) , a stronger concept than that of turing universality .
the set of busy beaver machines describes an ( enumerable ) infinite set of turing machines characterized by a particular specific behaviour . if the conjectures are true according to the evidence we have provided , the result is more surprising , because a describable property determines the computational power of this non - trivial infinite set of turing machines .
here we have taken these ideas a step further in the direction of an empirical proposal for considering statistical computational evidence of computational universality . because of the undecidability of the halting problem we may never obtain stronger evidence of the computational capabilities of these computer programs .
we have introduced a novel experimental and methodological bayesian approach to theoretical computing challenges that circumvents traditional limitations imposed by classical definitions , in particular related to undecidability , unreachability and universality and deals with pragmatic unconventional reprogramming by behavioural emulation rather than through attempting producing formal analytical proofs , which are not only difficult , but impossible in general , specially in the realm of natural computation where we think these new concepts and methods are more relevant . delahaye j .-
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223 - 240 , springer , 2012 . | we advance a bayesian concept of _ intrinsic asymptotic universality _ , taking to its final conclusions previous conceptual and numerical work based upon a concept of a _ reprogrammability _
test and an investigation of the complex qualitative behaviour of computer programs .
our method may quantify the trust and confidence of the computing capabilities of natural and classical systems , and quantify computers by their degree of reprogrammability .
we test the method to provide evidence in favour of a conjecture concerning the computing capabilities of busy beaver turing machines as candidates for turing universality .
the method has recently been used to quantify the number of _ intrinsically universal _ cellular automata , with results that point towards the pervasiveness of universality due to a widespread capacity for emulation .
our method represents an unconventional approach to the classical and seminal concept of turing universality , and it may be extended and applied in a broader context to natural computation , by ( in something like the spirit of the turing test ) observing the behaviour of a system under circumstances where formal proofs of universality are difficult , if not impossible to come by .
+ * keywords : * computer simulation / emulation ; busy beaver turing machines ; intrinsic universality ; turing - completeness ; dynamical systems ; reprogrammability ; behavioural methods | <s>[INST]attempts to answer even the simplest questions about the behaviour of computer programs are bedevilled by uncomputability .
the concept of asymptotic intrinsic universality introduced here is based upon a bayesian approach to emulation by computer programs of other computer programs .
the method provides a means to quantify their reprogramming capabilities , associating them with a deciding procedure that asymptotically recognizes computation with a confidence value and sets forth a hierarchy of reprogrammability ( see @xcite ) based upon the likelihood of a system being , in one degree or another , close to ( or removed from ) turing universality . in @xcite , a related conjecture concerning other kinds of simply defined programs
was presented , suggesting that all busy beaver turing machines may be capable of universal computation , as they seem to share some of the informational and complex properties of systems known to be capable of universal computational behaviour .
we have recently found that most computer programs can be reprogrammed to emulate an increasing number of other ( different ) computer programs of the same size @xcite under a similar _ block emulation _ transformation or set of compilers of increasing size .
we also previously advanced a conceptual framework for reprogrammability based upon the display of different qualitative output behaviours @xcite and modelled as a type of turing test to determine computational capabilities @xcite .
this has been used in connection with an instance of natural computation in an _ in - silico _ simulation of porphyrin molecules @xcite in the context of spatial computing . here
we advance a bayesian method , namely _
asymptotic intrinsic universality _
, that draws everything together and translates the seminal concept of computation universality to degrees of belief and confidence based upon emulation and reprogrammability capabilities applicable to natural computation .
we test the method with a case study of the set of turing machines defined by the busy beaver functions .
a turing machine consists of a finite alphabet set with symbols @xmath0 and states @xmath1 , with 0 the `` halting state '' .
the turing machine `` runs '' on an one - way unbounded tape and for each pair : the machine s current `` state '' @xmath2 ; and the tape symbol @xmath3 the machine s head is `` reading '' . for each pair @xmath4 there is a corresponding instruction @xmath5 : a state @xmath6 to transition into ( which may be the same as the one it was in ) . if 0 the machine halts ; a unique symbol @xmath7 to write on the tape ( the machine can overwrite a @xmath8 on a @xmath9 , a @xmath9 on a @xmath8 , a @xmath8 on a @xmath8 , and a @xmath9 on a @xmath9 ) , and a direction to move in @xmath10 : @xmath11 ( left ) , @xmath8 ( right ) or @xmath9 ( none , when halting ) . for @xmath12 ,
there are @xmath13 turing machines with @xmath14 states according to this formalism .
the output string is taken from the number of contiguous cells on the tape the head has gone through .
we denote by @xmath15 the set ( or space ) of all @xmath14-state 2-symbol turing machines ( with the halting state not included among the @xmath14 states ) and by @xmath16 a specific turing machine with @xmath14 states and @xmath17 symbols . a _ busy beaver turing machine _
@xcite is a turing machine that , when provided with a blank tape , does a lot of work .
formally , it is an @xmath14-state @xmath17-symbol turing machine started on an initially blank tape that writes a maximum number of 1s or moves the head a maximum number of times upon halting .
an online computer program showing the behaviour of these computer programs can be found in @xcite .
most turing machines never halt , yet busy beavers do halt ( by definition over the empty tape ) .
we know from algorithmic information theory that among those turing machines that do halt , most will halt quickly or will perform very little work , yet by definition busy beavers are those that perform the greatest amount of work . in a recent investigation @xcite
focused on cellular automata ( ca ) , we have also shown that most computer programs are candidates for intrinsic universality , and thus for turing universality .
there are known values for all 2-symbol busy beavers up to 4-state turing machines , and explicit constructions give exact or lower bounds for other state and symbol pairs . if @xmath18 is the number of 1s on the tape of a turing machine @xmath19 upon halting , then : @xmath20 . if @xmath21 is the number of steps that a machine @xmath19 takes upon halting , then @xmath22 .
@xmath23 and @xmath24 are noncomputable functions by reduction to the halting problem . yet values are known for @xmath15 with @xmath25 .
busy beavers are the turing machines that perform more computation among the machines if their same size ( by number of states but more appropriately by program length in bits ) needed .
this follows from rado s definitions and it means that busy beavers have also the greatest logical depth , as defined by bennett @xcite . yet a busy beaver is required to halt .
when running for the longest time or writing the largest number of non - blank symbols , @xmath26 has to be clever enough to make wise use of its resources and an instruction away to halt at the end .
there is thus evidence that these machines are far from trivial and that for several important measures of complexity they are among most complex , if not the most , yet their computational power is unknown and its investigation would represent a way to connect complexity to computational power .
here we undertake first steps with interesting results .
the notion of _ intrinsic _ computational universality used for cellular automata was an adaptation of classical turing - universality @xcite .
_ intrinsic universality _ is stronger than turing - universality @xcite and the concept can be extended and adapted to other computing systems , including computer programs in general .
a computer program of a given size is intrinsically universal if it is able to emulate the output behaviour of any other computer program under a coarse - graining compiler @xcite .
the so - called _ game of life _ is an example of 2-dimensional cellular automaton that is not only turing - universal but also intrinsic universal @xcite .
this means that the game of life does not only compute any computable function but can also emulate the behavior of any other 2d - dimensional cellular automaton ( under rescaling ) .
( emulation / simulation by rescaling / coarse - graining ) : let @xmath27 and @xmath28 be two computer programs
. then @xmath27 emulates / simulates @xmath28 if there exists a rescaling / projection @xmath29 of @xmath27 such that @xmath30 , where @xmath31 and @xmath32 are the computed functions of @xmath27 and @xmath28 .
we consider @xmath29 a compiler to translate @xmath27 into @xmath28 ( see fig .
[ fig_3 ] ) .
the exploration of the computing capabilities of computer programs can then proceed by _ block emulation _ , whereby the scale of space - time diagrams of a computation are found and rescaled / coarse - grained .
illustration of the process of one turing machine emulating another via a block transformation . in this case
( a ) shows a @xmath33 with initial tape @xmath34 after 2 steps . by performing the block transformation of length 3 ( b ) on the initial condition of ( a ) , after 6 steps using the same @xmath33 rule one gets ( c ) .
if the output of every 3rd step is taken and the back transformation ( d ) performed on these outputs , one gets the output ( e ) .
this is identical with the output of @xmath35 with rule number @xmath36 run on the same initial condition as in ( a ) for 2 steps . in other words ,
( e ) is the coarse - grained version of the block transformed @xmath37 ( a ) which in turn produces the same output as @xmath38 of rule number @xmath36 . in this picture
one can not see the compiler directly as it is encoded within the internal states of the @xmath37 .
[ fig_emul_visual ] , width=453 ] the emulations here explored are related to an even stronger form of _ intrinsic universality _ , namely linear - time intrinsic universality @xcite , which implies that all emulations carry only a linear overhead as a result of our brute force exploration of the compiler and rule space .
this is because the coarse - graining emulation is of a block of fixed length and therefore what one can consider a compiler ( another computer program of fixed size ) .
following these ideas , one can try out different possible compilers and see what type of computer programs a specific computer program is able to emulate .
the _ linear _ block transformation was suggested in @xcite .
the exploration of the emulating space of turing machines ( tm ) is more complicated than for cellular automata because the space - time diagram does not contain the head configuration state of the turing machine .
we ran the random tms and the busy beaver turing machines for the number of steps given by @xmath24 .
for example , for @xmath39 states , @xmath40 , given by the busy beaver @xmath41 .
we looked for all transformations which allow a back transformation for block sizes 2 to 4 and only considered ( 2-symbol , 4-state ) and 3-symbol , 2-state ) busy beaver turing machines and a sample of random turing machines of the same size .
flow diagram of emulation of tms.,title="fig:",width=472 ] + to ascertain which tm from the same rule space corresponded to the emulated busy beaver or tm , we adopted the following algorithm : for a @xmath14-state and @xmath17-symbol turing machine ( tm ) , we enumerated all possible block transformations @xmath42 of given block size @xmath14 ( @xmath14-tuples ) , e.g. @xmath43 for a 3-symbol , 2 state tm .
we found a total of @xmath44 possible transformations .
we applied each member of the set of possible transformations to a tm of the corresponding rule space , in this paper that of a busy beaver ( @xmath45 ) or a randomly selected tm given a randomly initialized tape .
we then let the tm evolve for n steps .
then we took every n output line of the tm and performed a back transformation on the output , e.g. @xmath46 . at the same time we drew a tm of the same rule space out of a random sample and let it evolve for @xmath14 steps using the same initial tape .
if the output was a valid output of a tm , we tried to match it with the output of the busy beaver or random tm described above . in order to exclude trivial emulations
, we filtered out all those emulated tms which are just a @xmath14-time repetition of the initial tape .
it is important to note that we are not taking the initial states of the tms into account .
we are just focusing on the output of tms when performing the block transformations .
these facts suggest the following conjectures , which are also relevant to the dynamic behaviour of a set of simply - described machines characterized by universal behaviour . in previous work we explored these conjectures relating to busy beavers with numerical approximations of their sensitivity to initial conditions @xcite and the qualitative behaviour that initial conditions induce over space - time diagrams @xcite . which was similar to work we did on the game of life @xcite
a _ weak _ universal turing machine is a machine that allows its initial tape to be in a non all-`blank ' configuration .
if @xmath26 is weak universal , then it is allowed to start either from a periodic tape configuration or an infinite sequence produced by e.g. a finite automaton . in other words , these are machines that are turing universal not necessarily running on non - empty tapes . [ conjecture ] the busy beaver conjecture(s ) as advanced in @xcite establish(es ) that : ( strong version ) : for all @xmath47 , @xmath26 is turing universal . ( sparse version ) : for some @xmath47 , @xmath26 is turing universal .
( weak version ) : for all @xmath47 , @xmath26 is weak turing universal .
( weakest version ) : for some @xmath47 , @xmath26 is ( weak ) turing universal . here we provide evidence in favour of all conjectures in the form of an increasingly monotonic asymptotic intrinsic universal behaviour .
it is known that among all 2-state 2-symbol turing machines , none can be universal .
@xmath26 , as defined by rado @xcite , is a turing machine with @xmath14 states plus the halting state .
@xmath48 is thus actually @xmath33 , a 3-state 2-symbol machine in which one state is specially reserved for halting only .
if @xmath45 is unary , then it will be assumed to be a 2-symbol turing machine , otherwise it will be denoted by @xmath49 .
typical space - time evolution / behaviour of _ busy beaver turing machines_. the first 6 figures from left to right correspond to busy beaver machines with 2-symbols and 2 to 6 states ( for illustration purposes only those @xmath50 were plotted with a background mesh ) for which the first 3 have exact ( @xmath24 ) runtime values ( 6 , 21 , 107 ) . for the rest
a cutoff value was arbitrarily chosen , so as to provide an optimally effective illustration .
the behaviour of a busy beaver can not be a trivial repetition because it does have to avoid getting into an infinite cycle in order to halt.,title="fig:",width=302 ] typical space - time evolution / behaviour of _ busy beaver turing machines_. the first 6 figures from left to right correspond to busy beaver machines with 2-symbols and 2 to 6 states ( for illustration purposes only those @xmath50 were plotted with a background mesh ) for which the first 3 have exact ( @xmath24 ) runtime values ( 6 , 21 , 107 ) . for the rest a cutoff value was arbitrarily chosen , so as to provide an optimally effective illustration .
the behaviour of a busy beaver can not be a trivial repetition because it does have to avoid getting into an infinite cycle in order to halt.,title="fig:",width=151 ]
we looked into the number of compilers up to a certain size for which a computer program can emulate other computer programs of the same size ( e.g. in number of states for tms , number neighbours for cas , or description bits in general ) .
given all the unknown priors and the uncertainty in the degree of belief , we need a basic function that : is increasingly monotonic .
normalizing by total number of explored compilers should provide a measure for comparison , but the function itself should only count the number of emulations .
@xmath51 when @xmath52 .
evidently any emulation should amount to a non - zero value .
nonlinearly converges to 1 .
we want a function that `` slowly '' converges to a positive value and incorporates a degree of belief weighting the number of emulations found .
because intrinsic universality implies turing universality @xcite , this approach is of relevance in finding the reprogramming capabilities of classical and unconventional computing systems .
asymptotic intrinsic universality curve ( @xmath53 , made continuous for illustration purposes ) is the bayesian approach to the otherwise seminal but abstract concept of computation universality applicable to both abstract and natural / unconventional computation .
for example , we found evidence in favour of a conjecture postulating that busy beaver turing machines are somewhere on the asymptotic universality curve , highly so if the degree of belief according to @xmath54 assigns it a higher confidence every time that such a machine in question is able to emulate some other.,width=340 ] the exact shape of the function has no essential meaning as long as it is concave and complies with the above requirements .
a canonical function is @xmath53 , where @xmath55 is the number of different non - trivial emulations of a system under evaluation and @xmath56 $ ] the degree of belief modifying the rate of convergence , in this case @xmath57 ( see fig .
[ universality ] ) .
we then define the asymptotic intrinsic universality of a computing system @xmath58 as : ( asymptotic intrinsic universality ) : let @xmath58 be a computing machine of fixed size and @xmath59 the number of non - equivalent ( e.g. under coarse - graining ) emulations of other computing systems of the same size that @xmath58 can emulate , then @xmath60 is the function that retrieves a confidence value of reprogrammability based upon the intrinsic universality of @xmath58 according to belief @xmath54 . here
we provide evidence in favour of the busy beaver conjectures by way of the different qualitative behavioural properties they display and their intrinsic universality capabilities . among the intuitions suggesting the truth of one of these conjectures ,
is that it is easier to find a machine capable of halting and performing unbounded computations for a turing machine if the machine already halts after performing a sophisticated calculation , than it is to find a machine showing sophisticated behaviour whose previous characteristic was simply to halt .
this claim can actually be quantified , given that the number of turing machines that halt after @xmath61 for increasing values of @xmath14 decreases exponentially @xcite .
in other words , if a machine capable of halting is chosen by chance , there is an exponentially increasing chance of finding that it will halt sooner rather than later , meaning that most of these machines will behave trivially because they will not have enough time to do anything interesting before halting .
a b + a - d : histograms of the compressed lengths ( @xmath59 axis using compress ) of the space - time diagrams of @xmath26 for @xmath623 to 6 for @xmath63 steps each , showing accumulation of different qualitative behaviours .
e : a right - left compressed behaviour of a busy beaver runnning for @xmath64 . only rows for which the head has moved further to the right or left than ever before are kept , a method suggested in @xcite .
f : function computed by the busy beaver @xmath65 for consecutive initial conditions 1 to 100 in binary.,title="fig:",width=188 ] a - d : histograms of the compressed lengths ( @xmath59 axis using compress ) of the space - time diagrams of @xmath26 for @xmath623 to 6 for @xmath63 steps each , showing accumulation of different qualitative behaviours .
e : a right - left compressed behaviour of a busy beaver runnning for @xmath64 . only rows for which the head has moved further to the right or left than ever before are kept , a method suggested in @xcite .
f : function computed by the busy beaver @xmath65 for consecutive initial conditions 1 to 100 in binary.,title="fig:",width=188 ] + c d + a - d : histograms of the compressed lengths ( @xmath59 axis using compress ) of the space - time diagrams of @xmath26 for @xmath623 to 6 for @xmath63 steps each , showing accumulation of different qualitative behaviours .
e : a right - left compressed behaviour of a busy beaver runnning for @xmath64 .
only rows for which the head has moved further to the right or left than ever before are kept , a method suggested in @xcite .
f : function computed by the busy beaver @xmath65 for consecutive initial conditions 1 to 100 in binary.,title="fig:",width=188 ] a - d : histograms of the compressed lengths ( @xmath59 axis using compress ) of the space - time diagrams of @xmath26 for @xmath623 to 6 for @xmath63 steps each , showing accumulation of different qualitative behaviours .
e : a right - left compressed behaviour of a busy beaver runnning for @xmath64 .
only rows for which the head has moved further to the right or left than ever before are kept , a method suggested in @xcite .
f : function computed by the busy beaver @xmath65 for consecutive initial conditions 1 to 100 in binary.,title="fig:",width=188 ] + e f + a - d : histograms of the compressed lengths ( @xmath59 axis using compress ) of the space - time diagrams of @xmath26 for @xmath623 to 6 for @xmath63 steps each , showing accumulation of different qualitative behaviours .
e : a right - left compressed behaviour of a busy beaver runnning for @xmath64 . only rows for which the head has moved further to the right or left than ever before are kept , a method suggested in @xcite .
f : function computed by the busy beaver @xmath65 for consecutive initial conditions 1 to 100 in binary.,title="fig:",width=170 ] a - d : histograms of the compressed lengths ( @xmath59 axis using compress ) of the space - time diagrams of @xmath26 for @xmath623 to 6 for @xmath63 steps each , showing accumulation of different qualitative behaviours .
e : a right - left compressed behaviour of a busy beaver runnning for @xmath64 . only rows for which the head has moved further to the right or left than ever before are kept , a method suggested in @xcite .
f : function computed by the busy beaver @xmath65 for consecutive initial conditions 1 to 100 in binary.,title="fig:",width=207 ] + left : state diagram after 20 steps ( state 1 is a down - tick , state 2 is an up - tick ) .
right : two runs from different `` random '' initial conditions of length 100 bits showing ( left ) a quick halting ( computation of the identity ) and ( right ) an apparently random movement of the head for another initial condition running on the same 4-state 3-symbol busy beaver turing machine.,title="fig:",width=207 ] left : state diagram after 20 steps ( state 1 is a down - tick , state 2 is an up - tick ) .
right : two runs from different `` random '' initial conditions of length 100 bits showing ( left ) a quick halting ( computation of the identity ) and ( right ) an apparently random movement of the head for another initial condition running on the same 4-state 3-symbol busy beaver turing machine.,title="fig:",width=75 ] left : state diagram after 20 steps ( state 1 is a down - tick , state 2 is an up - tick ) .
right : two runs from different `` random '' initial conditions of length 100 bits showing ( left ) a quick halting ( computation of the identity ) and ( right ) an apparently random movement of the head for another initial condition running on the same 4-state 3-symbol busy beaver turing machine.,title="fig:",width=73 ] fig .
[ mainfig ] provides a summation of the behavioural investigation of busy beaver machines .
histograms show the different qualitative behaviour in bimodal and multimodal discrete distributions .
the multimodality is not an effect of the size of the initial condition that grows smoothly by @xmath66 , nor of the stepwise behaviour of the lossless compression algorithm ( compress based upon deflate ) . if it were an effect of the length of the initial condition , then subfigs .
b - d would look like subfig .
a , which is not the case .
they display genuinely different behaviours ( see fig . [ mainfig2](right ) ) .
the state diagram in fig .
[ mainfig2](left ) suggests how to choose an initial configuration for the machine to enter into an infinite loop ( e.g. connected cycle on the left ) , and therefore how to enter into a never - halting computation , a requirement for ( weak ) turing universality .
[ mainfig2](right ) shows the behaviour of @xmath67 for 2 different initial conditions , one for which it halts ( or `` computes '' the identity ) and another for which the computation goes on in a rather complex head movement fashion .
top : boxplots showing the differences in the emulation power of ( left ) @xmath37 versus a set of randomly selected tms in @xmath68 , and ( right ) @xmath33 versus a set of randomly selected tms in @xmath69 .
the data show how many emulations on average a set of busy beavers of a given rule space and a set of random tms selected from the same rule space can produce for given block sizes .
the data shows a variance for both tm types , since the output of valid block transformations is compared with the output of a tm sample taken from the same rule space .
trivial tms ( c.f .
flow chart in fig [ diagram ] ) are excluded .
each emulation is counted , even if it corresponds to the same tm .
the diamond shapes represent the mean of the data points .
bottom : same plots , but only tm evolutions with different hash values ( from their evolution ) are counted , i.e. only distinct tms are counted , rendering the difference between busy beavers and random turing machines even more prominent.,title="fig:",width=204 ] top : boxplots showing the differences in the emulation power of ( left ) @xmath37 versus a set of randomly selected tms in @xmath68 , and ( right ) @xmath33 versus a set of randomly selected tms in @xmath69 .
the data show how many emulations on average a set of busy beavers of a given rule space and a set of random tms selected from the same rule space can produce for given block sizes .
the data shows a variance for both tm types , since the output of valid block transformations is compared with the output of a tm sample taken from the same rule space .
trivial tms ( c.f . flow chart in fig [ diagram ] ) are excluded .
each emulation is counted , even if it corresponds to the same tm .
the diamond shapes represent the mean of the data points .
bottom : same plots , but only tm evolutions with different hash values ( from their evolution ) are counted , i.e. only distinct tms are counted , rendering the difference between busy beavers and random turing machines even more prominent.,title="fig:",width=249 ] + top : boxplots showing the differences in the emulation power of ( left ) @xmath37 versus a set of randomly selected tms in @xmath68 , and ( right ) @xmath33 versus a set of randomly selected tms in @xmath69 .
the data show how many emulations on average a set of busy beavers of a given rule space and a set of random tms selected from the same rule space can produce for given block sizes .
the data shows a variance for both tm types , since the output of valid block transformations is compared with the output of a tm sample taken from the same rule space .
trivial tms ( c.f .
flow chart in fig [ diagram ] ) are excluded .
each emulation is counted , even if it corresponds to the same tm .
the diamond shapes represent the mean of the data points .
bottom : same plots , but only tm evolutions with different hash values ( from their evolution ) are counted , i.e. only distinct tms are counted , rendering the difference between busy beavers and random turing machines even more prominent.,title="fig:",width=204 ] top : boxplots showing the differences in the emulation power of ( left ) @xmath37 versus a set of randomly selected tms in @xmath68 , and ( right ) @xmath33 versus a set of randomly selected tms in @xmath69 .
the data show how many emulations on average a set of busy beavers of a given rule space and a set of random tms selected from the same rule space can produce for given block sizes .
the data shows a variance for both tm types , since the output of valid block transformations is compared with the output of a tm sample taken from the same rule space .
trivial tms ( c.f .
flow chart in fig [ diagram ] ) are excluded .
each emulation is counted , even if it corresponds to the same tm .
the diamond shapes represent the mean of the data points .
bottom : same plots , but only tm evolutions with different hash values ( from their evolution ) are counted , i.e. only distinct tms are counted , rendering the difference between busy beavers and random turing machines even more prominent.,title="fig:",width=249 ] fig . [ fig_2 ] shows that busy beavers are much more capable of emulating the behaviour of other ( non - trivial ) turing machines than the control case , a sample of random turing machines from the same rule space size ( i.e. all machines are of the same size ) .
this is consonant with theoretical expectations @xcite .
the capacity for universal behaviour implies that a system is capable of being reprogrammed and is therefore reactive to external input .
it is no surprise that universal systems should be capable of responding to their input and doing so succinctly , if the systems in question are efficient universal systems . if the system is incapable of reacting to any input or if the output is predictable ( decidable ) for any input , the system can not be universal .
we have here provided evidence that busy beavers comply with all the requirements for turing universality and must therefore be considered a very interesting non - trivial set of turing machines that are candidates for turing universality .
evidence in favour of the conjectures is based upon the following observations : busy beavers produce space - time diagrams of the highest complexity compared to the space - time diagrams of other rules in the same rule space .
busy beavers show qualitatively different behaviour for different initial conditions ; they can halt and it is not difficult to devise ways to perform non - halting computations based upon infinite loops , especially for non - empty inputs .
the small set of busy beavers investigated emulate a larger number of other ( non - trivial ) turing machines on average compared to random turing machines of the same size .
in other words , we found evidence indicating that @xmath70 , where @xmath71 is a random turing machine in the complement set of the busy beavers @xmath72 , and the confidence level @xmath54 is fixed .
thus the measure of asymptotic intrinsic universality that we defined @xmath73 converges to 1 much faster than @xmath74 .
asymptotic intrinsic universality is strictly stronger than turing universality .
[ fig_2 ] : random tm statistics serve as a control because we know that the set of machines that either quickly halt or never halt are of density measure 1 , and will therefore end up dominating the average emulation with @xmath75 for @xmath76 .
so if we find , as we in fact did , that @xmath77 grows faster than @xmath78 , we would be demonstrating with a high level of confidence that busy beaver turing machines have greater reprogramming capabilities and are candidates for intrinsic universality , and therefore turing universality .
we have brought together several concepts that are relevant and applicable to natural computation where , e.g. , resources are often scarce and computation occurs independently of the substrate , making for concepts that are disembodied , independent not only of specific hardware but of models and formalisms ( e.g. whether one can define a halting configuration ) . on the one hand , there is the use of the concept of intrinsic universality , which our definition of asymptotic universality relies upon .
intrinsic universality as originally formulated for cellular automata does not require a halting configuration .
this makes it applicable to natural computation , because a halting state is an arbitrary choice the option to design a state as a halting one which is meaningless in natural computation .
furthermore , the coarse - graining only takes into consideration the output configuration rather than the state configuration , which is consistent with recent extensions for _ membrane computing _ or p systems @xcite , where a computation with only one possible output can be reached through many different paths , regardless of the internal states transited through en route .
indeed , since we are not looking ` inside ' the tm ( its internal states ) , we are treating it as a black box ( see fig . [ fig_3 ] ) on which we perform an external observer test .
the compiler used to look at the internal states is a behaviourally shallow one .
interestingly , the transformed tm ( in fig .
[ fig_3 ] , a busy beaver ) does lock immediately into the same pattern .
again , one would need to visualize the internal states to see a difference between other emulations producing the same output . on the other hand , in a world where `` emptiness '' or simple / completely regular initial conditions can not be guaranteed , weak universality is more realistic .
the concept of asymptotic universality is based upon and adapted to deal with these situations in the context of natural computation where a system may be a black box but its behaviour can be reinterpreted ( by emulation ) and exploited . of course one difficulty is to identify different behaviours in order to undertake a behavioural comparison , and this is why we have also introduced complexity indices that can serve as tools to quantify the space - time evolutions of systems or their representations .
a limitation of any empirical approach is that of a non - universal system able to emulate an increasing number of non - universal systems may not be universal but an open question is whether there is a threshold n above which a system is universal after simulating n number of other systems .
this is also why the emulation results should be complemented by an analysis of the complexity of the emulations themselves .
while we do know that , for example , finite automata are bounded by the kind of complexity they can produce by the complexity of the set of regular languages , the connection between these qualitative differences and the computational power of the systems in this context is a future subject of further investigation .
the chief advantage of this approach is the amenability to non - formal evidence of the reprogrammability of less conventional systems , where formal proofs of universality are difficult , if not impossible to come by . in other words , while the method does disclose universal systems at the limit , it does not rule out non - universal ones , thus producing possible false positives .
however limited , any false positive is still a reprogrammable system , thereby providing a more natural / pragmatic definition of _ natural universality_. it would not have been possible to anticipate that the behaviour displayed would have been that of busy beavers , despite their complexity for empty inputs . nor could the low emulation capabilities of all other trivial and non - trivial machines in the complement set of the busy beavers @xmath72 have been anticipated , because they are no longer being tested and quantified over the full set of possible initial conditions but over the subset that allow the emulation of other computer programs ( turing machines ) of the same ( growing ) size .
in other words , what we are exploring is the cartesian product @xmath79 of the pairs @xmath80 , where @xmath81 is a computer program ( e.g. a turing machine ) and @xmath82 a compiler that maps @xmath83 onto @xmath84 of size @xmath85 ( in this case the number of states , but in the general the number of bits , i.e. its kolmogorov complexity @xcite ) .
here we explored the reprogrammable space , a subset of the the space of all computer programs for either a specific input or , equivalently ( per turing universality ) , for all inputs .
this also means that most of the machines that either halt almost immediately and therefore do nothing interesting , or else never halt , can actually be effectively reprogrammed , and the results obtained here and in @xcite strongly suggest that they may even be candidates for intrinsic universality ( i.e. the ability to emulate any other computer program under a coarse - graining compiler ) , a stronger concept than that of turing universality .
the set of busy beaver machines describes an ( enumerable ) infinite set of turing machines characterized by a particular specific behaviour . if the conjectures are true according to the evidence we have provided , the result is more surprising , because a describable property determines the computational power of this non - trivial infinite set of turing machines .
here we have taken these ideas a step further in the direction of an empirical proposal for considering statistical computational evidence of computational universality . because of the undecidability of the halting problem we may never obtain stronger evidence of the computational capabilities of these computer programs .
we have introduced a novel experimental and methodological bayesian approach to theoretical computing challenges that circumvents traditional limitations imposed by classical definitions , in particular related to undecidability , unreachability and universality and deals with pragmatic unconventional reprogramming by behavioural emulation rather than through attempting producing formal analytical proofs , which are not only difficult , but impossible in general , specially in the realm of natural computation where we think these new concepts and methods are more relevant . delahaye j .-
p . and zenil h. , numerical evaluation of the complexity of short strings : a glance into the innermost structure of algorithmic randomness , _ applied mathematics and computation _ , 219 , pp .
6377 , 2012 .
ollinger n. , the quest for small universal cellular automata , _ international colloquium on automata , languages and programming ( icalp2002 ) , _ widmayer p. , triguero f. , morales r , hennessy m. , eidenbenz s. and conejo r. ( eds ) , _ lncs _ 2380 , pp . 318329 , 2002 .
ollinger n. , the intrinsic universality problem of one - dimensional cellular automata , _ symposium on theoretical aspects of computer science ( stacs2003 ) _ , alt h. and habib m. ( eds ) , _ lncs _ 2607 , pp . 632641 , 2003 . zenil h. , algorithmicity and programmability in natural computing with the game of life as an in silico case study , _ journal of experimental & theoretical artificial intelligence _ , volume 27 ,
issue 1 , pp . 109121 , 2015 .
zenil h. , a behavioural foundation for natural computing and a programmability test . in g.
dodig - crnkovic and r. giovagnoli ( eds ) , _ computing nature : turing centenary perspective _ , springer sapere series vol . 7 , pp . 87113 , 2013 .
zenil , h. from computer runtimes to the length of proofs : with an algorithmic probabilistic application to waiting times in automatic theorem proving . in dinneen ,
khousainov , b. and nies , a. ( eds . ) , _ computation , physics and beyond international workshop on theoretical computer science _ ,
wtcs 2012 , lncs 7160 , pp .
223 - 240 , springer , 2012 .[/INST] we advance a bayesian concept of _ intrinsic asymptotic universality _ , taking to its final conclusions previous conceptual and numerical work based upon a concept of a _ reprogrammability _
test and an investigation of the complex qualitative behaviour of computer programs .
our method may quantify the trust and confidence of the computing capabilities of natural and classical systems , and quantify computers by their degree of reprogrammability .
we test the method to provide evidence in favour of a conjecture concerning the computing capabilities of busy beaver turing machines as candidates for turing universality .
the method has recently been used to quantify the number of _ intrinsically universal _ cellular automata , with results that point towards the pervasiveness of universality due to a widespread capacity for emulation .
our method represents an unconventional approach to the classical and seminal concept of turing universality , and it may be extended and applied in a broader context to natural computation , by ( in something like the spirit of the turing test ) observing the behaviour of a system under circumstances where formal proofs of universality are difficult , if not impossible to come by .
+ * keywords : * computer simulation / emulation ; busy beaver turing machines ; intrinsic universality ; turing - completeness ; dynamical systems ; reprogrammability ; behavioural methods </s> |
Two days after Malaysia Airlines Flight 17 crashed, killing 298 people, concerns are growing that rebel fighters are blocking access to the site and tampering with evidence. Photo: AP
DONETSK, Ukraine—When international observers arrived for the first time at the Flight 17 crash site outside this separatist-held capital on Friday afternoon, they found what they described as a field of already decomposing body parts and debris, lacking a secure cordon or any discernible on-site management. It was guarded by armed irregulars, some of whom the observers accused of being drunk.
The visit of monitors from the Organization for Security and Cooperation in Europe, limited to 75 minutes and two areas of debris,... ||||| Media playback is unsupported on your device Media caption The BBC's Richard Galpin describes "horrific scenes in beautiful fields" where MH17 came down
Ukraine has accused pro-Russian militiamen at the site of the Malaysia Airlines crash of trying to destroy evidence of an "international crime".
For a second day, OSCE monitors at the scene have had their movements restricted by militiamen.
Reports that bodies have been moved prompted anger from the Netherlands. Most of the passengers were Dutch.
The jet was reportedly hit by a missile over a rebel-held area in east Ukraine on Thursday. All 298 people died.
Both Ukraine and the rebels have accused each other of shooting it down.
The Boeing 777 flight MH17 was flying from Amsterdam to Kuala Lumpur. It fell between Krasni Luch in Luhansk region and Shakhtarsk in the neighbouring region of Donetsk.
The passenger list released by Malaysia Airlines shows the plane was carrying 193 Dutch nationals (including one with dual US nationality), 43 Malaysians (including 15 crew), 27 Australians, 12 Indonesians and 10 Britons (including one with dual South African nationality), four Germans, four Belgians, three from the Philippines, and one each from Canada and New Zealand.
Image copyright AFP Image caption The UN Security Council has called for a full and independent international investigation into the crash
Image copyright AFP Image caption The tragedy has shocked the world community
Image copyright AFP Image caption OSCE monitors say pro-Russian gunmen allowed them to visit more of the area on Saturday
Pressure on Russia
In a statement, the Ukrainian government complained that pro-Russian rebels had removed 38 bodies from the site near the village of Grabove and taken them to a morgue in the rebel-held city of Donetsk.
The BBC's Richard Galpin, who is at the crash site, says he saw bodies being removed by emergency workers, but it was not clear where they were being taken, nor whether the workers were loyal to the rebels or the government in Kiev.
Dutch Foreign Minister Frans Timmermans, who is visiting Ukraine, said he had been "shocked" by the reported removals.
"As soon as we receive proof, we will not rest until those guilty are put to trial - not only those who pulled the trigger, but also those who made it possible," he said.
At the scene: Fergal Keane, BBC News, Grabove
Image copyright AFP Image caption The OSCE monitors were forced to walk to the field where the plane crashed
At the main site the bodies were without covering. Some lay alone. Others were grouped together amid the twisted metal, the bags and cases, the child's playing cards, the guide books, the laptop computer, the duty free whiskey bottle, the woman's hat.
A militiaman with the nickname "Grumpy" - he was squat and barrel-chested with poor teeth and carried a machine gun - harangued me when I asked if the rebels would now stop fighting.
"You are only here because foreigners are dead," he said. And the old story was repeated, the same I have heard on numerous roadblocks - the Western media were all capitalists doing the bidding of their American and EU masters.
When the OSCE turned up in a convoy "Grumpy" came into his own. Now he was a man of power. He halted the OSCE and told them they would have to go forward on foot.
Scant respect for bodies at crash site
The world community, Ukraine added, must put pressure on Russia to pull back its "terrorists" and allow Ukrainian and international experts to carry out their inquiry.
Speaking in Kuala Lumpur, Malaysian Transport Minister Liow Tiong-Lai said it would be "inhumane" if Malaysian experts would not be given access to the crash site.
He also expressed concern that the site was not properly sealed and could be tampered with.
The monitors from the Organization for Security and Co-operation in Europe (OSCE) are now at the site.
Image copyright Reuters Image caption The UK urged Russia to use its influence over the rebels to improve access to the site
OSCE spokesman Michael Bociurkiw said access had improved from Friday and that the monitors were seeing parts of the field they had not seen before.
However he added that their movements were still being restricted. "We are unarmed civilians, we are not in the position to argue heavily with people with heavy arms," he said.
The monitors' mission is to observe the site pending the arrival of international experts being sent to investigate the cause of the crash.
'Act of terrorism'
On Saturday the Russian foreign ministry urged both sides in the Ukrainian conflict "to do everything possible to give international experts access to the aircraft crash".
Earlier, the Russian defence ministry accused the West of waging an information war against Moscow. It challenged Ukraine to produce details of what its anti-aircraft systems were doing at the time.
UK Prime Minister David Cameron and his Dutch counterpart Mark Rutte - who discussed the matter in a phone conversation on Saturday - called on the EU to "reconsider its approach to Russia" following the disaster.
Separatist leaders have denied earlier reports that the plane's flight recorders - the so-called black boxes - had been found.
Ukraine's government called Thursday's disaster an "act of terrorism" and released what they say are intercepted phone conversations that proved the plane was shot down by separatists.
Ukrainian officials also said they had evidence Russian military personnel operated a sophisticated Buk missile system that is thought to have been used to shoot down the plane.
The pro-Russian separatists claim a Ukrainian air force jet brought down the airliner. ||||| Kiev says pro-Russia rebels have removed bodies from crash site with help from Moscow, and are trying to destroy evidence
Ukraine's government accused pro-Russia rebels on Saturday of removing corpses from the MH17 crash site and destroying evidence.
"Terrorists brought 38 bodies to the mortuary in Donetsk," the government statement read, adding that Russian experts would presumably perform autopsies. "The terrorists are seeking for the heavy load trucks to carry the plane wreckage to Russia," the statement added.
A rebel, who identified himself as "Grumpy", neither confirmed nor denied the claims that bodies had been moved to Donetsk. "Maybe they did it, maybe not," he said. "I personally didn't do that."
On Saturday the rebels fired several shots in the air to prevent journalists from approaching to bodies at the crash site. They also fired the warning shots at OSCE monitors on Friday to prevent them from approaching the wreckage of the Malaysia Airlines flight.
The security of the crash site, outside the village of Grabovo in eastern Ukraine, is crucial to preserving evidence that will determine who and what brought the airliner down, but talks between Kiev and rebels who are in control of it have so far failed to establish a buffer zone where international investigators can work, or to give them access.
The head of Ukraine's security service, Valentyn Nalyvaychenko, said in televised remarks on Saturday that talks had agreed a 20km security zone around the site "so that Ukraine could fulfil the most important thing – identify the bodies hand them over to relatives". A senior official of the self-styled Donetsk People's Republic, however, said no agreement had been reached.
A spokesman for the Organisation for Security and Cooperation in Europe (OSCE), Michael Bociurkiw, also said he was not aware of any agreement, and reports from the scene said there was no security zone.
A team of nearly 30 OSCE observers attempted for second time to gain access to the crash site on Saturday after meeting resistance from armed rebels on Friday. The monitors were allowed to view one part of the site under escort.
Aleksander Borodai, prime minister of the self-styled Donetsk People's Republic, denied rebels had touched the crash site but said it would move the bodies for "humanitarian" reasons and called on Russia to help. "Bodies of innocent people are lying out in the heat. We reserve the right, if the delay continues ... to begin the process of taking away the bodies. We ask the Russian Federation to help us with this problem and send their experts," he said.
Workers at the scene have recovered more than 180 bodies, which have begun to decompose under the summer sun. All 298 on board the plane were killed in the crash.
Malaysia's transport minister, Liow Tiong Lai, called on the UN on Saturday to assist with a ceasefire in eastern Ukraine and ensure that investigators have safe access to the crash site so they can remove bodies as quickly as possible. Anything less would be inhumane, he said.
Investigators from the Netherlands, home to 192 of the victims, arrived in Kiev overnight. A team from Malaysia, home to 44, is also in Ukraine. The Malaysian transport minster is to join the team and attempt to gain access to the site.
Six investigators from the UK Air Accidents Investigation Branch are also to join the growing international investigation. The UK Foreign Office has sent extra consular staff to Ukraine and the Metropolitan police are liaising with international partners to send specialist officers to assist with the recovery, identification and repatriation of those killed. The dead include 10 British nationals.
There is growing international condemnation of pro-Russian separatists over the incident, with Washington pointing the finger of blame at the militias. The Pentagon confirmed a surface-to-air missile fired from territory controlled by separatists brought down the plane, but stopped short of accusing Russia of supplying the weapon.
In the UK, Downing Street said it appeared increasingly likely that the catastrophe was the result of a surface-to-air missile fired from near rebel-held Torez.
The Australian prime minster, Tony Abbott, repeated his assertion on Saturday that all evidence suggests that the missile came from an area controlled by Russian-backed separatists, using equipment likely supplied by Russia.
At a charged UN security council meeting on Friday the US ambassador, Samantha Power, said the US "cannot rule out technical assistance from Russia" while the Russian ambassador, Vitaly Churkin, said Moscow "places all blame on Kiev".
Barack Obama on Friday said the circumstances of the crash, which came at the end of a week in which pro-Russian separatists claimed to have shot down Ukrainian military aircraft, suggested some Russian assistance to the rebel forces.
"We don't yet know exactly what happened with respect to Malaysia Airlines, although obviously we are beginning to draw some conclusions given the nature of the shot that was fired. There are only certain types of anti-aircraft missiles that can reach up 30,000ft and shoot down a passenger jet.
"Set aside what's happened with respect to the Malaysian airliner, a group of separatists cannot shoot down military transport planes or, they claim, shoot down fighter jets without sophisticated equipment and sophisticated training and that's coming from Russia."
The Chinese president, Xi Jinping, who has avoided discussing the issue of responsibility, said on Saturday that he hoped "a fair and objective probe will be carried out to establish the truth as early as possible". | – The chances of a "credible international investigation" taking place in the aftermath of this week's Malaysian Airlines crash seem to be dwindling by the hour. Ukraine today accused pro-Russian separatists of removing bodies and wreckage from the crash site without proper authorization, reports the BBC. Specifically, it says that men with Russian accents took 38 bodies to a morgue in rebel-held Donetsk and threatened to conduct their own autopsies, and that they were trying to ship pieces of the wreckage to Moscow. The development comes after US intelligence suggested that the plane got shot down with a Russian-supplied missile system fired from rebel territory. "The government of Ukraine officially states that the terrorists, with the help of Russia, are trying to destroy evidence of international crimes," says the Ukraine statement, as per the Guardian. A team from the Organization for Security and Cooperation in Europe was to try to return to the crash site today after being allowed to visit for only 75 minutes yesterday and meeting some resistance from rebels, some of whom were believed to be drunk, reports the Wall Street Journal. "The whole world should unite, so as to enter that territory and investigate objectively," says Ukraine's deputy prime minister. | <s>[INST]Two days after Malaysia Airlines Flight 17 crashed, killing 298 people, concerns are growing that rebel fighters are blocking access to the site and tampering with evidence. Photo: AP
DONETSK, Ukraine—When international observers arrived for the first time at the Flight 17 crash site outside this separatist-held capital on Friday afternoon, they found what they described as a field of already decomposing body parts and debris, lacking a secure cordon or any discernible on-site management. It was guarded by armed irregulars, some of whom the observers accused of being drunk.
The visit of monitors from the Organization for Security and Cooperation in Europe, limited to 75 minutes and two areas of debris,... ||||| Media playback is unsupported on your device Media caption The BBC's Richard Galpin describes "horrific scenes in beautiful fields" where MH17 came down
Ukraine has accused pro-Russian militiamen at the site of the Malaysia Airlines crash of trying to destroy evidence of an "international crime".
For a second day, OSCE monitors at the scene have had their movements restricted by militiamen.
Reports that bodies have been moved prompted anger from the Netherlands. Most of the passengers were Dutch.
The jet was reportedly hit by a missile over a rebel-held area in east Ukraine on Thursday. All 298 people died.
Both Ukraine and the rebels have accused each other of shooting it down.
The Boeing 777 flight MH17 was flying from Amsterdam to Kuala Lumpur. It fell between Krasni Luch in Luhansk region and Shakhtarsk in the neighbouring region of Donetsk.
The passenger list released by Malaysia Airlines shows the plane was carrying 193 Dutch nationals (including one with dual US nationality), 43 Malaysians (including 15 crew), 27 Australians, 12 Indonesians and 10 Britons (including one with dual South African nationality), four Germans, four Belgians, three from the Philippines, and one each from Canada and New Zealand.
Image copyright AFP Image caption The UN Security Council has called for a full and independent international investigation into the crash
Image copyright AFP Image caption The tragedy has shocked the world community
Image copyright AFP Image caption OSCE monitors say pro-Russian gunmen allowed them to visit more of the area on Saturday
Pressure on Russia
In a statement, the Ukrainian government complained that pro-Russian rebels had removed 38 bodies from the site near the village of Grabove and taken them to a morgue in the rebel-held city of Donetsk.
The BBC's Richard Galpin, who is at the crash site, says he saw bodies being removed by emergency workers, but it was not clear where they were being taken, nor whether the workers were loyal to the rebels or the government in Kiev.
Dutch Foreign Minister Frans Timmermans, who is visiting Ukraine, said he had been "shocked" by the reported removals.
"As soon as we receive proof, we will not rest until those guilty are put to trial - not only those who pulled the trigger, but also those who made it possible," he said.
At the scene: Fergal Keane, BBC News, Grabove
Image copyright AFP Image caption The OSCE monitors were forced to walk to the field where the plane crashed
At the main site the bodies were without covering. Some lay alone. Others were grouped together amid the twisted metal, the bags and cases, the child's playing cards, the guide books, the laptop computer, the duty free whiskey bottle, the woman's hat.
A militiaman with the nickname "Grumpy" - he was squat and barrel-chested with poor teeth and carried a machine gun - harangued me when I asked if the rebels would now stop fighting.
"You are only here because foreigners are dead," he said. And the old story was repeated, the same I have heard on numerous roadblocks - the Western media were all capitalists doing the bidding of their American and EU masters.
When the OSCE turned up in a convoy "Grumpy" came into his own. Now he was a man of power. He halted the OSCE and told them they would have to go forward on foot.
Scant respect for bodies at crash site
The world community, Ukraine added, must put pressure on Russia to pull back its "terrorists" and allow Ukrainian and international experts to carry out their inquiry.
Speaking in Kuala Lumpur, Malaysian Transport Minister Liow Tiong-Lai said it would be "inhumane" if Malaysian experts would not be given access to the crash site.
He also expressed concern that the site was not properly sealed and could be tampered with.
The monitors from the Organization for Security and Co-operation in Europe (OSCE) are now at the site.
Image copyright Reuters Image caption The UK urged Russia to use its influence over the rebels to improve access to the site
OSCE spokesman Michael Bociurkiw said access had improved from Friday and that the monitors were seeing parts of the field they had not seen before.
However he added that their movements were still being restricted. "We are unarmed civilians, we are not in the position to argue heavily with people with heavy arms," he said.
The monitors' mission is to observe the site pending the arrival of international experts being sent to investigate the cause of the crash.
'Act of terrorism'
On Saturday the Russian foreign ministry urged both sides in the Ukrainian conflict "to do everything possible to give international experts access to the aircraft crash".
Earlier, the Russian defence ministry accused the West of waging an information war against Moscow. It challenged Ukraine to produce details of what its anti-aircraft systems were doing at the time.
UK Prime Minister David Cameron and his Dutch counterpart Mark Rutte - who discussed the matter in a phone conversation on Saturday - called on the EU to "reconsider its approach to Russia" following the disaster.
Separatist leaders have denied earlier reports that the plane's flight recorders - the so-called black boxes - had been found.
Ukraine's government called Thursday's disaster an "act of terrorism" and released what they say are intercepted phone conversations that proved the plane was shot down by separatists.
Ukrainian officials also said they had evidence Russian military personnel operated a sophisticated Buk missile system that is thought to have been used to shoot down the plane.
The pro-Russian separatists claim a Ukrainian air force jet brought down the airliner. ||||| Kiev says pro-Russia rebels have removed bodies from crash site with help from Moscow, and are trying to destroy evidence
Ukraine's government accused pro-Russia rebels on Saturday of removing corpses from the MH17 crash site and destroying evidence.
"Terrorists brought 38 bodies to the mortuary in Donetsk," the government statement read, adding that Russian experts would presumably perform autopsies. "The terrorists are seeking for the heavy load trucks to carry the plane wreckage to Russia," the statement added.
A rebel, who identified himself as "Grumpy", neither confirmed nor denied the claims that bodies had been moved to Donetsk. "Maybe they did it, maybe not," he said. "I personally didn't do that."
On Saturday the rebels fired several shots in the air to prevent journalists from approaching to bodies at the crash site. They also fired the warning shots at OSCE monitors on Friday to prevent them from approaching the wreckage of the Malaysia Airlines flight.
The security of the crash site, outside the village of Grabovo in eastern Ukraine, is crucial to preserving evidence that will determine who and what brought the airliner down, but talks between Kiev and rebels who are in control of it have so far failed to establish a buffer zone where international investigators can work, or to give them access.
The head of Ukraine's security service, Valentyn Nalyvaychenko, said in televised remarks on Saturday that talks had agreed a 20km security zone around the site "so that Ukraine could fulfil the most important thing – identify the bodies hand them over to relatives". A senior official of the self-styled Donetsk People's Republic, however, said no agreement had been reached.
A spokesman for the Organisation for Security and Cooperation in Europe (OSCE), Michael Bociurkiw, also said he was not aware of any agreement, and reports from the scene said there was no security zone.
A team of nearly 30 OSCE observers attempted for second time to gain access to the crash site on Saturday after meeting resistance from armed rebels on Friday. The monitors were allowed to view one part of the site under escort.
Aleksander Borodai, prime minister of the self-styled Donetsk People's Republic, denied rebels had touched the crash site but said it would move the bodies for "humanitarian" reasons and called on Russia to help. "Bodies of innocent people are lying out in the heat. We reserve the right, if the delay continues ... to begin the process of taking away the bodies. We ask the Russian Federation to help us with this problem and send their experts," he said.
Workers at the scene have recovered more than 180 bodies, which have begun to decompose under the summer sun. All 298 on board the plane were killed in the crash.
Malaysia's transport minister, Liow Tiong Lai, called on the UN on Saturday to assist with a ceasefire in eastern Ukraine and ensure that investigators have safe access to the crash site so they can remove bodies as quickly as possible. Anything less would be inhumane, he said.
Investigators from the Netherlands, home to 192 of the victims, arrived in Kiev overnight. A team from Malaysia, home to 44, is also in Ukraine. The Malaysian transport minster is to join the team and attempt to gain access to the site.
Six investigators from the UK Air Accidents Investigation Branch are also to join the growing international investigation. The UK Foreign Office has sent extra consular staff to Ukraine and the Metropolitan police are liaising with international partners to send specialist officers to assist with the recovery, identification and repatriation of those killed. The dead include 10 British nationals.
There is growing international condemnation of pro-Russian separatists over the incident, with Washington pointing the finger of blame at the militias. The Pentagon confirmed a surface-to-air missile fired from territory controlled by separatists brought down the plane, but stopped short of accusing Russia of supplying the weapon.
In the UK, Downing Street said it appeared increasingly likely that the catastrophe was the result of a surface-to-air missile fired from near rebel-held Torez.
The Australian prime minster, Tony Abbott, repeated his assertion on Saturday that all evidence suggests that the missile came from an area controlled by Russian-backed separatists, using equipment likely supplied by Russia.
At a charged UN security council meeting on Friday the US ambassador, Samantha Power, said the US "cannot rule out technical assistance from Russia" while the Russian ambassador, Vitaly Churkin, said Moscow "places all blame on Kiev".
Barack Obama on Friday said the circumstances of the crash, which came at the end of a week in which pro-Russian separatists claimed to have shot down Ukrainian military aircraft, suggested some Russian assistance to the rebel forces.
"We don't yet know exactly what happened with respect to Malaysia Airlines, although obviously we are beginning to draw some conclusions given the nature of the shot that was fired. There are only certain types of anti-aircraft missiles that can reach up 30,000ft and shoot down a passenger jet.
"Set aside what's happened with respect to the Malaysian airliner, a group of separatists cannot shoot down military transport planes or, they claim, shoot down fighter jets without sophisticated equipment and sophisticated training and that's coming from Russia."
The Chinese president, Xi Jinping, who has avoided discussing the issue of responsibility, said on Saturday that he hoped "a fair and objective probe will be carried out to establish the truth as early as possible".[/INST]– The chances of a "credible international investigation" taking place in the aftermath of this week's Malaysian Airlines crash seem to be dwindling by the hour. Ukraine today accused pro-Russian separatists of removing bodies and wreckage from the crash site without proper authorization, reports the BBC. Specifically, it says that men with Russian accents took 38 bodies to a morgue in rebel-held Donetsk and threatened to conduct their own autopsies, and that they were trying to ship pieces of the wreckage to Moscow. The development comes after US intelligence suggested that the plane got shot down with a Russian-supplied missile system fired from rebel territory. "The government of Ukraine officially states that the terrorists, with the help of Russia, are trying to destroy evidence of international crimes," says the Ukraine statement, as per the Guardian. A team from the Organization for Security and Cooperation in Europe was to try to return to the crash site today after being allowed to visit for only 75 minutes yesterday and meeting some resistance from rebels, some of whom were believed to be drunk, reports the Wall Street Journal. "The whole world should unite, so as to enter that territory and investigate objectively," says Ukraine's deputy prime minister.</s> |
DENVER (AP) — Hillary Rodham Clinton said on Tuesday her use of the term "illegal immigrants" was a "poor choice of words" and she pledged not to use it anymore, responding to criticism from immigration activists.
Democratic presidential candidate Hillary Rodham Clinton uses a supporter's mobile telephone to take a photograph after a rally Tuesday, Nov. 24, 2015, in a high school gymnasium in Denver. (AP Photo/David... (Associated Press)
Democratic presidential candidate Hillary Rodham Clinton holds up a mobile telephone to take a photograph with a supporter while working a rope line following a rally Tuesday, Nov. 24, 2015, in a high... (Associated Press)
The Democratic presidential candidate was asked about her use of the term to describe people who are in the U.S. illegally during a question-and-answer session on Facebook held by Telemundo. The question came from Jose Antonio Vargas, a filmmaker and journalist whose organization, Define American, has said the terminology is offensive and asked all presidential candidates to stop using it.
"Yes, I will," Clinton wrote during a stop in Boulder, Colorado. "That was a poor choice of words. As I've said throughout this campaign, the people at the heart of this issue are children, parents, families, DREAMers. They have names and hopes and dreams that deserve to be respected."
DREAMers take their name from the acronym for legislation that lays out a process toward citizenship for immigrants who were brought into the country illegally as children and grew up in the United States.
During a town-hall meeting in New Hampshire earlier this month, Clinton said she voted "numerous times when I was a senator to spend money to build a barrier to try to prevent illegal immigrants from coming in. And I do think you have to control your borders."
Clinton has called for expanding President Barack Obama's executive actions on immigration and overhauling U.S. immigration laws, providing a pathway to citizenship for those living in the U.S. illegally.
Her plans mark a sharp contrast with Republican White House hopefuls, who have vowed to roll back the president's immigration orders. Many GOP candidates also routinely use the term "illegals" to refer to immigrants in the country illegally.
Clinton, during a subsequent rally in Boulder, said the U.S. was "fighting for human rights and dignity and freedom" against terrorism and said the U.S. was justified in allowing refugees to enter the U.S. after a "strong vetting process." Republican presidential candidates have largely opposed allowing refugees from Syria into the country. GOP front-runner Donald Trump has suggested he would support ways to track Muslims in the U.S.
"I've heard all of this loose and inflammatory talk about refugees," Clinton said. "And I don't think that does us any good at all in waging and winning the fight against criminals and killers who misuse religion and promote a different set of values than the ones that we believe in."
Clinton met in Boulder early Tuesday with survivors of mass shooting victims, and she later vowed to fight gun violence with tougher gun control laws.
Clinton met with Jane Dougherty, sister of Mary Sherlach, who was slain at the Sandy Hook Elementary School shooting in 2012; Tom Sullivan and Matthew Jenks, the father and brother-in-law, respectively, of Alex Sullivan, who was killed in the 2012 Aurora theater shootings; and Coni Sanders, daughter of Dave Sanders, killed in the 1999 Columbine High School shootings.
"If 33,000 people were dying every year from something else, we'd surely do something about it," Clinton said of U.S. shooting deaths at a Denver rally.
Also Tuesday, the former secretary of state won the endorsement of the Laborers' International Union of North America, which represents about 500,000 construction workers. Clinton has won the support of several large unions representing about 11 million members in total.
___
This story has been corrected to show the name of Vargas' organization is Define American, not Define America.
___
Thomas reported from Washington. ||||| Tweet with a location
You can add location information to your Tweets, such as your city or precise location, from the web and via third-party applications. You always have the option to delete your Tweet location history. Learn more | – Hillary Clinton says the term "illegal immigrants" is no longer part of her vocabulary. In a Facebook chat hosted by Telemundo on Tuesday, she told #WordsMatter activist Jose Antonio Vargas that she will agree to his request to stop using the phrase to describe undocumented immigrants, the AP reports. It is "a poor choice of words," she agreed. "As I've said throughout this campaign, the people at the heart of this issue are children, parents, families, DREAMers. They have names and hopes and dreams that deserve to be respected." Vargas—a journalist who revealed his undocumented status in 2011—tells Yahoo News that he hopes Clinton will stick to the pledge and that other candidates will join her. He says the term is "offensive and hurtful," and the choice of words matters because "phrases like 'illegals,' 'illegal aliens,' and 'illegal immigrants’ frame the conversation, how politicians talk about the issue, and inevitably how policies are created." Earlier in the Telemundo chat, Clinton accused Donald Trump of "trafficking in prejudice and paranoia" and said "if you look at their policies, most of the other Republican candidates are just Trump without the pizazz or the hair. They don't support a real path to citizenship." | <s>[INST]DENVER (AP) — Hillary Rodham Clinton said on Tuesday her use of the term "illegal immigrants" was a "poor choice of words" and she pledged not to use it anymore, responding to criticism from immigration activists.
Democratic presidential candidate Hillary Rodham Clinton uses a supporter's mobile telephone to take a photograph after a rally Tuesday, Nov. 24, 2015, in a high school gymnasium in Denver. (AP Photo/David... (Associated Press)
Democratic presidential candidate Hillary Rodham Clinton holds up a mobile telephone to take a photograph with a supporter while working a rope line following a rally Tuesday, Nov. 24, 2015, in a high... (Associated Press)
The Democratic presidential candidate was asked about her use of the term to describe people who are in the U.S. illegally during a question-and-answer session on Facebook held by Telemundo. The question came from Jose Antonio Vargas, a filmmaker and journalist whose organization, Define American, has said the terminology is offensive and asked all presidential candidates to stop using it.
"Yes, I will," Clinton wrote during a stop in Boulder, Colorado. "That was a poor choice of words. As I've said throughout this campaign, the people at the heart of this issue are children, parents, families, DREAMers. They have names and hopes and dreams that deserve to be respected."
DREAMers take their name from the acronym for legislation that lays out a process toward citizenship for immigrants who were brought into the country illegally as children and grew up in the United States.
During a town-hall meeting in New Hampshire earlier this month, Clinton said she voted "numerous times when I was a senator to spend money to build a barrier to try to prevent illegal immigrants from coming in. And I do think you have to control your borders."
Clinton has called for expanding President Barack Obama's executive actions on immigration and overhauling U.S. immigration laws, providing a pathway to citizenship for those living in the U.S. illegally.
Her plans mark a sharp contrast with Republican White House hopefuls, who have vowed to roll back the president's immigration orders. Many GOP candidates also routinely use the term "illegals" to refer to immigrants in the country illegally.
Clinton, during a subsequent rally in Boulder, said the U.S. was "fighting for human rights and dignity and freedom" against terrorism and said the U.S. was justified in allowing refugees to enter the U.S. after a "strong vetting process." Republican presidential candidates have largely opposed allowing refugees from Syria into the country. GOP front-runner Donald Trump has suggested he would support ways to track Muslims in the U.S.
"I've heard all of this loose and inflammatory talk about refugees," Clinton said. "And I don't think that does us any good at all in waging and winning the fight against criminals and killers who misuse religion and promote a different set of values than the ones that we believe in."
Clinton met in Boulder early Tuesday with survivors of mass shooting victims, and she later vowed to fight gun violence with tougher gun control laws.
Clinton met with Jane Dougherty, sister of Mary Sherlach, who was slain at the Sandy Hook Elementary School shooting in 2012; Tom Sullivan and Matthew Jenks, the father and brother-in-law, respectively, of Alex Sullivan, who was killed in the 2012 Aurora theater shootings; and Coni Sanders, daughter of Dave Sanders, killed in the 1999 Columbine High School shootings.
"If 33,000 people were dying every year from something else, we'd surely do something about it," Clinton said of U.S. shooting deaths at a Denver rally.
Also Tuesday, the former secretary of state won the endorsement of the Laborers' International Union of North America, which represents about 500,000 construction workers. Clinton has won the support of several large unions representing about 11 million members in total.
___
This story has been corrected to show the name of Vargas' organization is Define American, not Define America.
___
Thomas reported from Washington. ||||| Tweet with a location
You can add location information to your Tweets, such as your city or precise location, from the web and via third-party applications. You always have the option to delete your Tweet location history. Learn more[/INST]– Hillary Clinton says the term "illegal immigrants" is no longer part of her vocabulary. In a Facebook chat hosted by Telemundo on Tuesday, she told #WordsMatter activist Jose Antonio Vargas that she will agree to his request to stop using the phrase to describe undocumented immigrants, the AP reports. It is "a poor choice of words," she agreed. "As I've said throughout this campaign, the people at the heart of this issue are children, parents, families, DREAMers. They have names and hopes and dreams that deserve to be respected." Vargas—a journalist who revealed his undocumented status in 2011—tells Yahoo News that he hopes Clinton will stick to the pledge and that other candidates will join her. He says the term is "offensive and hurtful," and the choice of words matters because "phrases like 'illegals,' 'illegal aliens,' and 'illegal immigrants’ frame the conversation, how politicians talk about the issue, and inevitably how policies are created." Earlier in the Telemundo chat, Clinton accused Donald Trump of "trafficking in prejudice and paranoia" and said "if you look at their policies, most of the other Republican candidates are just Trump without the pizazz or the hair. They don't support a real path to citizenship."</s> |
aflatoxins are secondary metabolites produced by different fungi of the species aspergillus , mainly a. flavus and a. parasiticus , but also a. nominus and a. tamarii ( kurtzman et al . , 1987 ;
( 2001 ) , and also a. niger , a. wentii , penicillum citrinum and p. frequentans ( caloni and nebbia , 2009 ) .
the aflatoxin group includes aflatoxin b1 ( afb1 ) , b2 , g1 and g2 , and their hydroxylated metabolites can be found in milk .
aflatoxins m1 ( afm1 ) and m2 are the metabolites of afb1 and b2 respectively .
afm1 is the most commonly occurring aflatoxin detected in milk of mammals exposed to afb1 ingestion .
afb1 is classified as group 1 ( carcinogenic to humans ) while afm1 is classified as group 2b ( possibly carcinogenic to humans ) by the international agency for research on cancer ( iarc ) ( caloni and nebbia , 2009 ) .
aflatoxin contamination risk is generally higher in geographical regions with a tropical or subtropical climate , but the abnormal hot and drought - growing seasons of maize have raised problems in crop management especially in southeast europe ( serraino et al . , 2003 ; trevisani et al . , 2014 ) .
maize grain , which is normally used to feed dairy cattle , is produced with the use of irrigation systems in this region .
maize can be infected by moulds when hot and dry environmental conditions occur during the pre - harvest phase , and weeds and crop disease contribute to grain contamination by aflatoxin ( giorni et al . , 2007 ; prandini et al . , 2009 ; kebede et al . ,
2012 ) . in 2003 and 2012 , unfavourable weather conditions , such as temperatures above 30c and the lack of precipitation over an extended period , caused a massive contamination of maize in northern italy resulting in an increase in afm1 in cow s milk ( canever et al . , 2004 ; marchetti et al . , 2013 ) .
the carryover of aflatoxin from cattle feed to milk depends on the animal breed , the lactation period and udder infections ( masoero et al . , 2007 ) .
the average value is approximately 2.5% , but a direct relation between carryover rate and milk yield was found with carryover percentages as high as 6.2% in high - yielding dairy cows with a production of up to 40 l of milk per day ( veldman et al . , 1992 ) . despite the high individual variability , the equation proposed by veldman et al .
( 1992 ) is used to estimate the carryover of afm1 in a whole dairy herd :
afm1 ( ng / kg milk)=1.19 x afb1
( g / cow / day)+1.19
using this equation is it possible to assume that , in order to obtain a concentration of afm1 below the maximum limit allowed by eu regulation 1881/2006 ( european commission , 2006 ) , the average intake of afb1 must be less than 40 g / day . considering that a complementary feed can be given to a dairy cow at levels of > 10 kg / day and that its aflatoxin contamination limit is 5 ppb ( ec regulation 574/2011 ; european commission , 2011 ) , it is easy to deduce that it is possible produce non compliant milk even feeding cows with compliant ( 5 ppb ) complementary feed . for this reason several integrated dairy chains require to the feed industry a lower afb1 content in their products and they provide a better information for dairy farmers . in 1993 the parmigiano reggiano ( pr ) consortium signed a protocol with feed industries to reduce the afb1 content in concentrates for dairy cow feed to a level below 3 ppb instead of the 5 ppb eu limit .
this work reports the results of an investigation , performed in the parmigiano reggiano area , on afb1 contamination in dairy cows complementary feed and on the related risk management implemented by feed industries .
during 2013 and 2014 , in the framework of a quality control program performed by the pr consortium ( ricci et al . , 2015 ) , data on afb1 risk management were collected in 29 feed industries .
the quality control program was based on a voluntary agreement between the feed industries and the pr consortium .
the agreement considered the application of requirements defined by the specification of parmigiano reggiano cheese ( for example a ban on the use of cotton seed , canola and others feedstuffs ) and additional requirements defining higher processing and composition standards compared to eu regulation n 574/2011 ( european commission , 2011 ) .
the additional requirements regard the aflatoxin content ( fixed at 3 ppb instead of 5 ppb ) , absence of gossypol , absence of volatile mustard oil , the implementation of procedures to avoid cross - contamination with prohibited raw materials like rice , rapeseed and cotton in dairy cow feed .
audits were performed twice in each of the 29 feed industries , once in 2013 , collecting one feed sample in each plant ( totally 29 samples ) and the second in 2014 collecting 41 feed samples , more than one in each plant .
samples collected in 2013 were analysed for the quantitative detection of afb1 by ridascreeen aflatoxin b1 30/15 biopharm kit ( darmstadt , germany ) whereas the samples collected in 2014 were first screened for total aflatoxin content by iscreen afla ( tecna , trieste , italy ) and afb1 was quantified only in samples with an aflatoxin b total content higher than 3 ppb by a lc - ms / ms method ( biancardi and dallasta , 2014 ) .
audit results showed that the afb1 contamination risk management applied by feed industries mainly focused , as expected , on maize and its by - products .
procedures performed by feed industries to reduce afb1 contamination of maize included : i ) purchase of maize in geographic areas with a low afb1 contamination risk due to favourable environmental conditions or to a particular organisation of the maize supply chain ; ii ) specific commercial agreements with suppliers that included a maximum limit of afb1 concentration ; iii ) a high frequency ( up to 100% ) of delivered maize analysis ; iv ) the selection of maize on the basis of afb1 content and differentiated use of afb1 in feed for different species ( for example low afb1 contaminated maize for dairy cow feed and high afb1 contaminated maize for swine feed ) ; v ) high frequency of maize purchasing reducing storage time in the feed mill .
the afb1 content was < 2 ppb in 28 out of 29 samples ( 96.6% ) collected during 2013 and 3.8 ppb in the last sample . in 41 samples collected during 2014 , the af total content was below the limit of detection ( 2 ppb ) , in the range 2 - 3 ppb , and > 3 ppb ( up to 4 ppb ) in 14 ( 34.1% ) , 24 ( 58.5% ) and 3 ( 7.3% ) samples , respectively .
the 3 samples showing aflatoxin contamination > 3 ppb were subsequently analysed by lc - ms / ms and afb1 concentration was < 1 ppb in all these samples .
few data are available on feed materials originating from europe ( european food safety authority , 2004 ) as aflatoxin formation was previously considered to occur mainly in geographic regions with a tropical or subtropical climate . on the other hand , afb1 contamination of feed and feed ingredients , mainly maize , appears to be a problem in southern europe , and the contamination level
out of 533 maize samples for animal feed collected in northern italy during the period 1995 - 1999 , pietri et al .
( 2004 ) reported high positive rates ( 42.9% ) , although levels were generally very low ( mean concentration between 1.3 and 5.1 ppb during years ) with the exception of 2 samples contaminated with afb1>100 ppb and 5 samples > 20 ppb .
( 1998 ) analysed 197 dairy cow feed samples and found all of them < 5 ppb and another 124 maize samples where only 9 showed values between 5 and 20 ppb , with no samples > 20 ppb . in the lombardy region ( 1999 - 2000 )
830 dairy cows feed samples were analysed and all feedstuffs showed afb1 levels < 5 ppb ( amodeo , 2001 ) .
on the contrary , during the 2003 crisis , several feed samples were analysed in dairy farms where afm1 milk contamination was above the legal limit of 50 ppt .
the results showed that 58.9% of complementary feeds and from 14.48 to 66.66% of maize and maize products exceeded the eu legal limit ( canever et al . ,
a study performed from the beginning of 2004 to the end of 2005 reported that afb1 in cattle feed was higher than the maximum limit in 8.1% of feed samples , whereas during 2005 found aflatoxin levels constantly below the limits of eu regulations ( decastelli et al . , 2007 ) .
more recently , a large 2012 survey conducted on corn produced in northern italy analysed 31,326 samples collected at storage plants .
the results showed that afb1 contamination above the eu limit of 20 ppb was detected in samples representative of about 784,000 tons of corn , corresponding to 45.2% of the total production ( causin , 2013 ) .
the results of the present study showed that no sample had afb1 levels above the eu legal limit of 5 ppb in the investigated feed mills .
moreover , auditing showed that a good level of afb1 risk management has been achieved by italian feed industries to counteract the unfavorable climatic conditions arising in some years . the special attention paid by the feed industry to maize af contamination is probably the result of the two seasonal crises in 2003 and 2012 when unfavorable climatic conditions led to a massive afb1 contamination of maize with up to 50% of national maize production non - compliant with eu regulations and unsuitable for feeding milking cows ( marchetti et al .
as a consequence , monitoring was stepped up by all the dairy production chains , including feed manufacturers and health authorities , also thanks to the availability of rapid and less expensive detection kits to test aflatoxin contamination in raw materials .
no limit is reported for afm1 in cheeses in the european community legislation , but the provisional limit of 450 ppt was fixed for hard and long maturing cheeses by the italian ministry ( italian ministry of health , 2004 ) . an investigation performed on grana padano cheese produced with naturally contaminated milk showed that afm1 concentration levels increase 4.5-fold in cheeses ( manetta et al . , 2009 ) .
this guarantees that the level of afm1 contamination of cheese will be lower than the 450 ppt limit even when milk with an afm1 contamination above the legal limit ( 50 ppt ) is used .
the application of a voluntary agreement to reduce the afb1 contamination of feedstuffs further reduces the health risk for consumers . | this study investigated aflatoxin b1 ( afb1 ) contamination in dairy cow feed and the risk management of afb1 content in concentrates undertaken by feed industries in the parmigiano reggiano area .
data on aflatoxin contamination risk management applied in 29 feed industries were collected and the afb1 content of 70 feed samples was analysed .
data were collected within the framework of a quality control programme promoted by the parmigiano reggiano consortium in 2013 and 2014 .
audit results showed that the control procedures to prevent afb1 contamination mainly focused on maize and its by - products .
afb1 concentration resulted lower than 5 ppb [ legal european union ( eu ) limit ] in all samples ; in one out of 70 samples , afb1 content was 3.8 ppb and in all the other samples it was lower than 3 ppb .
results showed that afb1 risk management applied by italian feed industries effectively monitors afb1 levels in feed below the eu legal limit . | <s>[INST]aflatoxins are secondary metabolites produced by different fungi of the species aspergillus , mainly a. flavus and a. parasiticus , but also a. nominus and a. tamarii ( kurtzman et al . , 1987 ;
( 2001 ) , and also a. niger , a. wentii , penicillum citrinum and p. frequentans ( caloni and nebbia , 2009 ) .
the aflatoxin group includes aflatoxin b1 ( afb1 ) , b2 , g1 and g2 , and their hydroxylated metabolites can be found in milk .
aflatoxins m1 ( afm1 ) and m2 are the metabolites of afb1 and b2 respectively .
afm1 is the most commonly occurring aflatoxin detected in milk of mammals exposed to afb1 ingestion .
afb1 is classified as group 1 ( carcinogenic to humans ) while afm1 is classified as group 2b ( possibly carcinogenic to humans ) by the international agency for research on cancer ( iarc ) ( caloni and nebbia , 2009 ) .
aflatoxin contamination risk is generally higher in geographical regions with a tropical or subtropical climate , but the abnormal hot and drought - growing seasons of maize have raised problems in crop management especially in southeast europe ( serraino et al . , 2003 ; trevisani et al . , 2014 ) .
maize grain , which is normally used to feed dairy cattle , is produced with the use of irrigation systems in this region .
maize can be infected by moulds when hot and dry environmental conditions occur during the pre - harvest phase , and weeds and crop disease contribute to grain contamination by aflatoxin ( giorni et al . , 2007 ; prandini et al . , 2009 ; kebede et al . ,
2012 ) . in 2003 and 2012 , unfavourable weather conditions , such as temperatures above 30c and the lack of precipitation over an extended period , caused a massive contamination of maize in northern italy resulting in an increase in afm1 in cow s milk ( canever et al . , 2004 ; marchetti et al . , 2013 ) .
the carryover of aflatoxin from cattle feed to milk depends on the animal breed , the lactation period and udder infections ( masoero et al . , 2007 ) .
the average value is approximately 2.5% , but a direct relation between carryover rate and milk yield was found with carryover percentages as high as 6.2% in high - yielding dairy cows with a production of up to 40 l of milk per day ( veldman et al . , 1992 ) . despite the high individual variability , the equation proposed by veldman et al .
( 1992 ) is used to estimate the carryover of afm1 in a whole dairy herd :
afm1 ( ng / kg milk)=1.19 x afb1
( g / cow / day)+1.19
using this equation is it possible to assume that , in order to obtain a concentration of afm1 below the maximum limit allowed by eu regulation 1881/2006 ( european commission , 2006 ) , the average intake of afb1 must be less than 40 g / day . considering that a complementary feed can be given to a dairy cow at levels of > 10 kg / day and that its aflatoxin contamination limit is 5 ppb ( ec regulation 574/2011 ; european commission , 2011 ) , it is easy to deduce that it is possible produce non compliant milk even feeding cows with compliant ( 5 ppb ) complementary feed . for this reason several integrated dairy chains require to the feed industry a lower afb1 content in their products and they provide a better information for dairy farmers . in 1993 the parmigiano reggiano ( pr ) consortium signed a protocol with feed industries to reduce the afb1 content in concentrates for dairy cow feed to a level below 3 ppb instead of the 5 ppb eu limit .
this work reports the results of an investigation , performed in the parmigiano reggiano area , on afb1 contamination in dairy cows complementary feed and on the related risk management implemented by feed industries .
during 2013 and 2014 , in the framework of a quality control program performed by the pr consortium ( ricci et al . , 2015 ) , data on afb1 risk management were collected in 29 feed industries .
the quality control program was based on a voluntary agreement between the feed industries and the pr consortium .
the agreement considered the application of requirements defined by the specification of parmigiano reggiano cheese ( for example a ban on the use of cotton seed , canola and others feedstuffs ) and additional requirements defining higher processing and composition standards compared to eu regulation n 574/2011 ( european commission , 2011 ) .
the additional requirements regard the aflatoxin content ( fixed at 3 ppb instead of 5 ppb ) , absence of gossypol , absence of volatile mustard oil , the implementation of procedures to avoid cross - contamination with prohibited raw materials like rice , rapeseed and cotton in dairy cow feed .
audits were performed twice in each of the 29 feed industries , once in 2013 , collecting one feed sample in each plant ( totally 29 samples ) and the second in 2014 collecting 41 feed samples , more than one in each plant .
samples collected in 2013 were analysed for the quantitative detection of afb1 by ridascreeen aflatoxin b1 30/15 biopharm kit ( darmstadt , germany ) whereas the samples collected in 2014 were first screened for total aflatoxin content by iscreen afla ( tecna , trieste , italy ) and afb1 was quantified only in samples with an aflatoxin b total content higher than 3 ppb by a lc - ms / ms method ( biancardi and dallasta , 2014 ) .
audit results showed that the afb1 contamination risk management applied by feed industries mainly focused , as expected , on maize and its by - products .
procedures performed by feed industries to reduce afb1 contamination of maize included : i ) purchase of maize in geographic areas with a low afb1 contamination risk due to favourable environmental conditions or to a particular organisation of the maize supply chain ; ii ) specific commercial agreements with suppliers that included a maximum limit of afb1 concentration ; iii ) a high frequency ( up to 100% ) of delivered maize analysis ; iv ) the selection of maize on the basis of afb1 content and differentiated use of afb1 in feed for different species ( for example low afb1 contaminated maize for dairy cow feed and high afb1 contaminated maize for swine feed ) ; v ) high frequency of maize purchasing reducing storage time in the feed mill .
the afb1 content was < 2 ppb in 28 out of 29 samples ( 96.6% ) collected during 2013 and 3.8 ppb in the last sample . in 41 samples collected during 2014 , the af total content was below the limit of detection ( 2 ppb ) , in the range 2 - 3 ppb , and > 3 ppb ( up to 4 ppb ) in 14 ( 34.1% ) , 24 ( 58.5% ) and 3 ( 7.3% ) samples , respectively .
the 3 samples showing aflatoxin contamination > 3 ppb were subsequently analysed by lc - ms / ms and afb1 concentration was < 1 ppb in all these samples .
few data are available on feed materials originating from europe ( european food safety authority , 2004 ) as aflatoxin formation was previously considered to occur mainly in geographic regions with a tropical or subtropical climate . on the other hand , afb1 contamination of feed and feed ingredients , mainly maize , appears to be a problem in southern europe , and the contamination level
out of 533 maize samples for animal feed collected in northern italy during the period 1995 - 1999 , pietri et al .
( 2004 ) reported high positive rates ( 42.9% ) , although levels were generally very low ( mean concentration between 1.3 and 5.1 ppb during years ) with the exception of 2 samples contaminated with afb1>100 ppb and 5 samples > 20 ppb .
( 1998 ) analysed 197 dairy cow feed samples and found all of them < 5 ppb and another 124 maize samples where only 9 showed values between 5 and 20 ppb , with no samples > 20 ppb . in the lombardy region ( 1999 - 2000 )
830 dairy cows feed samples were analysed and all feedstuffs showed afb1 levels < 5 ppb ( amodeo , 2001 ) .
on the contrary , during the 2003 crisis , several feed samples were analysed in dairy farms where afm1 milk contamination was above the legal limit of 50 ppt .
the results showed that 58.9% of complementary feeds and from 14.48 to 66.66% of maize and maize products exceeded the eu legal limit ( canever et al . ,
a study performed from the beginning of 2004 to the end of 2005 reported that afb1 in cattle feed was higher than the maximum limit in 8.1% of feed samples , whereas during 2005 found aflatoxin levels constantly below the limits of eu regulations ( decastelli et al . , 2007 ) .
more recently , a large 2012 survey conducted on corn produced in northern italy analysed 31,326 samples collected at storage plants .
the results showed that afb1 contamination above the eu limit of 20 ppb was detected in samples representative of about 784,000 tons of corn , corresponding to 45.2% of the total production ( causin , 2013 ) .
the results of the present study showed that no sample had afb1 levels above the eu legal limit of 5 ppb in the investigated feed mills .
moreover , auditing showed that a good level of afb1 risk management has been achieved by italian feed industries to counteract the unfavorable climatic conditions arising in some years . the special attention paid by the feed industry to maize af contamination is probably the result of the two seasonal crises in 2003 and 2012 when unfavorable climatic conditions led to a massive afb1 contamination of maize with up to 50% of national maize production non - compliant with eu regulations and unsuitable for feeding milking cows ( marchetti et al .
as a consequence , monitoring was stepped up by all the dairy production chains , including feed manufacturers and health authorities , also thanks to the availability of rapid and less expensive detection kits to test aflatoxin contamination in raw materials .
no limit is reported for afm1 in cheeses in the european community legislation , but the provisional limit of 450 ppt was fixed for hard and long maturing cheeses by the italian ministry ( italian ministry of health , 2004 ) . an investigation performed on grana padano cheese produced with naturally contaminated milk showed that afm1 concentration levels increase 4.5-fold in cheeses ( manetta et al . , 2009 ) .
this guarantees that the level of afm1 contamination of cheese will be lower than the 450 ppt limit even when milk with an afm1 contamination above the legal limit ( 50 ppt ) is used .
the application of a voluntary agreement to reduce the afb1 contamination of feedstuffs further reduces the health risk for consumers .[/INST]this study investigated aflatoxin b1 ( afb1 ) contamination in dairy cow feed and the risk management of afb1 content in concentrates undertaken by feed industries in the parmigiano reggiano area .
data on aflatoxin contamination risk management applied in 29 feed industries were collected and the afb1 content of 70 feed samples was analysed .
data were collected within the framework of a quality control programme promoted by the parmigiano reggiano consortium in 2013 and 2014 .
audit results showed that the control procedures to prevent afb1 contamination mainly focused on maize and its by - products .
afb1 concentration resulted lower than 5 ppb [ legal european union ( eu ) limit ] in all samples ; in one out of 70 samples , afb1 content was 3.8 ppb and in all the other samples it was lower than 3 ppb .
results showed that afb1 risk management applied by italian feed industries effectively monitors afb1 levels in feed below the eu legal limit .</s> |
the term magnetic frustration describes the inability of a magnetic system to satisfy all the competing interactions in order to establish a unique ground state .
@xcite in the presence of antiferromagnetic exchange interactions , magnets based on corner- or edge - sharing triangles @xcite or tetrahedra @xcite can exhibit geometric frustration .
common examples of systems in which frustration plays a fundamental role in establishing highly degenerate ground states and low - temperature properties such as reduced critical temperatures include the kagome , @xcite pyrochlore @xcite and garnet @xcite structures .
new magnets which exhibit the effects of geometric frustration are constantly being discovered .
the behaviour of these systems is often complex , with many magnets remaining disordered down to very low - temperatures - traditional examples being spin liquids @xcite and spin glasses .
@xcite in this paper we report on an investigation of single crystal samples of @xmath0 , a compound that displays no long - range order down to 0.05 k. more intriguingly , there appears to be two distinct types of short - range magnetic order coexisting in this material , which has no chemical instability or phase separation .
@xmath0 belongs to the sr@xmath8o@xmath9 ( where _ ln _ = lanthanide ) family of compounds , @xcite which crystallise in the form of calcium ferrite , @xcite space group _ pnam_.
this allows the magnetic _ ln _ ions to be linked in a network of triangles and hexagons , as shown in fig .
[ lnsublattice ] , with two crystallographically inequivalent sites of the rare earth ions shown in red and blue .
we believe that it is likely that the two different types of short - range order observed in @xmath0 can be attributed to the two different sites for the ho@xmath1 ions in the unit cell .
o@xmath9 compounds , with the two crystallographically inequivalent positions of the rare earth ions shown in different colors . when viewed in the _ a - b _ plane , honeycombs of the @xmath10 ions
are visible .
zigzag chains running along the @xmath7 axis connect the honeycomb layers and give rise to geometric frustration .
the box indicates the dimensions of the unit cell . ] for all the sr@xmath8o@xmath9 systems the magnetic ions form zigzag chains that run along the @xmath7 axis .
these triangular ladders can be frustrated , and are magnetically equivalent to one - dimensional chains with first- and second - nearest - neighbour interactions .
the chains of @xmath10 ions interconnect by forming a distorted _ honeycomb _ structure , a bipartite lattice made up of edge sharing hexagons , in the _ a - b _ plane .
the honeycomb lattice would only be frustrated if further neighbor exchange is considered , but receives substantial theoretical interest since it has the smallest possible coordination number in two - dimensions .
@xcite thus for these systems quantum fluctuations are expected to have a much larger effect on the stability of magnetic order than , for example , for square or triangular lattices .
a number of honeycomb lattice structures have been identified experimentally , including the spin-@xmath11 compound incu@xmath12v@xmath13o@xmath14 , @xcite the spin-@xmath15 systems bi@xmath14mn@xmath9o@xmath16(no@xmath14 ) @xcite and @xmath17cacr@xmath18o@xmath9 @xcite as well as other systems with larger spins like ba@xmath8o@xmath9 , @xcite eu@xmath8o@xmath9 @xcite and sr@xmath8o@xmath9 .
@xcite bulk property measurements of geometrically frustrated systems usually reveal anomalous behaviour , such as the presence of phase transitions at temperatures much lower than expected from the strength of the exchange interactions . magnetic susceptibility , @xmath19 , measured on powder samples of all the sr@xmath8o@xmath9 compounds
has revealed a disparity in the measured curie - weiss constants , @xmath20 , and the lack of long - range order down to 1.8 k. @xcite @xmath21 and @xmath0 show cusps in single crystal @xmath19 measurements at @xmath22 = 0.62 k for @xmath0 @xcite and at @xmath23 = 0.75 k for @xmath21 , @xcite and a @xmath24-anomaly is observed in the specific heat of @xmath25 at @xmath23 = 0.92 k. @xcite in contrast , @xmath26 does not show any anomalies in @xmath19 down to 0.5 k , @xcite and no @xmath24-type transitions have been observed in heat capacity measurements down to 0.39 k in zero applied field .
@xcite neutron diffraction on powder samples of @xmath26 reveals only broad diffuse scattering peaks and thus further corroborates the apparent lack of long - range order at least down to 20 mk for this compound .
@xcite low - temperature neutron diffraction studies of @xmath25 point to unusual magnetic behaviour , where the two inequivalent sites of the yb@xmath1 ion do not appear to have the same value of the ordered moment . @xcite the magnetism in @xmath21 is equally unconventional since powder neutron diffraction measurements indicate that the transition to nel order involves only half of the er@xmath1 sites ( either the red or blue sites in the notation of fig .
[ lnsublattice ] ) .
@xcite polarized neutron studies on single crystals of @xmath21 suggest that the long - range ordered ( * k * = 0 ) magnetic structure coexists with a shorter - range incommensurate ordering that has a pronounced low - dimensional character at temperatures below @xmath23 = 0.75 k. @xcite neutron diffraction on powder samples of @xmath0 @xcite appeared to indicate that a similar situation arises in this compound , with distinct long - range commensurate and shorter - range incommensurate magnetic structures present at low - temperatures . as a result of refining the data collected at 0.045 k , a magnetic structure with the propagation vector * k * = 0 was proposed , with only one of the crystallographically inequivalent ho@xmath1 ions carrying a significant magnetic moment .
all of the moments in the refined long - range structure point along the @xmath7 axis in ferromagnetic chains , with neighboring chains coupled antiferromagnetically .
in this paper we present the results of an investigation into the nature of the magnetism in single crystal samples of @xmath0 at low - temperatures .
we have measured neutron diffraction patterns for three orthogonal directions in the reciprocal space of @xmath0 .
our results indicate that in @xmath0 _ two _ distinct types of _ short - range _ magnetic order arise from the two sites for the ho@xmath1 ions . in the ( @xmath2 ) plane
, the first type of diffuse magnetic scattering appears around positions with the propagation vector * k * = 0 below 0.7 k ( with no long - range order present in contrast to previous measurements on powder samples of @xmath0 ) . whereas the second type of diffuse scattering appears as planes of scattering intensity at ( @xmath4 ) .
these planes are seen as `` rods '' of scattering intensity in both the ( @xmath27 ) and ( @xmath28 ) planes in reciprocal space at @xmath3 = ( 00@xmath11 ) and symmetry related positions .
therefore the second type of short - range order present in this material is one - dimensional in real space .
thus two members of the sr@xmath8o@xmath9 series , @xmath0 and @xmath21 , both show the coexistance of two types of magnetic ordering at low - temperatures , but @xmath21 has long- and short - range components , whereas in @xmath0 both types of magnetic correlations are short - ranged .
careful studies of the correlation lengths ( @xmath5 ) in @xmath0 indicate that the diffuse scattering in the ( @xmath2 ) plane is correlated to @xmath5 @xmath6 150 in the _ a - b _ plane at 0.18 k , and to @xmath5 @xmath6 190 along the @xmath7 axis at 0.16 k. the scattering is mostly isotropic in reciprocal space .
the diffuse intensity planes have a correlation length of @xmath5 @xmath6 230 along the @xmath7 axis at 0.15 k. finally by utilising an energy analyser we were able to deduce that the diffuse scattering in the ( @xmath2 ) plane is purely elastic , while the diffuse scattering that appears in planes along ( @xmath29 ) is mostly elastic .
large volume single crystals of @xmath0 were grown using the floating zone method , with details of the procedure reported elsewhere .
@xcite the samples were aligned using the backscattering laue technique and cut perpendicular to the principal crystal axes , within an estimated accuracy of @xmath30 for the d7 measurements and within @xmath31 for the wish experiment . for the wish experiment a single 0.9 g sample of @xmath0
was fixed to an oxygen free copper sample holder using kwikfill resin .
two more 0.9 g samples of @xmath0 ( one for each orientation ) were fixed to oxygen free copper sample holders using kwikfill resin during the d7 experiment ; with equivalent sample mountings used for background measurements . for the d10 experiment
single crystal samples of @xmath0 ( weighing 0.3 g and 0.1 g ) were fixed to oxygen free copper pins using stycast resin .
neutron diffraction measurements in the ( @xmath2 ) scattering plane were made using the cold neutron wish @xcite instrument at the isis facility ( rutherford appleton laboratory , uk ) in a range of temperatures from 0.05 to 1.5 k. wish is equipped with a continuous array of position sensitive @xmath32he detectors that cover an angular range of 10@xmath33 .
this provides the substantial @xmath3-space coverage required for single crystal experiments . depending on the experimental requirements
the wish instrument resolution and flux can be tuned , and out of plane neutron detection is also possible .
the diffuse scattering spectrometer d7 @xcite ( at the institut laue - langevin in grenoble , france ) with _ xyz _ polarization analysis was used to collect neutron scattering data for both ( @xmath27 ) and ( @xmath28 ) scattering planes in a range of temperatures from 0.055 to 4.5 k. the d7 instrument is equipped with 132 @xmath32he detectors which cover an angular range of 4@xmath34 . throughout the experiment cold neutrons monochromated to a wavelength of 3.1
were used , resulting in @xmath3-space coverage of 0.14 to 3.91 @xmath35 .
a quartz standard was used for normalising the polarization efficiency and a vanadium standard was used for normalising the detector efficiency of the instrument .
scans were performed in which the crystal was rotated about the vertical axis in steps of 1@xmath36 .
six measurements required to carry out full _ xyz _ polarization analysis were performed at each temperature for both sample orientations .
the reciprocal space maps were constructed in the usual manner using standard d7 data reduction functions .
the high - flux single - crystal diffractometer d10 ( located on a thermal neutron guide at the institute laue - langevin in grenoble , france ) was used in the four - circle dilution refrigerator mode to collect precise neutron scattering data .
the sample pins were attached to the eulerian cradle inside a helium flow cryostat with the dilution option to allow scanning along all reciprocal lattice directions at low - temperature .
a vertically focusing pyrolytic graphite ( pg ) ( 002 ) monochromator gave an incident wavelength of 2.36 , with the half - wavelength contamination suppressed by a pg filter .
a vertically focussing pg analyser was used to give improved resolution and suppressed background for some of the measurements .
the two - dimensional area detector was used for all the measurements except for those made with the energy analyser , where a single @xmath32he detector was used instead .
measurements were made in the temperature range 0.15 to 10 k. the integrated intensity of the magnetic diffuse scattering around the nuclear bragg peaks was extracted in the usual manner .
@xcite the plane like diffuse scattering features , however , often had a broad intensity profile which covered a large proportion of the two - dimensional d10 detector .
the selection of the integration box for these features required a compromise between getting adequate resolution and the correct representation of the diffuse scattering profile .
in the ( @xmath2 ) plane at a ) 0.055 k and b ) 0.7 k. the magnetic component was isolated by subtracting a 1 k background from the single crystal neutron diffraction data collected using wish , isis .
@xcite ] from earlier measurements on a powder sample of @xmath0 , * k * = 0 magnetic bragg peaks were expected in the ( @xmath2 ) scattering plane , @xcite similar to what has previously been observed for @xmath21 .
@xcite however , after cooling down the single crystal sample to 0.055 k , no long - range order was found in the wish measurements .
[ hk0 ] shows the observed magnetic scattering ( which was isolated by subtracting a 1 k background from the low - temperature data ) . from the single crystal data it is apparent that in the ( @xmath2 ) plane diffuse magnetic scattering appears around the * k * = 0 positions and that its intensity increases rapidly below 0.7 k. waiting at low - temperature for a long time for the sample to thermalise made no measurable difference to the intensity or width of the diffraction patterns .
it is important to note that in @xmath0 at temperatures below 0.7 k the diffuse scattering forms the same _ lozenge _ pattern that is seen at low - temperatures in @xmath21 .
@xcite this is a result of very similar positions of the magnetic @xmath10 ions in the respective unit cells for both compounds .
the positions of the observed broad diffuse scattering peaks in the ( @xmath2 ) scattering plane are in agreement with the positions previously reported for a * k * = 0 structure obtained from the powder refinement . however , from the single crystal experiment no long - range order is actually observed even though the onset of the diffuse scattering in the ( @xmath2 ) plane appears to go through a second - order phase transition ( see fig .
[ hk0_tdep ] and fig .
[ hk0_2ndorder ] ) , and can also be observed as a clear cusp in single crystal magnetic susceptibility measurements .
@xcite although the @xmath3 resolution of wish is good the sample was kept stationary during the experiments and in order to measure correlation length more accurately , high resolution scans across the nuclear and magnetic reflections in the ( @xmath2 ) plane were performed using the d10 instrument .
temperature dependence of the scattering intensity for two different types of reflections in the ( @xmath2 ) plane of @xmath0 are shown in fig .
[ 200peak ] , fig .
[ 030peak ] and fig .
[ 20lpeak ] . the data in fig .
[ 200peak ] have been fitted with gaussian and lorentzian components , to account for the nuclear ( temperature independent ) and magnetic scattering .
@xcite the nuclear ( gaussian ) component was fitted to data collected for ( 200 ) at higher temperature with high resolution , and this is shown in the inset to fig .
[ 200peak ] . the data in fig .
[ 030peak ] have been fitted using the lorentzian distribution only , since this is a forbidden reflection in _ pnam _ symmetry , and purely magnetic scattering is expected . the data in fig .
[ 20lpeak ] have been fitted using two gaussian components ( one for nuclear and one for magnetic contributions ) at all temperatures .
@xcite from the fwhm of the fitted lorentzian curves to the diffuse scattering , the correlation lengths were estimated using @xmath5 ( ) = @xmath37(fwhm ( @xmath38 .
@xcite at the lowest temperature , the magnetic order is correlated to @xmath5 @xmath6 150 in the _ a - b _ plane , and to @xmath5 @xmath6 190 along the @xmath7 axis .
the integrated intensity and fwhm along @xmath39 , and the calculated correlation length along the @xmath40 axis of the ( 030 ) reflection is plotted as a function of temperature in fig .
[ hk0_2ndorder ] . the data for the ( 030 ) reflection in fig .
[ hk0_2ndorder ] were collected using both the two - dimensional detector and energy analyser d10 instrument configurations .
a detailed comparison of these two types of measurements is presented later , see section [ analyser ] .
overall , the diffuse scattering in the ( @xmath2 ) plane shows second - order phase transition type behaviour , with a marked increase in correlation length below 0.62 k - the temperature at which a cusp was observed in single crystal magnetic susceptibility measurements .
@xcite finally , it is important to note that with the improved instrumental resolution offered by d10 , it is possible to see that there is a small amount of scattering intensity at positions forbidden by the @xmath41 symmetry .
this suggests that the proposed space group is not entirely appropriate for the sr@xmath8o@xmath9 family of compounds , although the relative intensity of the forbidden " peaks is systematically low compared to the intensity of the allowed nuclear peaks reflections , therefore much more accurate collection of the intensity of all the peaks is required in order to solve the crystal structure .
the intensity maps shown in fig .
[ d7 - 2planes ] summarise the main results of the single crystal neutron diffraction experiments to investigate the second type of diffuse scattering present in @xmath0 .
the polarized neutron experiments were configured to measure two independent components of the scattering function , here called the non - spin - flip ( nsf ) and spin - flip ( sf ) channels .
the @xmath42 polarization direction in our measurements coincides with the vertical axis , and hence the sum of @xmath42 nsf and @xmath42 sf measurements is what would be observed in unpolarized neutron experiments .
the standard data reduction formulas utilising all of the _ xyz _ polarized measurements to calculate the purely magnetic contribution to the scattering @xcite can not be applied to the @xmath0 system , because it is not an isotropically magnetic crystal at low - temperatures .
instead , fig .
[ d7 - 2planes](a ) shows the intensity measured in the ( @xmath27 ) plane @xmath42 nsf measurement ( here , the @xmath42 polarization direction coinsides with the @xmath43 axis ) .
no extra magnetic features associated with the ( @xmath4 ) planes are observed in the @xmath42 sf cross - section for this sample orientation .
[ d7 - 2planes](b ) shows the data for the ( @xmath28 ) plane @xmath42 sf measurements ( here , the @xmath42 polarization direction coinsides with the @xmath40 axis ) .
similarly , no extra magnetic features are observed in the @xmath42 nsf cross - section for the second sample orientation .
nonetheless , all of the measured @xmath42 polarization cross - sections are given in the supplimentary material .
this method of looking at the magnetic intensity ignores the contribution of components of the moments orthogonal to the @xmath42 axis in the ( @xmath27 ) plane and parallel to the @xmath42 axis for the ( @xmath28 ) plane , however our complimentary measurements with unpolarized neutrons on the e2 instrument @xcite also show no new information on the magnetic structure compared to the d7 results .
measurements of the ( @xmath27 ) and ( @xmath28 ) scattering planes reveal broad `` rod''-like features at half - integer positions along the @xmath44-axis observed at all measured temperatures .
the position of the rods along @xmath44 suggests that the unit cell for this magnetic structure is doubled along the @xmath7 axis . in the ( @xmath27 ) plane ,
the rods extend along the @xmath39-direction which implies that the magnetic moments are only weakly correlated along the @xmath40 axis .
also , in the ( @xmath28 ) plane , the rods extend along the @xmath45-direction , so the magnetic moments are only weakly correlated along the @xmath43 axis .
the presence of the `` rods '' along two orthogonal directions means that the diffuse scattering is a two - dimensional structure in reciprocal space .
hence the correlations of this type of short - range order in @xmath0 are @xmath46-dimensional in real space . at the lowest temperature of 0.055
k the `` rods '' of diffuse scattering are most intense and approximate straight lines perpendicular to the @xmath44-direction . in the ( @xmath27 ) plane areas of greater intensity along the rod can also be seen at even integer @xmath39 .
there is no pronounced decay of intensity for the `` rods '' with increasing @xmath39 , @xmath45 or @xmath44 than what is likely due to the magnetic form factor .
on warming the system to 0.75 k the one - dimensional scattering in both the ( @xmath27 ) and ( @xmath28 ) planes is still very intense , and for the ( @xmath28 ) plane it is little different to what is observed at base temperature .
however , in the ( @xmath27 ) plane there is no longer any modulation of the intensity along the rods .
thus the onset of the diffuse scattering in the ( @xmath2 ) plane below 0.7 k seems to only affect the modulation of the intensity along the rods in the ( @xmath27 ) plane , with no other effect on the diffraction pattern of the second diffuse phase . in order to explain this lack of coupling between the two types of short - range ordering
, we suggest that each of the crystallographically inequivalent ho@xmath1 sites in @xmath0 contributes to only one of the two coexisting structures . at much higher temperatures , @xmath47 k
, there is still some intensity in the diffuse component of the total scattering , for example shown in the righthand panels of figure [ d7 - 2planes ] .
the `` rods '' are now much wider along the @xmath44-direction , and they appear to be a lot less straight .
the one - dimensional order persists over a wide temperature range , and the onset of these correlations may be observed with bulk heat capacity measurements ( as the broad peak around 3.5 k shown in the inset of fig . 3 in ref . ) . from the @xmath42 polarization direction nsf and sf data
, some conclusions can be drawn about the nature of this diffuse magnetic scattering . in the ( @xmath28 ) measurement
the diffuse scattering appears at the ( @xmath48 ) and symmetry equivalent positions only in the sf channel .
this demonstrates that the spin structure has no components parallel to the @xmath42 direction which coincides with the crystallographic direction @xmath40 in this measurement , _
i.e. _ all of the magnetic moments lie in the _ b - c _ plane . in the ( @xmath27 ) measurement the diffuse scattering appears at the ( @xmath49 ) and symmetry equivalent positions only in the nsf measurement , which indicates that in this low - dimensional magnetic structure all of the spins lie _
parallel _ with the @xmath43 axis .
the diffuse scattering peaks associated with the * k * = 0 magnetic structure are only visible in the @xmath42 sf data for both the ( @xmath27 ) and ( @xmath28 ) scattering planes .
this means that all of the spins that give rise to the * k * = 0 scattering are _ parallel _ with the @xmath7 axis .
this is in agreement with the previously proposed magnetic structure that was established from a refinement performed using powder neutron diffraction data .
@xcite single ion anisotropy , due to the crystal field , may be responsible for the magnetic moments on the two crystallographically inequivalent sites pointing along two orthogonal principal axes .
the @xmath3 resolution of d7 does not allow for the precise investigation of the structure of the planes of diffuse scattering , so the d10 diffractometer was used to further examine the `` rod '' like features .
scans along the rods at 0.15 k indicate that there is a pronounced @xmath3-dependence to the scattering intensity , and to illustrate this , data for the ( @xmath49 ) rod is shown in fig .
[ difftdep1 ] . at the lowest temperature
the scattering appears to be most intense near the integer values of @xmath39 . upon raising the temperature
the @xmath3-dependence becomes less pronounced , but the scattering intensity remains measurable above background even at temperatures as high as 1.8 k , as expected from the d7 measurements . in order to have a complete picture of the one - dimensional scattering , scans across the `` rods '' along the @xmath44-direction were also performed .
the temperature dependence of the integrated intensity of the diffuse magnetic scattering across ( @xmath50 ) is shown in fig .
[ difftdep2 ] as an example . at the lowest temperature
the moments are highly correlated around @xmath44 = @xmath11 . upon raising the temperature
the scattering becomes less intense and less symmetrical about @xmath44 = @xmath11 . unlike the _ lozenge_-type diffuse scattering seen in the ( @xmath2 ) plane , the diffuse scattering intensity seen in the ( @xmath27 ) and ( @xmath28 ) planes appears to be a smooth function of temperature , with no well - defined transition , just a gradual building - up of one - dimensional correlations . from the fwhm of the fitted lorentzian curves to the diffuse scattering , the correlation lengths were estimated as described previously .
@xcite at the lowest temperature , the ( @xmath4 ) planes of diffuse scattering are correlated to @xmath5 @xmath6 230 along the @xmath7 axis .
the integrated intensity and fwhm along @xmath44 , and the calculated correlation length along the @xmath7 axis of the ( 20@xmath11 ) reflection are plotted as a function of temperature in fig .
the diffuse scattering does not show any abrupt transition , demonstrating a gradual build - up of correlations with decreasing temperature .
it is interesting to note that this type of diffuse scattering was expected from the previously collected diffraction data on powder samples of @xmath0 .
@xcite broad features were seen at @xmath3 = ( 00@xmath11 ) and symmetry related positions .
however , from the powder data alone it could not be established whether the diffuse scattering was one- or two - dimensional .
using the d10 instrument with the vertically focussing pg analyser both types of diffuse scattering found in @xmath0 were investigated .
comparison of the data collected with the analyser and with the 2-dimensional area detector data for the ( 030 ) magnetic reflection at the lowest temperature is shown in fig .
[ anapeak ] .
the statistics are much lower for the data collected in the analyser configuration .
the peaks are fitted with a lorentzian distribution , and the resulting fwhm for the two datasets is in reasonable agreement .
this indicates that the diffuse scattering that appears around the peaks in the ( @xmath2 ) plane is elastic within the energy resolution of the analyser .
scans along ( @xmath29 ) at several integer positions of @xmath39 were performed to check the diffuse scattering profile of the planes with an improved energy resolution .
the comparison of the data collected using the 2-dimensional area detector and that using the analyser configuration for the ( 20@xmath11 ) reflection at 0.60 k is shown in fig .
[ anadiff ] . here , the fwhm is fairly close for both datasets , taking into account that the statistics for data collected with the analyser configuration are significantly lower .
this indicates that the diffuse scattering that appears in planes at ( @xmath4 ) is mostly elastic within the energy resolution of the analyser .
we have probed the low - temperature magnetic structure of @xmath0 by measuring the neutron diffraction in three planes orthogonal to the principal axes of the crystal . for this compound there
appear to be two distinct types of short - range magnetic order , which can be inferred from the diffraction patterns , arising from the two crystallographically inequivalent sites for the ho@xmath1 ions in the unit cell . in the ( @xmath2 ) plane diffuse magnetic scattering
appears around the * k * = 0 positions at temperatures below 0.7 k. the ho@xmath1 spins that participate in this short - range structure are antiferromagnetically coupled and are collinear with the @xmath7 axis .
whereas another type of magnetic order forms nearly perfect planes of diffuse scattering which appear as `` rods '' of scattering intensity seen in both the ( @xmath27 ) and ( @xmath28 ) planes in reciprocal space at @xmath3 = ( 00@xmath11 ) and symmetry related positions .
this observation suggests that the second type of short - range order present in @xmath0 is almost perfectly one - dimensional in nature . from the _
xyz_-polarized neutron measurements it is obvious that the spins that participate in this second structure are antiferromagnetically coupled and point along the @xmath43 axis .
the planes of diffuse scattering have internal structure , with maxima of intensity occurring at even integer @xmath39 positions at the lowest temperature .
both types of diffuse scattering in @xmath0 appear to be elastic within the energy resolution of the analyser .
the coexistence of two distinct types of magnetism is similar to what is observed at low - temperatures in @xmath21 .
both compounds have a magnetic component with the propagation vector * k * = 0 in the ( @xmath2 ) plane below a well - defined transition temperature , as well as the one - dimensional scattering that is observed at much higher temperatures .
the authors would like to thank mr .
t. e. orton for the valuable technical support and acknowledge the dedication of the sample environment teams at both isis and ill .
a part of this work was financially supported by the epsrc , uk under grant ep / i007210/1 .
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the lorentzian or gaussian fitting functions were chosen because they gave the best fit to the data , assessed by comparing the value of @xmath52 and reduced @xmath53 for the different fits .
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taking into account the instrument resolution did not result in a significant difference to the calculated correlation lengths . | @xmath0 is a geometrically frustrated magnet in which the magnetic ho@xmath1 ions form honeycomb layers connected through a network of zigzag chains . at low - temperature two distinct types of short - range magnetic order can be inferred from single crystal diffraction data , collected using both polarized and unpolarized neutrons . in the ( @xmath2 ) plane
the diffuse scattering is most noticeable around the * k * = 0 positions and its intensity rapidly increases at temperatures below 0.7 k. in addition , planes of diffuse scattering at @xmath3 = ( @xmath4 ) are visible at temperatures as high as 4.5 k. these planes coexist with the broad peaks of diffuse scattering in the ( @xmath2 ) plane at low - temperatures .
correlation lengths associated with the broad peaks are @xmath5 @xmath6 150 in the _ a - b _ plane and @xmath5 @xmath6 190 along @xmath7 axis , while the correlation length associated with the diffuse scattering planes is @xmath5 @xmath6 230 along the @xmath7 axis at the lowest temperature .
both types of diffuse scattering are elastic in nature .
the highly unusual coexistance of the two types of diffuse scattering in @xmath0 is likely to be the result of the presence of two crystallographically inequivalent sites for ho@xmath1 in the unit cell . | <s>[INST]the term magnetic frustration describes the inability of a magnetic system to satisfy all the competing interactions in order to establish a unique ground state .
@xcite in the presence of antiferromagnetic exchange interactions , magnets based on corner- or edge - sharing triangles @xcite or tetrahedra @xcite can exhibit geometric frustration .
common examples of systems in which frustration plays a fundamental role in establishing highly degenerate ground states and low - temperature properties such as reduced critical temperatures include the kagome , @xcite pyrochlore @xcite and garnet @xcite structures .
new magnets which exhibit the effects of geometric frustration are constantly being discovered .
the behaviour of these systems is often complex , with many magnets remaining disordered down to very low - temperatures - traditional examples being spin liquids @xcite and spin glasses .
@xcite in this paper we report on an investigation of single crystal samples of @xmath0 , a compound that displays no long - range order down to 0.05 k. more intriguingly , there appears to be two distinct types of short - range magnetic order coexisting in this material , which has no chemical instability or phase separation .
@xmath0 belongs to the sr@xmath8o@xmath9 ( where _ ln _ = lanthanide ) family of compounds , @xcite which crystallise in the form of calcium ferrite , @xcite space group _ pnam_.
this allows the magnetic _ ln _ ions to be linked in a network of triangles and hexagons , as shown in fig .
[ lnsublattice ] , with two crystallographically inequivalent sites of the rare earth ions shown in red and blue .
we believe that it is likely that the two different types of short - range order observed in @xmath0 can be attributed to the two different sites for the ho@xmath1 ions in the unit cell .
o@xmath9 compounds , with the two crystallographically inequivalent positions of the rare earth ions shown in different colors . when viewed in the _ a - b _ plane , honeycombs of the @xmath10 ions
are visible .
zigzag chains running along the @xmath7 axis connect the honeycomb layers and give rise to geometric frustration .
the box indicates the dimensions of the unit cell . ] for all the sr@xmath8o@xmath9 systems the magnetic ions form zigzag chains that run along the @xmath7 axis .
these triangular ladders can be frustrated , and are magnetically equivalent to one - dimensional chains with first- and second - nearest - neighbour interactions .
the chains of @xmath10 ions interconnect by forming a distorted _ honeycomb _ structure , a bipartite lattice made up of edge sharing hexagons , in the _ a - b _ plane .
the honeycomb lattice would only be frustrated if further neighbor exchange is considered , but receives substantial theoretical interest since it has the smallest possible coordination number in two - dimensions .
@xcite thus for these systems quantum fluctuations are expected to have a much larger effect on the stability of magnetic order than , for example , for square or triangular lattices .
a number of honeycomb lattice structures have been identified experimentally , including the spin-@xmath11 compound incu@xmath12v@xmath13o@xmath14 , @xcite the spin-@xmath15 systems bi@xmath14mn@xmath9o@xmath16(no@xmath14 ) @xcite and @xmath17cacr@xmath18o@xmath9 @xcite as well as other systems with larger spins like ba@xmath8o@xmath9 , @xcite eu@xmath8o@xmath9 @xcite and sr@xmath8o@xmath9 .
@xcite bulk property measurements of geometrically frustrated systems usually reveal anomalous behaviour , such as the presence of phase transitions at temperatures much lower than expected from the strength of the exchange interactions . magnetic susceptibility , @xmath19 , measured on powder samples of all the sr@xmath8o@xmath9 compounds
has revealed a disparity in the measured curie - weiss constants , @xmath20 , and the lack of long - range order down to 1.8 k. @xcite @xmath21 and @xmath0 show cusps in single crystal @xmath19 measurements at @xmath22 = 0.62 k for @xmath0 @xcite and at @xmath23 = 0.75 k for @xmath21 , @xcite and a @xmath24-anomaly is observed in the specific heat of @xmath25 at @xmath23 = 0.92 k. @xcite in contrast , @xmath26 does not show any anomalies in @xmath19 down to 0.5 k , @xcite and no @xmath24-type transitions have been observed in heat capacity measurements down to 0.39 k in zero applied field .
@xcite neutron diffraction on powder samples of @xmath26 reveals only broad diffuse scattering peaks and thus further corroborates the apparent lack of long - range order at least down to 20 mk for this compound .
@xcite low - temperature neutron diffraction studies of @xmath25 point to unusual magnetic behaviour , where the two inequivalent sites of the yb@xmath1 ion do not appear to have the same value of the ordered moment . @xcite the magnetism in @xmath21 is equally unconventional since powder neutron diffraction measurements indicate that the transition to nel order involves only half of the er@xmath1 sites ( either the red or blue sites in the notation of fig .
[ lnsublattice ] ) .
@xcite polarized neutron studies on single crystals of @xmath21 suggest that the long - range ordered ( * k * = 0 ) magnetic structure coexists with a shorter - range incommensurate ordering that has a pronounced low - dimensional character at temperatures below @xmath23 = 0.75 k. @xcite neutron diffraction on powder samples of @xmath0 @xcite appeared to indicate that a similar situation arises in this compound , with distinct long - range commensurate and shorter - range incommensurate magnetic structures present at low - temperatures . as a result of refining the data collected at 0.045 k , a magnetic structure with the propagation vector * k * = 0 was proposed , with only one of the crystallographically inequivalent ho@xmath1 ions carrying a significant magnetic moment .
all of the moments in the refined long - range structure point along the @xmath7 axis in ferromagnetic chains , with neighboring chains coupled antiferromagnetically .
in this paper we present the results of an investigation into the nature of the magnetism in single crystal samples of @xmath0 at low - temperatures .
we have measured neutron diffraction patterns for three orthogonal directions in the reciprocal space of @xmath0 .
our results indicate that in @xmath0 _ two _ distinct types of _ short - range _ magnetic order arise from the two sites for the ho@xmath1 ions . in the ( @xmath2 ) plane
, the first type of diffuse magnetic scattering appears around positions with the propagation vector * k * = 0 below 0.7 k ( with no long - range order present in contrast to previous measurements on powder samples of @xmath0 ) . whereas the second type of diffuse scattering appears as planes of scattering intensity at ( @xmath4 ) .
these planes are seen as `` rods '' of scattering intensity in both the ( @xmath27 ) and ( @xmath28 ) planes in reciprocal space at @xmath3 = ( 00@xmath11 ) and symmetry related positions .
therefore the second type of short - range order present in this material is one - dimensional in real space .
thus two members of the sr@xmath8o@xmath9 series , @xmath0 and @xmath21 , both show the coexistance of two types of magnetic ordering at low - temperatures , but @xmath21 has long- and short - range components , whereas in @xmath0 both types of magnetic correlations are short - ranged .
careful studies of the correlation lengths ( @xmath5 ) in @xmath0 indicate that the diffuse scattering in the ( @xmath2 ) plane is correlated to @xmath5 @xmath6 150 in the _ a - b _ plane at 0.18 k , and to @xmath5 @xmath6 190 along the @xmath7 axis at 0.16 k. the scattering is mostly isotropic in reciprocal space .
the diffuse intensity planes have a correlation length of @xmath5 @xmath6 230 along the @xmath7 axis at 0.15 k. finally by utilising an energy analyser we were able to deduce that the diffuse scattering in the ( @xmath2 ) plane is purely elastic , while the diffuse scattering that appears in planes along ( @xmath29 ) is mostly elastic .
large volume single crystals of @xmath0 were grown using the floating zone method , with details of the procedure reported elsewhere .
@xcite the samples were aligned using the backscattering laue technique and cut perpendicular to the principal crystal axes , within an estimated accuracy of @xmath30 for the d7 measurements and within @xmath31 for the wish experiment . for the wish experiment a single 0.9 g sample of @xmath0
was fixed to an oxygen free copper sample holder using kwikfill resin .
two more 0.9 g samples of @xmath0 ( one for each orientation ) were fixed to oxygen free copper sample holders using kwikfill resin during the d7 experiment ; with equivalent sample mountings used for background measurements . for the d10 experiment
single crystal samples of @xmath0 ( weighing 0.3 g and 0.1 g ) were fixed to oxygen free copper pins using stycast resin .
neutron diffraction measurements in the ( @xmath2 ) scattering plane were made using the cold neutron wish @xcite instrument at the isis facility ( rutherford appleton laboratory , uk ) in a range of temperatures from 0.05 to 1.5 k. wish is equipped with a continuous array of position sensitive @xmath32he detectors that cover an angular range of 10@xmath33 .
this provides the substantial @xmath3-space coverage required for single crystal experiments . depending on the experimental requirements
the wish instrument resolution and flux can be tuned , and out of plane neutron detection is also possible .
the diffuse scattering spectrometer d7 @xcite ( at the institut laue - langevin in grenoble , france ) with _ xyz _ polarization analysis was used to collect neutron scattering data for both ( @xmath27 ) and ( @xmath28 ) scattering planes in a range of temperatures from 0.055 to 4.5 k. the d7 instrument is equipped with 132 @xmath32he detectors which cover an angular range of 4@xmath34 . throughout the experiment cold neutrons monochromated to a wavelength of 3.1
were used , resulting in @xmath3-space coverage of 0.14 to 3.91 @xmath35 .
a quartz standard was used for normalising the polarization efficiency and a vanadium standard was used for normalising the detector efficiency of the instrument .
scans were performed in which the crystal was rotated about the vertical axis in steps of 1@xmath36 .
six measurements required to carry out full _ xyz _ polarization analysis were performed at each temperature for both sample orientations .
the reciprocal space maps were constructed in the usual manner using standard d7 data reduction functions .
the high - flux single - crystal diffractometer d10 ( located on a thermal neutron guide at the institute laue - langevin in grenoble , france ) was used in the four - circle dilution refrigerator mode to collect precise neutron scattering data .
the sample pins were attached to the eulerian cradle inside a helium flow cryostat with the dilution option to allow scanning along all reciprocal lattice directions at low - temperature .
a vertically focusing pyrolytic graphite ( pg ) ( 002 ) monochromator gave an incident wavelength of 2.36 , with the half - wavelength contamination suppressed by a pg filter .
a vertically focussing pg analyser was used to give improved resolution and suppressed background for some of the measurements .
the two - dimensional area detector was used for all the measurements except for those made with the energy analyser , where a single @xmath32he detector was used instead .
measurements were made in the temperature range 0.15 to 10 k. the integrated intensity of the magnetic diffuse scattering around the nuclear bragg peaks was extracted in the usual manner .
@xcite the plane like diffuse scattering features , however , often had a broad intensity profile which covered a large proportion of the two - dimensional d10 detector .
the selection of the integration box for these features required a compromise between getting adequate resolution and the correct representation of the diffuse scattering profile .
in the ( @xmath2 ) plane at a ) 0.055 k and b ) 0.7 k. the magnetic component was isolated by subtracting a 1 k background from the single crystal neutron diffraction data collected using wish , isis .
@xcite ] from earlier measurements on a powder sample of @xmath0 , * k * = 0 magnetic bragg peaks were expected in the ( @xmath2 ) scattering plane , @xcite similar to what has previously been observed for @xmath21 .
@xcite however , after cooling down the single crystal sample to 0.055 k , no long - range order was found in the wish measurements .
[ hk0 ] shows the observed magnetic scattering ( which was isolated by subtracting a 1 k background from the low - temperature data ) . from the single crystal data it is apparent that in the ( @xmath2 ) plane diffuse magnetic scattering appears around the * k * = 0 positions and that its intensity increases rapidly below 0.7 k. waiting at low - temperature for a long time for the sample to thermalise made no measurable difference to the intensity or width of the diffraction patterns .
it is important to note that in @xmath0 at temperatures below 0.7 k the diffuse scattering forms the same _ lozenge _ pattern that is seen at low - temperatures in @xmath21 .
@xcite this is a result of very similar positions of the magnetic @xmath10 ions in the respective unit cells for both compounds .
the positions of the observed broad diffuse scattering peaks in the ( @xmath2 ) scattering plane are in agreement with the positions previously reported for a * k * = 0 structure obtained from the powder refinement . however , from the single crystal experiment no long - range order is actually observed even though the onset of the diffuse scattering in the ( @xmath2 ) plane appears to go through a second - order phase transition ( see fig .
[ hk0_tdep ] and fig .
[ hk0_2ndorder ] ) , and can also be observed as a clear cusp in single crystal magnetic susceptibility measurements .
@xcite although the @xmath3 resolution of wish is good the sample was kept stationary during the experiments and in order to measure correlation length more accurately , high resolution scans across the nuclear and magnetic reflections in the ( @xmath2 ) plane were performed using the d10 instrument .
temperature dependence of the scattering intensity for two different types of reflections in the ( @xmath2 ) plane of @xmath0 are shown in fig .
[ 200peak ] , fig .
[ 030peak ] and fig .
[ 20lpeak ] . the data in fig .
[ 200peak ] have been fitted with gaussian and lorentzian components , to account for the nuclear ( temperature independent ) and magnetic scattering .
@xcite the nuclear ( gaussian ) component was fitted to data collected for ( 200 ) at higher temperature with high resolution , and this is shown in the inset to fig .
[ 200peak ] . the data in fig .
[ 030peak ] have been fitted using the lorentzian distribution only , since this is a forbidden reflection in _ pnam _ symmetry , and purely magnetic scattering is expected . the data in fig .
[ 20lpeak ] have been fitted using two gaussian components ( one for nuclear and one for magnetic contributions ) at all temperatures .
@xcite from the fwhm of the fitted lorentzian curves to the diffuse scattering , the correlation lengths were estimated using @xmath5 ( ) = @xmath37(fwhm ( @xmath38 .
@xcite at the lowest temperature , the magnetic order is correlated to @xmath5 @xmath6 150 in the _ a - b _ plane , and to @xmath5 @xmath6 190 along the @xmath7 axis .
the integrated intensity and fwhm along @xmath39 , and the calculated correlation length along the @xmath40 axis of the ( 030 ) reflection is plotted as a function of temperature in fig .
[ hk0_2ndorder ] . the data for the ( 030 ) reflection in fig .
[ hk0_2ndorder ] were collected using both the two - dimensional detector and energy analyser d10 instrument configurations .
a detailed comparison of these two types of measurements is presented later , see section [ analyser ] .
overall , the diffuse scattering in the ( @xmath2 ) plane shows second - order phase transition type behaviour , with a marked increase in correlation length below 0.62 k - the temperature at which a cusp was observed in single crystal magnetic susceptibility measurements .
@xcite finally , it is important to note that with the improved instrumental resolution offered by d10 , it is possible to see that there is a small amount of scattering intensity at positions forbidden by the @xmath41 symmetry .
this suggests that the proposed space group is not entirely appropriate for the sr@xmath8o@xmath9 family of compounds , although the relative intensity of the forbidden " peaks is systematically low compared to the intensity of the allowed nuclear peaks reflections , therefore much more accurate collection of the intensity of all the peaks is required in order to solve the crystal structure .
the intensity maps shown in fig .
[ d7 - 2planes ] summarise the main results of the single crystal neutron diffraction experiments to investigate the second type of diffuse scattering present in @xmath0 .
the polarized neutron experiments were configured to measure two independent components of the scattering function , here called the non - spin - flip ( nsf ) and spin - flip ( sf ) channels .
the @xmath42 polarization direction in our measurements coincides with the vertical axis , and hence the sum of @xmath42 nsf and @xmath42 sf measurements is what would be observed in unpolarized neutron experiments .
the standard data reduction formulas utilising all of the _ xyz _ polarized measurements to calculate the purely magnetic contribution to the scattering @xcite can not be applied to the @xmath0 system , because it is not an isotropically magnetic crystal at low - temperatures .
instead , fig .
[ d7 - 2planes](a ) shows the intensity measured in the ( @xmath27 ) plane @xmath42 nsf measurement ( here , the @xmath42 polarization direction coinsides with the @xmath43 axis ) .
no extra magnetic features associated with the ( @xmath4 ) planes are observed in the @xmath42 sf cross - section for this sample orientation .
[ d7 - 2planes](b ) shows the data for the ( @xmath28 ) plane @xmath42 sf measurements ( here , the @xmath42 polarization direction coinsides with the @xmath40 axis ) .
similarly , no extra magnetic features are observed in the @xmath42 nsf cross - section for the second sample orientation .
nonetheless , all of the measured @xmath42 polarization cross - sections are given in the supplimentary material .
this method of looking at the magnetic intensity ignores the contribution of components of the moments orthogonal to the @xmath42 axis in the ( @xmath27 ) plane and parallel to the @xmath42 axis for the ( @xmath28 ) plane , however our complimentary measurements with unpolarized neutrons on the e2 instrument @xcite also show no new information on the magnetic structure compared to the d7 results .
measurements of the ( @xmath27 ) and ( @xmath28 ) scattering planes reveal broad `` rod''-like features at half - integer positions along the @xmath44-axis observed at all measured temperatures .
the position of the rods along @xmath44 suggests that the unit cell for this magnetic structure is doubled along the @xmath7 axis . in the ( @xmath27 ) plane ,
the rods extend along the @xmath39-direction which implies that the magnetic moments are only weakly correlated along the @xmath40 axis .
also , in the ( @xmath28 ) plane , the rods extend along the @xmath45-direction , so the magnetic moments are only weakly correlated along the @xmath43 axis .
the presence of the `` rods '' along two orthogonal directions means that the diffuse scattering is a two - dimensional structure in reciprocal space .
hence the correlations of this type of short - range order in @xmath0 are @xmath46-dimensional in real space . at the lowest temperature of 0.055
k the `` rods '' of diffuse scattering are most intense and approximate straight lines perpendicular to the @xmath44-direction . in the ( @xmath27 ) plane areas of greater intensity along the rod can also be seen at even integer @xmath39 .
there is no pronounced decay of intensity for the `` rods '' with increasing @xmath39 , @xmath45 or @xmath44 than what is likely due to the magnetic form factor .
on warming the system to 0.75 k the one - dimensional scattering in both the ( @xmath27 ) and ( @xmath28 ) planes is still very intense , and for the ( @xmath28 ) plane it is little different to what is observed at base temperature .
however , in the ( @xmath27 ) plane there is no longer any modulation of the intensity along the rods .
thus the onset of the diffuse scattering in the ( @xmath2 ) plane below 0.7 k seems to only affect the modulation of the intensity along the rods in the ( @xmath27 ) plane , with no other effect on the diffraction pattern of the second diffuse phase . in order to explain this lack of coupling between the two types of short - range ordering
, we suggest that each of the crystallographically inequivalent ho@xmath1 sites in @xmath0 contributes to only one of the two coexisting structures . at much higher temperatures , @xmath47 k
, there is still some intensity in the diffuse component of the total scattering , for example shown in the righthand panels of figure [ d7 - 2planes ] .
the `` rods '' are now much wider along the @xmath44-direction , and they appear to be a lot less straight .
the one - dimensional order persists over a wide temperature range , and the onset of these correlations may be observed with bulk heat capacity measurements ( as the broad peak around 3.5 k shown in the inset of fig . 3 in ref . ) . from the @xmath42 polarization direction nsf and sf data
, some conclusions can be drawn about the nature of this diffuse magnetic scattering . in the ( @xmath28 ) measurement
the diffuse scattering appears at the ( @xmath48 ) and symmetry equivalent positions only in the sf channel .
this demonstrates that the spin structure has no components parallel to the @xmath42 direction which coincides with the crystallographic direction @xmath40 in this measurement , _
i.e. _ all of the magnetic moments lie in the _ b - c _ plane . in the ( @xmath27 ) measurement the diffuse scattering appears at the ( @xmath49 ) and symmetry equivalent positions only in the nsf measurement , which indicates that in this low - dimensional magnetic structure all of the spins lie _
parallel _ with the @xmath43 axis .
the diffuse scattering peaks associated with the * k * = 0 magnetic structure are only visible in the @xmath42 sf data for both the ( @xmath27 ) and ( @xmath28 ) scattering planes .
this means that all of the spins that give rise to the * k * = 0 scattering are _ parallel _ with the @xmath7 axis .
this is in agreement with the previously proposed magnetic structure that was established from a refinement performed using powder neutron diffraction data .
@xcite single ion anisotropy , due to the crystal field , may be responsible for the magnetic moments on the two crystallographically inequivalent sites pointing along two orthogonal principal axes .
the @xmath3 resolution of d7 does not allow for the precise investigation of the structure of the planes of diffuse scattering , so the d10 diffractometer was used to further examine the `` rod '' like features .
scans along the rods at 0.15 k indicate that there is a pronounced @xmath3-dependence to the scattering intensity , and to illustrate this , data for the ( @xmath49 ) rod is shown in fig .
[ difftdep1 ] . at the lowest temperature
the scattering appears to be most intense near the integer values of @xmath39 . upon raising the temperature
the @xmath3-dependence becomes less pronounced , but the scattering intensity remains measurable above background even at temperatures as high as 1.8 k , as expected from the d7 measurements . in order to have a complete picture of the one - dimensional scattering , scans across the `` rods '' along the @xmath44-direction were also performed .
the temperature dependence of the integrated intensity of the diffuse magnetic scattering across ( @xmath50 ) is shown in fig .
[ difftdep2 ] as an example . at the lowest temperature
the moments are highly correlated around @xmath44 = @xmath11 . upon raising the temperature
the scattering becomes less intense and less symmetrical about @xmath44 = @xmath11 . unlike the _ lozenge_-type diffuse scattering seen in the ( @xmath2 ) plane , the diffuse scattering intensity seen in the ( @xmath27 ) and ( @xmath28 ) planes appears to be a smooth function of temperature , with no well - defined transition , just a gradual building - up of one - dimensional correlations . from the fwhm of the fitted lorentzian curves to the diffuse scattering , the correlation lengths were estimated as described previously .
@xcite at the lowest temperature , the ( @xmath4 ) planes of diffuse scattering are correlated to @xmath5 @xmath6 230 along the @xmath7 axis .
the integrated intensity and fwhm along @xmath44 , and the calculated correlation length along the @xmath7 axis of the ( 20@xmath11 ) reflection are plotted as a function of temperature in fig .
the diffuse scattering does not show any abrupt transition , demonstrating a gradual build - up of correlations with decreasing temperature .
it is interesting to note that this type of diffuse scattering was expected from the previously collected diffraction data on powder samples of @xmath0 .
@xcite broad features were seen at @xmath3 = ( 00@xmath11 ) and symmetry related positions .
however , from the powder data alone it could not be established whether the diffuse scattering was one- or two - dimensional .
using the d10 instrument with the vertically focussing pg analyser both types of diffuse scattering found in @xmath0 were investigated .
comparison of the data collected with the analyser and with the 2-dimensional area detector data for the ( 030 ) magnetic reflection at the lowest temperature is shown in fig .
[ anapeak ] .
the statistics are much lower for the data collected in the analyser configuration .
the peaks are fitted with a lorentzian distribution , and the resulting fwhm for the two datasets is in reasonable agreement .
this indicates that the diffuse scattering that appears around the peaks in the ( @xmath2 ) plane is elastic within the energy resolution of the analyser .
scans along ( @xmath29 ) at several integer positions of @xmath39 were performed to check the diffuse scattering profile of the planes with an improved energy resolution .
the comparison of the data collected using the 2-dimensional area detector and that using the analyser configuration for the ( 20@xmath11 ) reflection at 0.60 k is shown in fig .
[ anadiff ] . here , the fwhm is fairly close for both datasets , taking into account that the statistics for data collected with the analyser configuration are significantly lower .
this indicates that the diffuse scattering that appears in planes at ( @xmath4 ) is mostly elastic within the energy resolution of the analyser .
we have probed the low - temperature magnetic structure of @xmath0 by measuring the neutron diffraction in three planes orthogonal to the principal axes of the crystal . for this compound there
appear to be two distinct types of short - range magnetic order , which can be inferred from the diffraction patterns , arising from the two crystallographically inequivalent sites for the ho@xmath1 ions in the unit cell . in the ( @xmath2 ) plane diffuse magnetic scattering
appears around the * k * = 0 positions at temperatures below 0.7 k. the ho@xmath1 spins that participate in this short - range structure are antiferromagnetically coupled and are collinear with the @xmath7 axis .
whereas another type of magnetic order forms nearly perfect planes of diffuse scattering which appear as `` rods '' of scattering intensity seen in both the ( @xmath27 ) and ( @xmath28 ) planes in reciprocal space at @xmath3 = ( 00@xmath11 ) and symmetry related positions .
this observation suggests that the second type of short - range order present in @xmath0 is almost perfectly one - dimensional in nature . from the _
xyz_-polarized neutron measurements it is obvious that the spins that participate in this second structure are antiferromagnetically coupled and point along the @xmath43 axis .
the planes of diffuse scattering have internal structure , with maxima of intensity occurring at even integer @xmath39 positions at the lowest temperature .
both types of diffuse scattering in @xmath0 appear to be elastic within the energy resolution of the analyser .
the coexistence of two distinct types of magnetism is similar to what is observed at low - temperatures in @xmath21 .
both compounds have a magnetic component with the propagation vector * k * = 0 in the ( @xmath2 ) plane below a well - defined transition temperature , as well as the one - dimensional scattering that is observed at much higher temperatures .
the authors would like to thank mr .
t. e. orton for the valuable technical support and acknowledge the dedication of the sample environment teams at both isis and ill .
a part of this work was financially supported by the epsrc , uk under grant ep / i007210/1 .
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t. j. hayes , g. balakrishnan , p. p. deen , p. manuel , l. c. chapon , and o. a. petrenko , phys . rev .
b * 84 * , 174435 ( 2011 ) . o. young , l. c. chapon , and o. a. petrenko , j. phys . : conf . ser . *
391 * 012081 ( 2012 ) .
g. balakrishnan , t. j. hayes , o. a. petrenko , and d. @xmath51 paul , j. phys . : condens .
matter * 21 * , 012202 ( 2009 ) . l. c. chapon , p. manuel , p. g. radaelli , c. benson , l. perrott , s. ansell , n. rhodes , d. raspino , d. duxbury , e. spill , and j. norris , neutron news * 22 * , 22 ( 2011 ) .
o. schrpf and h. capellmann , z. phys .
b * 80 * , 253 ( 1990 ) .
o. schrpf and h. capellmann , phys .
status solidi * 135 * , 359 ( 1993 ) .
j. r. stewart , p. p. deen , k. h. andersen , h. schober , j .- f .
barthelemy , j. m. hillier , a. p. murani , t. hayes , and b. lindenauc , j. appl .
crystallogr . *
42 * , 69 ( 2009 ) . c. wilkinson
, h. w. khamis , r. f. d. stansfield , and g. j. mcintyre , j. appl . crystallogr . * 21 * , 471 ( 1988 ) . no assumptions were made about the nature of the magnetic scattering distribution .
the lorentzian or gaussian fitting functions were chosen because they gave the best fit to the data , assessed by comparing the value of @xmath52 and reduced @xmath53 for the different fits .
taking into account the instrument resolution by estimating the correletion lengths using @xmath5 = @xmath54 , where @xmath55 and @xmath56 are the full widths at half maximum in @xmath3 space for the lorentzian peak in question and a reference ( resolution - limited ) bragg peak obtained on the same instrument resulted in a difference in the calculated correlation length of less than 1 @xmath57 for the lengths along the @xmath40 and @xmath43 axes .
the instrument resolution is more important for the calculations of correlation lengths along the @xmath7 axis where the scattering profile is much narrower .
o. young , i. glavatskyi , and o. a. petrenko , hzb exp .
report phy-01 - 3098 .
s. ghosh , h. d. zhou , l. balicas , s. hill , j. s. gardner , y. qiu , and c. r. wiebe , j. phys . : condens .
matter * 23 * , 164203 ( 2011 ) .
taking into account the instrument resolution did not result in a significant difference to the calculated correlation lengths .[/INST] @xmath0 is a geometrically frustrated magnet in which the magnetic ho@xmath1 ions form honeycomb layers connected through a network of zigzag chains . at low - temperature two distinct types of short - range magnetic order can be inferred from single crystal diffraction data , collected using both polarized and unpolarized neutrons . in the ( @xmath2 ) plane
the diffuse scattering is most noticeable around the * k * = 0 positions and its intensity rapidly increases at temperatures below 0.7 k. in addition , planes of diffuse scattering at @xmath3 = ( @xmath4 ) are visible at temperatures as high as 4.5 k. these planes coexist with the broad peaks of diffuse scattering in the ( @xmath2 ) plane at low - temperatures .
correlation lengths associated with the broad peaks are @xmath5 @xmath6 150 in the _ a - b _ plane and @xmath5 @xmath6 190 along @xmath7 axis , while the correlation length associated with the diffuse scattering planes is @xmath5 @xmath6 230 along the @xmath7 axis at the lowest temperature .
both types of diffuse scattering are elastic in nature .
the highly unusual coexistance of the two types of diffuse scattering in @xmath0 is likely to be the result of the presence of two crystallographically inequivalent sites for ho@xmath1 in the unit cell . </s> |
o efeito antiplaca e antigengivite de um gel contendo extrato de rom a 10% foi avaliado utilizando um modelo de gengivite experimental parcial em humanos .
23 indivduos participaram voluntariamente deste estudo cruzado , duplo - cego , compreendendo dois perodos de 21 dias cada um .
uma moldeira de acrlico foi confeccionada para cada participante , a qual foi utilizada como carreadora dos gis sobre a rea a ser avaliada ( hemiarco inferior esquerdo ) .
os sujeitos foram aleatoriamente designados para usar o gel placebo ( grupo controle ) ou o gel teste ( grupo experimental ) , sendo instrudos a colocar o gel na moldeira e esta sobre os dentes teste , escovando os outros normalmente trs vezes ao dia .
no dia 0 e dia 21 os ndices de placa visvel ( ipv ) e ndice de sangramento gengival ( isg ) foram registrados .
os resultados no demonstraram diferena estatstica significante entre os grupos controle e experimental para nenhum dos ndices .
o gel contendo extrato de rom a 10% no foi eficiente em evitar a formao de placa bacteriana supragengival e prevenir a inflamao gengival .
gingivitis is a chronic inflammatory process limited to the gingiva and without either attachment or alveolar bone loss .
it is one of the most frequent oral diseases , affecting more than 90% of the population , regardless of age , sex or race .
the earliest clinical sign is the bleeding caused by a vasodilatory effect caused by an inflammatory response29 .
the prevention of gingivitis by daily and effective supragingival plaque control using toothbrushing and dental floss is necessary to arrest a possible progression to periodontitis3,11 .
although mechanical plaque control methods have the potential to maintain adequate levels of oral hygiene , clinical experience and population - based studies have shown that such methods are not being employed as accurately as they should by a large number of people .
therefore , several chemotherapeutic agents such as triclosan , essential oils and chlorhexidine have been developed to control bacterial plaque , aiming at improving the efficacy of daily hygiene control measures6,8,10,15 - 17,23,26 .
the interest in plants with antibacterial and antiinflammatory activity has increased as a consequence of current problems associated with the wide - scale misuse of antibiotics that induced microbial drug resistence7,18 .
natural products such as astronium urundeuva , calendula , aloe vera , curcuma zedoaria and other herbal products have been tested with effective results12,19,25,29 .
punica granatum linn ( family punicaceae ) , mostly known as " pomegranate " , is a shrub or small tree native from asia where several of its parts have been used as an astringent , haemostatic as well as for diabetes control5,13,24 . in brazil
, the fruit of this tree is known as " rom " and is commonly used for treatment of throat infections , coughs and fever due to its antiinflammatory properties13,14 . in the only study available evaluating the effects of pomegranate on gingivitis , pereira and sampaio21 ( 2003 ) showed a significant reduction of gingival bleeding after using a dentifrice containing pomegranate extract . however , a control group was not included in that study .
therefore , the purpose of the present investigation was to assess the effects of punica granatum linn extract on supragingival plaque formation and development of experimental gingivitis in comparison to a control formulation .
twenty - five dental students from the university of fortaleza ( unifor ) ( 12 male and 13 female aged 22 to 28 years ) were enrolled in this study .
all subjects had at least 20 natural teeth , among which the 4 posterior teeth in the lower left quadrant ( experimental teeth ) .
all participants , randomly screened , were informed about the nature of the study and signed an informed consent form in compliance with the guidelines of the brazilian health council .
students with medical disorders , severe periodontal disease and under antimicrobial therapy , as well as smokers , pregnant women and individuals presenting a probing depth 3 mm associated with any mandibular teeth were excluded from the trail .
the protocol was approved by the university 's ethics committee ( report cotica / unifor ) an alginate impression of the experimental teeth was taken and poured in die stone to obtain casts . on each stone
cast , a 0.3-mm - thick thermoplastic mouthguard material spacer was made using a vacuum former . upon the spacer
, an individual toothshield was made of a 2-mm - thick thermoplastic mouthguard material , using the same vacuum former .
the toothshield was trimmed 2 mm beyond the gingival margin to assure that gel would be in contact with the gingival margin of the experimental teeth during toothbrushing of the remaining teeth .
the control and experimental gels were formulated and packed into tubes in a commercial drugstore . the tubes were previously coded to warrant that neither the examiner nor the volunteers knew their content , which was revealed by the pharmacist only after the study was completed .
all students used both gels in alternate periods , according to a cross - over model .
an infusion was prepared with powdered material at a ratio of 100 g powder to 1000 ml distilled water , cooled at room temperature and filtered .
thereafter , 50 g of carboxymethylcellulose was added to the infusion ( 1000 ml ) and the mixture was kept boiling until complete dissolution to obtain the 10% gel concentration .
the pomegranate extract concentration used in this work was based on the findings of previous in vitro studies13,20 that tested the gel at different concentrations and found that the 10% concentration yielded the most favorable results . a glycerin / ethanol mixture ( 50 ml:50 ml )
was added and the solution was vigorously stirred during 15 minutes until gel formation . a very small amount of menthol ( flavoring ) and a conserving agent were then added .
this study was a randomized , double - blind comparison of 2 crossover groups of dental students performed in 2 experimental phases of 21 days each with a 1-month washout interval between them .
to standardize the groups , the students were submitted to a meticulous evaluation ( pre - experimental phase ) to score the visible plaque index ( vpi ) and the gingival bleeding index ( gbi)1 of each tooth .
all teeth of each subject were polished and flossed by the examiner to eliminate plaque remnants .
thirty days after the initial phase , the volunteers were randomly assigned to 2 groups and the experimental phase began . on day 0 of both experimental periods ,
vpi and gbi were recorded . a personal " kit " containing a toothshield , a tube with 90 g of control or experimental gel and a commercial dentifrice with no antigingivitis properties ( sorriso , kolynos do brazil ltda .
, osasco , sp , brazil ) was given to all students . during each 21-day experimental period
, the subjects were instructed to fill the toothshield with the gel prior to insertion in the mouth and seat it over the experimental teeth for at least 1 min .
the volunteers refrained from brushing the test quadrant , while the other teeth were normally brushed three times a day using the dentifrice ( same to all students ) .
in addition to verbal instructions , the subjects were given written recommendations to follow at home . on the last day of each period ( 21st day ) ,
vpi and gbi indexes were recorded by the same examiner on the mesiobuccal , buccal , distobuccal , mesiolingual , lingual and distolingual surfaces of the experimental teeth .
the gingival tissues were inspected for the presence of bleeding , recorded 10 seconds after running the tip of a who probe along the gingival margin ( 0.5-mm penetration into the sulci ) .
the values of six sites of each tooth were recorded to obtain the vpi and gbi means .
then , vpi and gbi means for the four test teeth were calculated to determine vpi and gbi means of each volunteer .
intra - examiner agreement for vpi and gbi was calculated by repeating the measurements in 10 patients , with at least 1 hour of interval4 .
twenty - five dental students from the university of fortaleza ( unifor ) ( 12 male and 13 female aged 22 to 28 years ) were enrolled in this study .
all subjects had at least 20 natural teeth , among which the 4 posterior teeth in the lower left quadrant ( experimental teeth ) .
all participants , randomly screened , were informed about the nature of the study and signed an informed consent form in compliance with the guidelines of the brazilian health council .
students with medical disorders , severe periodontal disease and under antimicrobial therapy , as well as smokers , pregnant women and individuals presenting a probing depth 3 mm associated with any mandibular teeth were excluded from the trail .
the protocol was approved by the university 's ethics committee ( report cotica / unifor )
an alginate impression of the experimental teeth was taken and poured in die stone to obtain casts . on each stone
cast , a 0.3-mm - thick thermoplastic mouthguard material spacer was made using a vacuum former . upon the spacer ,
an individual toothshield was made of a 2-mm - thick thermoplastic mouthguard material , using the same vacuum former .
the toothshield was trimmed 2 mm beyond the gingival margin to assure that gel would be in contact with the gingival margin of the experimental teeth during toothbrushing of the remaining teeth .
the control and experimental gels were formulated and packed into tubes in a commercial drugstore . the tubes were previously coded to warrant that neither the examiner nor the volunteers knew their content , which was revealed by the pharmacist only after the study was completed .
all students used both gels in alternate periods , according to a cross - over model .
an infusion was prepared with powdered material at a ratio of 100 g powder to 1000 ml distilled water , cooled at room temperature and filtered .
thereafter , 50 g of carboxymethylcellulose was added to the infusion ( 1000 ml ) and the mixture was kept boiling until complete dissolution to obtain the 10% gel concentration .
the pomegranate extract concentration used in this work was based on the findings of previous in vitro studies13,20 that tested the gel at different concentrations and found that the 10% concentration yielded the most favorable results . a glycerin / ethanol mixture ( 50 ml:50 ml )
was added and the solution was vigorously stirred during 15 minutes until gel formation . a very small amount of menthol ( flavoring ) and a conserving agent were then added .
this study was a randomized , double - blind comparison of 2 crossover groups of dental students performed in 2 experimental phases of 21 days each with a 1-month washout interval between them .
the students were submitted to a meticulous evaluation ( pre - experimental phase ) to score the visible plaque index ( vpi ) and the gingival bleeding index ( gbi)1 of each tooth .
all teeth of each subject were polished and flossed by the examiner to eliminate plaque remnants .
thirty days after the initial phase , the volunteers were randomly assigned to 2 groups and the experimental phase began . on day 0 of both experimental periods ,
vpi and gbi were recorded . a personal " kit " containing a toothshield , a tube with 90 g of control or experimental gel and a commercial dentifrice with no antigingivitis properties ( sorriso , kolynos do brazil ltda .
, osasco , sp , brazil ) was given to all students . during each 21-day experimental period
, the subjects were instructed to fill the toothshield with the gel prior to insertion in the mouth and seat it over the experimental teeth for at least 1 min .
the volunteers refrained from brushing the test quadrant , while the other teeth were normally brushed three times a day using the dentifrice ( same to all students ) .
in addition to verbal instructions , the subjects were given written recommendations to follow at home . on the last day of each period ( 21st day ) , vpi and gbi indexes were recorded and the teeth were polished with pumice .
vpi and gbi indexes were recorded by the same examiner on the mesiobuccal , buccal , distobuccal , mesiolingual , lingual and distolingual surfaces of the experimental teeth .
the gingival tissues were inspected for the presence of bleeding , recorded 10 seconds after running the tip of a who probe along the gingival margin ( 0.5-mm penetration into the sulci ) .
the values of six sites of each tooth were recorded to obtain the vpi and gbi means .
then , vpi and gbi means for the four test teeth were calculated to determine vpi and gbi means of each volunteer .
intra - examiner agreement for vpi and gbi was calculated by repeating the measurements in 10 patients , with at least 1 hour of interval4 .
the mann - whitney non - parametric test was used to evaluate statistical differences between control and experimental groups on days 0 and 21 . in each group ,
the mean scores of vpi and gbi were compared between baseline and the end of the trial by the wilcoxon test .
two students were excluded from the study during the experimental phase due to third molar extraction and restorative needs .
the experimental gel had good acceptance and did not show adverse effects , such as abscess , ulcerations or allergic reactions . on day 0 , in both experimental periods ,
the control and experimental groups did not show statistically significant difference to each other with respect to vpi ( p=0.5385 ) and gbi ( p=0.3392 ) means ( p>0.05 ) .
these results indicated that both groups were well balanced at baseline ( table 1 and 2 ) . at the 21st day ,
plaque ( p=0.4354 ) and gingival bleeding ( p=0.4685 ) were present in both groups , but the difference between them was not statistically significant ( table 1 and 2 ) .
* means followed by the same uppercase letters on day 0 and day 21 do not differ statistically ( p>0.05 ) * * means followed by different lowercase letters in a same column differ statistically ( p<0.05 ) * means followed by the same uppercase letters on day 0 and day 21 do not differ statistically ( p>0.05 ) * * means followed by different lowercase letters in a same column differ statistically ( p<0.05 ) comparing the means between day 0 and day 21 in each group , there was a statistically significant difference in the vpi ( p=0.0000 ) and gbi ( p=0.0001 ) indexes .
the inability of adult population to perform adequate mechanical toothcleaning has stimulated the search for chemotherapeutic agents added to dentifrices to improve plaque control and prevent gingivitis16 .
the antibacterial activity of punica granatum linn has been evaluated in previous studies with good results .
trivedi and kazmi28 ( 1979 ) , using extracts of fruit barks have observed an antibacterial activity of pomegranate extract against bacillus anthracis and vibrio cholerae while machado , et al.14 ( 2003 ) showed similar effect against staphylococcus aureus , in agreement with prashant and asha22 ( 2001 ) .
considering that flavoring agents can promote a moderate antiplaque effect16 and that the contents of test and control gels were different only with respect to the presence of pomegranate extract , this agent did not have additional effect in reducing dental plaque formation .
these data are not in agreement with those of a previous in vitro study20 that showed that a bacterial strain present in supragingival plaque , namely streptococcus sanguis , was sensitive to different concentrations of pomegranate extract , which demonstrated an inhibitory action similar to that of chlorhexidine2,9 .
it should be highlighted , however , that in vitro studies do not reproduce exactly the oral conditions . in the present study , the punica granatum linn
extract gel did not avoid plaque formation during the trial , as suggested by kakiuchi , et al.9 ( 1986 ) and pereira , et al.20 ( 2001 ) . as the gel was placed into on the toothshield in a non - diluted form , it may be speculated that gel solubilization by saliva would be necessary for its antimicrobial action to take place17 .
the antibacterial agents present in pomegranate - the hydrolysable tannins - form complexes of high molecular weight with proteins soluble , increase bacterial lysis and moreover interfere with bacterial adherence mechanisms to tooth surfaces9,13 - 14 .
there was no significant difference between the experimental and control groups in relation to gbi at the end of the trial .
these results are not consistent with those reported by pereira and sampaio21 ( 2003 ) , who showed a significant reduction on gingivitis in patients using a dentifrice containing pomegranate extract .
nevertheless , it is noteworthy that a control group was not included in that study , which does not allow accessing the actual gingivitis reduction rate related exclusively to mechanical plaque control . according to ross , et al.24 ( 2001 )
the antiinflammatory effect of pomegranate may be attributed to its considerable immunoregulatory activity over macrophages and t and b lymphocyte subsets .
however , in both experimental and control groups , there was a significant increase in marginal bleeding , showing that pomegranate did not avoid the development of gingivitis .
the binary score used in this study only evaluate the presence or absence of bleeding ; it does not allow the assessment of other characteristics of the inflammatory process , such as edema , changes in gingival contour and loss of tissue attachment .
therefore , the possible effect of punica granatum linn extract on controlling the severity of gingivitis can not be discussed . due to the lack of clinical trials with a similar design investigating the effect of pomegranate on gingivitis ,
the data of this study were evaluated by parallel inferences , taken off from non specialized articles .
therefore , more controlled trials using different concentrations of punica granatum linn extract are necessary to verify its action upon supragingival microflora in vivo and established gingivitis .
further research will be important to identify the real benefits of pomegranate as a therapeutic and preventive agent for gingivitis , in addition to its common use in popular medicine .
within the limits of this clinical study , it may be concluded that the gel containing 10% punica granatum linn extract was not efficient in preventing supragingival dental plaque formation and gingivitis . | objectives : the antiplaque and antigingivitis effects of a gel containing 10% punica granatum linn extract were evaluated using a 21-day partial - mouth experimental model of gingivitis.methods:23 volunteers participated in this cross - over , doubleblind study , carried out in 2 phases of 21 days each . for each period of the experiment ,
an acrylic toothshield was made for each volunteer to carry the test or placebo gel as well as to avoid brushing of the 4 experimental teeth ( posterior teeth in the lower left quadrant ) .
the subjects were randomly assigned to use either the placebo gel ( control group ) or the test gel ( experimental group ) and were instructed to brush the remaining teeth normally 3 times a day . on days 0 and 21 , the visible plaque index ( vpi ) and gingival bleeding index ( gbi ) were recorded.results:the results did not show statistically significant difference between control and experimental groups for either of the indices ( vpi and gbi).conclusion : the gel containing 10% punica granatum linn extract was not efficient in preventing supragingival dental plaque formation and gingivitis . | <s>[INST]o efeito antiplaca e antigengivite de um gel contendo extrato de rom a 10% foi avaliado utilizando um modelo de gengivite experimental parcial em humanos .
23 indivduos participaram voluntariamente deste estudo cruzado , duplo - cego , compreendendo dois perodos de 21 dias cada um .
uma moldeira de acrlico foi confeccionada para cada participante , a qual foi utilizada como carreadora dos gis sobre a rea a ser avaliada ( hemiarco inferior esquerdo ) .
os sujeitos foram aleatoriamente designados para usar o gel placebo ( grupo controle ) ou o gel teste ( grupo experimental ) , sendo instrudos a colocar o gel na moldeira e esta sobre os dentes teste , escovando os outros normalmente trs vezes ao dia .
no dia 0 e dia 21 os ndices de placa visvel ( ipv ) e ndice de sangramento gengival ( isg ) foram registrados .
os resultados no demonstraram diferena estatstica significante entre os grupos controle e experimental para nenhum dos ndices .
o gel contendo extrato de rom a 10% no foi eficiente em evitar a formao de placa bacteriana supragengival e prevenir a inflamao gengival .
gingivitis is a chronic inflammatory process limited to the gingiva and without either attachment or alveolar bone loss .
it is one of the most frequent oral diseases , affecting more than 90% of the population , regardless of age , sex or race .
the earliest clinical sign is the bleeding caused by a vasodilatory effect caused by an inflammatory response29 .
the prevention of gingivitis by daily and effective supragingival plaque control using toothbrushing and dental floss is necessary to arrest a possible progression to periodontitis3,11 .
although mechanical plaque control methods have the potential to maintain adequate levels of oral hygiene , clinical experience and population - based studies have shown that such methods are not being employed as accurately as they should by a large number of people .
therefore , several chemotherapeutic agents such as triclosan , essential oils and chlorhexidine have been developed to control bacterial plaque , aiming at improving the efficacy of daily hygiene control measures6,8,10,15 - 17,23,26 .
the interest in plants with antibacterial and antiinflammatory activity has increased as a consequence of current problems associated with the wide - scale misuse of antibiotics that induced microbial drug resistence7,18 .
natural products such as astronium urundeuva , calendula , aloe vera , curcuma zedoaria and other herbal products have been tested with effective results12,19,25,29 .
punica granatum linn ( family punicaceae ) , mostly known as " pomegranate " , is a shrub or small tree native from asia where several of its parts have been used as an astringent , haemostatic as well as for diabetes control5,13,24 . in brazil
, the fruit of this tree is known as " rom " and is commonly used for treatment of throat infections , coughs and fever due to its antiinflammatory properties13,14 . in the only study available evaluating the effects of pomegranate on gingivitis , pereira and sampaio21 ( 2003 ) showed a significant reduction of gingival bleeding after using a dentifrice containing pomegranate extract . however , a control group was not included in that study .
therefore , the purpose of the present investigation was to assess the effects of punica granatum linn extract on supragingival plaque formation and development of experimental gingivitis in comparison to a control formulation .
twenty - five dental students from the university of fortaleza ( unifor ) ( 12 male and 13 female aged 22 to 28 years ) were enrolled in this study .
all subjects had at least 20 natural teeth , among which the 4 posterior teeth in the lower left quadrant ( experimental teeth ) .
all participants , randomly screened , were informed about the nature of the study and signed an informed consent form in compliance with the guidelines of the brazilian health council .
students with medical disorders , severe periodontal disease and under antimicrobial therapy , as well as smokers , pregnant women and individuals presenting a probing depth 3 mm associated with any mandibular teeth were excluded from the trail .
the protocol was approved by the university 's ethics committee ( report cotica / unifor ) an alginate impression of the experimental teeth was taken and poured in die stone to obtain casts . on each stone
cast , a 0.3-mm - thick thermoplastic mouthguard material spacer was made using a vacuum former . upon the spacer
, an individual toothshield was made of a 2-mm - thick thermoplastic mouthguard material , using the same vacuum former .
the toothshield was trimmed 2 mm beyond the gingival margin to assure that gel would be in contact with the gingival margin of the experimental teeth during toothbrushing of the remaining teeth .
the control and experimental gels were formulated and packed into tubes in a commercial drugstore . the tubes were previously coded to warrant that neither the examiner nor the volunteers knew their content , which was revealed by the pharmacist only after the study was completed .
all students used both gels in alternate periods , according to a cross - over model .
an infusion was prepared with powdered material at a ratio of 100 g powder to 1000 ml distilled water , cooled at room temperature and filtered .
thereafter , 50 g of carboxymethylcellulose was added to the infusion ( 1000 ml ) and the mixture was kept boiling until complete dissolution to obtain the 10% gel concentration .
the pomegranate extract concentration used in this work was based on the findings of previous in vitro studies13,20 that tested the gel at different concentrations and found that the 10% concentration yielded the most favorable results . a glycerin / ethanol mixture ( 50 ml:50 ml )
was added and the solution was vigorously stirred during 15 minutes until gel formation . a very small amount of menthol ( flavoring ) and a conserving agent were then added .
this study was a randomized , double - blind comparison of 2 crossover groups of dental students performed in 2 experimental phases of 21 days each with a 1-month washout interval between them .
to standardize the groups , the students were submitted to a meticulous evaluation ( pre - experimental phase ) to score the visible plaque index ( vpi ) and the gingival bleeding index ( gbi)1 of each tooth .
all teeth of each subject were polished and flossed by the examiner to eliminate plaque remnants .
thirty days after the initial phase , the volunteers were randomly assigned to 2 groups and the experimental phase began . on day 0 of both experimental periods ,
vpi and gbi were recorded . a personal " kit " containing a toothshield , a tube with 90 g of control or experimental gel and a commercial dentifrice with no antigingivitis properties ( sorriso , kolynos do brazil ltda .
, osasco , sp , brazil ) was given to all students . during each 21-day experimental period
, the subjects were instructed to fill the toothshield with the gel prior to insertion in the mouth and seat it over the experimental teeth for at least 1 min .
the volunteers refrained from brushing the test quadrant , while the other teeth were normally brushed three times a day using the dentifrice ( same to all students ) .
in addition to verbal instructions , the subjects were given written recommendations to follow at home . on the last day of each period ( 21st day ) ,
vpi and gbi indexes were recorded by the same examiner on the mesiobuccal , buccal , distobuccal , mesiolingual , lingual and distolingual surfaces of the experimental teeth .
the gingival tissues were inspected for the presence of bleeding , recorded 10 seconds after running the tip of a who probe along the gingival margin ( 0.5-mm penetration into the sulci ) .
the values of six sites of each tooth were recorded to obtain the vpi and gbi means .
then , vpi and gbi means for the four test teeth were calculated to determine vpi and gbi means of each volunteer .
intra - examiner agreement for vpi and gbi was calculated by repeating the measurements in 10 patients , with at least 1 hour of interval4 .
twenty - five dental students from the university of fortaleza ( unifor ) ( 12 male and 13 female aged 22 to 28 years ) were enrolled in this study .
all subjects had at least 20 natural teeth , among which the 4 posterior teeth in the lower left quadrant ( experimental teeth ) .
all participants , randomly screened , were informed about the nature of the study and signed an informed consent form in compliance with the guidelines of the brazilian health council .
students with medical disorders , severe periodontal disease and under antimicrobial therapy , as well as smokers , pregnant women and individuals presenting a probing depth 3 mm associated with any mandibular teeth were excluded from the trail .
the protocol was approved by the university 's ethics committee ( report cotica / unifor )
an alginate impression of the experimental teeth was taken and poured in die stone to obtain casts . on each stone
cast , a 0.3-mm - thick thermoplastic mouthguard material spacer was made using a vacuum former . upon the spacer ,
an individual toothshield was made of a 2-mm - thick thermoplastic mouthguard material , using the same vacuum former .
the toothshield was trimmed 2 mm beyond the gingival margin to assure that gel would be in contact with the gingival margin of the experimental teeth during toothbrushing of the remaining teeth .
the control and experimental gels were formulated and packed into tubes in a commercial drugstore . the tubes were previously coded to warrant that neither the examiner nor the volunteers knew their content , which was revealed by the pharmacist only after the study was completed .
all students used both gels in alternate periods , according to a cross - over model .
an infusion was prepared with powdered material at a ratio of 100 g powder to 1000 ml distilled water , cooled at room temperature and filtered .
thereafter , 50 g of carboxymethylcellulose was added to the infusion ( 1000 ml ) and the mixture was kept boiling until complete dissolution to obtain the 10% gel concentration .
the pomegranate extract concentration used in this work was based on the findings of previous in vitro studies13,20 that tested the gel at different concentrations and found that the 10% concentration yielded the most favorable results . a glycerin / ethanol mixture ( 50 ml:50 ml )
was added and the solution was vigorously stirred during 15 minutes until gel formation . a very small amount of menthol ( flavoring ) and a conserving agent were then added .
this study was a randomized , double - blind comparison of 2 crossover groups of dental students performed in 2 experimental phases of 21 days each with a 1-month washout interval between them .
the students were submitted to a meticulous evaluation ( pre - experimental phase ) to score the visible plaque index ( vpi ) and the gingival bleeding index ( gbi)1 of each tooth .
all teeth of each subject were polished and flossed by the examiner to eliminate plaque remnants .
thirty days after the initial phase , the volunteers were randomly assigned to 2 groups and the experimental phase began . on day 0 of both experimental periods ,
vpi and gbi were recorded . a personal " kit " containing a toothshield , a tube with 90 g of control or experimental gel and a commercial dentifrice with no antigingivitis properties ( sorriso , kolynos do brazil ltda .
, osasco , sp , brazil ) was given to all students . during each 21-day experimental period
, the subjects were instructed to fill the toothshield with the gel prior to insertion in the mouth and seat it over the experimental teeth for at least 1 min .
the volunteers refrained from brushing the test quadrant , while the other teeth were normally brushed three times a day using the dentifrice ( same to all students ) .
in addition to verbal instructions , the subjects were given written recommendations to follow at home . on the last day of each period ( 21st day ) , vpi and gbi indexes were recorded and the teeth were polished with pumice .
vpi and gbi indexes were recorded by the same examiner on the mesiobuccal , buccal , distobuccal , mesiolingual , lingual and distolingual surfaces of the experimental teeth .
the gingival tissues were inspected for the presence of bleeding , recorded 10 seconds after running the tip of a who probe along the gingival margin ( 0.5-mm penetration into the sulci ) .
the values of six sites of each tooth were recorded to obtain the vpi and gbi means .
then , vpi and gbi means for the four test teeth were calculated to determine vpi and gbi means of each volunteer .
intra - examiner agreement for vpi and gbi was calculated by repeating the measurements in 10 patients , with at least 1 hour of interval4 .
the mann - whitney non - parametric test was used to evaluate statistical differences between control and experimental groups on days 0 and 21 . in each group ,
the mean scores of vpi and gbi were compared between baseline and the end of the trial by the wilcoxon test .
two students were excluded from the study during the experimental phase due to third molar extraction and restorative needs .
the experimental gel had good acceptance and did not show adverse effects , such as abscess , ulcerations or allergic reactions . on day 0 , in both experimental periods ,
the control and experimental groups did not show statistically significant difference to each other with respect to vpi ( p=0.5385 ) and gbi ( p=0.3392 ) means ( p>0.05 ) .
these results indicated that both groups were well balanced at baseline ( table 1 and 2 ) . at the 21st day ,
plaque ( p=0.4354 ) and gingival bleeding ( p=0.4685 ) were present in both groups , but the difference between them was not statistically significant ( table 1 and 2 ) .
* means followed by the same uppercase letters on day 0 and day 21 do not differ statistically ( p>0.05 ) * * means followed by different lowercase letters in a same column differ statistically ( p<0.05 ) * means followed by the same uppercase letters on day 0 and day 21 do not differ statistically ( p>0.05 ) * * means followed by different lowercase letters in a same column differ statistically ( p<0.05 ) comparing the means between day 0 and day 21 in each group , there was a statistically significant difference in the vpi ( p=0.0000 ) and gbi ( p=0.0001 ) indexes .
the inability of adult population to perform adequate mechanical toothcleaning has stimulated the search for chemotherapeutic agents added to dentifrices to improve plaque control and prevent gingivitis16 .
the antibacterial activity of punica granatum linn has been evaluated in previous studies with good results .
trivedi and kazmi28 ( 1979 ) , using extracts of fruit barks have observed an antibacterial activity of pomegranate extract against bacillus anthracis and vibrio cholerae while machado , et al.14 ( 2003 ) showed similar effect against staphylococcus aureus , in agreement with prashant and asha22 ( 2001 ) .
considering that flavoring agents can promote a moderate antiplaque effect16 and that the contents of test and control gels were different only with respect to the presence of pomegranate extract , this agent did not have additional effect in reducing dental plaque formation .
these data are not in agreement with those of a previous in vitro study20 that showed that a bacterial strain present in supragingival plaque , namely streptococcus sanguis , was sensitive to different concentrations of pomegranate extract , which demonstrated an inhibitory action similar to that of chlorhexidine2,9 .
it should be highlighted , however , that in vitro studies do not reproduce exactly the oral conditions . in the present study , the punica granatum linn
extract gel did not avoid plaque formation during the trial , as suggested by kakiuchi , et al.9 ( 1986 ) and pereira , et al.20 ( 2001 ) . as the gel was placed into on the toothshield in a non - diluted form , it may be speculated that gel solubilization by saliva would be necessary for its antimicrobial action to take place17 .
the antibacterial agents present in pomegranate - the hydrolysable tannins - form complexes of high molecular weight with proteins soluble , increase bacterial lysis and moreover interfere with bacterial adherence mechanisms to tooth surfaces9,13 - 14 .
there was no significant difference between the experimental and control groups in relation to gbi at the end of the trial .
these results are not consistent with those reported by pereira and sampaio21 ( 2003 ) , who showed a significant reduction on gingivitis in patients using a dentifrice containing pomegranate extract .
nevertheless , it is noteworthy that a control group was not included in that study , which does not allow accessing the actual gingivitis reduction rate related exclusively to mechanical plaque control . according to ross , et al.24 ( 2001 )
the antiinflammatory effect of pomegranate may be attributed to its considerable immunoregulatory activity over macrophages and t and b lymphocyte subsets .
however , in both experimental and control groups , there was a significant increase in marginal bleeding , showing that pomegranate did not avoid the development of gingivitis .
the binary score used in this study only evaluate the presence or absence of bleeding ; it does not allow the assessment of other characteristics of the inflammatory process , such as edema , changes in gingival contour and loss of tissue attachment .
therefore , the possible effect of punica granatum linn extract on controlling the severity of gingivitis can not be discussed . due to the lack of clinical trials with a similar design investigating the effect of pomegranate on gingivitis ,
the data of this study were evaluated by parallel inferences , taken off from non specialized articles .
therefore , more controlled trials using different concentrations of punica granatum linn extract are necessary to verify its action upon supragingival microflora in vivo and established gingivitis .
further research will be important to identify the real benefits of pomegranate as a therapeutic and preventive agent for gingivitis , in addition to its common use in popular medicine .
within the limits of this clinical study , it may be concluded that the gel containing 10% punica granatum linn extract was not efficient in preventing supragingival dental plaque formation and gingivitis .[/INST]objectives : the antiplaque and antigingivitis effects of a gel containing 10% punica granatum linn extract were evaluated using a 21-day partial - mouth experimental model of gingivitis.methods:23 volunteers participated in this cross - over , doubleblind study , carried out in 2 phases of 21 days each . for each period of the experiment ,
an acrylic toothshield was made for each volunteer to carry the test or placebo gel as well as to avoid brushing of the 4 experimental teeth ( posterior teeth in the lower left quadrant ) .
the subjects were randomly assigned to use either the placebo gel ( control group ) or the test gel ( experimental group ) and were instructed to brush the remaining teeth normally 3 times a day . on days 0 and 21 , the visible plaque index ( vpi ) and gingival bleeding index ( gbi ) were recorded.results:the results did not show statistically significant difference between control and experimental groups for either of the indices ( vpi and gbi).conclusion : the gel containing 10% punica granatum linn extract was not efficient in preventing supragingival dental plaque formation and gingivitis .</s> |
it appears that in the next decade the photon - nucleus interactions will be in the forefront of the small _ x _ qcd dynamics studies .
this is due to the possibilities of the studying coherent ( and for some channels incoherent ) photon - nucleus interactions at energies which exceed at least by a factor of 10 the energies of electron - nucleon interactions at hera .
such studies will be feasible at lhc within the program of the study of the ultra peripheral collisions ( upc ) @xcite .
this opens a challenging opportunity to get answers to a number of the fundamental questions which could be investigated in the coherent processes : how to achieve new qcd regime of strong interaction with small coupling constant , how interactions depend on the type of the projectile and how they change with an increase of the size / thickness of the target , etc .
several regimes appear possible depending on the incident energy and the target thickness . a hadronic projectile ( proton , pion , etc ) high - energy interactions with the nucleus rather rapidly approach the black body limit ( bbl ) in which the total cross section of the interaction is equal to @xmath5 ( @xmath6 ) .
another extreme limit is the interaction of small size projectiles ( or wave packages ) . in this case in a wide range of high energies the system remains almost frozen during the passage through the nucleus and the regime of color transparency is reached in which the interaction of the small size projectile with a nucleus is rather weak and proportional to a. this color transparency phenomenon in hard high energy projectile - nucleus interactions has been recently observed experimentally in the exclusive production of two jets by pions in the coherent diffraction off nuclei . at higher energies interactions of small dipole is expected to reach the regime of the perturbative color opacity . in this regime
the small size projectile still couples to the gluon field of the target via the ( skewed ) gluon density of the target , @xmath7 , like in the color transparency regime .
however , the scattering amplitude is not @xmath8 due to the leading twist ( lt ) shadowing , @xmath9 .
the onset of gluon shadowing tames somewhat the increase of @xmath10 between @xmath11 and @xmath12 and slows down the increase of the small dipole - nucleus interaction with energy .
the resulting taming is not strong enough to prevent the leading twist approximation result for the total inelastic cross section from reaching and even exceeding the bbl .
this violation of unitarity is an unambiguous signal that for sufficiently small @xmath3 the lt approximation breaks down .
an important practical issue for the studies of the small @xmath3 dynamics is whether the interactions of small dipoles with several nucleons of the target are strongly modified by the leading twist shadowing dynamics @xcite or one can neglect the lt gluon shadowing , like in the model of mclerran and venugopalan@xcite , and focus on the higher twist effects which are often modeled in the impact parameter space eikonal model @xcite .
if the leading twist shadowing was small and only higher twist effects were taming the increase of the dipole - nucleus cross section , the break down of the dglap approximation would occur at rather large @xmath3 .
the break down of dglap may result in onset of the bbl or taming of the cross sections at smaller values .
we will argue below that the relative importance of leading and higher twist interactions could be experimentally resolved using coherent onium photoproduction .
note also that if the lt gluon shadowing effects were small enough , the bbl for the interaction of @xmath13 dipoles of the size @xmath14 could be reached for central collisions with heavy nuclei already at @xmath15 that is in the kinematics where @xmath16 effects in the evolution of the parton densities are small . in any case , whatever is the limiting behavior for the interaction of the small size dipoles with heavy nuclei , it is of major theoretical interest since it represents a new regime of interactions when the leading twist approximation and therefore the whole notion of the parton distributions becomes inapplicable for the description of hard qcd processes in the small @xmath17 regime .
it is worth emphasizing that on the top of providing higher parton density targets , nuclei have another important advantage as compared to the nucleon target .
it is a weak dependence of the scattering amplitude on the impact parameter for a wide range of the impact parameters ( in fact , one can combine light and heavy nuclei to study the dependence of the amplitudes on the nuclear thickness ) . on the contrary , in the nucleon case
the scattering at large impact parameters is important even at very small @xmath3 working to mask the change of the regime of the interactions at small impact parameters .
theoretical studies of the limiting behavior of the small dipole - heavy nucleus cross sections did not lead so far to definitive results .
it is conceivable that the qcd dynamics will stop the increase of the cross section at central impact parameters at the values significantly smaller than allowed by the bbl . in the following discussion to emphasize the qualitative difference of the new regime we will use for simplicity the extreme hypothesis that the impact factor at small impact parameters reaches the value of one corresponding to the bbl pattern of the elastic and inelastic cross sections being equal .
there exist many processes where the projectile wave function is a superposition of configurations of different sizes , leading to the fluctuations of the interaction strength . in this respect ,
interactions of real and virtual photons with heavy nuclei provide unique opportunities since the photon wave function contains both the hadron - like configurations ( vector meson dominance ) and the direct photon configurations ( small @xmath13 components , heavy quark - antiquark components ) .
the important advantage of the photon is that at high energies the bbl is manifested in diffraction into a multitude of the hadronic final states ( elastic diffraction @xmath18 is negligible ) while in the hadron case only elastic diffraction survives in the bbl , and details of the dynamics responsible for this regime remain hidden .
moreover , one can _ post - select _ a small size or a large size initial state by selecting a particular final state , containing for example @xmath19 @xmath20 , or a leading light meson .
such post - selection is much easier in the photon case than in the hadron case since the distribution over the sizes of the configurations is much broader in the photon case .
spectacular manifestations of bbl in ( virtual ) photon diffraction include strong enhancement of the large mass tail of the diffractive spectrum as compared to the expectations of the triple pomeron limit , large cross section of the high @xmath21 dijet production @xcite .
we emphasize that the study of the diffractive channels will allow to distinguish between two extreme scenarios : large suppression of the cross section due to the leading twist shadowing and nonlinear regime of the bbl .
investigation of the coherent diffraction in bbl would allow to perform unique measurements of various components of the light cone wave function of the photon , providing a much more detailed information than similar measurements in the regime where leading twist dominates . in this review
we summarize our recent studies of the various regimes of the coherent photoproduction off nuclei @xcite : the onset of the bbl regime , phenomenon of color transparency and perturbative color opacity related to the leading twist nuclear gluon shadowing , and the pattern of soft qcd phenomena in the proximity to the black body limit .
in addition we consider hard leading twist diffraction off nuclei in dis .
we also outline how these effects can be studied in upc collisions and provide a comparison with the first upc data from rhic .
our consideration of the coherent photoproduction processes of light flavor and hidden charm is based on the use of the eikonal approximation that is the glauber model modified to take into account finite longitudinal momentum transfer @xcite .
the photoproduction cross section @xmath22 is given in the glauber model by the general expression @xmath23 here @xmath24 is the photon energy , @xmath25is the vector meson momentum , @xmath26 , @xmath27 is the longitudinal momentum transfer in the @xmath28 transition , and @xmath29 is the diffractive nuclear profile function .
depending on the considered vector meson production process , the glauber approach can be combined with either the traditional vector dominance model ( vdm ) ( for the detailed review see ref .
@xcite ) or with the generalized vector dominance model ( gvdm ) @xcite . more properly
this latter approximation should be called the gribov - glauber model @xcite because the space - time evolution of high energy processes is different in quantum mechanical models and in quantum field theory , and therefore theoretical foundations of the high - energy model are different . in particular , in qcd in difference from quantum mechanics a high - energy projectile interacts with all nucleons at the same impact parameter almost at the same time @xcite . due to the cancellations between diagonal and nondiagonal transitions
the gvdm allows to take into account the qcd effect of the suppression of interaction of spatially small quark - gluon wave packages with a hadron target - the so called color transparency phenomenon .
namely , cancellations occur between the amplitudes of the photon transition into a vector state @xmath30 with subsequent conversion to a state @xmath31 and direct production of the state @xmath31 , etc .
the importance of the nondiagonal transitions reveals itself in the precocious bjorken scaling for moderately small @xmath32 as due to the presence in the virtual photon of hadron - like and point - like type configurations @xcite .
these amplitudes are also crucial for ensuring a quantitative matching with perturbative qcd regime for @xmath33 few gev@xmath34 @xcite .
the amplitude of the vector meson production off a nucleon can be written within the gvdm as @xmath35 where @xmath36 are expressed through @xmath37 .
calculation of the vector meson production amplitude off nuclei within the glauber approximation requires taking into account both the nondiagonal transitions due to the transition of the photon to a different meson @xmath38 in the vertex @xmath39 and due to a change of the meson in multiple rescatterings like @xmath40 .
this physics is equivalent to inelastic shadowing phenomenon familiar from hadron - nucleus scattering @xcite .
then in the optical limit ( @xmath41 ) of the glauber multistep production theory one can introduce the eikonal functions , @xmath42 , which describe propagation of the produced objects through the medium and are related to the diffractive profile function by expression @xmath43 within the optical limit of the glauber based gvdm with accuracy @xmath44 the eikonal functions @xmath42 are determined by the solutions of the coupled channel equations @xmath45 , \label{cch}\end{aligned}\ ] ] with the initial condition @xmath46 .
the exponential factors @xmath47 $ ] are responsible for the coherent length effect , @xmath48 , @xmath49 .
the generalized glauber -based optical potentials in the short - range approximation are given by the expression @xmath50 here @xmath51 are the forward elementary amplitudes , and @xmath52 is the nuclear density normalized by the condition @xmath53 .
we calculated @xmath54 in the hartree - fock - skyrme ( hfs ) model which provided a very good(with an accuracy @xmath55 ) description of the global nuclear properties of spherical nuclei along the periodical table from carbon to uranium@xcite and the shell momentum distributions in the high energy ( p,2p)@xcite and ( e , ep)@xcite reactions .
if the nondiagonal rescattering amplitudes @xmath56 , one can easily integrate eq.[cch ] , and using the expression for the elementary amplitude @xmath57 obtain the expression for the photoproduction cross section : @xmath58 well known from early seventies ( see for example @xcite ) .
we have used the gvdm to describe coherent photoproduction of hadronic states of @xmath59 gev off nuclei and consider the onset of bbl in the soft regime . in ref .
@xcite the simplest nondiagonal model was considered with two states @xmath0 and @xmath60 .
then the gvdm comprises elementary amplitudes @xmath61 it was assumed that both @xmath0 and @xmath62 have the same diagonal amplitudes of scattering off a nucleon .
the ratio of coupling constants was fixed : @xmath63 , while the ratio of the nondiagonal and diagonal amplitudes @xmath64 , and the value @xmath65 were found from the fit to the forward @xmath66 cross sections measured at @xmath676.1 , 6.6 and 8.8 gev@xcite .
one should emphasize here that in such gvdm extension @xmath60-meson approximates the hadron production in the interval of hadron masses @xmath68 .
thus the values of the production cross section refer to the corresponding mass interval .
we refined this model in @xcite .
the dependence on the nuclear structure parameters was diminished by calculating the nuclear densities in the hartree - fock - skyrme ( hfs ) approach .
next , we used in all our calculations the parameterization of @xcite for the @xmath69 amplitude which was obtained from the fit to the experimental data on photoproduction off the proton target .
the value of @xmath70 was fixed at 0.18 to ensure the best fit of the measured differential cross section of the @xmath0-meson photoproduction off lead at @xmath71 gev and @xmath72 @xmath73 .
note that this value of @xmath74 leads to a suppression of the differential cross section of the @xmath0-photoproduction in @xmath75 by a factor of @xmath76 practically coinciding with phenomenological renormalization factor @xmath77 introduced in @xcite to achieve the best fit of the elementary @xmath0-meson photoproduction forward cross section in the vdm which neglects mixing effects . with all parameters fixed we calculated the differential cross sections of @xmath0-production off nuclei and found a good agreement with the data @xcite , see a detailed comparison in @xcite . in view of a good agreement of the model with the data on @xmath0-meson production in the low energy domain we used this model to consider the @xmath0-meson photoproduction at higher energies of photons .
the increase of the coherence length with the photon energy leads to a qualitative difference in the energy dependence of the coherent vector meson production off light and heavy nuclei and to a change of the a - dependence for the ratio of the forward @xmath60 and @xmath0-meson production cross sections between @xmath78 gev and @xmath79 gev ( fig.[rhoen ] ) .
the observed pattern reflects the difference of the coherence lengths of the @xmath0-meson and a heavier @xmath80-meson which is important for the intermediate photon energies @xmath81 gev .
the corrections due to nondiagonal transitions are relatively small ( @xmath82 15% ) for the case of @xmath0 production off a nuclei . as a result
, we find that the gvdm cross section is close to the one calculated in the vdm for heavy nuclei as well .
situation for @xmath60 production is much more interesting .
the cross section of @xmath60 production off a nucleon is strongly suppressed as compared to the case when the @xmath83 transitions are switched off .
the extra suppression factor is @xmath84 .
the non - diagonal transitions disappear in the limit of large a ( corresponding to the bbl ) due to the condition of orthogonality of hadronic wave functions in accordance with the general argument of gribov @xcite . therefore in the limit of @xmath85
we expect that the relation @xmath86 should be fulfilled for the productions of states @xmath87 of invariant masses @xmath88 at @xmath89 .
indeed we have found from calculations that in the case of the coherent photoproduction off lead the nondiagonal transitions becomes strongly suppressed with increase of the photon energy . as a result the @xmath90 ratio increases , exceeds the ratio of the @xmath91 forward cross sections calculated with accounting for @xmath92 transitions already at @xmath93 gev and becomes close to the value of @xmath94 which can be considered as the limit when one can treat the interaction with the heavy nucleus as a black one .
it is worth noting here that presence of nondiagonal transitions in terms of the formalism of the scattering eigen states @xcite corresponds to the fluctuations of the values of the interaction cross sections for the real photon .
the gvdm discussed in the paper leads to small ( @xmath95 ) color transparency effects at intermediate energies for the cross section of semiinclusive photoproduction processes .
really , this model corresponds to the propagation of states with cross sections : @xmath96 . in the case of electroproduction @xmath74
should be significantly larger : @xmath97 this equation follows from eq.([gvdm ] ) where the left hand side is put to zero because the cross section of the elastic vector meson electroproduction rapidly decreases with @xmath98 .
the presence of the ct phenomenon within the gvdm leads to a substantial modification of the pattern of the approach to bbl .
the nondiagonal transitions become more important with the increase of @xmath98 , leading to an enhancement of the effects discussed above . in particular
, the fluctuations of strengths of interaction would lead at large @xmath98 to the color transparency phenomenon .
presence in gvdm of significantly different masses of @xmath99 makes it impossible to describe all fluctuations of strengths of interaction in terms of one coherent length .
there is a qualitative difference between gvdm description of the light meson production described above and production of charmonium states . in the case of the photoproduction of light mesons the soft physics dominates both at low and high energies
hence , the gribov - glauber model should be applicable in a wide range of energies . at the same time the space - time picture of the process changes with energy . at low energies
the meson is formed at the distances smaller than the typical interaction length of a meson in the nucleus . with the increase of energy
the formation length starts to exceed the nuclear size and a photon converts to a system of @xmath13 and higher fock - components before the target , and one has to account for the interactions of this system with the media and subsequent transition of the system to a vector meson . the situation is much more involved in the case of ( charm)onium production . at high energies
both the coherence length @xmath101 and the formation length @xmath102}^{-1}$ ] ( distance on which the squeezed @xmath13 pair transforms into the ordinary meson ) are large and the color transparency phenomenon reveals itself .
in particular , it explains the fast increase of the cross section with energy observed at hera ( for reviews of small x phenomena see ref .
consequently , the value of the cross section extracted from the charmonium photoproduction characterizes the interaction of the squeezed @xmath19 pair with a nucleon rather than the charmonium - nucleon interaction . in the high energy limit the very small interquark distances in the wave function of the photon dominate , and
one has to treat the interaction of small dipoles with nuclei . in this case
the eikonal approximation gives a qualitatively wrong answer since it does not take into account the leading twist effect of the gluon shadowing(see the detailed analysis in @xcite ) , while the leading twist analysis predicts large shadowing effects @xcite , see discussion in section 3 . on the other hand , at the intermediate energies when onium states are formed inside the nucleus the nonperturbative effects at a transverse distance scale comparable to the charmonium size becomes important .
the hadronic basis description would be more relevant in this case .
however the vdm which takes into account only diagonal vector meson transitions does not account properly for the basic qcd dynamics of interaction .
in particular , slac data @xcite show that @xmath103 which within vdm corresponds to : @xmath104 .
this conclusion is in evident contradiction with the qcd expectation that the hadron interaction cross section should be scaled approximately as the transverse area occupied by color : @xmath105 .
thus in this naive qcd picture @xmath106 .
a qcd explanation of such failure of vdm is based on the observation @xcite that in photoproduction of both the @xmath107and @xmath108mesons the small relative distances @xmath109 dominate in the @xmath19 component of the photon wave function .
therefore the cross sections which enter into the ratio of @xmath107and @xmath108yields are cross sections of the interaction of the small dipoles , not genuine mesons .
the suppression of the production of @xmath108 in this picture is primarily due to a smaller leptonic decay width of @xmath108(a factor of 1/3 ) .
a significant additional suppression comes from importance of more massive @xmath19 intermediate states in the photon wave function ( @xmath110 respectively ) .
the exact value of the suppression is sensitive to the details of the onium wave functions and the dependence of the dipole - nucleon cross section on the size of the dipole @xcite .
the dominance of small @xmath19 configurations in photoproduction processes is relevant for the significant probability of nondiagonal @xmath111 diffractive transitions .
the gvdm adjusted to account for the color screening phenomenon @xcite allows to take into account qcd dynamics using a hadronic basis .
such a description is limited to the regime of small coherence lengths ( medium energies ) , where leading twist shadowing is not important .
we use the gvdm to consider the coherent photoproduction of hidden charm mesons off nuclei at moderate photon energies @xmath112 where the coherence length for the @xmath113 transition @xmath114 is still close enough to the internucleon distance in nuclei while the formation length @xmath115 is comparable to the radii of heavy nuclei . in this energy range
produced charmonium states have a noticeable probability to rescatter in sufficiently heavy nuclei .
therefore , one would be able to reveal the fluctuation of the charmonium - nucleon interaction strength as due to the diagonal @xmath116 and nondiagonal @xmath117 rescatterings for moderate energies .
the gvdm which we outlined above takes into account the coherence length effects via the glauber model approximation .
the key distinction from the @xmath118meson case is choosing the parameters of the model to account for the space - time evolution of spatially small @xmath19 pair .
it is important that the inelastic shadowing corrections related to the production of higher mass states @xcite are still insignificant .
a reasonable starting approximation to evaluate the amplitude of the charmonium - nucleon interaction is to restrict ourselves to the basis of @xmath107and @xmath108states for the photon wave function in eq.[gvdm ] .
then , similarly to the considered above case of @xmath119 production we have two equations comprising six elementary amplitudes .
the charmonium - nucleon coupling constants : @xmath120 , and @xmath121 are determined from the widths of the vector meson decays @xmath122 . since in
the photoproduction processes @xmath19 pair is produced within the spatially small configuration one can neglect for a moment by the direct photoproduction amplitude and obtain the approximative relations between rescattering amplitudes @xmath123 large values for nondiagonal amplitudes @xmath124 are a characteristic qcd property of hidden charm and beauty meson - nucleon interaction .
note that the negative sign of the nondiagonal amplitude is dictated by the qcd factorization theorem . a positive sign of the forward photoproduction @xmath125 amplitudes as well as the signs of the coupling constants @xmath126 and @xmath127 are determined by the signs of the charmonium wave functions at r=0 . from the approximative estimates above
it also follows that @xmath128 .
this is much larger than @xmath129 20 mb suggested by analyses of the data on @xmath130 absorption in nucleus - nucleus collisions @xcite .
when combined with the slac data @xcite , this corresponds to @xmath131 with large experimental and theoretical errors . to fix elementary amplitudes more accurately within gvdm ( see @xcite for details )
we parameterized the elementary photoproduction cross section in the form used by the experimentalists of hera to describe their data .
this form has no firm theoretical justification but it is convenient for the fit @xmath132 here @xmath133 is the invariant energy for the photon scattering off a free nucleon , @xmath134 is the reference point and @xmath135 is the two - gluon form factor of a nucleon .
we also used the slac results for the forward @xmath136 cross section @xcite and for the ratio @xmath137 besides , we fixed the @xmath138 cross section @xmath139 mb as measured at slac@xcite and used the reasonable assumption about the energy dependence of this cross section as the sum of soft and hard physics : @xmath140 the existence of a hard part of the @xmath141n cross section is consistent with the gvdm , because the photoproduction amplitude has a stronger energy dependence than the pomeron exchange , i.e. soft scattering amplitudes . next , we used this input , the optical theorem and the well known gribov - migdal relation @xmath142 to determine from eq.[gvdm ] all elementary amplitudes in the discussed energy range .
in particular , we found the value @xmath143 mb .
however , the input parameters of the gvdm , namely the experimental cross sections of the forward elementary photoproduction and , especially , the value of @xmath144 , are known with large uncertainties . in result
, we obtained elementary cross sections changing in the ranges : @xmath145 and @xmath146 , in the discussed energy range .
we checked how a variation of @xmath144 within the experimental errors influences our results .
= .9 = 1 .
in our papers@xcite,@xcite we analyzed the coherent photoproduction of charmonia off light(si ) and heavy(pb ) nuclei .
here we present the cross sections of the coherent photoproduction of @xmath141 and @xmath130 off ca .
the energy dependence of these cross sections is compared ( fig.[jpsipsi]a ) to that obtained in the impulse approximation where all rescatterings of the produced vector mesons are neglected , and the cross section is given by the simple formula @xmath147 the distinctive feature of the coherent charmonium photoproduction is that differential cross sections oscillate as a function of the photon energy .
the major source for such a behavior at intermediate energies is oscillating behavior of the longitudinal nuclear form factor at the relatively large values of @xmath148 in the photoproduction vertex .
the cross section of the @xmath107photoproduction in the gvdm is close to that calculated in the impulse approximation - the shapes of curves are very similar and the values of the cross sections are only slightly reduced at energies below 40 gev(fig.[jpsipsi]b ) .
this indicates that it would be very difficult to extract the total @xmath138 cross section from such a measurement . at the same time , since the the nuclear form factor is known with a high precision from the high energy elastic electron - nucleus scattering , one can use the coherent @xmath107photoproduction off the spherical nuclei to determine the elementary @xmath149 amplitude in a wide range of energies for @xmath150 .
the picture is qualitatively different for the coherent @xmath108photoproduction off nuclei . due to the higher threshold ( @xmath151 gev , the direct @xmath108production off nuclei is suppressed in the impulse approximation ( for the same incident energy ) as compared to the @xmath107production by the nuclear form factor . since @xmath152
, the minima of the impulse approximation distribution are shifted .
the contribution of the nondiagonal term @xmath153 essentially increases the @xmath108yield and produces an additional shift of the minima in the spectrum to lower photon energies ( fig .
[ jpsipsi]c ) .
this results in significant effects , especially , if one analyses the data as a function of the mass number a at different energies to extract a - dependence of the @xmath138 cross sections .
it is seen from fig.[adpsi ] that the oscillating form factor significantly influences the a - dependence that complicates extracting of the genuine @xmath138 and @xmath154 cross section from such analysis .
the oscillation of the cross section with energy can be used to measure in a new way the elementary charmonium photoproduction amplitudes as well as the charmonium - nucleon amplitudes using the coherent charmonium photoproduction off light nuclei@xcite . in particular , at the photon energies @xmath155 ( fig .
[ jpsipsi]d ) , the main contribution to the cross section originates from the nondiagonal rescattering . as a result
, one can extract from the data the nondiagonal elementary @xmath156 amplitude by measuring the ratio of the @xmath130 and @xmath141 yields at zero production angle , because other inputs to this ratio such as the elementary @xmath149 amplitude are fixed from the @xmath141 production .
moreover , since other parameters enter both in the numerator and denominator , the major uncertainties are canceled out .
on the other side , the energy dependence of this ratio should originate primarily due to the contribution of the direct @xmath130 production .
thus , one would be able to determine the @xmath157 amplitude from the measurement of the @xmath130-to-@xmath141 ratio .
we want to emphasize that the suggested procedure for extracting the nondiagonal amplitude and amplitudes of direct @xmath141 and @xmath130 photoproduction from the nuclear measurements is practically model independent .
it is much more difficult to determine the diagonal @xmath158 and @xmath159 amplitudes , which are relevant for the suppression of the charmonium yield in heavy ion collisions . a naive diagonal vdm with @xmath160 based on the slac data @xcite leads to a rather significant suppression of the @xmath141 yield : @xmath161 for light nuclei , and @xmath162 for heavy nuclei .
however , we find @xcite a strong compensation of the suppression due to the contribution of the nondiagonal transitions . as a result
we find that overall the suppression does not exceed @xmath163 for all nuclei along the periodical table .
hence , an extraction of the diagonal amplitudes from the measured cross sections would require a comparison of high precision data with very accurate theoretical calculations including the nondiagonal transitions .
another strategy is possible if the elementary @xmath164 , and @xmath157 photoproduction amplitudes , as well as the nondiagonal amplitude @xmath165 would be reliably determined from the medium energy data . in this case
it would be possible to determine the imaginary parts of the forward diagonal amplitudes from the gvdm equations ( [ gvdm ] ) @xmath166 the suggested procedure allows to determine all elementary amplitudes with a reasonable precision from the measurements of @xmath141 and @xmath130 photoproduction off the light nucleus at the medium photon energies .
the measurement of the coherent charmonium photoproduction off nuclei in this energy region are planned at slac @xcite .
the measurements of coherent production off heavy nuclei and of the quasielastic production with parameters of gvdm fixed from the analysis of light nuclei would provide a critical test of the model .
the main limitation of the suggested procedure is the restriction of the hadronic basis to the two lowest 1s , 2s charmonium states with the photon quantum numbers : @xmath141 , @xmath130 .
this is one of the key approximations in the discussed approach .
it seems quite reasonable since in the coherent production of vector meson states off nuclei at moderate energies contribution of high mass states is more suppressed by the target form factor .
however , we neglected by @xmath167 which is nearly degenerate in mass with @xmath130 : @xmath168 mev .
the properties of these two states are described well in the charmonium model @xcite . in this model
@xmath167-meson is described as a @xmath169 state with a small admixture of the @xmath170 wave , while @xmath130-meson has a small @xmath171-wave admixture .
namely @xmath172 since only the s - wave contributes to the decay of @xmath173 states into @xmath174 ( at least in the non - relativistic charmonium models ) the value @xmath175 can be determined from the data on the @xmath174 decay widths @xmath176 kev and the @xmath177 kev . due to the small difference of masses between the @xmath178 and @xmath179 mesons the produced s - wave @xmath180-state does not loose coherence while going through the media at any conceivable energies .
the soft interactions can not transform the @xmath170-state to @xmath171-state with any significant probability . in the soft qcd processes data
show that the cross sections of exclusive nondiagonal transitions are negligible for the forward angle scattering .
the same conclusion is valid in the pqcd model for the charm dipole - nucleon interactions .
thus , it is more appropriate to use the @xmath181 - @xmath182 basis for description of the propagation of @xmath19 through the nucleus .
the only resulting change is an increase of @xmath183 by a factor of @xmath184 as compared to @xmath127 which is within the uncertainties of the model .
since the @xmath182 state ultimately transforms into @xmath130 and @xmath185 we predict @xcite : ratio would be a universal number .
since @xmath185 can be easily observed via its characteristic @xmath186 decays in a number of the lepton , hadron and nucleus induced processes the study of the discussed process can provide a new way to probing dynamics of charmonium production in various reactions . ]
@xmath187 influence of the higher mass resonances is expected to be even weaker - the constants @xmath188 relevant for the transition of a photon to a charmonium state @xmath189 rapidly decrease with the resonance mass .
this is because the radius of a bound state , @xmath190 , is increasing with the mass of the resonance and therefore the probability of the small size configuration being @xmath191 is decreasing with an increase of mass ( for fixed s , l ) .
besides , the asymptotic freedom in qcd dictates decreasing of the coupling constant relevant for the behavior of the charmonium wave function at small relative distances .
experimentally one finds from the data on the leptonic decay widths that @xmath188 drops by a large factor with increasing mass .
an additional suppression arises due to the weakening of the soft exclusive nondiagonal @xmath192 amplitudes between states with the different number of nodes .
hence , it seems possible to determine the imaginary parts of diagonal rescattering amplitudes from analysis of the data using the gvdm equations .
since in the medium energy domain the energy dependence of soft rescattering amplitudes is well reproduced by a factor @xmath193 , one can determine the real parts of the amplitudes using the gribov - migdal relation ( eq .
[ gm ] ) .
the above analyses demonstrate that the relative importance of the non - diagonal transitions increases an increase of the quark mass .
it would be of interest to investigate experimentally the case of strangeness production .
it is likely to correspond to @xmath70 substantially larger than @xmath194 but much smaller than @xmath195 .
interaction of small size color singlet objects with hadrons is one of the most actively studied issues in high - energy qcd .
the qcd factorization theorem for exclusive meson electroproduction at large @xmath98 , and @xmath196 photoproduction @xcite allows to evaluate the amplitude of the production of a vector meson by a longitudinally polarized photon @xmath197 through the convolution of the wave function of the meson at the zero transverse separation , hard interaction block and the generalized ( skewed ) parton density .
production @xcite in the bfkl approximation and for the pion diffraction into two jets @xcite in the leading log @xmath98 approximation @xcite . ]
the lt approximation differs strongly from the expectations based on glauber model approaches and on the two gluon exchange models , because it accounts for the dominance of the electroproduction of spatially small quark - gluon wave package and its space - time evolution which leads to formation of a softer gluon field .
the latter effect results effectively in an increase of the size of the dipole with increase of the energy
. in perturbative qcd ( similar to qed ) the total cross section of the interaction of small systems with hadrons is proportional to the area occupied by color within projectile hadron @xcite leading to the expectation of the color transparency phenomenon for various hard processes with nuclei .
the cross sections of incoherent processes are expected to be proportional to the number of nucleons in the nuclei , while the coherent amplitude is proportional to number of nucleons times the nuclear form factor .
possibility to approximate projectile heavy quarkonium as colorless dipole of heavy quarks can be formally derived from qcd within the limit when mass of heavy quark @xmath198 but @xmath199 is fixed and not extremely small @xcite . in this
kinematics the size of heavy quarkonium is sufficiently small to justify applicability of pqcd . for practical purposes
the crucial question is at what @xmath98 squeezing becomes effective .
probably the most sensitive indicator is the @xmath200-dependence of the meson production .
the current hera data are consistent with the prediction of @xcite that the slopes of the @xmath0 and @xmath141 production amplitudes should converge to the same value .
this indicates that at small @xmath17 configurations much smaller than average configurations in light mesons ( @xmath201 ) dominate for @xmath0-meson production at @xmath202 gev@xmath34 , while the @xmath141 production is dominated by interaction in small size configurations for all @xmath98 .
therefore , one expects the regime of color transparency for @xmath203 where the gluon shadowing is very small / absent .
recently the color transparency ( ct ) phenomenon was observed at fnal by e791 experiment @xcite which studied the coherent process of dissociation of a 500 gev pion into two jets off the nuclei .
the measurement has confirmed a number of predictions of @xcite including the a - dependence , and the transverse and longitudinal momentum distributions of the jets .
previously the color transparency type behavior of the cross section was observed also in the coherent @xmath204 photoproduction at @xmath205 @xcite .
a natural question is whether the color transparency will hold for arbitrary high energies ?
two phenomena are expected to work against ct at high energies .
one is the lt gluon shadowing .
there are theoretical expectations ( see discussion below ) supported to some extent by the current analyses of the data on dis scattering off nuclei ( which do not extend deep enough into the shadowing region ) that the gluon distributions are shadowed in nuclei as compared to the nucleon : @xmath206 .
this obviously should lead to a gradual but calculable in qcd disappearance of color transparency @xcite , and to onset of a new regime , which we refer to as _ the color opacity regime _
( one can think of this regime also as a regime of generalized color transparency since a small @xmath13 dipole still couples to the gluon field of the target through a two gluon attachment and the amplitude is proportional to the generalized gluon density of the nucleus ) .
another mechanism for the violation of ct at high energies is the increase of the small dipole - nucleon cross section with energy @xmath207 . for sufficiently large energies
this cross section becomes comparable to the meson - nucleon cross sections .
one may expect that this would result in a significant suppression of the hard exclusive diffractive processes as compared to the lt approximation .
however it seems that this phenomenon is beyond the kinematics achievable for the photoproduction of @xmath141-mesons in upc of heavy ions at rhic ( @xmath208 ) but could be important at heavy ion upc at lhc . hence , a systematic study of the onium production in the coherent scattering off nuclei at collider energies will be very interesting .
one should emphasize here that with decrease of the size of the onium the eikonal ( higher twist ) contributions die out quickly ( provided @xmath3 is kept fixed ) .
in particular , for the @xmath209 case one probes nuclear gluon fields at the transverse scale of the order of 0.1 fm or @xmath210 . the @xmath141 case is closer to the border line between the perturbative and nonperturbative domains . as a result
the a nonperturbative region appears to give a significant contribution to the production amplitude @xcite .
= .50 let us discuss the photoproduction amplitude @xmath211 in more details .
we are interested here in the @xmath212 range which can be probed at lhc .
this region corresponds to rather small values of @xmath17 . in this situation interaction of @xmath13 pair , which in the final state forms a quarkonium state is still rather far from the bbl .
hence the key problem in the theoretical treatment of the process is taking into account the nuclear shadowing .
a number of mechanisms of coherent interactions with several were suggested for this process .
we focus here on the * the leading twist mechanism of shadowing * which is presented by diagrams in fig.[ltdiag ] .
there exists qualitative difference between the mechanism of interaction of a small dipole with several nucleons and the case of a similar interaction of an ordinary hadron .
let us for example consider interaction with two nucleons .
the leading twist contribution is described by the diagrams where two gluons are attached to the dipole . to ensure that nucleus remains intact in such a process
, the color singlet lines should be attached to both nucleons .
these diagrams ( especially the one of fig .
[ ltdiag]b ) are closely related to the diagrams describing the gluon diffractive parton densities ( which are measured at hera ) , and hence to the similar diagrams for the gluon nuclear shadowing @xcite .
the amplitude of high energy coherent heavy onium photoproduction is proportional to the generalized gluon density of the target , @xmath213 , which depends on the light - cone fractions @xmath214 and @xmath215 of gluons attached to the quark loop .
they satisfy a relation : @xmath216 if the quark fermi motion and binding effects were negligible , @xmath217 .
the resolution scale @xmath218 , where @xmath219 is the mass of the heavy quark .
numerical estimates for the photoproduction of @xmath141 give @xmath220@xcite reflecting a relatively small mass of c - quark and indicating that this process is on the verge between nonperturbative and perturbative regimes . on the contrary
, the mass of the beauty quark is huge on the scale of soft qcd . in this case
hard physics dominates , attachments of more than two gluons to @xmath20 are negligible and the qcd factorization theorem provides a reliable tool for description of the @xmath4 production .
this is especially true for the ratio of the cross sections of @xmath4 production from different targets since the higher twist effects due to the overlapping integral of the @xmath20 component of the photon and @xmath4 cancelled out in the ratio . as a result ,
in the leading twist shadowing approximation the cross section of the process @xmath221 is proportional to the squared nuclear gluon density distribution and can be written in the form @xmath222 ^ 2 \int \limits_{-\infty}^{t_{min } } dt { \left| \int d^2bdz e^{i{\vec q_t}\cdot { \vec b } } e^{-q_{l}z}\rho ( { \vec b},z ) \right| } ^2 . \label{phocs}\ ] ] numerical estimates using realistic potential model wave functions indicate that for @xmath141 , @xmath223 @xcite , and for @xmath4 , @xmath224 @xcite .
modeling of the generalized parton distributions at moderate @xmath98 suggests that to a good approximation @xmath225 can be approximated by the gluon density at @xmath226 @xcite . for large @xmath98 and small @xmath3 gpds
are dominated by the evolution from @xmath227 . since the evolution conserves @xmath228 , effect of skewedness
is determined primarily by the evolution from nearly diagonal distributions , see ref .
@xcite and references therein . in the case of the @xmath209 production
it increases the cross section by a factor @xmath229 @xcite and , potentially , this could even obscure the connection of the discussed effect with the shadowing of the nuclear gluon densities .
however , the analysis of @xcite shows that the ratio of gpd on a nucleus and on a nucleon at @xmath230 is a weak function of @xmath215 , slowly dropping from its diagonal value ( @xmath231 ) with the decrease of @xmath215 .
overall this observation is in a agreement with the general trend mentioned above that it is more appropriate to do comparison of diagonal and non - diagonal cases at @xmath226 . in the case of double scattering contribution
[ ltdiag]b ) there is another way to address the question of the accuracy of the substitution of the ratio of generalized gluon densities by the ratio of diagonal parton densities at the normalization scale .
we notice that the amplitude corresponding to fig .
[ ltdiag]b is expressed through the nondiagonal matrix element of the diffractive distribution function , @xmath232 , which is an analog of generalized parton distribution . in the diagonal limit of @xmath233
it coincides with the diffractive gluon distribution .
it depends on the light - cone fraction which nucleon lost in @xmath234 and @xmath235 states : @xmath236 @xmath237 respectively , @xmath238 , and @xmath239 .
if we make a natural assumption that @xmath240 we find that numerically in the kinematics we discuss the resulting skewedness effects are small as compared to the uncertainties in the input gluon diagonal diffractive pdfs . hence in the following we will approximate the ratio of generalized gluon densities in the nucleus and nucleon by the ratio of the gluon densities in nucleus and nucleon at @xmath241 . in the case of @xmath4 use of @xmath242
maybe more appropriate .
this would lead to slightly larger shadowing effect .
it was demonstrated in @xcite that one can express the quark and gluon nuclear shadowing for the interaction with two nucleons in a model independent way through the corresponding diffractive parton densities using the gribov theory of inelastic shadowing @xcite and the qcd factorization theorem for the hard diffraction @xcite .
an important discovery of hera is that hard diffraction is indeed dominated by the leading twist contribution and gluons play a very important role in the diffraction(this is loosely referred to as gluon dominance of the pomeron ) .
analysis of the hera diffractive data indicates that in the gluon induced processes probability of the diffraction is much larger than in the quark induced processes @xcite .
the recent h1 data on diffractive dijet production @xcite provide an additional confirmation of this observation .
large probability of diffraction in the gluon induced hard processes could be understood in the s - channel language as formation of color octet dipoles of rather large sizes which can diffractively scatter with a quite large cross section .
the strength of this interaction can be quantified using optical theorem and introducing @xmath243 for the hard process of scattering of a virtual photon off the gluon field of the nucleon . here
@xmath244 is the ratio of the real to imaginary parts of the elementary diffractive amplitude , @xmath98 is the momentum scale determining virtuality of the gluons , @xmath245 is the momentum fraction of the pomeron with the corresponding cut - off scale @xmath246 , and @xmath247 is the diffractive gluon density distribution of nucleon which is known from the h1 analysis of the diffractive data at the scale @xmath248 gev@xmath34 .
an important feature of this mechanism of coherent interaction is that it is practically absent for @xmath249 and may rather quickly become important with decrease of @xmath3 .
= .80 we calculated the ratio of the gluon density distributions in eq .
[ phocs ] using the leading twist shadowing model @xcite ( for the details of calculations see ref.@xcite ) . as the first step the nuclear gluon density distribution with account of the leading twist shadowing
is calculated at the starting evolution scale @xmath250 gev@xmath34 @xmath251 . \label{ga}\end{aligned}\ ] ] as an input we used the h1 parameterization of @xmath252 .
the effective cross section @xmath253 accounts for the elastic rescattering of the produced diffractive state off the nuclear nucleon and is determined by eq .
[ sigef ] .
numerically it is very large at the starting scale of the evolution , see fig .
[ figsigef ] , and corresponds to the probability of the gluon induced diffraction close to 50% .
this indicates that at the initial scale of the evolution interactions in the gluon sector are close to the bbl for @xmath254 for the nucleon case , and even more so for the nuclei , where similar regime should hold for a larger range of the impact parameters .
note that the double scattering term in eq .
[ ga ] for the nuclear parton densities satisfies qcd evolution , but the higher order terms do not . that is
if we use different starting scale of evolution we would obtain different results of @xmath255 .
the reason is that the terms @xmath256 are sensitive to degree of fluctuations in the cross sections of interaction of diffracting states .
these fluctuations increase with increase of @xmath98 .
this effect is automatically included in the qcd evolution , and it leads to violation of the glauber - like structure of the expression for the shadowing at @xmath257 .
approximation for the @xmath258 rescattering of eq .
[ ga ] corresponds to an assumption that fluctuations are small at @xmath259 scale since this scale is close enough to the scale of the soft interactions , see discussion in @xcite .
thus , at the second step of the calculation we use nlo qcd evolution equations to calculate the shadowing at larger @xmath98 using the calculation at @xmath260 as a boundary condition . in this way we also take into account the contribution of the gluon enhancement at @xmath261 which influences the shadowing at larger @xmath98 .
note here that proximity to the bbl in the gluon sector which is reflected in a large value of @xmath262 may result in corrections to the lt evolution which require further studies .
= 0.8 first we calculate the ratios of the cross sections of coherent photoproduction of @xmath141 and @xmath4 off nuclei and nucleon ( fig .
[ fshad ] ) .
such ratios do not depend on the uncertainties of the elementary cross sections and provide a sensitive test of the role of the lt shadowing effects . in a case of the @xmath141 photoproduction
the gluon virtuality scale is 3 - 4 gev@xmath34 with a significant fraction of the amplitude due to smaller virtualities @xcite .
hence we will take the gluon shadowing in the leading twist at @xmath263 .
taking a smaller value of @xmath98 would result in even larger shadowing effect . in calculations for the @xmath4
we take @xmath264 , though the result is not very sensitive to precise value of @xmath265 since the scaling violation for the gluon shadowing for these @xmath98 is rather small .
we find that in spite of a small size of @xmath4 , which essentially precludes higher twist shadowing effects up to very small x , the perturbative color opacity effect is quite appreciable .
it is worth noting that the effective cross section of the rescattering in the eikonal model is determined by the cross section of dipole -nucleon interactions at the distances @xmath266 in the @xmath141 case and @xmath267 in the @xmath4 case .
these cross sections are @xmath268 for @xmath141 and @xmath269 for @xmath4 case for @xmath12 and a factor of 1.5 - 2 smaller for @xmath270 , see fig . 13 in ref .
they are much smaller than the cross sections which enter into calculation of the gluon shadowing in the lt mechanism .
we also estimated the absolute cross section of onium photoproduction for a wide range of the photon energies .
this is of interest for the planned measurements of the onium production in the ultraperipheral heavy ion collisions at lhc .
the dependence of the momentum - integrated cross sections on the energy @xmath271 is presented in fig .
[ onics ] . in the case of @xmath141 production
the calculations are pretty straightforward as the accurate data are available from hera .
the situation is more complicated in the case of the photoproduction of @xmath4 .
so far the information about the elementary @xmath272 cross section is very limited .
there is the only zeus and h1 data on total cross section for the average energy of @xmath273 .
thus , to calculate the forward photoproduction cross section we used a simple parameterization : @xmath274 where @xmath275 gev@xmath34 , the slope parameter @xmath276 is fixed basing on the analysis of the two gluon form factor in ref .
@xcite , and the energy dependence follows from the calculations of ref .
@xcite of the photoproduction of @xmath4 in the leading @xmath277 approximation with an account for the skewedness of the partonic density distributions .
this elementary cross section is normalized so that the total cross section is in @xmath278 .
it is well known that inelastic diffraction at small @xmath200 gives information on the fluctuations of strength in the projectile - target interactions @xcite .
application of this logic to the hadron scattering off nuclei have allowed to explain the a - dependence of two measured diffractive channels in @xmath279 scattering assuming that it coincides with the a - dependence of the total cross section of the inelastic diffraction , and the absolute total cross section of pa diffraction ( the data exist for two nuclei only ) at the energies 200 - 400 gev , see @xcite for the review and references . with an increase of energy , the total cross section of @xmath280 interaction increases and fluctuations in the elementary amplitude lead to much smaller fluctuations of the absorption in the scattering off a heavy nuclei . as a result
, one can expect much weaker a - dependence of the diffractive cross section @xcite , in particular , @xmath281 at lhc energies @xcite as compared to @xmath282 at fixed target energies . for large produced masses we can also understand this suppression using the @xmath200 channel picture of the pomeron exchanges as due to the stronger screening of the triple pomeron exchange , for review and references see @xcite .
diffraction in deep inelastic scattering corresponds to the transition of the ( virtual ) photon into its hadronic components leaving the nucleus intact .
hence it is similar to elastic hadron - nucleus scattering rather than inelastic diffractive hadron - nucleus scattering .
it was demonstrated recently that in the upc collisions at lhc it would be possible to study nuclear parton densities using hard charm and beauty production in @xmath283 interactions @xcite .
naturally one can also use these and similar processes to measure diffractive parton densities of nuclei . since these quantities in the leading twist
satisfy the factorization theorem we can analyze them on the basis of the analysis of the diffraction in dis .
there is a deep connection between shadowing and phenomenon of diffractive scattering off nuclei .
the simplest way to investigate this connection is to apply the agk cutting rules @xcite .
several processes contribute to diffraction on nuclei : ( i ) coherent diffraction in which the nucleus remains intact , ( ii ) break - up of the nucleus without production of hadrons in the nucleus fragmentation region , ( iii ) rapidity gap events with hadron production in the nucleus fragmentation region . in ref .
@xcite we found that for @xmath284 gev@xmath34 , the fraction of the dis events with rapidity gaps reaches the value of about 30 - 40% for heavy nuclei , with a fraction of the events of type ( iii ) rapidly dropping with @xmath285 .
we can use the information on @xmath262 for quarks and gluons to estimate probability of diffraction for different hard triggers at the resolution scale @xmath286 .
first we consider the dependence of the fraction of the events due to coherent diffraction and due to the break - up of the nucleus on the strength of the interaction , @xmath287 , neglecting fluctuations of the interaction strength .
we find that for the realistic values of @xmath287 the probability of coherent diffraction is quite large but increases with @xmath262 very slowly and does not reach the asymptotic value of @xmath288 even for very large values of @xmath289 ( the later feature reflects presence of a significant diffuse edge even in heavy nuclei ) , see fig .
[ figcsratio ] .
thus , it is not sensitive to the fluctuations of @xmath262
. we also found that the ratio of diffraction with the nucleus break - up and with the nucleus remaining intact is small ( 10 - 20% ) in a wide range of nuclei , and slowly increasing with increase of @xmath262 , see fig .
[ figcsratio ] .
hence it would require high precision measurements to constrain the dynamics using @xmath290 ratios . comparing the values of the fraction of the diffractive events for quark and gluon induced processes off heavy nuclei and proton
, we find that the relative importance of the quark induced events is increasing .
therefore , the scaling violation at large @xmath291 for the diffractive quark distribution in nuclei will be stronger for nuclei than for a proton .
another interesting effect is that for heavy nuclei only genuine elastic components can be produced ( inelastic diffraction is zero ) .
hence , the soft contribution at @xmath260 due to triple pomeron exchange is strongly suppressed see e.g. @xcite . as a result ,
nuclear diffractive parton distributions at small @xmath291 are strongly suppressed ( by a factor @xmath292 ) at @xmath260 though this suppression will be less pronounced at large @xmath98 due to the qcd evolution .
this will lead to breakdown of the universality of the @xmath291 distributions as a function of a. though the diffractive parton densities change rather slowly with @xmath98 leading to a weak variation of the diffractive cross sections with @xmath98 ( modulus the scaling factor ) the fraction of the diffractive events at fixed @xmath3 should significantly drop with increase of @xmath98 due to a large increase of the inclusive nucleon parton densities and decrease of the nuclear shadowing .
for example , let us consider ultraperipheral collisions ( upc ) at lhc where one can measure a the process @xmath293 in the kinematics where direct photon process @xmath294 dominates . in this case
if we consider the process at say @xmath295 corresponding to @xmath296 the fraction of diffractive events will be of the order 10% .
the background from the strong interaction originates from glancing collisions in which two nucleons interact via a double diffractive process @xmath297 where @xmath298 contains jets .
probability of the hard processes with two gaps is very small at collider energies - even smaller than .the probability of the single diffractive hard processes , see e.g. @xcite .
therefore , we expect that the background conditions will be at least as good in the diffractive case as in the inclusive case considered in @xcite
. thus , it would be pretty straightforward to extract coherent diffraction by simply using anti - coincidence with the forward neutron detector , especially in the case of heavy nuclei , see discussion in @xcite . as a result it would be possible to measure in the upc the nuclear diffractive parton distributions with a high statistical accuracy .
it is important that in difference from the diffraction to a vector meson it would be possible to determine on the event by event basis the energy of the photon which induced the reaction , since the rapidity of the photon is close to the rapidity of two jets . as a result it would be possible to perform the measurements for large rapidities ( selecting the events generated by a photon of higher of two energies allowed by the kinematics of production particles in the interval of rapidities @xmath299 ) and to determine diffractive parton densities for pretty small @xmath3 .
one of the striking features of the bbl is the suppression of nondiagonal transitions in the photon interaction with heavy nuclei @xcite .
indeed , in the bbl the dominant contribution to the coherent diffraction originates from `` a shadow '' of the fully absorptive interactions at impact parameters @xmath300 , so the orthogonality argument is applicable .
we use it to derive the bbl expression for the differential cross section of the production of the invariant mass @xmath301 for scattering of ( virtual ) photons @xcite . for the real photon case : @xmath302 here @xmath303 .
comparison of the measured cross section of the diffractive production of states with certain masses with the bbl result ( eq . [ ccsb ] ) would allow to determine up to what masses in the photon wave function interaction remains black .
similar equation is valid in the bbl for the production of specific hadronic or quark - gluonic final states ( @xmath304 etc ) in the case of the coherent nuclear recoil .
this allows to measure any component of the light cone photon wave function which interacts with the bbl strength corresponding final states in the coherent processes .
the onset of bbl limit for hard processes should reveal itself also in a faster increase with energy of cross sections of photoproduction of excited states as compared to the cross section for the ground state meson
. it would be especially advantageous for these studies to use a set of nuclei - one in the medium range , like @xmath305 , and another with @xmath306 .
this would allow to remove the edge effects and use the length of about 10 fm of nuclear matter .
one especially interesting channel is exclusive diffractive dijet production by real photons .
one may expect that for the @xmath307 energies which will be available at eic or at lhc in upc the bbl in the scattering off heavy nuclei would be a good approximation for the masses @xmath308 in the photon wave function up to few gev .
this is the domain which is described by perturbative qcd for @xmath309 in the case of the proton targets , and larger @xmath3 for scattering off nuclei .
the condition of large longitudinal distances , a small longitudinal momentum transfer , will be applicable in this case up to quite large values of the produced diffractive mass . in the bbl
the dominant channel of diffraction to large masses is production of two jets with the total cross section given by eq.([ccsb ] ) and with a characteristic angular distribution @xmath310 , where @xmath311 is the c.m .
angle @xcite . on the contrary , in the perturbative qcd limit the diffractive dijet production , except the charmed dijet production ,
is strongly suppressed @xcite .
the suppression is due to the structure of coupling of the @xmath13 component of the real photon wave function to two gluons when calculated in the lowest order in @xmath312 . as a result , in the real photon case
hard diffraction involving light quarks is connected to production of @xmath313 and higher states .
distribution of diffractively produced jets over invariant mass provides an important test of the onset of bbl limit .
really , in the dglap / ct regime differential cross section of forward diffractive dijet production should be @xmath314 and be dominated by charm jet production .
this behavior is strikingly different from the bbl limit expressions of @xcite .
thus , the dijet photoproduction should be very sensitive to the onset of the bbl regime .
we want to draw attention that @xmath315 component of the photon light - cone wave function can be measured in three independent diffractive phenomena : in the bbl off the proton , in bbl off a heavy nuclei , in the ct regime where the wave function can be measured as a function of the interquark distance @xcite .
a competing process for photoproduction of dijets off heavy nuclei is production of dijets in @xmath316 collisions where the second photon is provided by the coulomb field of the nucleus .
the dijets produced in this process have positive c - parity and hence this amplitude does not interfere with the amplitude of the dijet production in the @xmath317 interaction which have negative c - parity .
our estimates indicate that this process will constitute a very small background over the wide range of energies @xcite .
ultraperipheral collisions(upc ) of relativistic heavy ions at rhic and lhc open a promising new avenue for experimental studies of the photon induced coherent and incoherent interactions with nuclei at high energies @xcite .
really , the lhc heavy ion program @xcite will allow studies of photon - proton and photon - nucleus collisions at the energies exceeding by far those available now at hera for @xmath318 scattering .
hence , we can analyze an opportunity to study the phenomena discussed above combining the theory of photo induced processes in the ultraperipheral aa collisions with our studies of the coherent photo(electro ) production of vector mesons .
we can use the standard weizsacker - williams approximation @xcite to calculate the cross section integrated over the momentum of the nucleus which emits the quasireal photons .
the cross section of the vector meson production integrated over the transverse momenta of the nucleus which emitted a photon can be written in the convoluted form : @xmath319 here y is the rapidity @xmath320 the flux of the equivalent photons @xmath321 is given by a simple expression @xcite : @xmath322.\ ] ] here @xmath323 and @xmath324 are modified bessel functions with argument @xmath325 , @xmath326 is lorentz factor and @xmath327 is the impact parameter .
the glauber profile factor @xmath328 accounts for the inelastic strong interactions of the nuclei at impact parameters @xmath329 and , hence , suppresses the corresponding contribution of the vector meson photoproduction .
recently the star collaboration released the first data on the cross section of the coherent @xmath330-meson production in gold - gold upc at @xmath331 gev @xcite .
this provides a first opportunity to check the basic features of the theoretical models and main approximations which include the weizscker - williams ( ww ) approximation for the spectrum of the equivalent photons , an approximate procedure for removing collisions at small impact parameters where nuclei interact strongly , and the model for the vector meson production in the @xmath332 interactions . in the case of the @xmath0-meson production the basic process
is understood much better than for other photoproduction processes .
hence , checking the theory for this case is especially important for proving that upc could be used for learning new information about photon - nucleus interactions .
note here that the inelastic shadowing effects which start to contribute at high energies still remain a few percent correction at energies @xmath333 100 gev relevant for the star kinematics . for lhc energy range one should account for the blackening of interaction with nuclei . in this case
cross section of inelastic diffraction in hadron - nucleus collisions should tend to 0 .
so major impact for the calculation of the process of diffractive photoproduction of @xmath0 meson would be necessity to neglect by the contribution of @xmath1 @xcite . the calculated momentum transfer distributions at the rapidity @xmath334 and the momentum transfer integrated rapidity distribution for gold - gold upc at @xmath335 gev are presented in figs .
[ figstar1]a , b @xcite .
= 0.8 = 0.8 let us briefly comment on our estimate of the incoherent @xmath330-meson production cross section .
the momentum transfer distribution ( dashed line in fig . [
figstar1]a ) is practically flat in the discussed @xmath336 range .
the total incoherent cross section obtained by integration over the wide range of @xmath336 is @xmath337 mb . to select the coherent production
the cut @xmath338 gev@xmath34 was used in the data analysis @xcite .
correspondingly , the calculated incoherent cross section for this region of @xmath336 is @xmath339 mb .
our calculations of incoherent production which are based on accounting for only the single elementary diffractive collision obviously present the lower limit
. the residual nucleus will be weakly excited and can evaporate only one - two neutrons .
the events @xmath340 were detected by the star and identified as a two - stage process - coherent @xmath330-production with the subsequent electromagnetic excitation and neutron decay of the colliding nuclei @xcite .
in particular , the cross section estimated by the star for the case when only one of the nuclei is excited and emits several neutrons is @xmath341 mb .
the momentum transfer distribution for these events is determined by the coherent production .
hence , it differs from that for incoherent events but in the region of very low @xmath336 it is hardly possible to separate them experimentally , and the measured cross section @xmath342 includes contribution of incoherent events on the level of @xmath343 .
the total rapidity - integrated cross section of coherent @xmath330-meson production calculated in the gvdm for the range of energies available at rhic is shown in fig .
[ figstar2](solid line ) .
we find @xmath344 mb at @xmath335 gev .
the value @xmath345 mb was obtained at this energy by the star from the data analysis at the low momentum transfer @xmath338 gev@xmath34 .
thus , before making a comparison we should take into account this cut .
it leads to a reduction of the cross section by @xmath346 ( the dashed line in fig .
[ figstar2 ] ) . in our calculations
we did nt account for the @xmath336-dependence of the elementary amplitudes which are rather flat in the considered range of energies and momentum transfers as compared to that for the nucleus form factor .
so , in the region of integration important for our analysis it is reasonable to neglect this slope .
nevertheless , an account of this effect would slightly reduce our estimate of the total cross section .
also we neglected a smearing due to the transverse momentum of photons and the interference of the production amplitudes from both nuclei @xcite .
.total cross sections of @xmath141 production in upc at lhc . [ cols="^,^,^",options="header " , ] this latter phenomenon results in the narrow dip in the coherent @xmath336-distribution at @xmath347 gev@xmath34 .
all these effects do not influence noticeably the value of the @xmath336-integrated cross section but can be easy treated and taken into account in a more refined analysis .
thus we find @xmath348 mb to be compared to the star value @xmath345 mb .
since our calculation does not have any free parameters , this can be considered as a reasonable agreement .
= 1.0 = 1.0 .
[ figlhc1 ] it was suggested in @xcite to look for color opacity phenomenon using @xmath204 ( photo ) electroproduction .
this however requires energies much larger than those available at the fixed target facilities and would require use of electron - nucleus colliders
. at the same time estimates of the counting rates performed within the framework of the felix study @xcite have demonstrated that the effective photon luminosities generated in peripheral heavy ion collisions at lhc would lead to significant rates of coherent photoproduction of vector mesons including @xmath4 in reaction @xmath349 as a result it would be possible to study at lhc photoproduction of vector mesons in pb - pb and ca - ca collisions at energies much higher than the range @xmath350 gev covered at the fixed target experiment at fnal @xcite .
note that even current experiments at rhic ( @xmath351 gev ) should also exceed this limit .
as it is clearly indicated by the star study the coherent photoproduction , leaving the both interacting nuclei intact , can be reliably identified by using the veto triggering from the two - side zero degree calorimeters which select the events not comprising the escaped neutrons . the additional requirement which enables to remove contribution of the incoherent events with the residual nucleus in the ground state is selection of the produced quarkonium with small transverse momentum . in fig .
[ lhcdst ] we compare the momentum transfer distributions for the coherent @xmath141 and @xmath4 photoproduction calculated in the leading twist shadowing model with the corresponding distributions for incoherent photoproduction .
note that we estimated the upper limit of incoherent cross section simply as the free elementary cross section on the nucleon target multiplied by the number of nucleons a. in fig .
[ figlhc1]a , b we present the rapidity distributions of the @xmath141 coherent production for peripheral collisions at lhc calculated including effects of gluon shadowing and in the impulse approximation . at the central rapidities we find suppression by a factor 4 for a case of ca and more strong , by a factor 6 for pb .
the total cross sections are given in table [ tcrsec1 ] .
the rapidity distributions for coherent @xmath4 production in the upc with ca and pb beams are shown in fig .
[ figlhc1]c , d and the corresponding total cross sections are given in table [ tcrsec2 ] . as it is seen from comparison of the leading twist shadowing based calculations to that performed in the impulse approximation the yield of @xmath4 is expected to be suppressed by a factor 2 at central rapidities due to the leading twist nuclear shadowing .
hence , study of the coherent photoproduction of the heavy quarkonium states at lhc opens an important avenue for investigating the nuclear gluon distributions and the shadowing effects in the kinematics which would be very hard to probe in any other experiments .
we demonstrated that coherent diffraction off nuclei provides an effective method of probing a possible onset of bbl regime in hard processes at small @xmath17 .
we predict a significant increase of the ratio of the yields of @xmath352 mesons in coherent processes off heavy nuclei due to the blackening of the soft qcd interactions in which fluctuations of the interaction strength are present .
an account of nondiagonal transitions leads to a prediction of a significant enhancement of production of heavier diffractive states especially production of high @xmath21 dijets .
study of these channels may allow to get an important information on the onset of the black body limit in the diffraction of real photons .
we argued that the fluctuations of strengths of interactions has been observed at intermediate energies in the diffractive photoproduction of vector mesons .
we discuss the opportunity to look for the transition from the nuclear color transparency to the regime of the color opacity in the ultrarelativistic peripheral ion collisions at lhc .
we thank j.bjorken , a.mueller , g.shaw , members of the upc study group , and our coauthors m.mcdermott , a.freund , v.guzey , l.gerland , for useful discussions and gif and doe for support . m.s . and
thank int for hospitality while this work was completed .
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l. frankfurt , l. gerland , m. strikman and m. zhalov , [ arxiv : hep - ph/0302009 ] . | we argue that study of the cross section of coherent photo(electro ) production of vector mesons off nuclear targets provides an effective method to probe the leading twist hard qcd regimes of color transparency and perturbative color opacity as well as the onset of black body limit ( bbl ) in the soft and hard qcd interactions . in the case of intermediate energies we use the generalized vector dominance model ( gvdm ) to take into account coherence effects for two distinctive limits - the soft interactions for production of @xmath0 and @xmath1-mesons and the color transparency regime for production of charmonium states .
we demonstrate that gvdm describes very well @xmath0-meson coherent photoproduction at @xmath2 gev and predict an oscillating energy dependence for the coherent charmonium production . in the limit of small @xmath3
we find that hard qcd leads to onset of the perturbative color opacity even for production of very small onium states , like @xmath4 .
the advantages of the process of coherent dijet photoproduction and hard diffractive processes in general for probing the onset of bbl and measuring the light - cone wave function of the photon in a hard scattering regime where decomposition over twists becomes inapplicable are explained .
we apply this analysis to the study of the photon induced coherent processes in ultra peripheral collisions of ions at lhc and demonstrate that the counting rates will be sufficient to study the physics of color opacity and color transparency at the energies beyond the reach of the electron - nucleon(nucleus ) colliders . | <s>[INST]it appears that in the next decade the photon - nucleus interactions will be in the forefront of the small _ x _ qcd dynamics studies .
this is due to the possibilities of the studying coherent ( and for some channels incoherent ) photon - nucleus interactions at energies which exceed at least by a factor of 10 the energies of electron - nucleon interactions at hera .
such studies will be feasible at lhc within the program of the study of the ultra peripheral collisions ( upc ) @xcite .
this opens a challenging opportunity to get answers to a number of the fundamental questions which could be investigated in the coherent processes : how to achieve new qcd regime of strong interaction with small coupling constant , how interactions depend on the type of the projectile and how they change with an increase of the size / thickness of the target , etc .
several regimes appear possible depending on the incident energy and the target thickness . a hadronic projectile ( proton , pion , etc ) high - energy interactions with the nucleus rather rapidly approach the black body limit ( bbl ) in which the total cross section of the interaction is equal to @xmath5 ( @xmath6 ) .
another extreme limit is the interaction of small size projectiles ( or wave packages ) . in this case in a wide range of high energies the system remains almost frozen during the passage through the nucleus and the regime of color transparency is reached in which the interaction of the small size projectile with a nucleus is rather weak and proportional to a. this color transparency phenomenon in hard high energy projectile - nucleus interactions has been recently observed experimentally in the exclusive production of two jets by pions in the coherent diffraction off nuclei . at higher energies interactions of small dipole is expected to reach the regime of the perturbative color opacity . in this regime
the small size projectile still couples to the gluon field of the target via the ( skewed ) gluon density of the target , @xmath7 , like in the color transparency regime .
however , the scattering amplitude is not @xmath8 due to the leading twist ( lt ) shadowing , @xmath9 .
the onset of gluon shadowing tames somewhat the increase of @xmath10 between @xmath11 and @xmath12 and slows down the increase of the small dipole - nucleus interaction with energy .
the resulting taming is not strong enough to prevent the leading twist approximation result for the total inelastic cross section from reaching and even exceeding the bbl .
this violation of unitarity is an unambiguous signal that for sufficiently small @xmath3 the lt approximation breaks down .
an important practical issue for the studies of the small @xmath3 dynamics is whether the interactions of small dipoles with several nucleons of the target are strongly modified by the leading twist shadowing dynamics @xcite or one can neglect the lt gluon shadowing , like in the model of mclerran and venugopalan@xcite , and focus on the higher twist effects which are often modeled in the impact parameter space eikonal model @xcite .
if the leading twist shadowing was small and only higher twist effects were taming the increase of the dipole - nucleus cross section , the break down of the dglap approximation would occur at rather large @xmath3 .
the break down of dglap may result in onset of the bbl or taming of the cross sections at smaller values .
we will argue below that the relative importance of leading and higher twist interactions could be experimentally resolved using coherent onium photoproduction .
note also that if the lt gluon shadowing effects were small enough , the bbl for the interaction of @xmath13 dipoles of the size @xmath14 could be reached for central collisions with heavy nuclei already at @xmath15 that is in the kinematics where @xmath16 effects in the evolution of the parton densities are small . in any case , whatever is the limiting behavior for the interaction of the small size dipoles with heavy nuclei , it is of major theoretical interest since it represents a new regime of interactions when the leading twist approximation and therefore the whole notion of the parton distributions becomes inapplicable for the description of hard qcd processes in the small @xmath17 regime .
it is worth emphasizing that on the top of providing higher parton density targets , nuclei have another important advantage as compared to the nucleon target .
it is a weak dependence of the scattering amplitude on the impact parameter for a wide range of the impact parameters ( in fact , one can combine light and heavy nuclei to study the dependence of the amplitudes on the nuclear thickness ) . on the contrary , in the nucleon case
the scattering at large impact parameters is important even at very small @xmath3 working to mask the change of the regime of the interactions at small impact parameters .
theoretical studies of the limiting behavior of the small dipole - heavy nucleus cross sections did not lead so far to definitive results .
it is conceivable that the qcd dynamics will stop the increase of the cross section at central impact parameters at the values significantly smaller than allowed by the bbl . in the following discussion to emphasize the qualitative difference of the new regime we will use for simplicity the extreme hypothesis that the impact factor at small impact parameters reaches the value of one corresponding to the bbl pattern of the elastic and inelastic cross sections being equal .
there exist many processes where the projectile wave function is a superposition of configurations of different sizes , leading to the fluctuations of the interaction strength . in this respect ,
interactions of real and virtual photons with heavy nuclei provide unique opportunities since the photon wave function contains both the hadron - like configurations ( vector meson dominance ) and the direct photon configurations ( small @xmath13 components , heavy quark - antiquark components ) .
the important advantage of the photon is that at high energies the bbl is manifested in diffraction into a multitude of the hadronic final states ( elastic diffraction @xmath18 is negligible ) while in the hadron case only elastic diffraction survives in the bbl , and details of the dynamics responsible for this regime remain hidden .
moreover , one can _ post - select _ a small size or a large size initial state by selecting a particular final state , containing for example @xmath19 @xmath20 , or a leading light meson .
such post - selection is much easier in the photon case than in the hadron case since the distribution over the sizes of the configurations is much broader in the photon case .
spectacular manifestations of bbl in ( virtual ) photon diffraction include strong enhancement of the large mass tail of the diffractive spectrum as compared to the expectations of the triple pomeron limit , large cross section of the high @xmath21 dijet production @xcite .
we emphasize that the study of the diffractive channels will allow to distinguish between two extreme scenarios : large suppression of the cross section due to the leading twist shadowing and nonlinear regime of the bbl .
investigation of the coherent diffraction in bbl would allow to perform unique measurements of various components of the light cone wave function of the photon , providing a much more detailed information than similar measurements in the regime where leading twist dominates . in this review
we summarize our recent studies of the various regimes of the coherent photoproduction off nuclei @xcite : the onset of the bbl regime , phenomenon of color transparency and perturbative color opacity related to the leading twist nuclear gluon shadowing , and the pattern of soft qcd phenomena in the proximity to the black body limit .
in addition we consider hard leading twist diffraction off nuclei in dis .
we also outline how these effects can be studied in upc collisions and provide a comparison with the first upc data from rhic .
our consideration of the coherent photoproduction processes of light flavor and hidden charm is based on the use of the eikonal approximation that is the glauber model modified to take into account finite longitudinal momentum transfer @xcite .
the photoproduction cross section @xmath22 is given in the glauber model by the general expression @xmath23 here @xmath24 is the photon energy , @xmath25is the vector meson momentum , @xmath26 , @xmath27 is the longitudinal momentum transfer in the @xmath28 transition , and @xmath29 is the diffractive nuclear profile function .
depending on the considered vector meson production process , the glauber approach can be combined with either the traditional vector dominance model ( vdm ) ( for the detailed review see ref .
@xcite ) or with the generalized vector dominance model ( gvdm ) @xcite . more properly
this latter approximation should be called the gribov - glauber model @xcite because the space - time evolution of high energy processes is different in quantum mechanical models and in quantum field theory , and therefore theoretical foundations of the high - energy model are different . in particular , in qcd in difference from quantum mechanics a high - energy projectile interacts with all nucleons at the same impact parameter almost at the same time @xcite . due to the cancellations between diagonal and nondiagonal transitions
the gvdm allows to take into account the qcd effect of the suppression of interaction of spatially small quark - gluon wave packages with a hadron target - the so called color transparency phenomenon .
namely , cancellations occur between the amplitudes of the photon transition into a vector state @xmath30 with subsequent conversion to a state @xmath31 and direct production of the state @xmath31 , etc .
the importance of the nondiagonal transitions reveals itself in the precocious bjorken scaling for moderately small @xmath32 as due to the presence in the virtual photon of hadron - like and point - like type configurations @xcite .
these amplitudes are also crucial for ensuring a quantitative matching with perturbative qcd regime for @xmath33 few gev@xmath34 @xcite .
the amplitude of the vector meson production off a nucleon can be written within the gvdm as @xmath35 where @xmath36 are expressed through @xmath37 .
calculation of the vector meson production amplitude off nuclei within the glauber approximation requires taking into account both the nondiagonal transitions due to the transition of the photon to a different meson @xmath38 in the vertex @xmath39 and due to a change of the meson in multiple rescatterings like @xmath40 .
this physics is equivalent to inelastic shadowing phenomenon familiar from hadron - nucleus scattering @xcite .
then in the optical limit ( @xmath41 ) of the glauber multistep production theory one can introduce the eikonal functions , @xmath42 , which describe propagation of the produced objects through the medium and are related to the diffractive profile function by expression @xmath43 within the optical limit of the glauber based gvdm with accuracy @xmath44 the eikonal functions @xmath42 are determined by the solutions of the coupled channel equations @xmath45 , \label{cch}\end{aligned}\ ] ] with the initial condition @xmath46 .
the exponential factors @xmath47 $ ] are responsible for the coherent length effect , @xmath48 , @xmath49 .
the generalized glauber -based optical potentials in the short - range approximation are given by the expression @xmath50 here @xmath51 are the forward elementary amplitudes , and @xmath52 is the nuclear density normalized by the condition @xmath53 .
we calculated @xmath54 in the hartree - fock - skyrme ( hfs ) model which provided a very good(with an accuracy @xmath55 ) description of the global nuclear properties of spherical nuclei along the periodical table from carbon to uranium@xcite and the shell momentum distributions in the high energy ( p,2p)@xcite and ( e , ep)@xcite reactions .
if the nondiagonal rescattering amplitudes @xmath56 , one can easily integrate eq.[cch ] , and using the expression for the elementary amplitude @xmath57 obtain the expression for the photoproduction cross section : @xmath58 well known from early seventies ( see for example @xcite ) .
we have used the gvdm to describe coherent photoproduction of hadronic states of @xmath59 gev off nuclei and consider the onset of bbl in the soft regime . in ref .
@xcite the simplest nondiagonal model was considered with two states @xmath0 and @xmath60 .
then the gvdm comprises elementary amplitudes @xmath61 it was assumed that both @xmath0 and @xmath62 have the same diagonal amplitudes of scattering off a nucleon .
the ratio of coupling constants was fixed : @xmath63 , while the ratio of the nondiagonal and diagonal amplitudes @xmath64 , and the value @xmath65 were found from the fit to the forward @xmath66 cross sections measured at @xmath676.1 , 6.6 and 8.8 gev@xcite .
one should emphasize here that in such gvdm extension @xmath60-meson approximates the hadron production in the interval of hadron masses @xmath68 .
thus the values of the production cross section refer to the corresponding mass interval .
we refined this model in @xcite .
the dependence on the nuclear structure parameters was diminished by calculating the nuclear densities in the hartree - fock - skyrme ( hfs ) approach .
next , we used in all our calculations the parameterization of @xcite for the @xmath69 amplitude which was obtained from the fit to the experimental data on photoproduction off the proton target .
the value of @xmath70 was fixed at 0.18 to ensure the best fit of the measured differential cross section of the @xmath0-meson photoproduction off lead at @xmath71 gev and @xmath72 @xmath73 .
note that this value of @xmath74 leads to a suppression of the differential cross section of the @xmath0-photoproduction in @xmath75 by a factor of @xmath76 practically coinciding with phenomenological renormalization factor @xmath77 introduced in @xcite to achieve the best fit of the elementary @xmath0-meson photoproduction forward cross section in the vdm which neglects mixing effects . with all parameters fixed we calculated the differential cross sections of @xmath0-production off nuclei and found a good agreement with the data @xcite , see a detailed comparison in @xcite . in view of a good agreement of the model with the data on @xmath0-meson production in the low energy domain we used this model to consider the @xmath0-meson photoproduction at higher energies of photons .
the increase of the coherence length with the photon energy leads to a qualitative difference in the energy dependence of the coherent vector meson production off light and heavy nuclei and to a change of the a - dependence for the ratio of the forward @xmath60 and @xmath0-meson production cross sections between @xmath78 gev and @xmath79 gev ( fig.[rhoen ] ) .
the observed pattern reflects the difference of the coherence lengths of the @xmath0-meson and a heavier @xmath80-meson which is important for the intermediate photon energies @xmath81 gev .
the corrections due to nondiagonal transitions are relatively small ( @xmath82 15% ) for the case of @xmath0 production off a nuclei . as a result
, we find that the gvdm cross section is close to the one calculated in the vdm for heavy nuclei as well .
situation for @xmath60 production is much more interesting .
the cross section of @xmath60 production off a nucleon is strongly suppressed as compared to the case when the @xmath83 transitions are switched off .
the extra suppression factor is @xmath84 .
the non - diagonal transitions disappear in the limit of large a ( corresponding to the bbl ) due to the condition of orthogonality of hadronic wave functions in accordance with the general argument of gribov @xcite . therefore in the limit of @xmath85
we expect that the relation @xmath86 should be fulfilled for the productions of states @xmath87 of invariant masses @xmath88 at @xmath89 .
indeed we have found from calculations that in the case of the coherent photoproduction off lead the nondiagonal transitions becomes strongly suppressed with increase of the photon energy . as a result the @xmath90 ratio increases , exceeds the ratio of the @xmath91 forward cross sections calculated with accounting for @xmath92 transitions already at @xmath93 gev and becomes close to the value of @xmath94 which can be considered as the limit when one can treat the interaction with the heavy nucleus as a black one .
it is worth noting here that presence of nondiagonal transitions in terms of the formalism of the scattering eigen states @xcite corresponds to the fluctuations of the values of the interaction cross sections for the real photon .
the gvdm discussed in the paper leads to small ( @xmath95 ) color transparency effects at intermediate energies for the cross section of semiinclusive photoproduction processes .
really , this model corresponds to the propagation of states with cross sections : @xmath96 . in the case of electroproduction @xmath74
should be significantly larger : @xmath97 this equation follows from eq.([gvdm ] ) where the left hand side is put to zero because the cross section of the elastic vector meson electroproduction rapidly decreases with @xmath98 .
the presence of the ct phenomenon within the gvdm leads to a substantial modification of the pattern of the approach to bbl .
the nondiagonal transitions become more important with the increase of @xmath98 , leading to an enhancement of the effects discussed above . in particular
, the fluctuations of strengths of interaction would lead at large @xmath98 to the color transparency phenomenon .
presence in gvdm of significantly different masses of @xmath99 makes it impossible to describe all fluctuations of strengths of interaction in terms of one coherent length .
there is a qualitative difference between gvdm description of the light meson production described above and production of charmonium states . in the case of the photoproduction of light mesons the soft physics dominates both at low and high energies
hence , the gribov - glauber model should be applicable in a wide range of energies . at the same time the space - time picture of the process changes with energy . at low energies
the meson is formed at the distances smaller than the typical interaction length of a meson in the nucleus . with the increase of energy
the formation length starts to exceed the nuclear size and a photon converts to a system of @xmath13 and higher fock - components before the target , and one has to account for the interactions of this system with the media and subsequent transition of the system to a vector meson . the situation is much more involved in the case of ( charm)onium production . at high energies
both the coherence length @xmath101 and the formation length @xmath102}^{-1}$ ] ( distance on which the squeezed @xmath13 pair transforms into the ordinary meson ) are large and the color transparency phenomenon reveals itself .
in particular , it explains the fast increase of the cross section with energy observed at hera ( for reviews of small x phenomena see ref .
consequently , the value of the cross section extracted from the charmonium photoproduction characterizes the interaction of the squeezed @xmath19 pair with a nucleon rather than the charmonium - nucleon interaction . in the high energy limit the very small interquark distances in the wave function of the photon dominate , and
one has to treat the interaction of small dipoles with nuclei . in this case
the eikonal approximation gives a qualitatively wrong answer since it does not take into account the leading twist effect of the gluon shadowing(see the detailed analysis in @xcite ) , while the leading twist analysis predicts large shadowing effects @xcite , see discussion in section 3 . on the other hand , at the intermediate energies when onium states are formed inside the nucleus the nonperturbative effects at a transverse distance scale comparable to the charmonium size becomes important .
the hadronic basis description would be more relevant in this case .
however the vdm which takes into account only diagonal vector meson transitions does not account properly for the basic qcd dynamics of interaction .
in particular , slac data @xcite show that @xmath103 which within vdm corresponds to : @xmath104 .
this conclusion is in evident contradiction with the qcd expectation that the hadron interaction cross section should be scaled approximately as the transverse area occupied by color : @xmath105 .
thus in this naive qcd picture @xmath106 .
a qcd explanation of such failure of vdm is based on the observation @xcite that in photoproduction of both the @xmath107and @xmath108mesons the small relative distances @xmath109 dominate in the @xmath19 component of the photon wave function .
therefore the cross sections which enter into the ratio of @xmath107and @xmath108yields are cross sections of the interaction of the small dipoles , not genuine mesons .
the suppression of the production of @xmath108 in this picture is primarily due to a smaller leptonic decay width of @xmath108(a factor of 1/3 ) .
a significant additional suppression comes from importance of more massive @xmath19 intermediate states in the photon wave function ( @xmath110 respectively ) .
the exact value of the suppression is sensitive to the details of the onium wave functions and the dependence of the dipole - nucleon cross section on the size of the dipole @xcite .
the dominance of small @xmath19 configurations in photoproduction processes is relevant for the significant probability of nondiagonal @xmath111 diffractive transitions .
the gvdm adjusted to account for the color screening phenomenon @xcite allows to take into account qcd dynamics using a hadronic basis .
such a description is limited to the regime of small coherence lengths ( medium energies ) , where leading twist shadowing is not important .
we use the gvdm to consider the coherent photoproduction of hidden charm mesons off nuclei at moderate photon energies @xmath112 where the coherence length for the @xmath113 transition @xmath114 is still close enough to the internucleon distance in nuclei while the formation length @xmath115 is comparable to the radii of heavy nuclei . in this energy range
produced charmonium states have a noticeable probability to rescatter in sufficiently heavy nuclei .
therefore , one would be able to reveal the fluctuation of the charmonium - nucleon interaction strength as due to the diagonal @xmath116 and nondiagonal @xmath117 rescatterings for moderate energies .
the gvdm which we outlined above takes into account the coherence length effects via the glauber model approximation .
the key distinction from the @xmath118meson case is choosing the parameters of the model to account for the space - time evolution of spatially small @xmath19 pair .
it is important that the inelastic shadowing corrections related to the production of higher mass states @xcite are still insignificant .
a reasonable starting approximation to evaluate the amplitude of the charmonium - nucleon interaction is to restrict ourselves to the basis of @xmath107and @xmath108states for the photon wave function in eq.[gvdm ] .
then , similarly to the considered above case of @xmath119 production we have two equations comprising six elementary amplitudes .
the charmonium - nucleon coupling constants : @xmath120 , and @xmath121 are determined from the widths of the vector meson decays @xmath122 . since in
the photoproduction processes @xmath19 pair is produced within the spatially small configuration one can neglect for a moment by the direct photoproduction amplitude and obtain the approximative relations between rescattering amplitudes @xmath123 large values for nondiagonal amplitudes @xmath124 are a characteristic qcd property of hidden charm and beauty meson - nucleon interaction .
note that the negative sign of the nondiagonal amplitude is dictated by the qcd factorization theorem . a positive sign of the forward photoproduction @xmath125 amplitudes as well as the signs of the coupling constants @xmath126 and @xmath127 are determined by the signs of the charmonium wave functions at r=0 . from the approximative estimates above
it also follows that @xmath128 .
this is much larger than @xmath129 20 mb suggested by analyses of the data on @xmath130 absorption in nucleus - nucleus collisions @xcite .
when combined with the slac data @xcite , this corresponds to @xmath131 with large experimental and theoretical errors . to fix elementary amplitudes more accurately within gvdm ( see @xcite for details )
we parameterized the elementary photoproduction cross section in the form used by the experimentalists of hera to describe their data .
this form has no firm theoretical justification but it is convenient for the fit @xmath132 here @xmath133 is the invariant energy for the photon scattering off a free nucleon , @xmath134 is the reference point and @xmath135 is the two - gluon form factor of a nucleon .
we also used the slac results for the forward @xmath136 cross section @xcite and for the ratio @xmath137 besides , we fixed the @xmath138 cross section @xmath139 mb as measured at slac@xcite and used the reasonable assumption about the energy dependence of this cross section as the sum of soft and hard physics : @xmath140 the existence of a hard part of the @xmath141n cross section is consistent with the gvdm , because the photoproduction amplitude has a stronger energy dependence than the pomeron exchange , i.e. soft scattering amplitudes . next , we used this input , the optical theorem and the well known gribov - migdal relation @xmath142 to determine from eq.[gvdm ] all elementary amplitudes in the discussed energy range .
in particular , we found the value @xmath143 mb .
however , the input parameters of the gvdm , namely the experimental cross sections of the forward elementary photoproduction and , especially , the value of @xmath144 , are known with large uncertainties . in result
, we obtained elementary cross sections changing in the ranges : @xmath145 and @xmath146 , in the discussed energy range .
we checked how a variation of @xmath144 within the experimental errors influences our results .
= .9 = 1 .
in our papers@xcite,@xcite we analyzed the coherent photoproduction of charmonia off light(si ) and heavy(pb ) nuclei .
here we present the cross sections of the coherent photoproduction of @xmath141 and @xmath130 off ca .
the energy dependence of these cross sections is compared ( fig.[jpsipsi]a ) to that obtained in the impulse approximation where all rescatterings of the produced vector mesons are neglected , and the cross section is given by the simple formula @xmath147 the distinctive feature of the coherent charmonium photoproduction is that differential cross sections oscillate as a function of the photon energy .
the major source for such a behavior at intermediate energies is oscillating behavior of the longitudinal nuclear form factor at the relatively large values of @xmath148 in the photoproduction vertex .
the cross section of the @xmath107photoproduction in the gvdm is close to that calculated in the impulse approximation - the shapes of curves are very similar and the values of the cross sections are only slightly reduced at energies below 40 gev(fig.[jpsipsi]b ) .
this indicates that it would be very difficult to extract the total @xmath138 cross section from such a measurement . at the same time , since the the nuclear form factor is known with a high precision from the high energy elastic electron - nucleus scattering , one can use the coherent @xmath107photoproduction off the spherical nuclei to determine the elementary @xmath149 amplitude in a wide range of energies for @xmath150 .
the picture is qualitatively different for the coherent @xmath108photoproduction off nuclei . due to the higher threshold ( @xmath151 gev , the direct @xmath108production off nuclei is suppressed in the impulse approximation ( for the same incident energy ) as compared to the @xmath107production by the nuclear form factor . since @xmath152
, the minima of the impulse approximation distribution are shifted .
the contribution of the nondiagonal term @xmath153 essentially increases the @xmath108yield and produces an additional shift of the minima in the spectrum to lower photon energies ( fig .
[ jpsipsi]c ) .
this results in significant effects , especially , if one analyses the data as a function of the mass number a at different energies to extract a - dependence of the @xmath138 cross sections .
it is seen from fig.[adpsi ] that the oscillating form factor significantly influences the a - dependence that complicates extracting of the genuine @xmath138 and @xmath154 cross section from such analysis .
the oscillation of the cross section with energy can be used to measure in a new way the elementary charmonium photoproduction amplitudes as well as the charmonium - nucleon amplitudes using the coherent charmonium photoproduction off light nuclei@xcite . in particular , at the photon energies @xmath155 ( fig .
[ jpsipsi]d ) , the main contribution to the cross section originates from the nondiagonal rescattering . as a result
, one can extract from the data the nondiagonal elementary @xmath156 amplitude by measuring the ratio of the @xmath130 and @xmath141 yields at zero production angle , because other inputs to this ratio such as the elementary @xmath149 amplitude are fixed from the @xmath141 production .
moreover , since other parameters enter both in the numerator and denominator , the major uncertainties are canceled out .
on the other side , the energy dependence of this ratio should originate primarily due to the contribution of the direct @xmath130 production .
thus , one would be able to determine the @xmath157 amplitude from the measurement of the @xmath130-to-@xmath141 ratio .
we want to emphasize that the suggested procedure for extracting the nondiagonal amplitude and amplitudes of direct @xmath141 and @xmath130 photoproduction from the nuclear measurements is practically model independent .
it is much more difficult to determine the diagonal @xmath158 and @xmath159 amplitudes , which are relevant for the suppression of the charmonium yield in heavy ion collisions . a naive diagonal vdm with @xmath160 based on the slac data @xcite leads to a rather significant suppression of the @xmath141 yield : @xmath161 for light nuclei , and @xmath162 for heavy nuclei .
however , we find @xcite a strong compensation of the suppression due to the contribution of the nondiagonal transitions . as a result
we find that overall the suppression does not exceed @xmath163 for all nuclei along the periodical table .
hence , an extraction of the diagonal amplitudes from the measured cross sections would require a comparison of high precision data with very accurate theoretical calculations including the nondiagonal transitions .
another strategy is possible if the elementary @xmath164 , and @xmath157 photoproduction amplitudes , as well as the nondiagonal amplitude @xmath165 would be reliably determined from the medium energy data . in this case
it would be possible to determine the imaginary parts of the forward diagonal amplitudes from the gvdm equations ( [ gvdm ] ) @xmath166 the suggested procedure allows to determine all elementary amplitudes with a reasonable precision from the measurements of @xmath141 and @xmath130 photoproduction off the light nucleus at the medium photon energies .
the measurement of the coherent charmonium photoproduction off nuclei in this energy region are planned at slac @xcite .
the measurements of coherent production off heavy nuclei and of the quasielastic production with parameters of gvdm fixed from the analysis of light nuclei would provide a critical test of the model .
the main limitation of the suggested procedure is the restriction of the hadronic basis to the two lowest 1s , 2s charmonium states with the photon quantum numbers : @xmath141 , @xmath130 .
this is one of the key approximations in the discussed approach .
it seems quite reasonable since in the coherent production of vector meson states off nuclei at moderate energies contribution of high mass states is more suppressed by the target form factor .
however , we neglected by @xmath167 which is nearly degenerate in mass with @xmath130 : @xmath168 mev .
the properties of these two states are described well in the charmonium model @xcite . in this model
@xmath167-meson is described as a @xmath169 state with a small admixture of the @xmath170 wave , while @xmath130-meson has a small @xmath171-wave admixture .
namely @xmath172 since only the s - wave contributes to the decay of @xmath173 states into @xmath174 ( at least in the non - relativistic charmonium models ) the value @xmath175 can be determined from the data on the @xmath174 decay widths @xmath176 kev and the @xmath177 kev . due to the small difference of masses between the @xmath178 and @xmath179 mesons the produced s - wave @xmath180-state does not loose coherence while going through the media at any conceivable energies .
the soft interactions can not transform the @xmath170-state to @xmath171-state with any significant probability . in the soft qcd processes data
show that the cross sections of exclusive nondiagonal transitions are negligible for the forward angle scattering .
the same conclusion is valid in the pqcd model for the charm dipole - nucleon interactions .
thus , it is more appropriate to use the @xmath181 - @xmath182 basis for description of the propagation of @xmath19 through the nucleus .
the only resulting change is an increase of @xmath183 by a factor of @xmath184 as compared to @xmath127 which is within the uncertainties of the model .
since the @xmath182 state ultimately transforms into @xmath130 and @xmath185 we predict @xcite : ratio would be a universal number .
since @xmath185 can be easily observed via its characteristic @xmath186 decays in a number of the lepton , hadron and nucleus induced processes the study of the discussed process can provide a new way to probing dynamics of charmonium production in various reactions . ]
@xmath187 influence of the higher mass resonances is expected to be even weaker - the constants @xmath188 relevant for the transition of a photon to a charmonium state @xmath189 rapidly decrease with the resonance mass .
this is because the radius of a bound state , @xmath190 , is increasing with the mass of the resonance and therefore the probability of the small size configuration being @xmath191 is decreasing with an increase of mass ( for fixed s , l ) .
besides , the asymptotic freedom in qcd dictates decreasing of the coupling constant relevant for the behavior of the charmonium wave function at small relative distances .
experimentally one finds from the data on the leptonic decay widths that @xmath188 drops by a large factor with increasing mass .
an additional suppression arises due to the weakening of the soft exclusive nondiagonal @xmath192 amplitudes between states with the different number of nodes .
hence , it seems possible to determine the imaginary parts of diagonal rescattering amplitudes from analysis of the data using the gvdm equations .
since in the medium energy domain the energy dependence of soft rescattering amplitudes is well reproduced by a factor @xmath193 , one can determine the real parts of the amplitudes using the gribov - migdal relation ( eq .
[ gm ] ) .
the above analyses demonstrate that the relative importance of the non - diagonal transitions increases an increase of the quark mass .
it would be of interest to investigate experimentally the case of strangeness production .
it is likely to correspond to @xmath70 substantially larger than @xmath194 but much smaller than @xmath195 .
interaction of small size color singlet objects with hadrons is one of the most actively studied issues in high - energy qcd .
the qcd factorization theorem for exclusive meson electroproduction at large @xmath98 , and @xmath196 photoproduction @xcite allows to evaluate the amplitude of the production of a vector meson by a longitudinally polarized photon @xmath197 through the convolution of the wave function of the meson at the zero transverse separation , hard interaction block and the generalized ( skewed ) parton density .
production @xcite in the bfkl approximation and for the pion diffraction into two jets @xcite in the leading log @xmath98 approximation @xcite . ]
the lt approximation differs strongly from the expectations based on glauber model approaches and on the two gluon exchange models , because it accounts for the dominance of the electroproduction of spatially small quark - gluon wave package and its space - time evolution which leads to formation of a softer gluon field .
the latter effect results effectively in an increase of the size of the dipole with increase of the energy
. in perturbative qcd ( similar to qed ) the total cross section of the interaction of small systems with hadrons is proportional to the area occupied by color within projectile hadron @xcite leading to the expectation of the color transparency phenomenon for various hard processes with nuclei .
the cross sections of incoherent processes are expected to be proportional to the number of nucleons in the nuclei , while the coherent amplitude is proportional to number of nucleons times the nuclear form factor .
possibility to approximate projectile heavy quarkonium as colorless dipole of heavy quarks can be formally derived from qcd within the limit when mass of heavy quark @xmath198 but @xmath199 is fixed and not extremely small @xcite . in this
kinematics the size of heavy quarkonium is sufficiently small to justify applicability of pqcd . for practical purposes
the crucial question is at what @xmath98 squeezing becomes effective .
probably the most sensitive indicator is the @xmath200-dependence of the meson production .
the current hera data are consistent with the prediction of @xcite that the slopes of the @xmath0 and @xmath141 production amplitudes should converge to the same value .
this indicates that at small @xmath17 configurations much smaller than average configurations in light mesons ( @xmath201 ) dominate for @xmath0-meson production at @xmath202 gev@xmath34 , while the @xmath141 production is dominated by interaction in small size configurations for all @xmath98 .
therefore , one expects the regime of color transparency for @xmath203 where the gluon shadowing is very small / absent .
recently the color transparency ( ct ) phenomenon was observed at fnal by e791 experiment @xcite which studied the coherent process of dissociation of a 500 gev pion into two jets off the nuclei .
the measurement has confirmed a number of predictions of @xcite including the a - dependence , and the transverse and longitudinal momentum distributions of the jets .
previously the color transparency type behavior of the cross section was observed also in the coherent @xmath204 photoproduction at @xmath205 @xcite .
a natural question is whether the color transparency will hold for arbitrary high energies ?
two phenomena are expected to work against ct at high energies .
one is the lt gluon shadowing .
there are theoretical expectations ( see discussion below ) supported to some extent by the current analyses of the data on dis scattering off nuclei ( which do not extend deep enough into the shadowing region ) that the gluon distributions are shadowed in nuclei as compared to the nucleon : @xmath206 .
this obviously should lead to a gradual but calculable in qcd disappearance of color transparency @xcite , and to onset of a new regime , which we refer to as _ the color opacity regime _
( one can think of this regime also as a regime of generalized color transparency since a small @xmath13 dipole still couples to the gluon field of the target through a two gluon attachment and the amplitude is proportional to the generalized gluon density of the nucleus ) .
another mechanism for the violation of ct at high energies is the increase of the small dipole - nucleon cross section with energy @xmath207 . for sufficiently large energies
this cross section becomes comparable to the meson - nucleon cross sections .
one may expect that this would result in a significant suppression of the hard exclusive diffractive processes as compared to the lt approximation .
however it seems that this phenomenon is beyond the kinematics achievable for the photoproduction of @xmath141-mesons in upc of heavy ions at rhic ( @xmath208 ) but could be important at heavy ion upc at lhc . hence , a systematic study of the onium production in the coherent scattering off nuclei at collider energies will be very interesting .
one should emphasize here that with decrease of the size of the onium the eikonal ( higher twist ) contributions die out quickly ( provided @xmath3 is kept fixed ) .
in particular , for the @xmath209 case one probes nuclear gluon fields at the transverse scale of the order of 0.1 fm or @xmath210 . the @xmath141 case is closer to the border line between the perturbative and nonperturbative domains . as a result
the a nonperturbative region appears to give a significant contribution to the production amplitude @xcite .
= .50 let us discuss the photoproduction amplitude @xmath211 in more details .
we are interested here in the @xmath212 range which can be probed at lhc .
this region corresponds to rather small values of @xmath17 . in this situation interaction of @xmath13 pair , which in the final state forms a quarkonium state is still rather far from the bbl .
hence the key problem in the theoretical treatment of the process is taking into account the nuclear shadowing .
a number of mechanisms of coherent interactions with several were suggested for this process .
we focus here on the * the leading twist mechanism of shadowing * which is presented by diagrams in fig.[ltdiag ] .
there exists qualitative difference between the mechanism of interaction of a small dipole with several nucleons and the case of a similar interaction of an ordinary hadron .
let us for example consider interaction with two nucleons .
the leading twist contribution is described by the diagrams where two gluons are attached to the dipole . to ensure that nucleus remains intact in such a process
, the color singlet lines should be attached to both nucleons .
these diagrams ( especially the one of fig .
[ ltdiag]b ) are closely related to the diagrams describing the gluon diffractive parton densities ( which are measured at hera ) , and hence to the similar diagrams for the gluon nuclear shadowing @xcite .
the amplitude of high energy coherent heavy onium photoproduction is proportional to the generalized gluon density of the target , @xmath213 , which depends on the light - cone fractions @xmath214 and @xmath215 of gluons attached to the quark loop .
they satisfy a relation : @xmath216 if the quark fermi motion and binding effects were negligible , @xmath217 .
the resolution scale @xmath218 , where @xmath219 is the mass of the heavy quark .
numerical estimates for the photoproduction of @xmath141 give @xmath220@xcite reflecting a relatively small mass of c - quark and indicating that this process is on the verge between nonperturbative and perturbative regimes . on the contrary
, the mass of the beauty quark is huge on the scale of soft qcd . in this case
hard physics dominates , attachments of more than two gluons to @xmath20 are negligible and the qcd factorization theorem provides a reliable tool for description of the @xmath4 production .
this is especially true for the ratio of the cross sections of @xmath4 production from different targets since the higher twist effects due to the overlapping integral of the @xmath20 component of the photon and @xmath4 cancelled out in the ratio . as a result ,
in the leading twist shadowing approximation the cross section of the process @xmath221 is proportional to the squared nuclear gluon density distribution and can be written in the form @xmath222 ^ 2 \int \limits_{-\infty}^{t_{min } } dt { \left| \int d^2bdz e^{i{\vec q_t}\cdot { \vec b } } e^{-q_{l}z}\rho ( { \vec b},z ) \right| } ^2 . \label{phocs}\ ] ] numerical estimates using realistic potential model wave functions indicate that for @xmath141 , @xmath223 @xcite , and for @xmath4 , @xmath224 @xcite .
modeling of the generalized parton distributions at moderate @xmath98 suggests that to a good approximation @xmath225 can be approximated by the gluon density at @xmath226 @xcite . for large @xmath98 and small @xmath3 gpds
are dominated by the evolution from @xmath227 . since the evolution conserves @xmath228 , effect of skewedness
is determined primarily by the evolution from nearly diagonal distributions , see ref .
@xcite and references therein . in the case of the @xmath209 production
it increases the cross section by a factor @xmath229 @xcite and , potentially , this could even obscure the connection of the discussed effect with the shadowing of the nuclear gluon densities .
however , the analysis of @xcite shows that the ratio of gpd on a nucleus and on a nucleon at @xmath230 is a weak function of @xmath215 , slowly dropping from its diagonal value ( @xmath231 ) with the decrease of @xmath215 .
overall this observation is in a agreement with the general trend mentioned above that it is more appropriate to do comparison of diagonal and non - diagonal cases at @xmath226 . in the case of double scattering contribution
[ ltdiag]b ) there is another way to address the question of the accuracy of the substitution of the ratio of generalized gluon densities by the ratio of diagonal parton densities at the normalization scale .
we notice that the amplitude corresponding to fig .
[ ltdiag]b is expressed through the nondiagonal matrix element of the diffractive distribution function , @xmath232 , which is an analog of generalized parton distribution . in the diagonal limit of @xmath233
it coincides with the diffractive gluon distribution .
it depends on the light - cone fraction which nucleon lost in @xmath234 and @xmath235 states : @xmath236 @xmath237 respectively , @xmath238 , and @xmath239 .
if we make a natural assumption that @xmath240 we find that numerically in the kinematics we discuss the resulting skewedness effects are small as compared to the uncertainties in the input gluon diagonal diffractive pdfs . hence in the following we will approximate the ratio of generalized gluon densities in the nucleus and nucleon by the ratio of the gluon densities in nucleus and nucleon at @xmath241 . in the case of @xmath4 use of @xmath242
maybe more appropriate .
this would lead to slightly larger shadowing effect .
it was demonstrated in @xcite that one can express the quark and gluon nuclear shadowing for the interaction with two nucleons in a model independent way through the corresponding diffractive parton densities using the gribov theory of inelastic shadowing @xcite and the qcd factorization theorem for the hard diffraction @xcite .
an important discovery of hera is that hard diffraction is indeed dominated by the leading twist contribution and gluons play a very important role in the diffraction(this is loosely referred to as gluon dominance of the pomeron ) .
analysis of the hera diffractive data indicates that in the gluon induced processes probability of the diffraction is much larger than in the quark induced processes @xcite .
the recent h1 data on diffractive dijet production @xcite provide an additional confirmation of this observation .
large probability of diffraction in the gluon induced hard processes could be understood in the s - channel language as formation of color octet dipoles of rather large sizes which can diffractively scatter with a quite large cross section .
the strength of this interaction can be quantified using optical theorem and introducing @xmath243 for the hard process of scattering of a virtual photon off the gluon field of the nucleon . here
@xmath244 is the ratio of the real to imaginary parts of the elementary diffractive amplitude , @xmath98 is the momentum scale determining virtuality of the gluons , @xmath245 is the momentum fraction of the pomeron with the corresponding cut - off scale @xmath246 , and @xmath247 is the diffractive gluon density distribution of nucleon which is known from the h1 analysis of the diffractive data at the scale @xmath248 gev@xmath34 .
an important feature of this mechanism of coherent interaction is that it is practically absent for @xmath249 and may rather quickly become important with decrease of @xmath3 .
= .80 we calculated the ratio of the gluon density distributions in eq .
[ phocs ] using the leading twist shadowing model @xcite ( for the details of calculations see ref.@xcite ) . as the first step the nuclear gluon density distribution with account of the leading twist shadowing
is calculated at the starting evolution scale @xmath250 gev@xmath34 @xmath251 . \label{ga}\end{aligned}\ ] ] as an input we used the h1 parameterization of @xmath252 .
the effective cross section @xmath253 accounts for the elastic rescattering of the produced diffractive state off the nuclear nucleon and is determined by eq .
[ sigef ] .
numerically it is very large at the starting scale of the evolution , see fig .
[ figsigef ] , and corresponds to the probability of the gluon induced diffraction close to 50% .
this indicates that at the initial scale of the evolution interactions in the gluon sector are close to the bbl for @xmath254 for the nucleon case , and even more so for the nuclei , where similar regime should hold for a larger range of the impact parameters .
note that the double scattering term in eq .
[ ga ] for the nuclear parton densities satisfies qcd evolution , but the higher order terms do not . that is
if we use different starting scale of evolution we would obtain different results of @xmath255 .
the reason is that the terms @xmath256 are sensitive to degree of fluctuations in the cross sections of interaction of diffracting states .
these fluctuations increase with increase of @xmath98 .
this effect is automatically included in the qcd evolution , and it leads to violation of the glauber - like structure of the expression for the shadowing at @xmath257 .
approximation for the @xmath258 rescattering of eq .
[ ga ] corresponds to an assumption that fluctuations are small at @xmath259 scale since this scale is close enough to the scale of the soft interactions , see discussion in @xcite .
thus , at the second step of the calculation we use nlo qcd evolution equations to calculate the shadowing at larger @xmath98 using the calculation at @xmath260 as a boundary condition . in this way we also take into account the contribution of the gluon enhancement at @xmath261 which influences the shadowing at larger @xmath98 .
note here that proximity to the bbl in the gluon sector which is reflected in a large value of @xmath262 may result in corrections to the lt evolution which require further studies .
= 0.8 first we calculate the ratios of the cross sections of coherent photoproduction of @xmath141 and @xmath4 off nuclei and nucleon ( fig .
[ fshad ] ) .
such ratios do not depend on the uncertainties of the elementary cross sections and provide a sensitive test of the role of the lt shadowing effects . in a case of the @xmath141 photoproduction
the gluon virtuality scale is 3 - 4 gev@xmath34 with a significant fraction of the amplitude due to smaller virtualities @xcite .
hence we will take the gluon shadowing in the leading twist at @xmath263 .
taking a smaller value of @xmath98 would result in even larger shadowing effect . in calculations for the @xmath4
we take @xmath264 , though the result is not very sensitive to precise value of @xmath265 since the scaling violation for the gluon shadowing for these @xmath98 is rather small .
we find that in spite of a small size of @xmath4 , which essentially precludes higher twist shadowing effects up to very small x , the perturbative color opacity effect is quite appreciable .
it is worth noting that the effective cross section of the rescattering in the eikonal model is determined by the cross section of dipole -nucleon interactions at the distances @xmath266 in the @xmath141 case and @xmath267 in the @xmath4 case .
these cross sections are @xmath268 for @xmath141 and @xmath269 for @xmath4 case for @xmath12 and a factor of 1.5 - 2 smaller for @xmath270 , see fig . 13 in ref .
they are much smaller than the cross sections which enter into calculation of the gluon shadowing in the lt mechanism .
we also estimated the absolute cross section of onium photoproduction for a wide range of the photon energies .
this is of interest for the planned measurements of the onium production in the ultraperipheral heavy ion collisions at lhc .
the dependence of the momentum - integrated cross sections on the energy @xmath271 is presented in fig .
[ onics ] . in the case of @xmath141 production
the calculations are pretty straightforward as the accurate data are available from hera .
the situation is more complicated in the case of the photoproduction of @xmath4 .
so far the information about the elementary @xmath272 cross section is very limited .
there is the only zeus and h1 data on total cross section for the average energy of @xmath273 .
thus , to calculate the forward photoproduction cross section we used a simple parameterization : @xmath274 where @xmath275 gev@xmath34 , the slope parameter @xmath276 is fixed basing on the analysis of the two gluon form factor in ref .
@xcite , and the energy dependence follows from the calculations of ref .
@xcite of the photoproduction of @xmath4 in the leading @xmath277 approximation with an account for the skewedness of the partonic density distributions .
this elementary cross section is normalized so that the total cross section is in @xmath278 .
it is well known that inelastic diffraction at small @xmath200 gives information on the fluctuations of strength in the projectile - target interactions @xcite .
application of this logic to the hadron scattering off nuclei have allowed to explain the a - dependence of two measured diffractive channels in @xmath279 scattering assuming that it coincides with the a - dependence of the total cross section of the inelastic diffraction , and the absolute total cross section of pa diffraction ( the data exist for two nuclei only ) at the energies 200 - 400 gev , see @xcite for the review and references . with an increase of energy , the total cross section of @xmath280 interaction increases and fluctuations in the elementary amplitude lead to much smaller fluctuations of the absorption in the scattering off a heavy nuclei . as a result
, one can expect much weaker a - dependence of the diffractive cross section @xcite , in particular , @xmath281 at lhc energies @xcite as compared to @xmath282 at fixed target energies . for large produced masses we can also understand this suppression using the @xmath200 channel picture of the pomeron exchanges as due to the stronger screening of the triple pomeron exchange , for review and references see @xcite .
diffraction in deep inelastic scattering corresponds to the transition of the ( virtual ) photon into its hadronic components leaving the nucleus intact .
hence it is similar to elastic hadron - nucleus scattering rather than inelastic diffractive hadron - nucleus scattering .
it was demonstrated recently that in the upc collisions at lhc it would be possible to study nuclear parton densities using hard charm and beauty production in @xmath283 interactions @xcite .
naturally one can also use these and similar processes to measure diffractive parton densities of nuclei . since these quantities in the leading twist
satisfy the factorization theorem we can analyze them on the basis of the analysis of the diffraction in dis .
there is a deep connection between shadowing and phenomenon of diffractive scattering off nuclei .
the simplest way to investigate this connection is to apply the agk cutting rules @xcite .
several processes contribute to diffraction on nuclei : ( i ) coherent diffraction in which the nucleus remains intact , ( ii ) break - up of the nucleus without production of hadrons in the nucleus fragmentation region , ( iii ) rapidity gap events with hadron production in the nucleus fragmentation region . in ref .
@xcite we found that for @xmath284 gev@xmath34 , the fraction of the dis events with rapidity gaps reaches the value of about 30 - 40% for heavy nuclei , with a fraction of the events of type ( iii ) rapidly dropping with @xmath285 .
we can use the information on @xmath262 for quarks and gluons to estimate probability of diffraction for different hard triggers at the resolution scale @xmath286 .
first we consider the dependence of the fraction of the events due to coherent diffraction and due to the break - up of the nucleus on the strength of the interaction , @xmath287 , neglecting fluctuations of the interaction strength .
we find that for the realistic values of @xmath287 the probability of coherent diffraction is quite large but increases with @xmath262 very slowly and does not reach the asymptotic value of @xmath288 even for very large values of @xmath289 ( the later feature reflects presence of a significant diffuse edge even in heavy nuclei ) , see fig .
[ figcsratio ] .
thus , it is not sensitive to the fluctuations of @xmath262
. we also found that the ratio of diffraction with the nucleus break - up and with the nucleus remaining intact is small ( 10 - 20% ) in a wide range of nuclei , and slowly increasing with increase of @xmath262 , see fig .
[ figcsratio ] .
hence it would require high precision measurements to constrain the dynamics using @xmath290 ratios . comparing the values of the fraction of the diffractive events for quark and gluon induced processes off heavy nuclei and proton
, we find that the relative importance of the quark induced events is increasing .
therefore , the scaling violation at large @xmath291 for the diffractive quark distribution in nuclei will be stronger for nuclei than for a proton .
another interesting effect is that for heavy nuclei only genuine elastic components can be produced ( inelastic diffraction is zero ) .
hence , the soft contribution at @xmath260 due to triple pomeron exchange is strongly suppressed see e.g. @xcite . as a result ,
nuclear diffractive parton distributions at small @xmath291 are strongly suppressed ( by a factor @xmath292 ) at @xmath260 though this suppression will be less pronounced at large @xmath98 due to the qcd evolution .
this will lead to breakdown of the universality of the @xmath291 distributions as a function of a. though the diffractive parton densities change rather slowly with @xmath98 leading to a weak variation of the diffractive cross sections with @xmath98 ( modulus the scaling factor ) the fraction of the diffractive events at fixed @xmath3 should significantly drop with increase of @xmath98 due to a large increase of the inclusive nucleon parton densities and decrease of the nuclear shadowing .
for example , let us consider ultraperipheral collisions ( upc ) at lhc where one can measure a the process @xmath293 in the kinematics where direct photon process @xmath294 dominates . in this case
if we consider the process at say @xmath295 corresponding to @xmath296 the fraction of diffractive events will be of the order 10% .
the background from the strong interaction originates from glancing collisions in which two nucleons interact via a double diffractive process @xmath297 where @xmath298 contains jets .
probability of the hard processes with two gaps is very small at collider energies - even smaller than .the probability of the single diffractive hard processes , see e.g. @xcite .
therefore , we expect that the background conditions will be at least as good in the diffractive case as in the inclusive case considered in @xcite
. thus , it would be pretty straightforward to extract coherent diffraction by simply using anti - coincidence with the forward neutron detector , especially in the case of heavy nuclei , see discussion in @xcite . as a result it would be possible to measure in the upc the nuclear diffractive parton distributions with a high statistical accuracy .
it is important that in difference from the diffraction to a vector meson it would be possible to determine on the event by event basis the energy of the photon which induced the reaction , since the rapidity of the photon is close to the rapidity of two jets . as a result it would be possible to perform the measurements for large rapidities ( selecting the events generated by a photon of higher of two energies allowed by the kinematics of production particles in the interval of rapidities @xmath299 ) and to determine diffractive parton densities for pretty small @xmath3 .
one of the striking features of the bbl is the suppression of nondiagonal transitions in the photon interaction with heavy nuclei @xcite .
indeed , in the bbl the dominant contribution to the coherent diffraction originates from `` a shadow '' of the fully absorptive interactions at impact parameters @xmath300 , so the orthogonality argument is applicable .
we use it to derive the bbl expression for the differential cross section of the production of the invariant mass @xmath301 for scattering of ( virtual ) photons @xcite . for the real photon case : @xmath302 here @xmath303 .
comparison of the measured cross section of the diffractive production of states with certain masses with the bbl result ( eq . [ ccsb ] ) would allow to determine up to what masses in the photon wave function interaction remains black .
similar equation is valid in the bbl for the production of specific hadronic or quark - gluonic final states ( @xmath304 etc ) in the case of the coherent nuclear recoil .
this allows to measure any component of the light cone photon wave function which interacts with the bbl strength corresponding final states in the coherent processes .
the onset of bbl limit for hard processes should reveal itself also in a faster increase with energy of cross sections of photoproduction of excited states as compared to the cross section for the ground state meson
. it would be especially advantageous for these studies to use a set of nuclei - one in the medium range , like @xmath305 , and another with @xmath306 .
this would allow to remove the edge effects and use the length of about 10 fm of nuclear matter .
one especially interesting channel is exclusive diffractive dijet production by real photons .
one may expect that for the @xmath307 energies which will be available at eic or at lhc in upc the bbl in the scattering off heavy nuclei would be a good approximation for the masses @xmath308 in the photon wave function up to few gev .
this is the domain which is described by perturbative qcd for @xmath309 in the case of the proton targets , and larger @xmath3 for scattering off nuclei .
the condition of large longitudinal distances , a small longitudinal momentum transfer , will be applicable in this case up to quite large values of the produced diffractive mass . in the bbl
the dominant channel of diffraction to large masses is production of two jets with the total cross section given by eq.([ccsb ] ) and with a characteristic angular distribution @xmath310 , where @xmath311 is the c.m .
angle @xcite . on the contrary , in the perturbative qcd limit the diffractive dijet production , except the charmed dijet production ,
is strongly suppressed @xcite .
the suppression is due to the structure of coupling of the @xmath13 component of the real photon wave function to two gluons when calculated in the lowest order in @xmath312 . as a result , in the real photon case
hard diffraction involving light quarks is connected to production of @xmath313 and higher states .
distribution of diffractively produced jets over invariant mass provides an important test of the onset of bbl limit .
really , in the dglap / ct regime differential cross section of forward diffractive dijet production should be @xmath314 and be dominated by charm jet production .
this behavior is strikingly different from the bbl limit expressions of @xcite .
thus , the dijet photoproduction should be very sensitive to the onset of the bbl regime .
we want to draw attention that @xmath315 component of the photon light - cone wave function can be measured in three independent diffractive phenomena : in the bbl off the proton , in bbl off a heavy nuclei , in the ct regime where the wave function can be measured as a function of the interquark distance @xcite .
a competing process for photoproduction of dijets off heavy nuclei is production of dijets in @xmath316 collisions where the second photon is provided by the coulomb field of the nucleus .
the dijets produced in this process have positive c - parity and hence this amplitude does not interfere with the amplitude of the dijet production in the @xmath317 interaction which have negative c - parity .
our estimates indicate that this process will constitute a very small background over the wide range of energies @xcite .
ultraperipheral collisions(upc ) of relativistic heavy ions at rhic and lhc open a promising new avenue for experimental studies of the photon induced coherent and incoherent interactions with nuclei at high energies @xcite .
really , the lhc heavy ion program @xcite will allow studies of photon - proton and photon - nucleus collisions at the energies exceeding by far those available now at hera for @xmath318 scattering .
hence , we can analyze an opportunity to study the phenomena discussed above combining the theory of photo induced processes in the ultraperipheral aa collisions with our studies of the coherent photo(electro ) production of vector mesons .
we can use the standard weizsacker - williams approximation @xcite to calculate the cross section integrated over the momentum of the nucleus which emits the quasireal photons .
the cross section of the vector meson production integrated over the transverse momenta of the nucleus which emitted a photon can be written in the convoluted form : @xmath319 here y is the rapidity @xmath320 the flux of the equivalent photons @xmath321 is given by a simple expression @xcite : @xmath322.\ ] ] here @xmath323 and @xmath324 are modified bessel functions with argument @xmath325 , @xmath326 is lorentz factor and @xmath327 is the impact parameter .
the glauber profile factor @xmath328 accounts for the inelastic strong interactions of the nuclei at impact parameters @xmath329 and , hence , suppresses the corresponding contribution of the vector meson photoproduction .
recently the star collaboration released the first data on the cross section of the coherent @xmath330-meson production in gold - gold upc at @xmath331 gev @xcite .
this provides a first opportunity to check the basic features of the theoretical models and main approximations which include the weizscker - williams ( ww ) approximation for the spectrum of the equivalent photons , an approximate procedure for removing collisions at small impact parameters where nuclei interact strongly , and the model for the vector meson production in the @xmath332 interactions . in the case of the @xmath0-meson production the basic process
is understood much better than for other photoproduction processes .
hence , checking the theory for this case is especially important for proving that upc could be used for learning new information about photon - nucleus interactions .
note here that the inelastic shadowing effects which start to contribute at high energies still remain a few percent correction at energies @xmath333 100 gev relevant for the star kinematics . for lhc energy range one should account for the blackening of interaction with nuclei . in this case
cross section of inelastic diffraction in hadron - nucleus collisions should tend to 0 .
so major impact for the calculation of the process of diffractive photoproduction of @xmath0 meson would be necessity to neglect by the contribution of @xmath1 @xcite . the calculated momentum transfer distributions at the rapidity @xmath334 and the momentum transfer integrated rapidity distribution for gold - gold upc at @xmath335 gev are presented in figs .
[ figstar1]a , b @xcite .
= 0.8 = 0.8 let us briefly comment on our estimate of the incoherent @xmath330-meson production cross section .
the momentum transfer distribution ( dashed line in fig . [
figstar1]a ) is practically flat in the discussed @xmath336 range .
the total incoherent cross section obtained by integration over the wide range of @xmath336 is @xmath337 mb . to select the coherent production
the cut @xmath338 gev@xmath34 was used in the data analysis @xcite .
correspondingly , the calculated incoherent cross section for this region of @xmath336 is @xmath339 mb .
our calculations of incoherent production which are based on accounting for only the single elementary diffractive collision obviously present the lower limit
. the residual nucleus will be weakly excited and can evaporate only one - two neutrons .
the events @xmath340 were detected by the star and identified as a two - stage process - coherent @xmath330-production with the subsequent electromagnetic excitation and neutron decay of the colliding nuclei @xcite .
in particular , the cross section estimated by the star for the case when only one of the nuclei is excited and emits several neutrons is @xmath341 mb .
the momentum transfer distribution for these events is determined by the coherent production .
hence , it differs from that for incoherent events but in the region of very low @xmath336 it is hardly possible to separate them experimentally , and the measured cross section @xmath342 includes contribution of incoherent events on the level of @xmath343 .
the total rapidity - integrated cross section of coherent @xmath330-meson production calculated in the gvdm for the range of energies available at rhic is shown in fig .
[ figstar2](solid line ) .
we find @xmath344 mb at @xmath335 gev .
the value @xmath345 mb was obtained at this energy by the star from the data analysis at the low momentum transfer @xmath338 gev@xmath34 .
thus , before making a comparison we should take into account this cut .
it leads to a reduction of the cross section by @xmath346 ( the dashed line in fig .
[ figstar2 ] ) . in our calculations
we did nt account for the @xmath336-dependence of the elementary amplitudes which are rather flat in the considered range of energies and momentum transfers as compared to that for the nucleus form factor .
so , in the region of integration important for our analysis it is reasonable to neglect this slope .
nevertheless , an account of this effect would slightly reduce our estimate of the total cross section .
also we neglected a smearing due to the transverse momentum of photons and the interference of the production amplitudes from both nuclei @xcite .
.total cross sections of @xmath141 production in upc at lhc . [ cols="^,^,^",options="header " , ] this latter phenomenon results in the narrow dip in the coherent @xmath336-distribution at @xmath347 gev@xmath34 .
all these effects do not influence noticeably the value of the @xmath336-integrated cross section but can be easy treated and taken into account in a more refined analysis .
thus we find @xmath348 mb to be compared to the star value @xmath345 mb .
since our calculation does not have any free parameters , this can be considered as a reasonable agreement .
= 1.0 = 1.0 .
[ figlhc1 ] it was suggested in @xcite to look for color opacity phenomenon using @xmath204 ( photo ) electroproduction .
this however requires energies much larger than those available at the fixed target facilities and would require use of electron - nucleus colliders
. at the same time estimates of the counting rates performed within the framework of the felix study @xcite have demonstrated that the effective photon luminosities generated in peripheral heavy ion collisions at lhc would lead to significant rates of coherent photoproduction of vector mesons including @xmath4 in reaction @xmath349 as a result it would be possible to study at lhc photoproduction of vector mesons in pb - pb and ca - ca collisions at energies much higher than the range @xmath350 gev covered at the fixed target experiment at fnal @xcite .
note that even current experiments at rhic ( @xmath351 gev ) should also exceed this limit .
as it is clearly indicated by the star study the coherent photoproduction , leaving the both interacting nuclei intact , can be reliably identified by using the veto triggering from the two - side zero degree calorimeters which select the events not comprising the escaped neutrons . the additional requirement which enables to remove contribution of the incoherent events with the residual nucleus in the ground state is selection of the produced quarkonium with small transverse momentum . in fig .
[ lhcdst ] we compare the momentum transfer distributions for the coherent @xmath141 and @xmath4 photoproduction calculated in the leading twist shadowing model with the corresponding distributions for incoherent photoproduction .
note that we estimated the upper limit of incoherent cross section simply as the free elementary cross section on the nucleon target multiplied by the number of nucleons a. in fig .
[ figlhc1]a , b we present the rapidity distributions of the @xmath141 coherent production for peripheral collisions at lhc calculated including effects of gluon shadowing and in the impulse approximation . at the central rapidities we find suppression by a factor 4 for a case of ca and more strong , by a factor 6 for pb .
the total cross sections are given in table [ tcrsec1 ] .
the rapidity distributions for coherent @xmath4 production in the upc with ca and pb beams are shown in fig .
[ figlhc1]c , d and the corresponding total cross sections are given in table [ tcrsec2 ] . as it is seen from comparison of the leading twist shadowing based calculations to that performed in the impulse approximation the yield of @xmath4 is expected to be suppressed by a factor 2 at central rapidities due to the leading twist nuclear shadowing .
hence , study of the coherent photoproduction of the heavy quarkonium states at lhc opens an important avenue for investigating the nuclear gluon distributions and the shadowing effects in the kinematics which would be very hard to probe in any other experiments .
we demonstrated that coherent diffraction off nuclei provides an effective method of probing a possible onset of bbl regime in hard processes at small @xmath17 .
we predict a significant increase of the ratio of the yields of @xmath352 mesons in coherent processes off heavy nuclei due to the blackening of the soft qcd interactions in which fluctuations of the interaction strength are present .
an account of nondiagonal transitions leads to a prediction of a significant enhancement of production of heavier diffractive states especially production of high @xmath21 dijets .
study of these channels may allow to get an important information on the onset of the black body limit in the diffraction of real photons .
we argued that the fluctuations of strengths of interactions has been observed at intermediate energies in the diffractive photoproduction of vector mesons .
we discuss the opportunity to look for the transition from the nuclear color transparency to the regime of the color opacity in the ultrarelativistic peripheral ion collisions at lhc .
we thank j.bjorken , a.mueller , g.shaw , members of the upc study group , and our coauthors m.mcdermott , a.freund , v.guzey , l.gerland , for useful discussions and gif and doe for support . m.s . and
thank int for hospitality while this work was completed .
r. j. glauber , boulder lectures in theoretical physics , vol.1 , + ( interscience publ .
ny)(1959 ) ; + k. gottfried and d. r. yennie , phys . rev . *
182 * , 1595 ( 1969 ) + erratum - ibid .
d * 2 * , 2737 ( 1970 ) ; + g. v. bochmann , phys .
d6 , 1938 ( 1972 ) .
a. donnachie and g. shaw , in electromagnetic interactions of hadrons , edited by + a. donnachie and g. shaw ( plenum , new york , 1978 ) , vol .
164 - 194 ; + h. fraas , b. read , and d. schildknecht , nucl .
* b86 * , 346 ( 1975 ) ; + p. ditsas and g. shaw , nucl .
b * 113 * , 246 ( 1976 ) .
e. eichten , k. gottfried , t. kinoshita , j. b. kogut , k. d. lane and t. m. yan , + phys .
lett . * 34 * , 369 ( 1975 ) ; [ erratum - ibid . *
36 * , 1276 ( 1976 ) ] .
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c * 4 * ( 1980 ) , 211 ( 1980 ) .
l. frankfurt , l. gerland , m. strikman and m. zhalov , [ arxiv : hep - ph/0302009 ] .[/INST] we argue that study of the cross section of coherent photo(electro ) production of vector mesons off nuclear targets provides an effective method to probe the leading twist hard qcd regimes of color transparency and perturbative color opacity as well as the onset of black body limit ( bbl ) in the soft and hard qcd interactions . in the case of intermediate energies we use the generalized vector dominance model ( gvdm ) to take into account coherence effects for two distinctive limits - the soft interactions for production of @xmath0 and @xmath1-mesons and the color transparency regime for production of charmonium states .
we demonstrate that gvdm describes very well @xmath0-meson coherent photoproduction at @xmath2 gev and predict an oscillating energy dependence for the coherent charmonium production . in the limit of small @xmath3
we find that hard qcd leads to onset of the perturbative color opacity even for production of very small onium states , like @xmath4 .
the advantages of the process of coherent dijet photoproduction and hard diffractive processes in general for probing the onset of bbl and measuring the light - cone wave function of the photon in a hard scattering regime where decomposition over twists becomes inapplicable are explained .
we apply this analysis to the study of the photon induced coherent processes in ultra peripheral collisions of ions at lhc and demonstrate that the counting rates will be sufficient to study the physics of color opacity and color transparency at the energies beyond the reach of the electron - nucleon(nucleus ) colliders . </s> |
Calgary and other devastated communities are starting a painstaking recovery after the worst flood in Alberta’s history, even as the southeast of the province braces for the arrival of the peak of surging waters early Monday.
Alberta Premier Alison Redford said that while Calgary, Canmore and High River are shifting into recovery mode, other communities such as Drumheller and Medicine Hat are bracing for their own ordeal. The government has examined river flows, rainfall and the flooding impact, and Ms. Redford says they have confirmed the floods of the last several days are the largest in Alberta’s history.
“It’s been shocking to see the unbelievable destruction and the powerful impact of these floods,” Ms. Redford told reporters Sunday night. “We will live with this forever.”
Tens of thousands of Calgarians were allowed to return to their homes Sunday as river waters receded, and the province’s largest city and business centre shifted to the daunting task of cleaning up – and paying for – the unprecedented flood damage.
Still, thousands of residents remain under evacuation orders and unable to survey the damage to their homes. And Calgary’s iconic Saddledome remains wet and muddied, less than two weeks before the Calgary Stampede, while parts of the downtown – the hub of Canada’s oil and gas sector – remain under water and without power.
In High River, the hardest-hit community, 80 per cent of the town is without power or basic services, and the RCMP expects search and rescue efforts to take days.
The financial impact on the province’s and country’s economy has yet to be tabulated, and Ms. Redford would not speculate on an amount. But it’s starting to become clear how long a road lies ahead. She announced the appointment of three junior cabinet ministers to oversee “reconstruction” and said the province will help people with uninsurable losses.
“This is like nothing that we’ve ever seen in Alberta and it is going to require monumental marshalling of resources, skills and people,” she said.
Three flood-related deaths in the High River area were confirmed on the weekend.
Although Calgary municipal officials had originally predicted it could take weeks or months for the downtown to be powered and open for business, late Sunday Mayor Naheed Nenshi said the buildings occupied by 90 to 95 per cent of the city’s downtown workers could be functioning again by Tuesday. Still, he advised companies to keep non-essential employees home for at least Monday and Tuesday.
But Mr. Nenshi is determined that the Stampede, the 101-year-old rodeo and festival that brings hundreds of thousands to the city each year, will go ahead, despite the Saddledome and Stampede grounds still being partly flooded Sunday. The mayor said the fairgrounds are draining “remarkably fast” and noted the Stampede has its own electrical generators.
“So Stampede 101 may look very, very different than the 100th Stampede, but it will happen 12 days from today.”
On Sunday, Isha Sharif was able to enter her Calgary home, for the first time since a frantic evacuation Thursday evening, to find her basement nearly full of water, and her living room and garage covered with water and mud. Her six-year-old son cried for his lost toys, but one of the family’s greatest losses is Ms. Sharif’s extensive library, which included a collection of 100-year-old medical textbooks.
“We have small children and we don’t want to be back in the house because of mould concerns,” Ms. Sharif said, acknowledging she’s still in shock over the damage, and the realization that her home may still have to be demolished. “We’ll have to do a full or partial tear-down. It’s pretty bad.”
The focus of concern has now shifted to the southeastern corner of the province. In preparation for flooding in Medicine Hat, more than 10,000 residents have been evacuated in the city of 61,000. Mayor Norm Boucher said that although peak water flows won’t be as high as the province originally predicted, the city was already seeing some homes and downtown parking garages flooded by midday Sunday. “The sandbagging didn’t help very much,” Mr. Boucher said. “But we think everyone is safe now.”
Siksika Nation chief Fred Rabbit Carrier said the community east of Calgary was heavily damaged from the floods, with nearly a quarter of the reserve’s population forced to flee. The chief said it was too soon to tell how many of the water-damaged houses can be salvaged or how much the cleanup will cost. “This is the worst flooding I have ever seen in my life,” he said over the phone from Siksika’s Deerfoot Sportsplex, which is serving as a shelter.
Across Alberta, there are now more than 2,200 Canadian Forces troops on the ground, plus seven Griffon and two Cormorant helicopters either on standby or being used.
Although city officials insist the Stampede will go on, a number of events have already been cancelled. The Conservative Party of Canada had planned to hold a convention in Calgary this summer but cancelled the event this weekend. On Sunday, Immigration Minister Jason Kenney said while the party remains committed to holding the policy convention in Calgary, it would postpone the event until at least the fall.
With files from Carrie Tait, Renata D’Aliesio, Kim Mackrael and Tu Thanh Ha
Report Typo/Error ||||| CALGARY, Alberta, June 23 Power outages in the Canadian oil capital of Calgary could last for weeks or even months, city authorities said on Sunday, after record-breaking floods that killed three people and forced more than 100,000 to flee their homes swept across southern Alberta.
Some Calgary residents were able to return to sodden homes as river levels slowly dropped and some mandatory evacuations orders were lifted.
But Bruce Burrell, director of the Calgary Emergency Management Agency, said power restoration in the downtown core, where many of Canada's oil companies have their headquarters, could take days, weeks or even months.
Many of oil companies were making plans for employees to work from home.
"This is an evolving situation and because of the volatility of electricity and water and the infrastructure that was damaged we have got a lot of issues with restoring power to different parts of the city of Calgary," Alderman John Mar told CBC radio.
"We are facing an absolutely gargantuan task."
Heavy rains were blamed for 750 barrels of synthetic oil spilling from a pipeline approximately 70 kilometers (43 miles) south of Fort McMurray in northern Alberta early on Saturday.
"We are still investigating the cause, however, we believe that unusually heavy rains in the area may have resulted in ground movement on the right-of way that may have impacted the pipeline," Enbridge, Canada's largest pipeline company, said in an emailed statement.
The company also has shut down two major oil pipelines serving Canada's oil sands region as a precaution.
Provincial authorities said it was too early to count the cost of the flood damage because rivers have not peaked in some places.
The South Saskatchewan River is expected to burst its banks in the city of Medicine Hat in southeastern Alberta on Monday. About 10,000 people have been evacuated.
The floods already look significantly worse than those of 2005, which caused C$400 million ($383 million) in damage in the western Canadian province.
The floods followed 36 hours of unusually heavy rainfall that pushed the volume of water in rivers to record levels. Some communities received six months of their normal rainfall in fewer than two days.
Evacuations started on Thursday and utility Enmax switched off power to central Calgary on Friday afternoon to avoid water damage to its downtown facilities. Troops were used on Sunday morning to shore up the east bank of the Bow River in Calgary and ensure the stability of an Enmax substation.
It was unclear how much crude trading would take place on Monday after little if any trade on Friday.
Shorcan Energy Brokers, which provides live prices for many Canadian crude grades, operated out of Toronto on Friday rather than from Calgary, although there were no trades in Western Canada Select heavy blend or light synthetic crude.
Net Energy Inc, the other main Calgary crude broker, was closed on Friday and no trading took place.
As the Bow and Elbow rivers in Calgary, which during the weekend hit five times their normal flow rate, slowly receded, the scale of the damage became apparent. Roads and pavements were left covered with a layer of thick silt, fallen trees lined the riverbanks and residents pumped dirty brown water out of basements.
Police said three bodies had been found near High River, about 60 km (40 miles) south of Calgary.
Flood water covered the grounds of the Calgary Stampede, an annual extravaganza of cows, cowboys and horses scheduled to start on July 5. City authorities insisted the show would go ahead despite the disruption. | – Calgary, the heart of Canada's energy sector, could be without power for weeks or even months in the wake of floods that have forced 100,000 people from their homes and killed at least four. In the aftermath of the floods, the worst in the province of Alberta's history, "we are facing an absolutely gargantuan task," to restore power and infrastructure, a city official says. The heavy rain was blamed for a 750-barrel spill from an oil pipeline in the north of the province, Reuters reports. The worst of the flooding has yet to reach the southeastern corner of the province, where 10,000 people have been evacuated from the city of Medicine Hat, the Globe and Mail reports. Calgary Mayor Naheed Nenshi says that despite the devastation, the city's iconic, 101-year-old Stampede rodeo festival will go ahead in less than two weeks. "Stampede 101 may look very, very different than the 100th Stampede, but it will happen 12 days from today," he says. | <s>[INST]Calgary and other devastated communities are starting a painstaking recovery after the worst flood in Alberta’s history, even as the southeast of the province braces for the arrival of the peak of surging waters early Monday.
Alberta Premier Alison Redford said that while Calgary, Canmore and High River are shifting into recovery mode, other communities such as Drumheller and Medicine Hat are bracing for their own ordeal. The government has examined river flows, rainfall and the flooding impact, and Ms. Redford says they have confirmed the floods of the last several days are the largest in Alberta’s history.
“It’s been shocking to see the unbelievable destruction and the powerful impact of these floods,” Ms. Redford told reporters Sunday night. “We will live with this forever.”
Tens of thousands of Calgarians were allowed to return to their homes Sunday as river waters receded, and the province’s largest city and business centre shifted to the daunting task of cleaning up – and paying for – the unprecedented flood damage.
Still, thousands of residents remain under evacuation orders and unable to survey the damage to their homes. And Calgary’s iconic Saddledome remains wet and muddied, less than two weeks before the Calgary Stampede, while parts of the downtown – the hub of Canada’s oil and gas sector – remain under water and without power.
In High River, the hardest-hit community, 80 per cent of the town is without power or basic services, and the RCMP expects search and rescue efforts to take days.
The financial impact on the province’s and country’s economy has yet to be tabulated, and Ms. Redford would not speculate on an amount. But it’s starting to become clear how long a road lies ahead. She announced the appointment of three junior cabinet ministers to oversee “reconstruction” and said the province will help people with uninsurable losses.
“This is like nothing that we’ve ever seen in Alberta and it is going to require monumental marshalling of resources, skills and people,” she said.
Three flood-related deaths in the High River area were confirmed on the weekend.
Although Calgary municipal officials had originally predicted it could take weeks or months for the downtown to be powered and open for business, late Sunday Mayor Naheed Nenshi said the buildings occupied by 90 to 95 per cent of the city’s downtown workers could be functioning again by Tuesday. Still, he advised companies to keep non-essential employees home for at least Monday and Tuesday.
But Mr. Nenshi is determined that the Stampede, the 101-year-old rodeo and festival that brings hundreds of thousands to the city each year, will go ahead, despite the Saddledome and Stampede grounds still being partly flooded Sunday. The mayor said the fairgrounds are draining “remarkably fast” and noted the Stampede has its own electrical generators.
“So Stampede 101 may look very, very different than the 100th Stampede, but it will happen 12 days from today.”
On Sunday, Isha Sharif was able to enter her Calgary home, for the first time since a frantic evacuation Thursday evening, to find her basement nearly full of water, and her living room and garage covered with water and mud. Her six-year-old son cried for his lost toys, but one of the family’s greatest losses is Ms. Sharif’s extensive library, which included a collection of 100-year-old medical textbooks.
“We have small children and we don’t want to be back in the house because of mould concerns,” Ms. Sharif said, acknowledging she’s still in shock over the damage, and the realization that her home may still have to be demolished. “We’ll have to do a full or partial tear-down. It’s pretty bad.”
The focus of concern has now shifted to the southeastern corner of the province. In preparation for flooding in Medicine Hat, more than 10,000 residents have been evacuated in the city of 61,000. Mayor Norm Boucher said that although peak water flows won’t be as high as the province originally predicted, the city was already seeing some homes and downtown parking garages flooded by midday Sunday. “The sandbagging didn’t help very much,” Mr. Boucher said. “But we think everyone is safe now.”
Siksika Nation chief Fred Rabbit Carrier said the community east of Calgary was heavily damaged from the floods, with nearly a quarter of the reserve’s population forced to flee. The chief said it was too soon to tell how many of the water-damaged houses can be salvaged or how much the cleanup will cost. “This is the worst flooding I have ever seen in my life,” he said over the phone from Siksika’s Deerfoot Sportsplex, which is serving as a shelter.
Across Alberta, there are now more than 2,200 Canadian Forces troops on the ground, plus seven Griffon and two Cormorant helicopters either on standby or being used.
Although city officials insist the Stampede will go on, a number of events have already been cancelled. The Conservative Party of Canada had planned to hold a convention in Calgary this summer but cancelled the event this weekend. On Sunday, Immigration Minister Jason Kenney said while the party remains committed to holding the policy convention in Calgary, it would postpone the event until at least the fall.
With files from Carrie Tait, Renata D’Aliesio, Kim Mackrael and Tu Thanh Ha
Report Typo/Error ||||| CALGARY, Alberta, June 23 Power outages in the Canadian oil capital of Calgary could last for weeks or even months, city authorities said on Sunday, after record-breaking floods that killed three people and forced more than 100,000 to flee their homes swept across southern Alberta.
Some Calgary residents were able to return to sodden homes as river levels slowly dropped and some mandatory evacuations orders were lifted.
But Bruce Burrell, director of the Calgary Emergency Management Agency, said power restoration in the downtown core, where many of Canada's oil companies have their headquarters, could take days, weeks or even months.
Many of oil companies were making plans for employees to work from home.
"This is an evolving situation and because of the volatility of electricity and water and the infrastructure that was damaged we have got a lot of issues with restoring power to different parts of the city of Calgary," Alderman John Mar told CBC radio.
"We are facing an absolutely gargantuan task."
Heavy rains were blamed for 750 barrels of synthetic oil spilling from a pipeline approximately 70 kilometers (43 miles) south of Fort McMurray in northern Alberta early on Saturday.
"We are still investigating the cause, however, we believe that unusually heavy rains in the area may have resulted in ground movement on the right-of way that may have impacted the pipeline," Enbridge, Canada's largest pipeline company, said in an emailed statement.
The company also has shut down two major oil pipelines serving Canada's oil sands region as a precaution.
Provincial authorities said it was too early to count the cost of the flood damage because rivers have not peaked in some places.
The South Saskatchewan River is expected to burst its banks in the city of Medicine Hat in southeastern Alberta on Monday. About 10,000 people have been evacuated.
The floods already look significantly worse than those of 2005, which caused C$400 million ($383 million) in damage in the western Canadian province.
The floods followed 36 hours of unusually heavy rainfall that pushed the volume of water in rivers to record levels. Some communities received six months of their normal rainfall in fewer than two days.
Evacuations started on Thursday and utility Enmax switched off power to central Calgary on Friday afternoon to avoid water damage to its downtown facilities. Troops were used on Sunday morning to shore up the east bank of the Bow River in Calgary and ensure the stability of an Enmax substation.
It was unclear how much crude trading would take place on Monday after little if any trade on Friday.
Shorcan Energy Brokers, which provides live prices for many Canadian crude grades, operated out of Toronto on Friday rather than from Calgary, although there were no trades in Western Canada Select heavy blend or light synthetic crude.
Net Energy Inc, the other main Calgary crude broker, was closed on Friday and no trading took place.
As the Bow and Elbow rivers in Calgary, which during the weekend hit five times their normal flow rate, slowly receded, the scale of the damage became apparent. Roads and pavements were left covered with a layer of thick silt, fallen trees lined the riverbanks and residents pumped dirty brown water out of basements.
Police said three bodies had been found near High River, about 60 km (40 miles) south of Calgary.
Flood water covered the grounds of the Calgary Stampede, an annual extravaganza of cows, cowboys and horses scheduled to start on July 5. City authorities insisted the show would go ahead despite the disruption.[/INST]– Calgary, the heart of Canada's energy sector, could be without power for weeks or even months in the wake of floods that have forced 100,000 people from their homes and killed at least four. In the aftermath of the floods, the worst in the province of Alberta's history, "we are facing an absolutely gargantuan task," to restore power and infrastructure, a city official says. The heavy rain was blamed for a 750-barrel spill from an oil pipeline in the north of the province, Reuters reports. The worst of the flooding has yet to reach the southeastern corner of the province, where 10,000 people have been evacuated from the city of Medicine Hat, the Globe and Mail reports. Calgary Mayor Naheed Nenshi says that despite the devastation, the city's iconic, 101-year-old Stampede rodeo festival will go ahead in less than two weeks. "Stampede 101 may look very, very different than the 100th Stampede, but it will happen 12 days from today," he says.</s> |
stromal cells isolated from fresh bone marrow aspirates have multilineage potential that can differentiate into a variety of cell populations1 .
note , however , that the optimization of gene delivery to bone marrow stromal cells ( bmscs ) from mammalian cells had limited efficiencies .
recently , gene delivery by polyethylenimine - conjugated supraparamagnetic nano - particle under a magnetic field - so - called magnetofection - was introduced .
scherer et al.2 and plank et al.3 first reported that the application of magnetic nanoparticles to gene vectors to various cells showed significantly enhanced uptake of these vectors and subsequent high target protein expression .
the magnetic force applied on gene vector - magnetic particle complex can increase the accumulation of these complexes on the surface of the various cells . in particular , cell lines that have only limited efficiencies with regard to target gene expression , such as human endothelial cells , can be successfully managed by magnetofection4 - 6 .
note , however , that there had been few attempts to apply magnetofection to enhanced gene delivery for bmsc .
bone morphogenic protein 2 ( bmp2 ) gene transfer by transfection of bmp2-cdna to bmsc can be differentiated into osteoprogenitor cells , affecting the neighboring cells by paracrine pathway to potentiate the regeneration of various types of bone defects7,8 .
bmp7 was also reported as a potent osteogenic mediator8 . to accelerate gene expression , various gene delivery systems with high transfection efficiency
although there had been advances in gene transfer using non - viral vectors , efficiency of gene transfer is reported to be approximately 10 compared to adenoviral vectors8 .
since enhanced transfection efficiency is key to investigating the function of gene and protein , the viral gene transfer method had been proposed as a good method for gene overexpression .
different bmp2 gene therapy approaches to bone regeneration have been studied , and viral vectors such as adenoviruses11 - 13 and retroviruses14 as carriers of bmp2 cdna had been used .
nonetheless , immunogenicity of viral capsid protein is a major problem ; exposure of cell to virus for a long period of time or at higher doses is toxic for several tissues and cells ; hence the need for a method of potentiating viral transduction to the target cell at low multiplicity of infection ( moi ) to minimize the side effects16 .
this study sought to investigate whether adenoviral magnetofection can be a suitable method for increasing the efficacy of gene delivery into bmsc . as far as we know , this is the first trial of osteogenic induction of bmsc using adenoviral magnetofection .
primary mouse bmsc were isolated from the tibia and femur of 8 - 10-week - old c57bl6 mice .
mice were sacrificed by cervical dislocation , both ends of the bilateral tibia and femur were snipped off , and bone marrow was flushed out with dulbecco 's modified eagle 's medium ( dmem ; gibco , grand island , ny , usa ) containing 10% fetal bovine serum ( fbs ) and antibiotics ( penicillin 100 u / ml , streptomycin 100 g/l ) .
the single cell suspension of bone marrow was collected by several repetitions of drawing the cells into a syringe .
the cells were seeded on a 100 mm dish , and non - adherent cells were removed by changing the media ( dmem with 10% fbs ) for three consecutive days .
these cells of the first passage culture were then re - plated prior to confluence .
the culture media was replaced every 2 days and cultured up to 4 weeks . for the experiments of the study , the cells at passage 3 were used for in vitro viral transduction and in vivo animal experiments .
the e1-deleted adenoviral vector containing human bmp2 or bmp7 cdna - which constitutively expresses bmp2 or bmp7 , respectively , under the control of the cmv promoter - was propagated in 293a cells .
viral lysates were then expanded and purified using the adeno - x virus purification kit ( clontech , mountain view , ca , usa ) and titrated with the adeno - x rapid titer kit ( clontech ) .
bmscs were plated in 24-well plates ( in vitro study ) or 10 cm culture dish ( in vivo study ) at a density of 35,000 cells / cm on the day before transduction . for the in vitro adenoviral transduction of bmsc , adenovirus ( adbmp-2 , -7 , adlacz ) at the desired titer
was added to cells in 500 l of serum - free dmem and incubated for 6 hours .
after 24 hours , the media were then changed to dmem with 10% fbs and ascorbic acid ( 50 g / ml ) and -glycerol phosphate ( 5 mm ) to enhance osteoblastic differentiation and were replaced every two days . for adenoviral
transduction with magnetofection , adbmp-2 , -7 and lacz were diluted with dmem to establish the desired titer and mixed with 2 l of magnetic particle ( magnetofectin , combimac ; chemicell gmbh , berlin , germany ) indicated otherwise .
the mixture was incubated for 20 minutes at room temperature and added dropwise to the cells .
the cell culture plate was placed upon a magnetic plate ( magnetofactor-24 plate ; chemicell gmbh ) for 30 minutes .
two days after transduction , the expression of galactosidase ( number of blue nuclei / field ) according to the varying amount of magnetic nanoparticles and viral particles was evaluated with x - gal staining kit ( oz bioscience , marseille , france ) based on the manufacturer protocol .
the dependence on moi at different magnetic nanoparticles 48 hours after magnetofection was also assessed .
the efficiency of gene transfer with adenoviral magnetofection was compared with that of conventional adenoviral transduction .
bmp2 and 7 proteins secreted into conditioned media at the indicated time points were measured after adenoviral transduction or adenoviral magnetofection with adbmp-2 , 7 or lacz , using commercially available elisa kit ( quantikine ; r&d systems , minneapolis , mn , usa ) .
the conditioned media were prepared by culturing cells in serum - free medium for 24 hours .
alkaline phosphatase ( alp ) activity measured in cell layers was evaluated with p - nitrophenyl phosphate substrate included in a commercially available kit ( quanti -chrom alp assay kit ; bioassay systems , hayward , ca , usa ) .
the sample was harvested in a lysis buffer containing 0.1% np 40 and homogenized through three cycles of -70 freezing and 36 thawing .
alp activity was measured according to the manufacturer 's instruction and expressed in terms of relative luminescence unit ( rlu)/mg protein .
protein content was measured with protein assay kit ( biorad , hercules , ca , usa . ) using bovine serum albumin .
for alp staining , cells were cultured for 8 days in mineralizing medium , and then fixed for 30 seconds in 4% formaldehyde , washed three times with pbs , and stained with alp kit ( sigma , st .
louis , mo , usa ) . to compare the relative toxicity caused by magne - tofection
bmscs were seeded into the 96-well plate ( 110 cells / well/100 l media ) , and magnetic particle was added 48 hours after seeding .
after 72 hours of incubation , 50 l of mtt ( cell proliferation kit i ; roche molecular biochemicals , mannheim , germany ) was added to each well .
after another 4 hours of incubation at 37 , the supernatant of the plate was removed , and 150 l dimethylsulfoxide ( dmso ) was added to the cell monolayer .
the statistical difference between groups was analyzed with anova using spss program ( version 10 ; spss inc . ,
primary mouse bmsc were isolated from the tibia and femur of 8 - 10-week - old c57bl6 mice .
mice were sacrificed by cervical dislocation , both ends of the bilateral tibia and femur were snipped off , and bone marrow was flushed out with dulbecco 's modified eagle 's medium ( dmem ; gibco , grand island , ny , usa ) containing 10% fetal bovine serum ( fbs ) and antibiotics ( penicillin 100 u / ml , streptomycin 100 g/l ) .
the single cell suspension of bone marrow was collected by several repetitions of drawing the cells into a syringe .
the cells were seeded on a 100 mm dish , and non - adherent cells were removed by changing the media ( dmem with 10% fbs ) for three consecutive days .
these cells of the first passage culture were then re - plated prior to confluence .
the culture media was replaced every 2 days and cultured up to 4 weeks . for the experiments of the study , the cells at passage 3 were used for in vitro viral transduction and in vivo animal experiments .
the e1-deleted adenoviral vector containing human bmp2 or bmp7 cdna - which constitutively expresses bmp2 or bmp7 , respectively , under the control of the cmv promoter - was propagated in 293a cells .
viral lysates were then expanded and purified using the adeno - x virus purification kit ( clontech , mountain view , ca , usa ) and titrated with the adeno - x rapid titer kit ( clontech ) .
bmscs were plated in 24-well plates ( in vitro study ) or 10 cm culture dish ( in vivo study ) at a density of 35,000 cells / cm on the day before transduction . for the in vitro adenoviral transduction of bmsc , adenovirus ( adbmp-2 , -7 , adlacz ) at the desired titer
was added to cells in 500 l of serum - free dmem and incubated for 6 hours .
after 24 hours , the media were then changed to dmem with 10% fbs and ascorbic acid ( 50 g / ml ) and -glycerol phosphate ( 5 mm ) to enhance osteoblastic differentiation and were replaced every two days .
for adenoviral transduction with magnetofection , adbmp-2 , -7 and lacz were diluted with dmem to establish the desired titer and mixed with 2 l of magnetic particle ( magnetofectin , combimac ; chemicell gmbh , berlin , germany ) indicated otherwise .
the mixture was incubated for 20 minutes at room temperature and added dropwise to the cells .
the cell culture plate was placed upon a magnetic plate ( magnetofactor-24 plate ; chemicell gmbh ) for 30 minutes .
two days after transduction , the expression of galactosidase ( number of blue nuclei / field ) according to the varying amount of magnetic nanoparticles and viral particles was evaluated with x - gal staining kit ( oz bioscience , marseille , france ) based on the manufacturer protocol .
the dependence on moi at different magnetic nanoparticles 48 hours after magnetofection was also assessed .
the efficiency of gene transfer with adenoviral magnetofection was compared with that of conventional adenoviral transduction .
bmp2 and 7 proteins secreted into conditioned media at the indicated time points were measured after adenoviral transduction or adenoviral magnetofection with adbmp-2 , 7 or lacz , using commercially available elisa kit ( quantikine ; r&d systems , minneapolis , mn , usa ) .
the conditioned media were prepared by culturing cells in serum - free medium for 24 hours .
alkaline phosphatase ( alp ) activity measured in cell layers was evaluated with p - nitrophenyl phosphate substrate included in a commercially available kit ( quanti -chrom alp assay kit ; bioassay systems , hayward , ca , usa ) .
the sample was harvested in a lysis buffer containing 0.1% np 40 and homogenized through three cycles of -70 freezing and 36 thawing .
alp activity was measured according to the manufacturer 's instruction and expressed in terms of relative luminescence unit ( rlu)/mg protein .
protein content was measured with protein assay kit ( biorad , hercules , ca , usa . ) using bovine serum albumin . for alp staining , cells were cultured for 8 days in mineralizing medium , and then fixed for 30 seconds in 4% formaldehyde , washed three times with pbs , and stained with alp kit ( sigma , st .
to compare the relative toxicity caused by magne - tofection , 3-(4,5-dimethylthiazol-2-yl)-2.5-dipheny - ltetrazoliumbromide ( mtt ) assay was utilized .
bmscs were seeded into the 96-well plate ( 110 cells / well/100 l media ) , and magnetic particle was added 48 hours after seeding .
after 72 hours of incubation , 50 l of mtt ( cell proliferation kit i ; roche molecular biochemicals , mannheim , germany ) was added to each well .
after another 4 hours of incubation at 37 , the supernatant of the plate was removed , and 150 l dimethylsulfoxide ( dmso ) was added to the cell monolayer .
the statistical difference between groups was analyzed with anova using spss program ( version 10 ; spss inc . ,
the staining result showed that galactosidase expression increased significantly with the increased viral titer of adlacz , and that there were definitively more staining positive cells in the magnetofection group.(fig .
a ) when the efficiency of adlacz transduction was calculated by stained cells per microscopic field , magnetofection revealed at least 400 times ' higher efficiency compared to conventional adenoviral transduction.(fig .
b ) the efficiency of the adlacz transdu - ction with 200 moi was dependent on the increased amount of magnetic particles ( from 1 to 9 l of magnetic nanoparticles ) .
there was no significant difference in the shape or viability of bmsc according to the increased amount of magnetic particles when applied to adlacz transduction.(fig .
2 ) the time course of bmp2 or 7 secretion after conventional adenoviral transduction vs. adenoviral magnetofection was investigated .
adbmp2 20 moi showed significantly ( 2.8 fold ) higher bmp2 secretion compared to bmsc . only 1 moi of adbmp2 , a suboptimal level for bmp2 induction , did not enhance bmp2 secretion .
note , however , that magnetofection with 1 moi of adbmp2 induced 7.2-fold higher bmp2 protein secretion compared to bmsc control or 1 moi of the adbmp2 transduction group .
this difference was highest at 3 days , slowly decreasing over time until 7 days after the transduction.(fig .
3 ) the bmp7 protein secretion in conditioned media of bmsc was examined using a method similar to bmp2 elisa . at day 3 , bmp7 was secreted by 6.7-fold when 1 moi of adbmp7 was transduced with magnetofection ; on the other hand , 20 moi of conventional adbmp7 increased secretion by 5.2-fold compared to the control ( all p<0.05 ) .
such magnetofection dramatically increased bmp7 secretion by 10-fold compared to the control until 7 days of the transduction . despite the decrease in cell viability over time after the magnetofection , the resultant bmp-2 or 7 expression remained at a high level until 7 days after the transduction with magnetofection in both adbmp2 and 7.(fig .
4 ) to measure the alp activity , bmscs were harvested 1 , 3 , and 7 days after transduction .
values were expressed as fold changes relative to untreated bmsc cells compared to the alp activity on the 1st day . on day 7 of transudation , adbmp2 adenoviral magnetofection showed 2.4-fold and 1.8-fold higher alp activity than non - transduced bmsc and conventional adbmp2 ( 1 moi)-transduced bmsc.(fig .
a ) bmscs transduced with the respective adenoviral vectors were cultured with osteogenic medium containing -glycerol phosphate and ascorbic acid and stained .
increased mineralization activity was noted at the alp staining in adenoviral magnetofection compared to the control.(fig .
b ) cell viability was accessed through the comparison of relative toxicity caused by magnetofection .
cytotoxicity was ob served when high dose ( 10 l ) of magnetic nanoparticle was applied with adbmp2 virus.(fig .
a ) this was not the case with the adlacz viral transduction given high dose of ma gnetic nanoparticle as shown in fig .
2 . the use of 2 l of magnetic nanoparticle for adlacz viral transduction did not show significantly increased cell apoptosis compared to conventional adenoviral transduction ( p>0.05).(fig . 6 .
the staining result showed that galactosidase expression increased significantly with the increased viral titer of adlacz , and that there were definitively more staining positive cells in the magnetofection group.(fig .
a ) when the efficiency of adlacz transduction was calculated by stained cells per microscopic field , magnetofection revealed at least 400 times ' higher efficiency compared to conventional adenoviral transduction.(fig .
b ) the efficiency of the adlacz transdu - ction with 200 moi was dependent on the increased amount of magnetic particles ( from 1 to 9 l of magnetic nanoparticles ) .
there was no significant difference in the shape or viability of bmsc according to the increased amount of magnetic particles when applied to adlacz transduction.(fig .
the time course of bmp2 or 7 secretion after conventional adenoviral transduction vs. adenoviral magnetofection was investigated .
adbmp2 20 moi showed significantly ( 2.8 fold ) higher bmp2 secretion compared to bmsc . only 1 moi of adbmp2 , a suboptimal level for bmp2 induction , did not enhance bmp2 secretion .
note , however , that magnetofection with 1 moi of adbmp2 induced 7.2-fold higher bmp2 protein secretion compared to bmsc control or 1 moi of the adbmp2 transduction group .
this difference was highest at 3 days , slowly decreasing over time until 7 days after the transduction.(fig .
3 ) the bmp7 protein secretion in conditioned media of bmsc was examined using a method similar to bmp2 elisa . at day 3 , bmp7 was secreted by 6.7-fold when 1 moi of adbmp7 was transduced with magnetofection ; on the other hand , 20 moi of conventional adbmp7 increased secretion by 5.2-fold compared to the control ( all p<0.05 ) .
such magnetofection dramatically increased bmp7 secretion by 10-fold compared to the control until 7 days of the transduction . despite the decrease in cell viability over time after the magnetofection , the resultant bmp-2 or 7 expression remained at a high level until 7 days after the transduction with magnetofection in both adbmp2 and 7.(fig .
to measure the alp activity , bmscs were harvested 1 , 3 , and 7 days after transduction .
values were expressed as fold changes relative to untreated bmsc cells compared to the alp activity on the 1st day . on day 7 of transudation , adbmp2 adenoviral magnetofection showed 2.4-fold and 1.8-fold higher alp activity than non - transduced bmsc and conventional adbmp2 ( 1 moi)-transduced bmsc.(fig .
a ) bmscs transduced with the respective adenoviral vectors were cultured with osteogenic medium containing -glycerol phosphate and ascorbic acid and stained .
increased mineralization activity was noted at the alp staining in adenoviral magnetofection compared to the control.(fig .
cytotoxicity was ob served when high dose ( 10 l ) of magnetic nanoparticle was applied with adbmp2 virus.(fig .
a ) this was not the case with the adlacz viral transduction given high dose of ma gnetic nanoparticle as shown in fig .
2 . the use of 2 l of magnetic nanoparticle for adlacz viral transduction did not show significantly increased cell apoptosis compared to conventional adenoviral transduction ( p>0.05).(fig . 6 .
acceleration of the osteogenic induction of bmsc can be achieved by the transduction of the cells to express proteins that enable differentiation of bmsc lineage to osteoblast . even though bmps had been widely used for bone regeneration in various clinical and experimental settings , problems of short half - life and difficulty in continuous protein delivery system remain17 . moreover
, large and single amount of bmp2 or 7 administrations can be accumulated in organs that were not targeted at the time of administration ; this can result in unwanted bone formation in kidneys or liver .
therefore , another system needs to be considered for continuous gene delivery . for this purpose
, the adenoviral gene delivery system has a definitive advantage in ex vivo or in vivo gene therapy since the adenovirus does not integrate into the host genomic dna ; there is also a low likelihood of malignant transformation of host cells18 .
adenoviruses containing bmp2 or 7 cdna under the control of acmv promoter adbmp2 and 7 can reportedly be used for gene therapy for bone regeneration19 .
note , however , that a serious side effect from the host immune reaction against the clinical application of adenovirus had been reported previously20 - 22 .
moreover , there is limitation in the application of suboptimal dose of adenoviral transduction if the target cell surface is deficient in coxakie - adenovirus receptor ( car)23 .
high efficiency ( > 90% ) of adenovirus transduction and consistent level of car expression in human marrow stromal cells24 as well as definitively higher gene expression level compared to conventional liposomal transfection had been reported .
the transduction efficiency of bmsc and other mesenchymal cells is lower compared to other cell lines .
for example , a previous study reported that adlacz at 250 - 500 pfu / cell showed transduction efficiency of 30 - 40%17 .
magnetic particle - associated adenoviral gene delivery had been introduced to enhance the efficiency of gene expression but minimize the associated risk by reducing the viral dose25 . according to krtz et al.6 ,
the increased effectiveness of magnetofection could be attributed to an increased concentration of pdna or viral particle / magnetic complexes at the outer cellular membrane .
adenovirus solutions are mixed with magnetic nanoparticle and usually incubated for 20 minutes at room temperature .
the negatively charged electrokinetic viral particles in aqueous media assemble with cationic polymer such as polyethyleneimine , a major component of the outer coating of magnetic nanoparticle core26 .
7 ) when the magnetic field is applied to magnetic nanoparticle - adenovirus complex , the transduction efficiency dramatically increased as also shown in our experiments .
definitive adenoviral transduction can reportedly be performed even on cells without car , which does not allow the penetration of adenovirus27 .
the results of this study showed no significant cell apoptosis even with high amount ( 10 l ) of magnetic nanoparticles with adlacz .
similarly , human umbilical vein endothelial cells showed that , although the 10 l of magnetic particle treatment showed increased cytotoxicity compared to 1 l , viability was maintained at above 85% level at optimal viral titer28 . when high adenoviral titer of adbmp2 ( 200 moi ) and high dose of magnetic particles were applied , however
magnetic particles of 2 l did not induce significant cell apoptosis in the adbmp2 adenoviral transduction .
this suggests that optimizing the transduction efficiency with relative low cytotoxicity would be possible , but it would differ according to the type of adenoviral gene . therefore , the optimal value of magnetic nanoparticles for mouse bmsc primary culture cells needs to be investigated based on the type of gene .
our result showed that adenoviral magnetofection induced continuously high gene expression until 6 days after the transduction of adbmp2 or 7 .
bmp2 secretion was dramatically accelerated by up to 7.2-fold compared to non - transduced bmsc or minimal dose ( 1 moi ) of conventional adbmp2-transduced bmsc .
adbmp7 adenoviral magnetofection also showed dramatically increased bmp7 secretion by up to 10-fold compared to the control until 7 days of the transduction .
clearly , a minimal amount of viral particles can be potentiated by the magnetic nanoparticle - induced gene expression system .
this result implies that magnetofection can be used for the optimal system for gene therapy for bone regeneration .
the magnetic nanoparticle - induced transduction or transfection is now widely accepted even for induced pluripotent stem ( ips ) cells resembling embryonic stem cells29 .
since the ips cell needs strong expression of the four defined transcription factors - oct3/4 , klf4 , sox2 , and c - myc - viral vector was the method of choice in a previous report30 .
now , magnetofection can be one of the methods of choice that circumvent the disadvantage of viral transduction31 .
a recent animal experiment had shown targeted vascular endothelial growth factor ( vegf ) gene delivery by using magnetic nanoparticle - adenoviral vectors and revealed enhanced cardiac regeneration in the targeted region29 . since the isolation of the magnetic cell separation was also applied to in vitro and in vivo settings , magnetofection can be a safe and promising strategy for gene therapy27 that can be applied to bone regeneration .
note , however , that potentiated protein secretion with viral vector at much lower dose of viral particles does not directly mean zero toxicity and immunologic response in humans .
the results of this study showed that magnetic particle - mediated gene transudation is a highly efficient method of gene delivery to bmsc , outweighing the problem of toxicity of magnetofection .
these results also suggest that magnetofection can reduce the effective minimal amount of adbmps for bone regeneration .
the magnetic particle - mediated gene transduction is a highly efficient method of gene delivery to bmsc .
magnetofection can lower the amount of viral particles ( moi ) while improving efficacy of gene delivery .
this advantageous effect can be useful in preventing adenovirus inactivation and minimizing immune response in gene therapy . | objectivesthis study investigated the question of whether adenoviral magnetofection can be a suitable method for increasing the efficacy of gene delivery into bone marrow stromal cell ( bmsc ) and for generation of a high level of bone morphogenic protein ( bmp ) secretion at a minimized viral titer.materials and methodsprimary bmscs were isolated from c57bl6 mice and transduced with adenoviral vectors encoding galactosidase or bmp2 and bmp7 .
the level of bmp secretion , activity of osteoblast differentiation , and cell viability of magnetofection were measured and compared with those of the control group.resultsthe expression level of galactosidase showed that the cell transduction efficiency of adlacz increased according to the increased amount of magnetic nanoparticles .
no change in cell viability was observed after magnetofection with 2 l of magnetic nanoparticle .
secretion of bmp2 or bmp7 was accelerated after transduction of adbmp2 and 7 with magnetofection .
adbmp2 adenoviral magnetofection resulted in up to 7.2-fold higher secretion of bmp2 , compared with conventional adbmp2-transduced bmscs .
magnetofection also induced a dramatic increase in secretion of bmp7 by up to 10-fold compared to the control .
use of only 1 multiplicity of infection ( moi ) of magnetofection with adenoviral transduction of adbmp2 or adbmp7 resulted in significantly higher transgene expression compared to 20 moi of conventional adenoviral transduction.conclusionmagnetic particle - mediated gene transudation is a highly efficient method of gene delivery to bmscs .
magnetofection can lower the amount of viral particles while improving the efficacy of gene delivery . | <s>[INST]stromal cells isolated from fresh bone marrow aspirates have multilineage potential that can differentiate into a variety of cell populations1 .
note , however , that the optimization of gene delivery to bone marrow stromal cells ( bmscs ) from mammalian cells had limited efficiencies .
recently , gene delivery by polyethylenimine - conjugated supraparamagnetic nano - particle under a magnetic field - so - called magnetofection - was introduced .
scherer et al.2 and plank et al.3 first reported that the application of magnetic nanoparticles to gene vectors to various cells showed significantly enhanced uptake of these vectors and subsequent high target protein expression .
the magnetic force applied on gene vector - magnetic particle complex can increase the accumulation of these complexes on the surface of the various cells . in particular , cell lines that have only limited efficiencies with regard to target gene expression , such as human endothelial cells , can be successfully managed by magnetofection4 - 6 .
note , however , that there had been few attempts to apply magnetofection to enhanced gene delivery for bmsc .
bone morphogenic protein 2 ( bmp2 ) gene transfer by transfection of bmp2-cdna to bmsc can be differentiated into osteoprogenitor cells , affecting the neighboring cells by paracrine pathway to potentiate the regeneration of various types of bone defects7,8 .
bmp7 was also reported as a potent osteogenic mediator8 . to accelerate gene expression , various gene delivery systems with high transfection efficiency
although there had been advances in gene transfer using non - viral vectors , efficiency of gene transfer is reported to be approximately 10 compared to adenoviral vectors8 .
since enhanced transfection efficiency is key to investigating the function of gene and protein , the viral gene transfer method had been proposed as a good method for gene overexpression .
different bmp2 gene therapy approaches to bone regeneration have been studied , and viral vectors such as adenoviruses11 - 13 and retroviruses14 as carriers of bmp2 cdna had been used .
nonetheless , immunogenicity of viral capsid protein is a major problem ; exposure of cell to virus for a long period of time or at higher doses is toxic for several tissues and cells ; hence the need for a method of potentiating viral transduction to the target cell at low multiplicity of infection ( moi ) to minimize the side effects16 .
this study sought to investigate whether adenoviral magnetofection can be a suitable method for increasing the efficacy of gene delivery into bmsc . as far as we know , this is the first trial of osteogenic induction of bmsc using adenoviral magnetofection .
primary mouse bmsc were isolated from the tibia and femur of 8 - 10-week - old c57bl6 mice .
mice were sacrificed by cervical dislocation , both ends of the bilateral tibia and femur were snipped off , and bone marrow was flushed out with dulbecco 's modified eagle 's medium ( dmem ; gibco , grand island , ny , usa ) containing 10% fetal bovine serum ( fbs ) and antibiotics ( penicillin 100 u / ml , streptomycin 100 g/l ) .
the single cell suspension of bone marrow was collected by several repetitions of drawing the cells into a syringe .
the cells were seeded on a 100 mm dish , and non - adherent cells were removed by changing the media ( dmem with 10% fbs ) for three consecutive days .
these cells of the first passage culture were then re - plated prior to confluence .
the culture media was replaced every 2 days and cultured up to 4 weeks . for the experiments of the study , the cells at passage 3 were used for in vitro viral transduction and in vivo animal experiments .
the e1-deleted adenoviral vector containing human bmp2 or bmp7 cdna - which constitutively expresses bmp2 or bmp7 , respectively , under the control of the cmv promoter - was propagated in 293a cells .
viral lysates were then expanded and purified using the adeno - x virus purification kit ( clontech , mountain view , ca , usa ) and titrated with the adeno - x rapid titer kit ( clontech ) .
bmscs were plated in 24-well plates ( in vitro study ) or 10 cm culture dish ( in vivo study ) at a density of 35,000 cells / cm on the day before transduction . for the in vitro adenoviral transduction of bmsc , adenovirus ( adbmp-2 , -7 , adlacz ) at the desired titer
was added to cells in 500 l of serum - free dmem and incubated for 6 hours .
after 24 hours , the media were then changed to dmem with 10% fbs and ascorbic acid ( 50 g / ml ) and -glycerol phosphate ( 5 mm ) to enhance osteoblastic differentiation and were replaced every two days . for adenoviral
transduction with magnetofection , adbmp-2 , -7 and lacz were diluted with dmem to establish the desired titer and mixed with 2 l of magnetic particle ( magnetofectin , combimac ; chemicell gmbh , berlin , germany ) indicated otherwise .
the mixture was incubated for 20 minutes at room temperature and added dropwise to the cells .
the cell culture plate was placed upon a magnetic plate ( magnetofactor-24 plate ; chemicell gmbh ) for 30 minutes .
two days after transduction , the expression of galactosidase ( number of blue nuclei / field ) according to the varying amount of magnetic nanoparticles and viral particles was evaluated with x - gal staining kit ( oz bioscience , marseille , france ) based on the manufacturer protocol .
the dependence on moi at different magnetic nanoparticles 48 hours after magnetofection was also assessed .
the efficiency of gene transfer with adenoviral magnetofection was compared with that of conventional adenoviral transduction .
bmp2 and 7 proteins secreted into conditioned media at the indicated time points were measured after adenoviral transduction or adenoviral magnetofection with adbmp-2 , 7 or lacz , using commercially available elisa kit ( quantikine ; r&d systems , minneapolis , mn , usa ) .
the conditioned media were prepared by culturing cells in serum - free medium for 24 hours .
alkaline phosphatase ( alp ) activity measured in cell layers was evaluated with p - nitrophenyl phosphate substrate included in a commercially available kit ( quanti -chrom alp assay kit ; bioassay systems , hayward , ca , usa ) .
the sample was harvested in a lysis buffer containing 0.1% np 40 and homogenized through three cycles of -70 freezing and 36 thawing .
alp activity was measured according to the manufacturer 's instruction and expressed in terms of relative luminescence unit ( rlu)/mg protein .
protein content was measured with protein assay kit ( biorad , hercules , ca , usa . ) using bovine serum albumin .
for alp staining , cells were cultured for 8 days in mineralizing medium , and then fixed for 30 seconds in 4% formaldehyde , washed three times with pbs , and stained with alp kit ( sigma , st .
louis , mo , usa ) . to compare the relative toxicity caused by magne - tofection
bmscs were seeded into the 96-well plate ( 110 cells / well/100 l media ) , and magnetic particle was added 48 hours after seeding .
after 72 hours of incubation , 50 l of mtt ( cell proliferation kit i ; roche molecular biochemicals , mannheim , germany ) was added to each well .
after another 4 hours of incubation at 37 , the supernatant of the plate was removed , and 150 l dimethylsulfoxide ( dmso ) was added to the cell monolayer .
the statistical difference between groups was analyzed with anova using spss program ( version 10 ; spss inc . ,
primary mouse bmsc were isolated from the tibia and femur of 8 - 10-week - old c57bl6 mice .
mice were sacrificed by cervical dislocation , both ends of the bilateral tibia and femur were snipped off , and bone marrow was flushed out with dulbecco 's modified eagle 's medium ( dmem ; gibco , grand island , ny , usa ) containing 10% fetal bovine serum ( fbs ) and antibiotics ( penicillin 100 u / ml , streptomycin 100 g/l ) .
the single cell suspension of bone marrow was collected by several repetitions of drawing the cells into a syringe .
the cells were seeded on a 100 mm dish , and non - adherent cells were removed by changing the media ( dmem with 10% fbs ) for three consecutive days .
these cells of the first passage culture were then re - plated prior to confluence .
the culture media was replaced every 2 days and cultured up to 4 weeks . for the experiments of the study , the cells at passage 3 were used for in vitro viral transduction and in vivo animal experiments .
the e1-deleted adenoviral vector containing human bmp2 or bmp7 cdna - which constitutively expresses bmp2 or bmp7 , respectively , under the control of the cmv promoter - was propagated in 293a cells .
viral lysates were then expanded and purified using the adeno - x virus purification kit ( clontech , mountain view , ca , usa ) and titrated with the adeno - x rapid titer kit ( clontech ) .
bmscs were plated in 24-well plates ( in vitro study ) or 10 cm culture dish ( in vivo study ) at a density of 35,000 cells / cm on the day before transduction . for the in vitro adenoviral transduction of bmsc , adenovirus ( adbmp-2 , -7 , adlacz ) at the desired titer
was added to cells in 500 l of serum - free dmem and incubated for 6 hours .
after 24 hours , the media were then changed to dmem with 10% fbs and ascorbic acid ( 50 g / ml ) and -glycerol phosphate ( 5 mm ) to enhance osteoblastic differentiation and were replaced every two days .
for adenoviral transduction with magnetofection , adbmp-2 , -7 and lacz were diluted with dmem to establish the desired titer and mixed with 2 l of magnetic particle ( magnetofectin , combimac ; chemicell gmbh , berlin , germany ) indicated otherwise .
the mixture was incubated for 20 minutes at room temperature and added dropwise to the cells .
the cell culture plate was placed upon a magnetic plate ( magnetofactor-24 plate ; chemicell gmbh ) for 30 minutes .
two days after transduction , the expression of galactosidase ( number of blue nuclei / field ) according to the varying amount of magnetic nanoparticles and viral particles was evaluated with x - gal staining kit ( oz bioscience , marseille , france ) based on the manufacturer protocol .
the dependence on moi at different magnetic nanoparticles 48 hours after magnetofection was also assessed .
the efficiency of gene transfer with adenoviral magnetofection was compared with that of conventional adenoviral transduction .
bmp2 and 7 proteins secreted into conditioned media at the indicated time points were measured after adenoviral transduction or adenoviral magnetofection with adbmp-2 , 7 or lacz , using commercially available elisa kit ( quantikine ; r&d systems , minneapolis , mn , usa ) .
the conditioned media were prepared by culturing cells in serum - free medium for 24 hours .
alkaline phosphatase ( alp ) activity measured in cell layers was evaluated with p - nitrophenyl phosphate substrate included in a commercially available kit ( quanti -chrom alp assay kit ; bioassay systems , hayward , ca , usa ) .
the sample was harvested in a lysis buffer containing 0.1% np 40 and homogenized through three cycles of -70 freezing and 36 thawing .
alp activity was measured according to the manufacturer 's instruction and expressed in terms of relative luminescence unit ( rlu)/mg protein .
protein content was measured with protein assay kit ( biorad , hercules , ca , usa . ) using bovine serum albumin . for alp staining , cells were cultured for 8 days in mineralizing medium , and then fixed for 30 seconds in 4% formaldehyde , washed three times with pbs , and stained with alp kit ( sigma , st .
to compare the relative toxicity caused by magne - tofection , 3-(4,5-dimethylthiazol-2-yl)-2.5-dipheny - ltetrazoliumbromide ( mtt ) assay was utilized .
bmscs were seeded into the 96-well plate ( 110 cells / well/100 l media ) , and magnetic particle was added 48 hours after seeding .
after 72 hours of incubation , 50 l of mtt ( cell proliferation kit i ; roche molecular biochemicals , mannheim , germany ) was added to each well .
after another 4 hours of incubation at 37 , the supernatant of the plate was removed , and 150 l dimethylsulfoxide ( dmso ) was added to the cell monolayer .
the statistical difference between groups was analyzed with anova using spss program ( version 10 ; spss inc . ,
the staining result showed that galactosidase expression increased significantly with the increased viral titer of adlacz , and that there were definitively more staining positive cells in the magnetofection group.(fig .
a ) when the efficiency of adlacz transduction was calculated by stained cells per microscopic field , magnetofection revealed at least 400 times ' higher efficiency compared to conventional adenoviral transduction.(fig .
b ) the efficiency of the adlacz transdu - ction with 200 moi was dependent on the increased amount of magnetic particles ( from 1 to 9 l of magnetic nanoparticles ) .
there was no significant difference in the shape or viability of bmsc according to the increased amount of magnetic particles when applied to adlacz transduction.(fig .
2 ) the time course of bmp2 or 7 secretion after conventional adenoviral transduction vs. adenoviral magnetofection was investigated .
adbmp2 20 moi showed significantly ( 2.8 fold ) higher bmp2 secretion compared to bmsc . only 1 moi of adbmp2 , a suboptimal level for bmp2 induction , did not enhance bmp2 secretion .
note , however , that magnetofection with 1 moi of adbmp2 induced 7.2-fold higher bmp2 protein secretion compared to bmsc control or 1 moi of the adbmp2 transduction group .
this difference was highest at 3 days , slowly decreasing over time until 7 days after the transduction.(fig .
3 ) the bmp7 protein secretion in conditioned media of bmsc was examined using a method similar to bmp2 elisa . at day 3 , bmp7 was secreted by 6.7-fold when 1 moi of adbmp7 was transduced with magnetofection ; on the other hand , 20 moi of conventional adbmp7 increased secretion by 5.2-fold compared to the control ( all p<0.05 ) .
such magnetofection dramatically increased bmp7 secretion by 10-fold compared to the control until 7 days of the transduction . despite the decrease in cell viability over time after the magnetofection , the resultant bmp-2 or 7 expression remained at a high level until 7 days after the transduction with magnetofection in both adbmp2 and 7.(fig .
4 ) to measure the alp activity , bmscs were harvested 1 , 3 , and 7 days after transduction .
values were expressed as fold changes relative to untreated bmsc cells compared to the alp activity on the 1st day . on day 7 of transudation , adbmp2 adenoviral magnetofection showed 2.4-fold and 1.8-fold higher alp activity than non - transduced bmsc and conventional adbmp2 ( 1 moi)-transduced bmsc.(fig .
a ) bmscs transduced with the respective adenoviral vectors were cultured with osteogenic medium containing -glycerol phosphate and ascorbic acid and stained .
increased mineralization activity was noted at the alp staining in adenoviral magnetofection compared to the control.(fig .
b ) cell viability was accessed through the comparison of relative toxicity caused by magnetofection .
cytotoxicity was ob served when high dose ( 10 l ) of magnetic nanoparticle was applied with adbmp2 virus.(fig .
a ) this was not the case with the adlacz viral transduction given high dose of ma gnetic nanoparticle as shown in fig .
2 . the use of 2 l of magnetic nanoparticle for adlacz viral transduction did not show significantly increased cell apoptosis compared to conventional adenoviral transduction ( p>0.05).(fig . 6 .
the staining result showed that galactosidase expression increased significantly with the increased viral titer of adlacz , and that there were definitively more staining positive cells in the magnetofection group.(fig .
a ) when the efficiency of adlacz transduction was calculated by stained cells per microscopic field , magnetofection revealed at least 400 times ' higher efficiency compared to conventional adenoviral transduction.(fig .
b ) the efficiency of the adlacz transdu - ction with 200 moi was dependent on the increased amount of magnetic particles ( from 1 to 9 l of magnetic nanoparticles ) .
there was no significant difference in the shape or viability of bmsc according to the increased amount of magnetic particles when applied to adlacz transduction.(fig .
the time course of bmp2 or 7 secretion after conventional adenoviral transduction vs. adenoviral magnetofection was investigated .
adbmp2 20 moi showed significantly ( 2.8 fold ) higher bmp2 secretion compared to bmsc . only 1 moi of adbmp2 , a suboptimal level for bmp2 induction , did not enhance bmp2 secretion .
note , however , that magnetofection with 1 moi of adbmp2 induced 7.2-fold higher bmp2 protein secretion compared to bmsc control or 1 moi of the adbmp2 transduction group .
this difference was highest at 3 days , slowly decreasing over time until 7 days after the transduction.(fig .
3 ) the bmp7 protein secretion in conditioned media of bmsc was examined using a method similar to bmp2 elisa . at day 3 , bmp7 was secreted by 6.7-fold when 1 moi of adbmp7 was transduced with magnetofection ; on the other hand , 20 moi of conventional adbmp7 increased secretion by 5.2-fold compared to the control ( all p<0.05 ) .
such magnetofection dramatically increased bmp7 secretion by 10-fold compared to the control until 7 days of the transduction . despite the decrease in cell viability over time after the magnetofection , the resultant bmp-2 or 7 expression remained at a high level until 7 days after the transduction with magnetofection in both adbmp2 and 7.(fig .
to measure the alp activity , bmscs were harvested 1 , 3 , and 7 days after transduction .
values were expressed as fold changes relative to untreated bmsc cells compared to the alp activity on the 1st day . on day 7 of transudation , adbmp2 adenoviral magnetofection showed 2.4-fold and 1.8-fold higher alp activity than non - transduced bmsc and conventional adbmp2 ( 1 moi)-transduced bmsc.(fig .
a ) bmscs transduced with the respective adenoviral vectors were cultured with osteogenic medium containing -glycerol phosphate and ascorbic acid and stained .
increased mineralization activity was noted at the alp staining in adenoviral magnetofection compared to the control.(fig .
cytotoxicity was ob served when high dose ( 10 l ) of magnetic nanoparticle was applied with adbmp2 virus.(fig .
a ) this was not the case with the adlacz viral transduction given high dose of ma gnetic nanoparticle as shown in fig .
2 . the use of 2 l of magnetic nanoparticle for adlacz viral transduction did not show significantly increased cell apoptosis compared to conventional adenoviral transduction ( p>0.05).(fig . 6 .
acceleration of the osteogenic induction of bmsc can be achieved by the transduction of the cells to express proteins that enable differentiation of bmsc lineage to osteoblast . even though bmps had been widely used for bone regeneration in various clinical and experimental settings , problems of short half - life and difficulty in continuous protein delivery system remain17 . moreover
, large and single amount of bmp2 or 7 administrations can be accumulated in organs that were not targeted at the time of administration ; this can result in unwanted bone formation in kidneys or liver .
therefore , another system needs to be considered for continuous gene delivery . for this purpose
, the adenoviral gene delivery system has a definitive advantage in ex vivo or in vivo gene therapy since the adenovirus does not integrate into the host genomic dna ; there is also a low likelihood of malignant transformation of host cells18 .
adenoviruses containing bmp2 or 7 cdna under the control of acmv promoter adbmp2 and 7 can reportedly be used for gene therapy for bone regeneration19 .
note , however , that a serious side effect from the host immune reaction against the clinical application of adenovirus had been reported previously20 - 22 .
moreover , there is limitation in the application of suboptimal dose of adenoviral transduction if the target cell surface is deficient in coxakie - adenovirus receptor ( car)23 .
high efficiency ( > 90% ) of adenovirus transduction and consistent level of car expression in human marrow stromal cells24 as well as definitively higher gene expression level compared to conventional liposomal transfection had been reported .
the transduction efficiency of bmsc and other mesenchymal cells is lower compared to other cell lines .
for example , a previous study reported that adlacz at 250 - 500 pfu / cell showed transduction efficiency of 30 - 40%17 .
magnetic particle - associated adenoviral gene delivery had been introduced to enhance the efficiency of gene expression but minimize the associated risk by reducing the viral dose25 . according to krtz et al.6 ,
the increased effectiveness of magnetofection could be attributed to an increased concentration of pdna or viral particle / magnetic complexes at the outer cellular membrane .
adenovirus solutions are mixed with magnetic nanoparticle and usually incubated for 20 minutes at room temperature .
the negatively charged electrokinetic viral particles in aqueous media assemble with cationic polymer such as polyethyleneimine , a major component of the outer coating of magnetic nanoparticle core26 .
7 ) when the magnetic field is applied to magnetic nanoparticle - adenovirus complex , the transduction efficiency dramatically increased as also shown in our experiments .
definitive adenoviral transduction can reportedly be performed even on cells without car , which does not allow the penetration of adenovirus27 .
the results of this study showed no significant cell apoptosis even with high amount ( 10 l ) of magnetic nanoparticles with adlacz .
similarly , human umbilical vein endothelial cells showed that , although the 10 l of magnetic particle treatment showed increased cytotoxicity compared to 1 l , viability was maintained at above 85% level at optimal viral titer28 . when high adenoviral titer of adbmp2 ( 200 moi ) and high dose of magnetic particles were applied , however
magnetic particles of 2 l did not induce significant cell apoptosis in the adbmp2 adenoviral transduction .
this suggests that optimizing the transduction efficiency with relative low cytotoxicity would be possible , but it would differ according to the type of adenoviral gene . therefore , the optimal value of magnetic nanoparticles for mouse bmsc primary culture cells needs to be investigated based on the type of gene .
our result showed that adenoviral magnetofection induced continuously high gene expression until 6 days after the transduction of adbmp2 or 7 .
bmp2 secretion was dramatically accelerated by up to 7.2-fold compared to non - transduced bmsc or minimal dose ( 1 moi ) of conventional adbmp2-transduced bmsc .
adbmp7 adenoviral magnetofection also showed dramatically increased bmp7 secretion by up to 10-fold compared to the control until 7 days of the transduction .
clearly , a minimal amount of viral particles can be potentiated by the magnetic nanoparticle - induced gene expression system .
this result implies that magnetofection can be used for the optimal system for gene therapy for bone regeneration .
the magnetic nanoparticle - induced transduction or transfection is now widely accepted even for induced pluripotent stem ( ips ) cells resembling embryonic stem cells29 .
since the ips cell needs strong expression of the four defined transcription factors - oct3/4 , klf4 , sox2 , and c - myc - viral vector was the method of choice in a previous report30 .
now , magnetofection can be one of the methods of choice that circumvent the disadvantage of viral transduction31 .
a recent animal experiment had shown targeted vascular endothelial growth factor ( vegf ) gene delivery by using magnetic nanoparticle - adenoviral vectors and revealed enhanced cardiac regeneration in the targeted region29 . since the isolation of the magnetic cell separation was also applied to in vitro and in vivo settings , magnetofection can be a safe and promising strategy for gene therapy27 that can be applied to bone regeneration .
note , however , that potentiated protein secretion with viral vector at much lower dose of viral particles does not directly mean zero toxicity and immunologic response in humans .
the results of this study showed that magnetic particle - mediated gene transudation is a highly efficient method of gene delivery to bmsc , outweighing the problem of toxicity of magnetofection .
these results also suggest that magnetofection can reduce the effective minimal amount of adbmps for bone regeneration .
the magnetic particle - mediated gene transduction is a highly efficient method of gene delivery to bmsc .
magnetofection can lower the amount of viral particles ( moi ) while improving efficacy of gene delivery .
this advantageous effect can be useful in preventing adenovirus inactivation and minimizing immune response in gene therapy .[/INST]objectivesthis study investigated the question of whether adenoviral magnetofection can be a suitable method for increasing the efficacy of gene delivery into bone marrow stromal cell ( bmsc ) and for generation of a high level of bone morphogenic protein ( bmp ) secretion at a minimized viral titer.materials and methodsprimary bmscs were isolated from c57bl6 mice and transduced with adenoviral vectors encoding galactosidase or bmp2 and bmp7 .
the level of bmp secretion , activity of osteoblast differentiation , and cell viability of magnetofection were measured and compared with those of the control group.resultsthe expression level of galactosidase showed that the cell transduction efficiency of adlacz increased according to the increased amount of magnetic nanoparticles .
no change in cell viability was observed after magnetofection with 2 l of magnetic nanoparticle .
secretion of bmp2 or bmp7 was accelerated after transduction of adbmp2 and 7 with magnetofection .
adbmp2 adenoviral magnetofection resulted in up to 7.2-fold higher secretion of bmp2 , compared with conventional adbmp2-transduced bmscs .
magnetofection also induced a dramatic increase in secretion of bmp7 by up to 10-fold compared to the control .
use of only 1 multiplicity of infection ( moi ) of magnetofection with adenoviral transduction of adbmp2 or adbmp7 resulted in significantly higher transgene expression compared to 20 moi of conventional adenoviral transduction.conclusionmagnetic particle - mediated gene transudation is a highly efficient method of gene delivery to bmscs .
magnetofection can lower the amount of viral particles while improving the efficacy of gene delivery .</s> |
recently , the study of complex systems has gained significant attention .
one of the basic aspects of this progress is related with the understanding of correlations in and between such complex systems , which is realized through the use of different complexity measures . among these
, one can mention the transinformation @xcite , the block entropies @xcite different types of correlation functions @xcite and number - theoretic notions @xcite .
one of the paradigms of complex systems is the logistic map .
the logistic map has a simple definition but presents complex behavior when fine tuning the control parameter values .
in particular , after feigenbaum s work , the period - doubling route to chaos has been fairly understood .
also , connections with the theory of second order phase transitions ( critical phenomena ) have been established and scaling relations have been reported nearby the accumulation point ( also called feigenbaum point ( fp ) ) with and without the presence of external noise .
furthermore , cantorian fractal structures have been revealed in the transition point connecting the physics of the non - chaotic attractor with self - similarity @xcite .
recently also , a direct connection with experimental mathematics has been established , too @xcite . on the other hand , in non - linear physics
, the importance of the study of the correlation function has been realized from the very beginning .
particularly inspiring have been the works of ruelle @xcite , daems and nicolis @xcite , and alonso et al .
@xcite , for the case of resonances of chaotic dynamical systems .
in addition , based on the analogies between the period doubling transition and critical phenomena , h. g. schuster has done a guess on the functional form of the correlation function of the trajectory @xcite . indeed , according to his arguments
the correlation function should follow a power law behaviour . more recently , using the feigenbaum renormalization group transformation it has been shown @xcite that the correlation function of the trajectory in the one dimensional nonlinear dissipative logistic map is made of a family of power laws with a common scaling factor given by the feigenbaum constant @xmath1 . in the present work in order to extract the form of the correlation function of the trajectory we propose some more elaborated arguments , using a different approach which is based on the structure of the symbol - to - symbol correlation function @xcite , that is the correlation function of symbolic dynamics .
after establishing rigorously in a previous work @xcite the detailed form of the symbol - to - symbol correlation function we turn now our attention to the structure of the correlation function of the trajectory . to be more concrete
, taking advantage from the analytic form of the symbol - to symbol correlation function and presenting simple arguments we shall show that one can extract up to a good approximation , that is apart from numerical constants , the detailed structure for the correlation function of the trajectory .
the above investigation is mainly supported by a detailed numerical study which takes into account a large enough statistical sample of the logistic map . in this manner
, we can justify the analytic form of the correlation function of the trajectory from first principles using the metropolis - stein and stein algorithm ( mss algorithm ) , apart from numerical constants , which depend on the detailed functional form of the map .
furthermore , we make an attempt to generalize these results for an arbitrary @xmath2 accumulation point @xcite , for @xmath3 , which correspond to the accumulation points of the bifurcation tree @xcite ( see also figure 1 ) . finally , a general form for the correlation function of the trajectory and that obtained from the symbolic dynamics is also suggested .
we believe that our results will inspire similar investigations on non - unimodal maps and give further insight providing new complexity measures on real experimental time - series .
the paper is organized as follows . in sec .
ii we introduce the logistic map and the definitions of different types of correlation functions that will be used . in sec .
iii we present our careful numerical experimentation for the symbol - to - symbol correlation function and for the correlation function of the trajectory at the ( first ) accumulation point . as it is shown
those functions obey to simple numerical prescriptions , which are explicitly outlined .
in addition , we propose some simple arguments which , up to a good approximation , allow for the justification of the functional form of the correlation function of the trajectory from the symbol - to - symbol correlation function apart from arithmetical constants in a systematic basis .
we then present analogous results and generalizations for the @xmath2 accumulation points . finally , in sec .
iv we draw the main conclusions and discuss future plans .
the logistic map is the archetype of a complex system .
let us elaborate .
we introduce the logistic map in its familiar form @xmath4 where @xmath5 is the control parameter value and @xmath6 denotes the respective iteration of the map . for the logistic map in this form the generating partition
is easily computed , following an argument dating back to the french mathematician gaston julia . to be more specific , for @xmath7
the equation @xmath8 gives c=0.5 , so that the partition of the phase space ( which in this case coincides with the unit interval i=[0,1 ] ) @xmath9=[0,0.5 ] and @xmath10=(0.5,1 ] is a generating one .
notice that according to metropolis et al .
@xcite the information content of the symbolic trajectory is the `` minimum distinguishing information '' .
needless to say , in this representation the logistic map can be viewed as an abstract information generator . -cycles .
it is shown the control parameter values @xmath11 for the first few bifurcation points and the values @xmath12 for the superstable orbits .
the figure has been taken from ref.@xcite.,scaledwidth=60.0% ] in particular , the period doubling route to chaos has been fairly studied and it is by now well understood .
these studies led us to the occurrence of the two feigenbaum constants @xmath13 and @xmath14 which can be defined by an approximate real space renormalization procedure .
especially , the constant @xmath15 is related with the spacing in the control parameter space of the successive values of occurrence of the superstable periodic orbits and can be roughly estimated by the bifurcation diagram @xcite .
if we denote as @xmath16 this set of values , @xmath15 is defined as @xmath17 and for the quadratic map reads @xmath18 moreover , the constant @xmath1 is related to the rescaling of the period doubling functional composition law and its value for the logistic map reads @xmath19 finally , note that the above two constants are not unrelated and a crude approximation gives @xmath20 more accurate relations can be found by more refined renormalization group arguments .
the values of the above two constants depend only on the order of the maximum and have long been studied .
they are thus , for instance , universal for quadratic maps irrespectively of the exact way one writes down the map .
figure 1 presents the control parameter values of the bifurcation points denoted as @xmath21 , @xmath22 , @xmath23 , ... while the corresponding values for the superstable orbits are depicted as @xmath24 , @xmath25 , @xmath26 , ... .
the values of @xmath27 figuring in the definition of the feigenbaum constant @xmath1 are also shown .
note here that feigenbaum and successors have shown that eq.(2 ) , holds if instead of @xmath28 we use @xmath29 . after the above brief introduction of the logistic map and its properties
, we shall next define the ( un - normalized ) correlation function of the trajectory as @xmath30 where the deviation from the real value of the map at the @xmath31 iteration is given by @xmath32 and the corresponding mean value of the map taking into account @xmath33 iterations ( sample ) is denoted by @xmath34 .
also , in direct analogy with the above defined un - normalized correlation function one can also introduce here the normalized correlation function @xmath35 where @xmath36 is the mean standard deviation , which normalizes the statistical data . from the above definitions
follows that @xmath37 ( or equally @xmath38 ) yields another measure for the irregularity of the sequence of iterates @xmath39 , @xmath40 , @xmath41, ... etc .
it tells us how much the deviations of the iterates from their average value , @xmath42 that are m steps apart ( i.e. @xmath43 and @xmath44 ) `` know '' about each other , on the average .
another remark here is that if @xmath45 as @xmath46 then the system does not have the mixing property .
we should here note that the problem of determining the correlation function of an arbitrary dynamical system is intractable in the general case .
this is the reason to resort to other computable observables such as the symbol - to - symbol correlation function @xcite .
thus , in direct analogy with the correlation function of the trajectory one can introduce the un - normalized symbol - to - symbol correlation function as @xmath47 where the corresponding symbolic functional composition is defined by @xmath48 , with the mean value @xmath49 . here , @xmath50 is the real value of the map at the @xmath31 iteration , @xmath33 denotes the size of the statistical sample that we take into account and @xmath51 is the corresponding distance between two symbols in the symbolic sequence that we examine .
in addition , as usual the functional composition @xmath52 takes the values @xmath53=0,1 when @xmath54 or @xmath55 respectively , i.e. it is a step function . , with initial condition @xmath56 .
the first @xmath57 iterations have been eliminated from our statistics in order to exclude transients , and the subsequent @xmath58 iterations have been taken into account for the numerical calculations .
the experimentally determined lyapunov exponent is @xmath59.,scaledwidth=60.0% ] finally , let us also note that one can define a more relevant quantity which is the normalized symbol - to - symbol correlation function @xmath60 where @xmath61 denotes the mean standard deviation obtained from the respective symbolic sequence .
it has been shown @xcite that the normalized symbol - to - symbol correlation function does not depend on the choice of the symbols ( i.e. @xmath9 to 0 and @xmath10 to 1 ) because for binary sequences the correlation functions are unique up to a constant factor , which varies with the choice of these numbers but cancels out via the normalization .
motivated by previous works on correlation functions @xcite , we explore here the properties of the symbol - to - symbol correlation function and the correlation function of the trajectory . in order to cope with the problem of the analytic form of correlation functions we have studied the correlation function numerically . for the logistic map at the feigenbaum point , i.e. @xmath62
, we have calculated both the normalized symbol - to - symbol correlation function ( see eq.(9 ) and figure 2 ) and the correlation function of the trajectory ( see eq.(7 ) and figure 2 ) . to do
that we start each time from the initial point @xmath63 and take a numerical sample consisting of @xmath58 iterations after the elimination of the first @xmath57 iterations ( to avoid transients ) . for reasons of completeness
let us note that we have checked that our results , presented below , pertain if we use a different initial condition in the unit interval e.g. @xmath64 or @xmath65 .
at this point we should remind that exactly at the feigenbaum point the lyapunov exponent , which is defined in general as @xmath66 , strictly vanishes i.e. @xmath67 ( see also table i ) , and we are in the presence of the non - chaotic multifractal attractor .
notice also that the same behaviour of the lyapunov exponent holds for the higher accumulation points . to indicate the behaviour of the map table i presents the numerically calculated lyapunov exponent for every accumulation point ( using eight decimals for the corresponding control parameter ) of the logistic map including and excluding transients from our statistics .
we observe that the lyapunov exponent in each case vanishes , while the transients play no essential role due to the augmented statistics that we use .
( cycle @xmath68 ) and initial condition @xmath56 .
the first @xmath57 iterations have been eliminated from our statistics in order to exclude transients , and the subsequent @xmath58 iterations have been taken into account for the numerical calculations.,scaledwidth=60.0% ] on the other hand , as it has already been mentioned , in a previous work @xcite providing some theoretical arguments from the viewpoint of the symbolic dynamics we have established the structure of the un - normalized symbol - to - symbol correlation function .
these results have also been supported from careful numerical experimentations leading to the compact form @xmath69 where for a given ( fixed ) @xmath70 , @xmath71 , @xmath72 is a constant depending only on @xmath70 , and @xmath73 takes all the values from the set of natural numbers @xmath74 . here , we have also used the fact that any integer @xmath51 can be decomposed in terms of a unique pair of natural numbers @xmath70 , @xmath73 such that @xmath75 .
the same holds for any other form of the correlation function that will be presented in the rest of the paper .
( cycle @xmath76 ) and initial condition @xmath56 .
the first @xmath57 iterations have been eliminated from our statistics in order to exclude transients , and the subsequent @xmath58 iterations have been taken into account for the numerical calculations.,scaledwidth=60.0% ] in @xcite , on the grounds of the metropolis - stein - stein algorithm , we have established a new theorem , namely that @xmath77 as it seems , these are the first few numerically obtained coefficients @xmath78 of eq.(10 ) .
we can extend this procedure to infinity and the above constructive scheme guarantees that this deep algorithmic structure is kept in all scales . from this infinite stratification , the infinite memory of the system at the feigenbaum point is revealed , as this scheme never ends . in the following ,
we proceed by extending our numerical experimentation to the structure of the normalized symbol - to - symbol correlation function taking again into account the first @xmath58 iterations of the logistic map ( this scheme is depicted in figure 2 ) with initial condition @xmath79 .
the corresponding functional structure now reads @xmath80 which has already been established in @xcite .
moreover , proceeding along the same lines one can calculate the correlation function of the trajectory as it is defined in eqs.(6,7 ) . in this manner , it can be easily confirmed numerically that its structure has the following simple form @xmath81 as it can be observed it possesses the known functional form of eq.(10 ) apart from the numerical constants @xmath82 , whereas @xmath83 as @xmath51 becomes large .
therefore , up to now we have established a general form for the correlation function of the trajectory exactly at the @xmath84 point supported from numerical calculations . in the following ,
we shall present some arguments in order to show that the correlation functions of the trajectory and that obtained from the symbolic sequence possesses the same time scales .
this discussion will lead us to a conceptual understanding for the reason that the correlation function of the trajectory ( as it is defined in eq.(6 ) ) contains the same time scales with the symbol - to - symbol correlation function ( see eq.(8 ) ) , that is @xmath85 here for a fixed @xmath71 the coefficients @xmath82 are constants , while @xmath73 takes all the values from the set of natural numbers @xmath86 .
note also that the properties of a single position of the trajectory have already been studied in another context @xcite , where it has been shown that the trajectory exhibits the above mentioned iteration - times property . in the following
, we would like to show that when the symbol - to - symbol correlation function augments , the correlation function of the path is augmented , too , and when the symbol - to - symbol correlation function diminishes , the correlation function of the path diminishes , too . towards this direction ,
let us consider the deviation from the critical value @xmath87 as @xmath88 with @xmath89 , which remains valid for all cases .
as a consequence of the above proposition we can distinguish the following four different cases : a ) a contribution in the symbolic correlation function by two terms @xmath90 ( so @xmath91 ) and @xmath92 ( @xmath93 ) is + 1 and gives a corresponding contribution to the trajectory correlation function of the order of @xmath94 , that is more than 0.25 .
b ) secondly , a contribution in the symbolic correlation function by the terms @xmath95 and @xmath96 is 0 and gives a corresponding contribution to the correlation function of the trajectory of the order of @xmath97 , that is less than 0.25 .
c ) on the other hand , a contribution in the symbolic correlation function by two terms @xmath90 and @xmath96 is 0 and gives a corresponding contribution to the trajectory correlation function of the order of @xmath98 , i.e. of the order of 0.25 .
d ) finally , a contribution in the symbolic correlation function by the terms @xmath95 and @xmath92 is 0 and gives a corresponding contribution to the trajectory correlation function of the order @xmath99 , that is of the order of 0.25 . in order to clarify the meaning of the above approximations
let us consider a specific example with @xmath100 and @xmath101 .
then , we have @xmath102 and @xmath103 .
so , the contribution to the symbolic correlation function is 1 and as a consequence the contribution to the real correlation function is @xmath104 .
thus , from the above it is clear that using such a simple argument one can predict correctly the functional form of the correlation function of the trajectory from the symbolic one .
[ cols="^,^,^,^ " , ] [ table : nonlin ] the first few numerical values of the above coefficients for the correlation function of the symbolic sequence are presented in table ii ( see second row ) .
as one can easily verify after a straightforward numerical computation the same structure is observed for the correlation function of the trajectory , apart from numerical constants @xmath105 , @xmath106 , @xmath107 which depend on the detailed form of the map ( see table iii , third row ) . in the same manner , one can perform the same calculations for the higher accumulation points and find a similar structure for both the correlation function of the trajectory and that obtained from the symbolic sequence .
indeed , in tables ii and iii we extend these considerations to the @xmath108 , @xmath109 , @xmath110 , @xmath111 , @xmath112 , @xmath113 , @xmath114 , @xmath115 and @xmath116 ( see also figures 3,4 ) accumulation points and we present the corresponding coefficients that may appear in the respective correlation function for each cycle . notice that the relevant information about the accumulations points and the corresponding patterns have been found in @xcite . as for the lower cycles both the correlation function of the trajectory and the symbolic one posses the same time scales . to illustrate
the above , figure 3 shows the symbol - to - symbol versus the correlation function of the trajectory for the @xmath117 cycle .
we observe that the correlation function for the trajectory is always larger from the symbolic one .
the latter can also be confirmed by a direct comparison of the coefficients @xmath118 or @xmath119 among the different types of correlations presented in tables ii and iii .
the previous observations also hold for higher accumulation points , e.g. the @xmath120 cycle as shown in figure 4 .
additionally , from the tables ii , iii it is clearly seen that for the same type of correlations the coefficients @xmath118 are increasing for higher accumulation points while some of the constants @xmath121 may coincide .
this is more rare for the correlation function of the trajectory .
as a result of the above studies we can conclude that the suggested general form for the symbol - to - symbol correlation function at the @xmath84 point of the @xmath122 attractor reads @xmath123 where as usual for a given @xmath71 the coefficients @xmath78 , @xmath124 , @xmath125, ... ,@xmath126 are constants depending only on @xmath70 , @xmath51 denotes the number of the accumulation point that we consider and @xmath73 takes all the values from the set of natural numbers @xmath86 .
the corresponding form for the correlation function of the trajectory remains the same apart from numerical constants @xmath105 , @xmath106 , @xmath107 , ... which as it has been mentioned previously they depend on the detailed form of the map .
the correlation function is an important quantity measuring correlations in many branches of physics . obviously , there are also other interesting quantities as for instance the ( conditional ) block - entropies , the transinformation , the kolmogorov - sinai entropy etc
. however , it does provide an important measure of correlations by itself . in the present paper the correlation function of the trajectory at the feigenbaum point
is numerically investigated with careful numerical experimentation . comparing with the symbol - to - symbol correlation function discovered in the literature
theoretically and numerically we observe that it contains the same time scales , that is , it has the same functional form .
this result has been also justified up to a good approximation by presenting simple arguments .
moreover , we have generalized these results for the case of an arbitrary @xmath127 feigenbaum non chaotic multifractal attractor .
finally , we have arrived to an empirical formula summarizing the results .
to recapitulate , we are in position to justify the analytical form of the correlation function of the trajectory from first principles ( the mss algorithm ) and in a systematic way , apart from numerical constants which depend on the detailed functional form of the map .
apart from their mathematical beauty such ideas find important practical applications ranging from precursory signals @xcite to dna sequence analysis @xcite , heart beat rhythms @xcite and linguistics processes . in this manner , it is still an open problem what information one can extract by using such complexity measures in real experimental time - series and the physical explanation of the correlation function of the trajectory and that obtained from the symbolic sequence for a specific problem
. a second path towards this direction would be the generalization of the form of the correlation function for more complex maps as well as non - unimodal maps , see for instance @xcite . | the correlation function of the trajectory exactly at the feigenbaum point of the logistic map is introduced and checked by numerical experiments .
taking advantage of recent closed analytical results on the symbol - to - symbol correlation function of the generating partition , we are in position to justify the deep algorithmic structure of the correlation function apart from numerical constants .
a generalization is given for arbitrary @xmath0 feigenbaum attractors .
+ keywords : correlation function ; symbolic dynamics ; bifurcation points ; feigenbaum attractors ; logistic map . | <s>[INST]recently , the study of complex systems has gained significant attention .
one of the basic aspects of this progress is related with the understanding of correlations in and between such complex systems , which is realized through the use of different complexity measures . among these
, one can mention the transinformation @xcite , the block entropies @xcite different types of correlation functions @xcite and number - theoretic notions @xcite .
one of the paradigms of complex systems is the logistic map .
the logistic map has a simple definition but presents complex behavior when fine tuning the control parameter values .
in particular , after feigenbaum s work , the period - doubling route to chaos has been fairly understood .
also , connections with the theory of second order phase transitions ( critical phenomena ) have been established and scaling relations have been reported nearby the accumulation point ( also called feigenbaum point ( fp ) ) with and without the presence of external noise .
furthermore , cantorian fractal structures have been revealed in the transition point connecting the physics of the non - chaotic attractor with self - similarity @xcite .
recently also , a direct connection with experimental mathematics has been established , too @xcite . on the other hand , in non - linear physics
, the importance of the study of the correlation function has been realized from the very beginning .
particularly inspiring have been the works of ruelle @xcite , daems and nicolis @xcite , and alonso et al .
@xcite , for the case of resonances of chaotic dynamical systems .
in addition , based on the analogies between the period doubling transition and critical phenomena , h. g. schuster has done a guess on the functional form of the correlation function of the trajectory @xcite . indeed , according to his arguments
the correlation function should follow a power law behaviour . more recently , using the feigenbaum renormalization group transformation it has been shown @xcite that the correlation function of the trajectory in the one dimensional nonlinear dissipative logistic map is made of a family of power laws with a common scaling factor given by the feigenbaum constant @xmath1 . in the present work in order to extract the form of the correlation function of the trajectory we propose some more elaborated arguments , using a different approach which is based on the structure of the symbol - to - symbol correlation function @xcite , that is the correlation function of symbolic dynamics .
after establishing rigorously in a previous work @xcite the detailed form of the symbol - to - symbol correlation function we turn now our attention to the structure of the correlation function of the trajectory . to be more concrete
, taking advantage from the analytic form of the symbol - to symbol correlation function and presenting simple arguments we shall show that one can extract up to a good approximation , that is apart from numerical constants , the detailed structure for the correlation function of the trajectory .
the above investigation is mainly supported by a detailed numerical study which takes into account a large enough statistical sample of the logistic map . in this manner
, we can justify the analytic form of the correlation function of the trajectory from first principles using the metropolis - stein and stein algorithm ( mss algorithm ) , apart from numerical constants , which depend on the detailed functional form of the map .
furthermore , we make an attempt to generalize these results for an arbitrary @xmath2 accumulation point @xcite , for @xmath3 , which correspond to the accumulation points of the bifurcation tree @xcite ( see also figure 1 ) . finally , a general form for the correlation function of the trajectory and that obtained from the symbolic dynamics is also suggested .
we believe that our results will inspire similar investigations on non - unimodal maps and give further insight providing new complexity measures on real experimental time - series .
the paper is organized as follows . in sec .
ii we introduce the logistic map and the definitions of different types of correlation functions that will be used . in sec .
iii we present our careful numerical experimentation for the symbol - to - symbol correlation function and for the correlation function of the trajectory at the ( first ) accumulation point . as it is shown
those functions obey to simple numerical prescriptions , which are explicitly outlined .
in addition , we propose some simple arguments which , up to a good approximation , allow for the justification of the functional form of the correlation function of the trajectory from the symbol - to - symbol correlation function apart from arithmetical constants in a systematic basis .
we then present analogous results and generalizations for the @xmath2 accumulation points . finally , in sec .
iv we draw the main conclusions and discuss future plans .
the logistic map is the archetype of a complex system .
let us elaborate .
we introduce the logistic map in its familiar form @xmath4 where @xmath5 is the control parameter value and @xmath6 denotes the respective iteration of the map . for the logistic map in this form the generating partition
is easily computed , following an argument dating back to the french mathematician gaston julia . to be more specific , for @xmath7
the equation @xmath8 gives c=0.5 , so that the partition of the phase space ( which in this case coincides with the unit interval i=[0,1 ] ) @xmath9=[0,0.5 ] and @xmath10=(0.5,1 ] is a generating one .
notice that according to metropolis et al .
@xcite the information content of the symbolic trajectory is the `` minimum distinguishing information '' .
needless to say , in this representation the logistic map can be viewed as an abstract information generator . -cycles .
it is shown the control parameter values @xmath11 for the first few bifurcation points and the values @xmath12 for the superstable orbits .
the figure has been taken from ref.@xcite.,scaledwidth=60.0% ] in particular , the period doubling route to chaos has been fairly studied and it is by now well understood .
these studies led us to the occurrence of the two feigenbaum constants @xmath13 and @xmath14 which can be defined by an approximate real space renormalization procedure .
especially , the constant @xmath15 is related with the spacing in the control parameter space of the successive values of occurrence of the superstable periodic orbits and can be roughly estimated by the bifurcation diagram @xcite .
if we denote as @xmath16 this set of values , @xmath15 is defined as @xmath17 and for the quadratic map reads @xmath18 moreover , the constant @xmath1 is related to the rescaling of the period doubling functional composition law and its value for the logistic map reads @xmath19 finally , note that the above two constants are not unrelated and a crude approximation gives @xmath20 more accurate relations can be found by more refined renormalization group arguments .
the values of the above two constants depend only on the order of the maximum and have long been studied .
they are thus , for instance , universal for quadratic maps irrespectively of the exact way one writes down the map .
figure 1 presents the control parameter values of the bifurcation points denoted as @xmath21 , @xmath22 , @xmath23 , ... while the corresponding values for the superstable orbits are depicted as @xmath24 , @xmath25 , @xmath26 , ... .
the values of @xmath27 figuring in the definition of the feigenbaum constant @xmath1 are also shown .
note here that feigenbaum and successors have shown that eq.(2 ) , holds if instead of @xmath28 we use @xmath29 . after the above brief introduction of the logistic map and its properties
, we shall next define the ( un - normalized ) correlation function of the trajectory as @xmath30 where the deviation from the real value of the map at the @xmath31 iteration is given by @xmath32 and the corresponding mean value of the map taking into account @xmath33 iterations ( sample ) is denoted by @xmath34 .
also , in direct analogy with the above defined un - normalized correlation function one can also introduce here the normalized correlation function @xmath35 where @xmath36 is the mean standard deviation , which normalizes the statistical data . from the above definitions
follows that @xmath37 ( or equally @xmath38 ) yields another measure for the irregularity of the sequence of iterates @xmath39 , @xmath40 , @xmath41, ... etc .
it tells us how much the deviations of the iterates from their average value , @xmath42 that are m steps apart ( i.e. @xmath43 and @xmath44 ) `` know '' about each other , on the average .
another remark here is that if @xmath45 as @xmath46 then the system does not have the mixing property .
we should here note that the problem of determining the correlation function of an arbitrary dynamical system is intractable in the general case .
this is the reason to resort to other computable observables such as the symbol - to - symbol correlation function @xcite .
thus , in direct analogy with the correlation function of the trajectory one can introduce the un - normalized symbol - to - symbol correlation function as @xmath47 where the corresponding symbolic functional composition is defined by @xmath48 , with the mean value @xmath49 . here , @xmath50 is the real value of the map at the @xmath31 iteration , @xmath33 denotes the size of the statistical sample that we take into account and @xmath51 is the corresponding distance between two symbols in the symbolic sequence that we examine .
in addition , as usual the functional composition @xmath52 takes the values @xmath53=0,1 when @xmath54 or @xmath55 respectively , i.e. it is a step function . , with initial condition @xmath56 .
the first @xmath57 iterations have been eliminated from our statistics in order to exclude transients , and the subsequent @xmath58 iterations have been taken into account for the numerical calculations .
the experimentally determined lyapunov exponent is @xmath59.,scaledwidth=60.0% ] finally , let us also note that one can define a more relevant quantity which is the normalized symbol - to - symbol correlation function @xmath60 where @xmath61 denotes the mean standard deviation obtained from the respective symbolic sequence .
it has been shown @xcite that the normalized symbol - to - symbol correlation function does not depend on the choice of the symbols ( i.e. @xmath9 to 0 and @xmath10 to 1 ) because for binary sequences the correlation functions are unique up to a constant factor , which varies with the choice of these numbers but cancels out via the normalization .
motivated by previous works on correlation functions @xcite , we explore here the properties of the symbol - to - symbol correlation function and the correlation function of the trajectory . in order to cope with the problem of the analytic form of correlation functions we have studied the correlation function numerically . for the logistic map at the feigenbaum point , i.e. @xmath62
, we have calculated both the normalized symbol - to - symbol correlation function ( see eq.(9 ) and figure 2 ) and the correlation function of the trajectory ( see eq.(7 ) and figure 2 ) . to do
that we start each time from the initial point @xmath63 and take a numerical sample consisting of @xmath58 iterations after the elimination of the first @xmath57 iterations ( to avoid transients ) . for reasons of completeness
let us note that we have checked that our results , presented below , pertain if we use a different initial condition in the unit interval e.g. @xmath64 or @xmath65 .
at this point we should remind that exactly at the feigenbaum point the lyapunov exponent , which is defined in general as @xmath66 , strictly vanishes i.e. @xmath67 ( see also table i ) , and we are in the presence of the non - chaotic multifractal attractor .
notice also that the same behaviour of the lyapunov exponent holds for the higher accumulation points . to indicate the behaviour of the map table i presents the numerically calculated lyapunov exponent for every accumulation point ( using eight decimals for the corresponding control parameter ) of the logistic map including and excluding transients from our statistics .
we observe that the lyapunov exponent in each case vanishes , while the transients play no essential role due to the augmented statistics that we use .
( cycle @xmath68 ) and initial condition @xmath56 .
the first @xmath57 iterations have been eliminated from our statistics in order to exclude transients , and the subsequent @xmath58 iterations have been taken into account for the numerical calculations.,scaledwidth=60.0% ] on the other hand , as it has already been mentioned , in a previous work @xcite providing some theoretical arguments from the viewpoint of the symbolic dynamics we have established the structure of the un - normalized symbol - to - symbol correlation function .
these results have also been supported from careful numerical experimentations leading to the compact form @xmath69 where for a given ( fixed ) @xmath70 , @xmath71 , @xmath72 is a constant depending only on @xmath70 , and @xmath73 takes all the values from the set of natural numbers @xmath74 . here , we have also used the fact that any integer @xmath51 can be decomposed in terms of a unique pair of natural numbers @xmath70 , @xmath73 such that @xmath75 .
the same holds for any other form of the correlation function that will be presented in the rest of the paper .
( cycle @xmath76 ) and initial condition @xmath56 .
the first @xmath57 iterations have been eliminated from our statistics in order to exclude transients , and the subsequent @xmath58 iterations have been taken into account for the numerical calculations.,scaledwidth=60.0% ] in @xcite , on the grounds of the metropolis - stein - stein algorithm , we have established a new theorem , namely that @xmath77 as it seems , these are the first few numerically obtained coefficients @xmath78 of eq.(10 ) .
we can extend this procedure to infinity and the above constructive scheme guarantees that this deep algorithmic structure is kept in all scales . from this infinite stratification , the infinite memory of the system at the feigenbaum point is revealed , as this scheme never ends . in the following ,
we proceed by extending our numerical experimentation to the structure of the normalized symbol - to - symbol correlation function taking again into account the first @xmath58 iterations of the logistic map ( this scheme is depicted in figure 2 ) with initial condition @xmath79 .
the corresponding functional structure now reads @xmath80 which has already been established in @xcite .
moreover , proceeding along the same lines one can calculate the correlation function of the trajectory as it is defined in eqs.(6,7 ) . in this manner , it can be easily confirmed numerically that its structure has the following simple form @xmath81 as it can be observed it possesses the known functional form of eq.(10 ) apart from the numerical constants @xmath82 , whereas @xmath83 as @xmath51 becomes large .
therefore , up to now we have established a general form for the correlation function of the trajectory exactly at the @xmath84 point supported from numerical calculations . in the following ,
we shall present some arguments in order to show that the correlation functions of the trajectory and that obtained from the symbolic sequence possesses the same time scales .
this discussion will lead us to a conceptual understanding for the reason that the correlation function of the trajectory ( as it is defined in eq.(6 ) ) contains the same time scales with the symbol - to - symbol correlation function ( see eq.(8 ) ) , that is @xmath85 here for a fixed @xmath71 the coefficients @xmath82 are constants , while @xmath73 takes all the values from the set of natural numbers @xmath86 .
note also that the properties of a single position of the trajectory have already been studied in another context @xcite , where it has been shown that the trajectory exhibits the above mentioned iteration - times property . in the following
, we would like to show that when the symbol - to - symbol correlation function augments , the correlation function of the path is augmented , too , and when the symbol - to - symbol correlation function diminishes , the correlation function of the path diminishes , too . towards this direction ,
let us consider the deviation from the critical value @xmath87 as @xmath88 with @xmath89 , which remains valid for all cases .
as a consequence of the above proposition we can distinguish the following four different cases : a ) a contribution in the symbolic correlation function by two terms @xmath90 ( so @xmath91 ) and @xmath92 ( @xmath93 ) is + 1 and gives a corresponding contribution to the trajectory correlation function of the order of @xmath94 , that is more than 0.25 .
b ) secondly , a contribution in the symbolic correlation function by the terms @xmath95 and @xmath96 is 0 and gives a corresponding contribution to the correlation function of the trajectory of the order of @xmath97 , that is less than 0.25 .
c ) on the other hand , a contribution in the symbolic correlation function by two terms @xmath90 and @xmath96 is 0 and gives a corresponding contribution to the trajectory correlation function of the order of @xmath98 , i.e. of the order of 0.25 .
d ) finally , a contribution in the symbolic correlation function by the terms @xmath95 and @xmath92 is 0 and gives a corresponding contribution to the trajectory correlation function of the order @xmath99 , that is of the order of 0.25 . in order to clarify the meaning of the above approximations
let us consider a specific example with @xmath100 and @xmath101 .
then , we have @xmath102 and @xmath103 .
so , the contribution to the symbolic correlation function is 1 and as a consequence the contribution to the real correlation function is @xmath104 .
thus , from the above it is clear that using such a simple argument one can predict correctly the functional form of the correlation function of the trajectory from the symbolic one .
[ cols="^,^,^,^ " , ] [ table : nonlin ] the first few numerical values of the above coefficients for the correlation function of the symbolic sequence are presented in table ii ( see second row ) .
as one can easily verify after a straightforward numerical computation the same structure is observed for the correlation function of the trajectory , apart from numerical constants @xmath105 , @xmath106 , @xmath107 which depend on the detailed form of the map ( see table iii , third row ) . in the same manner , one can perform the same calculations for the higher accumulation points and find a similar structure for both the correlation function of the trajectory and that obtained from the symbolic sequence .
indeed , in tables ii and iii we extend these considerations to the @xmath108 , @xmath109 , @xmath110 , @xmath111 , @xmath112 , @xmath113 , @xmath114 , @xmath115 and @xmath116 ( see also figures 3,4 ) accumulation points and we present the corresponding coefficients that may appear in the respective correlation function for each cycle . notice that the relevant information about the accumulations points and the corresponding patterns have been found in @xcite . as for the lower cycles both the correlation function of the trajectory and the symbolic one posses the same time scales . to illustrate
the above , figure 3 shows the symbol - to - symbol versus the correlation function of the trajectory for the @xmath117 cycle .
we observe that the correlation function for the trajectory is always larger from the symbolic one .
the latter can also be confirmed by a direct comparison of the coefficients @xmath118 or @xmath119 among the different types of correlations presented in tables ii and iii .
the previous observations also hold for higher accumulation points , e.g. the @xmath120 cycle as shown in figure 4 .
additionally , from the tables ii , iii it is clearly seen that for the same type of correlations the coefficients @xmath118 are increasing for higher accumulation points while some of the constants @xmath121 may coincide .
this is more rare for the correlation function of the trajectory .
as a result of the above studies we can conclude that the suggested general form for the symbol - to - symbol correlation function at the @xmath84 point of the @xmath122 attractor reads @xmath123 where as usual for a given @xmath71 the coefficients @xmath78 , @xmath124 , @xmath125, ... ,@xmath126 are constants depending only on @xmath70 , @xmath51 denotes the number of the accumulation point that we consider and @xmath73 takes all the values from the set of natural numbers @xmath86 .
the corresponding form for the correlation function of the trajectory remains the same apart from numerical constants @xmath105 , @xmath106 , @xmath107 , ... which as it has been mentioned previously they depend on the detailed form of the map .
the correlation function is an important quantity measuring correlations in many branches of physics . obviously , there are also other interesting quantities as for instance the ( conditional ) block - entropies , the transinformation , the kolmogorov - sinai entropy etc
. however , it does provide an important measure of correlations by itself . in the present paper the correlation function of the trajectory at the feigenbaum point
is numerically investigated with careful numerical experimentation . comparing with the symbol - to - symbol correlation function discovered in the literature
theoretically and numerically we observe that it contains the same time scales , that is , it has the same functional form .
this result has been also justified up to a good approximation by presenting simple arguments .
moreover , we have generalized these results for the case of an arbitrary @xmath127 feigenbaum non chaotic multifractal attractor .
finally , we have arrived to an empirical formula summarizing the results .
to recapitulate , we are in position to justify the analytical form of the correlation function of the trajectory from first principles ( the mss algorithm ) and in a systematic way , apart from numerical constants which depend on the detailed functional form of the map .
apart from their mathematical beauty such ideas find important practical applications ranging from precursory signals @xcite to dna sequence analysis @xcite , heart beat rhythms @xcite and linguistics processes . in this manner , it is still an open problem what information one can extract by using such complexity measures in real experimental time - series and the physical explanation of the correlation function of the trajectory and that obtained from the symbolic sequence for a specific problem
. a second path towards this direction would be the generalization of the form of the correlation function for more complex maps as well as non - unimodal maps , see for instance @xcite .[/INST] the correlation function of the trajectory exactly at the feigenbaum point of the logistic map is introduced and checked by numerical experiments .
taking advantage of recent closed analytical results on the symbol - to - symbol correlation function of the generating partition , we are in position to justify the deep algorithmic structure of the correlation function apart from numerical constants .
a generalization is given for arbitrary @xmath0 feigenbaum attractors .
+ keywords : correlation function ; symbolic dynamics ; bifurcation points ; feigenbaum attractors ; logistic map . </s> |
SAN ANTONIO, Texas Texas-based Blue Bell Creameries, which stopped production and distribution of ice cream to 25 states in April after the discovery of listeria bacteria, said on Friday that listeria was discovered again in a production facility.
The company did not specify in a statement in which of its three facilities listeria had been found but said that none was found in any of its ice cream. Blue Bell said it is moving to eliminate the bacteria through a "seek and destroy" process.
"We expect to periodically find microbiological indications in our facilities," said Blue Bell, which declined comment beyond the statement. The company credited its "enhanced, robust testing system" for why it found the bacteria.
The company noted that because listeria is commonly found in the natural environment, "no manufacturer can ever assume it will be entirely eradicated."
Blue Bell, ranked the No. 1 ice cream brand in the country in 2014, recalled all products last spring after 10 reported cases of listeria in four states were linked to Blue Bell frozen treats. Three of the people sickened, all hospital patients in Kansas, later died.
The disease, caused by eating food contaminated with listeria, primarily affects older adults, pregnant women, newborns and adults with weakened immune systems, according to the U.S. Centers for Disease Control and Prevention.
Blue Bell suspended production at its plants in Brenham, Texas; Broken Arrow, Oklahoma, and Sylacauga, Alabama last spring and said it conducted a major overhaul of production at all three plants.
Blue Bell laid off or furloughed hundreds of employees as a result of the shutdown.
Starting in November, the company began a phased process of returning its ice cream to store shelves. The company said the next phase of the process, in which ice cream will be distributed in Tennessee, Kentucky, the Carolinas, and Virginia, will proceed as planned.
(Reporting by Jim Forsyth in San Antonio; Editing by Mary Wisniewski and Steve Orlofsky) ||||| Story highlights The discovery shows enhanced testing procedures are working, Blue Bell says
It emphasizes it has found no confirmed cases of listeria
Blue Bell recalled all products nationwide last year after a fatal listeria outbreak
(CNN) Blue Bell Creameries, which is recovering from a nationwide recall prompted by a fatal listeria outbreak, says enhanced testing of its facilities has found locations where suspected listeria may be present.
The ice cream company said the new discoveries show its testing procedures are working, and it is now extensively cleaning and sanitizing the suspect areas.
Blue Bell emphasized that it has found no confirmed cases of listeria
Correction A previous version of this story incorrectly characterized the contents of a Blue Bell statement on its product-safety efforts. The Blue Bell statement, reflected in this updated story, refers only to the company having "... identified locations where suspected Listeria species may be present ... " and says that the company "... continues to extensively clean and sanitize those areas ... "
"The entire purpose of our enhanced environmental testing is to identify locations where bacteria could be found in our facility in order to properly clean and sanitize the surface and prevent contamination," Blue Bell said in a statement Friday.
Read More | – Only a week after the US Justice Department announced it was investigating Blue Bell Creameries over a fatal listeria outbreak last spring, the ice cream maker revealed the bacteria had again been found in one of its facilities, Reuters reports. Blue Bell stopped production and issued a mass recall in April after it was linked to 10 cases of listeria, three of which proved to be fatal. It had only recently started getting its products back into stores. According to CNN, Blue Bell planned to start shipping its products to Tennessee, Alabama, Georgia, and Florida on Jan. 18. "We expect to periodically find microbiological indications in our facilities," Reuters quotes a statement released Friday by Blue Bell. The company says it was able to find the listeria this time because of an "enhanced, robust testing system" put in place after the outbreak in April. According to CNN, Blue Bell says its products currently in stores are safe to eat. "Since our plants reopened, we have tested and will continue to test every batch of ice cream produced, and no products produced have tested positive for listeria," CNN quotes the company's statement. | <s>[INST]SAN ANTONIO, Texas Texas-based Blue Bell Creameries, which stopped production and distribution of ice cream to 25 states in April after the discovery of listeria bacteria, said on Friday that listeria was discovered again in a production facility.
The company did not specify in a statement in which of its three facilities listeria had been found but said that none was found in any of its ice cream. Blue Bell said it is moving to eliminate the bacteria through a "seek and destroy" process.
"We expect to periodically find microbiological indications in our facilities," said Blue Bell, which declined comment beyond the statement. The company credited its "enhanced, robust testing system" for why it found the bacteria.
The company noted that because listeria is commonly found in the natural environment, "no manufacturer can ever assume it will be entirely eradicated."
Blue Bell, ranked the No. 1 ice cream brand in the country in 2014, recalled all products last spring after 10 reported cases of listeria in four states were linked to Blue Bell frozen treats. Three of the people sickened, all hospital patients in Kansas, later died.
The disease, caused by eating food contaminated with listeria, primarily affects older adults, pregnant women, newborns and adults with weakened immune systems, according to the U.S. Centers for Disease Control and Prevention.
Blue Bell suspended production at its plants in Brenham, Texas; Broken Arrow, Oklahoma, and Sylacauga, Alabama last spring and said it conducted a major overhaul of production at all three plants.
Blue Bell laid off or furloughed hundreds of employees as a result of the shutdown.
Starting in November, the company began a phased process of returning its ice cream to store shelves. The company said the next phase of the process, in which ice cream will be distributed in Tennessee, Kentucky, the Carolinas, and Virginia, will proceed as planned.
(Reporting by Jim Forsyth in San Antonio; Editing by Mary Wisniewski and Steve Orlofsky) ||||| Story highlights The discovery shows enhanced testing procedures are working, Blue Bell says
It emphasizes it has found no confirmed cases of listeria
Blue Bell recalled all products nationwide last year after a fatal listeria outbreak
(CNN) Blue Bell Creameries, which is recovering from a nationwide recall prompted by a fatal listeria outbreak, says enhanced testing of its facilities has found locations where suspected listeria may be present.
The ice cream company said the new discoveries show its testing procedures are working, and it is now extensively cleaning and sanitizing the suspect areas.
Blue Bell emphasized that it has found no confirmed cases of listeria
Correction A previous version of this story incorrectly characterized the contents of a Blue Bell statement on its product-safety efforts. The Blue Bell statement, reflected in this updated story, refers only to the company having "... identified locations where suspected Listeria species may be present ... " and says that the company "... continues to extensively clean and sanitize those areas ... "
"The entire purpose of our enhanced environmental testing is to identify locations where bacteria could be found in our facility in order to properly clean and sanitize the surface and prevent contamination," Blue Bell said in a statement Friday.
Read More[/INST]– Only a week after the US Justice Department announced it was investigating Blue Bell Creameries over a fatal listeria outbreak last spring, the ice cream maker revealed the bacteria had again been found in one of its facilities, Reuters reports. Blue Bell stopped production and issued a mass recall in April after it was linked to 10 cases of listeria, three of which proved to be fatal. It had only recently started getting its products back into stores. According to CNN, Blue Bell planned to start shipping its products to Tennessee, Alabama, Georgia, and Florida on Jan. 18. "We expect to periodically find microbiological indications in our facilities," Reuters quotes a statement released Friday by Blue Bell. The company says it was able to find the listeria this time because of an "enhanced, robust testing system" put in place after the outbreak in April. According to CNN, Blue Bell says its products currently in stores are safe to eat. "Since our plants reopened, we have tested and will continue to test every batch of ice cream produced, and no products produced have tested positive for listeria," CNN quotes the company's statement.</s> |
inelastic hard sphere models are perhaps the simplest models able to capture the two salient features of granular fluids , namely the hard core repulsion between grains and the dissipation of kinetic energy due to the inelastic collisions .
since many of the equilibrium properties of the 1d elastic hard rods are known in closed analytical form , such a system represents an excellent reference model even for the inelastic case .
let us consider @xmath0 identical impenetrable rods , of coordinates @xmath8 , mass @xmath9 and size @xmath10 , constrained to move along a line of length @xmath1 .
periodic boundary conditions are assumed .
the hard - core character of the repulsive forces among particles reduces the interactions to single binary , instantaneous collision events occurring whenever two consecutive rods reach a distance @xmath11 equal to their length @xmath10 .
when two inelastic hard - rods collide , their post - collisional velocities ( primed symbols ) are related to pre - collisional velocities ( unprimed symbols ) through the rule : @xmath12 where @xmath13 indicates the coefficient of restitution .
the interaction of each particle with the heat - bath is represented by the combination of a viscous force proportional to the velocity and a stochastic force .
then each particle follows the so called kramers dynamics @xmath14 where @xmath3 is the viscous friction coefficient , @xmath15 is a gaussian white noise with zero average and correlation @xmath16 @xmath2 is the `` heat - bath temperature '' and @xmath17 indicates the average over a statistical ensemble of noise realizations . we have developed a numerical simulation code for hard rods interacting through momentum conserving but energy dissipating collisions . in our simulations
the motion between two consecutive collisions is governed by the dynamics ( [ kramers1],[kramers2 ] ) .
thus , we determine the instant when the first collision among the @xmath0 particles occurs and change their velocities and positions according to the equations of motion .
the effect of the collision is taken into account by updating the velocities after each collision according to the rule ( [ collision ] ) .
we tested our code on the elastic case ( @xmath18 ) and checked that our simulations faithfully reproduced the well known properties of the equilibrium hard rod system .
we begin by considering the steady state properties of the model .
the aim is to derive relations connecting the microscopic parameters to the `` thermodynamic '' observables such as temperature and pressure and eventually to obtain an `` equation of state '' relating these two quantities . in order to achieve this goal
we assume that the system is homogeneous , so that its density @xmath19 is constant . collisions and the kramers dynamics entail that the time derivative of the average kinetic energy per particle is @xmath20 where @xmath21 is the granular temperature and @xmath22 is the average power dissipated by collisions , given by @xmath23 , where @xmath24 is the difference between the pre - collisional velocities of the colliding pair .
the average collision time @xmath25 is estimated by assuming a mean free path @xmath26 , where @xmath27 is the free volume .
we obtain , in terms of the system density @xmath28 , @xmath29 thus the average power dissipated per grain reads : @xmath30 in order to estimate @xmath31 we assume that @xmath32 since the velocities of the colliding pairs are strongly correlated . thus imposing the solution of eq .
( [ collis ] ) to be stationary we obtain for @xmath31 the following expression : @xmath33 ) .
the simulation data refer to @xmath34 , @xmath35 , @xmath36 , @xmath37 and @xmath38 .
we kept the system size fixed to @xmath39 but varied the number of particles @xmath0 to change the density.,width=302 ] in figure [ fig_graftemp ] we compare formula ( [ tg ] ) with the results of numerical simulations at various densities . in spite of the simplicity of the argument used to derive eq .
( [ tg ] ) , the agreement between @xmath31 extracted by simulations and its theoretical estimate is fairly good . in a granular system the total pressure , @xmath40 , can be obtained via its mechanical or kinetic definition , i.e. as the impulse transferred across a surface in the unit of time.@xcite the pressure contains both the ideal gas and the collisional contribution ( @xmath41 and @xmath42 respectively ) @xmath43 where the second equality stems from the virial theorem .
@xcite here @xmath44 is the observation time , the sum runs over the @xmath45 collisions and @xmath46 represents the impulse variation due to the @xmath47-th collision . an approximate formula for @xmath42 can be derived as follows .
the average collision frequency per particle can be estimated as @xmath48 . by replacing in eq .
( [ ptot ] ) @xmath44 with @xmath49 and using @xmath25 given by eq .
( [ tauc ] ) , we obtain , for the excess part of the pressure , the expression @xmath50 collecting pieces together we arrive at @xmath51\;=\ ; t_g(\rho)\frac{\rho}{1-\sigma \rho } \label{pressure}\ ] ] which reproduces the well known tonks formula @xcite in the case of elastic particles and constitutes the sought equation of state for the inelastic system .
let us recall that in the elastic case , eq . ( [ pressure ] ) can be written in the virial form @xmath52 \label{pressure2}\ ] ] showing the connection between the macroscopic and the microscopic level , since @xmath53 is the equilibrium pair correlation at contact .
we see , from figure ( [ fig_pres ] ) , that the presence of the prefactor @xmath54 , which is decreasing function of the density , makes @xmath55 to increase more slowly than the corresponding pressure of the elastic system in the same physical conditions ( i.e. same density and contact with the same heat bath ) . equations ( [ tg ] ) and ( [ excpressure ] ) for temperature and pressure coincide , in the limit @xmath56 , @xmath57 , @xmath58 , with those derived by williams and mackintosh @xcite . following the standard approach to fluids ,
we define , even for the inelastic system , the response of the density to a uniform change of the pressure for a fixed value of the heat bath temperature : @xmath59 which is plotted in figure [ fig_compres ] .
we observe that the response of the inelastic system to a compression is much larger than the corresponding elastic system at the same density , due to the tendency to cluster . at different densities for inelastic hard rods with coefficients of restitution @xmath37 and @xmath38 .
the remaining parameters are the same as in figure [ fig_graftemp ] .
dashed line refers to the pressure of the corresponding elastic system.,width=302 ] ) , plotted versus density , for inelastic hard rods with coefficient @xmath37 ( the remaining parameters are the same as in figure [ fig_graftemp ] ) .
symbols refers to simulations while solid lines are the theoretical predictions obtained via the expression for the pressure ( [ pressure ] ) .
the curve for the elastic system @xmath18 ( dashed line ) is also reported for sake of comparison . in the inset
shows the ratio between the inelastic and elastic compressibility.,width=302 ]
so far we have considered only the global average properties of the granular gas .
it is well known , on the other hand , that these system may exhibit strong spontaneous deviations from their uniform state . in this section we shall study fluctuations of the main observables in order to understand the qualitative effect of inelasticity on such a peculiar fluid .
one of the signatures of the inelasticity of the collisions is represented by the shape of the velocity distribution function ( vdf ) , @xmath60 .
non - gaussian vdf s , displaying low velocity and high velocity overpopulated regions , have been measured experimentally @xcite and in numerical simulations.@xcite in figure [ velocitydistr ] we show two vdf corresponding to two different values of @xmath13 . for three values of the coefficient of restitution @xmath61 ( circles ) , @xmath62 ( squares ) , @xmath63 ( triangles ) .
the remaining parameters are @xmath64 , @xmath65 , @xmath34 , @xmath36 , @xmath35
. dashed lines indicates the corresponding gaussian fit.,width=302 ] theoretical , numerical and experimental studies have shown that the vdf for inelastic ( @xmath66 ) gases usually displays overpopulated tails .
the literature seems to indicate the lack of a universal vdf : in @xmath67 the solution of the homogeneous boltzmann equation with inelastic collisions ( with a stochastic driving similar to ours but without viscosity ) has overpopulated tails of the kind @xmath68.@xcite interestingly , the energy fluctuations of our system , @xmath69/2 , display a scaling with respect to the number of particles .
we are interested in the quantity @xmath70 as a function of @xmath0 ( at fixed density @xmath19 ) .
defining @xmath71 , we have @xmath72 under the hypothesis that the variables @xmath73 are independently distributed , we get @xmath74}\ ] ] since for gaussian variables @xmath75 , we find @xmath76 which is a well known formula for equilibrium systems @xcite .
this scaling is fairly well verified in figure [ tempflut ] . for @xmath77 .
the elastic case agrees with the theoretical prediction @xmath78 , whereas the inelastic case gives a value of the relative fluctuation slightly larger .
the remaining parameters are the same as in figure [ velocitydistr],width=302 ] in the case of a granular fluid , @xmath79 is no more gaussian , exhibiting fatter tails , so one observes @xmath80
( for example in the case @xmath37 we have @xmath81 ) .
this leads to the conclusion that the scaling @xmath82 of formula ( [ enerflut ] ) still holds , but with a coefficient larger than @xmath83 .
simulation runs for @xmath37 confirm this prediction ( fig .
[ tempflut ] ) .
the renormalization of the multiplicative constant occurring in the inelastic system could be interpreted also as an `` effective reduction '' of the number of degrees of freedom .
indeed , the inelastic system has the tendency to cluster , as it will be shown , and therefore the effective number of independent `` particles '' appears smaller .
another appealing interpretation is that the inelastic systems possesses an effective `` specific heat '' larger than that of elastic systems .
a universal signature of the inelasticity is the presence of correlations between the velocities of the particles .
we measured the structure function of the velocities @xmath73 , @xmath84 , where @xmath85 is the fourier transform of @xmath73 . in figure [ velcor ] , we show three @xmath86 corresponding to the elastic ( @xmath87 ) and inelastic system with @xmath38 and @xmath37 .
, for elastic and inelastic systems .
the control parameters are the same as in figure [ velocitydistr],width=302 ] as mentioned above , the elastic systems is characterized by uncorrelated velocities and this reflects on a constant structure function
. a certain degree of correlation is instead evident in the inelastic system .
in fact , the inelasticity reduces by a factor @xmath13 the relative velocity of two colliding particles and this leads to an increasing correlation among velocities
. however , the noise induced by the bath competes with these correlations , making the structure function not very steep .
more specifically , @xmath86 can be fitted , in the middle range of @xmath47 values , by an inverse power @xmath88 , while at high @xmath47 values it reaches a constant plateau .
this is the fingerprint of a persistent internal noise ( velocity fluctuations are not completely frozen by inelastic collisions).@xcite , for elastic and inelastic systems , with the same parameters used before .
the solid line indicates the exponential expected in the elastic case ( see text ) .
the state parameters are the same as in fig .
[ velocitydistr],width=302 ] the probability distribution , @xmath89 , of distances between nearest neighbor particles @xmath90 , shown in figure [ spacingsdistr ] , provides information about the spatial arrangement of the system . in the elastic case one
easily finds @xmath91\ ] ] for @xmath92 and @xmath93 for @xmath94 with @xmath95 .
the presence of inelasticity modifies such a simple exponential law in the way shown in figure [ spacingsdistr ] . in this case
, the probability of finding two particles at small separation increases together with that of finding large voids .
such a picture is consistent with the idea of the clustering phenomenon:@xcite two particles , after the inelastic collision , have a smaller relative velocity and therefore reach smaller distances , eventually producing dense clusters and leaving larger empty regions with respect to the elastic case . on the contrary ,
the probability distribution of collision times , shown in figure [ timesdistr ] , appears to always follow the theoretical ( elastic ) form @xmath96 .
apart from a trivial rescaling due to the change of the thermal velocity with @xmath13 , it seems not to depend appreciably on the coefficient of restitution .
.,width=302 ] such a finding is in contrast with the situation observed in 2d vibrated granular systems @xcite .
a possible explanation for this discrepancy is the following : in the inelastic 1d system , there is correlation between the relative velocities and the free - paths ( or free - times ) , otherwise the distribution @xmath97 and @xmath89 would have had the same shape due to the trivial relation @xmath98 , @xmath99 being the the average velocity of the rods .
in particular , the fact that the peak of @xmath89 in @xmath100 does not yield a corresponding peak in the @xmath101 region of @xmath97 suggests that the shorter the distance between particles the smaller their relative velocity .
we turn , now , to the study of the structural properties of the inelastic hard - rod gas , by considering the pair correlation function or the structure factor .
as mentioned in section ii , the virial equation ( [ pressure2 ] ) relates the pressure of an elastic hard - rod system to its microscopic structure . in the presence of inelasticity
, however , we expect that the tendency to cluster is mirrored by a change in the structural properties of the fluid .
therefore we considered the behavior of the static ( truly speaking steady state ) structure factor @xmath102 e^{ikx}\ ] ] for different values of @xmath103 and inelasticity .
the spatial structure of the system is determined , as in ordinary fluids , by the strong repulsive forces .
their role is seen in the oscillating structure of @xmath104 .
the inelastic nature of the collisions provides a correction to @xmath104 , which can be better appreciated by studying the small wavelength behavior of @xmath105 which develops a peak at small @xmath47 recalling the ornstein - zernike behavior @xmath106 the coefficient @xmath107 is negative for hard rods , whereas it is positive for the inelastic system .
for hard rods , @xmath105 is known @xcite and reads : @xmath108 with @xmath109 . for different values of the coefficients @xmath77 .
notice the growth of the peak at small @xmath47 when @xmath13 decreases.,width=302 ] figure [ fig : sk ] shows the typical behaviors of @xmath105 for elastic and inelastic systems .
the numerically computed structure factor of the elastic system agrees rather well with equation ( [ sk_elastic ] ) .
the inelastic system , instead , displays a peak in the small @xmath47 region reflecting the tendency of the fluid to cluster
. the peak increases with inelasticity , demonstrating that the energy dissipation in collisions is responsible for these long range correlations .
incidentally , we comment that such a behavior of @xmath105 could be attributed to the presence of a long range attractive effective potential between the rods , as a result of dynamical correlations.@xcite mackintosh and williams @xcite found that , in the case of randomly kicked rods in the absence of viscosity , the pair correlation function decays as an inverse power law , @xmath110 with @xmath111 for @xmath112 and @xmath113 for @xmath114 . correspondingly , one expects @xmath105 to diverge as @xmath115 as @xmath116 , for very inelastic systems .
in other words , the inelasticity leads to long range spatial correlations which are revealed by the peak at small @xmath47 of @xmath105 .
we remark that , in spite of the apparent similarity between the equations of state for elastic and inelastic system , their structural properties are radically different . such a phenomenon is the result of the coupling of the long - wavelength modes of the velocity field with the stochastic non - conserved driving force .
in fact , due to the inelastic collisions , the velocities of the particles tend to align , thus reducing the energy dissipation . on the other hand , these modes adsorb energy from the heat bath and grow in amplitude , and
only the presence of friction prevents these excitations from becoming unstable .
the density field , which is coupled to the velocity field by the continuity equation , also develops long range correlations , and the structure factor displays a peak at small wave - vectors .
one dimensional hard - core fluids exhibit an interesting connection between the microscopic structural properties and diffusive ones . in the present section , we present numerical results for the collective diffusion and for the diffusion of a tagged particle and show how these are connected to the structure .
let us turn to analyze the perhaps simplest transport property of the hard rods system , namely the self - diffusion , i.e. the dynamics of a grain in the presence of @xmath117 partners .
the problem is highly non - trivial since the single grain degrees of freedom are coupled to those of the remaining grains .
such a single - filing diffusion is also relevant in the study of transport of particles in narrow pores .
@xcite the diffusing particles can never pass each other .
the excluded volume effect represents a severe hindrance for the particles to diffuse .
in fact , a given particle in order to move must wait for a collective rearrangement of the entire system .
only when the cage of a particle expands , the tagged particle is free to diffuse further .
this is a peculiar form of the so called cage effect which is enhanced by the one - dimensional geometry .
in addition , the cage effect produces a negative region and a slow tail in the velocity autocorrelation function . as an appropriate measure of the self - diffusion , we consider the average square displacement of each particle from its position at a certain time , that we assume to be @xmath101 without loss of generality @xmath118 ^ 2 \rangle}{n } \label{eq : msd}\ ] ] at an early stage ,
the self - diffusion is expected to display ballistic behavior , @xmath119 , with @xmath120 , before any perturbation ( heat bath and collisions ) change the free motion of particles , i.e. when @xmath121 and @xmath122 . a system of non - interacting ( i.e. non - colliding ) particles subjected to kramers dynamics ( [ kramers1],[kramers2 ] ) displays , after the ballistic transient , normal self - diffusion of the form @xmath123 with @xmath124 .
this is well verified in figure [ fig : diff ] ( circles ) .
lebowitz and percus @xcite studied the tagged particle diffusion problem for systems governed by non - dissipative dynamics without heat bath and found a diffusive behavior described by @xmath125 with @xmath95 . since @xmath126 one obtains @xmath127 on the other hand , almost in the same years , harris @xcite studied the behavior of @xmath128 in the case of @xmath0 identical brownian particles with hard - core interactions , i.e. obeying a single - filing condition , and obtained a sub - diffusive behavior increasing as @xmath129 where @xmath130 is the single ( noninteracting ) particle diffusion coefficient . in figure [
fig : diff ] , we study the self - diffusion @xmath128 for elastic and inelastic systems in the presence of heat bath and viscosity , obtaining two different regimes separated by a typical time @xmath25 . in the first transient regime @xmath131 we we observe the ballistic motion . in the second stage , instead , we expect the sub - diffusive behavior , @xmath132 , predicted by harris and other authors .
the inelastic system displays the same sub - diffusive behavior , but with a multiplicative constant larger than @xmath133 , i.e. at equal times the granular ( inelastic ) fluid has a larger absolute value of @xmath128 .
it is interesting to analyze the connection between this transport property and the compressibility of the system , as remarked by kollmann .
@xcite for three different systems : one without collisions ( free particles ) , one with elastic collisions and the third with inelastic collisions ( @xmath37).,width=302 ] we follow alexander and pincus @xcite argument in order to derive a formula for the self - diffusion and show the connection with the compressibility of the system .
let us consider the two time correlator : @xmath134 we set @xmath135 , where @xmath136 are the nodes of the 1d lattice @xmath137 , ( @xmath138 being the lattice spacing ) .
expanding around @xmath136 @xmath139 hence @xmath140 we assume , now , that the density correlator varies as @xmath141 where @xmath142 ( this is demonstrated in appendix a ) is the collective diffusion coefficient , with @xmath143 .
now , the mean square displacement per particle ( [ eq : msd ] ) can be written as @xmath144 ^ 2
\rangle / n $ ] and , in fourier components , reads @xmath145 employing eq .
[ aggiunta ] we find @xmath146 approximating the sum with an integral ( @xmath147 and recalling that @xmath148 we obtain @xmath149 and therefore @xmath150 notice that such a formula in the case of hard - rods is identical to formula ( [ singlefile ] ) .
we see that the tagged particle diffusion depends on the structure of the fluid . in the granular
fluid the @xmath151 part of the spectrum is enhanced and thus we expect a stronger tagged particle diffusion .
this is what we observe .
physically there are larger voids and particles can move more freely .
let us notice that as far as the collective diffusion is involved the spread of a group of particles is faster in the presence of repulsive interactions than without .
in this paper we have studied a one - dimensional system of inelastic hard - rods coupled to a stochastic heat - bath with the idea that it can represent a reference system in the area of granular gases to test theories and approximations . due to the relative simplicity of the one dimensional geometry we have shown that it is possible to obtain relations between the macroscopic control parameters such as kinetic temperature , pressure and density .
we tested these analytical predictions against the numerical measurements and found a fairly good agreement .
it also appears that many properties of the heated one - dimensional inelastic hard rod system are similar to those of ordinary fluids .
however , when we have considered how various physical observables fluctuate about their equilibrium values , many relevant differences have emerged .
these range from the non - gaussian behavior of the velocity distribution , the peculiar form of the distribution of distances between particles and of the energy fluctuations to the shape of the structure factor at small wave - vectors .
finally , we have found that the diffusive properties of the system are affected by the inelasticity and in particular the self - diffusion is enhanced . to conclude , in spite of the similarity between ordinary fluids and granular fluids , which has been recognized for many years and has made possible to formulate hydrodynamical equations for granular media in rapid , dilute flow , the presence of anomalous fluctuations in the inelastic case indicates the necessity of a treatment which incorporates in a proper way both the local effects such as the excluded volume constraint and the long ranged velocity and density correlations .
such a program has been partially carried out by ernst and coworkers @xcite , but needs to be completed regarding the description of the fluid structure .
in the case of over - damped dynamics ( i.e. large values of @xmath3 ) one finds that the collective diffusion is given by @xcite @xmath152 where @xmath153 is the local chemical potential .
expanding @xmath154 about its average value @xmath155 we obtain : @xmath156_{\rho_0 } \frac{\partial \rho(x)}{\partial x}\ ] ] substituting into eq .
( [ collective ] ) we find @xmath157_{\rho_0 } \frac{\partial^2 \rho(x)}{\partial x^2}\ ] ] and using @xmath158_t\ ] ] in the case of elastic hard rods we obtain : | we study the properties of a one - dimensional ( 1d ) granular gas consisting of @xmath0 hard rods on a line of length @xmath1 ( with periodic boundary conditions ) .
the particles collide inelastically and are fluidized by a heat bath at temperature @xmath2 and viscosity @xmath3 .
the analysis is supported by molecular dynamics simulations .
the average properties of the system are first discussed , focusing on the relations between granular temperature @xmath4 , kinetic pressure and density @xmath5 .
thereafter , we consider the fluctuations around the average behavior obtaining a slightly non - gaussian behavior of the velocity distributions and a spatially correlated velocity field ; the density field displays clustering : this is reflected in the structure factor which has a peak in the @xmath6 region suggesting an analogy between inelastic hard core interactions and an effective attractive potential .
finally , we study the transport properties , showing the typical sub - diffusive behavior of 1d stochastically driven systems , i.e. @xmath7 introduction ------------ scientists and engineers have been studying granular materials for nearly two centuries for their relevance both in natural processes ( landslides , dunes , saturn rings ) and in industry ( handling of cereals and minerals , fabrication of pharmaceuticals etc . ) . @xcite the understanding of the `` granular state '' still represents an open challenge and one of the most active research topics in non - equilibrium statistical mechanics and fluid dynamics .
for instance , a way to attack the problem consists in fluidizing the grains by shaking them so that the system behaves as a non - ideal gas , a problem relatively easier to study .
the difficulty , but also the beauty , of the dynamics of granular gases , meant as rarefied assemblies of macroscopic particles , stems from the inelastic nature of their collisions which leads to a variety of very peculiar phenomena .
several theoretical methods have been employed to deal with granular gases ranging from hydrodynamic equations , kinetic theories to molecular dynamics .
engineers often prefer the strategy of the continuum description because it gives a better grasp of real life phenomena , while natural scientists tend to opt for a microscopic approach , to better control each step of the modelization .
the latter , as far as the interaction between particles is concerned , regards granular systems as peculiar fluids , and treats them through the same methods which have been successfully applied to ordinary fluids .
@xcite this allows not only , to employ concepts already developed by physicists and chemists , but also to stress analogies and substantial differences .
the purpose of the present paper is to establish such a connection for a system of stochastically driven inelastic hard - rods constrained to move on a ring .
the elastic version of this system has a long tradition @xcite and is particularly suitable to test approximations and theories since many of its equilibrium properties can be derived in a closed analytical form .
even though , the one dimensional geometry introduces some peculiarities not shared by real fluids , we shall show that the model provides many useful information and a very rich phenomenology which closely recalls the behavior of microscopic particles confined in tubules or cylindrical pores with little interconnection .
a second reason to investigate such a model is to show how the inelasticity of interactions influences not only the average global properties of a system , but also its microscopic local structure .
a basic requirement to a theoretical description of a granular gas is to provide an equation of state linking the relevant control parameters and possibly to relate it to the microscopic structure of the system .
this connection is well known for classical fluids , where thermodynamic and transport properties are linked to the microscopic level via the correlation function formalism .
one dimensional models have been employed by several authors as simple models of granular gases .
@xcite the differences between the various models stem chiefly from the choice of the thermalizing device .
in fact , granular gases would come to rest unless supplying energy compensating the losses due to the inelastic collisions .
we call , by analogy , `` _ heat bath _ '' the external driving mechanism maintaining the system in a statistically steady state . for the history , the first 1d models , which were proposed , had no periodic boundary conditions and the energy was injected by a vibrating wall ( stochastic or not ) . this kind of external driving however , was not able to keep the system homogeneous , because only the first and last particle had a direct interaction with the wall .
@xcite as an alternative , a uniform heating mechanism , namely a gaussian white noise acting on each particle , was introduced .
@xcite later puglisi et al.@xcite added a second ingredient , consisting of a friction term that prevents the kinetic energy from diverging .
with such a modification the system reaches a steady regime and time averages can be safely computed . in the present paper
we shall focus on this last model characterizing its steady state properties .
the layout is the following : in section ii we introduce the model , in section iii we obtain numerically and by approximate analytical arguments equations for the average kinetic energy and pressure .
section iv is devoted to fluctuations of the system observables around their average values . in section
v we study the diffusion properties of the system .
finally , in section vi we present the conclusions . | <s>[INST]inelastic hard sphere models are perhaps the simplest models able to capture the two salient features of granular fluids , namely the hard core repulsion between grains and the dissipation of kinetic energy due to the inelastic collisions .
since many of the equilibrium properties of the 1d elastic hard rods are known in closed analytical form , such a system represents an excellent reference model even for the inelastic case .
let us consider @xmath0 identical impenetrable rods , of coordinates @xmath8 , mass @xmath9 and size @xmath10 , constrained to move along a line of length @xmath1 .
periodic boundary conditions are assumed .
the hard - core character of the repulsive forces among particles reduces the interactions to single binary , instantaneous collision events occurring whenever two consecutive rods reach a distance @xmath11 equal to their length @xmath10 .
when two inelastic hard - rods collide , their post - collisional velocities ( primed symbols ) are related to pre - collisional velocities ( unprimed symbols ) through the rule : @xmath12 where @xmath13 indicates the coefficient of restitution .
the interaction of each particle with the heat - bath is represented by the combination of a viscous force proportional to the velocity and a stochastic force .
then each particle follows the so called kramers dynamics @xmath14 where @xmath3 is the viscous friction coefficient , @xmath15 is a gaussian white noise with zero average and correlation @xmath16 @xmath2 is the `` heat - bath temperature '' and @xmath17 indicates the average over a statistical ensemble of noise realizations . we have developed a numerical simulation code for hard rods interacting through momentum conserving but energy dissipating collisions . in our simulations
the motion between two consecutive collisions is governed by the dynamics ( [ kramers1],[kramers2 ] ) .
thus , we determine the instant when the first collision among the @xmath0 particles occurs and change their velocities and positions according to the equations of motion .
the effect of the collision is taken into account by updating the velocities after each collision according to the rule ( [ collision ] ) .
we tested our code on the elastic case ( @xmath18 ) and checked that our simulations faithfully reproduced the well known properties of the equilibrium hard rod system .
we begin by considering the steady state properties of the model .
the aim is to derive relations connecting the microscopic parameters to the `` thermodynamic '' observables such as temperature and pressure and eventually to obtain an `` equation of state '' relating these two quantities . in order to achieve this goal
we assume that the system is homogeneous , so that its density @xmath19 is constant . collisions and the kramers dynamics entail that the time derivative of the average kinetic energy per particle is @xmath20 where @xmath21 is the granular temperature and @xmath22 is the average power dissipated by collisions , given by @xmath23 , where @xmath24 is the difference between the pre - collisional velocities of the colliding pair .
the average collision time @xmath25 is estimated by assuming a mean free path @xmath26 , where @xmath27 is the free volume .
we obtain , in terms of the system density @xmath28 , @xmath29 thus the average power dissipated per grain reads : @xmath30 in order to estimate @xmath31 we assume that @xmath32 since the velocities of the colliding pairs are strongly correlated . thus imposing the solution of eq .
( [ collis ] ) to be stationary we obtain for @xmath31 the following expression : @xmath33 ) .
the simulation data refer to @xmath34 , @xmath35 , @xmath36 , @xmath37 and @xmath38 .
we kept the system size fixed to @xmath39 but varied the number of particles @xmath0 to change the density.,width=302 ] in figure [ fig_graftemp ] we compare formula ( [ tg ] ) with the results of numerical simulations at various densities . in spite of the simplicity of the argument used to derive eq .
( [ tg ] ) , the agreement between @xmath31 extracted by simulations and its theoretical estimate is fairly good . in a granular system the total pressure , @xmath40 , can be obtained via its mechanical or kinetic definition , i.e. as the impulse transferred across a surface in the unit of time.@xcite the pressure contains both the ideal gas and the collisional contribution ( @xmath41 and @xmath42 respectively ) @xmath43 where the second equality stems from the virial theorem .
@xcite here @xmath44 is the observation time , the sum runs over the @xmath45 collisions and @xmath46 represents the impulse variation due to the @xmath47-th collision . an approximate formula for @xmath42 can be derived as follows .
the average collision frequency per particle can be estimated as @xmath48 . by replacing in eq .
( [ ptot ] ) @xmath44 with @xmath49 and using @xmath25 given by eq .
( [ tauc ] ) , we obtain , for the excess part of the pressure , the expression @xmath50 collecting pieces together we arrive at @xmath51\;=\ ; t_g(\rho)\frac{\rho}{1-\sigma \rho } \label{pressure}\ ] ] which reproduces the well known tonks formula @xcite in the case of elastic particles and constitutes the sought equation of state for the inelastic system .
let us recall that in the elastic case , eq . ( [ pressure ] ) can be written in the virial form @xmath52 \label{pressure2}\ ] ] showing the connection between the macroscopic and the microscopic level , since @xmath53 is the equilibrium pair correlation at contact .
we see , from figure ( [ fig_pres ] ) , that the presence of the prefactor @xmath54 , which is decreasing function of the density , makes @xmath55 to increase more slowly than the corresponding pressure of the elastic system in the same physical conditions ( i.e. same density and contact with the same heat bath ) . equations ( [ tg ] ) and ( [ excpressure ] ) for temperature and pressure coincide , in the limit @xmath56 , @xmath57 , @xmath58 , with those derived by williams and mackintosh @xcite . following the standard approach to fluids ,
we define , even for the inelastic system , the response of the density to a uniform change of the pressure for a fixed value of the heat bath temperature : @xmath59 which is plotted in figure [ fig_compres ] .
we observe that the response of the inelastic system to a compression is much larger than the corresponding elastic system at the same density , due to the tendency to cluster . at different densities for inelastic hard rods with coefficients of restitution @xmath37 and @xmath38 .
the remaining parameters are the same as in figure [ fig_graftemp ] .
dashed line refers to the pressure of the corresponding elastic system.,width=302 ] ) , plotted versus density , for inelastic hard rods with coefficient @xmath37 ( the remaining parameters are the same as in figure [ fig_graftemp ] ) .
symbols refers to simulations while solid lines are the theoretical predictions obtained via the expression for the pressure ( [ pressure ] ) .
the curve for the elastic system @xmath18 ( dashed line ) is also reported for sake of comparison . in the inset
shows the ratio between the inelastic and elastic compressibility.,width=302 ]
so far we have considered only the global average properties of the granular gas .
it is well known , on the other hand , that these system may exhibit strong spontaneous deviations from their uniform state . in this section we shall study fluctuations of the main observables in order to understand the qualitative effect of inelasticity on such a peculiar fluid .
one of the signatures of the inelasticity of the collisions is represented by the shape of the velocity distribution function ( vdf ) , @xmath60 .
non - gaussian vdf s , displaying low velocity and high velocity overpopulated regions , have been measured experimentally @xcite and in numerical simulations.@xcite in figure [ velocitydistr ] we show two vdf corresponding to two different values of @xmath13 . for three values of the coefficient of restitution @xmath61 ( circles ) , @xmath62 ( squares ) , @xmath63 ( triangles ) .
the remaining parameters are @xmath64 , @xmath65 , @xmath34 , @xmath36 , @xmath35
. dashed lines indicates the corresponding gaussian fit.,width=302 ] theoretical , numerical and experimental studies have shown that the vdf for inelastic ( @xmath66 ) gases usually displays overpopulated tails .
the literature seems to indicate the lack of a universal vdf : in @xmath67 the solution of the homogeneous boltzmann equation with inelastic collisions ( with a stochastic driving similar to ours but without viscosity ) has overpopulated tails of the kind @xmath68.@xcite interestingly , the energy fluctuations of our system , @xmath69/2 , display a scaling with respect to the number of particles .
we are interested in the quantity @xmath70 as a function of @xmath0 ( at fixed density @xmath19 ) .
defining @xmath71 , we have @xmath72 under the hypothesis that the variables @xmath73 are independently distributed , we get @xmath74}\ ] ] since for gaussian variables @xmath75 , we find @xmath76 which is a well known formula for equilibrium systems @xcite .
this scaling is fairly well verified in figure [ tempflut ] . for @xmath77 .
the elastic case agrees with the theoretical prediction @xmath78 , whereas the inelastic case gives a value of the relative fluctuation slightly larger .
the remaining parameters are the same as in figure [ velocitydistr],width=302 ] in the case of a granular fluid , @xmath79 is no more gaussian , exhibiting fatter tails , so one observes @xmath80
( for example in the case @xmath37 we have @xmath81 ) .
this leads to the conclusion that the scaling @xmath82 of formula ( [ enerflut ] ) still holds , but with a coefficient larger than @xmath83 .
simulation runs for @xmath37 confirm this prediction ( fig .
[ tempflut ] ) .
the renormalization of the multiplicative constant occurring in the inelastic system could be interpreted also as an `` effective reduction '' of the number of degrees of freedom .
indeed , the inelastic system has the tendency to cluster , as it will be shown , and therefore the effective number of independent `` particles '' appears smaller .
another appealing interpretation is that the inelastic systems possesses an effective `` specific heat '' larger than that of elastic systems .
a universal signature of the inelasticity is the presence of correlations between the velocities of the particles .
we measured the structure function of the velocities @xmath73 , @xmath84 , where @xmath85 is the fourier transform of @xmath73 . in figure [ velcor ] , we show three @xmath86 corresponding to the elastic ( @xmath87 ) and inelastic system with @xmath38 and @xmath37 .
, for elastic and inelastic systems .
the control parameters are the same as in figure [ velocitydistr],width=302 ] as mentioned above , the elastic systems is characterized by uncorrelated velocities and this reflects on a constant structure function
. a certain degree of correlation is instead evident in the inelastic system .
in fact , the inelasticity reduces by a factor @xmath13 the relative velocity of two colliding particles and this leads to an increasing correlation among velocities
. however , the noise induced by the bath competes with these correlations , making the structure function not very steep .
more specifically , @xmath86 can be fitted , in the middle range of @xmath47 values , by an inverse power @xmath88 , while at high @xmath47 values it reaches a constant plateau .
this is the fingerprint of a persistent internal noise ( velocity fluctuations are not completely frozen by inelastic collisions).@xcite , for elastic and inelastic systems , with the same parameters used before .
the solid line indicates the exponential expected in the elastic case ( see text ) .
the state parameters are the same as in fig .
[ velocitydistr],width=302 ] the probability distribution , @xmath89 , of distances between nearest neighbor particles @xmath90 , shown in figure [ spacingsdistr ] , provides information about the spatial arrangement of the system . in the elastic case one
easily finds @xmath91\ ] ] for @xmath92 and @xmath93 for @xmath94 with @xmath95 .
the presence of inelasticity modifies such a simple exponential law in the way shown in figure [ spacingsdistr ] . in this case
, the probability of finding two particles at small separation increases together with that of finding large voids .
such a picture is consistent with the idea of the clustering phenomenon:@xcite two particles , after the inelastic collision , have a smaller relative velocity and therefore reach smaller distances , eventually producing dense clusters and leaving larger empty regions with respect to the elastic case . on the contrary ,
the probability distribution of collision times , shown in figure [ timesdistr ] , appears to always follow the theoretical ( elastic ) form @xmath96 .
apart from a trivial rescaling due to the change of the thermal velocity with @xmath13 , it seems not to depend appreciably on the coefficient of restitution .
.,width=302 ] such a finding is in contrast with the situation observed in 2d vibrated granular systems @xcite .
a possible explanation for this discrepancy is the following : in the inelastic 1d system , there is correlation between the relative velocities and the free - paths ( or free - times ) , otherwise the distribution @xmath97 and @xmath89 would have had the same shape due to the trivial relation @xmath98 , @xmath99 being the the average velocity of the rods .
in particular , the fact that the peak of @xmath89 in @xmath100 does not yield a corresponding peak in the @xmath101 region of @xmath97 suggests that the shorter the distance between particles the smaller their relative velocity .
we turn , now , to the study of the structural properties of the inelastic hard - rod gas , by considering the pair correlation function or the structure factor .
as mentioned in section ii , the virial equation ( [ pressure2 ] ) relates the pressure of an elastic hard - rod system to its microscopic structure . in the presence of inelasticity
, however , we expect that the tendency to cluster is mirrored by a change in the structural properties of the fluid .
therefore we considered the behavior of the static ( truly speaking steady state ) structure factor @xmath102 e^{ikx}\ ] ] for different values of @xmath103 and inelasticity .
the spatial structure of the system is determined , as in ordinary fluids , by the strong repulsive forces .
their role is seen in the oscillating structure of @xmath104 .
the inelastic nature of the collisions provides a correction to @xmath104 , which can be better appreciated by studying the small wavelength behavior of @xmath105 which develops a peak at small @xmath47 recalling the ornstein - zernike behavior @xmath106 the coefficient @xmath107 is negative for hard rods , whereas it is positive for the inelastic system .
for hard rods , @xmath105 is known @xcite and reads : @xmath108 with @xmath109 . for different values of the coefficients @xmath77 .
notice the growth of the peak at small @xmath47 when @xmath13 decreases.,width=302 ] figure [ fig : sk ] shows the typical behaviors of @xmath105 for elastic and inelastic systems .
the numerically computed structure factor of the elastic system agrees rather well with equation ( [ sk_elastic ] ) .
the inelastic system , instead , displays a peak in the small @xmath47 region reflecting the tendency of the fluid to cluster
. the peak increases with inelasticity , demonstrating that the energy dissipation in collisions is responsible for these long range correlations .
incidentally , we comment that such a behavior of @xmath105 could be attributed to the presence of a long range attractive effective potential between the rods , as a result of dynamical correlations.@xcite mackintosh and williams @xcite found that , in the case of randomly kicked rods in the absence of viscosity , the pair correlation function decays as an inverse power law , @xmath110 with @xmath111 for @xmath112 and @xmath113 for @xmath114 . correspondingly , one expects @xmath105 to diverge as @xmath115 as @xmath116 , for very inelastic systems .
in other words , the inelasticity leads to long range spatial correlations which are revealed by the peak at small @xmath47 of @xmath105 .
we remark that , in spite of the apparent similarity between the equations of state for elastic and inelastic system , their structural properties are radically different . such a phenomenon is the result of the coupling of the long - wavelength modes of the velocity field with the stochastic non - conserved driving force .
in fact , due to the inelastic collisions , the velocities of the particles tend to align , thus reducing the energy dissipation . on the other hand , these modes adsorb energy from the heat bath and grow in amplitude , and
only the presence of friction prevents these excitations from becoming unstable .
the density field , which is coupled to the velocity field by the continuity equation , also develops long range correlations , and the structure factor displays a peak at small wave - vectors .
one dimensional hard - core fluids exhibit an interesting connection between the microscopic structural properties and diffusive ones . in the present section , we present numerical results for the collective diffusion and for the diffusion of a tagged particle and show how these are connected to the structure .
let us turn to analyze the perhaps simplest transport property of the hard rods system , namely the self - diffusion , i.e. the dynamics of a grain in the presence of @xmath117 partners .
the problem is highly non - trivial since the single grain degrees of freedom are coupled to those of the remaining grains .
such a single - filing diffusion is also relevant in the study of transport of particles in narrow pores .
@xcite the diffusing particles can never pass each other .
the excluded volume effect represents a severe hindrance for the particles to diffuse .
in fact , a given particle in order to move must wait for a collective rearrangement of the entire system .
only when the cage of a particle expands , the tagged particle is free to diffuse further .
this is a peculiar form of the so called cage effect which is enhanced by the one - dimensional geometry .
in addition , the cage effect produces a negative region and a slow tail in the velocity autocorrelation function . as an appropriate measure of the self - diffusion , we consider the average square displacement of each particle from its position at a certain time , that we assume to be @xmath101 without loss of generality @xmath118 ^ 2 \rangle}{n } \label{eq : msd}\ ] ] at an early stage ,
the self - diffusion is expected to display ballistic behavior , @xmath119 , with @xmath120 , before any perturbation ( heat bath and collisions ) change the free motion of particles , i.e. when @xmath121 and @xmath122 . a system of non - interacting ( i.e. non - colliding ) particles subjected to kramers dynamics ( [ kramers1],[kramers2 ] ) displays , after the ballistic transient , normal self - diffusion of the form @xmath123 with @xmath124 .
this is well verified in figure [ fig : diff ] ( circles ) .
lebowitz and percus @xcite studied the tagged particle diffusion problem for systems governed by non - dissipative dynamics without heat bath and found a diffusive behavior described by @xmath125 with @xmath95 . since @xmath126 one obtains @xmath127 on the other hand , almost in the same years , harris @xcite studied the behavior of @xmath128 in the case of @xmath0 identical brownian particles with hard - core interactions , i.e. obeying a single - filing condition , and obtained a sub - diffusive behavior increasing as @xmath129 where @xmath130 is the single ( noninteracting ) particle diffusion coefficient . in figure [
fig : diff ] , we study the self - diffusion @xmath128 for elastic and inelastic systems in the presence of heat bath and viscosity , obtaining two different regimes separated by a typical time @xmath25 . in the first transient regime @xmath131 we we observe the ballistic motion . in the second stage , instead , we expect the sub - diffusive behavior , @xmath132 , predicted by harris and other authors .
the inelastic system displays the same sub - diffusive behavior , but with a multiplicative constant larger than @xmath133 , i.e. at equal times the granular ( inelastic ) fluid has a larger absolute value of @xmath128 .
it is interesting to analyze the connection between this transport property and the compressibility of the system , as remarked by kollmann .
@xcite for three different systems : one without collisions ( free particles ) , one with elastic collisions and the third with inelastic collisions ( @xmath37).,width=302 ] we follow alexander and pincus @xcite argument in order to derive a formula for the self - diffusion and show the connection with the compressibility of the system .
let us consider the two time correlator : @xmath134 we set @xmath135 , where @xmath136 are the nodes of the 1d lattice @xmath137 , ( @xmath138 being the lattice spacing ) .
expanding around @xmath136 @xmath139 hence @xmath140 we assume , now , that the density correlator varies as @xmath141 where @xmath142 ( this is demonstrated in appendix a ) is the collective diffusion coefficient , with @xmath143 .
now , the mean square displacement per particle ( [ eq : msd ] ) can be written as @xmath144 ^ 2
\rangle / n $ ] and , in fourier components , reads @xmath145 employing eq .
[ aggiunta ] we find @xmath146 approximating the sum with an integral ( @xmath147 and recalling that @xmath148 we obtain @xmath149 and therefore @xmath150 notice that such a formula in the case of hard - rods is identical to formula ( [ singlefile ] ) .
we see that the tagged particle diffusion depends on the structure of the fluid . in the granular
fluid the @xmath151 part of the spectrum is enhanced and thus we expect a stronger tagged particle diffusion .
this is what we observe .
physically there are larger voids and particles can move more freely .
let us notice that as far as the collective diffusion is involved the spread of a group of particles is faster in the presence of repulsive interactions than without .
in this paper we have studied a one - dimensional system of inelastic hard - rods coupled to a stochastic heat - bath with the idea that it can represent a reference system in the area of granular gases to test theories and approximations . due to the relative simplicity of the one dimensional geometry we have shown that it is possible to obtain relations between the macroscopic control parameters such as kinetic temperature , pressure and density .
we tested these analytical predictions against the numerical measurements and found a fairly good agreement .
it also appears that many properties of the heated one - dimensional inelastic hard rod system are similar to those of ordinary fluids .
however , when we have considered how various physical observables fluctuate about their equilibrium values , many relevant differences have emerged .
these range from the non - gaussian behavior of the velocity distribution , the peculiar form of the distribution of distances between particles and of the energy fluctuations to the shape of the structure factor at small wave - vectors .
finally , we have found that the diffusive properties of the system are affected by the inelasticity and in particular the self - diffusion is enhanced . to conclude , in spite of the similarity between ordinary fluids and granular fluids , which has been recognized for many years and has made possible to formulate hydrodynamical equations for granular media in rapid , dilute flow , the presence of anomalous fluctuations in the inelastic case indicates the necessity of a treatment which incorporates in a proper way both the local effects such as the excluded volume constraint and the long ranged velocity and density correlations .
such a program has been partially carried out by ernst and coworkers @xcite , but needs to be completed regarding the description of the fluid structure .
in the case of over - damped dynamics ( i.e. large values of @xmath3 ) one finds that the collective diffusion is given by @xcite @xmath152 where @xmath153 is the local chemical potential .
expanding @xmath154 about its average value @xmath155 we obtain : @xmath156_{\rho_0 } \frac{\partial \rho(x)}{\partial x}\ ] ] substituting into eq .
( [ collective ] ) we find @xmath157_{\rho_0 } \frac{\partial^2 \rho(x)}{\partial x^2}\ ] ] and using @xmath158_t\ ] ] in the case of elastic hard rods we obtain :[/INST] we study the properties of a one - dimensional ( 1d ) granular gas consisting of @xmath0 hard rods on a line of length @xmath1 ( with periodic boundary conditions ) .
the particles collide inelastically and are fluidized by a heat bath at temperature @xmath2 and viscosity @xmath3 .
the analysis is supported by molecular dynamics simulations .
the average properties of the system are first discussed , focusing on the relations between granular temperature @xmath4 , kinetic pressure and density @xmath5 .
thereafter , we consider the fluctuations around the average behavior obtaining a slightly non - gaussian behavior of the velocity distributions and a spatially correlated velocity field ; the density field displays clustering : this is reflected in the structure factor which has a peak in the @xmath6 region suggesting an analogy between inelastic hard core interactions and an effective attractive potential .
finally , we study the transport properties , showing the typical sub - diffusive behavior of 1d stochastically driven systems , i.e. @xmath7 introduction ------------ scientists and engineers have been studying granular materials for nearly two centuries for their relevance both in natural processes ( landslides , dunes , saturn rings ) and in industry ( handling of cereals and minerals , fabrication of pharmaceuticals etc . ) . @xcite the understanding of the `` granular state '' still represents an open challenge and one of the most active research topics in non - equilibrium statistical mechanics and fluid dynamics .
for instance , a way to attack the problem consists in fluidizing the grains by shaking them so that the system behaves as a non - ideal gas , a problem relatively easier to study .
the difficulty , but also the beauty , of the dynamics of granular gases , meant as rarefied assemblies of macroscopic particles , stems from the inelastic nature of their collisions which leads to a variety of very peculiar phenomena .
several theoretical methods have been employed to deal with granular gases ranging from hydrodynamic equations , kinetic theories to molecular dynamics .
engineers often prefer the strategy of the continuum description because it gives a better grasp of real life phenomena , while natural scientists tend to opt for a microscopic approach , to better control each step of the modelization .
the latter , as far as the interaction between particles is concerned , regards granular systems as peculiar fluids , and treats them through the same methods which have been successfully applied to ordinary fluids .
@xcite this allows not only , to employ concepts already developed by physicists and chemists , but also to stress analogies and substantial differences .
the purpose of the present paper is to establish such a connection for a system of stochastically driven inelastic hard - rods constrained to move on a ring .
the elastic version of this system has a long tradition @xcite and is particularly suitable to test approximations and theories since many of its equilibrium properties can be derived in a closed analytical form .
even though , the one dimensional geometry introduces some peculiarities not shared by real fluids , we shall show that the model provides many useful information and a very rich phenomenology which closely recalls the behavior of microscopic particles confined in tubules or cylindrical pores with little interconnection .
a second reason to investigate such a model is to show how the inelasticity of interactions influences not only the average global properties of a system , but also its microscopic local structure .
a basic requirement to a theoretical description of a granular gas is to provide an equation of state linking the relevant control parameters and possibly to relate it to the microscopic structure of the system .
this connection is well known for classical fluids , where thermodynamic and transport properties are linked to the microscopic level via the correlation function formalism .
one dimensional models have been employed by several authors as simple models of granular gases .
@xcite the differences between the various models stem chiefly from the choice of the thermalizing device .
in fact , granular gases would come to rest unless supplying energy compensating the losses due to the inelastic collisions .
we call , by analogy , `` _ heat bath _ '' the external driving mechanism maintaining the system in a statistically steady state . for the history , the first 1d models , which were proposed , had no periodic boundary conditions and the energy was injected by a vibrating wall ( stochastic or not ) . this kind of external driving however , was not able to keep the system homogeneous , because only the first and last particle had a direct interaction with the wall .
@xcite as an alternative , a uniform heating mechanism , namely a gaussian white noise acting on each particle , was introduced .
@xcite later puglisi et al.@xcite added a second ingredient , consisting of a friction term that prevents the kinetic energy from diverging .
with such a modification the system reaches a steady regime and time averages can be safely computed . in the present paper
we shall focus on this last model characterizing its steady state properties .
the layout is the following : in section ii we introduce the model , in section iii we obtain numerically and by approximate analytical arguments equations for the average kinetic energy and pressure .
section iv is devoted to fluctuations of the system observables around their average values . in section
v we study the diffusion properties of the system .
finally , in section vi we present the conclusions . </s> |
analyses in developed countries have found ses and adult health to be significantly positively correlated
, 2008)though gradients appear smaller at older ages than at earlier ages ( crimmins , 2005 ; elo & preston , 1996 ; turra & goldman , 2007 ) . in developing countries ,
there has been much less study of older adult health differentials , partly due to the paucity of appropriate data until recent years . now available surveys in elderly populations in asia and latin america do indeed appear to also show substantially poorer self - assessed health among the low educated ( palloni & mceniry , 2004 ; zimmer , natividad , ofstedal , & lin , 2002 )
. however , the ses gradient in less subjective indicators is much less consistent . in asia
, surveys such as in taiwan have found unclear relationships between ses and indicators of functional health , and ses differentials appear to even reverse for life - threatening measurements such as stroke , cancer , and diabetes ( zimmer et al . ,
in contrast , latin american surveys such as in mexico find that the ses gradient persists for chronic conditions like diabetes , although with less strength than that observed in self - assessed health indicators ( palloni & mceniry , 2004 ) . in both asian and latin american studies , socioeconomic differentials are often smaller than those observed in the high - income countries .
when studying mortality indicators , ses differentials for older adults are again not well understood in developing countries .
a few recent studies have found that mortality by cardiovascular diseases ( cvds ) and diabetes tends to be higher in the more developed areas of costa rica ( rosero - bixby , 1996 ) ; similarly , a 17-year follow - up study in costa ricans showed no significant differences in survival by ses among older people ( rosero - bixby , dow , & lacle , 2005 ) .
another challenging result is the so called hispanic paradox ; that is , the lower mortality of elderly hispanics compared with the much more affluent white population in the united states ( elo , turra , kestenbaum , & ferguson , 2004 ) , which some argue may be partly due to cultural differences in health behaviors and psychosocial support .
hispanics also show significantly smaller ses differentials in mortality than whites ( turra & goldman , 2007 ) .
by contrast , bangladesh data from a surveillance site shows the expected pattern of higher adult mortality at lower education ( hurt , ronsmans , & saha , 2004 ; mostafa & ginneken , 2000 ) .
various hypotheses have been suggested to explain different dimensions of the conflicting ses patterns in adult health .
some authors attribute to selection effects the weakening of ses differentials by age : that is , mortality eliminates the frailest individuals at early ages in groups with lower ses ( crimmins , 2005 ) . but selection effects can not easily explain the contrasting relationships across different domains of objective and subjectively reported health .
these puzzles could be partly due to systematic biases by ses in subjective self - reports , but they also may reflect true differences in ses gradients across different domains of health .
for example , it could be that low ses is associated with demanding physical labor across the life course that manifests in self - reported pain and mobility problems , whereas middle and higher income is associated with developed country lifestyles that elevate cardiovascular risks for mortality .
buffers to low ses may also operate differentially on different health domains , with national health insurance enabling low ses to buffer the ill effects of certain medically manageable cardiovascular risk factors , but with fewer buffers potentially available against the adverse effects of cumulative insults from low social and occupational status .
its life expectancy at birth ( 78 years ) is the second highest in the americas ( canada is first ) , higher even than in the united states ( world bank , 2006 ) .
broad explanations of costa rica 's health achievements in the literature include the orientation of the government toward equity and social development , with large social investments being possible in part due to the absence of military expenditures , given that the 1949 constitution abolished the armed forces ( rosero - bixby , 1991 ) .
investments in education and the very high coverage of health insurance are often mentioned as key factors ( caldwell , 1986 ) .
the social security system , which is funded from deductions from payrolls and from contributions by employers and the government , is the provider of health insurance and health services with an almost universal coverage , especially for the elderly population .
all workers in the formal sector and many workers in the informal sector contribute to the system and are entitled to health insurance that allows them and their families to receive free health care services and free medications at any hospital , clinic , or community health center .
additionally , the government provides free health insurance to poor people . according to the 2000 census
, health insurance covers 82% of the population , including 9% destitute individuals whose insurance is paid by the government ( rosero - bixby , 2004a ) .
provision of primary health care , particularly to remote or poor populations , has had a quantifiable impact on death rates ( rosero - bixby , 2004b ) . in economic terms , costa rica does not differ from the latin american average . according to the world bank ( 2006 ) , its per capita income is about $ 4,600 per year , compared with the $ 3,600 average for latin america .
however , in terms of equity in income distribution , social security coverage , access to public health services and sanitation , labor laws , and protection of the environment , costa rica ranks among the highest in the continent .
costa rica has a mixed economy with open markets and , at the same time ,
government control of key areas such as health , education , banking , energy , communications , and insurance ( mesa - lago , 2000 ) .
the human development index of the united nations ranks costa rica 48th in the world and fourth in latin america ( after chile , argentina , and uruguay ) .
this article follows a simple framework ( figure 1 ) to organize the different dimensions and indicators of health ( crimmins & seeman , 2004 ) .
general health outcomes such as mortality and physical functioning are the end points of the framework .
proximate determinants very close to these outcomes are specific biological risk factors , usually measured by biomarkers such as blood pressure , obesity , and glucose levels
. then , one step back in the explanation hierarchy , there are health behaviors ( diet , smoking , exercising ) and health care services .
some demographic factors , such as age , sex , and marital status , are considered at the same hierarchical level and ses , and therefore their confounding effects must be controlled for .
the purpose of the article is to fill the breach in the literature regarding ses gradients in objectively measured adult health indicators in developing countries . does the well - documented
, strong connection of poor health and low ses among adults of rich countries and among children of developing countries persist in hard data for adults in middle - income countries like costa rica ?
first , ses disparities in health outcomes are interesting in and of themselves and have received a great deal of public attention in other settings ( such as in the united states or among children in latin america ) .
yet they have rarely been documented in latin american adult populations , primarily due to lack of data , except on a few select indicators .
a key contribution of this article is the availability in creles of a wide range of both subjective and objective health measures , which we analyze within a uniform empirical framework , creating an unparalleled opportunity in latin america to make ses gradient comparisons across them .
second , the analysis is of interest because once we have established stylized facts about health disparities in this population , we can begin to evaluate existing hypotheses and generate new ones about the determinants of health patterns in this setting .
there are many hypotheses about why health is typically worse in low ses populations . similarly , many hypotheses have been advanced about how a middle - income country such as costa rica has been able to obtain exceptionally good population average health outcomes , such as higher life expectancy than the united states .
these generally relate to models of the social determinants of population health : health care access , health behaviors , environmental health exposures , psychosocial stressors ( inequality ) , and the ability to buffer against negative health shocks ( social safety nets , social capital , and interpersonal ties ) .
although we do not formally test such hypotheses in this article , our analyses speak to the face validity of how some of these may or may not operate in costa rica .
because this is the first nationwide survey of adult health in costa rica , this article provides the first opportunity for beginning to evaluate such hypotheses .
the main hypothesis that we do test in this article is the provocative proposition that there is no ses gradient in costa rican adult health .
this hypothesis is based on prior findings of no education or wealth gradients in costa rican mortality , from the only previous study on the subject , using data from a single peri - urban community ( rosero - bixby et al . , 2005 ) .
observers have hypothesized that costa rica may have little ses gradient due to factors such as universal health insurance ( which has allowed low ses groups similar access to care as high ses groups ) in combination with costa rica perhaps being an unusually equitable society . for these factors to have been instrumental in minimizing ses gradients , however , it should be the case that ses gradients would be minimal across a wide range of health indicators beyond just mortality which is exactly what our analyses test .
the purpose of the article is to fill the breach in the literature regarding ses gradients in objectively measured adult health indicators in developing countries .
does the well - documented , strong connection of poor health and low ses among adults of rich countries and among children of developing countries persist in hard data for adults in middle - income countries like costa rica ?
first , ses disparities in health outcomes are interesting in and of themselves and have received a great deal of public attention in other settings ( such as in the united states or among children in latin america ) .
yet they have rarely been documented in latin american adult populations , primarily due to lack of data , except on a few select indicators . a key contribution of this article is the availability in creles of a wide range of both subjective and objective health measures , which we analyze within a uniform empirical framework , creating an unparalleled opportunity in latin america to make ses gradient comparisons across them .
second , the analysis is of interest because once we have established stylized facts about health disparities in this population , we can begin to evaluate existing hypotheses and generate new ones about the determinants of health patterns in this setting .
similarly , many hypotheses have been advanced about how a middle - income country such as costa rica has been able to obtain exceptionally good population average health outcomes , such as higher life expectancy than the united states .
these generally relate to models of the social determinants of population health : health care access , health behaviors , environmental health exposures , psychosocial stressors ( inequality ) , and the ability to buffer against negative health shocks ( social safety nets , social capital , and interpersonal ties ) .
although we do not formally test such hypotheses in this article , our analyses speak to the face validity of how some of these may or may not operate in costa rica .
because this is the first nationwide survey of adult health in costa rica , this article provides the first opportunity for beginning to evaluate such hypotheses .
the main hypothesis that we do test in this article is the provocative proposition that there is no ses gradient in costa rican adult health .
this hypothesis is based on prior findings of no education or wealth gradients in costa rican mortality , from the only previous study on the subject , using data from a single peri - urban community ( rosero - bixby et al . , 2005 ) .
observers have hypothesized that costa rica may have little ses gradient due to factors such as universal health insurance ( which has allowed low ses groups similar access to care as high ses groups ) in combination with costa rica perhaps being an unusually equitable society . for these factors to have been instrumental in minimizing ses gradients , however , it should be the case that ses gradients would be minimal across a wide range of health indicators beyond just mortality which is exactly what our analyses test .
data for this analysis come from creles , an on - going longitudinal study of a nationally representative sample of about 9,000 adults aged 60 years and over and residing in costa rica in the year 2000 , with oversampling of the oldest old and with an in - depth , longitudinal survey in a subsample of about 3,000 of them .
for this analysis , we use mortality data from the computer follow - up of the sample in the national death registry from september 2000 to september 2006 . the data on health ( mostly prevalence of conditions ) come from the first wave of interviews in the 3,000 subsample , conducted from november 2004 to september 2006 .
the mother sample of 9,000 individuals was randomly selected from the 2000 census database after stratification by 5-year age groups .
sampling fractions ranged from 1.1% among those born in 19411945 to 100% for those born before 1905 .
for the in - depth longitudinal survey , creles took from the mother sample a systematic subsample of 60 health areas
this subsample included originally more than 4,000 individuals : 2,827 of them were finally interviewed .
the subsample , which covers 59% of costa rican territory , yielded the following nonresponse rates : 19% of the individuals were deceased by the contact date , 18% were not found in the field , 2% moved to other addresses , 2% rejected the interview , and 2% remain as pending interviews after several visits ( likely rejections ) .
the individuals we did not find in the field originated mostly in the vagueness of the census address ( and the lack of an accurate address system in costa rica ) , as well as from address changes during the approximately 5-year lag between the census and our visit .
thus , it would be unlikely that this group 's ses patterns in health would be so different from the interviewed population so as to create significant selection effects that bias the estimated health ses relationships . among those interviewed , 95% provided a blood sample , 92% collected urine overnight , 91% had all anthropometric measures , and 24% required a proxy to answer the questionnaire .
all the data and specimens in the subsample were collected at the participants homes , usually in two visits . in the first visit ,
participants provided informed consent and answered a 90-min questionnaire ( including some mobility tests and two blood pressure measures ) as well as a 10-min frequency of tracer food consumption questionnaire . in a second visit early the next day ,
fasting blood samples were collected by venipuncture : one edta tube ( for 34 ml of whole blood ) and two serum - separating tubes , with a clot activator ( for 1012 ml of blood , to obtain 46 ml of serum ) . in this visit
, the field team also picked up a cooler containing 12-h overnight urine and took the anthropometric measures .
all field data were collected using personal digital assistants , also known as palm computers , with software applications developed by the central american population center for this study .
a field team of five interviewers , two phlebotomists , and a supervisor collected the information and the blood and urine specimens using a continuous fieldwork design over a period of nearly 2 years .
several costa rican laboratories analyzed the blood and urine specimens , depending on the type of biomarker .
all laboratories were certified by a national reference center of clinical chemistry , an agency under the ministry of health .
in addition to the internal reliability tests that these laboratories must conduct as part of their quality control procedures , we conducted reliability analyses in subsamples of 2040 specimens that were reanalyzed for each biomarker in a different laboratory .
we report elsewhere the results of these reliability analyses , as well as some adjustments introduced to standardize measures across laboratories ( mndez - chacn , rosero - bixby , fernndez - rojas , & barrantes - jimnez , 2007 ) .
we identified deaths of the 8,000 individuals in the original sample by computer follow - up in the national death registry during the period 20002007 , using the unique identification number ( the cdula ) that all costa ricans have .
prior research has indicated that the death registry is virtually 100% complete ( rosero - bixby , 2008 ) . to further validate the registry quality
, we were able to successfully match in the registry all of the several hundred deaths that we identified while attempting to contact individuals in the field for the household survey , thus finding no deaths missing from the registry .
all are coded as 0 , 1 dichotomous indicators , with 1 measuring unfavorable conditions or events : ( a ) general health outcomes , ( b ) specific poor health conditions , including biomarkers , and ( c ) unhealthy lifestyles.seven general health outcomes : death in the period september 2000 to september 2007 , in the sample of about 8,000 individuals .
about 1,000 foreigners are excluded from the original mother sample of 9,000 because they do not have the personal identification i d that allows the computer follow - up to establish death and its date .
the information on age is computed from the birth date in the birth record , avoiding the possibility of age - exaggeration errors.ordinal general srh status . from the five possible answers
, we took the two lowest ( mala and regular ) as defining poor srh.functional disability when respondents have difficulties doing 50% or more of 14 activities and instrumental activities and instrumental activities of daily living ( activities of daily living ( adls)/instrumental activities of daily living ( iadls ) ) , namely : walking on the streets , climbing stairs , pushing objects , raising an arm , crossing the bedroom on your feet , bathing , eating , going to bed , using the toilet , trimming toe nails , cooking , handling money , shopping , and taking medicines . even though many studies distinguish basic , instrumental , and functional disabilities , we combine all these dimensions in a single indicator after checking that the cronbach s alpha of the scale was an excellent .92 for the 14 items .
a person with basic disability ( i.e. , can not use the toilet ) is very likely to also have functional and instrumental disability ( i.e. , can not cut toenails).physical frailty : respondents failing two or more out of five physical tests grip strength with a dynamometer , pulmonary peak flow , standing up from a chair several times , picking an object up from the floor , and standing and walking 3 m.cognitive disability according to the folstein ( folstein & folstein , 1975 ) mini - mental state examination ( mmse ) ( quiroga , albala , & klaasen , 2004 ) .
we considered disabled those with less than 75% right answers of 15 items . the scale from adding the 15 items had an acceptable cronbach s alpha of .72.geriatric depression refers to individuals with nine or more out of 15 yesavage symptoms of depression ( sheikh & yesavage , 1986 ) .
the cronbach s alpha of the scale was .85.metabolic syndrome , which is a combination of five health conditions ( abdominal girth , diabetes , triglycerides , high density lipoprotein ( hdl ) cholesterol , and high blood pressure ) that increase a respondent 's risk for cvd as defined by the international diabetes federation ( idf , 2006 ) .
the syndrome is present when individuals have high abdominal girth and at least two of the other four conditions.specific biological risk factors ( table 2 shows the cutoff points to define at risk ) .
most are components of the concept of allostatic load or biological dysregulation ( seeman et al . , 2004 ) .
details about specific indicators can be found in crimmins and seeman ( 2004).2.1 cvd factors : abdominal girth ( waist > 80 cm women , 94 cm men)diabetes , controlled or not ( glycosylated hemoglobin 6.5% or taking medicine)high blood pressure , controlled or not ( diastolic > 90 and systolic > 140 mmhg in at least three out of four measurements or taking medicine)high triglycerides in fasting serum ( 50 mg / dl)high cholesterol ratio ( total to hdl 5.92)2.2 various deregulation indicators ( some are also related to cvd)low creatinine clearance ( 44.64 mg / dl ) , an indicator of kidney functionhigh cortisol ( 25.69 g / g ) , indicator of activity in the hypothalamic pituitary ( hpa ) axis in response to stressorslow dehydroepiandrosterone sulfate ( dhea - s , 35 mg / dl ) . antagonist to hpa activityhigh epinephrine ( 4.99 g / g ) in 12-h overnight urine .
indicator of neuroendocrine functioning in response to stresshigh norepinephrine ( 48 g / g ) in 12-h overnight urine .
similar to epinephrinehigh c - reactive protein ( crp ) concentrations ( 10 mg / l ) .
also a risk factor for cvdweak handgrip strength ( dynamometer 20 kg)unhealthy lifestylesobesity ( body mass index > 30 ) .
( note this is redundant with abdominal girth , which was included among cvd factors .
it is included in this group as a summary indicator of unhealthy lifestyles regarding food consumption and physical activity.)smoking currentno regular exercise in last yearno flu vaccine last year ( a tracer of preventive care seeking)high - calorie diet ( > 3000 day)low - calorie diet ( < 1500 day)high - carbohydrate diet ( > 400 g day)high - fat diet ( > 40 g day ) seven general health outcomes : death in the period september 2000 to september 2007 , in the sample of about 8,000 individuals .
about 1,000 foreigners are excluded from the original mother sample of 9,000 because they do not have the personal identification i d that allows the computer follow - up to establish death and its date .
the information on age is computed from the birth date in the birth record , avoiding the possibility of age - exaggeration errors .
, we took the two lowest ( mala and regular ) as defining poor srh .
functional disability when respondents have difficulties doing 50% or more of 14 activities and instrumental activities and instrumental activities of daily living ( activities of daily living ( adls)/instrumental activities of daily living ( iadls ) ) , namely : walking on the streets , climbing stairs , pushing objects , raising an arm , crossing the bedroom on your feet , bathing , eating , going to bed , using the toilet , trimming toe nails , cooking , handling money , shopping , and taking medicines .
even though many studies distinguish basic , instrumental , and functional disabilities , we combine all these dimensions in a single indicator after checking that the cronbach s alpha of the scale was an excellent .92 for the 14 items .
a person with basic disability ( i.e. , can not use the toilet ) is very likely to also have functional and instrumental disability ( i.e. , can not cut toenails ) .
physical frailty : respondents failing two or more out of five physical tests grip strength with a dynamometer , pulmonary peak flow , standing up from a chair several times , picking an object up from the floor , and standing and walking 3 m. cognitive disability according to the folstein ( folstein & folstein , 1975 ) mini - mental state examination ( mmse ) ( quiroga , albala , & klaasen , 2004 ) .
the scale from adding the 15 items had an acceptable cronbach s alpha of .72 .
geriatric depression refers to individuals with nine or more out of 15 yesavage symptoms of depression ( sheikh & yesavage , 1986 ) .
metabolic syndrome , which is a combination of five health conditions ( abdominal girth , diabetes , triglycerides , high density lipoprotein ( hdl ) cholesterol , and high blood pressure ) that increase a respondent 's risk for cvd as defined by the international diabetes federation ( idf , 2006 ) .
the syndrome is present when individuals have high abdominal girth and at least two of the other four conditions .
specific biological risk factors ( table 2 shows the cutoff points to define at risk ) .
most are components of the concept of allostatic load or biological dysregulation ( seeman et al . , 2004 ) .
abdominal girth ( waist > 80 cm women , 94 cm men ) diabetes , controlled or not ( glycosylated hemoglobin 6.5% or taking medicine ) high blood pressure , controlled or not ( diastolic > 90 and systolic > 140 mmhg in at least three out of four measurements or taking medicine ) high triglycerides in fasting serum ( 50 mg / dl ) high cholesterol ratio ( total to hdl 5.92 ) 2.2 various deregulation indicators ( some are also related to cvd ) low creatinine clearance ( 44.64 mg / dl ) , an indicator of kidney function high cortisol ( 25.69 g / g ) , indicator of activity in the hypothalamic pituitary ( hpa ) axis in response to stressors low dehydroepiandrosterone sulfate ( dhea - s , 35 mg / dl ) . antagonist to hpa activity high epinephrine ( 4.99 g / g ) in 12-h overnight urine .
indicator of neuroendocrine functioning in response to stress high norepinephrine ( 48 g / g ) in 12-h overnight urine .
also a risk factor for cvd weak handgrip strength ( dynamometer 20 kg ) obesity ( body mass index > 30 ) .
( note this is redundant with abdominal girth , which was included among cvd factors .
it is included in this group as a summary indicator of unhealthy lifestyles regarding food consumption and physical activity . ) no regular exercise in last year no flu vaccine last year ( a tracer of preventive care seeking ) high - calorie diet ( > 3000 day ) low - calorie diet ( < 1500 day ) high - carbohydrate diet ( > 400 g day ) high - fat diet ( > 40 g day ) we have a total of 27 health indicators .
although there is some degree of overlap for several of them , this large number reflects the multidimensional character of the health concept and the complexities of measuring it . to facilitate interpretation and comparisons of results among the different outcomes
, we opted for measuring them all with binary or dichotomous indicators of bad health .
we recognize that there is some loss of information from translating continuous variables into dichotomous indicators .
however , this loss is compensated by the gain in comparability and interpretability as well as by the gain of avoiding the distorting effects from extreme outlier values . where possible , we dichotomized variables with cutoff values commonly used in clinical practice and the literature , including mmse cognitive disability , yesavage geriatric depression , triglycerides , crp , obesity , abdominal obesity , and high- and low - calorie diet .
there are also several indicators that are naturally dichotomous , including death , metabolic syndrome , diabetes , high blood pressure , smoking , lack of physical exercise , and flu vaccine . for
the remaining 12 ( out of 27 ) variables , our choice of cutoff values was driven by the observation of natural breaks in the distribution ( srh , functional disability , frailty , grip strength , and carbohydrate and fat intake ) or was borrowed from the macarthur study of healthy aging ( crimmins & seeman , 2004 ; seeman et al . , 2004 ) .
we examine the effect on health of three ses variables : place of residence , education , and household wealth .
all three are categorized in three levels in order to ascertain the two sides of ses gradients : pertaining to a low - ses stratum or being a high - ses individual . for comparison purposes ,
these three variables are considered constant over time , and we are taking them as reported in the 2000 census , years prior to health measurement ( note that mortality is studied for the period 20002007 , prevalence of health conditions in the 20052006 survey , and the ses indicators are the same in both data sets).place of residence in 2000 : ( 1 ) in the less developed lowlands , which include coastal regions at the pacific ocean and caribbean , as well as the northern plains bordering nicaragua and the southern region bordering panama ; ( 2 ) in the rest of the highlands at the central valley , which includes some suburbs and satellite towns of san jose ; ( 3 ) in the more developed metropolitan area of san jose , the capital city . although
is not an individual - level variable , there is a large literature considering the role of place in health disparities ( e.g. , curtis and rees - jones , 1998 ) .
our simple categorization distinguishing urban and these other settings is consistent with a long literature that has documented rural
urban differences in health in various settings.educational attainment in three naturally defined groups : ( a ) none , ( b ) elementary ( one to six grades ) , and ( c ) some secondary ( postelementary ) school or higher .
the effects of education are some of the most studied among ses variables , given that education is easy to measure , does not change in adult life , is easily comparable , and has a number of socioeconomic influences related to factors such as empowerment , income generation , information gathering , and health - seeking behavior ( elo & preston , 1996 ; hummer , rogers , & eberstein , 1998).household wealth in three groups : poor , middle , and rich .
it is based on a simple count of 14 goods and conveniences in the household , ranging from no - dirt floors and having water connection and electricity to ( at the high end ) having a computer and a car .
wealth is in essence income accumulation or permanent income and thus an indicator of economic well - being during long periods ( menchik , 1993 ) .
place of residence in 2000 : ( 1 ) in the less developed lowlands , which include coastal regions at the pacific ocean and caribbean , as well as the northern plains bordering nicaragua and the southern region bordering panama ; ( 2 ) in the rest of the highlands at the central valley , which includes some suburbs and satellite towns of san jose ; ( 3 ) in the more developed metropolitan area of san jose , the capital city .
is not an individual - level variable , there is a large literature considering the role of place in health disparities ( e.g. , curtis and rees - jones , 1998 ) .
our simple categorization distinguishing urban and these other settings is consistent with a long literature that has documented rural
educational attainment in three naturally defined groups : ( a ) none , ( b ) elementary ( one to six grades ) , and ( c ) some secondary ( postelementary ) school or higher .
the effects of education are some of the most studied among ses variables , given that education is easy to measure , does not change in adult life , is easily comparable , and has a number of socioeconomic influences related to factors such as empowerment , income generation , information gathering , and health - seeking behavior ( elo & preston , 1996 ; hummer , rogers , & eberstein , 1998 ) .
it is based on a simple count of 14 goods and conveniences in the household , ranging from no - dirt floors and having water connection and electricity to ( at the high end ) having a computer and a car .
wealth is in essence income accumulation or permanent income and thus an indicator of economic well - being during long periods ( menchik , 1993 ) . as far as possible , we present all health results adjusted by three demographic variables : ( a ) age ( single year ) , ( b ) sex , and ( c ) marital status ( whether or not currently married including consensual unions ) . age and marital status refer to the situation at the interview in all prevalence analyses . in the mortality analysis , age is time varying ( each observation was split into single - age segments ) , and marital status is in the census interview in the year 2000 .
we also controlled in the regression models for the field worker who conducted the interview or took the anthropometric measures or other exams to correct potential interviewer and measurement biases ( all data were gathered by seven field workers over a period of 2 years ) .
although all field workers received the same training , and visited the same areas , and the work load was more or less randomly distributed , it is always possible that idiosyncratic behavior of a specific field worker might introduce some measurement bias .
for example , female examiners may tend to measure significantly lower values of waist circumference in female participants .
controlling for field worker in the multivariate analyses prevented the remote possibility that these biases were also correlated to ses of participants and thus were confounders of the relationship between health and ses . to study mortality
, we set the data as survival time ( statacorp , 2005 ) , with entry date at september 2000 ( 3 months after the census interview to avoid likely biases in case some hospitalized or very sick individuals were not interviewed in the june census ) and exit or right censoring at september 2007 .
we split observations into single - year segments ( approximately seven segments per individual ) .
mortality rates were computed as the ratio of deaths to the exact count of person - years .
we model some ses gradients in mortality with parametric hazard regression ( streg command in stata ) , assuming a gompertz distribution ( hosmer & lemeshow , 1999 ) .
the models control for demographic confounding effects as well as for the studied ses effects . to consider the possibility that age effects are nonlinear and differential by sex
, we included in the models a quadratic term for age and an interaction term for age and sex . to compare odds ratios across models , we reanalyzed mortality using a logistic model with the probability of dying in each age of the observation period as the dependent variable . in this model , we used robust estimates that take into account the lack of independence of age segments within each individual .
the standard errors in the logistic models were estimated considering the clustering effect of selecting whole health areas in the subsample .
this relaxed the assumption of independence among observations and required only that observations be independent across clusters . in some analyses , we assessed the significance of the joint effect of the three ses variables with a chi - square test of the improvement in the log - likelihood ratio resulting from including ses in the regression model .
all are coded as 0 , 1 dichotomous indicators , with 1 measuring unfavorable conditions or events : ( a ) general health outcomes , ( b ) specific poor health conditions , including biomarkers , and ( c ) unhealthy lifestyles.seven general health outcomes : death in the period september 2000 to september 2007 , in the sample of about 8,000 individuals .
about 1,000 foreigners are excluded from the original mother sample of 9,000 because they do not have the personal identification i d that allows the computer follow - up to establish death and its date .
the information on age is computed from the birth date in the birth record , avoiding the possibility of age - exaggeration errors.ordinal general srh status . from the five possible answers
, we took the two lowest ( mala and regular ) as defining poor srh.functional disability when respondents have difficulties doing 50% or more of 14 activities and instrumental activities and instrumental activities of daily living ( activities of daily living ( adls)/instrumental activities of daily living ( iadls ) ) , namely : walking on the streets , climbing stairs , pushing objects , raising an arm , crossing the bedroom on your feet , bathing , eating , going to bed , using the toilet , trimming toe nails , cooking , handling money , shopping , and taking medicines . even though many studies distinguish basic , instrumental , and functional disabilities , we combine all these dimensions in a single indicator after checking that the cronbach s alpha of the scale was an excellent .92 for the 14 items .
a person with basic disability ( i.e. , can not use the toilet ) is very likely to also have functional and instrumental disability ( i.e. , can not cut toenails).physical frailty : respondents failing two or more out of five physical tests
grip strength with a dynamometer , pulmonary peak flow , standing up from a chair several times , picking an object up from the floor , and standing and walking 3 m.cognitive disability according to the folstein ( folstein & folstein , 1975 ) mini - mental state examination ( mmse ) ( quiroga , albala , & klaasen , 2004 ) .
the scale from adding the 15 items had an acceptable cronbach s alpha of .72.geriatric depression refers to individuals with nine or more out of 15 yesavage symptoms of depression ( sheikh & yesavage , 1986 ) .
the cronbach s alpha of the scale was .85.metabolic syndrome , which is a combination of five health conditions ( abdominal girth , diabetes , triglycerides , high density lipoprotein ( hdl ) cholesterol , and high blood pressure ) that increase a respondent 's risk for cvd as defined by the international diabetes federation ( idf , 2006 ) .
the syndrome is present when individuals have high abdominal girth and at least two of the other four conditions.specific biological risk factors ( table 2 shows the cutoff points to define at risk ) .
most are components of the concept of allostatic load or biological dysregulation ( seeman et al . , 2004 ) .
details about specific indicators can be found in crimmins and seeman ( 2004).2.1 cvd factors : abdominal girth ( waist > 80 cm women , 94 cm men)diabetes , controlled or not ( glycosylated hemoglobin 6.5% or taking medicine)high blood pressure , controlled or not ( diastolic > 90 and systolic > 140 mmhg in at least three out of four measurements or taking medicine)high triglycerides in fasting serum ( 50 mg / dl)high cholesterol ratio ( total to hdl 5.92)2.2 various deregulation indicators ( some are also related to cvd)low creatinine clearance ( 44.64 mg / dl ) , an indicator of kidney functionhigh cortisol ( 25.69 g / g ) , indicator of activity in the hypothalamic pituitary ( hpa ) axis in response to stressorslow dehydroepiandrosterone sulfate ( dhea - s , 35 mg / dl ) .
antagonist to hpa activityhigh epinephrine ( 4.99 g / g ) in 12-h overnight urine .
indicator of neuroendocrine functioning in response to stresshigh norepinephrine ( 48 g / g ) in 12-h overnight urine .
similar to epinephrinehigh c - reactive protein ( crp ) concentrations ( 10 mg / l ) .
also a risk factor for cvdweak handgrip strength ( dynamometer 20 kg)unhealthy lifestylesobesity ( body mass index > 30 ) .
( note this is redundant with abdominal girth , which was included among cvd factors .
it is included in this group as a summary indicator of unhealthy lifestyles regarding food consumption and physical activity.)smoking currentno regular exercise in last yearno flu vaccine last year ( a tracer of preventive care seeking)high - calorie diet ( > 3000 day)low - calorie diet ( < 1500 day)high - carbohydrate diet ( > 400 g day)high - fat diet ( > 40 g day ) seven general health outcomes : death in the period september 2000 to september 2007 , in the sample of about 8,000 individuals .
about 1,000 foreigners are excluded from the original mother sample of 9,000 because they do not have the personal identification i d that allows the computer follow - up to establish death and its date .
the information on age is computed from the birth date in the birth record , avoiding the possibility of age - exaggeration errors .
, we took the two lowest ( mala and regular ) as defining poor srh .
functional disability when respondents have difficulties doing 50% or more of 14 activities and instrumental activities and instrumental activities of daily living ( activities of daily living ( adls)/instrumental activities of daily living ( iadls ) ) , namely : walking on the streets , climbing stairs , pushing objects , raising an arm , crossing the bedroom on your feet , bathing , eating , going to bed , using the toilet , trimming toe nails , cooking , handling money , shopping , and taking medicines . even though many studies distinguish basic , instrumental , and functional disabilities ,
we combine all these dimensions in a single indicator after checking that the cronbach s alpha of the scale was an excellent .92 for the 14 items .
a person with basic disability ( i.e. , can not use the toilet ) is very likely to also have functional and instrumental disability ( i.e. , can not cut toenails ) .
physical frailty : respondents failing two or more out of five physical tests grip strength with a dynamometer , pulmonary peak flow , standing up from a chair several times , picking an object up from the floor , and standing and walking 3 m. cognitive disability according to the folstein ( folstein & folstein , 1975 ) mini - mental state examination ( mmse ) ( quiroga , albala , & klaasen , 2004 ) .
the scale from adding the 15 items had an acceptable cronbach s alpha of .72 .
geriatric depression refers to individuals with nine or more out of 15 yesavage symptoms of depression ( sheikh & yesavage , 1986 ) .
metabolic syndrome , which is a combination of five health conditions ( abdominal girth , diabetes , triglycerides , high density lipoprotein ( hdl ) cholesterol , and high blood pressure ) that increase a respondent 's risk for cvd as defined by the international diabetes federation ( idf , 2006 ) .
the syndrome is present when individuals have high abdominal girth and at least two of the other four conditions .
specific biological risk factors ( table 2 shows the cutoff points to define at risk ) . some of them are components of the previous health outcomes .
most are components of the concept of allostatic load or biological dysregulation ( seeman et al . , 2004 ) .
abdominal girth ( waist > 80 cm women , 94 cm men ) diabetes , controlled or not ( glycosylated hemoglobin 6.5% or taking medicine ) high blood pressure , controlled or not ( diastolic > 90 and systolic > 140 mmhg in at least three out of four measurements or taking medicine ) high triglycerides in fasting serum ( 50 mg / dl ) high cholesterol ratio ( total to hdl 5.92 ) 2.2 various deregulation indicators ( some are also related to cvd ) low creatinine clearance ( 44.64 mg / dl ) , an indicator of kidney function high cortisol ( 25.69 g / g ) , indicator of activity in the hypothalamic pituitary ( hpa ) axis in response to stressors low dehydroepiandrosterone sulfate ( dhea - s , 35 mg / dl ) . antagonist to hpa activity high epinephrine ( 4.99 g / g ) in 12-h overnight urine
. indicator of neuroendocrine functioning in response to stress high norepinephrine ( 48 g / g ) in 12-h overnight urine .
similar to epinephrine high c - reactive protein ( crp ) concentrations ( 10 mg / l ) .
also a risk factor for cvd weak handgrip strength ( dynamometer 20 kg ) obesity ( body mass index > 30 ) .
( note this is redundant with abdominal girth , which was included among cvd factors .
it is included in this group as a summary indicator of unhealthy lifestyles regarding food consumption and physical activity . ) no regular exercise in last year no flu vaccine last year ( a tracer of preventive care seeking ) high - calorie diet ( > 3000 day ) low - calorie diet ( < 1500 day ) high - carbohydrate diet ( > 400 g day ) high - fat diet ( > 40 g day ) we have a total of 27 health indicators .
although there is some degree of overlap for several of them , this large number reflects the multidimensional character of the health concept and the complexities of measuring it . to facilitate interpretation and comparisons of results among the different outcomes , we opted for measuring them all with binary or dichotomous indicators of bad health .
we recognize that there is some loss of information from translating continuous variables into dichotomous indicators .
however , this loss is compensated by the gain in comparability and interpretability as well as by the gain of avoiding the distorting effects from extreme outlier values . where possible , we dichotomized variables with cutoff values commonly used in clinical practice and the literature , including mmse cognitive disability , yesavage geriatric depression , triglycerides , crp , obesity , abdominal obesity , and high- and low - calorie diet .
there are also several indicators that are naturally dichotomous , including death , metabolic syndrome , diabetes , high blood pressure , smoking , lack of physical exercise , and flu vaccine . for the remaining 12 ( out of 27 ) variables ,
our choice of cutoff values was driven by the observation of natural breaks in the distribution ( srh , functional disability , frailty , grip strength , and carbohydrate and fat intake ) or was borrowed from the macarthur study of healthy aging ( crimmins & seeman , 2004 ; seeman et al . , 2004 ) .
we examine the effect on health of three ses variables : place of residence , education , and household wealth .
all three are categorized in three levels in order to ascertain the two sides of ses gradients : pertaining to a low - ses stratum or being a high - ses individual . for comparison purposes ,
these three variables are considered constant over time , and we are taking them as reported in the 2000 census , years prior to health measurement ( note that mortality is studied for the period 20002007 , prevalence of health conditions in the 20052006 survey , and the ses indicators are the same in both data sets).place of residence in 2000 : ( 1 ) in the less developed lowlands , which include coastal regions at the pacific ocean and caribbean , as well as the northern plains bordering nicaragua and the southern region bordering panama ; ( 2 ) in the rest of the highlands at the central valley , which includes some suburbs and satellite towns of san jose ; ( 3 ) in the more developed metropolitan area of san jose , the capital city .
is not an individual - level variable , there is a large literature considering the role of place in health disparities ( e.g. , curtis and rees - jones , 1998 ) .
our simple categorization distinguishing urban and these other settings is consistent with a long literature that has documented rural
urban differences in health in various settings.educational attainment in three naturally defined groups : ( a ) none , ( b ) elementary ( one to six grades ) , and ( c ) some secondary ( postelementary ) school or higher .
the effects of education are some of the most studied among ses variables , given that education is easy to measure , does not change in adult life , is easily comparable , and has a number of socioeconomic influences related to factors such as empowerment , income generation , information gathering , and health - seeking behavior ( elo & preston , 1996 ; hummer , rogers , & eberstein , 1998).household wealth in three groups : poor , middle , and rich .
it is based on a simple count of 14 goods and conveniences in the household , ranging from no - dirt floors and having water connection and electricity to ( at the high end ) having a computer and a car .
wealth is in essence income accumulation or permanent income and thus an indicator of economic well - being during long periods ( menchik , 1993 ) .
place of residence in 2000 : ( 1 ) in the less developed lowlands , which include coastal regions at the pacific ocean and caribbean , as well as the northern plains bordering nicaragua and the southern region bordering panama ; ( 2 ) in the rest of the highlands at the central valley , which includes some suburbs and satellite towns of san jose ; ( 3 ) in the more developed metropolitan area of san jose , the capital city .
is not an individual - level variable , there is a large literature considering the role of place in health disparities ( e.g. , curtis and rees - jones , 1998 ) .
our simple categorization distinguishing urban and these other settings is consistent with a long literature that has documented rural
educational attainment in three naturally defined groups : ( a ) none , ( b ) elementary ( one to six grades ) , and ( c ) some secondary ( postelementary ) school or higher . the effects of education are some of the most studied among ses variables , given that education is easy to measure , does not change in adult life , is easily comparable , and has a number of socioeconomic influences related to factors such as empowerment , income generation , information gathering , and health - seeking behavior ( elo & preston , 1996 ; hummer , rogers , & eberstein , 1998 ) . household wealth in three groups : poor , middle , and rich .
it is based on a simple count of 14 goods and conveniences in the household , ranging from no - dirt floors and having water connection and electricity to ( at the high end ) having a computer and a car .
wealth is in essence income accumulation or permanent income and thus an indicator of economic well - being during long periods ( menchik , 1993 ) .
as far as possible , we present all health results adjusted by three demographic variables : ( a ) age ( single year ) , ( b ) sex , and ( c ) marital status ( whether or not currently married including consensual unions ) . age and marital status refer to the situation at the interview in all prevalence analyses . in the mortality analysis
, age is time varying ( each observation was split into single - age segments ) , and marital status is in the census interview in the year 2000 .
we also controlled in the regression models for the field worker who conducted the interview or took the anthropometric measures or other exams to correct potential interviewer and measurement biases ( all data were gathered by seven field workers over a period of 2 years ) .
although all field workers received the same training , and visited the same areas , and the work load was more or less randomly distributed , it is always possible that idiosyncratic behavior of a specific field worker might introduce some measurement bias .
for example , female examiners may tend to measure significantly lower values of waist circumference in female participants .
controlling for field worker in the multivariate analyses prevented the remote possibility that these biases were also correlated to ses of participants and thus were confounders of the relationship between health and ses .
to study mortality , we set the data as survival time ( statacorp , 2005 ) , with entry date at september 2000 ( 3 months after the census interview to avoid likely biases in case some hospitalized or very sick individuals were not interviewed in the june census ) and exit or right censoring at september 2007 .
we split observations into single - year segments ( approximately seven segments per individual ) .
mortality rates were computed as the ratio of deaths to the exact count of person - years .
we model some ses gradients in mortality with parametric hazard regression ( streg command in stata ) , assuming a gompertz distribution ( hosmer & lemeshow , 1999 ) .
the models control for demographic confounding effects as well as for the studied ses effects . to consider the possibility that age effects are nonlinear and differential by sex
, we included in the models a quadratic term for age and an interaction term for age and sex . to compare odds ratios across models , we reanalyzed mortality using a logistic model with the probability of dying in each age of the observation period as the dependent variable . in this model , we used robust estimates that take into account the lack of independence of age segments within each individual .
the standard errors in the logistic models were estimated considering the clustering effect of selecting whole health areas in the subsample .
this relaxed the assumption of independence among observations and required only that observations be independent across clusters . in some analyses , we assessed the significance of the joint effect of the three ses variables with a chi - square test of the improvement in the log - likelihood ratio resulting from including ses in the regression model .
table 1 shows the sizes and the composition by ses and demographic characteristics of the sample .
the three categories by place of residence are about the same size . in contrast ,
the low - end and high - end groups for these two variables comprise between 10% and 25% of observations .
the distribution by age reflects oversampling of old - age groups by design . as usual in elderly populations , there are more women than men . about 50% of the sample is married or in consensual union
. socioeconomic status ( ses ) and demographic variables in the mortality sample and prevalence subsample note : age at the middle of the mortality period ( 2000/2006 ) or at the interview in 2005/2006 .
sample size varies depending on the studied outcome ( table 2 ) . for studying mortality ,
our sample is more than 8,000 individuals or more than 50,000 person - years . for prevalence outcomes ,
the sample size is generally between 2,500 and 2,800 . for some specific indicators , the size further diminishes by a few hundred because of noncompliance or refusals in blood sample and urine collection .
the index of geriatric depression can be computed only for respondents who did not require a proxy in the interview ( 76% ) .
we also have smaller sample size ( about 1,600 ) for epinephrine and norepinephrine analyses because of degradation of stored urine samples .
health outcomes and specific health conditions in the analysis by age notes : rate or percentage computed considering sampling weights .
srh = self - rated health ; adl / iadl = activities of daily living / instrumental activities of daily living ; mmse = mini mental state examination ; hdl = high - density lipoprotein ; bmi = body mass index .
table 2 shows the observed values for the 27 health indicators by two large age brackets : 6079 years and 80 or more years .
comparing the two age groups provides an initial snapshot of how indicators shift with age , although it does not allow us to separate out potential confounding from cohort - specific effects ( e.g. , younger cohorts adopting western lifestyles that influence their health ) as well as selection effects ( e.g. , smokers may die at younger ages , which means that they are underrepresented at older ages ) .
given that all are poor - health indicators , one would expect substantial increments with age ( although evidence from other studies shows that some of these risk factors , such as obesity , cholesterol , and high blood pressure , may decline in late life as a result of other serious comorbidities ) .
cognitive and functional disabilities show a fivefold increment , with age being the closest to mortality .
srh and depression change little with age , and metabolic syndrome actually moves in the opposite direction from the expected age effect declining ( which is a health improvement ) 20% for older people .
health conditions that do not worsen , and even improve , with aging include the five components of metabolic syndrome : obesity , diabetes , high blood pressure , high cholesterol , and high triglycerides .
these age trends could be a reflection of improved cv health with aging within each individual .
or they could simply come from changes in the composition of the population with aging in a selection in frailty process ( vaupel , manton , & stallard , 1979 ) that eliminates the frail and sick at earlier ages .
the remaining biomarkers in the second panel of table 2 deteriorate ( increase ) with age , although at rates substantially lower than mortality .
low creatinine clearance , a marker of kidney malfunction , and grip strength are the only ones with a substantial aging increase ( ratio higher than 2 ) . most behavioral or lifestyle indicators in the third panel of table 2 improve ( diminish ) with age .
prevalence of smoking and obesity are less than half after age 80 than in the 6079 age group , high - calorie diet diminishes by 40% , and high - carbohydrate diet by one third .
the only behavioral deteriorations in the table are the lack of exercise and an increase in the proportion of individuals with a hypocaloric diet ( probably because of loss of appetite ) .
turning to the ses gradient issue , the exceptionally good health indicators of the costa rican population are by themselves a challenge to the notion of an inevitable ses gradient .
death rates of costa rican adults in the creles sample are lower than in the united states and not very different than in japan , especially at higher ages ( figure 2 ) , in spite of the substantially lower ses of the latin american population measured by any traditional indicator such as education , income , or health expenditure .
it is remarkable that a population with a per capita income that is one fifth of the united states ' and per capita health expenditures that are one tenth of the united states ' can have lower death rates than the united states .
life expectancy at age 60 implicit in the mortality rates in figure 2 is 22.4 years for men and 24.8 for women in the costa rican sample .
the corresponding values are 20.2 and 23.4 for the united states and 21.9 and 27.3 for japan . age - specific death rates .
often demographers have found that apparently low mortality at old ages in developing countries are solely an artifact of mismeasurement , particularly because of age exaggeration in census data that inflates the denominator and depletes the rates ( coale & kisker , 1986 ; preston , elo , & stewart , 1999 ) . in the costa rican sample , however , age errors are very unlikely because we are using data on exact birthdates as they appear in civil registration records and on the universal identity card , the cdula .
the possibility that we are finding low rates because of missing deaths in our computer follow - up is also remote because in the subsample of about 4,000 individuals creles visited , there was not a single case of a deceased person that was not also recorded in the national death registry computer follow - up .
furthermore , two other studies of old age mortality in costa rica have found similarly low rates ( rosero - bixby , 2008 ; rosero - bixby et al . , 2005 ) .
within costa rica , there is not a clear ses gradient in adult mortality or , if anything , the gradient is contrary to expectations . table 3 and figure 3 show that in our sample , there are slight increases in mortality with higher levels of education and wealth , net of other influences , and the least developed lowlands have lower mortality than the more developed highlands .
only the more developed capital city behaves according to expectations , showing lower mortality , although by a small margin .
socioeconomic status ( ses ) gradients in five health outcomes as estimated by logistic regression odds ratios notes : lr is the log - likelihood ratio chi
square of including the six ses variables in the model . significant at p < .05 .
socioeconomic status ( ses ) gradients in mortality and poor self - rated health ( srh ) .
rates or proportions relative to total population , controlled for age , sex , and marital status with regression : logistic for proportions and gompertz hazard for rates .
these mortality gradients contrast dramatically with the observed differentials by srh in table 3 and figure 3 .
the affluent and those with high school education self - report 40% less poor health than the national population .
the poor , those with no formal education , and those living in the lowlands report 20% more poor health than the national average .
this contradiction between mortality and srh is the motivation for the adjective of surprising ses gradients in this article 's title . in four other health outcomes , ses
high - ses individuals are less affected by functional , physical , and cognitive disabilities , or by depression . however , metabolic syndrome ( a multidimensional risk factor for cvd ) behaves more like mortality with no significant ses differentials .
there are also peculiarities of metabolic syndrome variation with age ( no gradient ) , sex ( much lower in men ) , and conjugal status ( higher among the married ) , but these are not the focus of this article .
given the enormous importance of cvd in adult mortality ( nearly half of old - age deaths are cardiovascular related in costa rica ) , this cvd risk factor helps explain the observed lack of ses gradients in overall mortality . to more finely explore the ses gradients in 20 intermediate health conditions , table 4 summarizes the results obtained from a series of logistic regressions . with a regression model for each health condition , we first estimated the net effects of the three ses variables and whether there was a significant joint effect of including the three variables in each model . in one third of the health indicators in the table ( 6 out of 20 ) , there are no significant joint ses effects . in the rest , the ses gradient sometimes behaves as expected with below - one odds ratio for the high - ses categories and above one for the low ses .
however , the reverse also is present in several indicators , such as obesity and triglycerides . to make things more complicated
, there are several cases of a curvilinear ses gradient , in which the middle - ses group is the worse off .
that is the case for triglycerides by wealth ; cholesterol and abdominal girth by education ; and dhea - s , epinephrine , and norepinephrine by place of residence .
figure 4 summarizes the large amount of information presented in tables 3 and 4 . with a logistic regression model for each health condition , the net effect of the three high - ses characteristics ( metro san jose , high school education , and rich wealth ) .
we then summarized the three odds ratios by computing the one that would correspond to an individual with simultaneously the three high - ses characteristics ; that is , by multiplication of the three odds ratios , and ( except in six cases as described subsequently ) we report this product in figure 4 .
given that this procedure presumes no interactions among the three ses variables , we also tested models with the triple interaction of the three low - ses indicators and with the triple interaction of the three high - ses indicators ( these extreme groups of all low ses and all high ses each represent only 4% of the sample ) . in the six ( out of 54 )
regression models where these interactions proved significant , we instead report in figure 4 an odds ratio that includes this triple interaction , rather than the previously described product of the odds ratios in the uninteracted model . in five of the six significant triple - interacted models ,
figure 4 shows these hypothetical odds ratios , sorted descending by the low - ses effect , which conversely results in approximately ascending sorting by the high - ses effects .
figures below 1 ( dots at the left ) denote good health ; that is , the risk of suffering the condition is lower in the group with respect to the rest of the population .
socioeconomic status ( ses ) gradients in intermediate health indicators as estimated by logistic regression odds ratios notes : these results are controlled for by age , age square , sex , age sex interaction , marital status , and field worker .
diet indicators also controlled for knee height , and carbohydrates and fat are controlled for calorie intake .
the reference groups for the three ses variables are highlands , grade school , and intermediate wealth , respectively .
lr is the log - likelihood ratio chi square including the six ses variables in the model .
poor - health indicators odds ratio prevalence in high - socioeconomic status ( ses ) and low - ses individuals .
see text for method to calculate odds ratios from models controlling for age , sex , and marital status with logistic regression .
high ses are wealthy metro san jose residents with postprimary education ; low ses are poor lowland residents with no education .
srh = self - rated health ; crp = c - reactive protein ; dhea - s = dehydroepiandrosterone sulfate if the ses gradient behaved as expected in figure 4 , the high - ses triangles should line up at the left of the figure and the low - ses circles should be at the right .
reality , as depicted by this costa rican sample , is far from that expected gradient .
there are three groups in our 27 health indicators : ( a ) 11 health indicators with the expected gradient of better health at high ses , ( b ) 9 health conditions , including death , in which low - ses individuals are better off , and ( 3 ) 7 indicators with no significant ses effects .
the expected ses gradient ( figure 4 ) occurs in five of our seven health outcomes ( srh ; cognitive , functional , and physical disability ; and depression ) , as well as in just two biomarkers ( norepinephrine and grip strength ) and two behavioral conditions ( smoking and lack of exercise ) .
counterbalancing the aforementioned health indicators , there are 10 conditions in which low - ses individuals do significantly better than high - ses groups : death , creatinine clearance , high - calorie diet , high blood pressure , obesity , high epinephrine , triglycerides , and low dhea - s levels , as well as the metabolic syndrome and its main component : abdominal girth . the pattern of the flu vaccine ( although marginally nonsignificant ) is on line with earlier findings that the costa rican primary health care system equalizes access to health in all ses levels
. it has been shown , for example , that there is a lower coverage of immunization among children of more affluent mothers ( chen - mok et al . , 2001 ) .
it is interesting to note that in several cvd risk factors , the ses disadvantaged groups do better , including triglycerides , cholesterol ratio , high blood pressure , diabetes , and fatty diet , although some of the effects are not significant .
rich data for elderly costa ricans from the creles project , which include a 6-year follow - up of a sample of 8,000 as well as biomarkers in a subsample of about 2,500 , show puzzling ses gradients in 26 health indicators .
disadvantaged groups in terms of education , wealth , and residence show steep health deficits in srh as well as in indicators of functionality and physical and mental fitness .
in contrast , in the single most important health outcome , mortality , there are no significant ses differentials ; on the contrary , there are even hints that low - ses groups might be better off .
metabolic syndrome , a risk factor for cvd , shows a similar pattern as mortality .
the direct relationship between ses and mortality found in these data may occur only in the elderly population under study ( 60 years and over ) .
the usual inverse relationship may persist in younger ages , which were not included in the analyzed sample .
this study intentionally considers a large number of health indicators to reflect the multidimensional character of the health concept .
the results show that these multiple dimensions of health do not behave in a monolithic way .
ses , and aging as well , generates very diverse responses in different aspects of health . cognitive impairment , for example , is substantially higher at older age and low ses ( although the strong negative association with education may be exaggerated by a cultural bias in the mini mental test ) . similarly , geriatric depression in our data is one of the most clear correlates with low ses , but it changes little with age ( though the latter may be due to the large proportion of missing responses among the oldest old needing a proxy in the interview ) .
our stress - related biomarkers epinephrine and norepinephrine also show an advantage for the affluent and educated .
these costa rican data show that socioeconomically disadvantaged populations have lower prevalence of obesity , hypercholesterolemia , triglycerides , hypertension , and hyperglycemia .
the changing association between ses and cvd merits careful monitoring in countries like costa rica .
dhea - s , a hormone some consider a marker of aging , also shows a more favorable situation in low - ses individuals .
smoking , sedentariness , and high - carbohydrate diets are less prevalent among the better off . but obesity , high fat , and high - calorie diets diminish consistently and substantially with ses .
interestingly , there are no negative ses gradients in our indicator of access to preventive care : having had the flu vaccine .
this is an indication of an important attribute of the public primary health care system in costa rica
its coverage of the lower strata of society to equalize access to health care ( rosero - bixby , 2004a ) .
viewing the diet - related biomarkers in conjunction with the dietary intake data , we can hypothesize that worse nutritional behaviors among higher ses groups may be playing a significant role in driving the worse cvd risks , and hence higher mortality , among the higher ses .
moreover , the low - calorie diet of low - ses individuals might be a protective factor because it has been shown that dietary caloric restriction slows ageing in other species ( roth et al . , 2002 ) .
this raises the question of what the time path has been and will be of ses gradients in nutritional behaviors .
a substantial literature has documented the transition of middle - income countries from positive ses obesity relationships to negative ones as countries develop ( e.g. , monteiro , moura , conde , & popkin , 2004 ) ; whereas countries such as mexico appear to have already moved through this nutritional transition , costa rica appears to lag .
it will be useful for future work to document the history of this ses nutrition relationship in costa rica , as well as to closely track its evolution , as this may have major implications for whether costa rica 's mortality gradient reverses in the future to the more usual negative relationship with ses .
for the broader set of health indicators examined , however , we do not know whether the findings in this article are unique to costa rica or whether they are common in other middle- and low - income countries .
reliable data to study ses gradients in adult mortality and in hard health indicators are rare .
however , this article shows that one can not jump from there to conclusions on other health outcomes . more research
costa rica is a special case of exceptional achievements in health and social development in spite of a weak economy .
two decades ago it was included , along with sri lanka , kerala , china , and cuba , among the world showcases of good health at low cost
( halstead , walsh , & warren , 1985 ) , and it has remained in that category . some have explained the country 's longevity achievements with its investments in education and health insurance ( caldwell , 1986 ) .
however , those can only be part of the explanation because even those with no education are doing fine in important aspects of health , including health dimensions not clearly influenced by medical care access
. it could even be that if a poor or traditional society completes the first stage of the epidemiologic transition by controlling communicable diseases , some traditional lifestyles can protect it from health problems like obesity and take it to better general health indicators such as lower mortality .
this evidence of success is tempered , however , by our strong evidence of a significant ses gradient in functional and mental health indicators , suggesting that disability - free life expectancy is indeed worse among more vulnerable adults even in costa rica .
the creles project is a longitudinal study of the universidad de costa rica , carried on by the centro centroamericano de poblacin in collaboration with the instituto de investigaciones en salud , with the support of the wellcome trust foundation ( grant no . | backgroundto determine socioeconomic status ( ses ) gradients in the different dimensions of health among elderly costa ricans .
hypothesis : ses disparities in adult health are minimal in costa rican society.methodsdata from the costa rican study on longevity and healthy aging study : 8,000 elderly costa ricans to determine mortality in the period 20002007 and a subsample of 3,000 to determine prevalence of several health conditions and biomarkers from anthropometry and blood and urine specimens.resultsthe ultimate health indicator , mortality , as well as the metabolic syndrome , reveals that better educated and wealthier individuals are worse off .
in contrast , quality of life related measures such as functional and cognitive disabilities , physical frailty , and depression all clearly worsen with lower ses .
overall self - reported health ( srh ) also shows a strong positive ses gradient .
traditional cardiovascular risk factors such as diabetes and cholesterol are not significantly related to ses , but hypertension and obesity are worse among high - ses individuals . reflecting mixed ses gradients in behaviors , smoking and lack of exercise are more common among low ses , but high calorie diets are more common among high ses.conclusionsnegative modern behaviors among high - ses groups may be reversing cardiovascular risks across ses groups , hence reversing mortality risks . but negative ses gradients in healthy years of life persist . | <s>[INST]analyses in developed countries have found ses and adult health to be significantly positively correlated
, 2008)though gradients appear smaller at older ages than at earlier ages ( crimmins , 2005 ; elo & preston , 1996 ; turra & goldman , 2007 ) . in developing countries ,
there has been much less study of older adult health differentials , partly due to the paucity of appropriate data until recent years . now available surveys in elderly populations in asia and latin america do indeed appear to also show substantially poorer self - assessed health among the low educated ( palloni & mceniry , 2004 ; zimmer , natividad , ofstedal , & lin , 2002 )
. however , the ses gradient in less subjective indicators is much less consistent . in asia
, surveys such as in taiwan have found unclear relationships between ses and indicators of functional health , and ses differentials appear to even reverse for life - threatening measurements such as stroke , cancer , and diabetes ( zimmer et al . ,
in contrast , latin american surveys such as in mexico find that the ses gradient persists for chronic conditions like diabetes , although with less strength than that observed in self - assessed health indicators ( palloni & mceniry , 2004 ) . in both asian and latin american studies , socioeconomic differentials are often smaller than those observed in the high - income countries .
when studying mortality indicators , ses differentials for older adults are again not well understood in developing countries .
a few recent studies have found that mortality by cardiovascular diseases ( cvds ) and diabetes tends to be higher in the more developed areas of costa rica ( rosero - bixby , 1996 ) ; similarly , a 17-year follow - up study in costa ricans showed no significant differences in survival by ses among older people ( rosero - bixby , dow , & lacle , 2005 ) .
another challenging result is the so called hispanic paradox ; that is , the lower mortality of elderly hispanics compared with the much more affluent white population in the united states ( elo , turra , kestenbaum , & ferguson , 2004 ) , which some argue may be partly due to cultural differences in health behaviors and psychosocial support .
hispanics also show significantly smaller ses differentials in mortality than whites ( turra & goldman , 2007 ) .
by contrast , bangladesh data from a surveillance site shows the expected pattern of higher adult mortality at lower education ( hurt , ronsmans , & saha , 2004 ; mostafa & ginneken , 2000 ) .
various hypotheses have been suggested to explain different dimensions of the conflicting ses patterns in adult health .
some authors attribute to selection effects the weakening of ses differentials by age : that is , mortality eliminates the frailest individuals at early ages in groups with lower ses ( crimmins , 2005 ) . but selection effects can not easily explain the contrasting relationships across different domains of objective and subjectively reported health .
these puzzles could be partly due to systematic biases by ses in subjective self - reports , but they also may reflect true differences in ses gradients across different domains of health .
for example , it could be that low ses is associated with demanding physical labor across the life course that manifests in self - reported pain and mobility problems , whereas middle and higher income is associated with developed country lifestyles that elevate cardiovascular risks for mortality .
buffers to low ses may also operate differentially on different health domains , with national health insurance enabling low ses to buffer the ill effects of certain medically manageable cardiovascular risk factors , but with fewer buffers potentially available against the adverse effects of cumulative insults from low social and occupational status .
its life expectancy at birth ( 78 years ) is the second highest in the americas ( canada is first ) , higher even than in the united states ( world bank , 2006 ) .
broad explanations of costa rica 's health achievements in the literature include the orientation of the government toward equity and social development , with large social investments being possible in part due to the absence of military expenditures , given that the 1949 constitution abolished the armed forces ( rosero - bixby , 1991 ) .
investments in education and the very high coverage of health insurance are often mentioned as key factors ( caldwell , 1986 ) .
the social security system , which is funded from deductions from payrolls and from contributions by employers and the government , is the provider of health insurance and health services with an almost universal coverage , especially for the elderly population .
all workers in the formal sector and many workers in the informal sector contribute to the system and are entitled to health insurance that allows them and their families to receive free health care services and free medications at any hospital , clinic , or community health center .
additionally , the government provides free health insurance to poor people . according to the 2000 census
, health insurance covers 82% of the population , including 9% destitute individuals whose insurance is paid by the government ( rosero - bixby , 2004a ) .
provision of primary health care , particularly to remote or poor populations , has had a quantifiable impact on death rates ( rosero - bixby , 2004b ) . in economic terms , costa rica does not differ from the latin american average . according to the world bank ( 2006 ) , its per capita income is about $ 4,600 per year , compared with the $ 3,600 average for latin america .
however , in terms of equity in income distribution , social security coverage , access to public health services and sanitation , labor laws , and protection of the environment , costa rica ranks among the highest in the continent .
costa rica has a mixed economy with open markets and , at the same time ,
government control of key areas such as health , education , banking , energy , communications , and insurance ( mesa - lago , 2000 ) .
the human development index of the united nations ranks costa rica 48th in the world and fourth in latin america ( after chile , argentina , and uruguay ) .
this article follows a simple framework ( figure 1 ) to organize the different dimensions and indicators of health ( crimmins & seeman , 2004 ) .
general health outcomes such as mortality and physical functioning are the end points of the framework .
proximate determinants very close to these outcomes are specific biological risk factors , usually measured by biomarkers such as blood pressure , obesity , and glucose levels
. then , one step back in the explanation hierarchy , there are health behaviors ( diet , smoking , exercising ) and health care services .
some demographic factors , such as age , sex , and marital status , are considered at the same hierarchical level and ses , and therefore their confounding effects must be controlled for .
the purpose of the article is to fill the breach in the literature regarding ses gradients in objectively measured adult health indicators in developing countries . does the well - documented
, strong connection of poor health and low ses among adults of rich countries and among children of developing countries persist in hard data for adults in middle - income countries like costa rica ?
first , ses disparities in health outcomes are interesting in and of themselves and have received a great deal of public attention in other settings ( such as in the united states or among children in latin america ) .
yet they have rarely been documented in latin american adult populations , primarily due to lack of data , except on a few select indicators .
a key contribution of this article is the availability in creles of a wide range of both subjective and objective health measures , which we analyze within a uniform empirical framework , creating an unparalleled opportunity in latin america to make ses gradient comparisons across them .
second , the analysis is of interest because once we have established stylized facts about health disparities in this population , we can begin to evaluate existing hypotheses and generate new ones about the determinants of health patterns in this setting .
there are many hypotheses about why health is typically worse in low ses populations . similarly , many hypotheses have been advanced about how a middle - income country such as costa rica has been able to obtain exceptionally good population average health outcomes , such as higher life expectancy than the united states .
these generally relate to models of the social determinants of population health : health care access , health behaviors , environmental health exposures , psychosocial stressors ( inequality ) , and the ability to buffer against negative health shocks ( social safety nets , social capital , and interpersonal ties ) .
although we do not formally test such hypotheses in this article , our analyses speak to the face validity of how some of these may or may not operate in costa rica .
because this is the first nationwide survey of adult health in costa rica , this article provides the first opportunity for beginning to evaluate such hypotheses .
the main hypothesis that we do test in this article is the provocative proposition that there is no ses gradient in costa rican adult health .
this hypothesis is based on prior findings of no education or wealth gradients in costa rican mortality , from the only previous study on the subject , using data from a single peri - urban community ( rosero - bixby et al . , 2005 ) .
observers have hypothesized that costa rica may have little ses gradient due to factors such as universal health insurance ( which has allowed low ses groups similar access to care as high ses groups ) in combination with costa rica perhaps being an unusually equitable society . for these factors to have been instrumental in minimizing ses gradients , however , it should be the case that ses gradients would be minimal across a wide range of health indicators beyond just mortality which is exactly what our analyses test .
the purpose of the article is to fill the breach in the literature regarding ses gradients in objectively measured adult health indicators in developing countries .
does the well - documented , strong connection of poor health and low ses among adults of rich countries and among children of developing countries persist in hard data for adults in middle - income countries like costa rica ?
first , ses disparities in health outcomes are interesting in and of themselves and have received a great deal of public attention in other settings ( such as in the united states or among children in latin america ) .
yet they have rarely been documented in latin american adult populations , primarily due to lack of data , except on a few select indicators . a key contribution of this article is the availability in creles of a wide range of both subjective and objective health measures , which we analyze within a uniform empirical framework , creating an unparalleled opportunity in latin america to make ses gradient comparisons across them .
second , the analysis is of interest because once we have established stylized facts about health disparities in this population , we can begin to evaluate existing hypotheses and generate new ones about the determinants of health patterns in this setting .
similarly , many hypotheses have been advanced about how a middle - income country such as costa rica has been able to obtain exceptionally good population average health outcomes , such as higher life expectancy than the united states .
these generally relate to models of the social determinants of population health : health care access , health behaviors , environmental health exposures , psychosocial stressors ( inequality ) , and the ability to buffer against negative health shocks ( social safety nets , social capital , and interpersonal ties ) .
although we do not formally test such hypotheses in this article , our analyses speak to the face validity of how some of these may or may not operate in costa rica .
because this is the first nationwide survey of adult health in costa rica , this article provides the first opportunity for beginning to evaluate such hypotheses .
the main hypothesis that we do test in this article is the provocative proposition that there is no ses gradient in costa rican adult health .
this hypothesis is based on prior findings of no education or wealth gradients in costa rican mortality , from the only previous study on the subject , using data from a single peri - urban community ( rosero - bixby et al . , 2005 ) .
observers have hypothesized that costa rica may have little ses gradient due to factors such as universal health insurance ( which has allowed low ses groups similar access to care as high ses groups ) in combination with costa rica perhaps being an unusually equitable society . for these factors to have been instrumental in minimizing ses gradients , however , it should be the case that ses gradients would be minimal across a wide range of health indicators beyond just mortality which is exactly what our analyses test .
data for this analysis come from creles , an on - going longitudinal study of a nationally representative sample of about 9,000 adults aged 60 years and over and residing in costa rica in the year 2000 , with oversampling of the oldest old and with an in - depth , longitudinal survey in a subsample of about 3,000 of them .
for this analysis , we use mortality data from the computer follow - up of the sample in the national death registry from september 2000 to september 2006 . the data on health ( mostly prevalence of conditions ) come from the first wave of interviews in the 3,000 subsample , conducted from november 2004 to september 2006 .
the mother sample of 9,000 individuals was randomly selected from the 2000 census database after stratification by 5-year age groups .
sampling fractions ranged from 1.1% among those born in 19411945 to 100% for those born before 1905 .
for the in - depth longitudinal survey , creles took from the mother sample a systematic subsample of 60 health areas
this subsample included originally more than 4,000 individuals : 2,827 of them were finally interviewed .
the subsample , which covers 59% of costa rican territory , yielded the following nonresponse rates : 19% of the individuals were deceased by the contact date , 18% were not found in the field , 2% moved to other addresses , 2% rejected the interview , and 2% remain as pending interviews after several visits ( likely rejections ) .
the individuals we did not find in the field originated mostly in the vagueness of the census address ( and the lack of an accurate address system in costa rica ) , as well as from address changes during the approximately 5-year lag between the census and our visit .
thus , it would be unlikely that this group 's ses patterns in health would be so different from the interviewed population so as to create significant selection effects that bias the estimated health ses relationships . among those interviewed , 95% provided a blood sample , 92% collected urine overnight , 91% had all anthropometric measures , and 24% required a proxy to answer the questionnaire .
all the data and specimens in the subsample were collected at the participants homes , usually in two visits . in the first visit ,
participants provided informed consent and answered a 90-min questionnaire ( including some mobility tests and two blood pressure measures ) as well as a 10-min frequency of tracer food consumption questionnaire . in a second visit early the next day ,
fasting blood samples were collected by venipuncture : one edta tube ( for 34 ml of whole blood ) and two serum - separating tubes , with a clot activator ( for 1012 ml of blood , to obtain 46 ml of serum ) . in this visit
, the field team also picked up a cooler containing 12-h overnight urine and took the anthropometric measures .
all field data were collected using personal digital assistants , also known as palm computers , with software applications developed by the central american population center for this study .
a field team of five interviewers , two phlebotomists , and a supervisor collected the information and the blood and urine specimens using a continuous fieldwork design over a period of nearly 2 years .
several costa rican laboratories analyzed the blood and urine specimens , depending on the type of biomarker .
all laboratories were certified by a national reference center of clinical chemistry , an agency under the ministry of health .
in addition to the internal reliability tests that these laboratories must conduct as part of their quality control procedures , we conducted reliability analyses in subsamples of 2040 specimens that were reanalyzed for each biomarker in a different laboratory .
we report elsewhere the results of these reliability analyses , as well as some adjustments introduced to standardize measures across laboratories ( mndez - chacn , rosero - bixby , fernndez - rojas , & barrantes - jimnez , 2007 ) .
we identified deaths of the 8,000 individuals in the original sample by computer follow - up in the national death registry during the period 20002007 , using the unique identification number ( the cdula ) that all costa ricans have .
prior research has indicated that the death registry is virtually 100% complete ( rosero - bixby , 2008 ) . to further validate the registry quality
, we were able to successfully match in the registry all of the several hundred deaths that we identified while attempting to contact individuals in the field for the household survey , thus finding no deaths missing from the registry .
all are coded as 0 , 1 dichotomous indicators , with 1 measuring unfavorable conditions or events : ( a ) general health outcomes , ( b ) specific poor health conditions , including biomarkers , and ( c ) unhealthy lifestyles.seven general health outcomes : death in the period september 2000 to september 2007 , in the sample of about 8,000 individuals .
about 1,000 foreigners are excluded from the original mother sample of 9,000 because they do not have the personal identification i d that allows the computer follow - up to establish death and its date .
the information on age is computed from the birth date in the birth record , avoiding the possibility of age - exaggeration errors.ordinal general srh status . from the five possible answers
, we took the two lowest ( mala and regular ) as defining poor srh.functional disability when respondents have difficulties doing 50% or more of 14 activities and instrumental activities and instrumental activities of daily living ( activities of daily living ( adls)/instrumental activities of daily living ( iadls ) ) , namely : walking on the streets , climbing stairs , pushing objects , raising an arm , crossing the bedroom on your feet , bathing , eating , going to bed , using the toilet , trimming toe nails , cooking , handling money , shopping , and taking medicines . even though many studies distinguish basic , instrumental , and functional disabilities , we combine all these dimensions in a single indicator after checking that the cronbach s alpha of the scale was an excellent .92 for the 14 items .
a person with basic disability ( i.e. , can not use the toilet ) is very likely to also have functional and instrumental disability ( i.e. , can not cut toenails).physical frailty : respondents failing two or more out of five physical tests grip strength with a dynamometer , pulmonary peak flow , standing up from a chair several times , picking an object up from the floor , and standing and walking 3 m.cognitive disability according to the folstein ( folstein & folstein , 1975 ) mini - mental state examination ( mmse ) ( quiroga , albala , & klaasen , 2004 ) .
we considered disabled those with less than 75% right answers of 15 items . the scale from adding the 15 items had an acceptable cronbach s alpha of .72.geriatric depression refers to individuals with nine or more out of 15 yesavage symptoms of depression ( sheikh & yesavage , 1986 ) .
the cronbach s alpha of the scale was .85.metabolic syndrome , which is a combination of five health conditions ( abdominal girth , diabetes , triglycerides , high density lipoprotein ( hdl ) cholesterol , and high blood pressure ) that increase a respondent 's risk for cvd as defined by the international diabetes federation ( idf , 2006 ) .
the syndrome is present when individuals have high abdominal girth and at least two of the other four conditions.specific biological risk factors ( table 2 shows the cutoff points to define at risk ) .
most are components of the concept of allostatic load or biological dysregulation ( seeman et al . , 2004 ) .
details about specific indicators can be found in crimmins and seeman ( 2004).2.1 cvd factors : abdominal girth ( waist > 80 cm women , 94 cm men)diabetes , controlled or not ( glycosylated hemoglobin 6.5% or taking medicine)high blood pressure , controlled or not ( diastolic > 90 and systolic > 140 mmhg in at least three out of four measurements or taking medicine)high triglycerides in fasting serum ( 50 mg / dl)high cholesterol ratio ( total to hdl 5.92)2.2 various deregulation indicators ( some are also related to cvd)low creatinine clearance ( 44.64 mg / dl ) , an indicator of kidney functionhigh cortisol ( 25.69 g / g ) , indicator of activity in the hypothalamic pituitary ( hpa ) axis in response to stressorslow dehydroepiandrosterone sulfate ( dhea - s , 35 mg / dl ) . antagonist to hpa activityhigh epinephrine ( 4.99 g / g ) in 12-h overnight urine .
indicator of neuroendocrine functioning in response to stresshigh norepinephrine ( 48 g / g ) in 12-h overnight urine .
similar to epinephrinehigh c - reactive protein ( crp ) concentrations ( 10 mg / l ) .
also a risk factor for cvdweak handgrip strength ( dynamometer 20 kg)unhealthy lifestylesobesity ( body mass index > 30 ) .
( note this is redundant with abdominal girth , which was included among cvd factors .
it is included in this group as a summary indicator of unhealthy lifestyles regarding food consumption and physical activity.)smoking currentno regular exercise in last yearno flu vaccine last year ( a tracer of preventive care seeking)high - calorie diet ( > 3000 day)low - calorie diet ( < 1500 day)high - carbohydrate diet ( > 400 g day)high - fat diet ( > 40 g day ) seven general health outcomes : death in the period september 2000 to september 2007 , in the sample of about 8,000 individuals .
about 1,000 foreigners are excluded from the original mother sample of 9,000 because they do not have the personal identification i d that allows the computer follow - up to establish death and its date .
the information on age is computed from the birth date in the birth record , avoiding the possibility of age - exaggeration errors .
, we took the two lowest ( mala and regular ) as defining poor srh .
functional disability when respondents have difficulties doing 50% or more of 14 activities and instrumental activities and instrumental activities of daily living ( activities of daily living ( adls)/instrumental activities of daily living ( iadls ) ) , namely : walking on the streets , climbing stairs , pushing objects , raising an arm , crossing the bedroom on your feet , bathing , eating , going to bed , using the toilet , trimming toe nails , cooking , handling money , shopping , and taking medicines .
even though many studies distinguish basic , instrumental , and functional disabilities , we combine all these dimensions in a single indicator after checking that the cronbach s alpha of the scale was an excellent .92 for the 14 items .
a person with basic disability ( i.e. , can not use the toilet ) is very likely to also have functional and instrumental disability ( i.e. , can not cut toenails ) .
physical frailty : respondents failing two or more out of five physical tests grip strength with a dynamometer , pulmonary peak flow , standing up from a chair several times , picking an object up from the floor , and standing and walking 3 m. cognitive disability according to the folstein ( folstein & folstein , 1975 ) mini - mental state examination ( mmse ) ( quiroga , albala , & klaasen , 2004 ) .
the scale from adding the 15 items had an acceptable cronbach s alpha of .72 .
geriatric depression refers to individuals with nine or more out of 15 yesavage symptoms of depression ( sheikh & yesavage , 1986 ) .
metabolic syndrome , which is a combination of five health conditions ( abdominal girth , diabetes , triglycerides , high density lipoprotein ( hdl ) cholesterol , and high blood pressure ) that increase a respondent 's risk for cvd as defined by the international diabetes federation ( idf , 2006 ) .
the syndrome is present when individuals have high abdominal girth and at least two of the other four conditions .
specific biological risk factors ( table 2 shows the cutoff points to define at risk ) .
most are components of the concept of allostatic load or biological dysregulation ( seeman et al . , 2004 ) .
abdominal girth ( waist > 80 cm women , 94 cm men ) diabetes , controlled or not ( glycosylated hemoglobin 6.5% or taking medicine ) high blood pressure , controlled or not ( diastolic > 90 and systolic > 140 mmhg in at least three out of four measurements or taking medicine ) high triglycerides in fasting serum ( 50 mg / dl ) high cholesterol ratio ( total to hdl 5.92 ) 2.2 various deregulation indicators ( some are also related to cvd ) low creatinine clearance ( 44.64 mg / dl ) , an indicator of kidney function high cortisol ( 25.69 g / g ) , indicator of activity in the hypothalamic pituitary ( hpa ) axis in response to stressors low dehydroepiandrosterone sulfate ( dhea - s , 35 mg / dl ) . antagonist to hpa activity high epinephrine ( 4.99 g / g ) in 12-h overnight urine .
indicator of neuroendocrine functioning in response to stress high norepinephrine ( 48 g / g ) in 12-h overnight urine .
also a risk factor for cvd weak handgrip strength ( dynamometer 20 kg ) obesity ( body mass index > 30 ) .
( note this is redundant with abdominal girth , which was included among cvd factors .
it is included in this group as a summary indicator of unhealthy lifestyles regarding food consumption and physical activity . ) no regular exercise in last year no flu vaccine last year ( a tracer of preventive care seeking ) high - calorie diet ( > 3000 day ) low - calorie diet ( < 1500 day ) high - carbohydrate diet ( > 400 g day ) high - fat diet ( > 40 g day ) we have a total of 27 health indicators .
although there is some degree of overlap for several of them , this large number reflects the multidimensional character of the health concept and the complexities of measuring it . to facilitate interpretation and comparisons of results among the different outcomes
, we opted for measuring them all with binary or dichotomous indicators of bad health .
we recognize that there is some loss of information from translating continuous variables into dichotomous indicators .
however , this loss is compensated by the gain in comparability and interpretability as well as by the gain of avoiding the distorting effects from extreme outlier values . where possible , we dichotomized variables with cutoff values commonly used in clinical practice and the literature , including mmse cognitive disability , yesavage geriatric depression , triglycerides , crp , obesity , abdominal obesity , and high- and low - calorie diet .
there are also several indicators that are naturally dichotomous , including death , metabolic syndrome , diabetes , high blood pressure , smoking , lack of physical exercise , and flu vaccine . for
the remaining 12 ( out of 27 ) variables , our choice of cutoff values was driven by the observation of natural breaks in the distribution ( srh , functional disability , frailty , grip strength , and carbohydrate and fat intake ) or was borrowed from the macarthur study of healthy aging ( crimmins & seeman , 2004 ; seeman et al . , 2004 ) .
we examine the effect on health of three ses variables : place of residence , education , and household wealth .
all three are categorized in three levels in order to ascertain the two sides of ses gradients : pertaining to a low - ses stratum or being a high - ses individual . for comparison purposes ,
these three variables are considered constant over time , and we are taking them as reported in the 2000 census , years prior to health measurement ( note that mortality is studied for the period 20002007 , prevalence of health conditions in the 20052006 survey , and the ses indicators are the same in both data sets).place of residence in 2000 : ( 1 ) in the less developed lowlands , which include coastal regions at the pacific ocean and caribbean , as well as the northern plains bordering nicaragua and the southern region bordering panama ; ( 2 ) in the rest of the highlands at the central valley , which includes some suburbs and satellite towns of san jose ; ( 3 ) in the more developed metropolitan area of san jose , the capital city . although
is not an individual - level variable , there is a large literature considering the role of place in health disparities ( e.g. , curtis and rees - jones , 1998 ) .
our simple categorization distinguishing urban and these other settings is consistent with a long literature that has documented rural
urban differences in health in various settings.educational attainment in three naturally defined groups : ( a ) none , ( b ) elementary ( one to six grades ) , and ( c ) some secondary ( postelementary ) school or higher .
the effects of education are some of the most studied among ses variables , given that education is easy to measure , does not change in adult life , is easily comparable , and has a number of socioeconomic influences related to factors such as empowerment , income generation , information gathering , and health - seeking behavior ( elo & preston , 1996 ; hummer , rogers , & eberstein , 1998).household wealth in three groups : poor , middle , and rich .
it is based on a simple count of 14 goods and conveniences in the household , ranging from no - dirt floors and having water connection and electricity to ( at the high end ) having a computer and a car .
wealth is in essence income accumulation or permanent income and thus an indicator of economic well - being during long periods ( menchik , 1993 ) .
place of residence in 2000 : ( 1 ) in the less developed lowlands , which include coastal regions at the pacific ocean and caribbean , as well as the northern plains bordering nicaragua and the southern region bordering panama ; ( 2 ) in the rest of the highlands at the central valley , which includes some suburbs and satellite towns of san jose ; ( 3 ) in the more developed metropolitan area of san jose , the capital city .
is not an individual - level variable , there is a large literature considering the role of place in health disparities ( e.g. , curtis and rees - jones , 1998 ) .
our simple categorization distinguishing urban and these other settings is consistent with a long literature that has documented rural
educational attainment in three naturally defined groups : ( a ) none , ( b ) elementary ( one to six grades ) , and ( c ) some secondary ( postelementary ) school or higher .
the effects of education are some of the most studied among ses variables , given that education is easy to measure , does not change in adult life , is easily comparable , and has a number of socioeconomic influences related to factors such as empowerment , income generation , information gathering , and health - seeking behavior ( elo & preston , 1996 ; hummer , rogers , & eberstein , 1998 ) .
it is based on a simple count of 14 goods and conveniences in the household , ranging from no - dirt floors and having water connection and electricity to ( at the high end ) having a computer and a car .
wealth is in essence income accumulation or permanent income and thus an indicator of economic well - being during long periods ( menchik , 1993 ) . as far as possible , we present all health results adjusted by three demographic variables : ( a ) age ( single year ) , ( b ) sex , and ( c ) marital status ( whether or not currently married including consensual unions ) . age and marital status refer to the situation at the interview in all prevalence analyses . in the mortality analysis , age is time varying ( each observation was split into single - age segments ) , and marital status is in the census interview in the year 2000 .
we also controlled in the regression models for the field worker who conducted the interview or took the anthropometric measures or other exams to correct potential interviewer and measurement biases ( all data were gathered by seven field workers over a period of 2 years ) .
although all field workers received the same training , and visited the same areas , and the work load was more or less randomly distributed , it is always possible that idiosyncratic behavior of a specific field worker might introduce some measurement bias .
for example , female examiners may tend to measure significantly lower values of waist circumference in female participants .
controlling for field worker in the multivariate analyses prevented the remote possibility that these biases were also correlated to ses of participants and thus were confounders of the relationship between health and ses . to study mortality
, we set the data as survival time ( statacorp , 2005 ) , with entry date at september 2000 ( 3 months after the census interview to avoid likely biases in case some hospitalized or very sick individuals were not interviewed in the june census ) and exit or right censoring at september 2007 .
we split observations into single - year segments ( approximately seven segments per individual ) .
mortality rates were computed as the ratio of deaths to the exact count of person - years .
we model some ses gradients in mortality with parametric hazard regression ( streg command in stata ) , assuming a gompertz distribution ( hosmer & lemeshow , 1999 ) .
the models control for demographic confounding effects as well as for the studied ses effects . to consider the possibility that age effects are nonlinear and differential by sex
, we included in the models a quadratic term for age and an interaction term for age and sex . to compare odds ratios across models , we reanalyzed mortality using a logistic model with the probability of dying in each age of the observation period as the dependent variable . in this model , we used robust estimates that take into account the lack of independence of age segments within each individual .
the standard errors in the logistic models were estimated considering the clustering effect of selecting whole health areas in the subsample .
this relaxed the assumption of independence among observations and required only that observations be independent across clusters . in some analyses , we assessed the significance of the joint effect of the three ses variables with a chi - square test of the improvement in the log - likelihood ratio resulting from including ses in the regression model .
all are coded as 0 , 1 dichotomous indicators , with 1 measuring unfavorable conditions or events : ( a ) general health outcomes , ( b ) specific poor health conditions , including biomarkers , and ( c ) unhealthy lifestyles.seven general health outcomes : death in the period september 2000 to september 2007 , in the sample of about 8,000 individuals .
about 1,000 foreigners are excluded from the original mother sample of 9,000 because they do not have the personal identification i d that allows the computer follow - up to establish death and its date .
the information on age is computed from the birth date in the birth record , avoiding the possibility of age - exaggeration errors.ordinal general srh status . from the five possible answers
, we took the two lowest ( mala and regular ) as defining poor srh.functional disability when respondents have difficulties doing 50% or more of 14 activities and instrumental activities and instrumental activities of daily living ( activities of daily living ( adls)/instrumental activities of daily living ( iadls ) ) , namely : walking on the streets , climbing stairs , pushing objects , raising an arm , crossing the bedroom on your feet , bathing , eating , going to bed , using the toilet , trimming toe nails , cooking , handling money , shopping , and taking medicines . even though many studies distinguish basic , instrumental , and functional disabilities , we combine all these dimensions in a single indicator after checking that the cronbach s alpha of the scale was an excellent .92 for the 14 items .
a person with basic disability ( i.e. , can not use the toilet ) is very likely to also have functional and instrumental disability ( i.e. , can not cut toenails).physical frailty : respondents failing two or more out of five physical tests
grip strength with a dynamometer , pulmonary peak flow , standing up from a chair several times , picking an object up from the floor , and standing and walking 3 m.cognitive disability according to the folstein ( folstein & folstein , 1975 ) mini - mental state examination ( mmse ) ( quiroga , albala , & klaasen , 2004 ) .
the scale from adding the 15 items had an acceptable cronbach s alpha of .72.geriatric depression refers to individuals with nine or more out of 15 yesavage symptoms of depression ( sheikh & yesavage , 1986 ) .
the cronbach s alpha of the scale was .85.metabolic syndrome , which is a combination of five health conditions ( abdominal girth , diabetes , triglycerides , high density lipoprotein ( hdl ) cholesterol , and high blood pressure ) that increase a respondent 's risk for cvd as defined by the international diabetes federation ( idf , 2006 ) .
the syndrome is present when individuals have high abdominal girth and at least two of the other four conditions.specific biological risk factors ( table 2 shows the cutoff points to define at risk ) .
most are components of the concept of allostatic load or biological dysregulation ( seeman et al . , 2004 ) .
details about specific indicators can be found in crimmins and seeman ( 2004).2.1 cvd factors : abdominal girth ( waist > 80 cm women , 94 cm men)diabetes , controlled or not ( glycosylated hemoglobin 6.5% or taking medicine)high blood pressure , controlled or not ( diastolic > 90 and systolic > 140 mmhg in at least three out of four measurements or taking medicine)high triglycerides in fasting serum ( 50 mg / dl)high cholesterol ratio ( total to hdl 5.92)2.2 various deregulation indicators ( some are also related to cvd)low creatinine clearance ( 44.64 mg / dl ) , an indicator of kidney functionhigh cortisol ( 25.69 g / g ) , indicator of activity in the hypothalamic pituitary ( hpa ) axis in response to stressorslow dehydroepiandrosterone sulfate ( dhea - s , 35 mg / dl ) .
antagonist to hpa activityhigh epinephrine ( 4.99 g / g ) in 12-h overnight urine .
indicator of neuroendocrine functioning in response to stresshigh norepinephrine ( 48 g / g ) in 12-h overnight urine .
similar to epinephrinehigh c - reactive protein ( crp ) concentrations ( 10 mg / l ) .
also a risk factor for cvdweak handgrip strength ( dynamometer 20 kg)unhealthy lifestylesobesity ( body mass index > 30 ) .
( note this is redundant with abdominal girth , which was included among cvd factors .
it is included in this group as a summary indicator of unhealthy lifestyles regarding food consumption and physical activity.)smoking currentno regular exercise in last yearno flu vaccine last year ( a tracer of preventive care seeking)high - calorie diet ( > 3000 day)low - calorie diet ( < 1500 day)high - carbohydrate diet ( > 400 g day)high - fat diet ( > 40 g day ) seven general health outcomes : death in the period september 2000 to september 2007 , in the sample of about 8,000 individuals .
about 1,000 foreigners are excluded from the original mother sample of 9,000 because they do not have the personal identification i d that allows the computer follow - up to establish death and its date .
the information on age is computed from the birth date in the birth record , avoiding the possibility of age - exaggeration errors .
, we took the two lowest ( mala and regular ) as defining poor srh .
functional disability when respondents have difficulties doing 50% or more of 14 activities and instrumental activities and instrumental activities of daily living ( activities of daily living ( adls)/instrumental activities of daily living ( iadls ) ) , namely : walking on the streets , climbing stairs , pushing objects , raising an arm , crossing the bedroom on your feet , bathing , eating , going to bed , using the toilet , trimming toe nails , cooking , handling money , shopping , and taking medicines . even though many studies distinguish basic , instrumental , and functional disabilities ,
we combine all these dimensions in a single indicator after checking that the cronbach s alpha of the scale was an excellent .92 for the 14 items .
a person with basic disability ( i.e. , can not use the toilet ) is very likely to also have functional and instrumental disability ( i.e. , can not cut toenails ) .
physical frailty : respondents failing two or more out of five physical tests grip strength with a dynamometer , pulmonary peak flow , standing up from a chair several times , picking an object up from the floor , and standing and walking 3 m. cognitive disability according to the folstein ( folstein & folstein , 1975 ) mini - mental state examination ( mmse ) ( quiroga , albala , & klaasen , 2004 ) .
the scale from adding the 15 items had an acceptable cronbach s alpha of .72 .
geriatric depression refers to individuals with nine or more out of 15 yesavage symptoms of depression ( sheikh & yesavage , 1986 ) .
metabolic syndrome , which is a combination of five health conditions ( abdominal girth , diabetes , triglycerides , high density lipoprotein ( hdl ) cholesterol , and high blood pressure ) that increase a respondent 's risk for cvd as defined by the international diabetes federation ( idf , 2006 ) .
the syndrome is present when individuals have high abdominal girth and at least two of the other four conditions .
specific biological risk factors ( table 2 shows the cutoff points to define at risk ) . some of them are components of the previous health outcomes .
most are components of the concept of allostatic load or biological dysregulation ( seeman et al . , 2004 ) .
abdominal girth ( waist > 80 cm women , 94 cm men ) diabetes , controlled or not ( glycosylated hemoglobin 6.5% or taking medicine ) high blood pressure , controlled or not ( diastolic > 90 and systolic > 140 mmhg in at least three out of four measurements or taking medicine ) high triglycerides in fasting serum ( 50 mg / dl ) high cholesterol ratio ( total to hdl 5.92 ) 2.2 various deregulation indicators ( some are also related to cvd ) low creatinine clearance ( 44.64 mg / dl ) , an indicator of kidney function high cortisol ( 25.69 g / g ) , indicator of activity in the hypothalamic pituitary ( hpa ) axis in response to stressors low dehydroepiandrosterone sulfate ( dhea - s , 35 mg / dl ) . antagonist to hpa activity high epinephrine ( 4.99 g / g ) in 12-h overnight urine
. indicator of neuroendocrine functioning in response to stress high norepinephrine ( 48 g / g ) in 12-h overnight urine .
similar to epinephrine high c - reactive protein ( crp ) concentrations ( 10 mg / l ) .
also a risk factor for cvd weak handgrip strength ( dynamometer 20 kg ) obesity ( body mass index > 30 ) .
( note this is redundant with abdominal girth , which was included among cvd factors .
it is included in this group as a summary indicator of unhealthy lifestyles regarding food consumption and physical activity . ) no regular exercise in last year no flu vaccine last year ( a tracer of preventive care seeking ) high - calorie diet ( > 3000 day ) low - calorie diet ( < 1500 day ) high - carbohydrate diet ( > 400 g day ) high - fat diet ( > 40 g day ) we have a total of 27 health indicators .
although there is some degree of overlap for several of them , this large number reflects the multidimensional character of the health concept and the complexities of measuring it . to facilitate interpretation and comparisons of results among the different outcomes , we opted for measuring them all with binary or dichotomous indicators of bad health .
we recognize that there is some loss of information from translating continuous variables into dichotomous indicators .
however , this loss is compensated by the gain in comparability and interpretability as well as by the gain of avoiding the distorting effects from extreme outlier values . where possible , we dichotomized variables with cutoff values commonly used in clinical practice and the literature , including mmse cognitive disability , yesavage geriatric depression , triglycerides , crp , obesity , abdominal obesity , and high- and low - calorie diet .
there are also several indicators that are naturally dichotomous , including death , metabolic syndrome , diabetes , high blood pressure , smoking , lack of physical exercise , and flu vaccine . for the remaining 12 ( out of 27 ) variables ,
our choice of cutoff values was driven by the observation of natural breaks in the distribution ( srh , functional disability , frailty , grip strength , and carbohydrate and fat intake ) or was borrowed from the macarthur study of healthy aging ( crimmins & seeman , 2004 ; seeman et al . , 2004 ) .
we examine the effect on health of three ses variables : place of residence , education , and household wealth .
all three are categorized in three levels in order to ascertain the two sides of ses gradients : pertaining to a low - ses stratum or being a high - ses individual . for comparison purposes ,
these three variables are considered constant over time , and we are taking them as reported in the 2000 census , years prior to health measurement ( note that mortality is studied for the period 20002007 , prevalence of health conditions in the 20052006 survey , and the ses indicators are the same in both data sets).place of residence in 2000 : ( 1 ) in the less developed lowlands , which include coastal regions at the pacific ocean and caribbean , as well as the northern plains bordering nicaragua and the southern region bordering panama ; ( 2 ) in the rest of the highlands at the central valley , which includes some suburbs and satellite towns of san jose ; ( 3 ) in the more developed metropolitan area of san jose , the capital city .
is not an individual - level variable , there is a large literature considering the role of place in health disparities ( e.g. , curtis and rees - jones , 1998 ) .
our simple categorization distinguishing urban and these other settings is consistent with a long literature that has documented rural
urban differences in health in various settings.educational attainment in three naturally defined groups : ( a ) none , ( b ) elementary ( one to six grades ) , and ( c ) some secondary ( postelementary ) school or higher .
the effects of education are some of the most studied among ses variables , given that education is easy to measure , does not change in adult life , is easily comparable , and has a number of socioeconomic influences related to factors such as empowerment , income generation , information gathering , and health - seeking behavior ( elo & preston , 1996 ; hummer , rogers , & eberstein , 1998).household wealth in three groups : poor , middle , and rich .
it is based on a simple count of 14 goods and conveniences in the household , ranging from no - dirt floors and having water connection and electricity to ( at the high end ) having a computer and a car .
wealth is in essence income accumulation or permanent income and thus an indicator of economic well - being during long periods ( menchik , 1993 ) .
place of residence in 2000 : ( 1 ) in the less developed lowlands , which include coastal regions at the pacific ocean and caribbean , as well as the northern plains bordering nicaragua and the southern region bordering panama ; ( 2 ) in the rest of the highlands at the central valley , which includes some suburbs and satellite towns of san jose ; ( 3 ) in the more developed metropolitan area of san jose , the capital city .
is not an individual - level variable , there is a large literature considering the role of place in health disparities ( e.g. , curtis and rees - jones , 1998 ) .
our simple categorization distinguishing urban and these other settings is consistent with a long literature that has documented rural
educational attainment in three naturally defined groups : ( a ) none , ( b ) elementary ( one to six grades ) , and ( c ) some secondary ( postelementary ) school or higher . the effects of education are some of the most studied among ses variables , given that education is easy to measure , does not change in adult life , is easily comparable , and has a number of socioeconomic influences related to factors such as empowerment , income generation , information gathering , and health - seeking behavior ( elo & preston , 1996 ; hummer , rogers , & eberstein , 1998 ) . household wealth in three groups : poor , middle , and rich .
it is based on a simple count of 14 goods and conveniences in the household , ranging from no - dirt floors and having water connection and electricity to ( at the high end ) having a computer and a car .
wealth is in essence income accumulation or permanent income and thus an indicator of economic well - being during long periods ( menchik , 1993 ) .
as far as possible , we present all health results adjusted by three demographic variables : ( a ) age ( single year ) , ( b ) sex , and ( c ) marital status ( whether or not currently married including consensual unions ) . age and marital status refer to the situation at the interview in all prevalence analyses . in the mortality analysis
, age is time varying ( each observation was split into single - age segments ) , and marital status is in the census interview in the year 2000 .
we also controlled in the regression models for the field worker who conducted the interview or took the anthropometric measures or other exams to correct potential interviewer and measurement biases ( all data were gathered by seven field workers over a period of 2 years ) .
although all field workers received the same training , and visited the same areas , and the work load was more or less randomly distributed , it is always possible that idiosyncratic behavior of a specific field worker might introduce some measurement bias .
for example , female examiners may tend to measure significantly lower values of waist circumference in female participants .
controlling for field worker in the multivariate analyses prevented the remote possibility that these biases were also correlated to ses of participants and thus were confounders of the relationship between health and ses .
to study mortality , we set the data as survival time ( statacorp , 2005 ) , with entry date at september 2000 ( 3 months after the census interview to avoid likely biases in case some hospitalized or very sick individuals were not interviewed in the june census ) and exit or right censoring at september 2007 .
we split observations into single - year segments ( approximately seven segments per individual ) .
mortality rates were computed as the ratio of deaths to the exact count of person - years .
we model some ses gradients in mortality with parametric hazard regression ( streg command in stata ) , assuming a gompertz distribution ( hosmer & lemeshow , 1999 ) .
the models control for demographic confounding effects as well as for the studied ses effects . to consider the possibility that age effects are nonlinear and differential by sex
, we included in the models a quadratic term for age and an interaction term for age and sex . to compare odds ratios across models , we reanalyzed mortality using a logistic model with the probability of dying in each age of the observation period as the dependent variable . in this model , we used robust estimates that take into account the lack of independence of age segments within each individual .
the standard errors in the logistic models were estimated considering the clustering effect of selecting whole health areas in the subsample .
this relaxed the assumption of independence among observations and required only that observations be independent across clusters . in some analyses , we assessed the significance of the joint effect of the three ses variables with a chi - square test of the improvement in the log - likelihood ratio resulting from including ses in the regression model .
table 1 shows the sizes and the composition by ses and demographic characteristics of the sample .
the three categories by place of residence are about the same size . in contrast ,
the low - end and high - end groups for these two variables comprise between 10% and 25% of observations .
the distribution by age reflects oversampling of old - age groups by design . as usual in elderly populations , there are more women than men . about 50% of the sample is married or in consensual union
. socioeconomic status ( ses ) and demographic variables in the mortality sample and prevalence subsample note : age at the middle of the mortality period ( 2000/2006 ) or at the interview in 2005/2006 .
sample size varies depending on the studied outcome ( table 2 ) . for studying mortality ,
our sample is more than 8,000 individuals or more than 50,000 person - years . for prevalence outcomes ,
the sample size is generally between 2,500 and 2,800 . for some specific indicators , the size further diminishes by a few hundred because of noncompliance or refusals in blood sample and urine collection .
the index of geriatric depression can be computed only for respondents who did not require a proxy in the interview ( 76% ) .
we also have smaller sample size ( about 1,600 ) for epinephrine and norepinephrine analyses because of degradation of stored urine samples .
health outcomes and specific health conditions in the analysis by age notes : rate or percentage computed considering sampling weights .
srh = self - rated health ; adl / iadl = activities of daily living / instrumental activities of daily living ; mmse = mini mental state examination ; hdl = high - density lipoprotein ; bmi = body mass index .
table 2 shows the observed values for the 27 health indicators by two large age brackets : 6079 years and 80 or more years .
comparing the two age groups provides an initial snapshot of how indicators shift with age , although it does not allow us to separate out potential confounding from cohort - specific effects ( e.g. , younger cohorts adopting western lifestyles that influence their health ) as well as selection effects ( e.g. , smokers may die at younger ages , which means that they are underrepresented at older ages ) .
given that all are poor - health indicators , one would expect substantial increments with age ( although evidence from other studies shows that some of these risk factors , such as obesity , cholesterol , and high blood pressure , may decline in late life as a result of other serious comorbidities ) .
cognitive and functional disabilities show a fivefold increment , with age being the closest to mortality .
srh and depression change little with age , and metabolic syndrome actually moves in the opposite direction from the expected age effect declining ( which is a health improvement ) 20% for older people .
health conditions that do not worsen , and even improve , with aging include the five components of metabolic syndrome : obesity , diabetes , high blood pressure , high cholesterol , and high triglycerides .
these age trends could be a reflection of improved cv health with aging within each individual .
or they could simply come from changes in the composition of the population with aging in a selection in frailty process ( vaupel , manton , & stallard , 1979 ) that eliminates the frail and sick at earlier ages .
the remaining biomarkers in the second panel of table 2 deteriorate ( increase ) with age , although at rates substantially lower than mortality .
low creatinine clearance , a marker of kidney malfunction , and grip strength are the only ones with a substantial aging increase ( ratio higher than 2 ) . most behavioral or lifestyle indicators in the third panel of table 2 improve ( diminish ) with age .
prevalence of smoking and obesity are less than half after age 80 than in the 6079 age group , high - calorie diet diminishes by 40% , and high - carbohydrate diet by one third .
the only behavioral deteriorations in the table are the lack of exercise and an increase in the proportion of individuals with a hypocaloric diet ( probably because of loss of appetite ) .
turning to the ses gradient issue , the exceptionally good health indicators of the costa rican population are by themselves a challenge to the notion of an inevitable ses gradient .
death rates of costa rican adults in the creles sample are lower than in the united states and not very different than in japan , especially at higher ages ( figure 2 ) , in spite of the substantially lower ses of the latin american population measured by any traditional indicator such as education , income , or health expenditure .
it is remarkable that a population with a per capita income that is one fifth of the united states ' and per capita health expenditures that are one tenth of the united states ' can have lower death rates than the united states .
life expectancy at age 60 implicit in the mortality rates in figure 2 is 22.4 years for men and 24.8 for women in the costa rican sample .
the corresponding values are 20.2 and 23.4 for the united states and 21.9 and 27.3 for japan . age - specific death rates .
often demographers have found that apparently low mortality at old ages in developing countries are solely an artifact of mismeasurement , particularly because of age exaggeration in census data that inflates the denominator and depletes the rates ( coale & kisker , 1986 ; preston , elo , & stewart , 1999 ) . in the costa rican sample , however , age errors are very unlikely because we are using data on exact birthdates as they appear in civil registration records and on the universal identity card , the cdula .
the possibility that we are finding low rates because of missing deaths in our computer follow - up is also remote because in the subsample of about 4,000 individuals creles visited , there was not a single case of a deceased person that was not also recorded in the national death registry computer follow - up .
furthermore , two other studies of old age mortality in costa rica have found similarly low rates ( rosero - bixby , 2008 ; rosero - bixby et al . , 2005 ) .
within costa rica , there is not a clear ses gradient in adult mortality or , if anything , the gradient is contrary to expectations . table 3 and figure 3 show that in our sample , there are slight increases in mortality with higher levels of education and wealth , net of other influences , and the least developed lowlands have lower mortality than the more developed highlands .
only the more developed capital city behaves according to expectations , showing lower mortality , although by a small margin .
socioeconomic status ( ses ) gradients in five health outcomes as estimated by logistic regression odds ratios notes : lr is the log - likelihood ratio chi
square of including the six ses variables in the model . significant at p < .05 .
socioeconomic status ( ses ) gradients in mortality and poor self - rated health ( srh ) .
rates or proportions relative to total population , controlled for age , sex , and marital status with regression : logistic for proportions and gompertz hazard for rates .
these mortality gradients contrast dramatically with the observed differentials by srh in table 3 and figure 3 .
the affluent and those with high school education self - report 40% less poor health than the national population .
the poor , those with no formal education , and those living in the lowlands report 20% more poor health than the national average .
this contradiction between mortality and srh is the motivation for the adjective of surprising ses gradients in this article 's title . in four other health outcomes , ses
high - ses individuals are less affected by functional , physical , and cognitive disabilities , or by depression . however , metabolic syndrome ( a multidimensional risk factor for cvd ) behaves more like mortality with no significant ses differentials .
there are also peculiarities of metabolic syndrome variation with age ( no gradient ) , sex ( much lower in men ) , and conjugal status ( higher among the married ) , but these are not the focus of this article .
given the enormous importance of cvd in adult mortality ( nearly half of old - age deaths are cardiovascular related in costa rica ) , this cvd risk factor helps explain the observed lack of ses gradients in overall mortality . to more finely explore the ses gradients in 20 intermediate health conditions , table 4 summarizes the results obtained from a series of logistic regressions . with a regression model for each health condition , we first estimated the net effects of the three ses variables and whether there was a significant joint effect of including the three variables in each model . in one third of the health indicators in the table ( 6 out of 20 ) , there are no significant joint ses effects . in the rest , the ses gradient sometimes behaves as expected with below - one odds ratio for the high - ses categories and above one for the low ses .
however , the reverse also is present in several indicators , such as obesity and triglycerides . to make things more complicated
, there are several cases of a curvilinear ses gradient , in which the middle - ses group is the worse off .
that is the case for triglycerides by wealth ; cholesterol and abdominal girth by education ; and dhea - s , epinephrine , and norepinephrine by place of residence .
figure 4 summarizes the large amount of information presented in tables 3 and 4 . with a logistic regression model for each health condition , the net effect of the three high - ses characteristics ( metro san jose , high school education , and rich wealth ) .
we then summarized the three odds ratios by computing the one that would correspond to an individual with simultaneously the three high - ses characteristics ; that is , by multiplication of the three odds ratios , and ( except in six cases as described subsequently ) we report this product in figure 4 .
given that this procedure presumes no interactions among the three ses variables , we also tested models with the triple interaction of the three low - ses indicators and with the triple interaction of the three high - ses indicators ( these extreme groups of all low ses and all high ses each represent only 4% of the sample ) . in the six ( out of 54 )
regression models where these interactions proved significant , we instead report in figure 4 an odds ratio that includes this triple interaction , rather than the previously described product of the odds ratios in the uninteracted model . in five of the six significant triple - interacted models ,
figure 4 shows these hypothetical odds ratios , sorted descending by the low - ses effect , which conversely results in approximately ascending sorting by the high - ses effects .
figures below 1 ( dots at the left ) denote good health ; that is , the risk of suffering the condition is lower in the group with respect to the rest of the population .
socioeconomic status ( ses ) gradients in intermediate health indicators as estimated by logistic regression odds ratios notes : these results are controlled for by age , age square , sex , age sex interaction , marital status , and field worker .
diet indicators also controlled for knee height , and carbohydrates and fat are controlled for calorie intake .
the reference groups for the three ses variables are highlands , grade school , and intermediate wealth , respectively .
lr is the log - likelihood ratio chi square including the six ses variables in the model .
poor - health indicators odds ratio prevalence in high - socioeconomic status ( ses ) and low - ses individuals .
see text for method to calculate odds ratios from models controlling for age , sex , and marital status with logistic regression .
high ses are wealthy metro san jose residents with postprimary education ; low ses are poor lowland residents with no education .
srh = self - rated health ; crp = c - reactive protein ; dhea - s = dehydroepiandrosterone sulfate if the ses gradient behaved as expected in figure 4 , the high - ses triangles should line up at the left of the figure and the low - ses circles should be at the right .
reality , as depicted by this costa rican sample , is far from that expected gradient .
there are three groups in our 27 health indicators : ( a ) 11 health indicators with the expected gradient of better health at high ses , ( b ) 9 health conditions , including death , in which low - ses individuals are better off , and ( 3 ) 7 indicators with no significant ses effects .
the expected ses gradient ( figure 4 ) occurs in five of our seven health outcomes ( srh ; cognitive , functional , and physical disability ; and depression ) , as well as in just two biomarkers ( norepinephrine and grip strength ) and two behavioral conditions ( smoking and lack of exercise ) .
counterbalancing the aforementioned health indicators , there are 10 conditions in which low - ses individuals do significantly better than high - ses groups : death , creatinine clearance , high - calorie diet , high blood pressure , obesity , high epinephrine , triglycerides , and low dhea - s levels , as well as the metabolic syndrome and its main component : abdominal girth . the pattern of the flu vaccine ( although marginally nonsignificant ) is on line with earlier findings that the costa rican primary health care system equalizes access to health in all ses levels
. it has been shown , for example , that there is a lower coverage of immunization among children of more affluent mothers ( chen - mok et al . , 2001 ) .
it is interesting to note that in several cvd risk factors , the ses disadvantaged groups do better , including triglycerides , cholesterol ratio , high blood pressure , diabetes , and fatty diet , although some of the effects are not significant .
rich data for elderly costa ricans from the creles project , which include a 6-year follow - up of a sample of 8,000 as well as biomarkers in a subsample of about 2,500 , show puzzling ses gradients in 26 health indicators .
disadvantaged groups in terms of education , wealth , and residence show steep health deficits in srh as well as in indicators of functionality and physical and mental fitness .
in contrast , in the single most important health outcome , mortality , there are no significant ses differentials ; on the contrary , there are even hints that low - ses groups might be better off .
metabolic syndrome , a risk factor for cvd , shows a similar pattern as mortality .
the direct relationship between ses and mortality found in these data may occur only in the elderly population under study ( 60 years and over ) .
the usual inverse relationship may persist in younger ages , which were not included in the analyzed sample .
this study intentionally considers a large number of health indicators to reflect the multidimensional character of the health concept .
the results show that these multiple dimensions of health do not behave in a monolithic way .
ses , and aging as well , generates very diverse responses in different aspects of health . cognitive impairment , for example , is substantially higher at older age and low ses ( although the strong negative association with education may be exaggerated by a cultural bias in the mini mental test ) . similarly , geriatric depression in our data is one of the most clear correlates with low ses , but it changes little with age ( though the latter may be due to the large proportion of missing responses among the oldest old needing a proxy in the interview ) .
our stress - related biomarkers epinephrine and norepinephrine also show an advantage for the affluent and educated .
these costa rican data show that socioeconomically disadvantaged populations have lower prevalence of obesity , hypercholesterolemia , triglycerides , hypertension , and hyperglycemia .
the changing association between ses and cvd merits careful monitoring in countries like costa rica .
dhea - s , a hormone some consider a marker of aging , also shows a more favorable situation in low - ses individuals .
smoking , sedentariness , and high - carbohydrate diets are less prevalent among the better off . but obesity , high fat , and high - calorie diets diminish consistently and substantially with ses .
interestingly , there are no negative ses gradients in our indicator of access to preventive care : having had the flu vaccine .
this is an indication of an important attribute of the public primary health care system in costa rica
its coverage of the lower strata of society to equalize access to health care ( rosero - bixby , 2004a ) .
viewing the diet - related biomarkers in conjunction with the dietary intake data , we can hypothesize that worse nutritional behaviors among higher ses groups may be playing a significant role in driving the worse cvd risks , and hence higher mortality , among the higher ses .
moreover , the low - calorie diet of low - ses individuals might be a protective factor because it has been shown that dietary caloric restriction slows ageing in other species ( roth et al . , 2002 ) .
this raises the question of what the time path has been and will be of ses gradients in nutritional behaviors .
a substantial literature has documented the transition of middle - income countries from positive ses obesity relationships to negative ones as countries develop ( e.g. , monteiro , moura , conde , & popkin , 2004 ) ; whereas countries such as mexico appear to have already moved through this nutritional transition , costa rica appears to lag .
it will be useful for future work to document the history of this ses nutrition relationship in costa rica , as well as to closely track its evolution , as this may have major implications for whether costa rica 's mortality gradient reverses in the future to the more usual negative relationship with ses .
for the broader set of health indicators examined , however , we do not know whether the findings in this article are unique to costa rica or whether they are common in other middle- and low - income countries .
reliable data to study ses gradients in adult mortality and in hard health indicators are rare .
however , this article shows that one can not jump from there to conclusions on other health outcomes . more research
costa rica is a special case of exceptional achievements in health and social development in spite of a weak economy .
two decades ago it was included , along with sri lanka , kerala , china , and cuba , among the world showcases of good health at low cost
( halstead , walsh , & warren , 1985 ) , and it has remained in that category . some have explained the country 's longevity achievements with its investments in education and health insurance ( caldwell , 1986 ) .
however , those can only be part of the explanation because even those with no education are doing fine in important aspects of health , including health dimensions not clearly influenced by medical care access
. it could even be that if a poor or traditional society completes the first stage of the epidemiologic transition by controlling communicable diseases , some traditional lifestyles can protect it from health problems like obesity and take it to better general health indicators such as lower mortality .
this evidence of success is tempered , however , by our strong evidence of a significant ses gradient in functional and mental health indicators , suggesting that disability - free life expectancy is indeed worse among more vulnerable adults even in costa rica .
the creles project is a longitudinal study of the universidad de costa rica , carried on by the centro centroamericano de poblacin in collaboration with the instituto de investigaciones en salud , with the support of the wellcome trust foundation ( grant no .[/INST]backgroundto determine socioeconomic status ( ses ) gradients in the different dimensions of health among elderly costa ricans .
hypothesis : ses disparities in adult health are minimal in costa rican society.methodsdata from the costa rican study on longevity and healthy aging study : 8,000 elderly costa ricans to determine mortality in the period 20002007 and a subsample of 3,000 to determine prevalence of several health conditions and biomarkers from anthropometry and blood and urine specimens.resultsthe ultimate health indicator , mortality , as well as the metabolic syndrome , reveals that better educated and wealthier individuals are worse off .
in contrast , quality of life related measures such as functional and cognitive disabilities , physical frailty , and depression all clearly worsen with lower ses .
overall self - reported health ( srh ) also shows a strong positive ses gradient .
traditional cardiovascular risk factors such as diabetes and cholesterol are not significantly related to ses , but hypertension and obesity are worse among high - ses individuals . reflecting mixed ses gradients in behaviors , smoking and lack of exercise are more common among low ses , but high calorie diets are more common among high ses.conclusionsnegative modern behaviors among high - ses groups may be reversing cardiovascular risks across ses groups , hence reversing mortality risks . but negative ses gradients in healthy years of life persist .</s> |
Anthony Weiner spent $100,000 on polling and research in March By Daniel Strauss - Tweet Former Rep. Anthony Weiner's (D-N.Y.) spent roughly $100,000 on polling and research in March, according to campaign filings released Friday.
The New York Democrat has long been rumored to be seriously considering running for mayor, either through a challenge to New York Mayor Michael Bloomberg (I) or as a successor when Bloomberg left office.
According to the campaign filings, Weiner's campaign spent $52,500 on campaign consulting research and $54,000 on polling. The research and polling was done by David Binder Research in San Francisco, California. Weiner also spent about $7,000 on rent for office space in New York, according to the campaign filings.
The filings will add to speculation that Weiner is planning a return to politics and will campaign for mayor of New York. Weiner reportedly also has a warchest $4.3 million in campaign funds.
But the polling and research is essentially the only spending Weiner did for March, which could also suggest that he is not planning a serious run for mayor.
Asked if he was planning to run for mayor Weiner responded in an email that there was "nothing to report,"
Tweet View Comments Former Rep. Anthony Weiner's (D-N.Y.) spent roughly $100,000 on polling and research in March, according to campaign filings released Friday.Weiner has kept a low profile since he resigned office in June 2011 after news surfaced that he had been texting explicit pictures to women through text messages.The New York Democrat has long been rumored to be seriously considering running for mayor, either through a challenge to New York Mayor Michael Bloomberg (I) or as a successor when Bloomberg left office.According to the campaign filings, Weiner's campaign spent $52,500 on campaign consulting research and $54,000 on polling. The research and polling was done by David Binder Research in San Francisco, California. Weiner also spent about $7,000 on rent for office space in New York, according to the campaign filings.The filings will add to speculation that Weiner is planning a return to politics and will campaign for mayor of New York. Weiner reportedly also has a warchest $4.3 million in campaign funds.But the polling and research is essentially the only spending Weiner did for March, which could also suggest that he is not planning a serious run for mayor.Asked if he was planning to run for mayor Weiner responded in an email that there was "nothing to report," according to DNAinfo.com New York. Source:
http://thehill.com/blogs/ballot-box/other-races/288545-anthony-weiner-spent-100000-on-polling-and-research-in-march The Hill Archives: Senate | House | Administration | Campaign | Business & Lobbying | Capital Living | Opinion View News by Subject:
Defense & Homeland Security | Energy & Environment | Healthcare | Finance & Economy | Technology | Foreign Policy | Labor | Transportation & Infrastructure ||||| There may still be some life in the old Weiner yet.
Campaign filings show that former Rep. Anthony Weiner, who is contemplating a possible political comeback, spent $106,500 on polls this month.
Weiner paid David Binder, a San Francisco-based pollster, $52,500 for one survey and $54,000 for a second just days apart.
The Post previously reported that the former Brooklyn congressman, brought down in a texting scandal, was considering making a late entry into the race for either comptroller or mayor.
But he’s taken no action as of today and political insiders now consider him unlikely to become a candidate this year.
Public polls show that voters still haven’t forgiven Weiner for sending racy photos of himself to females he met over the Internet.
Whatever he decides to do, Weiner won’t have to worry about fundraising. He’s still got $4.3 million left in his campaign account after spending $115,477 over the last two months. ||||| Former Rep. Anthony Weiner, who resigned from Congress after misfiring a racy photo over Twitter, spent more than $50,000 on polling in recent months, according to New York City campaign finance filings.
The latest filing with the city’s Campaign Finance Board for Weiner’s close-to-dormant mayoral campaign account shows he spent $54,000 on polling by David Binder Research on March 5. He spent another $52,500 on the firm for consulting work a day earlier, the filings show.
Text Size -
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reset FLASHBACK: Weiner admits to tweeting lewd photos
Weiner declined comment, and it’s unclear precisely what the polling was for. The New York Post reported earlier this year on a polling survey being conducted tossing Weiner’s name into the mix for city comptroller and for mayor.
A path to the mayoralty is more complicated for Weiner in a crowded field, while the comptroller’s race is all but certain to be won by Manhattan Borough President Scott Stringer.
While Weiner would face questions about the scandal, there is a window for him to run for mayor. The Democratic field has yet to gel, with only one candidate, City Council Speaker Christine Quinn, showing relatively high name recognition in comparison to the others.
Weiner has done some toe-dips in terms of media interviews, but would face questions about the scandal that cost him his Queens seat — once held by Sen. Chuck Schumer — in 2011.
He was the favorite for the Democratic mayoral primary in 2009 but ultimately decided not to run, following Mayor Mike Bloomberg’s decision to extend term limits for a single election so he could run again himself. | – Anthony Weiner isn't saying anything publicly, but his wallet suggests he's serious about getting back into politics soon. The former congressman spent more than $100,000 on consulting and polling this month, reports the New York Post, setting off all kinds of renewed speculation that he plans to run for either mayor or comptroller. Even with that spending, the Post estimates that he still has $4.3 million in campaign funds left over from his days in Congress. "Nothing to report," Weiner tells DNAinfo via email. He might be right, at least in regard to this election cycle. While there's no denying that he shelled out the money to the pollster, thanks to campaign finance records, the Hill thinks it's unlikely he could mount a run for mayor at this late date without having done anything else. And Politico says the comptroller's race is all but wrapped up already. Weiner has kept a mostly low profile since resigning in 2011 over his dirty-photo texting scandal, though in an interview last summer, the stay-at-home dad shot down rumors of a mayoral run that were circulating even back then. | <s>[INST]Anthony Weiner spent $100,000 on polling and research in March By Daniel Strauss - Tweet Former Rep. Anthony Weiner's (D-N.Y.) spent roughly $100,000 on polling and research in March, according to campaign filings released Friday.
The New York Democrat has long been rumored to be seriously considering running for mayor, either through a challenge to New York Mayor Michael Bloomberg (I) or as a successor when Bloomberg left office.
According to the campaign filings, Weiner's campaign spent $52,500 on campaign consulting research and $54,000 on polling. The research and polling was done by David Binder Research in San Francisco, California. Weiner also spent about $7,000 on rent for office space in New York, according to the campaign filings.
The filings will add to speculation that Weiner is planning a return to politics and will campaign for mayor of New York. Weiner reportedly also has a warchest $4.3 million in campaign funds.
But the polling and research is essentially the only spending Weiner did for March, which could also suggest that he is not planning a serious run for mayor.
Asked if he was planning to run for mayor Weiner responded in an email that there was "nothing to report,"
Tweet View Comments Former Rep. Anthony Weiner's (D-N.Y.) spent roughly $100,000 on polling and research in March, according to campaign filings released Friday.Weiner has kept a low profile since he resigned office in June 2011 after news surfaced that he had been texting explicit pictures to women through text messages.The New York Democrat has long been rumored to be seriously considering running for mayor, either through a challenge to New York Mayor Michael Bloomberg (I) or as a successor when Bloomberg left office.According to the campaign filings, Weiner's campaign spent $52,500 on campaign consulting research and $54,000 on polling. The research and polling was done by David Binder Research in San Francisco, California. Weiner also spent about $7,000 on rent for office space in New York, according to the campaign filings.The filings will add to speculation that Weiner is planning a return to politics and will campaign for mayor of New York. Weiner reportedly also has a warchest $4.3 million in campaign funds.But the polling and research is essentially the only spending Weiner did for March, which could also suggest that he is not planning a serious run for mayor.Asked if he was planning to run for mayor Weiner responded in an email that there was "nothing to report," according to DNAinfo.com New York. Source:
http://thehill.com/blogs/ballot-box/other-races/288545-anthony-weiner-spent-100000-on-polling-and-research-in-march The Hill Archives: Senate | House | Administration | Campaign | Business & Lobbying | Capital Living | Opinion View News by Subject:
Defense & Homeland Security | Energy & Environment | Healthcare | Finance & Economy | Technology | Foreign Policy | Labor | Transportation & Infrastructure ||||| There may still be some life in the old Weiner yet.
Campaign filings show that former Rep. Anthony Weiner, who is contemplating a possible political comeback, spent $106,500 on polls this month.
Weiner paid David Binder, a San Francisco-based pollster, $52,500 for one survey and $54,000 for a second just days apart.
The Post previously reported that the former Brooklyn congressman, brought down in a texting scandal, was considering making a late entry into the race for either comptroller or mayor.
But he’s taken no action as of today and political insiders now consider him unlikely to become a candidate this year.
Public polls show that voters still haven’t forgiven Weiner for sending racy photos of himself to females he met over the Internet.
Whatever he decides to do, Weiner won’t have to worry about fundraising. He’s still got $4.3 million left in his campaign account after spending $115,477 over the last two months. ||||| Former Rep. Anthony Weiner, who resigned from Congress after misfiring a racy photo over Twitter, spent more than $50,000 on polling in recent months, according to New York City campaign finance filings.
The latest filing with the city’s Campaign Finance Board for Weiner’s close-to-dormant mayoral campaign account shows he spent $54,000 on polling by David Binder Research on March 5. He spent another $52,500 on the firm for consulting work a day earlier, the filings show.
Text Size -
+
reset FLASHBACK: Weiner admits to tweeting lewd photos
Weiner declined comment, and it’s unclear precisely what the polling was for. The New York Post reported earlier this year on a polling survey being conducted tossing Weiner’s name into the mix for city comptroller and for mayor.
A path to the mayoralty is more complicated for Weiner in a crowded field, while the comptroller’s race is all but certain to be won by Manhattan Borough President Scott Stringer.
While Weiner would face questions about the scandal, there is a window for him to run for mayor. The Democratic field has yet to gel, with only one candidate, City Council Speaker Christine Quinn, showing relatively high name recognition in comparison to the others.
Weiner has done some toe-dips in terms of media interviews, but would face questions about the scandal that cost him his Queens seat — once held by Sen. Chuck Schumer — in 2011.
He was the favorite for the Democratic mayoral primary in 2009 but ultimately decided not to run, following Mayor Mike Bloomberg’s decision to extend term limits for a single election so he could run again himself.[/INST]– Anthony Weiner isn't saying anything publicly, but his wallet suggests he's serious about getting back into politics soon. The former congressman spent more than $100,000 on consulting and polling this month, reports the New York Post, setting off all kinds of renewed speculation that he plans to run for either mayor or comptroller. Even with that spending, the Post estimates that he still has $4.3 million in campaign funds left over from his days in Congress. "Nothing to report," Weiner tells DNAinfo via email. He might be right, at least in regard to this election cycle. While there's no denying that he shelled out the money to the pollster, thanks to campaign finance records, the Hill thinks it's unlikely he could mount a run for mayor at this late date without having done anything else. And Politico says the comptroller's race is all but wrapped up already. Weiner has kept a mostly low profile since resigning in 2011 over his dirty-photo texting scandal, though in an interview last summer, the stay-at-home dad shot down rumors of a mayoral run that were circulating even back then.</s> |
. disabilities of the arm , shoulder , and hand ( dash ) questionnaire is a patient - reported outcome measure ( prom ) that measures the magnitude of disability for the upper extremity .
it consists of 30 items , 21 of which assess the ability to perform physical activities , 5 items measure pain , and 4 items measure the psychosocial effects . item elimination in order to shorten the questionnaire resulted in an 11-item instrument , which proved to be as reliable as the original dash instrument .
retention of the clinically oriented questions in the quick - dash made it a comparable instrument to the full dash questionnaire .
the quick - dash is more appealing than the dash because it can be administered in the clinic in a shorter time .
a well - translated and adapted questionnaire would facilitate multicenter studies and increases the feasibility of meta - analysis studies .
farsi is spoken in several countries including iran , tajikistan , afghanistan , and some regions of pakistan and iraq .
validity of the quick - dash has been tested in several other languages . in this study ,
our aim was to assess the validity and reliability of the persian version of the quick - dash in patients with upper extremity conditions .
in total , 202 patients with upper extremity problems enrolled in this study from january 2013 to december 2013 .
inclusion criteria were age above 18 years , ability to read and write persian as a mother tongue , and a minimum of 4-week symptom duration [ table 1 ] . at the first visit
, all patients responded to the persian quick - dash as well as the persian short form 36 health survey ( sf-36 ) and the michigan hand outcome questionnaire ( mhoq ) [ table 2 ] . to test the reliability , 71 patients accepted to return for the second visit after 3 days to fill the persian quick - dash without receiving any major treatment or changes in symptoms .
this study was reviewed and approved by the committee of research and patients consented verbally to participate in the study .
characteristics of patients with upper extremity conditions ( n=202 ) average functional score of patients with upper extremity conditoins ( n=202 ) reliability can be test by either measuring the cronbach 's alpha for internal consistency or intra - class correlation coefficient ( icc ) for test - retest reliability ( reproducibility ) .
commonly accepted values for cronbach 's alpha are described as excellent for > 0.9 , good for 0.9 > > 0.7 , acceptable for 0.7 > > 0.6 , poor for 0.6 > > 0.5 , and unacceptable for < 0.5 .
test - retest reliability is tested by administering a questionnaire to a patient on two separate occasions without any substantial changes in his / her symptoms .
a correlation coefficient of 0 indicates no reliability , whereas a value of 1 indicates excellent reliability . to measure
test - retest reliability in our study , 71 patients randomly filled the persian quick - dash for a 2 time 3 days after the first visit , without being given any major treatment or surgery . to test the construct validity , the new questionnaire is tested against a validated questionnaire with similar or relevant context to assess the correlation between the two questionnaires .
we tested the persian quick - dash against the sf-36 questionnaire and mhoq , which have been validated in persian .
statistical analysis performed using spss version 11.5 ( spss inc . , chicago , il , usa ) .
the sf-36 is an easily administered prom that is frequently used to measure the quality of life .
it consists of 36 questions divided into two major domains of physical and mental components , each one consisting of four sub - domains physical function , role - physical , bodily pain , and general health are sub - domains of functional health .
vitality , social function , role - emotional and mental health are sub - domains of psychometrical health .
it consists of 37 items divided into six subscales , including hand function , pain , activities of daily living , work , esthetics , and patient satisfaction .
in total , 202 patients with upper extremity problems enrolled in this study from january 2013 to december 2013 .
inclusion criteria were age above 18 years , ability to read and write persian as a mother tongue , and a minimum of 4-week symptom duration [ table 1 ] . at the first visit
, all patients responded to the persian quick - dash as well as the persian short form 36 health survey ( sf-36 ) and the michigan hand outcome questionnaire ( mhoq ) [ table 2 ] . to test the reliability , 71 patients accepted to return for the second visit after 3 days to fill the persian quick - dash without receiving any major treatment or changes in symptoms .
this study was reviewed and approved by the committee of research and patients consented verbally to participate in the study .
characteristics of patients with upper extremity conditions ( n=202 ) average functional score of patients with upper extremity conditoins ( n=202 )
reliability can be test by either measuring the cronbach 's alpha for internal consistency or intra - class correlation coefficient ( icc ) for test - retest reliability ( reproducibility ) .
internal consistency measures the consistency of responses across the questionnaire and the subscales . commonly accepted values for cronbach 's alpha are described as excellent for > 0.9 , good for 0.9 > > 0.7 , acceptable for 0.7 >
> 0.6 , poor for 0.6 > > 0.5 , and unacceptable for < 0.5 .
test - retest reliability is tested by administering a questionnaire to a patient on two separate occasions without any substantial changes in his / her symptoms .
a correlation coefficient of 0 indicates no reliability , whereas a value of 1 indicates excellent reliability . to measure
test - retest reliability in our study , 71 patients randomly filled the persian quick - dash for a 2 time 3 days after the first visit , without being given any major treatment or surgery .
to test the construct validity , the new questionnaire is tested against a validated questionnaire with similar or relevant context to assess the correlation between the two questionnaires .
we tested the persian quick - dash against the sf-36 questionnaire and mhoq , which have been validated in persian .
statistical analysis performed using spss version 11.5 ( spss inc . , chicago , il , usa ) .
statistical analysis performed using spss version 11.5 ( spss inc . , chicago , il , usa ) .
the sf-36 is an easily administered prom that is frequently used to measure the quality of life .
it consists of 36 questions divided into two major domains of physical and mental components , each one consisting of four sub - domains physical function , role - physical , bodily pain , and general health are sub - domains of functional health .
vitality , social function , role - emotional and mental health are sub - domains of psychometrical health .
it consists of 37 items divided into six subscales , including hand function , pain , activities of daily living , work , esthetics , and patient satisfaction .
icc was 0.89 , indicating good to excellent test - retest reliability [ table 3 ] .
there was a high and significant inverse correlation between the quick - dash and the mhoq , and the sub - domains of the sf-36 , indicating a strong correlation between the quick - dash and the other validated questionnaire in the same domain [ table 4 ] .
convergent validity was confirmed , as the spearman correlation between the quick - dash and mhoq was 0.67 and ranged from 0.24 to 0.56 between the sub - domains of the sf-36 and quick - dash [ table 4 ] . internal consistency and test - retest reliability of the farsi version of the quick - dash convergent validity expressed by spearman 's rho correlation coefficient between quick - dash and subdomins of the sf-36 and mhoq
the purpose of this study was to establish the validity of the persian version of the quick - dash in patients with upper extremity conditions .
our results indicate that farsi quick - dash is a reliable and valid instrument for studying outcomes in patients with upper extremity conditions . in the current study , internal consistency and
test - retest reliability indicated the excellent reliability of the farsi version of the quick - dash .
testing the construct validity revealed moderate to strong correlation between quick - dash and the mhq and subscales of the sf-36 .
first of all , this is a single - center study , which may not represent the general patient population .
however , this is a major tertiary referral center , providing care to the entire north east and east , and south east provinces of iran .
another limitation was the administration of sf-36 questionnaire , which is more general than quick - dash , and mhoq , which is more specific compared to the quick - dash , to test construct validity ; however , some studies have shown relatively small differences in the responsiveness of the more general and more specific measures of disability .
translations of the dash questionnaire are available in most languages ; however , less work has been done in the cross - cultural adaptation of the quick - dash .
japanese , and turkish versions , cronbach 's alpha was 0.89 , 0.88 and 0.84 , respectively , showing good internal consistency . similarly , icc was 0.94 , 0.93 , and 0.82 in french , turkish , and japanese versions , respectively , showing good test - retest reliability . in our study ,
cronbach 's alpha and icc were 0.90 and 0.89 respectively , showing comparable results with previously validated versions , indicating the reliability of our study .
we compared the quick - dash with sf-36 and mhoq to test the construct validity , using spearman 's correlation coefficient . in order to test the construct validity of the turkish version of the quick - dash , koldas dogan et al .
studied patients with carpal tunnel syndrome using the boston carpal tunnel questionnaire , visual analogue scale - pain ( vas - pain ) , and pinch and grip strength tests to measure the correlation in responsiveness with quick - dash .
quick - dash showed moderate correlations with vas - pain and grip strength test , a good correlation with the pinch strength test , and high correlation with boston carpal tunnel questionnaire .
the japanese version of the quick - dash was tested against the dash , sf-36 and vas .
the correlation coefficients were 0.92 and 0.52 when compared with dash and vas , respectively .
in addition , correlations between quick - dash and sf-36 subscales ranged from 0.29 to 0.73 . in a study to validate the french version ,
the correlation was tested using subjective assessment of activities of daily living ( adl ) , active range of motion ( rom ) , and measurement of abduction strength ( strength ) .
correlation of the french quick - dash score with scores for french dash ( r = 0.96 ) , perceived handicap score ( r = 0.79 ) , adl ( r = 0.73 ) , pain during activities ( r = 0.63 ) , strength ( r = 0.58 ) , pain at rest ( r = 0.57 ) , and rom ( r = 0.51 ) indicated good construct validity .
in this study , we evaluated the reliability and validity of the persian version of the quick - dash .
observation of excellent internal consistency , good to excellent test - retest reliability , and moderate to strong construct validity confirms the validity and reliability of the persian quick - dash in the evaluation of the magnitude of disability for upper extremity conditions . | background : the aim was to assess the validity and reliability of the persian version of shortened disabilities of the arm , shoulder , and hand ( quick - dash ) questionnaire in patients with upper extremity conditions.methods:we administered the persian version of quick - dash to 202 patients with upper extremity conditions , of which 71 patients randomly returned after 3 days to respond to the questionnaire for the 2nd time . in order to test the construct validity of the questionnaire
, patients responded to the michigan hand outcome questionnaire ( mhoq ) and short form 36 health survey ( sf-36 ) as well .
internal consistency was tested using the cronbach 's alpha , and test - retest reliability was measured using intra - class correlation coefficient ( icc).results : cronbach 's alpha was 0.90 .
icc was 0.89 .
convergent validity was confirmed , as the spearman correlation between the quick - dash and mhoq was 0.67 and ranged from 0.24 to 0.56 between the subscales of the sf-36 and quick-dash.conclusions:observation of excellent internal consistency , good to excellent test - retest reliability , and moderate to strong construct validity confirms the validity and reliability of the persian version of quick - dash for evaluating the magnitude and level of disability in upper extremity conditions . | <s>[INST]. disabilities of the arm , shoulder , and hand ( dash ) questionnaire is a patient - reported outcome measure ( prom ) that measures the magnitude of disability for the upper extremity .
it consists of 30 items , 21 of which assess the ability to perform physical activities , 5 items measure pain , and 4 items measure the psychosocial effects . item elimination in order to shorten the questionnaire resulted in an 11-item instrument , which proved to be as reliable as the original dash instrument .
retention of the clinically oriented questions in the quick - dash made it a comparable instrument to the full dash questionnaire .
the quick - dash is more appealing than the dash because it can be administered in the clinic in a shorter time .
a well - translated and adapted questionnaire would facilitate multicenter studies and increases the feasibility of meta - analysis studies .
farsi is spoken in several countries including iran , tajikistan , afghanistan , and some regions of pakistan and iraq .
validity of the quick - dash has been tested in several other languages . in this study ,
our aim was to assess the validity and reliability of the persian version of the quick - dash in patients with upper extremity conditions .
in total , 202 patients with upper extremity problems enrolled in this study from january 2013 to december 2013 .
inclusion criteria were age above 18 years , ability to read and write persian as a mother tongue , and a minimum of 4-week symptom duration [ table 1 ] . at the first visit
, all patients responded to the persian quick - dash as well as the persian short form 36 health survey ( sf-36 ) and the michigan hand outcome questionnaire ( mhoq ) [ table 2 ] . to test the reliability , 71 patients accepted to return for the second visit after 3 days to fill the persian quick - dash without receiving any major treatment or changes in symptoms .
this study was reviewed and approved by the committee of research and patients consented verbally to participate in the study .
characteristics of patients with upper extremity conditions ( n=202 ) average functional score of patients with upper extremity conditoins ( n=202 ) reliability can be test by either measuring the cronbach 's alpha for internal consistency or intra - class correlation coefficient ( icc ) for test - retest reliability ( reproducibility ) .
commonly accepted values for cronbach 's alpha are described as excellent for > 0.9 , good for 0.9 > > 0.7 , acceptable for 0.7 > > 0.6 , poor for 0.6 > > 0.5 , and unacceptable for < 0.5 .
test - retest reliability is tested by administering a questionnaire to a patient on two separate occasions without any substantial changes in his / her symptoms .
a correlation coefficient of 0 indicates no reliability , whereas a value of 1 indicates excellent reliability . to measure
test - retest reliability in our study , 71 patients randomly filled the persian quick - dash for a 2 time 3 days after the first visit , without being given any major treatment or surgery . to test the construct validity , the new questionnaire is tested against a validated questionnaire with similar or relevant context to assess the correlation between the two questionnaires .
we tested the persian quick - dash against the sf-36 questionnaire and mhoq , which have been validated in persian .
statistical analysis performed using spss version 11.5 ( spss inc . , chicago , il , usa ) .
the sf-36 is an easily administered prom that is frequently used to measure the quality of life .
it consists of 36 questions divided into two major domains of physical and mental components , each one consisting of four sub - domains physical function , role - physical , bodily pain , and general health are sub - domains of functional health .
vitality , social function , role - emotional and mental health are sub - domains of psychometrical health .
it consists of 37 items divided into six subscales , including hand function , pain , activities of daily living , work , esthetics , and patient satisfaction .
in total , 202 patients with upper extremity problems enrolled in this study from january 2013 to december 2013 .
inclusion criteria were age above 18 years , ability to read and write persian as a mother tongue , and a minimum of 4-week symptom duration [ table 1 ] . at the first visit
, all patients responded to the persian quick - dash as well as the persian short form 36 health survey ( sf-36 ) and the michigan hand outcome questionnaire ( mhoq ) [ table 2 ] . to test the reliability , 71 patients accepted to return for the second visit after 3 days to fill the persian quick - dash without receiving any major treatment or changes in symptoms .
this study was reviewed and approved by the committee of research and patients consented verbally to participate in the study .
characteristics of patients with upper extremity conditions ( n=202 ) average functional score of patients with upper extremity conditoins ( n=202 )
reliability can be test by either measuring the cronbach 's alpha for internal consistency or intra - class correlation coefficient ( icc ) for test - retest reliability ( reproducibility ) .
internal consistency measures the consistency of responses across the questionnaire and the subscales . commonly accepted values for cronbach 's alpha are described as excellent for > 0.9 , good for 0.9 > > 0.7 , acceptable for 0.7 >
> 0.6 , poor for 0.6 > > 0.5 , and unacceptable for < 0.5 .
test - retest reliability is tested by administering a questionnaire to a patient on two separate occasions without any substantial changes in his / her symptoms .
a correlation coefficient of 0 indicates no reliability , whereas a value of 1 indicates excellent reliability . to measure
test - retest reliability in our study , 71 patients randomly filled the persian quick - dash for a 2 time 3 days after the first visit , without being given any major treatment or surgery .
to test the construct validity , the new questionnaire is tested against a validated questionnaire with similar or relevant context to assess the correlation between the two questionnaires .
we tested the persian quick - dash against the sf-36 questionnaire and mhoq , which have been validated in persian .
statistical analysis performed using spss version 11.5 ( spss inc . , chicago , il , usa ) .
statistical analysis performed using spss version 11.5 ( spss inc . , chicago , il , usa ) .
the sf-36 is an easily administered prom that is frequently used to measure the quality of life .
it consists of 36 questions divided into two major domains of physical and mental components , each one consisting of four sub - domains physical function , role - physical , bodily pain , and general health are sub - domains of functional health .
vitality , social function , role - emotional and mental health are sub - domains of psychometrical health .
it consists of 37 items divided into six subscales , including hand function , pain , activities of daily living , work , esthetics , and patient satisfaction .
icc was 0.89 , indicating good to excellent test - retest reliability [ table 3 ] .
there was a high and significant inverse correlation between the quick - dash and the mhoq , and the sub - domains of the sf-36 , indicating a strong correlation between the quick - dash and the other validated questionnaire in the same domain [ table 4 ] .
convergent validity was confirmed , as the spearman correlation between the quick - dash and mhoq was 0.67 and ranged from 0.24 to 0.56 between the sub - domains of the sf-36 and quick - dash [ table 4 ] . internal consistency and test - retest reliability of the farsi version of the quick - dash convergent validity expressed by spearman 's rho correlation coefficient between quick - dash and subdomins of the sf-36 and mhoq
the purpose of this study was to establish the validity of the persian version of the quick - dash in patients with upper extremity conditions .
our results indicate that farsi quick - dash is a reliable and valid instrument for studying outcomes in patients with upper extremity conditions . in the current study , internal consistency and
test - retest reliability indicated the excellent reliability of the farsi version of the quick - dash .
testing the construct validity revealed moderate to strong correlation between quick - dash and the mhq and subscales of the sf-36 .
first of all , this is a single - center study , which may not represent the general patient population .
however , this is a major tertiary referral center , providing care to the entire north east and east , and south east provinces of iran .
another limitation was the administration of sf-36 questionnaire , which is more general than quick - dash , and mhoq , which is more specific compared to the quick - dash , to test construct validity ; however , some studies have shown relatively small differences in the responsiveness of the more general and more specific measures of disability .
translations of the dash questionnaire are available in most languages ; however , less work has been done in the cross - cultural adaptation of the quick - dash .
japanese , and turkish versions , cronbach 's alpha was 0.89 , 0.88 and 0.84 , respectively , showing good internal consistency . similarly , icc was 0.94 , 0.93 , and 0.82 in french , turkish , and japanese versions , respectively , showing good test - retest reliability . in our study ,
cronbach 's alpha and icc were 0.90 and 0.89 respectively , showing comparable results with previously validated versions , indicating the reliability of our study .
we compared the quick - dash with sf-36 and mhoq to test the construct validity , using spearman 's correlation coefficient . in order to test the construct validity of the turkish version of the quick - dash , koldas dogan et al .
studied patients with carpal tunnel syndrome using the boston carpal tunnel questionnaire , visual analogue scale - pain ( vas - pain ) , and pinch and grip strength tests to measure the correlation in responsiveness with quick - dash .
quick - dash showed moderate correlations with vas - pain and grip strength test , a good correlation with the pinch strength test , and high correlation with boston carpal tunnel questionnaire .
the japanese version of the quick - dash was tested against the dash , sf-36 and vas .
the correlation coefficients were 0.92 and 0.52 when compared with dash and vas , respectively .
in addition , correlations between quick - dash and sf-36 subscales ranged from 0.29 to 0.73 . in a study to validate the french version ,
the correlation was tested using subjective assessment of activities of daily living ( adl ) , active range of motion ( rom ) , and measurement of abduction strength ( strength ) .
correlation of the french quick - dash score with scores for french dash ( r = 0.96 ) , perceived handicap score ( r = 0.79 ) , adl ( r = 0.73 ) , pain during activities ( r = 0.63 ) , strength ( r = 0.58 ) , pain at rest ( r = 0.57 ) , and rom ( r = 0.51 ) indicated good construct validity .
in this study , we evaluated the reliability and validity of the persian version of the quick - dash .
observation of excellent internal consistency , good to excellent test - retest reliability , and moderate to strong construct validity confirms the validity and reliability of the persian quick - dash in the evaluation of the magnitude of disability for upper extremity conditions .[/INST]background : the aim was to assess the validity and reliability of the persian version of shortened disabilities of the arm , shoulder , and hand ( quick - dash ) questionnaire in patients with upper extremity conditions.methods:we administered the persian version of quick - dash to 202 patients with upper extremity conditions , of which 71 patients randomly returned after 3 days to respond to the questionnaire for the 2nd time . in order to test the construct validity of the questionnaire
, patients responded to the michigan hand outcome questionnaire ( mhoq ) and short form 36 health survey ( sf-36 ) as well .
internal consistency was tested using the cronbach 's alpha , and test - retest reliability was measured using intra - class correlation coefficient ( icc).results : cronbach 's alpha was 0.90 .
icc was 0.89 .
convergent validity was confirmed , as the spearman correlation between the quick - dash and mhoq was 0.67 and ranged from 0.24 to 0.56 between the subscales of the sf-36 and quick-dash.conclusions:observation of excellent internal consistency , good to excellent test - retest reliability , and moderate to strong construct validity confirms the validity and reliability of the persian version of quick - dash for evaluating the magnitude and level of disability in upper extremity conditions .</s> |
the era of unconventional computers implementations of computing schemes in physical , chemical and biological substrates , and interpretation of the behaviour of natural systems in terms of computation has brought us a plethora of original prototypes of future and emerging computing architectures .
some examples of this new paradigm are polymer- and conductive foam based extended analog computers @xcite , chemical reaction - diffusion computers @xcite , aromatic molecular computers @xcite , slime mould computers @xcite , micro - fluidic based computers @xcite , enzymatic logical circuits @xcite , molecular arithmetical circuits @xcite to name but a few .
many of these novel computing devices work on the principle that information is represented by localised states of natural systems ( phase or diffusive waves , propagating pseudopodia , electron density , conformation ) which can then be represented by cellular automata or other discrete automata models ( at least in principle ) @xcite .
most models of unconventional computers suffer , up to different degrees , from boundary problems .
the systems are confined to some experimental arena , e.g. test tube or a petri dish , or even be controlled and programmed by externally imposed geometrical constraints ( e.g. channels in excitable chemical computers )
. it would be incredible useful to produce a model which is self - contained , is not dependent on external constraints and which can , subject to resources and energy supplied , function indefinitely .
a particle `` super collider '' may be the best candidate for such a universal model of boundary free computation . in his seminal paper `` symbol super colliders ''
@xcite tommaso toffoli envisaged far fetching analogies between physical implementations of particle super colliders , lattice gas and one - dimensional cellular automata .
he suggested that the concept of symbol super collider where myriad of tokens run along intersecting rings and interact with each other to produce new tokens can be used in designing novel types of nature - inspired computing devices @xcite .
in present paper we develop toffoli s ideas further and provide computational implementations of particle ` accelerator ' or test rigs , implemented in elementary cellular automata .
the paper is structured as follows .
one - dimensional cellular automata , ahistoric and with memory , are introduced in sect .
the concepts of supercollider and ballistic computing are presented in sect .
[ collider ] .
section [ ballisticcollision ] shows how essential elements of collision - based computers can be implemented via glider interactions in one - dimensional cellular automata , and computational capacities are presented in sect .
[ routing ] .
outcomes of the presented results and directions for further studies are discussed in sect .
[ summary ] .
a cellular automaton ( ca ) is a quintuple @xmath2 based on a one - dimensional lattice @xmath3 of cells , where each cell @xmath4 , @xmath5 , takes a state from a finite alphabet @xmath6 .
a sequence @xmath7 of @xmath8 cell - states represents a string or a global configuration @xmath9 on @xmath6 .
we write a set of finite configurations as @xmath10 .
cells update their states via an evolution rule @xmath11 , such that @xmath12 represents a cell neighbourhood that consists of a central cell and a number of neighbours connected locally
. there are @xmath13 different neighbourhoods and if @xmath14 then we have @xmath15 different evolution rules . an evolution diagram for a ca
is represented by a sequence of configurations @xmath16 generated by the global mapping @xmath17 , where a global relation is given by as @xmath18 .
@xmath19 is the initial configuration .
cell states of a configuration @xmath20 are updated simultaneously by the evolution rule as : @xmath21 where @xmath22 indicates cell position and @xmath23 is the radius of neighbourhood @xmath12 .
thus , the elementary basic ca class represents a system of order @xmath24 ( in wolfram s nomenclature @xcite ) , the well - known eca . to represent a specific evolution rule we write name of the rule in a decimal notation , e.g. @xmath25 .
conventional cellular automata are memoryless : the new state of a cell depends on the neighbourhood configuration solely at the preceding time step of @xmath26 .
ca with memory are an extension of eca in such a way that every cell @xmath4 is allowed to remember its states during some fixed period of its evolution .
ca with memory have been proposed originally by alonso - sanz @xcite .
we implement a memory function @xmath27 as follow : @xmath28 where @xmath29 determines the degree of memory and each cell @xmath30 is a state function of the series of states of the cell @xmath4 with memory up @xmath31 . to execute the evolution we apply the original rule @xmath32 .
thus in ca with memory , while the mapping @xmath26 remains unaltered , historic memory of all past iterations is retained by featuring each cell as a summary of its past states from @xmath27 .
we can say that cells canalize memory to the map @xmath26 @xcite .
let us consider the memory function @xmath27 as a majority memory @xmath33 , where in case of a tie given by @xmath34 from @xmath27 we take the last value @xmath4 .
so @xmath35 function represents the classic majority function for three values @xcite as follows : @xmath36 that represents the cells @xmath37 and defines a temporal ring before to get the next global configuration @xmath9 .
of course , this evaluation can be for any number of values . in this way
, a number of functional memories may be used such as : minority , parity , alpha , etc .
( see @xcite ) .
evolution rules representation in eca with memory as given in @xcite is as follows : @xmath38 where @xmath39 is a decimal notation of a particular eca rule and @xmath40 is a kind of memory used given with a specific value of @xmath31 .
thus for example , the majority memory ( @xmath41 ) incorporated in eca rule 30 employing five step of a cell s history ( @xmath42 ) is denoted as @xmath43 . the memory is a function of the ca itself , see schematic explanation in fig .
[ memevol ] .
in the late 1970s fredkin and toffoli developed a concept of a general - purpose computation based on ballistic interactions between quanta of information that are represented by abstract particles @xcite .
the boolean states of logical variables are represented by balls or atoms , which preserve their identity when they collide with each other .
they came up with the idea of a billiard - ball model of computation , with underpinning mechanics of elastically colliding balls and mirrors reflecting the balls trajectories .
later margolus developed a special class of ca which implement the billiard - ball model .
margolus partitioned ca exhibited computational universality because they simulated fredkin gate via collision of soft spheres @xcite .
the following basic functions with two input arguments @xmath44 and @xmath45 can be expressed via collision between two localizations : 1 .
@xmath46 , fusion ( fig . [ particles]a ) 2 .
@xmath47 , interaction and subsequent change of state ( fig .
[ particles]b ) 3 .
@xmath48 identity , solitonic collision ( fig .
[ particles]c ) ; 4 .
@xmath49 reflection , elastic collision ( fig . [ particles]d ) ; to map toffoli s supercollider @xcite onto a one - dimensional ca we use the notion of an idealized particle @xmath50 ( without energy and potential energy ) .
the particle @xmath51 is represented by a binary string of cell states .
figure [ beamrouting ] shows two typical scenarios where particles @xmath52 and @xmath53 travel in a ca cyclotron .
the first scenario ( fig .
[ beamrouting]a ) shows two particles travelling in opposite directions which then collide .
their collision site is shown by a dark circle in ( fig .
[ beamrouting]a ) .
the second scenario demonstrates a typical beam routing where a fast particle @xmath52 eventually catches up with a slow particle @xmath54 at a collision site ( fig .
[ beamrouting]b ) . if the particles collide like solitons @xcite , then the faster particle @xmath52 simply overtakes the slower particle @xmath54 and continues its motion ( fig .
[ beamrouting]c ) . .
particle @xmath55 collides with particle @xmath56 giving rise to three new particles @xmath57 , @xmath58 , and @xmath59 that are generated as a result of the collision .
, width=288 ] typically , we can find all types of particles manifest in ca gliders , including positive @xmath60 , negative @xmath61 , and neutral @xmath62 displacements @xcite , and also composite particles assembled from elementary localizations .
let us consider the case where a quiescent state is substituted by cells synchronized together as an ether ( periodic background ) .
this phenomenon is associated with eca rule 110 @xmath25 .
its evolution space is dominated by a number of particles emerging in various different orders , some of which are really quite complex constructions .
consequently , the number of collisions between particles is increased .
each particle has a period , displacement , velocity , mass , volume , and phase @xcite .
figure [ splitparticler110 ] displays a typical collision between two particles in @xmath25 . as a result of the collision one particle
is split into three different particles ( for details please see @xcite ) .
the pre - collision positions of particles determines the outcomes of the collision . to represent particles on a given beam routing scheme ( see fig .
[ beamrouting ] ) , we do not consider ether configuration in @xmath25 because this does not affect on collisions .
figure [ solitonr110 ] displays a one - dimensional configuration where two particles collide repeatedly and interact as solitonic so that the identities of the particles are preserved in the collisions .
a negative particle @xmath63 collides and overtakes a neutral particle @xmath64 . figure [ solitonr110]a presents a whole set of cells in state 1 ( dark points ) where the ether configuration makes it impossible to distinguish the particles : @xmath63 and @xmath64 .
however , we can apply a filter and thereby select particles from their background ether ( fig .
[ solitonr110]b ) .
space - time configurations of a cellular automaton exhibiting a collision between particles @xmath63 and @xmath64 are shown in fig .
[ solitonr110]c .
filters selected in ca are a useful tool for understand `` hidden '' properties of ca .
this tool was amply developed by wuensche in the context of automatic classification of ca @xcite .
the filters were derived from mechanical computation techniques @xcite , pattern recognition @xcite , and analysis of cell - state frequencies @xcite .
thus , a filter is a sequence of cells that have a high frequency in the evolution space .
such @xmath65-dimensional string repeat periodically , coexisting with any complex structure without altering or disturbing the global dynamics .
in this section we analyze examples of ballistic collisions between particles in eca and eca with memory .
let us start with eca with memory governed by the rule @xmath66
there are only two types of particles in this rule @xmath67@xmath68 .
their properties are easy to infer : both particles have a volume of a perfect square of @xmath69 cells , a mass of 35 cells , and they translate 2 cells per 11 time steps ( or iterations of ca evolution ) .
the particle @xmath70 has a negative slope with a velocity of @xmath71 and the particle @xmath72 has a positive slope with a velocity of @xmath73 .
the rule @xmath66 supports two types of ballistic collisions : @xmath74 and @xmath75 .
figure [ ballistic]a shows how a number of soliton interactions can be synchronized as a identity collision @xmath76 , where both particles can cross their own trajectories .
this result can be achieved by selecting a particular phase of each particle as encoded by its initial condition .
different initial conditions lead to different reactions @xcite .
for example , in fig .
[ ballistic]b we can see particles undergoing elastic collisions similarly to a lattice gas model @xcite .
this is a reflection collisions @xmath77 .
.properties of particles in rule @xmath78 @xcite . [ cols="^,^",options="header " , ] eca @xmath25 has a unique complexity due to great number of particles that emerge in the automaton evolution .
table [ margenesgliders ] presents a summary of the basic particle properties in @xmath25 , following cook s nomenclature
. we can appreciate how diverse they are .
there are even particles that can expand size forever which increases the number of collisions that we can produce on this eca .
initially , a cts works as a traditional tag system @xcite , i.e. , as a substitution system reading the first symbol on the tape , deleting and putting new symbols .
cts are new machines proposed by cook @xcite as a tool to implement computations in @xmath25 .
cts are a variant of tag systems : they have the same action of reading a tape in the front and adding characters at the end , nevertheless there are some new features as follows : 1 .
a cts needs at least two letters in its alphabet ( @xmath79 ) .
only the first character is deleted ( @xmath80 ) and its respective sequence is added .
if the machine reads a character zero then the production rule is always null ( @xmath81 , where @xmath82 represents the empty word ) .
4 . there are @xmath83 sequences from @xmath84 which are periodically accessed to specify the current production rule when a nonzero character is taken by the system .
therefore the period of each cycle is determinate by @xmath83 .
this way a cycle determines a partial computation over the tape .
no particular halt conditions are specified in the original paper @xcite , possibly because the halting is a direct consequence of tag systems .
let us see some samples of a cts working with @xmath85 , @xmath86 and the production rules : @xmath87 , @xmath88 and @xmath89 .
.,width=432 ] our intention is to represent cts function in @xmath25 based beam routing of symbols .
we employ transition beam routings to explain critical changes that occur due to collisions and sets of particles that are present on each beam routing at every instant description of the machine .
we start with a description of main stages of encoding packages of particles in their initial condition .
this will be an equivalent of beam routing diagram .
we will first show how particles and their collisions emulate a cts in @xmath25 .
we use packages of particles to represent data and operators .
we read , transform and delete data in the tape using reactions between the particles .
the approach is a delicate one and requires a laborious task of setting initial configurations for the particles in the beams .
a diagram of such representation is shown in fig . [ cts - diagram ] , particular features of the diagram are explain below .
a construction of the cts in @xmath25 can be partitioned , essentially , in three parts : * first , is the left periodic part , controlled by packages of 4_@xmath90 particles .
this part is static and controls the production of @xmath91 s and @xmath92 s . *
the second part is the center , determining the initial value in the tape . *
the third one is the right cyclic part , which has the data to process , adding a leader component which specifies data added to or erased from the tape in the evolution space . in the left part , the four packages of @xmath90 ( fig .
[ beamroutingr110]c ) particles must be carefully explained because although they are static , their phases change periodically .
the important point is to implement these components in defining both distances and phases , because a distinct phase or a distance induces an undesirable reaction ; in fact all components obey this restriction because every glider of each component must be correctly aligned . the central part is constituted by an initial 1 on the tape represented by a package of four @xmath93 particles .
this way , an element 1ele@xmath94 ( fig .
[ beamroutingr110]b ) represents a 1 and the element 0ele@xmath94 ( fig . [ beamroutingr110]a ) represents a 0 in the tape . the element 0blo@xmath95 is formed by 12@xmath96 particles . for the 1blo@xmath95 element , cook establishes the existence of two components to represent 1 s : 1blop@xmath95 ( fig .
[ beamroutingr110]f ) named _ primary _ and 1blos@xmath95 ( fig .
[ beamroutingr110]g ) named _ standard_. in essence both blocks produce the same element 1add@xmath95 , although coming from different intervals .
the reason to use both blocks is that @xmath25 is not symmetric ; thus , if we use only one element then although we would obtain a good production in the first collision , generating an element 1add@xmath95 , when the second package of 4_@xmath90 particles finds the second block , the system is completely destroyed .
a leader element sepinit@xmath97 ( fig . [ beamroutingr110]d ) is important in order to separate packages of data and determine their incorporation into of the tape . the elements 1add@xmath95 ( fig . [ beamroutingr110]i ) and
0add@xmath95 ( fig .
[ beamroutingr110]h ) are produced by two previous different packages of data .
an element 1add@xmath95 must be generated by a block 1blop@xmath95 or by 1blos@xmath95 .
this way , both elements can produce the same element . while an element 0add@xmath95 is generated by a block 0blo@xmath95 ( fig .
[ beamroutingr110]e ) .
finally , in terms of periodic phases , this cts can be written as follow : * \{@xmath98 - 4@xmath99(f@xmath100 ) } , for @xmath101 in sequential order * @xmath102 - 1ele@xmath103c2(a , f@xmath104_1)-@xmath105-@xmath106(f@xmath104_1 ) * \{sepinit@xmath97(#,f@xmath107_1)-1blop@xmath95(#,f@xmath107_1)-sepinit@xmath97(#,f@xmath107_1)-1blop@xmath95(#,f@xmath107_1)-0blo@xmath95(#,f@xmath107_1)-1blos@xmath95(#,f@xmath107_1 ) } ( where @xmath108 and # represents a particular phase ) .
for a complete and full description of such reproduction by phases f@xmath109 , please see @xcite . to get a cts emulation in @xmath25 by beam routings
, we will use connections between beam routing , as we have proposed in fig [ beamroutingtransition ] .
.,width=345 ] transitions between beam routings connect each set of collisions to enter to the next beam routing diagram .
we need some fine details to get a cts operation by beam routings .
figure [ ctsbeamrouting ] shows the general diagram to reproduce a cts by particle collisions in @xmath25 with beam routing transitions . while fig .
[ beamroutingr110 ] describes each component to code particles in @xmath25 , fig .
[ ctsbeamrouting ] display how to connect such components and control the transition of collisions .
some notes are necessary to better understand this schematic diagram . for the components 1ele@xmath110 and
0ele@xmath110 they are compressed only for one dark circle ( that represents the point of collisions ) .
both elements are constituted for four @xmath111 particles in different distances , although they have a static position @xmath62 that can be confined to this dark circle , as @xmath112 and @xmath113 respectively .
when a leader component ( sepinit@xmath97 ) is transformed , given previous binary value on the tape , it collides with @xmath114 component , i.e. a @xmath112 or @xmath113 element .
if @xmath114 is 0 , then a cascade of collisions start to _ delete _ all components that come with three particles successively and change this reaction to reach a new leader component and return to the beginning .
but , if @xmath114 is 1 then a cascade of _ transformations _ dominated by additional particles @xmath62 starts , in order to reach the next leader component . here , we have more variants because pre - transformed package of particles is encoded to binary values that is then included on the machine tape .
if a block of particles is 1blop@xmath95 or 1blos@xmath95 this means that such a component will be transformed to one 1add@xmath95 element .
but , if a block of particles is 0blo@xmath95 , then such a component will be transformed to 0add@xmath95 element . at this stage ,
when both components are prepared then a binary value is introduced on the tape , a 1add@xmath95 element stores a 1 ( 1ele@xmath110 ) , and a 0add@xmath95 element stores a 0 ( 0ele@xmath110 ) , which eventually is deleted for the next leader component and starts a new cycle in the cts machine .
the relevant point here is how to control and code particles by beam routings .
that will offer a better chance to perform a computation with this architecture before implementing the complicated and laborious task of setting up initial condition .
of course , such an idea can be carried out in any ca handling signals , waves , particles , gliders or mobile self - localizations @xcite .
the package particles codification for a cts in @xcite is represented for the expression @xmath115 while that in @xcite is represented for the expression @xmath116 .
finally in all cases , this cts beam routing may simulate such operations .
we advanced a concept of symbol super collider @xcite and implemented it in one - dimensional cellular automata .
two types of automaton rings were considered elementary cellular automata ( binary cell state , ternary neighbourhoods ) and elementary cellular automata with memory .
we demonstrated that , for certain rules of cell - state transition functions , the automata exhibit a wide range of particles ( mobile self - localizations or gliders ) in their evolution .
high degree of morphological diversity and richness of collision dynamics of the particles in memory - enriched cellular automata make them particularly promising objects for constructing computational schemes . in present paper we advanced over twenty years old studies in identifying and classifying gliders and localisations in ca .
there is a number of approaches varying in their degrees of efficiency and discovery potentials .
thus , wuensche successfully classified ca evolution rules with his z parameter , and provided power structures of a substantial number of glider - generating rules @xcite .
other studies focus on specification of sets of strings as patterns and gliders .
for example , redeker developed a compact algebraic representation of 1d ca evolution , known as _
flexible time_. suing his approach one can construct specific periodic structures @xcite .
evolution programming techniques are also proved to be very successful , e.g. in situations when a genetic algorithm undertakes a search for gliders and patterns on fixed small arrays of bits @xcite .
as well , freire _ et .
al _ developed an approach to select specific sets of vectors , initial configurations , that determine development of gliders and localised patterns @xcite .
finally , the de bruijn diagrams is a time - tested and reliable tool to classify sets of periodic structures or gliders using exhaustive approach @xcite .
said that in present paper we did not aim to deal with identification of mobile patterns but rather consider glider sets in collision - based computing perspective .
concretely , we only aimed to develop the idea of cyclotrons as an abstract model of super - colliders @xcite .
we proved experimentally that the dynamics of these particles support all basic types of ballistic collisions and consequently that the cellular automata cyclotrons can be used to implement certain schemes and operations of collision - based computing .
we designed schemes with several beams of particles and provided a means of beam routing and programming interactions between particles . to demonstrate the high degree of computational universality of cellular automaton cyclotrons we took into account that each particle is essentially a finite - size binary string travelling along a one - dimensional lattice ` cyclotron . '
when a string with lower velocity overtaken by a string with higher velocity the content of one or both strings can be modified .
thus , for carefully selected initial configuration of particles and types of particles on a ring , the cellular automaton cyclotron imitates a cyclic tag systems , and thus is computationally universal . what are advantages of the proposed approach ? in cellular - automaton models particles can run along the rings indefinitely . with suitable beam routing schemes some particles (
the results of computation or the products of reactions ) can be removed from the system and new particles can be added .
the cellular - automaton super collider is a universal computing devices based on interactions between particles due to the particles different speeds .
this give our constructs an enormous advantage when compared to more `` traditional '' constructs , where particles collide only due to different orientations of velocity vectors .
also most existing unconventional designs of universal computing devices have certain issues of boundary conditions , e.g. infinite versus finite , the cellular - automaton super - colliders by using periodic boundary conditions removes the effect of any boundary being equivalent to an infinite periodic system .
the theoretical models of cellular - automaton super colliders open new perspectives in laboratory implementations of collision based computing devices .
the opportunities are virtually endless .
hundreds of chemical , physical and biological systems exhibit travelling localizations in their dynamics .
examples include co - aligned dipole groups in tubulin microtubules ( e.g. @xcite , kinks , breathers and solitons in molecular chains and polymers ( e.g. @xcite , phasons in quasi - crystals @xcite , kinks in ferromagnets @xcite , dissipative solitons in gas - discharge systems @xcite , localizations of electron density in monolayers of aromatic molecules @xcite , wave - fragments in excitable chemical media @xcite .
we envisage that molecular chains and polymers would be the best candidates for experimental laboratory realisation of symbol super colliders .
this will be a subject of further studies .
genaro j. martnez thanks to support given by dgapa - unam and epsrc grant ep / f054343/1 .
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* 73(3 ) * 036104 , 2005 . | gliders in one - dimensional cellular automata are compact groups of non - quiescent and non - ether patterns ( ether represents a periodic background ) translating along automaton lattice .
they are cellular - automaton analogous of localizations or quasi - local collective excitations travelling in a spatially extended non - linear medium .
they can be considered as binary strings or symbols travelling along a one - dimensional ring , interacting with each other and changing their states , or symbolic values , as a result of interactions .
we analyse what types of interaction occur between gliders travelling on a cellular automaton ` cyclotron ' and build a catalog of the most common reactions .
we demonstrate that collisions between gliders emulate the basic types of interaction that occur between localizations in non - linear media : fusion , elastic collision , and soliton - like collision .
computational outcomes of a swarm of gliders circling on a one - dimensional torus are analysed via implementation of cyclic tag systems .
+ * keywords : * cellular automata , particles , travelling localizations , collisions , beam routing , universality @xmath0 unconventional computing centre , university of the west of england , bristol bs16 1qy , united kingdom .
+ \{genaro.martinez , andrew.adamatzky}@uwe.ac.uk + @xmath1 instituto de ciencias nucleares and centro de ciencias de la complejidad , universidad nacional autnoma de mxico , mxico .
+ \{stephens , frank}@nucleares.unam.mx + | <s>[INST]the era of unconventional computers implementations of computing schemes in physical , chemical and biological substrates , and interpretation of the behaviour of natural systems in terms of computation has brought us a plethora of original prototypes of future and emerging computing architectures .
some examples of this new paradigm are polymer- and conductive foam based extended analog computers @xcite , chemical reaction - diffusion computers @xcite , aromatic molecular computers @xcite , slime mould computers @xcite , micro - fluidic based computers @xcite , enzymatic logical circuits @xcite , molecular arithmetical circuits @xcite to name but a few .
many of these novel computing devices work on the principle that information is represented by localised states of natural systems ( phase or diffusive waves , propagating pseudopodia , electron density , conformation ) which can then be represented by cellular automata or other discrete automata models ( at least in principle ) @xcite .
most models of unconventional computers suffer , up to different degrees , from boundary problems .
the systems are confined to some experimental arena , e.g. test tube or a petri dish , or even be controlled and programmed by externally imposed geometrical constraints ( e.g. channels in excitable chemical computers )
. it would be incredible useful to produce a model which is self - contained , is not dependent on external constraints and which can , subject to resources and energy supplied , function indefinitely .
a particle `` super collider '' may be the best candidate for such a universal model of boundary free computation . in his seminal paper `` symbol super colliders ''
@xcite tommaso toffoli envisaged far fetching analogies between physical implementations of particle super colliders , lattice gas and one - dimensional cellular automata .
he suggested that the concept of symbol super collider where myriad of tokens run along intersecting rings and interact with each other to produce new tokens can be used in designing novel types of nature - inspired computing devices @xcite .
in present paper we develop toffoli s ideas further and provide computational implementations of particle ` accelerator ' or test rigs , implemented in elementary cellular automata .
the paper is structured as follows .
one - dimensional cellular automata , ahistoric and with memory , are introduced in sect .
the concepts of supercollider and ballistic computing are presented in sect .
[ collider ] .
section [ ballisticcollision ] shows how essential elements of collision - based computers can be implemented via glider interactions in one - dimensional cellular automata , and computational capacities are presented in sect .
[ routing ] .
outcomes of the presented results and directions for further studies are discussed in sect .
[ summary ] .
a cellular automaton ( ca ) is a quintuple @xmath2 based on a one - dimensional lattice @xmath3 of cells , where each cell @xmath4 , @xmath5 , takes a state from a finite alphabet @xmath6 .
a sequence @xmath7 of @xmath8 cell - states represents a string or a global configuration @xmath9 on @xmath6 .
we write a set of finite configurations as @xmath10 .
cells update their states via an evolution rule @xmath11 , such that @xmath12 represents a cell neighbourhood that consists of a central cell and a number of neighbours connected locally
. there are @xmath13 different neighbourhoods and if @xmath14 then we have @xmath15 different evolution rules . an evolution diagram for a ca
is represented by a sequence of configurations @xmath16 generated by the global mapping @xmath17 , where a global relation is given by as @xmath18 .
@xmath19 is the initial configuration .
cell states of a configuration @xmath20 are updated simultaneously by the evolution rule as : @xmath21 where @xmath22 indicates cell position and @xmath23 is the radius of neighbourhood @xmath12 .
thus , the elementary basic ca class represents a system of order @xmath24 ( in wolfram s nomenclature @xcite ) , the well - known eca . to represent a specific evolution rule we write name of the rule in a decimal notation , e.g. @xmath25 .
conventional cellular automata are memoryless : the new state of a cell depends on the neighbourhood configuration solely at the preceding time step of @xmath26 .
ca with memory are an extension of eca in such a way that every cell @xmath4 is allowed to remember its states during some fixed period of its evolution .
ca with memory have been proposed originally by alonso - sanz @xcite .
we implement a memory function @xmath27 as follow : @xmath28 where @xmath29 determines the degree of memory and each cell @xmath30 is a state function of the series of states of the cell @xmath4 with memory up @xmath31 . to execute the evolution we apply the original rule @xmath32 .
thus in ca with memory , while the mapping @xmath26 remains unaltered , historic memory of all past iterations is retained by featuring each cell as a summary of its past states from @xmath27 .
we can say that cells canalize memory to the map @xmath26 @xcite .
let us consider the memory function @xmath27 as a majority memory @xmath33 , where in case of a tie given by @xmath34 from @xmath27 we take the last value @xmath4 .
so @xmath35 function represents the classic majority function for three values @xcite as follows : @xmath36 that represents the cells @xmath37 and defines a temporal ring before to get the next global configuration @xmath9 .
of course , this evaluation can be for any number of values . in this way
, a number of functional memories may be used such as : minority , parity , alpha , etc .
( see @xcite ) .
evolution rules representation in eca with memory as given in @xcite is as follows : @xmath38 where @xmath39 is a decimal notation of a particular eca rule and @xmath40 is a kind of memory used given with a specific value of @xmath31 .
thus for example , the majority memory ( @xmath41 ) incorporated in eca rule 30 employing five step of a cell s history ( @xmath42 ) is denoted as @xmath43 . the memory is a function of the ca itself , see schematic explanation in fig .
[ memevol ] .
in the late 1970s fredkin and toffoli developed a concept of a general - purpose computation based on ballistic interactions between quanta of information that are represented by abstract particles @xcite .
the boolean states of logical variables are represented by balls or atoms , which preserve their identity when they collide with each other .
they came up with the idea of a billiard - ball model of computation , with underpinning mechanics of elastically colliding balls and mirrors reflecting the balls trajectories .
later margolus developed a special class of ca which implement the billiard - ball model .
margolus partitioned ca exhibited computational universality because they simulated fredkin gate via collision of soft spheres @xcite .
the following basic functions with two input arguments @xmath44 and @xmath45 can be expressed via collision between two localizations : 1 .
@xmath46 , fusion ( fig . [ particles]a ) 2 .
@xmath47 , interaction and subsequent change of state ( fig .
[ particles]b ) 3 .
@xmath48 identity , solitonic collision ( fig .
[ particles]c ) ; 4 .
@xmath49 reflection , elastic collision ( fig . [ particles]d ) ; to map toffoli s supercollider @xcite onto a one - dimensional ca we use the notion of an idealized particle @xmath50 ( without energy and potential energy ) .
the particle @xmath51 is represented by a binary string of cell states .
figure [ beamrouting ] shows two typical scenarios where particles @xmath52 and @xmath53 travel in a ca cyclotron .
the first scenario ( fig .
[ beamrouting]a ) shows two particles travelling in opposite directions which then collide .
their collision site is shown by a dark circle in ( fig .
[ beamrouting]a ) .
the second scenario demonstrates a typical beam routing where a fast particle @xmath52 eventually catches up with a slow particle @xmath54 at a collision site ( fig .
[ beamrouting]b ) . if the particles collide like solitons @xcite , then the faster particle @xmath52 simply overtakes the slower particle @xmath54 and continues its motion ( fig .
[ beamrouting]c ) . .
particle @xmath55 collides with particle @xmath56 giving rise to three new particles @xmath57 , @xmath58 , and @xmath59 that are generated as a result of the collision .
, width=288 ] typically , we can find all types of particles manifest in ca gliders , including positive @xmath60 , negative @xmath61 , and neutral @xmath62 displacements @xcite , and also composite particles assembled from elementary localizations .
let us consider the case where a quiescent state is substituted by cells synchronized together as an ether ( periodic background ) .
this phenomenon is associated with eca rule 110 @xmath25 .
its evolution space is dominated by a number of particles emerging in various different orders , some of which are really quite complex constructions .
consequently , the number of collisions between particles is increased .
each particle has a period , displacement , velocity , mass , volume , and phase @xcite .
figure [ splitparticler110 ] displays a typical collision between two particles in @xmath25 . as a result of the collision one particle
is split into three different particles ( for details please see @xcite ) .
the pre - collision positions of particles determines the outcomes of the collision . to represent particles on a given beam routing scheme ( see fig .
[ beamrouting ] ) , we do not consider ether configuration in @xmath25 because this does not affect on collisions .
figure [ solitonr110 ] displays a one - dimensional configuration where two particles collide repeatedly and interact as solitonic so that the identities of the particles are preserved in the collisions .
a negative particle @xmath63 collides and overtakes a neutral particle @xmath64 . figure [ solitonr110]a presents a whole set of cells in state 1 ( dark points ) where the ether configuration makes it impossible to distinguish the particles : @xmath63 and @xmath64 .
however , we can apply a filter and thereby select particles from their background ether ( fig .
[ solitonr110]b ) .
space - time configurations of a cellular automaton exhibiting a collision between particles @xmath63 and @xmath64 are shown in fig .
[ solitonr110]c .
filters selected in ca are a useful tool for understand `` hidden '' properties of ca .
this tool was amply developed by wuensche in the context of automatic classification of ca @xcite .
the filters were derived from mechanical computation techniques @xcite , pattern recognition @xcite , and analysis of cell - state frequencies @xcite .
thus , a filter is a sequence of cells that have a high frequency in the evolution space .
such @xmath65-dimensional string repeat periodically , coexisting with any complex structure without altering or disturbing the global dynamics .
in this section we analyze examples of ballistic collisions between particles in eca and eca with memory .
let us start with eca with memory governed by the rule @xmath66
there are only two types of particles in this rule @xmath67@xmath68 .
their properties are easy to infer : both particles have a volume of a perfect square of @xmath69 cells , a mass of 35 cells , and they translate 2 cells per 11 time steps ( or iterations of ca evolution ) .
the particle @xmath70 has a negative slope with a velocity of @xmath71 and the particle @xmath72 has a positive slope with a velocity of @xmath73 .
the rule @xmath66 supports two types of ballistic collisions : @xmath74 and @xmath75 .
figure [ ballistic]a shows how a number of soliton interactions can be synchronized as a identity collision @xmath76 , where both particles can cross their own trajectories .
this result can be achieved by selecting a particular phase of each particle as encoded by its initial condition .
different initial conditions lead to different reactions @xcite .
for example , in fig .
[ ballistic]b we can see particles undergoing elastic collisions similarly to a lattice gas model @xcite .
this is a reflection collisions @xmath77 .
.properties of particles in rule @xmath78 @xcite . [ cols="^,^",options="header " , ] eca @xmath25 has a unique complexity due to great number of particles that emerge in the automaton evolution .
table [ margenesgliders ] presents a summary of the basic particle properties in @xmath25 , following cook s nomenclature
. we can appreciate how diverse they are .
there are even particles that can expand size forever which increases the number of collisions that we can produce on this eca .
initially , a cts works as a traditional tag system @xcite , i.e. , as a substitution system reading the first symbol on the tape , deleting and putting new symbols .
cts are new machines proposed by cook @xcite as a tool to implement computations in @xmath25 .
cts are a variant of tag systems : they have the same action of reading a tape in the front and adding characters at the end , nevertheless there are some new features as follows : 1 .
a cts needs at least two letters in its alphabet ( @xmath79 ) .
only the first character is deleted ( @xmath80 ) and its respective sequence is added .
if the machine reads a character zero then the production rule is always null ( @xmath81 , where @xmath82 represents the empty word ) .
4 . there are @xmath83 sequences from @xmath84 which are periodically accessed to specify the current production rule when a nonzero character is taken by the system .
therefore the period of each cycle is determinate by @xmath83 .
this way a cycle determines a partial computation over the tape .
no particular halt conditions are specified in the original paper @xcite , possibly because the halting is a direct consequence of tag systems .
let us see some samples of a cts working with @xmath85 , @xmath86 and the production rules : @xmath87 , @xmath88 and @xmath89 .
.,width=432 ] our intention is to represent cts function in @xmath25 based beam routing of symbols .
we employ transition beam routings to explain critical changes that occur due to collisions and sets of particles that are present on each beam routing at every instant description of the machine .
we start with a description of main stages of encoding packages of particles in their initial condition .
this will be an equivalent of beam routing diagram .
we will first show how particles and their collisions emulate a cts in @xmath25 .
we use packages of particles to represent data and operators .
we read , transform and delete data in the tape using reactions between the particles .
the approach is a delicate one and requires a laborious task of setting initial configurations for the particles in the beams .
a diagram of such representation is shown in fig . [ cts - diagram ] , particular features of the diagram are explain below .
a construction of the cts in @xmath25 can be partitioned , essentially , in three parts : * first , is the left periodic part , controlled by packages of 4_@xmath90 particles .
this part is static and controls the production of @xmath91 s and @xmath92 s . *
the second part is the center , determining the initial value in the tape . *
the third one is the right cyclic part , which has the data to process , adding a leader component which specifies data added to or erased from the tape in the evolution space . in the left part , the four packages of @xmath90 ( fig .
[ beamroutingr110]c ) particles must be carefully explained because although they are static , their phases change periodically .
the important point is to implement these components in defining both distances and phases , because a distinct phase or a distance induces an undesirable reaction ; in fact all components obey this restriction because every glider of each component must be correctly aligned . the central part is constituted by an initial 1 on the tape represented by a package of four @xmath93 particles .
this way , an element 1ele@xmath94 ( fig .
[ beamroutingr110]b ) represents a 1 and the element 0ele@xmath94 ( fig . [ beamroutingr110]a ) represents a 0 in the tape . the element 0blo@xmath95 is formed by 12@xmath96 particles . for the 1blo@xmath95 element , cook establishes the existence of two components to represent 1 s : 1blop@xmath95 ( fig .
[ beamroutingr110]f ) named _ primary _ and 1blos@xmath95 ( fig .
[ beamroutingr110]g ) named _ standard_. in essence both blocks produce the same element 1add@xmath95 , although coming from different intervals .
the reason to use both blocks is that @xmath25 is not symmetric ; thus , if we use only one element then although we would obtain a good production in the first collision , generating an element 1add@xmath95 , when the second package of 4_@xmath90 particles finds the second block , the system is completely destroyed .
a leader element sepinit@xmath97 ( fig . [ beamroutingr110]d ) is important in order to separate packages of data and determine their incorporation into of the tape . the elements 1add@xmath95 ( fig . [ beamroutingr110]i ) and
0add@xmath95 ( fig .
[ beamroutingr110]h ) are produced by two previous different packages of data .
an element 1add@xmath95 must be generated by a block 1blop@xmath95 or by 1blos@xmath95 .
this way , both elements can produce the same element . while an element 0add@xmath95 is generated by a block 0blo@xmath95 ( fig .
[ beamroutingr110]e ) .
finally , in terms of periodic phases , this cts can be written as follow : * \{@xmath98 - 4@xmath99(f@xmath100 ) } , for @xmath101 in sequential order * @xmath102 - 1ele@xmath103c2(a , f@xmath104_1)-@xmath105-@xmath106(f@xmath104_1 ) * \{sepinit@xmath97(#,f@xmath107_1)-1blop@xmath95(#,f@xmath107_1)-sepinit@xmath97(#,f@xmath107_1)-1blop@xmath95(#,f@xmath107_1)-0blo@xmath95(#,f@xmath107_1)-1blos@xmath95(#,f@xmath107_1 ) } ( where @xmath108 and # represents a particular phase ) .
for a complete and full description of such reproduction by phases f@xmath109 , please see @xcite . to get a cts emulation in @xmath25 by beam routings
, we will use connections between beam routing , as we have proposed in fig [ beamroutingtransition ] .
.,width=345 ] transitions between beam routings connect each set of collisions to enter to the next beam routing diagram .
we need some fine details to get a cts operation by beam routings .
figure [ ctsbeamrouting ] shows the general diagram to reproduce a cts by particle collisions in @xmath25 with beam routing transitions . while fig .
[ beamroutingr110 ] describes each component to code particles in @xmath25 , fig .
[ ctsbeamrouting ] display how to connect such components and control the transition of collisions .
some notes are necessary to better understand this schematic diagram . for the components 1ele@xmath110 and
0ele@xmath110 they are compressed only for one dark circle ( that represents the point of collisions ) .
both elements are constituted for four @xmath111 particles in different distances , although they have a static position @xmath62 that can be confined to this dark circle , as @xmath112 and @xmath113 respectively .
when a leader component ( sepinit@xmath97 ) is transformed , given previous binary value on the tape , it collides with @xmath114 component , i.e. a @xmath112 or @xmath113 element .
if @xmath114 is 0 , then a cascade of collisions start to _ delete _ all components that come with three particles successively and change this reaction to reach a new leader component and return to the beginning .
but , if @xmath114 is 1 then a cascade of _ transformations _ dominated by additional particles @xmath62 starts , in order to reach the next leader component . here , we have more variants because pre - transformed package of particles is encoded to binary values that is then included on the machine tape .
if a block of particles is 1blop@xmath95 or 1blos@xmath95 this means that such a component will be transformed to one 1add@xmath95 element .
but , if a block of particles is 0blo@xmath95 , then such a component will be transformed to 0add@xmath95 element . at this stage ,
when both components are prepared then a binary value is introduced on the tape , a 1add@xmath95 element stores a 1 ( 1ele@xmath110 ) , and a 0add@xmath95 element stores a 0 ( 0ele@xmath110 ) , which eventually is deleted for the next leader component and starts a new cycle in the cts machine .
the relevant point here is how to control and code particles by beam routings .
that will offer a better chance to perform a computation with this architecture before implementing the complicated and laborious task of setting up initial condition .
of course , such an idea can be carried out in any ca handling signals , waves , particles , gliders or mobile self - localizations @xcite .
the package particles codification for a cts in @xcite is represented for the expression @xmath115 while that in @xcite is represented for the expression @xmath116 .
finally in all cases , this cts beam routing may simulate such operations .
we advanced a concept of symbol super collider @xcite and implemented it in one - dimensional cellular automata .
two types of automaton rings were considered elementary cellular automata ( binary cell state , ternary neighbourhoods ) and elementary cellular automata with memory .
we demonstrated that , for certain rules of cell - state transition functions , the automata exhibit a wide range of particles ( mobile self - localizations or gliders ) in their evolution .
high degree of morphological diversity and richness of collision dynamics of the particles in memory - enriched cellular automata make them particularly promising objects for constructing computational schemes . in present paper we advanced over twenty years old studies in identifying and classifying gliders and localisations in ca .
there is a number of approaches varying in their degrees of efficiency and discovery potentials .
thus , wuensche successfully classified ca evolution rules with his z parameter , and provided power structures of a substantial number of glider - generating rules @xcite .
other studies focus on specification of sets of strings as patterns and gliders .
for example , redeker developed a compact algebraic representation of 1d ca evolution , known as _
flexible time_. suing his approach one can construct specific periodic structures @xcite .
evolution programming techniques are also proved to be very successful , e.g. in situations when a genetic algorithm undertakes a search for gliders and patterns on fixed small arrays of bits @xcite .
as well , freire _ et .
al _ developed an approach to select specific sets of vectors , initial configurations , that determine development of gliders and localised patterns @xcite .
finally , the de bruijn diagrams is a time - tested and reliable tool to classify sets of periodic structures or gliders using exhaustive approach @xcite .
said that in present paper we did not aim to deal with identification of mobile patterns but rather consider glider sets in collision - based computing perspective .
concretely , we only aimed to develop the idea of cyclotrons as an abstract model of super - colliders @xcite .
we proved experimentally that the dynamics of these particles support all basic types of ballistic collisions and consequently that the cellular automata cyclotrons can be used to implement certain schemes and operations of collision - based computing .
we designed schemes with several beams of particles and provided a means of beam routing and programming interactions between particles . to demonstrate the high degree of computational universality of cellular automaton cyclotrons we took into account that each particle is essentially a finite - size binary string travelling along a one - dimensional lattice ` cyclotron . '
when a string with lower velocity overtaken by a string with higher velocity the content of one or both strings can be modified .
thus , for carefully selected initial configuration of particles and types of particles on a ring , the cellular automaton cyclotron imitates a cyclic tag systems , and thus is computationally universal . what are advantages of the proposed approach ? in cellular - automaton models particles can run along the rings indefinitely . with suitable beam routing schemes some particles (
the results of computation or the products of reactions ) can be removed from the system and new particles can be added .
the cellular - automaton super collider is a universal computing devices based on interactions between particles due to the particles different speeds .
this give our constructs an enormous advantage when compared to more `` traditional '' constructs , where particles collide only due to different orientations of velocity vectors .
also most existing unconventional designs of universal computing devices have certain issues of boundary conditions , e.g. infinite versus finite , the cellular - automaton super - colliders by using periodic boundary conditions removes the effect of any boundary being equivalent to an infinite periodic system .
the theoretical models of cellular - automaton super colliders open new perspectives in laboratory implementations of collision based computing devices .
the opportunities are virtually endless .
hundreds of chemical , physical and biological systems exhibit travelling localizations in their dynamics .
examples include co - aligned dipole groups in tubulin microtubules ( e.g. @xcite , kinks , breathers and solitons in molecular chains and polymers ( e.g. @xcite , phasons in quasi - crystals @xcite , kinks in ferromagnets @xcite , dissipative solitons in gas - discharge systems @xcite , localizations of electron density in monolayers of aromatic molecules @xcite , wave - fragments in excitable chemical media @xcite .
we envisage that molecular chains and polymers would be the best candidates for experimental laboratory realisation of symbol super colliders .
this will be a subject of further studies .
genaro j. martnez thanks to support given by dgapa - unam and epsrc grant ep / f054343/1 .
boccara , nino , nasser , j. , and roger , m. `` particle like structures and their interactions in spatio - temporal patterns generated by one - dimensional deterministic cellular automaton rules , '' _ physical review a _ * 44(2 ) * 866875 , 1991 .
r. coldea , d. a. tennant , e. m. wheeler , e. wawrzynska , d. prabhakaran , m. telling , k. habicht , p. smeibidl , and k. kiefer , `` quantum criticality in an ising chain : experimental evidence for emergent e8 symmetry , '' _ science _ * 327 * 177180 , 2010 .
freire , joana g. , brison , owen j. , and gallas , jason a.c .
( 2010 ) `` complete sets of initial vectors for pattern growth with elementary cellular automata , '' _ computer physics communications _ * 181 * 750755 .
michael j. fuerstman , pascal deschatelets , ravi kane , alexander schwartz , paul j. a. kenis , john m. deutch , and george m. whitesides , `` solving mazes using microfluidic networks , '' _ langmuir _ * 19 * 47144722 , 2003 .
martnez , genaro j. , adamatzky , andrew , seck - tuoh - mora , j. c. , and alonso - sanz , ramon , `` how to make dull cellular automata complex by adding memory : rule 126 case study , '' _ complexity _ * 15(6 ) * 3449 , 2010 .
martnez , genaro j. , adamatzky , andrew , and mcintosh , harold v. , `` phenomenology of glider collisions in cellular automaton rule 54 and associated logical gates , '' _ chaos , solitons and fractals _ * 28 * 100111 , 2006 .
martnez , genaro j. , adamatzky , andrew , and mcintosh , harold v. , `` on the representation of gliders in rule 54 by de bruijn and cycle diagrams , '' _ lecture notes in computer science _ * 5191 * 8391 , 2008 .
mershin a. , kolomenski a. a. , schuessler h. a. , nanopoulos d. v. , `` tubulin dipole moment , dielectric constant and quantum behavior : computer simulations , experimental results and suggestions , '' _
biosystems _ * 77 * 7385 , 2004 .
arxiv : physics/0402053v1 martnez , genaro j. , mcintosh , harold v. , seck - tuoh - mora , juan c. , and chapa - vergara , sergio v. , `` determining a regular language by glider - based structures called _
phases f@xmath117_1 _ in rule 110 , '' _ journal of cellular automata _
* 3(3 ) * 231270 , 2008 .
martnez , genaro j. , mcintosh , harold v. , seck - tuoh - mora , juan c. , and chapa - vergara , sergio v. , `` reproducing the cyclic tag system developed by matthew cook with rule 110 using the phases f@xmath118_1 , '' _ journal of cellular automata _ * 6(2 - 3 ) * 121161 , 2011 .
moreira , andrs , boccara , nino , and goles , eric , `` on conservative and monotone one - dimensional cellular automata and their particle representation , '' _ theoretical computer science _
* 352(2 ) * 285316 , 2004 .
rasmussen , s. , karampurwala , h. , vaidyanath , r. , jensen , k.s . , and hameroff , s. , `` computational connectionism within neurons : a model of cytoskeletal automata subserving neural networks , '' _ physica d _ * 42 * 428449 , 1990 .
shalizi , cosma r. , haslinger , robert , rouquier , jean - baptiste , klinkner , kristina l. , and moore , cristopher , `` automatic filters for the detection of coherent structure in spatiotemporal systems '' , _ physical review e _
* 73(3 ) * 036104 , 2005 .[/INST] gliders in one - dimensional cellular automata are compact groups of non - quiescent and non - ether patterns ( ether represents a periodic background ) translating along automaton lattice .
they are cellular - automaton analogous of localizations or quasi - local collective excitations travelling in a spatially extended non - linear medium .
they can be considered as binary strings or symbols travelling along a one - dimensional ring , interacting with each other and changing their states , or symbolic values , as a result of interactions .
we analyse what types of interaction occur between gliders travelling on a cellular automaton ` cyclotron ' and build a catalog of the most common reactions .
we demonstrate that collisions between gliders emulate the basic types of interaction that occur between localizations in non - linear media : fusion , elastic collision , and soliton - like collision .
computational outcomes of a swarm of gliders circling on a one - dimensional torus are analysed via implementation of cyclic tag systems .
+ * keywords : * cellular automata , particles , travelling localizations , collisions , beam routing , universality @xmath0 unconventional computing centre , university of the west of england , bristol bs16 1qy , united kingdom .
+ \{genaro.martinez , andrew.adamatzky}@uwe.ac.uk + @xmath1 instituto de ciencias nucleares and centro de ciencias de la complejidad , universidad nacional autnoma de mxico , mxico .
+ \{stephens , frank}@nucleares.unam.mx + </s> |
What kind of Pathetic, coward shoots and kills a family dog? The kind that work here it seems. Never mind the fact the officer was at t
about 7 months ago 1 star | – Deputies in North Carolina say they're seeking a teenager who robbed a 9-year-old's lemonade stand at gunpoint, per the AP. The Union County Sheriff's Office said Sunday that the stickup happened near a traffic roundabout in Monroe, about 30 miles southeast of Charlotte. Deputies say the young drink vendor reported that a male teenager with a camouflage hat and black shirt placed a black handgun to the boy's stomach Saturday, demanded money and then fled on foot. Sheriff's spokesman Tony Underwood tells The Charlotte Observer less than $20 in cash was stolen. According to a statement the sheriff's office posted to Facebook, authorities found a camouflage hat, a black BB handgun and a stolen metal tin along a trail in some nearby woods. Deputies believe the suspect left a bicycle in the brush for his getaway. Authorities said they're unsure if the BB gun they found is the same weapon used in the holdup, but that is appears to likely to be the case because of where it was recovered along with the other items. | <s>[INST]What kind of Pathetic, coward shoots and kills a family dog? The kind that work here it seems. Never mind the fact the officer was at t
about 7 months ago 1 star[/INST]– Deputies in North Carolina say they're seeking a teenager who robbed a 9-year-old's lemonade stand at gunpoint, per the AP. The Union County Sheriff's Office said Sunday that the stickup happened near a traffic roundabout in Monroe, about 30 miles southeast of Charlotte. Deputies say the young drink vendor reported that a male teenager with a camouflage hat and black shirt placed a black handgun to the boy's stomach Saturday, demanded money and then fled on foot. Sheriff's spokesman Tony Underwood tells The Charlotte Observer less than $20 in cash was stolen. According to a statement the sheriff's office posted to Facebook, authorities found a camouflage hat, a black BB handgun and a stolen metal tin along a trail in some nearby woods. Deputies believe the suspect left a bicycle in the brush for his getaway. Authorities said they're unsure if the BB gun they found is the same weapon used in the holdup, but that is appears to likely to be the case because of where it was recovered along with the other items.</s> |
D.C. Circuit Judges Top List of Potential Supreme Court Picks
By Todd Ruger
At the top of many lists of the potential picks that President Barack Obama could make to fill Justice Antonin Scalia’s seat on the Supreme Court is an appeals court judge the Senate unanimously confirmed in May 2013.
The Senate voted 97-0 to confirm Sri Srinivasan to the U.S. Court of Appeals for the D.C. Circuit, sometimes referred to as the second-highest court in the land behind the Supreme Court because it decides many regulatory issues that have a nationwide scope.
In the confirmation process, Srinivasan garnered broad support from both Democrats and Republicans, including Majority Leader Mitch McConnell, R-Ky., Sen. Charles E. Grassley, R-Iowa, Sen. Orrin G. Hatch, R-Utah., and Sen. Ted Cruz, R-Texas.
“We have been friends for a long time – so I am hopeful that our friendship will not be seen as a strike against you by some,” Cruz said, a remark that drew laughter in the hearing room. Cruz, now seeking the Republican nomination for president, noted that both he and Srinivasan served as law clerks for judges on the 4th Circuit Court of Appeals in 1995 and 1996.
Hatch told him, “I think you’re going to make a great circuit court of appeals judge and I intend to support you.”
McConnell and Grassley issued statements Saturday that the president shouldn’t make a nomination before the November presidential election. Supreme Court decisions often become political issues and the appointment to fill a vacancy is likely to add to the debate on the campaign trail this year. Scalia was one of the court’s conservatives. Democrats hope they can replace him with a more liberal justice and Republicans want another conservative on the bench.
Srinivasan, responding to a question from Cruz, said he did not believe in the idea of “a living constitution” with a meaning that judges change as social conditions change. “The Constitution has an enduring, fixed quality to it,” he said.
His confirmation hearing in 2013 was also held in the presence of a large South Asian community, potentially adding a variable to the political calculus that surrounds high court nominations.
Srinivasan would be a consensus candidate that Obama could pick “if he wanted to try to lower the temperature” of Senate politics, said appellate lawyer John Elwood, a partner at Vinson & Elkins in Washington. Obama also could consider nominating another woman to the court in an effort to make it five men and four women, Elwood said.
Potential picks could be Judges Patricia Millette or Cornelia “Nina” Pillard, both widely praised judges on the D.C. Circuit but both filibustered in the Senate when Republicans objected to how many judges Obama was picking for the D.C. Circuit. Both were eventually confirmed in 2013 after Democrats changed the filibuster rules to make it easier to confirm some appointees.
Norman Ornstein, a scholar at the American Enterprise Institute and long-time observer of Congress, floated the possibility of Democratic Sen. Amy Klobuchar of Minnesota, as well as Merrick Garland, the chief judge of the D.C. Circuit.
Sen. Lindsey Graham, R-S.C., reportedly floated the idea Saturday of Utah Republican Sen. Orrin G. Hatch as a potential nominee that some Republicans might support.
Srinivasan is a potential nominee who first comes to mind because his work history is bipartisan. He clerked for Supreme Court Justice Sandra Day O’Connor, a Reagan appointee. He worked in the Justice Department during the George W. Bush administration, and at the time of his appointment was principal deputy solicitor general at the Justice Department under Obama who was frequently an advocate before the Supreme Court.
Of course, the scrutiny for a Supreme Court pick is vastly elevated from that for even the D.C. Circuit. And even his broad support didn’t keep his nomination from being held up in Senate politics for almost 11 months. McConnnell and Grassley have already said the pick to fill Scalia’s seat should fall to the next president.
Tom Curry contributed to this report.
Related:
See photos, follies, HOH Hits and Misses and more at Roll Call’s new video site.
NEW! Download the Roll Call app for the best coverage of people, politics and personalities of Capitol Hill. ||||| CLOSE In what's likely to be a political quagmire, President Obama looks to appoint another Supreme Court justice before leaving office. USA TODAY
President Obama speaks at the Rose Garden with Patricia Millett in June 2013. (Photo: Manuel Balce Ceneta, AP)
WASHINGTON — Who could replace Supreme Court Justice Antonin Scalia if Republicans don't block all of President Obama's nominees, as appears likely? Here are 10 possibilities:
Sri Srinivasan: The 48-year-old federal appeals court judge was confirmed unanimously in 2013 for a seat on the U.S. Court of Appeals for the D.C. Circuit — a traditional steppingstone to the Supreme Court. He would be the court's first Indian-American justice.
Patricia Millett: Srinivasan's 52-year-old colleague on the D.C. Circuit is popular in both parties and is frequently mentioned as a possible candidate. She argued 32 cases before the Supreme Court as an advocate.
Merrick Garland: At 63, Garland is older than most nominees, since presidents want their choices to stick around for decades on the bench. He is a moderate who serves as chief judge on the D.C. Circuit court and could be a compromise choice.
Kamala Harris: California's attorney general, 51, could be another leading candidate. She has the added luster of holding political office, a life experience that is sorely lacking on the Supreme Court. But she's currently running for the U.S. Senate seat of retiring Sen. Barbara Boxer, so she likely wouldn't want a fated nomination.
Jacqueline Nguyen: The Asian-American judge, who sits on the U.S. Court of Appeals for the 9th Circuit, has been mentioned frequently in the initial hours after Scalia's death. At 50, she is the perfect age for a nominee.
Amy Klobuchar: If the Senate would be less inclined to block one of its own, the senior senator from Minnesota, 55, might be someone Obama would consider.
Adalberto Jordan: This Cuban-American appellate judge sits on the 11th Circuit, where he was named by Obama in 2012. At 54, he is the right age and could bring a new ethnicity to the court.
Loretta Lynch: The U.S. attorney general. 56, just went through a lengthy confirmation process and has the scars to prove it. She is a black woman with prosecutorial experience and is being touted as one of the most likely nominees.
Paul Watford: A judge on the U.S. Court of Appeals for the 9th Circuit, Watford, 48, is another Obama nominee with a potentially stellar future. Some court-watchers expect the African-American judge to be Obama's first choice -- but possibly not for a fated nomination.
Jane Kelly: She is a 51-year-old judge on the U.S. Court of Appeals for the 8th Circuit who was a career public defender. From Iowa, she has enjoyed the prior support of Republican Sen. Chuck Grassley, who heads the Senate Judiciary Committee. And Iowa is a purple state.
More on the death of Justice Scalia:
CLOSE President Obama remembered and honored Supreme Court Justice Antonin Scalia who died at the age of 79, and vowed to nominate a replacement. USA TODAY
Read or Share this story: http://usat.ly/1XqItgU | – With the death of Antonin Scalia, the longest-serving justice on the Supreme Court, comes the inevitable question of who might succeed him on the bench. Some of the bigger names being floated, via USA Today and Roll Call: Sri Srinivasan: The 48-year-old Court of Appeals for the DC Circuit judge tops both lists. He sailed unanimously through Senate confirmation in 2013, and he'd be the first Indian-American to sit on the high court. Patricia Millett: The 52-year-old sits on the DC Circuit Court with Srinivasan, and has argued 32 cases before the Supreme Court. Merrick Garland: Another DC Circuit Court justice; he's moderate, and his name was brought up for the Supreme Court nomination that ultimately went to Elena Kagan. Possible down side: He's 63, and a bit older than most potential nominees. Amy Klobuchar: The 55-year-old Minnesota senator's name is mentioned with an eye toward a contentious Senate that might be less likely to block one of their own. Deval Patrick: The 59-year-old former Massachusetts governor spent time in the Justice Department, and is a close friend of President Obama. Kamala Harris: California's 51-year-old attorney general is seen as a rising Democratic star, and is currently running for Barbara Boxer's Senate seat. The rest of the list is here. | <s>[INST]D.C. Circuit Judges Top List of Potential Supreme Court Picks
By Todd Ruger
At the top of many lists of the potential picks that President Barack Obama could make to fill Justice Antonin Scalia’s seat on the Supreme Court is an appeals court judge the Senate unanimously confirmed in May 2013.
The Senate voted 97-0 to confirm Sri Srinivasan to the U.S. Court of Appeals for the D.C. Circuit, sometimes referred to as the second-highest court in the land behind the Supreme Court because it decides many regulatory issues that have a nationwide scope.
In the confirmation process, Srinivasan garnered broad support from both Democrats and Republicans, including Majority Leader Mitch McConnell, R-Ky., Sen. Charles E. Grassley, R-Iowa, Sen. Orrin G. Hatch, R-Utah., and Sen. Ted Cruz, R-Texas.
“We have been friends for a long time – so I am hopeful that our friendship will not be seen as a strike against you by some,” Cruz said, a remark that drew laughter in the hearing room. Cruz, now seeking the Republican nomination for president, noted that both he and Srinivasan served as law clerks for judges on the 4th Circuit Court of Appeals in 1995 and 1996.
Hatch told him, “I think you’re going to make a great circuit court of appeals judge and I intend to support you.”
McConnell and Grassley issued statements Saturday that the president shouldn’t make a nomination before the November presidential election. Supreme Court decisions often become political issues and the appointment to fill a vacancy is likely to add to the debate on the campaign trail this year. Scalia was one of the court’s conservatives. Democrats hope they can replace him with a more liberal justice and Republicans want another conservative on the bench.
Srinivasan, responding to a question from Cruz, said he did not believe in the idea of “a living constitution” with a meaning that judges change as social conditions change. “The Constitution has an enduring, fixed quality to it,” he said.
His confirmation hearing in 2013 was also held in the presence of a large South Asian community, potentially adding a variable to the political calculus that surrounds high court nominations.
Srinivasan would be a consensus candidate that Obama could pick “if he wanted to try to lower the temperature” of Senate politics, said appellate lawyer John Elwood, a partner at Vinson & Elkins in Washington. Obama also could consider nominating another woman to the court in an effort to make it five men and four women, Elwood said.
Potential picks could be Judges Patricia Millette or Cornelia “Nina” Pillard, both widely praised judges on the D.C. Circuit but both filibustered in the Senate when Republicans objected to how many judges Obama was picking for the D.C. Circuit. Both were eventually confirmed in 2013 after Democrats changed the filibuster rules to make it easier to confirm some appointees.
Norman Ornstein, a scholar at the American Enterprise Institute and long-time observer of Congress, floated the possibility of Democratic Sen. Amy Klobuchar of Minnesota, as well as Merrick Garland, the chief judge of the D.C. Circuit.
Sen. Lindsey Graham, R-S.C., reportedly floated the idea Saturday of Utah Republican Sen. Orrin G. Hatch as a potential nominee that some Republicans might support.
Srinivasan is a potential nominee who first comes to mind because his work history is bipartisan. He clerked for Supreme Court Justice Sandra Day O’Connor, a Reagan appointee. He worked in the Justice Department during the George W. Bush administration, and at the time of his appointment was principal deputy solicitor general at the Justice Department under Obama who was frequently an advocate before the Supreme Court.
Of course, the scrutiny for a Supreme Court pick is vastly elevated from that for even the D.C. Circuit. And even his broad support didn’t keep his nomination from being held up in Senate politics for almost 11 months. McConnnell and Grassley have already said the pick to fill Scalia’s seat should fall to the next president.
Tom Curry contributed to this report.
Related:
See photos, follies, HOH Hits and Misses and more at Roll Call’s new video site.
NEW! Download the Roll Call app for the best coverage of people, politics and personalities of Capitol Hill. ||||| CLOSE In what's likely to be a political quagmire, President Obama looks to appoint another Supreme Court justice before leaving office. USA TODAY
President Obama speaks at the Rose Garden with Patricia Millett in June 2013. (Photo: Manuel Balce Ceneta, AP)
WASHINGTON — Who could replace Supreme Court Justice Antonin Scalia if Republicans don't block all of President Obama's nominees, as appears likely? Here are 10 possibilities:
Sri Srinivasan: The 48-year-old federal appeals court judge was confirmed unanimously in 2013 for a seat on the U.S. Court of Appeals for the D.C. Circuit — a traditional steppingstone to the Supreme Court. He would be the court's first Indian-American justice.
Patricia Millett: Srinivasan's 52-year-old colleague on the D.C. Circuit is popular in both parties and is frequently mentioned as a possible candidate. She argued 32 cases before the Supreme Court as an advocate.
Merrick Garland: At 63, Garland is older than most nominees, since presidents want their choices to stick around for decades on the bench. He is a moderate who serves as chief judge on the D.C. Circuit court and could be a compromise choice.
Kamala Harris: California's attorney general, 51, could be another leading candidate. She has the added luster of holding political office, a life experience that is sorely lacking on the Supreme Court. But she's currently running for the U.S. Senate seat of retiring Sen. Barbara Boxer, so she likely wouldn't want a fated nomination.
Jacqueline Nguyen: The Asian-American judge, who sits on the U.S. Court of Appeals for the 9th Circuit, has been mentioned frequently in the initial hours after Scalia's death. At 50, she is the perfect age for a nominee.
Amy Klobuchar: If the Senate would be less inclined to block one of its own, the senior senator from Minnesota, 55, might be someone Obama would consider.
Adalberto Jordan: This Cuban-American appellate judge sits on the 11th Circuit, where he was named by Obama in 2012. At 54, he is the right age and could bring a new ethnicity to the court.
Loretta Lynch: The U.S. attorney general. 56, just went through a lengthy confirmation process and has the scars to prove it. She is a black woman with prosecutorial experience and is being touted as one of the most likely nominees.
Paul Watford: A judge on the U.S. Court of Appeals for the 9th Circuit, Watford, 48, is another Obama nominee with a potentially stellar future. Some court-watchers expect the African-American judge to be Obama's first choice -- but possibly not for a fated nomination.
Jane Kelly: She is a 51-year-old judge on the U.S. Court of Appeals for the 8th Circuit who was a career public defender. From Iowa, she has enjoyed the prior support of Republican Sen. Chuck Grassley, who heads the Senate Judiciary Committee. And Iowa is a purple state.
More on the death of Justice Scalia:
CLOSE President Obama remembered and honored Supreme Court Justice Antonin Scalia who died at the age of 79, and vowed to nominate a replacement. USA TODAY
Read or Share this story: http://usat.ly/1XqItgU[/INST]– With the death of Antonin Scalia, the longest-serving justice on the Supreme Court, comes the inevitable question of who might succeed him on the bench. Some of the bigger names being floated, via USA Today and Roll Call: Sri Srinivasan: The 48-year-old Court of Appeals for the DC Circuit judge tops both lists. He sailed unanimously through Senate confirmation in 2013, and he'd be the first Indian-American to sit on the high court. Patricia Millett: The 52-year-old sits on the DC Circuit Court with Srinivasan, and has argued 32 cases before the Supreme Court. Merrick Garland: Another DC Circuit Court justice; he's moderate, and his name was brought up for the Supreme Court nomination that ultimately went to Elena Kagan. Possible down side: He's 63, and a bit older than most potential nominees. Amy Klobuchar: The 55-year-old Minnesota senator's name is mentioned with an eye toward a contentious Senate that might be less likely to block one of their own. Deval Patrick: The 59-year-old former Massachusetts governor spent time in the Justice Department, and is a close friend of President Obama. Kamala Harris: California's 51-year-old attorney general is seen as a rising Democratic star, and is currently running for Barbara Boxer's Senate seat. The rest of the list is here.</s> |
resistance weight training was reported to have a positive effect on the reduction of body
fat by increasing muscle tissues ; maintenance of muscular strength and increase of fat - free
mass ; and reduction of blood lipid and lipoprotein metabolism , emphasizing the necessity of
resistance weight training as an effective method for weight control , controling the
interset rest time during weight training can have a significant have a positive effect on
the change of blood lipid concentration and body construction1 . likewise , weight training increases bmr , improves insulin reaction ,
increases bone density or prevents its loss , and prevents the loss of muscle mass and
muscular strength resulting from aging , which emphasizes the importance of weight
training2 .
in addition , weight training
is reported to increase muscle strength and transversal area of muscle not only in men , but
also in women who are middle age / old aged . from this viewpoint , it is recommendable that an
exercise program for the safest and most efficient weight loss should be composed of
contents that comprehensively combine aerobic exercise with resistance weight training based
on the person s level .
even recently conducted precedent studies found that compound
training with aerobic exercise and resistance weight training aimed at middle - aged women
with obesity had a positive effect on body composition and blood lipids3 , 4 .
the study reported
the importance of dietary therapy as well as exercise therapy and stated that exercise
therapy without considering dietary therapy could not reduce body fat5 .
recently , there have been more than a few findings regarding the effect of compound
exercises on middle - aged women with obesity who had experienced health risks due to exposure to
various adult diseases and illnesses , but the number of studies is still insufficient ;
further , more specific and diverse experiments and research are necessary with regard to how
dietary exercises and resistance weight training can be mixed into an ideal compound
physical activity program that is suitable for a person s own characteristics .
the purpose
of this study was to investigate the effect of a compound physical activity program on
muscular strength in obese women .
they were selected based on a body fat
rate of over 30% obtained using a bioelectric impedance method .
the subjects had not
participated in physical activity or training for at least 6 months .
they were randomly
assigned to two groups , the experimental group , n=20 , and the control , n=20 ( table 1 ) .
aerobic physical activity was performed 5 times per week ,
and anaerobic physical activity was performed every two days ; the exercise program each day
was composed of warm - up , the main exercise , and cooldown .
the compound physical activity
method used to reach the objective of this study was determined based on exercise
prescriptions , such as the intensity , frequency , and duration of exercise suggested by the
acsm ( 2009 ) after implementing an exercise load test .
the type of exercise focused on
walking at a quick pace , and the intensity of the exercise focused long periods of at low
intensity rather than short periods of exercise at high intensity with the level of hrmax
being 4060% .
the weight training , as a type of kinetic load exercise , was applied with a composition
( intensity of 4060% of 1rm and 1015 repetitions ) recommended by the acsm for muscle
fitness , and circulatory weight training , which was useful for beginners , was also used and
was designed to stimulate the glodbal muscles . in regard to exercise methods , exercise were
performed with 15 repetiions and 23 sets by each exercise with an intensity of 4060% of
1rm , and the subjects trained for 4050 minutes , with a break of 30 seconds between events
and 2 minutes between sets .
[ maximum muscle strength ( 1 rm ) = ( 1.06 lifted weight ( kg ) ) +
( 0.58 repeat count ) ( 0.20 age ) 3.41 ] spss version 16.0 was used to analyze the data .
the t - test and analysis of covariance
( ancova ) were used for statistical analyses .
chest muscular strength of the control group was 41.39.7 before the treatment and
39.99.52 after the treatment , and chest muscular strength of the treatment group was
40.411.15 before the treatment and 51.1410.1 after the treatment ( table 2 ) .
leg muscular strength of the control group was 83.47.3 before the treatment and 86.68.421
after the treatment , and leg muscular strength of the treatment group was 81.78.47 before
the treatment and 101.67.51 after the physical activity ( table 3 ) .
abdominal muscular strength of the control group was 51.577.27 before the treatment and
51.757.6 after the treatment , and abdominal muscular strength of the exercise group was
53.279.14 before the treatment and 68.166.16 after the treatment ( table 4 ) .
weight training receives a fervent response , and it is a highly appropriate training method
for promoting physical strength in men and women of all ages including children .
weight
training is an physical activity that raises contractible or extensible contraction by using
fixed or adjustable resistance and utilizes free weight equipment including barbells or
dumbbells , or contractible or adjustable resistance machines .
moreover , the effect on muscle
strength of weight training has been shown in precedent studies .
weight training reportedly
results in statistically meaningful increases in muscle strength and muscle endurance
meaningfully in statistics6 .
a
statistically significant increase in muscle strength and endurance was also reported in
another study7 . in the present study ,
weight training was found to enhance isometric muscle function , which
hints that there would be various factors relating to this finding .
the improvement of
muscle strength can come with the increase of muscle size as a priority . if no physical
activity is performed for a long time , muscle area and muscle strength decrease rapidly .
analysis of
the changes in muscles and muscle endurance revealed that training efficiency is influenced
by the difference in exercise intensity with regard to motor unit recruitment7,8,9 .
the motor unit of fast - twitch muscle fibers contains more muscle fibers than the motor
units of slow - twitch muscle fibers .
therefore , fast - twitch muscle fibers have an outstanding
ability to add more .
it was reported that selective recruitment was not determined by the
locomotion speed but by the power level required by muscles6 , 10,11,12,13 .
therefore , the program provided in this study exhibits a
difference in the selective recruitment aspect of muscle fiber , and this phenomenon had an
influence on the change in training effect .
this indicates that the change in muscle
strength and muscle endurance caused by resistance training is critically influenced by
exercise intensity . | [ purpose ] the aim of this study was to determine how compound physical activity affects
muscular strength of middle - aged obese women . [ subjects ] the research subjects were
4050 year - old middle - aged women with excess body fat ( 30% ) . [ methods ] the subjects were
randomly assigned to two group , the experimental group and the control group .
the
experimental group performed two types of exercise programs for 16 weeks .
aerobic physical
activity was performed 5 times per week , and anaerobic physical activity was performed
every two days , and the exercise program each day was composed of a warm - up , the main
exercise , and cooldown .
the type of exercise focused on walking at a quick pace , and the
intensity of the exercise focused on long periods of exercise at low intensity with the
level of hrmax being 4060% .
the weight training , which was useful for beginners , as a
type of kinetic load exercise , was applied with a composition recommended by the acsm for
muscle fitness ( intensity of 4060% of 1 rm and 1015 repetitions ) .
spss version 16.0 was
used to analyze the data by ancova and the t - test .
[ results ] the chest , leg , and abdominal
strengths were significantly increased in the experimental group , and this indicates that
compound physical activity is effective for improvement of muscular strength . [ conclusion ]
in conclusion , there were significant differences between groups in terms of muscular
strength . | <s>[INST]resistance weight training was reported to have a positive effect on the reduction of body
fat by increasing muscle tissues ; maintenance of muscular strength and increase of fat - free
mass ; and reduction of blood lipid and lipoprotein metabolism , emphasizing the necessity of
resistance weight training as an effective method for weight control , controling the
interset rest time during weight training can have a significant have a positive effect on
the change of blood lipid concentration and body construction1 . likewise , weight training increases bmr , improves insulin reaction ,
increases bone density or prevents its loss , and prevents the loss of muscle mass and
muscular strength resulting from aging , which emphasizes the importance of weight
training2 .
in addition , weight training
is reported to increase muscle strength and transversal area of muscle not only in men , but
also in women who are middle age / old aged . from this viewpoint , it is recommendable that an
exercise program for the safest and most efficient weight loss should be composed of
contents that comprehensively combine aerobic exercise with resistance weight training based
on the person s level .
even recently conducted precedent studies found that compound
training with aerobic exercise and resistance weight training aimed at middle - aged women
with obesity had a positive effect on body composition and blood lipids3 , 4 .
the study reported
the importance of dietary therapy as well as exercise therapy and stated that exercise
therapy without considering dietary therapy could not reduce body fat5 .
recently , there have been more than a few findings regarding the effect of compound
exercises on middle - aged women with obesity who had experienced health risks due to exposure to
various adult diseases and illnesses , but the number of studies is still insufficient ;
further , more specific and diverse experiments and research are necessary with regard to how
dietary exercises and resistance weight training can be mixed into an ideal compound
physical activity program that is suitable for a person s own characteristics .
the purpose
of this study was to investigate the effect of a compound physical activity program on
muscular strength in obese women .
they were selected based on a body fat
rate of over 30% obtained using a bioelectric impedance method .
the subjects had not
participated in physical activity or training for at least 6 months .
they were randomly
assigned to two groups , the experimental group , n=20 , and the control , n=20 ( table 1 ) .
aerobic physical activity was performed 5 times per week ,
and anaerobic physical activity was performed every two days ; the exercise program each day
was composed of warm - up , the main exercise , and cooldown .
the compound physical activity
method used to reach the objective of this study was determined based on exercise
prescriptions , such as the intensity , frequency , and duration of exercise suggested by the
acsm ( 2009 ) after implementing an exercise load test .
the type of exercise focused on
walking at a quick pace , and the intensity of the exercise focused long periods of at low
intensity rather than short periods of exercise at high intensity with the level of hrmax
being 4060% .
the weight training , as a type of kinetic load exercise , was applied with a composition
( intensity of 4060% of 1rm and 1015 repetitions ) recommended by the acsm for muscle
fitness , and circulatory weight training , which was useful for beginners , was also used and
was designed to stimulate the glodbal muscles . in regard to exercise methods , exercise were
performed with 15 repetiions and 23 sets by each exercise with an intensity of 4060% of
1rm , and the subjects trained for 4050 minutes , with a break of 30 seconds between events
and 2 minutes between sets .
[ maximum muscle strength ( 1 rm ) = ( 1.06 lifted weight ( kg ) ) +
( 0.58 repeat count ) ( 0.20 age ) 3.41 ] spss version 16.0 was used to analyze the data .
the t - test and analysis of covariance
( ancova ) were used for statistical analyses .
chest muscular strength of the control group was 41.39.7 before the treatment and
39.99.52 after the treatment , and chest muscular strength of the treatment group was
40.411.15 before the treatment and 51.1410.1 after the treatment ( table 2 ) .
leg muscular strength of the control group was 83.47.3 before the treatment and 86.68.421
after the treatment , and leg muscular strength of the treatment group was 81.78.47 before
the treatment and 101.67.51 after the physical activity ( table 3 ) .
abdominal muscular strength of the control group was 51.577.27 before the treatment and
51.757.6 after the treatment , and abdominal muscular strength of the exercise group was
53.279.14 before the treatment and 68.166.16 after the treatment ( table 4 ) .
weight training receives a fervent response , and it is a highly appropriate training method
for promoting physical strength in men and women of all ages including children .
weight
training is an physical activity that raises contractible or extensible contraction by using
fixed or adjustable resistance and utilizes free weight equipment including barbells or
dumbbells , or contractible or adjustable resistance machines .
moreover , the effect on muscle
strength of weight training has been shown in precedent studies .
weight training reportedly
results in statistically meaningful increases in muscle strength and muscle endurance
meaningfully in statistics6 .
a
statistically significant increase in muscle strength and endurance was also reported in
another study7 . in the present study ,
weight training was found to enhance isometric muscle function , which
hints that there would be various factors relating to this finding .
the improvement of
muscle strength can come with the increase of muscle size as a priority . if no physical
activity is performed for a long time , muscle area and muscle strength decrease rapidly .
analysis of
the changes in muscles and muscle endurance revealed that training efficiency is influenced
by the difference in exercise intensity with regard to motor unit recruitment7,8,9 .
the motor unit of fast - twitch muscle fibers contains more muscle fibers than the motor
units of slow - twitch muscle fibers .
therefore , fast - twitch muscle fibers have an outstanding
ability to add more .
it was reported that selective recruitment was not determined by the
locomotion speed but by the power level required by muscles6 , 10,11,12,13 .
therefore , the program provided in this study exhibits a
difference in the selective recruitment aspect of muscle fiber , and this phenomenon had an
influence on the change in training effect .
this indicates that the change in muscle
strength and muscle endurance caused by resistance training is critically influenced by
exercise intensity .[/INST][ purpose ] the aim of this study was to determine how compound physical activity affects
muscular strength of middle - aged obese women . [ subjects ] the research subjects were
4050 year - old middle - aged women with excess body fat ( 30% ) . [ methods ] the subjects were
randomly assigned to two group , the experimental group and the control group .
the
experimental group performed two types of exercise programs for 16 weeks .
aerobic physical
activity was performed 5 times per week , and anaerobic physical activity was performed
every two days , and the exercise program each day was composed of a warm - up , the main
exercise , and cooldown .
the type of exercise focused on walking at a quick pace , and the
intensity of the exercise focused on long periods of exercise at low intensity with the
level of hrmax being 4060% .
the weight training , which was useful for beginners , as a
type of kinetic load exercise , was applied with a composition recommended by the acsm for
muscle fitness ( intensity of 4060% of 1 rm and 1015 repetitions ) .
spss version 16.0 was
used to analyze the data by ancova and the t - test .
[ results ] the chest , leg , and abdominal
strengths were significantly increased in the experimental group , and this indicates that
compound physical activity is effective for improvement of muscular strength . [ conclusion ]
in conclusion , there were significant differences between groups in terms of muscular
strength .</s> |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Microfinance and Microenterprise
Enhancement Act of 2011''.
SEC. 2. FINDINGS.
Congress makes the following findings:
(1) A growing body of research shows that, where markets
are inclusive and income gaps are relatively small, growth
translates into poverty reduction much more quickly,
efficiently, and sustainably.
(2) Microenterprises, including smallholder and pastoral
farms, are important actors in most developing economies and
contribute significantly to employment generation, food
security, and family financial stability.
(3) Microfinance institutions and providers have played an
increasingly important role in enabling micro-entrepreneurs to
graduate from extreme poverty to sustainable living patterns
through financial services such as micro-credit, savings, and
micro-insurance, as well as skills development, business
mentoring, value-chain linkages, and facilitation of producer
groups.
(4) Congress has demonstrated its support for
microenterprise development assistance programs through the
enactment of three comprehensive microenterprise laws. Support
for microenterprise and microfinance remains a key tenet of
foreign assistance programs under the Foreign Assistance Act of
1961 (22 U.S.C. 2151 et seq.), including pursuant to the
following Acts:
(A) The Microenterprise for Self-Reliance Act of
2000 (title I of Public Law 106-309; 114 Stat. 1079).
(B) Public Law 108-31 (117 Stat. 775).
(C) The Microenterprise Results and Accountability
Act of 2004 (Public Law 108-484; 118 Stat. 3922).
(5) Microcredit alone is insufficient to sustainably reduce
poverty and facilitate inclusive economic growth. In addition
to access to credit, poor households need savings tools to
build assets, mitigate risks, increase social capital, enhance
skills, and integrate into competitive, growing value-chains,
as well as to access good-quality health and education
services.
(6) Over the last three decades, the United States Agency
for International Development has made microenterprise
development an important feature of its programming and has
continually sought to enhance the positive impact of
investments on poor households. In fiscal year 2010, the United
States Agency for International Development provided not less
than $262,000,000 in funding for microenterprise development in
at least 64 countries through at least 145 diverse implementing
partners, including private voluntary organizations,
nongovernmental organizations, banks and enterprise development
service providers, benefitting over 1,600,000
microentrepreneurs and 1,900,000 savers.
(7) New approaches are essential to keep pace with global
technology, not only to alleviate poverty, but also to
sustainably reduce poverty by linking poor households to
economic opportunities so that they can contribute to and
benefit from economic growth in their countries.
(8) Public funding for microfinance and microenterprise
should be available to benefit the poor in all countries, and,
in particular, among countries with a high concentration of the
very poor.
SEC. 3. SENSE OF CONGRESS ON TARGETED AND EFFECTIVE PROGRAMMING.
It is the sense of Congress that the United States Agency for
International Development should continue and expand programming in
microfinance that adheres to the following principles and basic
considerations:
(1) The United States Agency for International Development
should advance access to economic opportunities for very poor
and vulnerable populations, including orphans and vulnerable
children, single mothers, those affected by HIV/AIDS, those
affected by regional conflict, and the food insecure to ensure
that the poorest are included and benefit from broad-based
economic growth.
(2) To the greatest extent possible, the United States
Agency for International Development should set clear country
or regional funding targets based on greatest need, as
evidenced by poverty indicators and should strive to fill a gap
in unmet demand by the very poor for financial services.
(3) The United States Agency for International Development
should place special emphasis on aiding poor women, who
constitute a substantial portion of microentrepreneurs and who
face a wide range of disadvantages, as a means of promoting
financial self-reliance, empowering gender equality, including
land rights and access, and bringing a host of development
benefits to families through improved nutrition, health, and
education.
(4) The United States Agency for International Development
should ensure that providers of financial services benefitting
from United States Agency for International Development
assistance adhere to client protection principles, such as the
Client Protection Principles of the ``Smart Campaign'', and
take concrete steps to protect clients from potentially harmful
financial products and to support equitable and fair treatment,
including--
(A) avoidance of over-indebtedness;
(B) transparent and responsible pricing;
(C) appropriate collection practices;
(D) mechanisms for redress of grievances; and
(E) privacy of client data.
(5) The United States Agency for International Development
should encourage providers of financial services benefitting
from assistance programs to provide cost-effective services and
make steady progress toward full financial sustainability as a
means to achieve large-scale impact and institutional
viability, while also maintaining focus on their target
population of poor micro-entrepreneurs and smallholder farmers.
(6) The United States Agency for International Development
should strive to increase access to financial services to poor
and very poor, rural, and other underserved populations by
supporting a diverse range of financial intermediaries,
including nongovernmental organizations and private and state-
owned banks; postal and savings banks and savings and credit
cooperatives; voluntary savings associations; member-owned
community organizations; and other non-bank intermediaries,
such as mobile network operators, finance, and insurance
companies.
(7) The United States Agency for International Development
should promote and make use of existing technologies that show
promise for lowering costs, managing risks, and rapidly scaling
up access to financial products and services, including mobile
phones, smart phones, tablets, point-of-sale devices linked to
smart cards, automatic teller machines (ATMs), geographic
information system (GIS) mapping, and cloud computing, among
other information and communication technologies (ICT).
(8) The United States Agency for International Development
should make efforts to identify and support smaller, community-
led partner organizations, including local collectives and
consortia.
SEC. 4. SENSE OF CONGRESS ON EXPANDED INTEGRATED APPROACHES.
It is the sense of Congress that the next generation of programming
in microfinance and microenterprise development should advance
holistic, integrated strategies that focus on the myriad financial and
non-financial needs, including nutrition, health, and education, of
households, as well as the functioning of enterprises, markets, and
their inter-relationships in the economy.
SEC. 5. HOUSEHOLD-BASED APPROACHES.
(a) Responsive Financial Services.--The Administrator of the United
States Agency for International Development shall promote responsive
financial services to meet the diverse needs of poor households for
cash flow management and asset accumulation by supporting the
development of savings, remittances, and money transfer services.
(b) Consumption Smoothing, Risk Aggregation, and Mitigation.--The
Administrator of the United States Agency for International Development
shall promote tools that aggregate risks, mitigate shocks, and smooth
consumption, such as insurance and savings deposit services, so that
the poor can better manage, cope with, and recover from expected and
unexpected income fluctuations and crises like family emergencies and
crop failures.
(c) Partners.--The Administrator of the United States Agency for
International Development shall identify and support partners that
support informal savings-led and asset building approaches to
microfinance, including organizations that work to provide linkages
between savings-led groups to institutions in the formal financial
sector.
(d) Social Protection Programs.--Because some people are too poor
or otherwise unable to make use of microfinance or microenterprise
development services without special assistance to prepare them for
participation, the Administrator of the United States Agency for
International Development should identify and support organizations
that link social protection programs, including food assistance, cash
or asset transfers, life and livelihood skills development, and health
and nutrition education, with microfinance services, savings services,
and business development services. Such linkages should attempt to
enable poor people to stabilize food consumption, survive extreme
poverty, develop sustainable livelihoods, and take advantage of
economic opportunities.
SEC. 6. ENTERPRISE AND MARKET-BASED APPROACHES.
(a) Interventions.--The Administrator of the United States Agency
for International Development shall align household-level interventions
for the poor with interventions that catalyze more inclusive markets
and link the poor to expanding economic opportunities.
(b) Development of Financial Products.--The Administrator of the
United States Agency for International Development shall support the
development of a range of financial products adapted to the needs of
enterprises, including working capital for inputs, labor, and
production services; long-term asset finance; and agriculture, animal
husbandry, and rural enterprise loans. Such products should be provided
through a diversity of financing schemes, including financiers along
the value chain such as input suppliers, traders, and processors.
(c) Support for Agriculture Specific Tools.--The Administrator of
the United States Agency for International Development shall support
microfinance institutions and providers that are using agriculture-
specific tools, including--
(1) household profiling, crop analysis, and land mapping;
(2) diversification of loan portfolio to include a variety
of sectors and crops;
(3) linkages to extension and formal financial services;
and
(4) linking farmers to clients and larger supply chains.
(d) Linked Approaches.--To ensure that the poor are not left out of
economic growth strategies, the Administrator of the United States
Agency for International Development shall focus investments on linking
microenterprises into global, regional, and local value chains where
they have a comparative advantage. The Agency should consider issues
such as the business enabling environment, market competitiveness,
inter-firm cooperation, firm-level upgrading, and the relationships
between firms that create incentives or disincentives for investing in
improved performance or upgrading.
(e) Support for Small- and Medium-Sized Enterprises.--The
Administrator of the United States Agency for International Development
should consider support for small- and medium-sized enterprises as a
means to improve productivity and competitiveness in key subsectors in
which large numbers of poor micro-entrepreneurs participate, as well as
to strengthen the channels, such as employment, by which the benefits
of growth are transmitted to the poor.
SEC. 7. MEASURING AND REPORTING RESULTS.
(a) Modification of Poverty Assessment Tools.--The Administrator of
the United States Agency for International Development shall modify the
Poverty Assessment Tools (PATs) of the Agency so that partner
organizations can use them for expanded data management purposes.
(b) Alternatives to Poverty Assessment Tools.--Notwithstanding any
other provision of law, not later than one year after the date of the
enactment of this Act, the Administrator of the United States Agency
for International Development shall identify and approve alternatives
to the Poverty Assessment Tools, such as those commonly used within the
industry and development community.
SEC. 8. FINANCIAL ACCESS AND MICROENTERPRISE INNOVATION FUND.
(a) Establishment.--The Administrator of the United States Agency
for International Development is authorized to utilize one percent of
the Agency's development assistance account budget for fiscal years
2013 through 2017 for the creation of a financial access and
microenterprise innovation challenge fund.
(b) Use of Fund.--The fund established under this section shall be
used to--
(1) identify, test, and support cost-effective and
innovative products and technologies that improve the delivery
of financial services to the poor and very poor, particularly
in rural locations;
(2) identify, test, and support new microfinance and
microenterprise products, services, and delivery systems that
show potential to become cost-effective at large scale; and
(3) help transition such methods and technologies to
widespread adoption.
(c) Grants.--The financial access and microenterprise innovation
challenge fund shall make grants to organizations and companies,
including those interested in eventual commercialization. Where
appropriate, grants should reward or require recipients to
substantially invest their own funds. The mechanisms may include
challenge grants that require recipients to match grant funds with
their own funds in minimum ratios and bounties for achievement of
targets, such as the number of poor customers reached. | Microfinance and Microenterprise Enhancement Act of 2011 - Expresses the sense of Congress that the United States Agency for International Development (USAID) should expand specified microfinance programming.
Directs USAID to: (1) modify the Poverty Assessment Tools so that partner organizations can use them for expanded data management purposes, (2) align household-level interventions with interventions that link the poor to expanding economic opportunities, (3) support the development of financial products adapted to the needs of enterprises, (4) support microfinance institutions and providers that are using agriculture-specific tools, (5) promote financial services to meet the needs of poor households for cash flow management and asset accumulation, and (6) support partners that provide informal savings-led and asset building approaches to microfinance.
Urges USAID to: (1) consider support for small- and medium-sized enterprises as a means to improve productivity and competitiveness in key subsectors in which large numbers of poor micro-entrepreneurs participate; and (2) support organizations that link social protection programs with microfinance services, savings services, and business development services.
Authorizes USAID to utilize 1% of its development assistance account budget for FY2013 through FY2017 for the creation of a financial access and microenterprise innovation challenge fund that shall: (1) support cost-effective and innovative products and technologies that improve the delivery of financial services to the poor, particularly in rural locations; (2) support new microfinance and microenterprise products, services, and delivery systems that show potential to become cost-effective at large scale; and (3) help transition such methods and technologies to widespread adoption. | <s>[INST]SECTION 1. SHORT TITLE.
This Act may be cited as the ``Microfinance and Microenterprise
Enhancement Act of 2011''.
SEC. 2. FINDINGS.
Congress makes the following findings:
(1) A growing body of research shows that, where markets
are inclusive and income gaps are relatively small, growth
translates into poverty reduction much more quickly,
efficiently, and sustainably.
(2) Microenterprises, including smallholder and pastoral
farms, are important actors in most developing economies and
contribute significantly to employment generation, food
security, and family financial stability.
(3) Microfinance institutions and providers have played an
increasingly important role in enabling micro-entrepreneurs to
graduate from extreme poverty to sustainable living patterns
through financial services such as micro-credit, savings, and
micro-insurance, as well as skills development, business
mentoring, value-chain linkages, and facilitation of producer
groups.
(4) Congress has demonstrated its support for
microenterprise development assistance programs through the
enactment of three comprehensive microenterprise laws. Support
for microenterprise and microfinance remains a key tenet of
foreign assistance programs under the Foreign Assistance Act of
1961 (22 U.S.C. 2151 et seq.), including pursuant to the
following Acts:
(A) The Microenterprise for Self-Reliance Act of
2000 (title I of Public Law 106-309; 114 Stat. 1079).
(B) Public Law 108-31 (117 Stat. 775).
(C) The Microenterprise Results and Accountability
Act of 2004 (Public Law 108-484; 118 Stat. 3922).
(5) Microcredit alone is insufficient to sustainably reduce
poverty and facilitate inclusive economic growth. In addition
to access to credit, poor households need savings tools to
build assets, mitigate risks, increase social capital, enhance
skills, and integrate into competitive, growing value-chains,
as well as to access good-quality health and education
services.
(6) Over the last three decades, the United States Agency
for International Development has made microenterprise
development an important feature of its programming and has
continually sought to enhance the positive impact of
investments on poor households. In fiscal year 2010, the United
States Agency for International Development provided not less
than $262,000,000 in funding for microenterprise development in
at least 64 countries through at least 145 diverse implementing
partners, including private voluntary organizations,
nongovernmental organizations, banks and enterprise development
service providers, benefitting over 1,600,000
microentrepreneurs and 1,900,000 savers.
(7) New approaches are essential to keep pace with global
technology, not only to alleviate poverty, but also to
sustainably reduce poverty by linking poor households to
economic opportunities so that they can contribute to and
benefit from economic growth in their countries.
(8) Public funding for microfinance and microenterprise
should be available to benefit the poor in all countries, and,
in particular, among countries with a high concentration of the
very poor.
SEC. 3. SENSE OF CONGRESS ON TARGETED AND EFFECTIVE PROGRAMMING.
It is the sense of Congress that the United States Agency for
International Development should continue and expand programming in
microfinance that adheres to the following principles and basic
considerations:
(1) The United States Agency for International Development
should advance access to economic opportunities for very poor
and vulnerable populations, including orphans and vulnerable
children, single mothers, those affected by HIV/AIDS, those
affected by regional conflict, and the food insecure to ensure
that the poorest are included and benefit from broad-based
economic growth.
(2) To the greatest extent possible, the United States
Agency for International Development should set clear country
or regional funding targets based on greatest need, as
evidenced by poverty indicators and should strive to fill a gap
in unmet demand by the very poor for financial services.
(3) The United States Agency for International Development
should place special emphasis on aiding poor women, who
constitute a substantial portion of microentrepreneurs and who
face a wide range of disadvantages, as a means of promoting
financial self-reliance, empowering gender equality, including
land rights and access, and bringing a host of development
benefits to families through improved nutrition, health, and
education.
(4) The United States Agency for International Development
should ensure that providers of financial services benefitting
from United States Agency for International Development
assistance adhere to client protection principles, such as the
Client Protection Principles of the ``Smart Campaign'', and
take concrete steps to protect clients from potentially harmful
financial products and to support equitable and fair treatment,
including--
(A) avoidance of over-indebtedness;
(B) transparent and responsible pricing;
(C) appropriate collection practices;
(D) mechanisms for redress of grievances; and
(E) privacy of client data.
(5) The United States Agency for International Development
should encourage providers of financial services benefitting
from assistance programs to provide cost-effective services and
make steady progress toward full financial sustainability as a
means to achieve large-scale impact and institutional
viability, while also maintaining focus on their target
population of poor micro-entrepreneurs and smallholder farmers.
(6) The United States Agency for International Development
should strive to increase access to financial services to poor
and very poor, rural, and other underserved populations by
supporting a diverse range of financial intermediaries,
including nongovernmental organizations and private and state-
owned banks; postal and savings banks and savings and credit
cooperatives; voluntary savings associations; member-owned
community organizations; and other non-bank intermediaries,
such as mobile network operators, finance, and insurance
companies.
(7) The United States Agency for International Development
should promote and make use of existing technologies that show
promise for lowering costs, managing risks, and rapidly scaling
up access to financial products and services, including mobile
phones, smart phones, tablets, point-of-sale devices linked to
smart cards, automatic teller machines (ATMs), geographic
information system (GIS) mapping, and cloud computing, among
other information and communication technologies (ICT).
(8) The United States Agency for International Development
should make efforts to identify and support smaller, community-
led partner organizations, including local collectives and
consortia.
SEC. 4. SENSE OF CONGRESS ON EXPANDED INTEGRATED APPROACHES.
It is the sense of Congress that the next generation of programming
in microfinance and microenterprise development should advance
holistic, integrated strategies that focus on the myriad financial and
non-financial needs, including nutrition, health, and education, of
households, as well as the functioning of enterprises, markets, and
their inter-relationships in the economy.
SEC. 5. HOUSEHOLD-BASED APPROACHES.
(a) Responsive Financial Services.--The Administrator of the United
States Agency for International Development shall promote responsive
financial services to meet the diverse needs of poor households for
cash flow management and asset accumulation by supporting the
development of savings, remittances, and money transfer services.
(b) Consumption Smoothing, Risk Aggregation, and Mitigation.--The
Administrator of the United States Agency for International Development
shall promote tools that aggregate risks, mitigate shocks, and smooth
consumption, such as insurance and savings deposit services, so that
the poor can better manage, cope with, and recover from expected and
unexpected income fluctuations and crises like family emergencies and
crop failures.
(c) Partners.--The Administrator of the United States Agency for
International Development shall identify and support partners that
support informal savings-led and asset building approaches to
microfinance, including organizations that work to provide linkages
between savings-led groups to institutions in the formal financial
sector.
(d) Social Protection Programs.--Because some people are too poor
or otherwise unable to make use of microfinance or microenterprise
development services without special assistance to prepare them for
participation, the Administrator of the United States Agency for
International Development should identify and support organizations
that link social protection programs, including food assistance, cash
or asset transfers, life and livelihood skills development, and health
and nutrition education, with microfinance services, savings services,
and business development services. Such linkages should attempt to
enable poor people to stabilize food consumption, survive extreme
poverty, develop sustainable livelihoods, and take advantage of
economic opportunities.
SEC. 6. ENTERPRISE AND MARKET-BASED APPROACHES.
(a) Interventions.--The Administrator of the United States Agency
for International Development shall align household-level interventions
for the poor with interventions that catalyze more inclusive markets
and link the poor to expanding economic opportunities.
(b) Development of Financial Products.--The Administrator of the
United States Agency for International Development shall support the
development of a range of financial products adapted to the needs of
enterprises, including working capital for inputs, labor, and
production services; long-term asset finance; and agriculture, animal
husbandry, and rural enterprise loans. Such products should be provided
through a diversity of financing schemes, including financiers along
the value chain such as input suppliers, traders, and processors.
(c) Support for Agriculture Specific Tools.--The Administrator of
the United States Agency for International Development shall support
microfinance institutions and providers that are using agriculture-
specific tools, including--
(1) household profiling, crop analysis, and land mapping;
(2) diversification of loan portfolio to include a variety
of sectors and crops;
(3) linkages to extension and formal financial services;
and
(4) linking farmers to clients and larger supply chains.
(d) Linked Approaches.--To ensure that the poor are not left out of
economic growth strategies, the Administrator of the United States
Agency for International Development shall focus investments on linking
microenterprises into global, regional, and local value chains where
they have a comparative advantage. The Agency should consider issues
such as the business enabling environment, market competitiveness,
inter-firm cooperation, firm-level upgrading, and the relationships
between firms that create incentives or disincentives for investing in
improved performance or upgrading.
(e) Support for Small- and Medium-Sized Enterprises.--The
Administrator of the United States Agency for International Development
should consider support for small- and medium-sized enterprises as a
means to improve productivity and competitiveness in key subsectors in
which large numbers of poor micro-entrepreneurs participate, as well as
to strengthen the channels, such as employment, by which the benefits
of growth are transmitted to the poor.
SEC. 7. MEASURING AND REPORTING RESULTS.
(a) Modification of Poverty Assessment Tools.--The Administrator of
the United States Agency for International Development shall modify the
Poverty Assessment Tools (PATs) of the Agency so that partner
organizations can use them for expanded data management purposes.
(b) Alternatives to Poverty Assessment Tools.--Notwithstanding any
other provision of law, not later than one year after the date of the
enactment of this Act, the Administrator of the United States Agency
for International Development shall identify and approve alternatives
to the Poverty Assessment Tools, such as those commonly used within the
industry and development community.
SEC. 8. FINANCIAL ACCESS AND MICROENTERPRISE INNOVATION FUND.
(a) Establishment.--The Administrator of the United States Agency
for International Development is authorized to utilize one percent of
the Agency's development assistance account budget for fiscal years
2013 through 2017 for the creation of a financial access and
microenterprise innovation challenge fund.
(b) Use of Fund.--The fund established under this section shall be
used to--
(1) identify, test, and support cost-effective and
innovative products and technologies that improve the delivery
of financial services to the poor and very poor, particularly
in rural locations;
(2) identify, test, and support new microfinance and
microenterprise products, services, and delivery systems that
show potential to become cost-effective at large scale; and
(3) help transition such methods and technologies to
widespread adoption.
(c) Grants.--The financial access and microenterprise innovation
challenge fund shall make grants to organizations and companies,
including those interested in eventual commercialization. Where
appropriate, grants should reward or require recipients to
substantially invest their own funds. The mechanisms may include
challenge grants that require recipients to match grant funds with
their own funds in minimum ratios and bounties for achievement of
targets, such as the number of poor customers reached.[/INST]Microfinance and Microenterprise Enhancement Act of 2011 - Expresses the sense of Congress that the United States Agency for International Development (USAID) should expand specified microfinance programming.
Directs USAID to: (1) modify the Poverty Assessment Tools so that partner organizations can use them for expanded data management purposes, (2) align household-level interventions with interventions that link the poor to expanding economic opportunities, (3) support the development of financial products adapted to the needs of enterprises, (4) support microfinance institutions and providers that are using agriculture-specific tools, (5) promote financial services to meet the needs of poor households for cash flow management and asset accumulation, and (6) support partners that provide informal savings-led and asset building approaches to microfinance.
Urges USAID to: (1) consider support for small- and medium-sized enterprises as a means to improve productivity and competitiveness in key subsectors in which large numbers of poor micro-entrepreneurs participate; and (2) support organizations that link social protection programs with microfinance services, savings services, and business development services.
Authorizes USAID to utilize 1% of its development assistance account budget for FY2013 through FY2017 for the creation of a financial access and microenterprise innovation challenge fund that shall: (1) support cost-effective and innovative products and technologies that improve the delivery of financial services to the poor, particularly in rural locations; (2) support new microfinance and microenterprise products, services, and delivery systems that show potential to become cost-effective at large scale; and (3) help transition such methods and technologies to widespread adoption.</s> |
sunspots have been studied scientifically since the invention of the telescope , and reliable daily sunspot number records are available from the early 1800s .
the accepted quantity to characterise solar activity is the international sunspot number @xmath0 where @xmath1 is the number of individual sunspots , @xmath2 is the number of sunspot groups , and @xmath3 is a correction factor @xcite . the sunspot number changes in a secular or long - term fashion with the semi - regular 11-year sunspot cycle , driven by an internal magnetic dynamo which generates the magnetic field @xcite .
the secular change in sunspot number exhibits apparent randomness , as evidenced by the extensive literature describing the smoothed daily sunspot number ( typically a monthly average ) as a stochastic , or chaotic time series .
in particular , the peak and timing of the different solar cycles shows considerable variation @xcite .
sunspot numbers also vary on shorter time scales , in particular daily , as a result of the complicated local processes associated with sunspot formation , evolution , and decay .
the short - timescale variation produces large excursions in sunspot number , up to 100 per day in extreme cases @xcite . the large day to day variations
are caused by the rapid evolution of magnetic structures , and the sudden appearance / disappearance of large active regions .
these rapid developments can have important consequences for the space weather experienced on earth @xcite .
recently , it was demonstrated that the change @xmath4 in the daily sunspot number ( for days on which the number does change ) follows a laplace , or double exponential distribution @xcite . including the case of days with no changes , @xcite modelled the distribution @xmath5 of the change in sunspot number with the functional form @xmath6 where @xmath7 , and @xmath8 are constants , and where @xmath9 is the indicator function defined by @xmath10 for @xmath11 true , and @xmath12 for @xmath11 false .
the parameter @xmath8 determines the fraction of zero changes , and @xmath13 is the mean absolute change for days on which the number does change .
normalisation of equation ( [ eq : pop_law ] ) requires @xmath14 .
figure [ fig : f1 ] shows the observed distribution for the daily sunspot number using the ngdc data for 18502011 , and illustrates the exponential form identified by @xcite .
the top panel is a histogram of daily changes @xmath4 .
the bottom panel shows the cumulative number of changes greater than @xmath15 , for positive changes : @xmath16 and the cumulative number less than @xmath15 for negative changes : @xmath17 both panels use a logarithmic scaling on the vertical axis .
the red dots in the panels show the data , and the blue curves show the model distribution defined by equation ( [ eq : pop_law ] ) , with parameters @xmath13 and @xmath8 estimated from the data using maximum likelihood @xcite .
the adherence to the exponential form in figure [ fig : f1 ] is striking .
there are a large number of days with no change in sunspot number , and @xcite refers to @xmath18 as a `` special state '' .
the distribution is remarkably symmetric about @xmath18 .
@xcite also investigated the solar cycle dependence of the observed distribution , and found that the exponential rule in absolute changes is most closely adhered to over whole cycles , with the greatest departure near minima of cycles .
it is surprising that the laplace distribution in the change in daily sunspot number was not identified and discussed in the literature earlier .
the behaviour was previously noted in smoothed data @xcite , and an approximate exponential dependence in the distribution of overall sunspot numbers , related to equation ( [ eq : pop_law ] ) , was also commented on @xcite .
however , @xcite showed that the adherence of the observed changes in daily sunspot number to the laplace distribution defined by equation ( [ eq : pop_law ] ) is much stricter than the approximate exponential distribution of overall sunspot number .
the laplace distribution ( equation ( [ eq : pop_law ] ) ) represents a newly identified phenomenological rule describing the way in which the daily sunspot number varies , which should have application for modelling and prediction .
the origin of the distribution is not obvious .
changes in sunspot number occur daily due to sunspot group formation , evolution and decay , the appearance / disappearance of spots and spot splitting ( referred to here as spot evolution ) , and also due to sunspot groups and individual spots rotating onto and off the visible disc .
if the law is due to spot and group evolution , then the phenomenological rule must have a physical origin . in this paper
we demonstrate that the laplace distribution of changes in sunspot number is caused by sunspots forming , evolving , and decaying , and is not a result of rotation on and off the disc .
we then also present a simple monte carlo method , based on equation ( [ eq : pop_law ] ) and some additional assumptions , for simulating sunspot numbers over solar cycles .
to investigate the origin of the observed distribution in changes in sunspot number we use reports of sunspot groups on the sun , for 1981 - 2011 , compiled by us national oceanic and atmospheric administration ( usaf / noaa ) .
the daily change in sunspot number @xmath19 can be decomposed into changes due to rotation of regions and spots onto and off the disc @xmath20 , and changes due to group and sunspot evolution @xmath21 : @xmath22 similarly the terms @xmath23 and @xmath24 on the right hand side of equation ( [ eq : changeins ] ) can be decomposed in this way . to approximate the change due to rotation @xmath20
we assume that active regions first appearing on the disc within @xmath25 of the eastern limb arrive due to rotation within a day , and regions last observed on the disc within @xmath26 of the western limb disappear due to rotation within a day .
the factor of 14 days is the approximate time to rotate across the disc @xcite .
figure [ fig : f2 ] shows the result of the analysis of the data .
the figure presents the cumulative distribution of the total change in sunspot number @xmath4 using the complete data set ( black ) , the change due to rotation of spots and groups onto and off the disc @xmath27 ( blue ) , and the changes due to the evolution of spots and groups @xmath28 ( red ) .
the distributions of the total change @xmath4 and change due to evolution @xmath29 are very similar , and both clearly show the laplace distribution of equation ( [ eq : pop_law ] ) .
the distribution of @xmath20 exhibits significant falls in number at @xmath30 , which may be attributed to entire sunspot groups rotating onto and off the disc ( groups are weighted with a factor of 10 in the definition of the international sunspot number see equation ( [ eq : issn ] ) ) .
an important feature of figure [ fig : f2 ] is that the number of changes due to rotation onto and off the visible disc is at least an order of magnitude smaller than the number of changes due to evolution .
there are too few changes associated with active regions rotating onto and off the visible disc for this to influence the overall distribution of changes in sunspot number .
it is very unlikely that the observed double exponential distribution of changes , for days on which the sunspot number does change , is influenced by the small number of active regions which rotate onto or off the disc in a day .
it is possible that the observed laplace distribution arises from an averaging of locally non - exponential distributions across the disk . to test this
we also calculate the cumulative fraction of changes occurring in particular 26@xmath31 strips on the disc . in other words ,
we identify the active regions in the strips on a given day , and calculate the sunspot number due to these regions only . on the next day
we identify the regions in the strips , and again count the sunspot number due to these regions .
the difference between these two counts is the change in sunspot number in a day occurring in the particular strips .
this count includes both changes due to rotations into and out of the strips , and changes due to evolution in the strips .
figure [ fig : f2x ] shows the results .
changes occurring in the region @xmath32 and @xmath33 are in blue , changes occurring in the region @xmath34 and @xmath35 are in black , changes occurring in the region @xmath36 and @xmath37 are in green , and changes occurring at the limbs ( _ i.e. _ @xmath38 and @xmath39 ) are in red .
figure [ fig : f2x ] shows that changes associated with regions in a restricted range of longitudes reproduce the observed laplace distribution .
the exception is the distribution of changes at each limb , which shows large falls in probability due to changes in the number of groups in the strips , and a significantly smaller proportion of large changes in sunspot number .
presumably these differences arise due to the difficulty of accurately observing sunspot regions at the limb , and in particular , resolving the number of individual spots in a group .
this may explain why this particular distribution is dominated by changes in the number of groups .
figure [ fig : f2x ] shows that the observed laplace distribution in total changes does not arise from averaging over non - exponential local distributions in particular strips .
the conclusion is that the laplace distribution form is representative of changes in daily sunspot number due to the local evolution of sunspot groups on the sun .
it reflects the physical processes occurring .
@xcite investigated the daily change in sunspot number @xmath4 using data over complete cycles , which involve days with a range of different initial values @xmath40 of the sunspot number at each change .
the phenomenological rule represented by equation ( [ eq : pop_law ] ) was found to hold to a very good approximation for the range @xmath41 over the last 14 cycles , although departures from the rule for small changes in sunspot number were noted .
this departure may be attributed to the discrete nature of sunspot number , which means that the minimum sunspot number larger than zero is @xmath42 ( where @xmath3 is typically less than unity ) .
this causes a discrete jump in the tabulated daily values of the international sunspot number from zero to seven ( and implies that the average value of @xmath3 used by observers is @xmath43 ) .
departures for large changes in sunspot number were also noted . this may be attributed to the finite size of the sunspot number over any cycle .
large negative changes in sunspot number are unlikely because the sunspot number is unlikely to have a sufficiently large value at any given time over a cycle to allow that change .
the distribution of a change @xmath4 on a given day is dependent on the value of sunspot number on that day .
to model this we introduce transition probabilities @xmath44 for changes from an initial sunspot number @xmath40 to a final sunspot number @xmath45 on a day , given that the sunspot number is initially @xmath40 .
the function on the right hand side is a conditional distribution , and in section [ subsection : transition ] we consider a suitable functional form for this distribution . in section [
subsection : relationship ] we relate the chosen form of the conditional distribution @xmath46 and @xcite s exponential distribution @xmath5 of changes over complete cycles , and demonstrate how to estimate parameters from the data , for the proposed conditional distribution . to gain insight into a suitable function form for the conditional distribution in equation ( [ eq : trans1 ] ) we re - examine the data .
figure [ fig:2x ] is a two - dimensional ( 2d ) histogram @xmath47 of the number of days for which the sunspot number simultaneously has the value @xmath40 ( enumerated along the vertical axis ) , and increases by @xmath4 to the next day ( horizontal axis ) , for the ngdc data for 1815 - 2010 .
the bins are chosen to be of size two in @xmath4 and @xmath40 , and the figure shows the normalised histogram @xmath48 so that the greyscale density along each row shows the relative probability of a given change @xmath15 , for the given initial sunspot number @xmath49 . a nonlinear scaling
is applied to the greyscale density , to better show the bins with small numbers of days .
figure [ fig:2x ] illustrates the influence of the lower boundary @xmath50 required by the non negativity of sunspot number .
the distribution is relatively symmetric about @xmath51 for any given initial sunspot number @xmath40 , except for an excess of days at the @xmath52 boundary ( which correspond to changes leading to a zero sunspot number ) , and an excess of days with no change ( _ i.e. _ @xmath51 ) .
based on figure [ fig:2x ] , a suitable approximate model form for equation ( [ eq : trans1 ] ) is a simple exponential distribution symmetric about @xmath18 for each value of @xmath40 , with the same coefficient in the exponent for both negative and positive changes .
the ( asymmetric ) non negativity of sunspot number may be imposed by requiring that transitions producing a negative final sunspot number @xmath53 lead to zero sunspot number @xmath54 instead .
this may be written as : @xmath55\mathbb{i}(s'<s ) + d\exp\left[(s - s')/e\right ] \mathbb{i}(s'>s)\nonumber \\ & & + g\delta(s ' ) + h\delta(s'-s),\end{aligned}\ ] ] where @xmath56 , and @xmath57 are constants , and where the two terms involving delta functions describe the excess of days with changes leading to zero final sunspot number , and the excess of days on which the sunspot number does not change , respectively .
the data show that for the observed changes in daily sunspot number for 18502011 the fraction of negative and positive jumps are approximately equal ( 42@xmath58 and @xmath59 respectively ) , so we assume the same symmetry holds for each value of @xmath40 in equation ( [ eq : pop_law_cond ] ) : @xmath60 normalising over all final sunspot numbers @xmath45 , _
i.e. _ requiring @xmath61 leads to @xmath62 and @xmath63 the model conditional distribution ( equation ( [ eq : pop_law_cond ] ) ) then has two parameters , @xmath64 and @xmath57 .
the parameter @xmath64 determines the size of changes on days when there is a change ( a typical value , based on the data , is @xmath65 ) .
the parameter @xmath57 is the probability of no change in daily sunspot number .
the overall distribution of changes @xmath5 may be calculated from the transitional distribution ( equation ( [ eq : pop_law_cond ] ) ) by integrating over all starting values @xmath40 , _
i.e. _ calculating @xmath66 where @xmath67 is a constant imposing normalisation over changes in sunspot number : @xmath68 and @xmath69 is the probability of an initial sunspot number @xmath40 in the observations . a suitable choice to approximately describe the distribution of sunspot number @xmath69 over a complete solar cycle is an exponential @xcite , the adherence of the overall sunspot number to an exponential distribution is only very approximate ( by comparison with the observed distribution of changes in daily sunspot number , which follows the laplace distribution quite strictly ) .
] @xmath70 where the mean value of daily sunspot number ( based on observations for 18502011 ) is @xmath71 . calculating the integral in equation ( [ eq : formula ] ) gives @xmath72 \mathbb{i}(\delta s < 0 ) + \frac{1-h}{2e}{\rm e}^{-\delta s / e } \mathbb{i}(\delta s > 0 ) \nonumber \\ & + h \delta ( \delta s ) \end{aligned}\ ] ] and the normalisation by equation ( [ eq : deltanorm ] ) implies @xmath73 for the case of negative changes ( @xmath74 ) , equation ( [ eq : modelchanges ] ) contains a term @xmath75 which makes the distribution @xmath76 asymmetric about @xmath18 , and which is produced by changes leading to zero sunspot number .
the characteristic size of this term is @xmath77 , suggesting that the asymmetry in the distribution in @xmath4 produced by the lower boundary @xmath50 is not a strong effect . in the absence of the extra term
the normalisation constant is @xmath78 , and based on the data we find @xmath79 .
neglecting the extra term and setting @xmath78 , the distribution of changes implied by the conditional distribution ( equation ( [ eq : pop_law_cond ] ) ) is @xmath80 which is the same functional form as equation ( [ eq : pop_law ] ) , the @xcite distribution of changes .
the correspondence between the conditional distribution ( equation ( [ eq : pop_law_cond ] ) ) and the overall distribution of changes ( equation ( [ eq : approxmodelchanges ] ) ) allows the parameters @xmath64 and @xmath57 of the conditional distribution to be estimated from the daily changes @xmath4 over a cycle using maximum likelihood .
specifically , the exponential coefficient @xmath13 ( see equation ( [ eq : pop_law_cond ] ) ) estimated for the overall distribution may be taken as the estimate for coefficient @xmath64 in the conditional distribution , and the fraction of days @xmath8 with no change in sunspot number ( see equation ( [ eq : pop_law_cond ] ) ) in the overall distribution may be taken as the estimate of the corresponding parameter @xmath57 in the conditional distribution .
in this section we apply the conditional distribution ( equation ( [ eq : pop_law_cond ] ) ) in a monte carlo simulation of daily sunspot numbers @xmath81 , where @xmath82 refers to a day . the daily random variation in sunspot number
is described by the stochastic differential equation ( stochastic de ) @xmath83 where @xmath84 is the number of days and the daily change @xmath15 is generated by sampling from the distribution @xmath85 with @xmath46 given by equation ( [ eq : pop_law_cond ] ) . to solve the stochastic de ( equation ( [ eq : sde_trans ] ) ) we need to sample from the conditional distribution @xmath46 given by equation ( [ eq : pop_law_cond ] ) , with our maximum likelihood estimate of the parameters @xmath64 and @xmath57 .
this is achieved as follows . for a given initial sunspot number @xmath40 and the estimates of @xmath64 and @xmath57
we generate a final sunspot number @xmath86 by generating an exponential random variable @xmath4 with parameter @xmath64 _ i.e. _ a random deviate @xmath4 distributed according to @xmath87 . a random variable @xmath88 which is uniformly distribution on @xmath89
is also generated , and then the final change @xmath4 is calculated according to the rule : * if @xmath90 , then @xmath91 ; * if @xmath92 , then @xmath93 ; * otherwise @xmath51 .
this procedure assigns no change in sunspot number ( _ i.e. _ @xmath18 ) with probability @xmath57 , and the remaining changes are exponentially distributed over positive and negative @xmath4 with equal total probability .
the mean absolute size of changes ( on days when @xmath94 ) is @xmath64 . finally , to prevent the final sunspot number @xmath95 from being negative , if @xmath96 , then we take @xmath50 .
this procedure assigns values correctly according to equation ( [ eq : pop_law_cond ] ) .
equation ( [ eq : sde_trans ] ) is solved for a given initial sunspot number @xmath97 at time @xmath98 by generating a sequence of transitions @xmath15 ( with @xmath99 ) according to this recipe , and adding these successively to @xmath97 .
this model accounts for the stochastic variation in sunspot number according to the conditional distribution given by equation ( [ eq : pop_law_cond ] ) , but it does not account for the secular or long time - scale variation of the sunspot number over a solar cycle ( the `` shape '' of the cycle ) .
recently @xcite presented a method for modelling the solar cycle variation in a general fokker - planck description of stochastic variation in sunspot number , and the same procedure is applied here .
a term may be added to the stochastic de ( equation ( [ eq : sde_trans ] ) ) causing the fluctuating sunspot number to return to a prescribed time evolution @xmath100 : @xmath101 + \sum_{i=1}^{n}\delta s_i.\ ] ] the function @xmath102 is referred to as the driver function , and factor @xmath103 is the rate at which sunspot number @xmath40 returns to the value specified by the driver function .
the two terms on the right hand side of equation ( [ eq : sde_sec_trans ] ) are deterministic and stochastic terms , respectively . equation ( [ eq : sde_sec_trans ] ) is solved for a given initial sunspot number @xmath97 by adding daily stochastic transitions @xmath15 in the same way as for equation ( [ eq : sde_trans ] ) . in between the transitions
the sunspot number is evolved according to equation ( [ eq : sde_sec_trans ] ) with just the deterministic term included .
the solution to the differential equation with just the deterministic term is @xmath104 where @xmath81 is the value of the sunspot number on the most recent day , and @xmath105 . to summarise , the procedure for simulating the sunspot number evolution for day @xmath106 , given the sunspot number @xmath107 on day @xmath108 , is to evaluate a deterministic value for the sunspot number @xmath109 using equation ( [ eq : sde_sec_sol ] ) , to generate a random change @xmath110 using equation ( [ eq : pop_law_cond ] ) with initial sunspot number @xmath111 , and then the sunspot number on day @xmath106 is @xmath112 .
the driver function @xmath100 in the deterministic term in equation ( [ eq : sde_sec_trans ] ) represents the functional form of the solar cycle variation in sunspot number , _
i.e. _ the shape of a cycle .
the driver function describes basic empirical features of a solar cycle , such as the time taken to reach maximum , the size of the maximum , and so on .
additionally , @xmath102 may account for detailed features of the shape of a cycles such as the gnevyshev gap @xcite .
here we use a function introduced by @xcite ( @xcite , hereafter hwr94 ) : @xmath113 - c},\ ] ] where @xmath98 is the start time for a cycle , and @xmath114 , @xmath115 , and @xmath116 represent the cycle amplitude , period , and asymmetry , respectively . equation ( [ eq : hath ] ) was used by @xcite to investigate daily variation in sunspot number , and to forecast sunspot number and solar cycles . a statistical procedure for calculating estimates of the parameters @xmath114 , @xmath115 , @xmath116 , and @xmath103 from daily sunspot data , and the values of the estimates for cycles 1123 ,
was given in @xcite .
here we re use these parameter estimates describing the shapes of the cycle to simulate three recent solar cycles ( 21 , 22 , and 23 ) .
figure [ fig : f4 ] shows the daily sunspot numbers over cycle 23 , for the years 1996 to 2008 ( red points ) , and our simulation of sunspot numbers for this cycle based on equation ( [ eq : sde_sec_trans ] ) ( blue points ) .
the hwr94 driver function , equation ( [ eq : hath ] ) , enforces the secular variation in the solar cycle , with the parameter values @xmath117 , @xmath118 , @xmath119 , and @xmath120 ( taken from table i in @xcite ) .
we also use the estimates @xmath121 and @xmath122 for the conditional distribution ( equation ( [ eq : pop_law_cond ] ) ) , which are maximum likelihood values on the changes in daily sunspot data for cycle 23 , as discussed in section [ section : section2 ] . for the hwr94 driver function it is not possible to solve equation ( [ eq : sde_sec_sol ] ) analytically ,
and instead we integrate @xmath123\ ] ] numerically using a fourth order runge - kutta scheme @xcite .
figure [ fig : f5 ] shows the daily changes in sunspot number for cycle 23 ( red points ) , and the corresponding changes in our simulation ( blue points ) .
the upper panel of figure [ fig : f5 ] shows the distribution of changes and the lower panel shows the cumulative distribution in the same format as figure [ fig : f1 ] .
figure [ fig : f5 ] confirms that the simulation of daily sunspot number over cycle 23 based on the stochastic de ( equation ( [ eq : sde_sec_trans ] ) ) and the conditional distribution ( equation ( [ eq : pop_law_cond ] ) ) , together with the hwr94 model for the shape of the solar cycle , generates a distribution of changes @xmath5 over the cycle that closely resembles the exponential form identified by @xcite .
figure [ fig : f6 ] presents the results of the simulation procedure for cycle 22 ( years 1986 to 1996 ) in the same format as figure [ fig : f5 ] .
the parameter estimates for the hwr94 driver function are @xmath124 , @xmath125 , @xmath126 , and @xmath127 , again taken from table i in @xcite . the estimates @xmath128 and @xmath129 are used for the parameters in the conditional distribution equation ( [ eq : pop_law_cond ] ) , based on maximum likelihood applied to the daily data for cycle 22 .
figure [ fig : f7 ] presents the results of the simulation procedure for cycle 21 ( years 1976 to 1986 ) , again in the same format as figure [ fig : f5 ] .
the parameter estimates for the hwr94 driver function are @xmath130 , @xmath131 , @xmath132 , and @xmath127 , again taken from table i in @xcite .
the maximum likelihood estimates @xmath133 and @xmath134 are used for the parameters in the conditional distribution ( equation ( [ eq : pop_law_cond ] ) ) .
figures [ fig : f6 ] and [ fig : f7 ] confirm that the simulation procedure succeeds in reproducing the phenomenological exponential rule for daily changes in sunspot number when applied to cycles 22 and 21 , respectively .
this paper establishes that the observed laplace , or double exponential distribution of changes @xmath4 in daily sunspot number @xmath40 ( for days on which the sunspot number does change ) recently identified by @xcite , is due to the evolution of observed sunspot groups ( _ i.e. _ group formation , spot splitting , spot / group decay ) rather than being due to the artificial variation caused by groups rotating onto and off the visible disc .
the implication is that the distribution has a physical basis .
sunspot emergence , evolution , and eventual decay produces daily changes in sunspot number which may be positive or negative , and changes of this kind in separate active regions may add or cancel .
the sum of these daily changes , remarkably , produces a simple laplace distribution , with a marked excess of days with no change in sunspot number . in this paper
we show also how to simulate daily sunspot number via a monte carlo method , using a conditional distribution based on the exponential rule together with a model for the solar cycle variation in sunspot number .
the conditional distribution @xmath46 introduced describes the probability of a change from a current sunspot number @xmath40 to a value @xmath86 in one day , given the initial sunspot number , and ensures that @xmath135 .
the simulation procedure involves calculating a secular or deterministic change in sunspot number due to the underlying solar cycle , and then adding a random change in sunspot number according to the conditional distribution .
the monte carlo method is demonstrated in application to three recent solar cycles ( cycles 21 , 22 , and 23 ) .
the simulated sunspot numbers exhibit a distribution of changes @xmath5 over each cycle that closely reproduces the laplace distribution identified by @xcite .
it is interesting to consider possible explanations for the observed laplace distribution .
the origin of the surface changes in sunspot number described by the rule are changes in the structure of the subphotospheric magnetic fields , which are not directly amenable to observation @xcite , although local helioseismology is beginning to provide some insights @xcite . in the absence of detailed physical models for the surface changes provided by this field evolution
, it may be possible to construct statistical models for daily changes in sunspot number based on simple statistical descriptions of spot and group evolution , for given numbers of spots and groups .
for example , probabilities could be assigned to given spots or groups increasing or decreasing their number in a day .
such a description may be modelled by a type of birth
death process , which have been used in the natural and social sciences ( _ e.g. _ see for example ) .
it may also be possible to use other known statistical rules for the distribution and evolution of spot groups , for example the log normal distribution of spot areas ( @xcite @xcite ) , and various rules for the decay rate of sunspot area ( in area per unit time ) per sunspot within a group ( see ) . given the complexity of the combinations implied by this consideration of possible modelling , we note again how remarkable it is that a simple double exponential form arises .
we leave the development of a detailed model to a future investigation . degree strips .
the daily changes in sunspot number in the strip from @xmath136 to @xmath137 are shown in blue , the changes in the strip from @xmath138 to @xmath139 and from @xmath140 to @xmath141 are shown in black , the change in the strip from @xmath142 to @xmath143 and from @xmath144 to @xmath145 are in green , and changes in the strip from @xmath146 to @xmath147 and from @xmath148 to @xmath149 are shown in red . , width=384,height=240 ] ) , and for our simulation of the sunspot numbers .
the red points show the data and the blue points the simulation .
the upper panel shows the numbers of days with the given change in sunspot number and the lower panel shows the corresponding cumulative distribution .
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j. _ * 351 * , 309 . | recently pop ( _ solar phys . _ * 276 * , 351 , 2012 ) identified a laplace ( or double exponential ) distribution in the number of days with a given absolute value in the change over a day , in sunspot number , for days on which the sunspot number does change .
we show this phenomenological rule has a physical origin attributable to sunspot formation , evolution , and decay , rather than being due to the changes in sunspot number caused by groups rotating onto and off the visible disc .
we also demonstrate a simple method to simulate daily sunspot numbers over a solar cycle using the @xcite result , together with a model for the cycle variation in the mean sunspot number .
the procedure is applied to three recent solar cycles .
we check that the simulated sunspot numbers reproduce the observed distribution of daily changes over those cycles . | <s>[INST]sunspots have been studied scientifically since the invention of the telescope , and reliable daily sunspot number records are available from the early 1800s .
the accepted quantity to characterise solar activity is the international sunspot number @xmath0 where @xmath1 is the number of individual sunspots , @xmath2 is the number of sunspot groups , and @xmath3 is a correction factor @xcite . the sunspot number changes in a secular or long - term fashion with the semi - regular 11-year sunspot cycle , driven by an internal magnetic dynamo which generates the magnetic field @xcite .
the secular change in sunspot number exhibits apparent randomness , as evidenced by the extensive literature describing the smoothed daily sunspot number ( typically a monthly average ) as a stochastic , or chaotic time series .
in particular , the peak and timing of the different solar cycles shows considerable variation @xcite .
sunspot numbers also vary on shorter time scales , in particular daily , as a result of the complicated local processes associated with sunspot formation , evolution , and decay .
the short - timescale variation produces large excursions in sunspot number , up to 100 per day in extreme cases @xcite . the large day to day variations
are caused by the rapid evolution of magnetic structures , and the sudden appearance / disappearance of large active regions .
these rapid developments can have important consequences for the space weather experienced on earth @xcite .
recently , it was demonstrated that the change @xmath4 in the daily sunspot number ( for days on which the number does change ) follows a laplace , or double exponential distribution @xcite . including the case of days with no changes , @xcite modelled the distribution @xmath5 of the change in sunspot number with the functional form @xmath6 where @xmath7 , and @xmath8 are constants , and where @xmath9 is the indicator function defined by @xmath10 for @xmath11 true , and @xmath12 for @xmath11 false .
the parameter @xmath8 determines the fraction of zero changes , and @xmath13 is the mean absolute change for days on which the number does change .
normalisation of equation ( [ eq : pop_law ] ) requires @xmath14 .
figure [ fig : f1 ] shows the observed distribution for the daily sunspot number using the ngdc data for 18502011 , and illustrates the exponential form identified by @xcite .
the top panel is a histogram of daily changes @xmath4 .
the bottom panel shows the cumulative number of changes greater than @xmath15 , for positive changes : @xmath16 and the cumulative number less than @xmath15 for negative changes : @xmath17 both panels use a logarithmic scaling on the vertical axis .
the red dots in the panels show the data , and the blue curves show the model distribution defined by equation ( [ eq : pop_law ] ) , with parameters @xmath13 and @xmath8 estimated from the data using maximum likelihood @xcite .
the adherence to the exponential form in figure [ fig : f1 ] is striking .
there are a large number of days with no change in sunspot number , and @xcite refers to @xmath18 as a `` special state '' .
the distribution is remarkably symmetric about @xmath18 .
@xcite also investigated the solar cycle dependence of the observed distribution , and found that the exponential rule in absolute changes is most closely adhered to over whole cycles , with the greatest departure near minima of cycles .
it is surprising that the laplace distribution in the change in daily sunspot number was not identified and discussed in the literature earlier .
the behaviour was previously noted in smoothed data @xcite , and an approximate exponential dependence in the distribution of overall sunspot numbers , related to equation ( [ eq : pop_law ] ) , was also commented on @xcite .
however , @xcite showed that the adherence of the observed changes in daily sunspot number to the laplace distribution defined by equation ( [ eq : pop_law ] ) is much stricter than the approximate exponential distribution of overall sunspot number .
the laplace distribution ( equation ( [ eq : pop_law ] ) ) represents a newly identified phenomenological rule describing the way in which the daily sunspot number varies , which should have application for modelling and prediction .
the origin of the distribution is not obvious .
changes in sunspot number occur daily due to sunspot group formation , evolution and decay , the appearance / disappearance of spots and spot splitting ( referred to here as spot evolution ) , and also due to sunspot groups and individual spots rotating onto and off the visible disc .
if the law is due to spot and group evolution , then the phenomenological rule must have a physical origin . in this paper
we demonstrate that the laplace distribution of changes in sunspot number is caused by sunspots forming , evolving , and decaying , and is not a result of rotation on and off the disc .
we then also present a simple monte carlo method , based on equation ( [ eq : pop_law ] ) and some additional assumptions , for simulating sunspot numbers over solar cycles .
to investigate the origin of the observed distribution in changes in sunspot number we use reports of sunspot groups on the sun , for 1981 - 2011 , compiled by us national oceanic and atmospheric administration ( usaf / noaa ) .
the daily change in sunspot number @xmath19 can be decomposed into changes due to rotation of regions and spots onto and off the disc @xmath20 , and changes due to group and sunspot evolution @xmath21 : @xmath22 similarly the terms @xmath23 and @xmath24 on the right hand side of equation ( [ eq : changeins ] ) can be decomposed in this way . to approximate the change due to rotation @xmath20
we assume that active regions first appearing on the disc within @xmath25 of the eastern limb arrive due to rotation within a day , and regions last observed on the disc within @xmath26 of the western limb disappear due to rotation within a day .
the factor of 14 days is the approximate time to rotate across the disc @xcite .
figure [ fig : f2 ] shows the result of the analysis of the data .
the figure presents the cumulative distribution of the total change in sunspot number @xmath4 using the complete data set ( black ) , the change due to rotation of spots and groups onto and off the disc @xmath27 ( blue ) , and the changes due to the evolution of spots and groups @xmath28 ( red ) .
the distributions of the total change @xmath4 and change due to evolution @xmath29 are very similar , and both clearly show the laplace distribution of equation ( [ eq : pop_law ] ) .
the distribution of @xmath20 exhibits significant falls in number at @xmath30 , which may be attributed to entire sunspot groups rotating onto and off the disc ( groups are weighted with a factor of 10 in the definition of the international sunspot number see equation ( [ eq : issn ] ) ) .
an important feature of figure [ fig : f2 ] is that the number of changes due to rotation onto and off the visible disc is at least an order of magnitude smaller than the number of changes due to evolution .
there are too few changes associated with active regions rotating onto and off the visible disc for this to influence the overall distribution of changes in sunspot number .
it is very unlikely that the observed double exponential distribution of changes , for days on which the sunspot number does change , is influenced by the small number of active regions which rotate onto or off the disc in a day .
it is possible that the observed laplace distribution arises from an averaging of locally non - exponential distributions across the disk . to test this
we also calculate the cumulative fraction of changes occurring in particular 26@xmath31 strips on the disc . in other words ,
we identify the active regions in the strips on a given day , and calculate the sunspot number due to these regions only . on the next day
we identify the regions in the strips , and again count the sunspot number due to these regions .
the difference between these two counts is the change in sunspot number in a day occurring in the particular strips .
this count includes both changes due to rotations into and out of the strips , and changes due to evolution in the strips .
figure [ fig : f2x ] shows the results .
changes occurring in the region @xmath32 and @xmath33 are in blue , changes occurring in the region @xmath34 and @xmath35 are in black , changes occurring in the region @xmath36 and @xmath37 are in green , and changes occurring at the limbs ( _ i.e. _ @xmath38 and @xmath39 ) are in red .
figure [ fig : f2x ] shows that changes associated with regions in a restricted range of longitudes reproduce the observed laplace distribution .
the exception is the distribution of changes at each limb , which shows large falls in probability due to changes in the number of groups in the strips , and a significantly smaller proportion of large changes in sunspot number .
presumably these differences arise due to the difficulty of accurately observing sunspot regions at the limb , and in particular , resolving the number of individual spots in a group .
this may explain why this particular distribution is dominated by changes in the number of groups .
figure [ fig : f2x ] shows that the observed laplace distribution in total changes does not arise from averaging over non - exponential local distributions in particular strips .
the conclusion is that the laplace distribution form is representative of changes in daily sunspot number due to the local evolution of sunspot groups on the sun .
it reflects the physical processes occurring .
@xcite investigated the daily change in sunspot number @xmath4 using data over complete cycles , which involve days with a range of different initial values @xmath40 of the sunspot number at each change .
the phenomenological rule represented by equation ( [ eq : pop_law ] ) was found to hold to a very good approximation for the range @xmath41 over the last 14 cycles , although departures from the rule for small changes in sunspot number were noted .
this departure may be attributed to the discrete nature of sunspot number , which means that the minimum sunspot number larger than zero is @xmath42 ( where @xmath3 is typically less than unity ) .
this causes a discrete jump in the tabulated daily values of the international sunspot number from zero to seven ( and implies that the average value of @xmath3 used by observers is @xmath43 ) .
departures for large changes in sunspot number were also noted . this may be attributed to the finite size of the sunspot number over any cycle .
large negative changes in sunspot number are unlikely because the sunspot number is unlikely to have a sufficiently large value at any given time over a cycle to allow that change .
the distribution of a change @xmath4 on a given day is dependent on the value of sunspot number on that day .
to model this we introduce transition probabilities @xmath44 for changes from an initial sunspot number @xmath40 to a final sunspot number @xmath45 on a day , given that the sunspot number is initially @xmath40 .
the function on the right hand side is a conditional distribution , and in section [ subsection : transition ] we consider a suitable functional form for this distribution . in section [
subsection : relationship ] we relate the chosen form of the conditional distribution @xmath46 and @xcite s exponential distribution @xmath5 of changes over complete cycles , and demonstrate how to estimate parameters from the data , for the proposed conditional distribution . to gain insight into a suitable function form for the conditional distribution in equation ( [ eq : trans1 ] ) we re - examine the data .
figure [ fig:2x ] is a two - dimensional ( 2d ) histogram @xmath47 of the number of days for which the sunspot number simultaneously has the value @xmath40 ( enumerated along the vertical axis ) , and increases by @xmath4 to the next day ( horizontal axis ) , for the ngdc data for 1815 - 2010 .
the bins are chosen to be of size two in @xmath4 and @xmath40 , and the figure shows the normalised histogram @xmath48 so that the greyscale density along each row shows the relative probability of a given change @xmath15 , for the given initial sunspot number @xmath49 . a nonlinear scaling
is applied to the greyscale density , to better show the bins with small numbers of days .
figure [ fig:2x ] illustrates the influence of the lower boundary @xmath50 required by the non negativity of sunspot number .
the distribution is relatively symmetric about @xmath51 for any given initial sunspot number @xmath40 , except for an excess of days at the @xmath52 boundary ( which correspond to changes leading to a zero sunspot number ) , and an excess of days with no change ( _ i.e. _ @xmath51 ) .
based on figure [ fig:2x ] , a suitable approximate model form for equation ( [ eq : trans1 ] ) is a simple exponential distribution symmetric about @xmath18 for each value of @xmath40 , with the same coefficient in the exponent for both negative and positive changes .
the ( asymmetric ) non negativity of sunspot number may be imposed by requiring that transitions producing a negative final sunspot number @xmath53 lead to zero sunspot number @xmath54 instead .
this may be written as : @xmath55\mathbb{i}(s'<s ) + d\exp\left[(s - s')/e\right ] \mathbb{i}(s'>s)\nonumber \\ & & + g\delta(s ' ) + h\delta(s'-s),\end{aligned}\ ] ] where @xmath56 , and @xmath57 are constants , and where the two terms involving delta functions describe the excess of days with changes leading to zero final sunspot number , and the excess of days on which the sunspot number does not change , respectively .
the data show that for the observed changes in daily sunspot number for 18502011 the fraction of negative and positive jumps are approximately equal ( 42@xmath58 and @xmath59 respectively ) , so we assume the same symmetry holds for each value of @xmath40 in equation ( [ eq : pop_law_cond ] ) : @xmath60 normalising over all final sunspot numbers @xmath45 , _
i.e. _ requiring @xmath61 leads to @xmath62 and @xmath63 the model conditional distribution ( equation ( [ eq : pop_law_cond ] ) ) then has two parameters , @xmath64 and @xmath57 .
the parameter @xmath64 determines the size of changes on days when there is a change ( a typical value , based on the data , is @xmath65 ) .
the parameter @xmath57 is the probability of no change in daily sunspot number .
the overall distribution of changes @xmath5 may be calculated from the transitional distribution ( equation ( [ eq : pop_law_cond ] ) ) by integrating over all starting values @xmath40 , _
i.e. _ calculating @xmath66 where @xmath67 is a constant imposing normalisation over changes in sunspot number : @xmath68 and @xmath69 is the probability of an initial sunspot number @xmath40 in the observations . a suitable choice to approximately describe the distribution of sunspot number @xmath69 over a complete solar cycle is an exponential @xcite , the adherence of the overall sunspot number to an exponential distribution is only very approximate ( by comparison with the observed distribution of changes in daily sunspot number , which follows the laplace distribution quite strictly ) .
] @xmath70 where the mean value of daily sunspot number ( based on observations for 18502011 ) is @xmath71 . calculating the integral in equation ( [ eq : formula ] ) gives @xmath72 \mathbb{i}(\delta s < 0 ) + \frac{1-h}{2e}{\rm e}^{-\delta s / e } \mathbb{i}(\delta s > 0 ) \nonumber \\ & + h \delta ( \delta s ) \end{aligned}\ ] ] and the normalisation by equation ( [ eq : deltanorm ] ) implies @xmath73 for the case of negative changes ( @xmath74 ) , equation ( [ eq : modelchanges ] ) contains a term @xmath75 which makes the distribution @xmath76 asymmetric about @xmath18 , and which is produced by changes leading to zero sunspot number .
the characteristic size of this term is @xmath77 , suggesting that the asymmetry in the distribution in @xmath4 produced by the lower boundary @xmath50 is not a strong effect . in the absence of the extra term
the normalisation constant is @xmath78 , and based on the data we find @xmath79 .
neglecting the extra term and setting @xmath78 , the distribution of changes implied by the conditional distribution ( equation ( [ eq : pop_law_cond ] ) ) is @xmath80 which is the same functional form as equation ( [ eq : pop_law ] ) , the @xcite distribution of changes .
the correspondence between the conditional distribution ( equation ( [ eq : pop_law_cond ] ) ) and the overall distribution of changes ( equation ( [ eq : approxmodelchanges ] ) ) allows the parameters @xmath64 and @xmath57 of the conditional distribution to be estimated from the daily changes @xmath4 over a cycle using maximum likelihood .
specifically , the exponential coefficient @xmath13 ( see equation ( [ eq : pop_law_cond ] ) ) estimated for the overall distribution may be taken as the estimate for coefficient @xmath64 in the conditional distribution , and the fraction of days @xmath8 with no change in sunspot number ( see equation ( [ eq : pop_law_cond ] ) ) in the overall distribution may be taken as the estimate of the corresponding parameter @xmath57 in the conditional distribution .
in this section we apply the conditional distribution ( equation ( [ eq : pop_law_cond ] ) ) in a monte carlo simulation of daily sunspot numbers @xmath81 , where @xmath82 refers to a day . the daily random variation in sunspot number
is described by the stochastic differential equation ( stochastic de ) @xmath83 where @xmath84 is the number of days and the daily change @xmath15 is generated by sampling from the distribution @xmath85 with @xmath46 given by equation ( [ eq : pop_law_cond ] ) . to solve the stochastic de ( equation ( [ eq : sde_trans ] ) ) we need to sample from the conditional distribution @xmath46 given by equation ( [ eq : pop_law_cond ] ) , with our maximum likelihood estimate of the parameters @xmath64 and @xmath57 .
this is achieved as follows . for a given initial sunspot number @xmath40 and the estimates of @xmath64 and @xmath57
we generate a final sunspot number @xmath86 by generating an exponential random variable @xmath4 with parameter @xmath64 _ i.e. _ a random deviate @xmath4 distributed according to @xmath87 . a random variable @xmath88 which is uniformly distribution on @xmath89
is also generated , and then the final change @xmath4 is calculated according to the rule : * if @xmath90 , then @xmath91 ; * if @xmath92 , then @xmath93 ; * otherwise @xmath51 .
this procedure assigns no change in sunspot number ( _ i.e. _ @xmath18 ) with probability @xmath57 , and the remaining changes are exponentially distributed over positive and negative @xmath4 with equal total probability .
the mean absolute size of changes ( on days when @xmath94 ) is @xmath64 . finally , to prevent the final sunspot number @xmath95 from being negative , if @xmath96 , then we take @xmath50 .
this procedure assigns values correctly according to equation ( [ eq : pop_law_cond ] ) .
equation ( [ eq : sde_trans ] ) is solved for a given initial sunspot number @xmath97 at time @xmath98 by generating a sequence of transitions @xmath15 ( with @xmath99 ) according to this recipe , and adding these successively to @xmath97 .
this model accounts for the stochastic variation in sunspot number according to the conditional distribution given by equation ( [ eq : pop_law_cond ] ) , but it does not account for the secular or long time - scale variation of the sunspot number over a solar cycle ( the `` shape '' of the cycle ) .
recently @xcite presented a method for modelling the solar cycle variation in a general fokker - planck description of stochastic variation in sunspot number , and the same procedure is applied here .
a term may be added to the stochastic de ( equation ( [ eq : sde_trans ] ) ) causing the fluctuating sunspot number to return to a prescribed time evolution @xmath100 : @xmath101 + \sum_{i=1}^{n}\delta s_i.\ ] ] the function @xmath102 is referred to as the driver function , and factor @xmath103 is the rate at which sunspot number @xmath40 returns to the value specified by the driver function .
the two terms on the right hand side of equation ( [ eq : sde_sec_trans ] ) are deterministic and stochastic terms , respectively . equation ( [ eq : sde_sec_trans ] ) is solved for a given initial sunspot number @xmath97 by adding daily stochastic transitions @xmath15 in the same way as for equation ( [ eq : sde_trans ] ) . in between the transitions
the sunspot number is evolved according to equation ( [ eq : sde_sec_trans ] ) with just the deterministic term included .
the solution to the differential equation with just the deterministic term is @xmath104 where @xmath81 is the value of the sunspot number on the most recent day , and @xmath105 . to summarise , the procedure for simulating the sunspot number evolution for day @xmath106 , given the sunspot number @xmath107 on day @xmath108 , is to evaluate a deterministic value for the sunspot number @xmath109 using equation ( [ eq : sde_sec_sol ] ) , to generate a random change @xmath110 using equation ( [ eq : pop_law_cond ] ) with initial sunspot number @xmath111 , and then the sunspot number on day @xmath106 is @xmath112 .
the driver function @xmath100 in the deterministic term in equation ( [ eq : sde_sec_trans ] ) represents the functional form of the solar cycle variation in sunspot number , _
i.e. _ the shape of a cycle .
the driver function describes basic empirical features of a solar cycle , such as the time taken to reach maximum , the size of the maximum , and so on .
additionally , @xmath102 may account for detailed features of the shape of a cycles such as the gnevyshev gap @xcite .
here we use a function introduced by @xcite ( @xcite , hereafter hwr94 ) : @xmath113 - c},\ ] ] where @xmath98 is the start time for a cycle , and @xmath114 , @xmath115 , and @xmath116 represent the cycle amplitude , period , and asymmetry , respectively . equation ( [ eq : hath ] ) was used by @xcite to investigate daily variation in sunspot number , and to forecast sunspot number and solar cycles . a statistical procedure for calculating estimates of the parameters @xmath114 , @xmath115 , @xmath116 , and @xmath103 from daily sunspot data , and the values of the estimates for cycles 1123 ,
was given in @xcite .
here we re use these parameter estimates describing the shapes of the cycle to simulate three recent solar cycles ( 21 , 22 , and 23 ) .
figure [ fig : f4 ] shows the daily sunspot numbers over cycle 23 , for the years 1996 to 2008 ( red points ) , and our simulation of sunspot numbers for this cycle based on equation ( [ eq : sde_sec_trans ] ) ( blue points ) .
the hwr94 driver function , equation ( [ eq : hath ] ) , enforces the secular variation in the solar cycle , with the parameter values @xmath117 , @xmath118 , @xmath119 , and @xmath120 ( taken from table i in @xcite ) .
we also use the estimates @xmath121 and @xmath122 for the conditional distribution ( equation ( [ eq : pop_law_cond ] ) ) , which are maximum likelihood values on the changes in daily sunspot data for cycle 23 , as discussed in section [ section : section2 ] . for the hwr94 driver function it is not possible to solve equation ( [ eq : sde_sec_sol ] ) analytically ,
and instead we integrate @xmath123\ ] ] numerically using a fourth order runge - kutta scheme @xcite .
figure [ fig : f5 ] shows the daily changes in sunspot number for cycle 23 ( red points ) , and the corresponding changes in our simulation ( blue points ) .
the upper panel of figure [ fig : f5 ] shows the distribution of changes and the lower panel shows the cumulative distribution in the same format as figure [ fig : f1 ] .
figure [ fig : f5 ] confirms that the simulation of daily sunspot number over cycle 23 based on the stochastic de ( equation ( [ eq : sde_sec_trans ] ) ) and the conditional distribution ( equation ( [ eq : pop_law_cond ] ) ) , together with the hwr94 model for the shape of the solar cycle , generates a distribution of changes @xmath5 over the cycle that closely resembles the exponential form identified by @xcite .
figure [ fig : f6 ] presents the results of the simulation procedure for cycle 22 ( years 1986 to 1996 ) in the same format as figure [ fig : f5 ] .
the parameter estimates for the hwr94 driver function are @xmath124 , @xmath125 , @xmath126 , and @xmath127 , again taken from table i in @xcite . the estimates @xmath128 and @xmath129 are used for the parameters in the conditional distribution equation ( [ eq : pop_law_cond ] ) , based on maximum likelihood applied to the daily data for cycle 22 .
figure [ fig : f7 ] presents the results of the simulation procedure for cycle 21 ( years 1976 to 1986 ) , again in the same format as figure [ fig : f5 ] .
the parameter estimates for the hwr94 driver function are @xmath130 , @xmath131 , @xmath132 , and @xmath127 , again taken from table i in @xcite .
the maximum likelihood estimates @xmath133 and @xmath134 are used for the parameters in the conditional distribution ( equation ( [ eq : pop_law_cond ] ) ) .
figures [ fig : f6 ] and [ fig : f7 ] confirm that the simulation procedure succeeds in reproducing the phenomenological exponential rule for daily changes in sunspot number when applied to cycles 22 and 21 , respectively .
this paper establishes that the observed laplace , or double exponential distribution of changes @xmath4 in daily sunspot number @xmath40 ( for days on which the sunspot number does change ) recently identified by @xcite , is due to the evolution of observed sunspot groups ( _ i.e. _ group formation , spot splitting , spot / group decay ) rather than being due to the artificial variation caused by groups rotating onto and off the visible disc .
the implication is that the distribution has a physical basis .
sunspot emergence , evolution , and eventual decay produces daily changes in sunspot number which may be positive or negative , and changes of this kind in separate active regions may add or cancel .
the sum of these daily changes , remarkably , produces a simple laplace distribution , with a marked excess of days with no change in sunspot number . in this paper
we show also how to simulate daily sunspot number via a monte carlo method , using a conditional distribution based on the exponential rule together with a model for the solar cycle variation in sunspot number .
the conditional distribution @xmath46 introduced describes the probability of a change from a current sunspot number @xmath40 to a value @xmath86 in one day , given the initial sunspot number , and ensures that @xmath135 .
the simulation procedure involves calculating a secular or deterministic change in sunspot number due to the underlying solar cycle , and then adding a random change in sunspot number according to the conditional distribution .
the monte carlo method is demonstrated in application to three recent solar cycles ( cycles 21 , 22 , and 23 ) .
the simulated sunspot numbers exhibit a distribution of changes @xmath5 over each cycle that closely reproduces the laplace distribution identified by @xcite .
it is interesting to consider possible explanations for the observed laplace distribution .
the origin of the surface changes in sunspot number described by the rule are changes in the structure of the subphotospheric magnetic fields , which are not directly amenable to observation @xcite , although local helioseismology is beginning to provide some insights @xcite . in the absence of detailed physical models for the surface changes provided by this field evolution
, it may be possible to construct statistical models for daily changes in sunspot number based on simple statistical descriptions of spot and group evolution , for given numbers of spots and groups .
for example , probabilities could be assigned to given spots or groups increasing or decreasing their number in a day .
such a description may be modelled by a type of birth
death process , which have been used in the natural and social sciences ( _ e.g. _ see for example ) .
it may also be possible to use other known statistical rules for the distribution and evolution of spot groups , for example the log normal distribution of spot areas ( @xcite @xcite ) , and various rules for the decay rate of sunspot area ( in area per unit time ) per sunspot within a group ( see ) . given the complexity of the combinations implied by this consideration of possible modelling , we note again how remarkable it is that a simple double exponential form arises .
we leave the development of a detailed model to a future investigation . degree strips .
the daily changes in sunspot number in the strip from @xmath136 to @xmath137 are shown in blue , the changes in the strip from @xmath138 to @xmath139 and from @xmath140 to @xmath141 are shown in black , the change in the strip from @xmath142 to @xmath143 and from @xmath144 to @xmath145 are in green , and changes in the strip from @xmath146 to @xmath147 and from @xmath148 to @xmath149 are shown in red . , width=384,height=240 ] ) , and for our simulation of the sunspot numbers .
the red points show the data and the blue points the simulation .
the upper panel shows the numbers of days with the given change in sunspot number and the lower panel shows the corresponding cumulative distribution .
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j. _ * 351 * , 309 .[/INST] recently pop ( _ solar phys . _ * 276 * , 351 , 2012 ) identified a laplace ( or double exponential ) distribution in the number of days with a given absolute value in the change over a day , in sunspot number , for days on which the sunspot number does change .
we show this phenomenological rule has a physical origin attributable to sunspot formation , evolution , and decay , rather than being due to the changes in sunspot number caused by groups rotating onto and off the visible disc .
we also demonstrate a simple method to simulate daily sunspot numbers over a solar cycle using the @xcite result , together with a model for the cycle variation in the mean sunspot number .
the procedure is applied to three recent solar cycles .
we check that the simulated sunspot numbers reproduce the observed distribution of daily changes over those cycles . </s> |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Learning Differences Act of 1998''.
SEC. 2. FINDINGS AND PURPOSES.
(a) Findings.--The Congress finds the following:
(1) Disability is a natural part of the human experience
and encompasses physical, mental, and cognitive impairments.
The term ``learning disability'' refers to a number of specific
learning disabilities, such as dyslexia. These disorders may
manifest themselves in an imperfect ability to listen, think,
speak, read, write, spell, reason, or perform mathematical
calculations. Learning disabilities tend to endure from
childhood into adulthood.
(2) 2,600,000 of the 5,100,000 children with disabilities
served under the Individuals with Disabilities Education Act in
elementary and secondary education are children with learning
disabilities.
(3) About 2 percent of all undergraduate students
nationwide report having a learning disability. Different
teaching strategies are needed to enable them to develop their
talents and perform up to their capacity.
(4) A greater number of individuals with learning
disabilities can benefit from postsecondary education, and
contribute more fully to society and the economy, with adequate
and appropriate programs, services, adaptations, and
accommodations.
(5) Civil rights laws protect individuals with
disabilities, including individuals with learning disabilities,
in postsecondary education, and institutions of higher
education require assistance to comply with these laws.
(6) Exemplary institutions of higher education dedicated to
meeting the needs of individuals with learning disabilities
exist and can serve as a national resource for other
institutions in educating these students.
(b) Purposes.--The purposes of this Act are as follows:
(1) To assist model institutions of higher education with
demonstrated prior experience in serving individuals with
learning disabilities.
(2) To demonstrate and disseminate programs, services,
adaptations, accommodations, strategies, and approaches to
teaching individuals with disabilities in postsecondary
education.
SEC. 3. PROGRAM AUTHORITY.
(a) In General.--The Secretary of Education may award grants to,
and enter into contracts and cooperative agreements with, not more than
5 institutions of higher education that are described in section 4 for
demonstration projects to develop, test, and disseminate, in accordance
with section 5, methods, techniques, and procedures for ensuring equal
educational opportunity for individuals with learning disabilities in
postsecondary education.
(b) Award Basis.--Grants, contracts, and cooperative agreements
shall be awarded on a competitive basis.
(c) Award Period.--Grants, contracts, and cooperative agreements
shall be awarded for a period of 3 years.
SEC. 4. ELIGIBLE ENTITIES.
Entities eligible to apply for a grant, contract, or cooperative
agreement under this Act are institutions of higher education (as
defined in section 1201 of the Higher Education Act of 1956) with
demonstrated prior experience with meeting the postsecondary
educational needs of individuals with learning disabilities.
SEC. 5. REQUIRED ACTIVITIES.
A recipient of a grant, contract, or cooperative agreement under
this Act shall use the funds received under this Act to carry out each
of the following activities:
(1) Developing or identifying innovative, effective, and
efficient approaches, strategies, supports, modifications,
adaptations, and accommodations that enable individuals with
learning disabilities to fully participate in postsecondary
education.
(2) Synthesizing research and other information related to
the provision of services to individuals with learning
disabilities in postsecondary education.
(3) Conducting training sessions for personnel from other
institutions of higher education to enable them to meet the
special needs of postsecondary students with learning
disabilities.
(4) Preparing and disseminating products based upon the
activities described in paragraphs (1) through (3).
(5) Coordinating findings and products from the activities
described in paragraphs (1) through (4) with other similar
products and findings through participation in conferences,
groups, and professional networks involved in the dissemination
of technical assistance and information on postsecondary
education.
SEC. 6. PRIORITY.
The Secretary of Education shall ensure that, to the extent
feasible, there is a national geographic distribution of grants,
contracts, and cooperative agreements awarded under this Act throughout
the States, except that the Secretary may give priority to a
historically Black college or university that satisfies the
requirements of section 4.
SEC. 7. AUTHORIZATION OF APPROPRIATIONS.
There are authorized to be appropriated to carry out this Act
$10,000,000 for each of the fiscal years 1999 through 2001. | Learning Differences Act of 1998 - Authorizes the Secretary of Education to award grants to, and enter into contracts and cooperative agreements with, as many as five institutions of higher education, on a competitive basis, for demonstration projects to develop, test, and disseminate methods, techniques, and procedures for ensuring equal educational opportunity in postsecondary education for individuals with learning disabilities.
Requires national geographic distribution of such awards, to the extent feasible, but authorizes giving priority to a historically Black college or university that meets specified eligibility requirements.
Authorizes appropriations. | <s>[INST]SECTION 1. SHORT TITLE.
This Act may be cited as the ``Learning Differences Act of 1998''.
SEC. 2. FINDINGS AND PURPOSES.
(a) Findings.--The Congress finds the following:
(1) Disability is a natural part of the human experience
and encompasses physical, mental, and cognitive impairments.
The term ``learning disability'' refers to a number of specific
learning disabilities, such as dyslexia. These disorders may
manifest themselves in an imperfect ability to listen, think,
speak, read, write, spell, reason, or perform mathematical
calculations. Learning disabilities tend to endure from
childhood into adulthood.
(2) 2,600,000 of the 5,100,000 children with disabilities
served under the Individuals with Disabilities Education Act in
elementary and secondary education are children with learning
disabilities.
(3) About 2 percent of all undergraduate students
nationwide report having a learning disability. Different
teaching strategies are needed to enable them to develop their
talents and perform up to their capacity.
(4) A greater number of individuals with learning
disabilities can benefit from postsecondary education, and
contribute more fully to society and the economy, with adequate
and appropriate programs, services, adaptations, and
accommodations.
(5) Civil rights laws protect individuals with
disabilities, including individuals with learning disabilities,
in postsecondary education, and institutions of higher
education require assistance to comply with these laws.
(6) Exemplary institutions of higher education dedicated to
meeting the needs of individuals with learning disabilities
exist and can serve as a national resource for other
institutions in educating these students.
(b) Purposes.--The purposes of this Act are as follows:
(1) To assist model institutions of higher education with
demonstrated prior experience in serving individuals with
learning disabilities.
(2) To demonstrate and disseminate programs, services,
adaptations, accommodations, strategies, and approaches to
teaching individuals with disabilities in postsecondary
education.
SEC. 3. PROGRAM AUTHORITY.
(a) In General.--The Secretary of Education may award grants to,
and enter into contracts and cooperative agreements with, not more than
5 institutions of higher education that are described in section 4 for
demonstration projects to develop, test, and disseminate, in accordance
with section 5, methods, techniques, and procedures for ensuring equal
educational opportunity for individuals with learning disabilities in
postsecondary education.
(b) Award Basis.--Grants, contracts, and cooperative agreements
shall be awarded on a competitive basis.
(c) Award Period.--Grants, contracts, and cooperative agreements
shall be awarded for a period of 3 years.
SEC. 4. ELIGIBLE ENTITIES.
Entities eligible to apply for a grant, contract, or cooperative
agreement under this Act are institutions of higher education (as
defined in section 1201 of the Higher Education Act of 1956) with
demonstrated prior experience with meeting the postsecondary
educational needs of individuals with learning disabilities.
SEC. 5. REQUIRED ACTIVITIES.
A recipient of a grant, contract, or cooperative agreement under
this Act shall use the funds received under this Act to carry out each
of the following activities:
(1) Developing or identifying innovative, effective, and
efficient approaches, strategies, supports, modifications,
adaptations, and accommodations that enable individuals with
learning disabilities to fully participate in postsecondary
education.
(2) Synthesizing research and other information related to
the provision of services to individuals with learning
disabilities in postsecondary education.
(3) Conducting training sessions for personnel from other
institutions of higher education to enable them to meet the
special needs of postsecondary students with learning
disabilities.
(4) Preparing and disseminating products based upon the
activities described in paragraphs (1) through (3).
(5) Coordinating findings and products from the activities
described in paragraphs (1) through (4) with other similar
products and findings through participation in conferences,
groups, and professional networks involved in the dissemination
of technical assistance and information on postsecondary
education.
SEC. 6. PRIORITY.
The Secretary of Education shall ensure that, to the extent
feasible, there is a national geographic distribution of grants,
contracts, and cooperative agreements awarded under this Act throughout
the States, except that the Secretary may give priority to a
historically Black college or university that satisfies the
requirements of section 4.
SEC. 7. AUTHORIZATION OF APPROPRIATIONS.
There are authorized to be appropriated to carry out this Act
$10,000,000 for each of the fiscal years 1999 through 2001.[/INST]Learning Differences Act of 1998 - Authorizes the Secretary of Education to award grants to, and enter into contracts and cooperative agreements with, as many as five institutions of higher education, on a competitive basis, for demonstration projects to develop, test, and disseminate methods, techniques, and procedures for ensuring equal educational opportunity in postsecondary education for individuals with learning disabilities.
Requires national geographic distribution of such awards, to the extent feasible, but authorizes giving priority to a historically Black college or university that meets specified eligibility requirements.
Authorizes appropriations.</s> |
neutrino oscillations between two flavors in vacuum are governed by the frequency @xmath0 where @xmath1 is the energy of a given mode .
therefore , if the energy spectrum is broad , the energy dependence of the oscillation frequency quickly leads to kinematical decoherence , i.e. , along a neutrino beam the overall flavor content quickly approaches an average value .
the situation changes radically when neutrinos themselves provide a significant refractive effect , leading to collective oscillation modes @xcite that can be of practical interest in the early universe @xcite or in core - collapse supernovae @xcite . defining the parameter @xmath2 the neutrino gas is `` dense '' when @xmath3 , i.e. , when a typical neutrino - neutrino interaction energy exceeds the energy corresponding to the vacuum oscillation frequency .
when this condition is satisfied , collective effects are important , even if the ordinary matter effect is much larger than that from the neutrino - neutrino interaction @xcite .
one characteristic feature of collective oscillations is the phenomenon of `` self - maintained coherence '' @xcite , meaning that all modes oscillate with the same frequency even though the energy spectrum may be broad .
it was recently stressed , however , that this is not the complete story @xcite .
perhaps the most interesting case for collective effects is provided by neutrinos streaming off a supernova core , a situation that is far from isotropic .
the current - current nature of the weak - interaction hamiltonian implies that the interaction energy between particles of momenta @xmath4 and @xmath5 is proportional to @xmath6 where @xmath7 is the velocity .
if the medium is isotropic , the @xmath8 term averages to zero , but if there is a net current , test particles moving in different directions experience different refractive effects . therefore , neutrinos moving in a background with a net current will decohere between different directions of motion , even if the energy spectrum is monochromatic .
to avoid confusion about terminology we stress that we always mean `` kinematical decoherence '' when we say `` decoherence . ''
different modes oscillate differently , leading to `` de - phasing '' and thus to the depolarization of the overall ensemble .
if we use the common language of polarization vectors @xmath9 for each mode @xmath4 , then the length of each @xmath9 is conserved , whereas the length of the overall polarization vector @xmath10 shrinks ( kinematical decoherence ) or is conserved ( kinematical coherence ) .
the effect of _ dynamical _ decoherence , caused by collisions among the neutrinos or with a thermal background medium , is that each individual polarization vector @xmath9 shrinks , i.e. , neutrinos in individual modes can not be represented as pure states .
this effect , relevant for open quantum systems , does not occur in our case where oscillations are the only form of evolution .
the multi - angle decoherence effect becomes nontrivial in the most interesting case when the `` background current '' consists of the neutrinos themselves as for neutrinos streaming off a supernova core .
numerical examples reveal significant decoherence effects , but on the other hand they also show collective modes very similar to the isotropic ( `` single - angle '' ) case @xcite .
the overall behavior is determined by a complicated interplay between the collective evolution and decoherence . rather than trying to understand the supernova case in its full complexity , we here take the opposite approach and study the simplest example that shows decoherence caused by the neutrino - neutrino multi - angle effect .
therefore , we consider a dense neutrino gas that is monochromatic , symmetric ( equal @xmath11 and @xmath12 densities ) , and homogeneous , but not isotropic .
even this simple model has a rich phenomenology that helps one to develop a better understanding of the full problem . on the other hand ,
it is simple enough that the most puzzling aspects of its behavior are analytically tractable . a symmetric @xmath13 gas oscillates in the `` bipolar mode '' where pairs of neutrinos of a given flavor coherently oscillate into the other flavor and back with the `` bipolar frequency '' @xcite @xmath14 as an example we consider a dense neutrino gas initially consisting of @xmath15 and assume that the mixing angle @xmath16 with another flavor is small , a situation that could represent 13-oscillations .
we characterize the overall flavor content of the ensemble in the usual way by a polarization vector where the positive @xmath17-direction corresponds to the @xmath18-flavor whereas the mass direction is defined by a unit vector that we call @xmath19 .
it is tilted against the @xmath17-direction by @xmath20 and we always choose it to lie in the @xmath21-@xmath17-plane with @xmath22 for the normal hierarchy and @xmath23 for the inverted hierarchy . in vacuum ,
the polarization vectors precess around @xmath19 with frequency @xmath24 . in a dense neutrino gas with @xmath25 , their motion
is largely confined to the @xmath21-@xmath17-plane where they perform pendular motions with frequency @xmath26 and where @xmath27 is the `` force direction . ''
the maximum excursion is @xmath20 , indicated by the dotted lines in fig .
[ fig : trajectory ] where we show the trajectory in the @xmath21-@xmath17-plane .
for the normal hierarchy , the pendulum swings between the dotted lines . for the inverted hierarchy ( bottom ) , it performs almost full - circle oscillations as indicated by the diamonds .
if the gas is not isotropic , the picture changes completely . taking the `` half - isotropic '' case as a generic example where only one half - space of momentum modes is occupied ( neutrinos streaming off a plane surface ) , we show in fig .
[ fig : trajectory ] the trajectory of the average polarization vector .
for both hierarchies , its length shrinks to zero so that the final state of the ensemble is an equal mixture of both flavors .
in other words , the ensemble quickly decoheres , independently of the mass hierarchy .
this behavior is perhaps intuitive because we have assumed a large neutrino current .
however , this effect is self - accelerating in that it is triggered even by the smallest nonzero anisotropy . whereas for perfect isotropy
the neutrino - neutrino interaction provides for self - maintained coherence between modes of different energy , even an infinitesimal anisotropy has the opposite effect of causing self - induced decoherence between modes with different propagation directions .
the average flavor content of the ensemble always approaches an equal mixture of both flavors .
this instability is a nonlinear effect caused by the neutrino - neutrino interaction .
in other words , the pendular motion of the isotropic ensemble is an unstable limit cycle , whereas the equal flavor mixture is a stable fixed point .
our goal is to explain this behavior . as a first step we formulate in sect .
[ sec : eom ] the equations of motion for the multi - angle system in terms of the multipole components of the neutrino angular distribution
. the special role of the flux ( the dipole term of the angular distribution ) becomes manifest .
we begin with the full @xmath28-flavor problem and then consider two flavors in terms of polarization vectors . in sect .
[ sec : anisotropy ] we study the role of a large anisotropy in causing decoherence .
our main result is developed in sect .
[ sec : smallanisotropy ] where we show that a @xmath13 gas is unstable in flavor space and always decoheres if there is an infinitesimally small initial anisotropy .
we conclude in sec .
[ sec : conclusions ] with a summary and outlook .
a statistical ensemble of unmixed neutrinos is represented by the occupation numbers @xmath29 for each momentum mode @xmath4 , where @xmath30 and @xmath31 are the relevant creation and annihilation operators and @xmath32 is the expectation value .
the corresponding expression for antineutrinos is @xmath33 , where here and henceforth overbarred quantities refer to antiparticles . for several flavors ,
the occupation numbers are generalized to `` matrices of densities '' in flavor space @xmath34 that really are matrices of occupation numbers .
the reversed order of the flavor indices @xmath35 and @xmath36 in the r.h.s . for antineutrinos ensures that under a flavor transformation , @xmath37 , antineutrinos transform in the same way , @xmath38 .
sums and differences of @xmath39 and @xmath40 then transform consistently .
for the seemingly intuitive equal order of flavor indices that is almost universally used in the literature , @xmath39 , @xmath40 , @xmath41 and @xmath42 all appear in the equations instead of @xmath39 and @xmath40 alone .
analogous matrices @xmath43 can be defined for the charged leptons .
we assume that the neutrino ensemble is completely described by these one - particle occupation number matrices , i.e. , that genuine many - body effects play no role @xcite . in this
case flavor oscillations of an ensemble of neutrinos and antineutrinos are described by an equation of motion for each mode @xmath44 + \sqrt{2}\,g_{\rm f}\left [ \int\!\frac{d^3{\bf q}}{(2\pi)^3 } \left(\ell_{\bf q}-\bar\ell_{\bf q } + \varrho_{\bf q}-\bar\varrho_{\bf q}\right ) ( 1-{\bf v}_{\bf q}\cdot{\bf v}_{\bf p } ) , \varrho_{\bf p}\right ] , \nonumber\\ { \rm i}\,\partial_t\bar\varrho_{\bf p}&= & -\left[\omega_{\bf p},\bar\varrho_{\bf p}\right ] + \sqrt{2}\,g_{\rm f}\left [ \int\!\frac{d^3{\bf q}}{(2\pi)^3 } \left(\ell_{\bf q}-\bar\ell_{\bf q } + \varrho_{\bf q}-\bar\varrho_{\bf q}\right ) ( 1-{\bf v}_{\bf q}\cdot{\bf v}_{\bf p } ) , \bar\varrho_{\bf p}\right],\end{aligned}\ ] ] where @xmath45 $ ] is a commutator and @xmath46 is the fermi constant . for ultrarelativistic neutrinos ,
the matrix of vacuum oscillation frequencies , expressed in the mass basis , is @xmath47 with @xmath48 .
further , @xmath49 is the velocity of a particle ( neutrino or charged lepton ) with momentum @xmath4
. the total conserved energy of the neutrino ensemble is an important quantity for understanding its evolution @xcite .
we find for the energy density @xmath50 ^ 2 -\frac{\sqrt2\,g_{\rm f}}{2}\left [ \int\!\frac{d^3{\bf p}}{(2\pi)^3}\ , ( \varrho_{\bf p}-\bar\varrho_{\bf p}){\bf v}_{\bf p}\right]^2 \biggr\rbrace\,.\end{aligned}\ ] ] this quantity actually represents the energy _ shift _ caused by the neutrino masses and by neutrino interactions .
it is straightfoward to show that indeed @xmath51 by taking the time derivative on the r.h.s . of eq .
( [ eq : energydensity ] ) , inserting the equations of motion eq .
( [ eq : eom1 ] ) , and using cyclic permutations of matrices under the trace .
for completeness we mention that one can also define the entropy density @xcite @xmath52\,.\end{aligned}\ ] ] this expression is well defined because @xmath39 and @xmath53 are positive semi - definite matrices . in our case where the equation of motion for each @xmath39 is of the form @xmath54 $ ] , the entropy density is conserved .
oscillations alone do not lead to a loss of information .
kinematical decoherence does not lead to an increase of entropy .
since we wish to study the simplest example that shows nontrivial multi - angle effects , we now restrict the neutrino energy distribution to be monochromatic and the geometry to axial symmetry .
we then integrate the matrices of densities over all variables except @xmath55 where the angle is relative to the direction of symmetry .
therefore , we consider the matrices @xmath56 implying the normalization @xmath57 for convenience we have arbitrarily normalized the @xmath58 matrices to the neutrino density .
we further define the matrix representing the particle flux along the direction of symmetry , @xmath59 where @xmath60 is the velocity along the symmetry direction . for relativistic particles @xmath61 . for charged leptons
we proceed in the same way , except that we normalize to the electron density @xmath62 .
we denote with @xmath63 the matrix of vacuum oscillation frequencies for our fixed neutrino energy @xmath1 .
the equations of motion then simplify to @xmath64 + \left[\lambda\left(\ell-\bar\ell)_0 + \mu(\varrho-\bar\varrho\right)_0,\varrho_u\right ] \nonumber\\ & & \kern2.8em{}-\left[\lambda\left(\ell-\bar\ell)_1 + \mu(\varrho-\bar\varrho\right)_1,u\varrho_u\right]\,,\end{aligned}\ ] ] where @xmath65 .
the same equation applies for @xmath66 except for a sign change of the vacuum oscillation term .
evidently the isotropic part of the medium ( index 0 ) affects all modes in the same way and is ultimately responsible for the phenomenon of self - maintained coherence . on the other hand ,
the flux term ( index 1 ) involves a factor @xmath67 for every mode @xmath68 . even in the absence of a neutrino - neutrino term
, a charged - lepton flux alone causes a trivial multi - angle decoherence effect .
the conserved energy of the axially symmetric neutrino ensemble is @xmath69 \nonumber\\ & & { } + \lambda\,{\rm tr}\left [ ( \ell-\bar\ell)_0(\varrho-\bar\varrho)_0 -(\ell-\bar\ell)_1(\varrho-\bar\varrho)_1\right ] \nonumber\\ & & { } + \frac{\mu}{2}\,{\rm tr}\left [ ( \varrho-\bar\varrho)_0 ^ 2 -(\varrho-\bar\varrho)_1 ^ 2\right]\,.\end{aligned}\ ] ] because of our normalization of the @xmath58 matrices the quantity @xmath70 is the energy per @xmath11 . the structure of these equations becomes more transparent if we expand the angular dependence of the matrices in legendre polynomials .
( had we not assumed axial symmetry , spherical harmonics would be the appropriate basis . )
the first few legendre polynomials are @xmath71 we thus define @xmath72 the normalisation @xmath73 implies that the original function is @xmath74 the previously defined overall density @xmath75 and the flux @xmath76 are but the zeroth and first case of eq .
( [ eq : expansion1 ] ) . multiplying both sides of eq .
( [ eq : eom2 ] ) with @xmath77 and integrating over @xmath78 leads to the equation of motion @xmath79 + \mu\left[(\varrho-\bar\varrho)_0,\varrho_n\right ] \nonumber\\ & & { } -\mu\left[(\varrho-\bar\varrho)_1 , { \textstyle\int_{-1}^{+1}}du\,u\varrho_u l_n(u)\right]\,.\end{aligned}\ ] ] here and henceforth we no longer show the ordinary matter term . its structure is similar to the neutrino - neutrino term so that it is easily reinstated . with the expansion eq .
( [ eq : expansion2 ] ) the remaining integral is @xmath80 we use the `` dipole matrix element '' of the legendre polynomials @xmath81 with this result the equations of motion are @xmath82 + \mu\left[(\varrho-\bar\varrho)_0,\varrho_n\right ] \nonumber\\ & & { } -\frac{\mu}{2 } \left[(\varrho-\bar\varrho)_1 , ( a_n\varrho_{n-1}+b_n\varrho_{n+1})\right]\,,\end{aligned}\ ] ] where @xmath83 note that the equation for @xmath75 is consistent even though the quantity @xmath84 is not defined because the coefficient @xmath85 for @xmath86 .
the equations of motion eq .
( [ eq : eom3 ] ) together with the corresponding equations for @xmath87 ( sign change for the vacuum term ) form a closed set of equations . if we also include the ordinary matter term they are equivalent to eq .
( [ eq : eom2 ] ) for the momentum - space matrices @xmath58 .
one important difference is that @xmath88 is conserved , reflecting the absence of decoherence for individual momentum modes , whereas @xmath89 is not in general conserved , reflecting the effect of kinematical decoherence .
we note that in general @xmath90 when the equation of motion is of the form @xmath91 $ ] .
this is the case for @xmath58 , but not for the multipole matrices @xmath92 . of course
, in a numerical implementation the series @xmath92 has to be truncated at some value @xmath93 , leading to limited angular resolution .
this is analogous to the coarse graining of phase space required for the @xmath94 where one needs to use discrete angular bins of nonzero width .
the equations of motion for the flux terms are special in that they involve one power of @xmath76 or @xmath95 in each term of the equation .
therefore , if initially there is no flux term ( @xmath96 ) , none will develop . in this case the equations for @xmath75 and @xmath97 form a closed set , describing the dynamics of the `` flavor pendulum '' studied in ref .
in addition , the higher multipoles @xmath92 with @xmath98 , if initially nonzero , will simply oscillate under the action of the vacuum term and of the density term @xmath99 .
the interpretation of the equations of motion in multipole space becomes clearer if we observe that for some function @xmath100 one has to second order @xmath101 taking the sum and difference of these equations provides @xmath102 with eq .
( [ eq : abcoefficients ] ) we may write @xmath103 where we interpret a prime as a derivative with respect to @xmath104 that is now viewed as a continuous variable . if we further observe that in the discrete equation @xmath105 we may write eq .
( [ eq : eom3 ] ) in the continuous form @xmath106 + \mu\left[(\varrho-\bar\varrho)_0-(\varrho-\bar\varrho)_1 , \varrho_n\right ] \nonumber\\ & & \kern2.7em{}-\mu \left[(\varrho-\bar\varrho)_1,\left ( \frac{\varrho^\prime_n}{2n+1}+\frac{\varrho^{\prime\prime}_n}{2 } \right)\right]\,.\end{aligned}\ ] ] therefore , the lowest multipole ( monopole ) is equivalent to the pendulum in flavor space @xcite , the high multipoles are akin to a continuous medium carrying flavor waves .
equation ( [ eq : eom4 ] ) is a diffusion equation .
the periodic excitation caused by the flavor pendulum then diffuses to higher multipoles ( smaller scales ) .
the flavor waves as a function of neutrino direction visible in numerical simulations @xcite are the result of this process . in the equations of motion
the difference of the particle and antiparticle densities , @xmath107 , plays a special role in that it is this matrix of net lepton number densities that plays the role of a potential for the other neutrino modes . as noted by several authors
, it is sometimes useful to write the equations of motion in terms of the sum and difference of @xmath39 and @xmath40 instead of these matrices themselves .
we therefore define the matrix of particle densities ( sum @xmath108 ) and the matrix of lepton number densities ( difference @xmath109 ) by virtue of @xmath110 analogous definitions apply to the case of axial symmetry , @xmath111 and @xmath112 , and their multipole expansion @xmath113 and @xmath114 .
the equations of motion for the particle and lepton number matrices are found by adding and subtracting the two lines of eq .
( [ eq : eom1 ] ) and the equivalent equations for axial symmetry or the multipoles .
we find explicitly for the multipoles @xmath115 + \mu[{\sf d}_0,{\sf s}_n ] -\mu\left[{\sf d}_1 , \frac{a_n{\sf s}_{n-1}+b_n{\sf s}_{n+1}}{2}\right ] , \nonumber\\ { \rm i}\dot{\sf d}_n&=&[\omega,{\sf s}_n ] + \mu[{\sf d}_0,{\sf d}_n ] -\mu\left[{\sf d}_1 , \frac{a_n{\sf d}_{n-1}\!+\!b_n{\sf d}_{n+1}}{2}\right ] .
\nonumber\\\end{aligned}\ ] ] one can easily restore the ordinary matter term because it has the same structure as the neutrino - neutrino term with the substitution @xmath116 and @xmath117 , the latter being the charged - lepton matrix of net lepton - number densities and the corresponding flux , respectively . the commutator structure of the r.h.s . of eq .
( [ eq : eom5 ] ) implies that its trace vanishes .
therefore , the particle and lepton numbers for all multipoles , @xmath118 and @xmath119 , are conserved . with the expressions
( [ eq : abcoefficients ] ) for @xmath120 and @xmath121 the lowest - order multipole equation is @xmath122 + \mu[{\sf d}_0,{\sf s}_0 ]
-\mu[{\sf d}_1,{\sf s}_{1}]\ , , \nonumber\\ { \rm i}\dot{\sf d}_0&=&[\omega,{\sf s}_0]\,.\end{aligned}\ ] ] one immediate consequence of the second equation is @xmath123 i.e. , in the mass basis a certain combination of flavor - lepton numbers is conserved . the explicit equation for the flux term is @xmath124 + \mu[{\sf d}_0,{\sf s}_1 ] + \frac{\mu}{3}\,[{\sf s}_{0}+2{\sf s}_{2},{\sf d}_1]\ , , \nonumber\\ { \rm i}\dot{\sf d}_1&=&[\omega,{\sf s}_1 ] + \frac{2\mu}{3}\,[{\sf d}_0-{\sf d}_2,{\sf d}_{1}]\,.\end{aligned}\ ] ] as stated earlier , these equations are special in that they involve one power of @xmath125 or @xmath126 in each term . therefore , @xmath125 and @xmath126 vanish at all times if they vanish initially . in this case , the monopole terms ( overall densities ) form a closed set of equations . defining @xmath127
the equations of motion take on the simple form @xmath128\ , , \nonumber\\ { \rm i}\dot{\sf d}&=&[\omega,{\sf q}]\,.\end{aligned}\ ] ] conserved quantities are @xmath129 , @xmath130 , @xmath131 , and @xmath132 .
up to a constant , the last quantity is the energy per neutrino . for two flavors ,
these simplifications are at the origin of the pendulum analogy @xcite where @xmath129 corresponds to its length , @xmath130 its spin , and @xmath131 to the orbital angular momentum around the force direction ( the mass direction in flavor space ) .
returning to the general case with arbitrary initial conditions , the energy per neutrino is @xmath133\,.\ ] ] energy conservation @xmath134 is easily verified by using the equations of motion for @xmath135 , @xmath136 and @xmath126 . in the two - flavor case where the @xmath39 are hermitian @xmath137 matrices ,
a representation in terms of polarization vectors is useful .
a hermitian @xmath137 matrix @xmath138 is represented as @xmath139 where @xmath140 is the vector of pauli matrices and @xmath141 the polarization vector .
the commutation relations of the pauli matrices imply that an equation of motion of the form @xmath142\ ] ] is represented by @xmath143 moreover , @xmath144 for any two matrices @xmath138 and @xmath145 . as usual , we denote with @xmath9 and @xmath146 the polarization vectors representing @xmath39 and @xmath40 , respectively , and analogous expressions for @xmath147 and @xmath148 .
the particle and lepton - number matrices are represented by @xmath149 and @xmath150 , in each case with the subscripts @xmath151 , @xmath68 or @xmath104 for the different variables .
finally , we represent the matrix of oscillation frequencies in the form @xmath152 where @xmath153 we have defined the oscillation frequency @xmath24 as a positive number .
the `` magnetic field '' is a unit vector that in the interaction basis is explicitly @xmath154 where @xmath16 is the vacuum mixing angle .
we have arbitrarily chosen its @xmath155-component to vanish , corresponding to a choice of overall phase of the mixing matrix . in the following , when we say that `` the mixing angle is small , '' we mean that @xmath156 .
the sign of @xmath157 is physically irrelevant whereas @xmath22 represents the normal , @xmath23 the inverted hierarchy .
the equations of motion for the particle- and lepton - number polarization vectors are explicitly @xmath158 the two lowest - order equations are explicitly @xmath159 and @xmath160 the conserved energy eq .
( [ eq : energy2 ] ) becomes , with the help of eq .
( [ eq : doubletrace ] ) , @xmath161\bigr\rbrace\,.\end{aligned}\ ] ] we have already noted that the individual traces @xmath162 , @xmath163 and @xmath164 are conserved so that is missing in the equivalent expression in our previous paper @xcite . ] @xmath165\ ] ] is the conserved energy per neutrino , up to an irrelevant constant .
we use the notation @xmath166 for what is the `` potential energy '' in the pendulum analogy .
its minimum is chosen at zero .
the `` kinetic energy '' ( neutrino - neutrino interaction energy ) is denoted by @xmath167 where we have introduced @xmath168 for the monopole and dipole contributions .
in order to study the impact of kinematical decoherence in the simplest nontrivial case we study a homogeneous ensemble consisting of equal numbers of neutrinos and antineutrinos that are all initially in the electron flavor . before turning to issues of decoherence
, we briefly recall the evolution of the isotropic case . to this end
we show in fig .
[ fig : isotropic ] in the upper panels the @xmath17-component of the overall polarization vector @xmath169 for the inverted and normal hierarchy .
the @xmath18 or @xmath170 survival probability is @xmath171 because in our normalization @xmath172 . in the lower panels we show the corresponding energy components . for the normal hierarchy ( left )
the motion is a small - excursion harmonic oscillation with the bipolar frequency @xmath26 .
we show one full cycle of oscillation .
the potential energy @xmath173 ( solid line in the lower panel ) is measured against the mass direction so that it is back at its maximum after a half - period as behooves an ordinary pendulum .
the dashed line shows the `` kinetic pendulum energy '' @xmath174 .
the isotropy of the ensemble implies @xmath175 and thus @xmath176 .
for the inverted hierarchy ( right ) the motion is that of an inverted oscillator .
we show approximately one full cycle that for the chosen mixing angle lasts approximately 3 times the bipolar period @xmath177 .
the polarization vector starts in the positive @xmath17 direction , swings almost one full circle and almost arrives back at the vertical direction ( maximum in the middle of the plot ) , then swings back , reaching its original vertical position , and then starts over again .
the maximum potential energy is @xmath178 because the energy is normalized to the total energy per @xmath11 and because there are equal numbers of neutrinos and antineutrinos , i.e. , two particles per @xmath11 . reducing the mixing angle has the effect of reducing the oscillation amplitude for the normal hierarchy , whereas it increases logarithmically the duration of the `` plateau phases '' for the inverted hierarchy . for quantitative discussions of the isotropic case in terms of the pendulum analogy
see ref .
@xcite .
next we consider the same example , but assume a large degree of anisotropy where only one half - space of momentum modes is occupied . in fig .
[ fig : halfisotropic ] we show , in the upper panels , the evolution of @xmath179 .
moreover , we show the length of the overall polarization vector , @xmath180 , as a thin dashed line .
both in the normal hierarchy ( left ) and the inverted hierarchy ( right ) , an equal mixture of the two flavors is quickly achieved . in the isotropic case
the length of @xmath181 and @xmath182 is conserved and that of @xmath183 is approximately conserved , up to corrections of order @xmath184 . here
, the lengths of @xmath185 , @xmath182 and @xmath183 shrink to zero , reflecting kinematical decoherence . of course
, @xmath179 can become small or zero without its length shrinking as during the first swing in the inverted hierarchy case .
it is the length of the polarization vector , not its @xmath17-component , that is a measure of decoherence .
of course , in the normal hierarchy , @xmath183 performs only small - excursion oscillations so that a significant change of its @xmath17-component can be achieved only by a change of its length . in this case @xmath186 and @xmath187 are almost identical . the evolution of @xmath183 was also illustrated in fig .
[ fig : trajectory ] where we showed its trajectory in the @xmath21-@xmath17-plane . for our chosen geometry where @xmath19 is in the @xmath21-@xmath17-plane , @xmath188 at all times . for the inverted hierarchy ( bottom )
we indicate the isotropic - gas trajectory with diamonds at time intervals of @xmath189 where the motion starts in the vertical position . in the half - isotropic case ,
the particle - number polarization vector @xmath183 spirals in to a position close to the origin .
the final offset is very small and depends on the magnitude of @xmath190 for which we have chosen @xmath191 . in the normal hierarchy ( top ) , the isotropic - case motion is a small - excursion harmonic oscillation between the dotted lines . in the half - isotropic case ,
the evolution begins from the vertical position .
a full oscillation back to the vertical position is performed before the shrinking of @xmath183 becomes noticeable . in the lower panels of fig .
[ fig : halfisotropic ] we show the evolution of the different energy components .
the simpler case is the inverted hierarchy ( right ) where the `` potential '' and `` kinetic '' energies begin to oscillate as in the isotropic case of fig .
[ fig : isotropic ] . on the time scale of a few bipolar oscillation periods , the two components essentially equipartition ,
although asymptotically a small offset remains that depends on @xmath190 .
moreover , the neutrino - neutrino energy ( `` kinetic energy '' ) now develops a nonvanishing flux term @xmath192 that inevitably is negative .
the normal hierarchy ( left ) is initially similar in that @xmath173 and @xmath174 oscillate as for a pendulum , even though this motion is not visible on the scale of the plot .
as decoherence sets in , a qualitatively different mode of behavior obtains in that the neutrino - neutrino energy @xmath174 is dominated almost entirely by the negative @xmath193 whereas @xmath194 now is subdominant .
all individual polarization vectors of all modes start aligned with the @xmath17-direction , i.e. , almost aligned with the force direction since the mixing angle is small .
therefore , the initial @xmath173 is near its minimum .
if the overall polarization vector @xmath183 is supposed to shrink , the individual polarization vectors must develop significant deviations from each other and thus the potential energy must increase .
energy conservation then dictates that @xmath174 becomes negative .
one important conclusion is that the angular dependence of the neutrino - neutrino interaction alone is not enough to cause kinematical decoherence , but its absolute sign is also crucial .
if @xmath193 were not negative , energy conservation would prevent significant decoherence for the normal hierarchy . changing this sign in a numerical example indeed
reveals the absence of decoherence for the normal hierarchy , but no significant change of behavior for the inverted case . in the real world
there is no choice about this sign .
it derives from the negative sign of the spatial part in the neutrino current - current interaction , i.e. , it is the negative sign inherent in the lorentz metric . from the equations of motion in the form eq .
( [ eq : eom6 ] ) one would have never guessed that the absolute sign of the term proportional to @xmath195 plays a crucial role .
it is also instructive to study the evolution of the higher multipole components @xmath196 .
we consider the same example as in the previous section .
for a half - isotropic gas the initial relative length of the multipole components is @xmath197 where @xmath198 and all of them are initially oriented in the @xmath17-direction . here
, @xmath199 is an integer , i.e. , the even multipoles vanish initially except for @xmath200 . instead of using these initial values , we calculate the evolution for a case where all multipoles vanish initially except for @xmath201 and @xmath202 , i.e. , we use the same density and flux terms as in the half - isotropic case .
the evolution is very similar .
we show the evolution of the first 21 multipoles in fig .
[ fig : multipoleevolution ] for the inverted hierarchy ; the picture is similar for the normal hierarchy .
the initial horizontal part of the curves corresponds to their zero initial value so that the offset by 0.1 vertical units between the curves is directly apparent .
initially , @xmath200 and @xmath203 are large , but quickly decay away by decoherence , whereas the higher multipoles vanish initially and get excited one after another , but then decrease again . the length of each multipole sports `` wiggles , '' i.e.
, the evolution is not monotonic .
moreover , they have large relative angles in the @xmath21-@xmath17 plane ( not shown here ) , i.e. , the spread of the inital excitation to larger and larger multipoles is far from simple in detail , but the overall process is as expected . in fig .
[ fig : multipoleevolution2 ] we show @xmath204 and @xmath205 as a function of @xmath104 at @xmath206 for the example of fig .
[ fig : multipoleevolution ] . at @xmath206 , multipoles @xmath207 are not yet excited
. the nearly linear increase of the phases between individual polarization vectors corresponds here to a diffusion of the `` multipole wave '' to larger @xmath104 with approximately constant speed , @xmath208 .
qualitatively , this can be understood as follows . the second line in eq .
( [ eq : eom6 ] ) together with the analogue of eq .
( [ eq : diffusion ] ) implies that @xmath209 the last term does not contribute to the growth of @xmath210 and can be ignored .
approximate equipartition between potential and kinetic energies in eq .
( [ eq : energy4 ] ) implies @xmath211 , as indeed was observed in fig .
[ fig : halfisotropic ] . the second term in eq .
( [ eq : n_growth ] ) then represents a combination of a drift in @xmath212space with velocity @xmath213 and diffusion with diffusion coefficient @xmath214 .
up to a factor @xmath215 this gives rise to an exponential factor @xmath216 $ ] . on the other hand , since @xmath217 for @xmath98 , the first term in eq .
( [ eq : n_growth ] ) can give rise to exponential growth whenever @xmath218 .
this growth will be non - monotonic , but can roughly be estimated as @xmath219 before @xmath220 saturates .
using perturbation theory , we will find a similar growth rate for @xmath221 at early times in sect .
[ sec : analytic ] . combining these two factors
, one sees that at time @xmath222 the wave front of @xmath223 , and thus also of @xmath196 , should be located at @xmath208 , which , according to figs .
[ fig : multipoleevolution ] and [ fig : multipoleevolution2 ] indeed it is within about @xmath224% .
the slow decrease of @xmath196 and @xmath220 at late times can be interpreted as due to the @xmath215 factor in the diffusive behavior .
the overall behavior of the inverted - hierarchy case is qualitatively easy to understand . to this end
we consider an ensemble of polarization vectors @xmath225 , initially oriented in the @xmath17-direction , that rotate around the @xmath155-axis , each with a frequency @xmath68 , so that @xmath226 both @xmath68 and @xmath222 are normalized to be dimensionless .
if the frequencies are spread over @xmath227 , then the overall polarization vector evolves as @xmath228-\sin(t)}{t}\ , , \nonumber\\ p^x_0&=&\int_1^{1+\delta u}\!\!du\,\sin(u t ) = \frac{\cos(t)-\cos[(1+\delta u)\,t]}{t}\ , , \nonumber\\ |{\bf p}_0|&=&\left[(p^x_0)^2+(p^z_0)^2\right]^{1/2 } = \frac{2\,|\sin(\delta u\,t/2)|}{t}\,.\end{aligned}\ ] ] for @xmath229 we show in fig .
[ fig : toy1 ] the evolution of @xmath230 ( solid line ) and the length @xmath231 ( dashed line ) . in fig .
[ fig : toy2 ] we show the trajectory of @xmath181 in the @xmath21-@xmath17-plane .
unsurprisingly , this simple model represents qualitatively the features of the inverted - hierarchy case . in particular , the trajectory in the @xmath21-@xmath17-plane is not a true spiral , but there are many crossings of the origin as the length of the overall polarization vector shrinks .
its length does not shrink monotonically .
its envelope decreases as a power law @xmath232 , not exponentially .
this example also shows that it is not trivial to define a useful measure of kinematical decoherence .
the @xmath17-component of the polarization vector is not useful because @xmath181 can tilt so that its @xmath17-component vanishes , i.e. , both flavors are present with the same probability , yet the flavor content of the ensemble is perfectly coherent . the length of @xmath181 is a much better measure in analogy to dynamical decoherence of a single mode where the length of @xmath9 is a measure of dynamical decoherence ; unit length would correspond to a pure state . in our case ,
the length of the individual @xmath9 is conserved , whereas the length of the total @xmath181 shrinks , but not monotonically .
it is not evident if there is an `` entropy '' measure that evolves monotonically as a consequence of kinematical decoherence .
we note , however , that the origin of kinematical decoherence is the differential evolution between neighboring polarization vectors . in our toy example
, the angle between neighboring polarization vectors grows linearly as @xmath233 and thus is a measure of decoherence .
motivated by this observation we can define the `` winding number '' @xmath234 in the symmetric case where the evolution of the polarization vectors is essentially restricted to the @xmath21-@xmath17-plane , this quantity tells us the number of windings around the @xmath155-direction of the full ensemble of polarization vectors . in fig .
[ fig : windingnumber ] we show the evolution of this quantity for the normal and inverted hierarchy examples of fig .
[ fig : halfisotropic ] .
@xmath28 counts how often the length of @xmath183 shrinks to zero .
closely related to kinematical decoherence are recurrence effects that arise when one uses a limited number of polarization vectors , i.e. , when the full ensemble is represented by a coarse - grained ( binned ) ensemble of polarization vectors or , in multipole space , when the series is truncated at some multipole @xmath93 . binning or truncation are unavoidable in numerical treatments and represent equivalent approximations .
if the phase differences evolve linearly between different polarization vectors as in the toy example of the previous section , then the initial state will recur when each polarization vector has turned around the @xmath155-axis by @xmath235 relative to its neighbors .
put another way , if we use @xmath236 bins to represent the polarization vectors , we expect recurrence to begin when @xmath237 .
we demonstrate this effect in fig .
[ fig : recurrence ] for the same example as in fig .
[ fig : halfisotropic ] , normal hierarchy , using @xmath238 .
indeed , the winding number increases until approximately @xmath239 and then decreases back to almost zero , and so forth .
this system is almost periodic on the recurrence time scale , reflecting that nonlinear effects play a subleading role here .
since a large flux term is present from the start , kinematical decoherence is very similar to the linear toy example of the previous section where recurrence would be exact and the system would be periodic with a frequency proportional to @xmath240 times the individual polarization vector s oscillation frequency . using the multipoles as the primary variables ,
the same recurrence effects occur due to the truncation @xmath93 of the multipole series .
the `` multipole wave '' of fig .
[ fig : multipoleevolution2 ] can only propagate up to @xmath241 , is then reflected , and eventually returns back to @xmath86 .
this is the moment of maximum recurrence of the overall polarization vector . for a more complicated example such as a realistic simulation of the supernova case
, recurrence effects may not be so obvious as here .
therefore , in a numerical treatment one must make sure that the largest relative angle developed between any two neighboring polarization vectors never grows to order unity , i.e. , one should monitor the largest relative angle between neighboring polarization vectors as a measure of accuracy of the calculation .
in other words , kinematical decoherence is a property of the entire ensemble , but can also be a a property of individual bins if they are too coarse .
one must make sure that within all individual bins kinematical decoherence remains negligible .
we next turn to a symmetric system that is perfectly isotropic except for an arbitrarily small but nonzero initial anisotropy .
we work in the multipole picture and assume that initially @xmath242 for all @xmath104 , @xmath243 for @xmath244 , @xmath245 and @xmath246 .
note that @xmath247 corresponds to a flux term equivalent to the half - isotropic case . as a first example we show in fig .
[ fig : nearisotropic ] the evolution of the overall polarization vector @xmath183 ( top ) for the normal hierarchy ( left ) and the inverted hierarchy ( right ) .
the initial anisotropy is @xmath248 and @xmath249 . for both hierarchies , kinematical decoherence eventually obtains . in the bottom panels we show the evolution of @xmath250 ( solid line ) as a proxy for @xmath195 which is the primary quantity that causes decoherence .
for the symmetric neutrino gas only the component @xmath251 is nonzero , but it can be negative and can change sign so that it is difficult to display on a logarithmic scale .
we also show the evolution of the `` potential energy '' @xmath173 ( dotted line ) .
for the normal hierarchy , @xmath251 grows exponentially after a short initial transient . while @xmath251 is small
, the potential energy @xmath173 performs the usual oscillations of a harmonic oscillator , complemented by the opposite oscillations of the kinetic energy @xmath252 ( not shown ) that is entirely dominated by @xmath194 .
as @xmath251 grows , it eventually dominates the kinetic energy and the end state is approximately @xmath253 and @xmath254 , with @xmath193 dominating @xmath174 . in other words ,
the end state is exactly as in the previous case with a large initial anisotropy .
the crucial novel feature is that the flux term grows exponentially from a small value .
this is a purely nonlinear effect caused by neutrino - neutrino interactions . for smaller mixing angles and/or other values of @xmath255 ,
the behavior is analogous .
the rising part of the @xmath193 curve is the same , except that it shifts vertically in direct proportion to @xmath255 and @xmath256 . for the inverted hierarchy ,
the evolution is far more complicated .
while @xmath251 grows in an average sense , this evolution is overlaid with oscillations and in fact @xmath251 changes sign at each spike in the @xmath193 curve . moreover ,
the evolution of the envelope of the @xmath193 curve is not monotonic .
it can perform complicated motions , with growing , declining , and nearly flat phases , until finally decoherence obtains . from these numerical observations
we tentatively conclude that an isotropic neutrino ensemble of equal densities of neutrinos and antineutrinos is not stable .
a small flux term triggers a run - away evolution towards kinematical decoherence . as a starting point for an analytic understanding of this instability
we use the equations of motion eq .
( [ eq : eom6 ] ) for the vectors @xmath196 and @xmath220 .
initially only @xmath183 is of order one , @xmath257 , and all others vanish .
as long as @xmath195 is sufficiently small , none of the higher multipoles can grow large so that we can limit our attention to the equations for @xmath86 and @xmath258 , i.e. , to eqs .
( [ eq : eom6a ] ) and ( [ eq : eom6b ] ) .
we further observe that the @xmath86 equations are coupled to the higher multipoles only by the term @xmath259 , consisting of a product of two small quantities , i.e. , it is at least of order @xmath260 .
therefore , the evolution of the near - isotropic ensemble is identical with that of the isotropic case until @xmath195 has grown sufficiently large . in other words , up to second order in @xmath255 the @xmath86 equation is that of the isotropic case .
therefore , what remains to be solved is the @xmath258 equation . after neglecting terms involving @xmath244
all we need to study is @xmath261 where @xmath262 and @xmath263 are the solutions of the unperturbed pendulum equations .
the equations simplify further in our case of equal @xmath11 and @xmath12 densities where symmetry dictates that all polarization vectors @xmath9 and @xmath146 evolve as each other s mirror images relative to the @xmath21-@xmath17-plane , the latter being singled out by our choice that @xmath19 lies in that plane . in this case
all @xmath220 vectors are parallel to the @xmath155-axis , whereas all @xmath196 vectors are confined to the @xmath21-@xmath17-plane . as a consequence ,
the @xmath264 term drops out .
the second equation then implies @xmath265 , and with the first equation yields @xmath266 + \omega\mu{\bf b}\times\left({\bf d}_0\times{\bf s}_1\right)\,.\ ] ] expanding the triple product , observing that in our case @xmath267 , and using @xmath268 this is @xmath269 we repeat that all @xmath220 are here parallel to each other and to the @xmath155-axis . in the absence of neutrino - neutrino interactions ( @xmath270 )
, @xmath195 obeys a harmonic - oscillator equation . in a dense neutrino gas , @xmath271
, we may ignore the term proportional to @xmath272 . since during the growth phase , @xmath273 and @xmath274 , the last term in eq .
( [ eq : ddot ] ) can also be neglected . a possible exponential growth is then accounted for by the term @xmath275 where we have used the bipolar oscillation frequency @xmath276 and we note that initially @xmath172 and that its length remains nearly constant if @xmath277 unless there is kinematical decoherence .
if the mixing angle is small , the `` normal hierarchy '' is defined by neutrinos being essentially in the lower mass eigenstate or @xmath278 up to corrections of order @xmath279 .
therefore , the critical part of the equation of motion for the flux term is approximately @xmath280 the solution includes growing modes of the form @xmath281 where @xmath282 is the dimensionless time variable used in all of our plots , i.e. , time in units of the bipolar oscillation period .
this behavior is numerically verified in the lower - left panel of fig .
[ fig : nearisotropic ] if we recall that the plotted quantity is @xmath283 $ ] .
once more we note that the crucial absolute sign in eq .
( [ eq : expgrowth2 ] ) is traced back to the negative sign in the term @xmath284 in eq .
( [ eq : eom1 ] ) .
therefore , the instability of the near - isotropic neutrino gas , for the normal hierarchy , is not just caused by different angular modes experiencing different neutrino - neutrino effects .
this would also be the case for a hypothetical term @xmath285 that naively looks very similar , but causes a completely different overall behavior . in more complicated numerical situations , e.g. , for a full supernova simulation , it is easy to change this sign in order to diagnose the relevance of the term eq .
( [ eq : expgrowth1 ] ) for the overall behavior of the system .
initially @xmath286 so that the exponential growth term alone is not enough .
the initial evolution is dominated by the second line of eq .
( [ eq : eom6c ] ) that is initially @xmath287 where @xmath288 and we have used @xmath289 and @xmath290 . here the absolute sign is not critical because it does not matter if @xmath195 grows in the positive or negative @xmath155-direction .
the first factor @xmath291 sets the overall scale for @xmath195 . from the expression for the energy we note that @xmath292 and @xmath293 appear in the combinations @xmath294 .
the quantities @xmath196 are of order unity , whereas the natural scale for @xmath220 is @xmath291 .
the initial evolution is @xmath295 where , again , @xmath296 is our usual measure of time .
this linear growth is shown in fig .
[ fig : initialevolution ] as a dotted line and agrees with the numerical examples . besides a transient caused by the other terms in the equation , the exponential growth takes over after a time of order @xmath177 .
we conclude that the initial value of @xmath297 for its exponential growth is of order @xmath298 so that it grows to order unity within a time scale of order @xmath299 . for the inverted hierarchy
, the initial growth of @xmath300 is the same ( dashed line in fig .
[ fig : initialevolution ] ) . after that , however , the situation is entirely different because initially @xmath301 .
this corresponds to the pendulum starting in a nearly upright position from where it starts almost full - circle oscillations . for our usual assumption
@xmath156 the term @xmath302 is almost identical with @xmath179 shown in the upper - right panel of fig .
[ fig : nearisotropic ] . this term changes sign during every swing of the pendulum . during the phases when @xmath303 , @xmath195 oscillates whereas during the phases @xmath304 exponential growth obtains .
these are the relatively short phases when the pendulum is oriented downward , whereas it stays upright for long periods if the mixing angle is small .
we illustrate this behavior in fig .
[ fig : initialevolution2 ] where we show the evolution of @xmath300 overlaid with that of @xmath179 .
we have chosen an extremely small mixing angle , @xmath305 , to obtain long plateaus for @xmath179 where the pendulum stands almost still in an almost upright position . during these phases we have
@xmath306 so that eq .
( [ eq : expgrowth1 ] ) implies harmonic oscillations of @xmath300 with the frequency @xmath307 as borne out by the example in fig .
[ fig : initialevolution2 ] .
the frequency @xmath307 is not matched to the pendulum s oscillation period because the duration of the `` plateaus '' depend logarithmically on @xmath256 .
therefore , the short exponential growth phases when @xmath308 occur at erratic instances relative to the harmonic @xmath195 oscillation .
this interplay explains the erratic behavior of the @xmath195 evolution that is apparent in fig .
[ fig : nearisotropic ] and that obtains in all numerical examples .
this interplay also explains why small changes of parameters such as @xmath256 can completely change the overall @xmath195 evolution .
therefore , we can not prove if there is some specific combination of parameters where kinematical decoherence will not occur , although this would have to be isolated parameter points that presumably have measure zero in parameter space if they exist at all . except for this caveat
we conclude that both for the normal and inverted hierarchy kinematical decoherence is an unavoidable consequence of the nonlinear neutrino - neutrino interaction terms .
an infinitesimally small , but nonzero , deviation from isotropy is enough to trigger an exponential evolution towards flavor equilibrium .
therefore , the pendulum solution that describes the behavior of a perfectly isotropic gas is merely an unstable limit cycle of this nonlinear system .
we have investigated multi - angle kinematical decoherence effects in a dense neutrino gas consisting of equal @xmath11 and @xmath12 densities .
the current - current nature of the weak - interaction hamiltonian implies that a current of the background medium causes kinematical decoherence between neutrinos propagating in different directions .
this simple effect becomes entirely nontrivial in the most interesting case when the `` background current '' is caused by the neutrinos themselves .
we have shown that a neutrino gas of this sort is not stable in flavor space .
if one prepares the ensemble in a given flavor state , even a small deviation from isotropy is enough to trigger an exponential evolution towards flavor equipartition , even when the mixing angle is small .
up to logarithmic corrections , the time scale is determined by the bipolar oscillation period .
we thus have to do with a self - induced macroscopic pair conversion process that proceeds much faster than ordinary pair processes that occur at order @xmath309 .
with hindsight this is probably the same `` speed - up effect '' discussed in ref .
however , the fast speed @xmath310 is not introduced by the multi - angle effect as is perhaps suggested in ref .
rather , @xmath26 is the bipolar oscillation frequency that is inherent even in the isotropic system . for the normal hierarchy
`` nothing '' seems to happen in the isotropic case , although this would be a misperception because the system moves with the speed @xmath26 , but the amplitude is small if @xmath311 . in any event , we agree with the importance of multi - angle effects and with the end result conjectured in ref .
@xcite that complete flavor equipartition obtains on a time scale @xmath312 .
however , we have found no indication that an even faster time scale @xmath313 plays any role , in contrast to what was conjectured in ref .
@xcite .
of course , flavor equipartition obtains only in a macroscopic sense with some degree of coarse graining in phase space .
it is the nature of kinematical decoherence that information is not lost and the entropy does not increase . on the other hand , kinematical and dynamical decoherence are not always operationally distinguishable .
it is not necessarily possible to distinguish between a neutrino gas in true chemical equilibrium and one where neighboring modes are simply `` de - phased '' relative to each other . either way , the `` self - maintained coherence '' of a dense neutrino gas represents only an unstable limiting form of behavior of the perfectly isotropic case . since no gas can be perfectly isotropic , self - induced decoherence is the generic behavior of a symmetric @xmath13 gas .
contrary to a naive expectation , the fact that neutrinos propagating in different directions experience different weak potentials is necessary , but not sufficient , to cause multi - angle decoherence .
the negative sign in the lorentz metric plays a crucial role because it determines that the flux term grows exponentially rather than oscillating .
the occurrence of kinematical decoherence is a subtle feature of the nonlinear equations .
we have studied the simplest possible case where decoherence effects obtain .
a more realistic case is provided by neutrinos streaming off a supernova core . in this case
the fluxes of neutrinos and antineutrinos are different and geometry implies that the neutrino - neutrino interaction strength declines with the fourth power of radius .
the evolution of an asymmetric system is far more complicated , even in the isotropic case , where the simple pendular motion turns into one of a spinning top that can precess , nutate , or simply swing , depending on the @xmath13 asymmetry . in the supernova context ,
transitions between these modes occur as @xmath314 declines as a function of radius .
multi - angle decoherence can not occur , for example , in regions where synchronized oscillations prevail .
numerical simulations suggest that for neutrinos streaming off a supernova core , the collective behavior characteristic of an isotropic gas prevails in many situations , i.e. , kinematical decoherence occurs , but is not the dominating feature of the system , contrary to what we have found here for the symmetric @xmath13 gas . evidently it is not straightforward to apply the insights gained from our present study to the supernova case .
we imagine , however , that the methods developed here may take us one step further to understand the supernova problem .
we have formulated the equations of motion in a novel form adapted to the problem of multi - angle propagation , i.e. , we have used a multipole expansion rather than the usual momentum modes and we have used the particle number and lepton number polarization vectors ( or density matrices ) as the fundamental variables . in this way ,
the crucial exponentially growing quantity , our @xmath195 , could be isolated as the primary cause of kinematical decoherence .
this approach may prove useful for understanding the supernova problem as well .
for numerical three - flavor studies we have provided an expression for the conserved energy of the system in terms of the density matrices .
the conserved energy and its three components @xmath173 , @xmath194 and @xmath193 provide a useful diagnostic tool for the behavior of the system .
even simple nonlinear systems can exhibit a surprisingly rich phenomenology .
it is fascinating that the neutrinos streaming off a supernova core provide an intriguing case in point where many aspects of its behavior remain to be understood .
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d * 49 * , 2710 ( 1994 ) . | dense neutrino gases exhibit collective oscillations where `` self - maintained coherence '' is a characteristic feature , i.e. , neutrinos of different energies oscillate with the same frequency . in a non - isotropic gas , however , the flux term of the neutrino - neutrino interaction has the opposite effect of causing kinematical decoherence of neutrinos propagating in different directions , an effect that is at the origin of the `` multi - angle behavior '' of neutrinos streaming off a supernova core .
we cast the equations of motion in a form where the role of the flux term is manifest .
we study in detail the symmetric case of equal neutrino and antineutrino densities where the evolution consists of collective pair conversions ( `` bipolar oscillations '' ) .
a gas of this sort is unstable in that an infinitesimal anisotropy is enough to trigger a run - away towards flavor equipartition .
the `` self - maintained coherence '' of a perfectly isotropic gas gives way to `` self - induced decoherence . '' | <s>[INST]neutrino oscillations between two flavors in vacuum are governed by the frequency @xmath0 where @xmath1 is the energy of a given mode .
therefore , if the energy spectrum is broad , the energy dependence of the oscillation frequency quickly leads to kinematical decoherence , i.e. , along a neutrino beam the overall flavor content quickly approaches an average value .
the situation changes radically when neutrinos themselves provide a significant refractive effect , leading to collective oscillation modes @xcite that can be of practical interest in the early universe @xcite or in core - collapse supernovae @xcite . defining the parameter @xmath2 the neutrino gas is `` dense '' when @xmath3 , i.e. , when a typical neutrino - neutrino interaction energy exceeds the energy corresponding to the vacuum oscillation frequency .
when this condition is satisfied , collective effects are important , even if the ordinary matter effect is much larger than that from the neutrino - neutrino interaction @xcite .
one characteristic feature of collective oscillations is the phenomenon of `` self - maintained coherence '' @xcite , meaning that all modes oscillate with the same frequency even though the energy spectrum may be broad .
it was recently stressed , however , that this is not the complete story @xcite .
perhaps the most interesting case for collective effects is provided by neutrinos streaming off a supernova core , a situation that is far from isotropic .
the current - current nature of the weak - interaction hamiltonian implies that the interaction energy between particles of momenta @xmath4 and @xmath5 is proportional to @xmath6 where @xmath7 is the velocity .
if the medium is isotropic , the @xmath8 term averages to zero , but if there is a net current , test particles moving in different directions experience different refractive effects . therefore , neutrinos moving in a background with a net current will decohere between different directions of motion , even if the energy spectrum is monochromatic .
to avoid confusion about terminology we stress that we always mean `` kinematical decoherence '' when we say `` decoherence . ''
different modes oscillate differently , leading to `` de - phasing '' and thus to the depolarization of the overall ensemble .
if we use the common language of polarization vectors @xmath9 for each mode @xmath4 , then the length of each @xmath9 is conserved , whereas the length of the overall polarization vector @xmath10 shrinks ( kinematical decoherence ) or is conserved ( kinematical coherence ) .
the effect of _ dynamical _ decoherence , caused by collisions among the neutrinos or with a thermal background medium , is that each individual polarization vector @xmath9 shrinks , i.e. , neutrinos in individual modes can not be represented as pure states .
this effect , relevant for open quantum systems , does not occur in our case where oscillations are the only form of evolution .
the multi - angle decoherence effect becomes nontrivial in the most interesting case when the `` background current '' consists of the neutrinos themselves as for neutrinos streaming off a supernova core .
numerical examples reveal significant decoherence effects , but on the other hand they also show collective modes very similar to the isotropic ( `` single - angle '' ) case @xcite .
the overall behavior is determined by a complicated interplay between the collective evolution and decoherence . rather than trying to understand the supernova case in its full complexity , we here take the opposite approach and study the simplest example that shows decoherence caused by the neutrino - neutrino multi - angle effect .
therefore , we consider a dense neutrino gas that is monochromatic , symmetric ( equal @xmath11 and @xmath12 densities ) , and homogeneous , but not isotropic .
even this simple model has a rich phenomenology that helps one to develop a better understanding of the full problem . on the other hand ,
it is simple enough that the most puzzling aspects of its behavior are analytically tractable . a symmetric @xmath13 gas oscillates in the `` bipolar mode '' where pairs of neutrinos of a given flavor coherently oscillate into the other flavor and back with the `` bipolar frequency '' @xcite @xmath14 as an example we consider a dense neutrino gas initially consisting of @xmath15 and assume that the mixing angle @xmath16 with another flavor is small , a situation that could represent 13-oscillations .
we characterize the overall flavor content of the ensemble in the usual way by a polarization vector where the positive @xmath17-direction corresponds to the @xmath18-flavor whereas the mass direction is defined by a unit vector that we call @xmath19 .
it is tilted against the @xmath17-direction by @xmath20 and we always choose it to lie in the @xmath21-@xmath17-plane with @xmath22 for the normal hierarchy and @xmath23 for the inverted hierarchy . in vacuum ,
the polarization vectors precess around @xmath19 with frequency @xmath24 . in a dense neutrino gas with @xmath25 , their motion
is largely confined to the @xmath21-@xmath17-plane where they perform pendular motions with frequency @xmath26 and where @xmath27 is the `` force direction . ''
the maximum excursion is @xmath20 , indicated by the dotted lines in fig .
[ fig : trajectory ] where we show the trajectory in the @xmath21-@xmath17-plane .
for the normal hierarchy , the pendulum swings between the dotted lines . for the inverted hierarchy ( bottom ) , it performs almost full - circle oscillations as indicated by the diamonds .
if the gas is not isotropic , the picture changes completely . taking the `` half - isotropic '' case as a generic example where only one half - space of momentum modes is occupied ( neutrinos streaming off a plane surface ) , we show in fig .
[ fig : trajectory ] the trajectory of the average polarization vector .
for both hierarchies , its length shrinks to zero so that the final state of the ensemble is an equal mixture of both flavors .
in other words , the ensemble quickly decoheres , independently of the mass hierarchy .
this behavior is perhaps intuitive because we have assumed a large neutrino current .
however , this effect is self - accelerating in that it is triggered even by the smallest nonzero anisotropy . whereas for perfect isotropy
the neutrino - neutrino interaction provides for self - maintained coherence between modes of different energy , even an infinitesimal anisotropy has the opposite effect of causing self - induced decoherence between modes with different propagation directions .
the average flavor content of the ensemble always approaches an equal mixture of both flavors .
this instability is a nonlinear effect caused by the neutrino - neutrino interaction .
in other words , the pendular motion of the isotropic ensemble is an unstable limit cycle , whereas the equal flavor mixture is a stable fixed point .
our goal is to explain this behavior . as a first step we formulate in sect .
[ sec : eom ] the equations of motion for the multi - angle system in terms of the multipole components of the neutrino angular distribution
. the special role of the flux ( the dipole term of the angular distribution ) becomes manifest .
we begin with the full @xmath28-flavor problem and then consider two flavors in terms of polarization vectors . in sect .
[ sec : anisotropy ] we study the role of a large anisotropy in causing decoherence .
our main result is developed in sect .
[ sec : smallanisotropy ] where we show that a @xmath13 gas is unstable in flavor space and always decoheres if there is an infinitesimally small initial anisotropy .
we conclude in sec .
[ sec : conclusions ] with a summary and outlook .
a statistical ensemble of unmixed neutrinos is represented by the occupation numbers @xmath29 for each momentum mode @xmath4 , where @xmath30 and @xmath31 are the relevant creation and annihilation operators and @xmath32 is the expectation value .
the corresponding expression for antineutrinos is @xmath33 , where here and henceforth overbarred quantities refer to antiparticles . for several flavors ,
the occupation numbers are generalized to `` matrices of densities '' in flavor space @xmath34 that really are matrices of occupation numbers .
the reversed order of the flavor indices @xmath35 and @xmath36 in the r.h.s . for antineutrinos ensures that under a flavor transformation , @xmath37 , antineutrinos transform in the same way , @xmath38 .
sums and differences of @xmath39 and @xmath40 then transform consistently .
for the seemingly intuitive equal order of flavor indices that is almost universally used in the literature , @xmath39 , @xmath40 , @xmath41 and @xmath42 all appear in the equations instead of @xmath39 and @xmath40 alone .
analogous matrices @xmath43 can be defined for the charged leptons .
we assume that the neutrino ensemble is completely described by these one - particle occupation number matrices , i.e. , that genuine many - body effects play no role @xcite . in this
case flavor oscillations of an ensemble of neutrinos and antineutrinos are described by an equation of motion for each mode @xmath44 + \sqrt{2}\,g_{\rm f}\left [ \int\!\frac{d^3{\bf q}}{(2\pi)^3 } \left(\ell_{\bf q}-\bar\ell_{\bf q } + \varrho_{\bf q}-\bar\varrho_{\bf q}\right ) ( 1-{\bf v}_{\bf q}\cdot{\bf v}_{\bf p } ) , \varrho_{\bf p}\right ] , \nonumber\\ { \rm i}\,\partial_t\bar\varrho_{\bf p}&= & -\left[\omega_{\bf p},\bar\varrho_{\bf p}\right ] + \sqrt{2}\,g_{\rm f}\left [ \int\!\frac{d^3{\bf q}}{(2\pi)^3 } \left(\ell_{\bf q}-\bar\ell_{\bf q } + \varrho_{\bf q}-\bar\varrho_{\bf q}\right ) ( 1-{\bf v}_{\bf q}\cdot{\bf v}_{\bf p } ) , \bar\varrho_{\bf p}\right],\end{aligned}\ ] ] where @xmath45 $ ] is a commutator and @xmath46 is the fermi constant . for ultrarelativistic neutrinos ,
the matrix of vacuum oscillation frequencies , expressed in the mass basis , is @xmath47 with @xmath48 .
further , @xmath49 is the velocity of a particle ( neutrino or charged lepton ) with momentum @xmath4
. the total conserved energy of the neutrino ensemble is an important quantity for understanding its evolution @xcite .
we find for the energy density @xmath50 ^ 2 -\frac{\sqrt2\,g_{\rm f}}{2}\left [ \int\!\frac{d^3{\bf p}}{(2\pi)^3}\ , ( \varrho_{\bf p}-\bar\varrho_{\bf p}){\bf v}_{\bf p}\right]^2 \biggr\rbrace\,.\end{aligned}\ ] ] this quantity actually represents the energy _ shift _ caused by the neutrino masses and by neutrino interactions .
it is straightfoward to show that indeed @xmath51 by taking the time derivative on the r.h.s . of eq .
( [ eq : energydensity ] ) , inserting the equations of motion eq .
( [ eq : eom1 ] ) , and using cyclic permutations of matrices under the trace .
for completeness we mention that one can also define the entropy density @xcite @xmath52\,.\end{aligned}\ ] ] this expression is well defined because @xmath39 and @xmath53 are positive semi - definite matrices . in our case where the equation of motion for each @xmath39 is of the form @xmath54 $ ] , the entropy density is conserved .
oscillations alone do not lead to a loss of information .
kinematical decoherence does not lead to an increase of entropy .
since we wish to study the simplest example that shows nontrivial multi - angle effects , we now restrict the neutrino energy distribution to be monochromatic and the geometry to axial symmetry .
we then integrate the matrices of densities over all variables except @xmath55 where the angle is relative to the direction of symmetry .
therefore , we consider the matrices @xmath56 implying the normalization @xmath57 for convenience we have arbitrarily normalized the @xmath58 matrices to the neutrino density .
we further define the matrix representing the particle flux along the direction of symmetry , @xmath59 where @xmath60 is the velocity along the symmetry direction . for relativistic particles @xmath61 . for charged leptons
we proceed in the same way , except that we normalize to the electron density @xmath62 .
we denote with @xmath63 the matrix of vacuum oscillation frequencies for our fixed neutrino energy @xmath1 .
the equations of motion then simplify to @xmath64 + \left[\lambda\left(\ell-\bar\ell)_0 + \mu(\varrho-\bar\varrho\right)_0,\varrho_u\right ] \nonumber\\ & & \kern2.8em{}-\left[\lambda\left(\ell-\bar\ell)_1 + \mu(\varrho-\bar\varrho\right)_1,u\varrho_u\right]\,,\end{aligned}\ ] ] where @xmath65 .
the same equation applies for @xmath66 except for a sign change of the vacuum oscillation term .
evidently the isotropic part of the medium ( index 0 ) affects all modes in the same way and is ultimately responsible for the phenomenon of self - maintained coherence . on the other hand ,
the flux term ( index 1 ) involves a factor @xmath67 for every mode @xmath68 . even in the absence of a neutrino - neutrino term
, a charged - lepton flux alone causes a trivial multi - angle decoherence effect .
the conserved energy of the axially symmetric neutrino ensemble is @xmath69 \nonumber\\ & & { } + \lambda\,{\rm tr}\left [ ( \ell-\bar\ell)_0(\varrho-\bar\varrho)_0 -(\ell-\bar\ell)_1(\varrho-\bar\varrho)_1\right ] \nonumber\\ & & { } + \frac{\mu}{2}\,{\rm tr}\left [ ( \varrho-\bar\varrho)_0 ^ 2 -(\varrho-\bar\varrho)_1 ^ 2\right]\,.\end{aligned}\ ] ] because of our normalization of the @xmath58 matrices the quantity @xmath70 is the energy per @xmath11 . the structure of these equations becomes more transparent if we expand the angular dependence of the matrices in legendre polynomials .
( had we not assumed axial symmetry , spherical harmonics would be the appropriate basis . )
the first few legendre polynomials are @xmath71 we thus define @xmath72 the normalisation @xmath73 implies that the original function is @xmath74 the previously defined overall density @xmath75 and the flux @xmath76 are but the zeroth and first case of eq .
( [ eq : expansion1 ] ) . multiplying both sides of eq .
( [ eq : eom2 ] ) with @xmath77 and integrating over @xmath78 leads to the equation of motion @xmath79 + \mu\left[(\varrho-\bar\varrho)_0,\varrho_n\right ] \nonumber\\ & & { } -\mu\left[(\varrho-\bar\varrho)_1 , { \textstyle\int_{-1}^{+1}}du\,u\varrho_u l_n(u)\right]\,.\end{aligned}\ ] ] here and henceforth we no longer show the ordinary matter term . its structure is similar to the neutrino - neutrino term so that it is easily reinstated . with the expansion eq .
( [ eq : expansion2 ] ) the remaining integral is @xmath80 we use the `` dipole matrix element '' of the legendre polynomials @xmath81 with this result the equations of motion are @xmath82 + \mu\left[(\varrho-\bar\varrho)_0,\varrho_n\right ] \nonumber\\ & & { } -\frac{\mu}{2 } \left[(\varrho-\bar\varrho)_1 , ( a_n\varrho_{n-1}+b_n\varrho_{n+1})\right]\,,\end{aligned}\ ] ] where @xmath83 note that the equation for @xmath75 is consistent even though the quantity @xmath84 is not defined because the coefficient @xmath85 for @xmath86 .
the equations of motion eq .
( [ eq : eom3 ] ) together with the corresponding equations for @xmath87 ( sign change for the vacuum term ) form a closed set of equations . if we also include the ordinary matter term they are equivalent to eq .
( [ eq : eom2 ] ) for the momentum - space matrices @xmath58 .
one important difference is that @xmath88 is conserved , reflecting the absence of decoherence for individual momentum modes , whereas @xmath89 is not in general conserved , reflecting the effect of kinematical decoherence .
we note that in general @xmath90 when the equation of motion is of the form @xmath91 $ ] .
this is the case for @xmath58 , but not for the multipole matrices @xmath92 . of course
, in a numerical implementation the series @xmath92 has to be truncated at some value @xmath93 , leading to limited angular resolution .
this is analogous to the coarse graining of phase space required for the @xmath94 where one needs to use discrete angular bins of nonzero width .
the equations of motion for the flux terms are special in that they involve one power of @xmath76 or @xmath95 in each term of the equation .
therefore , if initially there is no flux term ( @xmath96 ) , none will develop . in this case the equations for @xmath75 and @xmath97 form a closed set , describing the dynamics of the `` flavor pendulum '' studied in ref .
in addition , the higher multipoles @xmath92 with @xmath98 , if initially nonzero , will simply oscillate under the action of the vacuum term and of the density term @xmath99 .
the interpretation of the equations of motion in multipole space becomes clearer if we observe that for some function @xmath100 one has to second order @xmath101 taking the sum and difference of these equations provides @xmath102 with eq .
( [ eq : abcoefficients ] ) we may write @xmath103 where we interpret a prime as a derivative with respect to @xmath104 that is now viewed as a continuous variable . if we further observe that in the discrete equation @xmath105 we may write eq .
( [ eq : eom3 ] ) in the continuous form @xmath106 + \mu\left[(\varrho-\bar\varrho)_0-(\varrho-\bar\varrho)_1 , \varrho_n\right ] \nonumber\\ & & \kern2.7em{}-\mu \left[(\varrho-\bar\varrho)_1,\left ( \frac{\varrho^\prime_n}{2n+1}+\frac{\varrho^{\prime\prime}_n}{2 } \right)\right]\,.\end{aligned}\ ] ] therefore , the lowest multipole ( monopole ) is equivalent to the pendulum in flavor space @xcite , the high multipoles are akin to a continuous medium carrying flavor waves .
equation ( [ eq : eom4 ] ) is a diffusion equation .
the periodic excitation caused by the flavor pendulum then diffuses to higher multipoles ( smaller scales ) .
the flavor waves as a function of neutrino direction visible in numerical simulations @xcite are the result of this process . in the equations of motion
the difference of the particle and antiparticle densities , @xmath107 , plays a special role in that it is this matrix of net lepton number densities that plays the role of a potential for the other neutrino modes . as noted by several authors
, it is sometimes useful to write the equations of motion in terms of the sum and difference of @xmath39 and @xmath40 instead of these matrices themselves .
we therefore define the matrix of particle densities ( sum @xmath108 ) and the matrix of lepton number densities ( difference @xmath109 ) by virtue of @xmath110 analogous definitions apply to the case of axial symmetry , @xmath111 and @xmath112 , and their multipole expansion @xmath113 and @xmath114 .
the equations of motion for the particle and lepton number matrices are found by adding and subtracting the two lines of eq .
( [ eq : eom1 ] ) and the equivalent equations for axial symmetry or the multipoles .
we find explicitly for the multipoles @xmath115 + \mu[{\sf d}_0,{\sf s}_n ] -\mu\left[{\sf d}_1 , \frac{a_n{\sf s}_{n-1}+b_n{\sf s}_{n+1}}{2}\right ] , \nonumber\\ { \rm i}\dot{\sf d}_n&=&[\omega,{\sf s}_n ] + \mu[{\sf d}_0,{\sf d}_n ] -\mu\left[{\sf d}_1 , \frac{a_n{\sf d}_{n-1}\!+\!b_n{\sf d}_{n+1}}{2}\right ] .
\nonumber\\\end{aligned}\ ] ] one can easily restore the ordinary matter term because it has the same structure as the neutrino - neutrino term with the substitution @xmath116 and @xmath117 , the latter being the charged - lepton matrix of net lepton - number densities and the corresponding flux , respectively . the commutator structure of the r.h.s . of eq .
( [ eq : eom5 ] ) implies that its trace vanishes .
therefore , the particle and lepton numbers for all multipoles , @xmath118 and @xmath119 , are conserved . with the expressions
( [ eq : abcoefficients ] ) for @xmath120 and @xmath121 the lowest - order multipole equation is @xmath122 + \mu[{\sf d}_0,{\sf s}_0 ]
-\mu[{\sf d}_1,{\sf s}_{1}]\ , , \nonumber\\ { \rm i}\dot{\sf d}_0&=&[\omega,{\sf s}_0]\,.\end{aligned}\ ] ] one immediate consequence of the second equation is @xmath123 i.e. , in the mass basis a certain combination of flavor - lepton numbers is conserved . the explicit equation for the flux term is @xmath124 + \mu[{\sf d}_0,{\sf s}_1 ] + \frac{\mu}{3}\,[{\sf s}_{0}+2{\sf s}_{2},{\sf d}_1]\ , , \nonumber\\ { \rm i}\dot{\sf d}_1&=&[\omega,{\sf s}_1 ] + \frac{2\mu}{3}\,[{\sf d}_0-{\sf d}_2,{\sf d}_{1}]\,.\end{aligned}\ ] ] as stated earlier , these equations are special in that they involve one power of @xmath125 or @xmath126 in each term . therefore , @xmath125 and @xmath126 vanish at all times if they vanish initially . in this case , the monopole terms ( overall densities ) form a closed set of equations . defining @xmath127
the equations of motion take on the simple form @xmath128\ , , \nonumber\\ { \rm i}\dot{\sf d}&=&[\omega,{\sf q}]\,.\end{aligned}\ ] ] conserved quantities are @xmath129 , @xmath130 , @xmath131 , and @xmath132 .
up to a constant , the last quantity is the energy per neutrino . for two flavors ,
these simplifications are at the origin of the pendulum analogy @xcite where @xmath129 corresponds to its length , @xmath130 its spin , and @xmath131 to the orbital angular momentum around the force direction ( the mass direction in flavor space ) .
returning to the general case with arbitrary initial conditions , the energy per neutrino is @xmath133\,.\ ] ] energy conservation @xmath134 is easily verified by using the equations of motion for @xmath135 , @xmath136 and @xmath126 . in the two - flavor case where the @xmath39 are hermitian @xmath137 matrices ,
a representation in terms of polarization vectors is useful .
a hermitian @xmath137 matrix @xmath138 is represented as @xmath139 where @xmath140 is the vector of pauli matrices and @xmath141 the polarization vector .
the commutation relations of the pauli matrices imply that an equation of motion of the form @xmath142\ ] ] is represented by @xmath143 moreover , @xmath144 for any two matrices @xmath138 and @xmath145 . as usual , we denote with @xmath9 and @xmath146 the polarization vectors representing @xmath39 and @xmath40 , respectively , and analogous expressions for @xmath147 and @xmath148 .
the particle and lepton - number matrices are represented by @xmath149 and @xmath150 , in each case with the subscripts @xmath151 , @xmath68 or @xmath104 for the different variables .
finally , we represent the matrix of oscillation frequencies in the form @xmath152 where @xmath153 we have defined the oscillation frequency @xmath24 as a positive number .
the `` magnetic field '' is a unit vector that in the interaction basis is explicitly @xmath154 where @xmath16 is the vacuum mixing angle .
we have arbitrarily chosen its @xmath155-component to vanish , corresponding to a choice of overall phase of the mixing matrix . in the following , when we say that `` the mixing angle is small , '' we mean that @xmath156 .
the sign of @xmath157 is physically irrelevant whereas @xmath22 represents the normal , @xmath23 the inverted hierarchy .
the equations of motion for the particle- and lepton - number polarization vectors are explicitly @xmath158 the two lowest - order equations are explicitly @xmath159 and @xmath160 the conserved energy eq .
( [ eq : energy2 ] ) becomes , with the help of eq .
( [ eq : doubletrace ] ) , @xmath161\bigr\rbrace\,.\end{aligned}\ ] ] we have already noted that the individual traces @xmath162 , @xmath163 and @xmath164 are conserved so that is missing in the equivalent expression in our previous paper @xcite . ] @xmath165\ ] ] is the conserved energy per neutrino , up to an irrelevant constant .
we use the notation @xmath166 for what is the `` potential energy '' in the pendulum analogy .
its minimum is chosen at zero .
the `` kinetic energy '' ( neutrino - neutrino interaction energy ) is denoted by @xmath167 where we have introduced @xmath168 for the monopole and dipole contributions .
in order to study the impact of kinematical decoherence in the simplest nontrivial case we study a homogeneous ensemble consisting of equal numbers of neutrinos and antineutrinos that are all initially in the electron flavor . before turning to issues of decoherence
, we briefly recall the evolution of the isotropic case . to this end
we show in fig .
[ fig : isotropic ] in the upper panels the @xmath17-component of the overall polarization vector @xmath169 for the inverted and normal hierarchy .
the @xmath18 or @xmath170 survival probability is @xmath171 because in our normalization @xmath172 . in the lower panels we show the corresponding energy components . for the normal hierarchy ( left )
the motion is a small - excursion harmonic oscillation with the bipolar frequency @xmath26 .
we show one full cycle of oscillation .
the potential energy @xmath173 ( solid line in the lower panel ) is measured against the mass direction so that it is back at its maximum after a half - period as behooves an ordinary pendulum .
the dashed line shows the `` kinetic pendulum energy '' @xmath174 .
the isotropy of the ensemble implies @xmath175 and thus @xmath176 .
for the inverted hierarchy ( right ) the motion is that of an inverted oscillator .
we show approximately one full cycle that for the chosen mixing angle lasts approximately 3 times the bipolar period @xmath177 .
the polarization vector starts in the positive @xmath17 direction , swings almost one full circle and almost arrives back at the vertical direction ( maximum in the middle of the plot ) , then swings back , reaching its original vertical position , and then starts over again .
the maximum potential energy is @xmath178 because the energy is normalized to the total energy per @xmath11 and because there are equal numbers of neutrinos and antineutrinos , i.e. , two particles per @xmath11 . reducing the mixing angle has the effect of reducing the oscillation amplitude for the normal hierarchy , whereas it increases logarithmically the duration of the `` plateau phases '' for the inverted hierarchy . for quantitative discussions of the isotropic case in terms of the pendulum analogy
see ref .
@xcite .
next we consider the same example , but assume a large degree of anisotropy where only one half - space of momentum modes is occupied . in fig .
[ fig : halfisotropic ] we show , in the upper panels , the evolution of @xmath179 .
moreover , we show the length of the overall polarization vector , @xmath180 , as a thin dashed line .
both in the normal hierarchy ( left ) and the inverted hierarchy ( right ) , an equal mixture of the two flavors is quickly achieved . in the isotropic case
the length of @xmath181 and @xmath182 is conserved and that of @xmath183 is approximately conserved , up to corrections of order @xmath184 . here
, the lengths of @xmath185 , @xmath182 and @xmath183 shrink to zero , reflecting kinematical decoherence . of course
, @xmath179 can become small or zero without its length shrinking as during the first swing in the inverted hierarchy case .
it is the length of the polarization vector , not its @xmath17-component , that is a measure of decoherence .
of course , in the normal hierarchy , @xmath183 performs only small - excursion oscillations so that a significant change of its @xmath17-component can be achieved only by a change of its length . in this case @xmath186 and @xmath187 are almost identical . the evolution of @xmath183 was also illustrated in fig .
[ fig : trajectory ] where we showed its trajectory in the @xmath21-@xmath17-plane . for our chosen geometry where @xmath19 is in the @xmath21-@xmath17-plane , @xmath188 at all times . for the inverted hierarchy ( bottom )
we indicate the isotropic - gas trajectory with diamonds at time intervals of @xmath189 where the motion starts in the vertical position . in the half - isotropic case ,
the particle - number polarization vector @xmath183 spirals in to a position close to the origin .
the final offset is very small and depends on the magnitude of @xmath190 for which we have chosen @xmath191 . in the normal hierarchy ( top ) , the isotropic - case motion is a small - excursion harmonic oscillation between the dotted lines . in the half - isotropic case ,
the evolution begins from the vertical position .
a full oscillation back to the vertical position is performed before the shrinking of @xmath183 becomes noticeable . in the lower panels of fig .
[ fig : halfisotropic ] we show the evolution of the different energy components .
the simpler case is the inverted hierarchy ( right ) where the `` potential '' and `` kinetic '' energies begin to oscillate as in the isotropic case of fig .
[ fig : isotropic ] . on the time scale of a few bipolar oscillation periods , the two components essentially equipartition ,
although asymptotically a small offset remains that depends on @xmath190 .
moreover , the neutrino - neutrino energy ( `` kinetic energy '' ) now develops a nonvanishing flux term @xmath192 that inevitably is negative .
the normal hierarchy ( left ) is initially similar in that @xmath173 and @xmath174 oscillate as for a pendulum , even though this motion is not visible on the scale of the plot .
as decoherence sets in , a qualitatively different mode of behavior obtains in that the neutrino - neutrino energy @xmath174 is dominated almost entirely by the negative @xmath193 whereas @xmath194 now is subdominant .
all individual polarization vectors of all modes start aligned with the @xmath17-direction , i.e. , almost aligned with the force direction since the mixing angle is small .
therefore , the initial @xmath173 is near its minimum .
if the overall polarization vector @xmath183 is supposed to shrink , the individual polarization vectors must develop significant deviations from each other and thus the potential energy must increase .
energy conservation then dictates that @xmath174 becomes negative .
one important conclusion is that the angular dependence of the neutrino - neutrino interaction alone is not enough to cause kinematical decoherence , but its absolute sign is also crucial .
if @xmath193 were not negative , energy conservation would prevent significant decoherence for the normal hierarchy . changing this sign in a numerical example indeed
reveals the absence of decoherence for the normal hierarchy , but no significant change of behavior for the inverted case . in the real world
there is no choice about this sign .
it derives from the negative sign of the spatial part in the neutrino current - current interaction , i.e. , it is the negative sign inherent in the lorentz metric . from the equations of motion in the form eq .
( [ eq : eom6 ] ) one would have never guessed that the absolute sign of the term proportional to @xmath195 plays a crucial role .
it is also instructive to study the evolution of the higher multipole components @xmath196 .
we consider the same example as in the previous section .
for a half - isotropic gas the initial relative length of the multipole components is @xmath197 where @xmath198 and all of them are initially oriented in the @xmath17-direction . here
, @xmath199 is an integer , i.e. , the even multipoles vanish initially except for @xmath200 . instead of using these initial values , we calculate the evolution for a case where all multipoles vanish initially except for @xmath201 and @xmath202 , i.e. , we use the same density and flux terms as in the half - isotropic case .
the evolution is very similar .
we show the evolution of the first 21 multipoles in fig .
[ fig : multipoleevolution ] for the inverted hierarchy ; the picture is similar for the normal hierarchy .
the initial horizontal part of the curves corresponds to their zero initial value so that the offset by 0.1 vertical units between the curves is directly apparent .
initially , @xmath200 and @xmath203 are large , but quickly decay away by decoherence , whereas the higher multipoles vanish initially and get excited one after another , but then decrease again . the length of each multipole sports `` wiggles , '' i.e.
, the evolution is not monotonic .
moreover , they have large relative angles in the @xmath21-@xmath17 plane ( not shown here ) , i.e. , the spread of the inital excitation to larger and larger multipoles is far from simple in detail , but the overall process is as expected . in fig .
[ fig : multipoleevolution2 ] we show @xmath204 and @xmath205 as a function of @xmath104 at @xmath206 for the example of fig .
[ fig : multipoleevolution ] . at @xmath206 , multipoles @xmath207 are not yet excited
. the nearly linear increase of the phases between individual polarization vectors corresponds here to a diffusion of the `` multipole wave '' to larger @xmath104 with approximately constant speed , @xmath208 .
qualitatively , this can be understood as follows . the second line in eq .
( [ eq : eom6 ] ) together with the analogue of eq .
( [ eq : diffusion ] ) implies that @xmath209 the last term does not contribute to the growth of @xmath210 and can be ignored .
approximate equipartition between potential and kinetic energies in eq .
( [ eq : energy4 ] ) implies @xmath211 , as indeed was observed in fig .
[ fig : halfisotropic ] . the second term in eq .
( [ eq : n_growth ] ) then represents a combination of a drift in @xmath212space with velocity @xmath213 and diffusion with diffusion coefficient @xmath214 .
up to a factor @xmath215 this gives rise to an exponential factor @xmath216 $ ] . on the other hand , since @xmath217 for @xmath98 , the first term in eq .
( [ eq : n_growth ] ) can give rise to exponential growth whenever @xmath218 .
this growth will be non - monotonic , but can roughly be estimated as @xmath219 before @xmath220 saturates .
using perturbation theory , we will find a similar growth rate for @xmath221 at early times in sect .
[ sec : analytic ] . combining these two factors
, one sees that at time @xmath222 the wave front of @xmath223 , and thus also of @xmath196 , should be located at @xmath208 , which , according to figs .
[ fig : multipoleevolution ] and [ fig : multipoleevolution2 ] indeed it is within about @xmath224% .
the slow decrease of @xmath196 and @xmath220 at late times can be interpreted as due to the @xmath215 factor in the diffusive behavior .
the overall behavior of the inverted - hierarchy case is qualitatively easy to understand . to this end
we consider an ensemble of polarization vectors @xmath225 , initially oriented in the @xmath17-direction , that rotate around the @xmath155-axis , each with a frequency @xmath68 , so that @xmath226 both @xmath68 and @xmath222 are normalized to be dimensionless .
if the frequencies are spread over @xmath227 , then the overall polarization vector evolves as @xmath228-\sin(t)}{t}\ , , \nonumber\\ p^x_0&=&\int_1^{1+\delta u}\!\!du\,\sin(u t ) = \frac{\cos(t)-\cos[(1+\delta u)\,t]}{t}\ , , \nonumber\\ |{\bf p}_0|&=&\left[(p^x_0)^2+(p^z_0)^2\right]^{1/2 } = \frac{2\,|\sin(\delta u\,t/2)|}{t}\,.\end{aligned}\ ] ] for @xmath229 we show in fig .
[ fig : toy1 ] the evolution of @xmath230 ( solid line ) and the length @xmath231 ( dashed line ) . in fig .
[ fig : toy2 ] we show the trajectory of @xmath181 in the @xmath21-@xmath17-plane .
unsurprisingly , this simple model represents qualitatively the features of the inverted - hierarchy case . in particular , the trajectory in the @xmath21-@xmath17-plane is not a true spiral , but there are many crossings of the origin as the length of the overall polarization vector shrinks .
its length does not shrink monotonically .
its envelope decreases as a power law @xmath232 , not exponentially .
this example also shows that it is not trivial to define a useful measure of kinematical decoherence .
the @xmath17-component of the polarization vector is not useful because @xmath181 can tilt so that its @xmath17-component vanishes , i.e. , both flavors are present with the same probability , yet the flavor content of the ensemble is perfectly coherent . the length of @xmath181 is a much better measure in analogy to dynamical decoherence of a single mode where the length of @xmath9 is a measure of dynamical decoherence ; unit length would correspond to a pure state . in our case ,
the length of the individual @xmath9 is conserved , whereas the length of the total @xmath181 shrinks , but not monotonically .
it is not evident if there is an `` entropy '' measure that evolves monotonically as a consequence of kinematical decoherence .
we note , however , that the origin of kinematical decoherence is the differential evolution between neighboring polarization vectors . in our toy example
, the angle between neighboring polarization vectors grows linearly as @xmath233 and thus is a measure of decoherence .
motivated by this observation we can define the `` winding number '' @xmath234 in the symmetric case where the evolution of the polarization vectors is essentially restricted to the @xmath21-@xmath17-plane , this quantity tells us the number of windings around the @xmath155-direction of the full ensemble of polarization vectors . in fig .
[ fig : windingnumber ] we show the evolution of this quantity for the normal and inverted hierarchy examples of fig .
[ fig : halfisotropic ] .
@xmath28 counts how often the length of @xmath183 shrinks to zero .
closely related to kinematical decoherence are recurrence effects that arise when one uses a limited number of polarization vectors , i.e. , when the full ensemble is represented by a coarse - grained ( binned ) ensemble of polarization vectors or , in multipole space , when the series is truncated at some multipole @xmath93 . binning or truncation are unavoidable in numerical treatments and represent equivalent approximations .
if the phase differences evolve linearly between different polarization vectors as in the toy example of the previous section , then the initial state will recur when each polarization vector has turned around the @xmath155-axis by @xmath235 relative to its neighbors .
put another way , if we use @xmath236 bins to represent the polarization vectors , we expect recurrence to begin when @xmath237 .
we demonstrate this effect in fig .
[ fig : recurrence ] for the same example as in fig .
[ fig : halfisotropic ] , normal hierarchy , using @xmath238 .
indeed , the winding number increases until approximately @xmath239 and then decreases back to almost zero , and so forth .
this system is almost periodic on the recurrence time scale , reflecting that nonlinear effects play a subleading role here .
since a large flux term is present from the start , kinematical decoherence is very similar to the linear toy example of the previous section where recurrence would be exact and the system would be periodic with a frequency proportional to @xmath240 times the individual polarization vector s oscillation frequency . using the multipoles as the primary variables ,
the same recurrence effects occur due to the truncation @xmath93 of the multipole series .
the `` multipole wave '' of fig .
[ fig : multipoleevolution2 ] can only propagate up to @xmath241 , is then reflected , and eventually returns back to @xmath86 .
this is the moment of maximum recurrence of the overall polarization vector . for a more complicated example such as a realistic simulation of the supernova case
, recurrence effects may not be so obvious as here .
therefore , in a numerical treatment one must make sure that the largest relative angle developed between any two neighboring polarization vectors never grows to order unity , i.e. , one should monitor the largest relative angle between neighboring polarization vectors as a measure of accuracy of the calculation .
in other words , kinematical decoherence is a property of the entire ensemble , but can also be a a property of individual bins if they are too coarse .
one must make sure that within all individual bins kinematical decoherence remains negligible .
we next turn to a symmetric system that is perfectly isotropic except for an arbitrarily small but nonzero initial anisotropy .
we work in the multipole picture and assume that initially @xmath242 for all @xmath104 , @xmath243 for @xmath244 , @xmath245 and @xmath246 .
note that @xmath247 corresponds to a flux term equivalent to the half - isotropic case . as a first example we show in fig .
[ fig : nearisotropic ] the evolution of the overall polarization vector @xmath183 ( top ) for the normal hierarchy ( left ) and the inverted hierarchy ( right ) .
the initial anisotropy is @xmath248 and @xmath249 . for both hierarchies , kinematical decoherence eventually obtains . in the bottom panels we show the evolution of @xmath250 ( solid line ) as a proxy for @xmath195 which is the primary quantity that causes decoherence .
for the symmetric neutrino gas only the component @xmath251 is nonzero , but it can be negative and can change sign so that it is difficult to display on a logarithmic scale .
we also show the evolution of the `` potential energy '' @xmath173 ( dotted line ) .
for the normal hierarchy , @xmath251 grows exponentially after a short initial transient . while @xmath251 is small
, the potential energy @xmath173 performs the usual oscillations of a harmonic oscillator , complemented by the opposite oscillations of the kinetic energy @xmath252 ( not shown ) that is entirely dominated by @xmath194 .
as @xmath251 grows , it eventually dominates the kinetic energy and the end state is approximately @xmath253 and @xmath254 , with @xmath193 dominating @xmath174 . in other words ,
the end state is exactly as in the previous case with a large initial anisotropy .
the crucial novel feature is that the flux term grows exponentially from a small value .
this is a purely nonlinear effect caused by neutrino - neutrino interactions . for smaller mixing angles and/or other values of @xmath255 ,
the behavior is analogous .
the rising part of the @xmath193 curve is the same , except that it shifts vertically in direct proportion to @xmath255 and @xmath256 . for the inverted hierarchy ,
the evolution is far more complicated .
while @xmath251 grows in an average sense , this evolution is overlaid with oscillations and in fact @xmath251 changes sign at each spike in the @xmath193 curve . moreover ,
the evolution of the envelope of the @xmath193 curve is not monotonic .
it can perform complicated motions , with growing , declining , and nearly flat phases , until finally decoherence obtains . from these numerical observations
we tentatively conclude that an isotropic neutrino ensemble of equal densities of neutrinos and antineutrinos is not stable .
a small flux term triggers a run - away evolution towards kinematical decoherence . as a starting point for an analytic understanding of this instability
we use the equations of motion eq .
( [ eq : eom6 ] ) for the vectors @xmath196 and @xmath220 .
initially only @xmath183 is of order one , @xmath257 , and all others vanish .
as long as @xmath195 is sufficiently small , none of the higher multipoles can grow large so that we can limit our attention to the equations for @xmath86 and @xmath258 , i.e. , to eqs .
( [ eq : eom6a ] ) and ( [ eq : eom6b ] ) .
we further observe that the @xmath86 equations are coupled to the higher multipoles only by the term @xmath259 , consisting of a product of two small quantities , i.e. , it is at least of order @xmath260 .
therefore , the evolution of the near - isotropic ensemble is identical with that of the isotropic case until @xmath195 has grown sufficiently large . in other words , up to second order in @xmath255 the @xmath86 equation is that of the isotropic case .
therefore , what remains to be solved is the @xmath258 equation . after neglecting terms involving @xmath244
all we need to study is @xmath261 where @xmath262 and @xmath263 are the solutions of the unperturbed pendulum equations .
the equations simplify further in our case of equal @xmath11 and @xmath12 densities where symmetry dictates that all polarization vectors @xmath9 and @xmath146 evolve as each other s mirror images relative to the @xmath21-@xmath17-plane , the latter being singled out by our choice that @xmath19 lies in that plane . in this case
all @xmath220 vectors are parallel to the @xmath155-axis , whereas all @xmath196 vectors are confined to the @xmath21-@xmath17-plane . as a consequence ,
the @xmath264 term drops out .
the second equation then implies @xmath265 , and with the first equation yields @xmath266 + \omega\mu{\bf b}\times\left({\bf d}_0\times{\bf s}_1\right)\,.\ ] ] expanding the triple product , observing that in our case @xmath267 , and using @xmath268 this is @xmath269 we repeat that all @xmath220 are here parallel to each other and to the @xmath155-axis . in the absence of neutrino - neutrino interactions ( @xmath270 )
, @xmath195 obeys a harmonic - oscillator equation . in a dense neutrino gas , @xmath271
, we may ignore the term proportional to @xmath272 . since during the growth phase , @xmath273 and @xmath274 , the last term in eq .
( [ eq : ddot ] ) can also be neglected . a possible exponential growth is then accounted for by the term @xmath275 where we have used the bipolar oscillation frequency @xmath276 and we note that initially @xmath172 and that its length remains nearly constant if @xmath277 unless there is kinematical decoherence .
if the mixing angle is small , the `` normal hierarchy '' is defined by neutrinos being essentially in the lower mass eigenstate or @xmath278 up to corrections of order @xmath279 .
therefore , the critical part of the equation of motion for the flux term is approximately @xmath280 the solution includes growing modes of the form @xmath281 where @xmath282 is the dimensionless time variable used in all of our plots , i.e. , time in units of the bipolar oscillation period .
this behavior is numerically verified in the lower - left panel of fig .
[ fig : nearisotropic ] if we recall that the plotted quantity is @xmath283 $ ] .
once more we note that the crucial absolute sign in eq .
( [ eq : expgrowth2 ] ) is traced back to the negative sign in the term @xmath284 in eq .
( [ eq : eom1 ] ) .
therefore , the instability of the near - isotropic neutrino gas , for the normal hierarchy , is not just caused by different angular modes experiencing different neutrino - neutrino effects .
this would also be the case for a hypothetical term @xmath285 that naively looks very similar , but causes a completely different overall behavior . in more complicated numerical situations , e.g. , for a full supernova simulation , it is easy to change this sign in order to diagnose the relevance of the term eq .
( [ eq : expgrowth1 ] ) for the overall behavior of the system .
initially @xmath286 so that the exponential growth term alone is not enough .
the initial evolution is dominated by the second line of eq .
( [ eq : eom6c ] ) that is initially @xmath287 where @xmath288 and we have used @xmath289 and @xmath290 . here the absolute sign is not critical because it does not matter if @xmath195 grows in the positive or negative @xmath155-direction .
the first factor @xmath291 sets the overall scale for @xmath195 . from the expression for the energy we note that @xmath292 and @xmath293 appear in the combinations @xmath294 .
the quantities @xmath196 are of order unity , whereas the natural scale for @xmath220 is @xmath291 .
the initial evolution is @xmath295 where , again , @xmath296 is our usual measure of time .
this linear growth is shown in fig .
[ fig : initialevolution ] as a dotted line and agrees with the numerical examples . besides a transient caused by the other terms in the equation , the exponential growth takes over after a time of order @xmath177 .
we conclude that the initial value of @xmath297 for its exponential growth is of order @xmath298 so that it grows to order unity within a time scale of order @xmath299 . for the inverted hierarchy
, the initial growth of @xmath300 is the same ( dashed line in fig .
[ fig : initialevolution ] ) . after that , however , the situation is entirely different because initially @xmath301 .
this corresponds to the pendulum starting in a nearly upright position from where it starts almost full - circle oscillations . for our usual assumption
@xmath156 the term @xmath302 is almost identical with @xmath179 shown in the upper - right panel of fig .
[ fig : nearisotropic ] . this term changes sign during every swing of the pendulum . during the phases when @xmath303 , @xmath195 oscillates whereas during the phases @xmath304 exponential growth obtains .
these are the relatively short phases when the pendulum is oriented downward , whereas it stays upright for long periods if the mixing angle is small .
we illustrate this behavior in fig .
[ fig : initialevolution2 ] where we show the evolution of @xmath300 overlaid with that of @xmath179 .
we have chosen an extremely small mixing angle , @xmath305 , to obtain long plateaus for @xmath179 where the pendulum stands almost still in an almost upright position . during these phases we have
@xmath306 so that eq .
( [ eq : expgrowth1 ] ) implies harmonic oscillations of @xmath300 with the frequency @xmath307 as borne out by the example in fig .
[ fig : initialevolution2 ] .
the frequency @xmath307 is not matched to the pendulum s oscillation period because the duration of the `` plateaus '' depend logarithmically on @xmath256 .
therefore , the short exponential growth phases when @xmath308 occur at erratic instances relative to the harmonic @xmath195 oscillation .
this interplay explains the erratic behavior of the @xmath195 evolution that is apparent in fig .
[ fig : nearisotropic ] and that obtains in all numerical examples .
this interplay also explains why small changes of parameters such as @xmath256 can completely change the overall @xmath195 evolution .
therefore , we can not prove if there is some specific combination of parameters where kinematical decoherence will not occur , although this would have to be isolated parameter points that presumably have measure zero in parameter space if they exist at all . except for this caveat
we conclude that both for the normal and inverted hierarchy kinematical decoherence is an unavoidable consequence of the nonlinear neutrino - neutrino interaction terms .
an infinitesimally small , but nonzero , deviation from isotropy is enough to trigger an exponential evolution towards flavor equilibrium .
therefore , the pendulum solution that describes the behavior of a perfectly isotropic gas is merely an unstable limit cycle of this nonlinear system .
we have investigated multi - angle kinematical decoherence effects in a dense neutrino gas consisting of equal @xmath11 and @xmath12 densities .
the current - current nature of the weak - interaction hamiltonian implies that a current of the background medium causes kinematical decoherence between neutrinos propagating in different directions .
this simple effect becomes entirely nontrivial in the most interesting case when the `` background current '' is caused by the neutrinos themselves .
we have shown that a neutrino gas of this sort is not stable in flavor space .
if one prepares the ensemble in a given flavor state , even a small deviation from isotropy is enough to trigger an exponential evolution towards flavor equipartition , even when the mixing angle is small .
up to logarithmic corrections , the time scale is determined by the bipolar oscillation period .
we thus have to do with a self - induced macroscopic pair conversion process that proceeds much faster than ordinary pair processes that occur at order @xmath309 .
with hindsight this is probably the same `` speed - up effect '' discussed in ref .
however , the fast speed @xmath310 is not introduced by the multi - angle effect as is perhaps suggested in ref .
rather , @xmath26 is the bipolar oscillation frequency that is inherent even in the isotropic system . for the normal hierarchy
`` nothing '' seems to happen in the isotropic case , although this would be a misperception because the system moves with the speed @xmath26 , but the amplitude is small if @xmath311 . in any event , we agree with the importance of multi - angle effects and with the end result conjectured in ref .
@xcite that complete flavor equipartition obtains on a time scale @xmath312 .
however , we have found no indication that an even faster time scale @xmath313 plays any role , in contrast to what was conjectured in ref .
@xcite .
of course , flavor equipartition obtains only in a macroscopic sense with some degree of coarse graining in phase space .
it is the nature of kinematical decoherence that information is not lost and the entropy does not increase . on the other hand , kinematical and dynamical decoherence are not always operationally distinguishable .
it is not necessarily possible to distinguish between a neutrino gas in true chemical equilibrium and one where neighboring modes are simply `` de - phased '' relative to each other . either way , the `` self - maintained coherence '' of a dense neutrino gas represents only an unstable limiting form of behavior of the perfectly isotropic case . since no gas can be perfectly isotropic , self - induced decoherence is the generic behavior of a symmetric @xmath13 gas .
contrary to a naive expectation , the fact that neutrinos propagating in different directions experience different weak potentials is necessary , but not sufficient , to cause multi - angle decoherence .
the negative sign in the lorentz metric plays a crucial role because it determines that the flux term grows exponentially rather than oscillating .
the occurrence of kinematical decoherence is a subtle feature of the nonlinear equations .
we have studied the simplest possible case where decoherence effects obtain .
a more realistic case is provided by neutrinos streaming off a supernova core . in this case
the fluxes of neutrinos and antineutrinos are different and geometry implies that the neutrino - neutrino interaction strength declines with the fourth power of radius .
the evolution of an asymmetric system is far more complicated , even in the isotropic case , where the simple pendular motion turns into one of a spinning top that can precess , nutate , or simply swing , depending on the @xmath13 asymmetry . in the supernova context ,
transitions between these modes occur as @xmath314 declines as a function of radius .
multi - angle decoherence can not occur , for example , in regions where synchronized oscillations prevail .
numerical simulations suggest that for neutrinos streaming off a supernova core , the collective behavior characteristic of an isotropic gas prevails in many situations , i.e. , kinematical decoherence occurs , but is not the dominating feature of the system , contrary to what we have found here for the symmetric @xmath13 gas . evidently it is not straightforward to apply the insights gained from our present study to the supernova case .
we imagine , however , that the methods developed here may take us one step further to understand the supernova problem .
we have formulated the equations of motion in a novel form adapted to the problem of multi - angle propagation , i.e. , we have used a multipole expansion rather than the usual momentum modes and we have used the particle number and lepton number polarization vectors ( or density matrices ) as the fundamental variables . in this way ,
the crucial exponentially growing quantity , our @xmath195 , could be isolated as the primary cause of kinematical decoherence .
this approach may prove useful for understanding the supernova problem as well .
for numerical three - flavor studies we have provided an expression for the conserved energy of the system in terms of the density matrices .
the conserved energy and its three components @xmath173 , @xmath194 and @xmath193 provide a useful diagnostic tool for the behavior of the system .
even simple nonlinear systems can exhibit a surprisingly rich phenomenology .
it is fascinating that the neutrinos streaming off a supernova core provide an intriguing case in point where many aspects of its behavior remain to be understood .
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a gas of this sort is unstable in that an infinitesimal anisotropy is enough to trigger a run - away towards flavor equipartition .
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SECTION 1. SHORT TITLE.
This Act may be cited as the ``Infant Crib Safety Act''.
SEC. 2. FINDINGS; PURPOSE.
(a) Findings.--Congress makes the following findings:
(1) The disability and death of infants resulting from
injuries sustained in crib incidents are a serious threat to
the public health, welfare, and safety of people of this
country.
(2) The design and construction of a baby crib must ensure
that it is safe to leave an infant unattended for extended
periods of time. A parent or caregiver has a right to believe
that the crib in use is a safe place to leave an infant.
(3) Each year more than 12,000 children ages 2 and under
are injured in cribs seriously enough to require hospital
treatment.
(4) Each year at least 50 children ages 2 and under die
from injuries sustained in cribs.
(5) The United States Consumer Product Safety Commission
estimates that the cost to society resulting from deaths due to
cribs is at least $225,000,000 per year.
(6) Secondhand, hand-me-down, and heirloom cribs pose a
special problem. There are nearly 4 million infants born in
this country each year, but only one million new cribs sold. As
many as 2 out of 4 infants are placed in secondhand, hand-me-
down, or heirloom cribs.
(7) Most crib deaths occur in secondhand, hand-me-down, or
heirloom cribs.
(8) Existing State and Federal legislation is inadequate to
deal with the hazard presented by secondhand, hand-me-down, or
heirloom cribs.
(9) Prohibiting the contracting to sell, resell, lease,
sublease of unsafe cribs that are not new, or otherwise place
in the stream of commerce unsafe secondhand, hand-me-down, or
heirloom cribs, will prevent injuries and deaths caused by
cribs.
(b) Purpose.--The purpose of this Act is to prevent the occurrence
of injuries and deaths to infants as a result of unsafe cribs by making
it illegal--
(1) to manufacture, sell, or contract to sell any crib that
is unsafe for any infant using it; or
(2) to resell, lease, sublet, or otherwise place in the
stream of commerce, after the effective date of this Act, any
unsafe crib, particularly any unsafe secondhand, hand-me-down,
or heirloom crib.
SEC. 3. DEFINITIONS.
As used in this Act:
(1) Commercial user.--The term ``commercial user'' means
any person--
(A) who manufactures, sells, or contracts to sell
full-size cribs or nonfull-size cribs; or
(B) who--
(i) deals in full-size or nonfull-size
cribs that are not new or who otherwise by
one's occupation holds oneself out as having
knowledge or skill peculiar to full-size cribs
or nonfull-size cribs, including child care
facilities and family child care homes; or
(ii) is in the business of contracting to
sell or resell, lease, sublet, or otherwise
placing in the stream of commerce full-size
cribs or nonfull-size cribs that are not new.
(2) Crib.--The term ``crib'' means a full-size crib or
nonfull-size crib.
(3) Full-size crib.--The term ``full-size crib'' means a
full-size baby crib as defined in section 1508.1 of title 16 of
the Code of Federal Regulations.
(4) Infant.--The term ``infant'' means any person less than
35 inches tall or less than 2 years of age.
(5) Nonfull-size crib.--The term ``nonfull-size crib''
means a nonfull-size baby crib as defined in section 1509.2(b)
of title 16 of the Code of Federal Regulations (including a
portable crib and a crib-pen described in paragraph (2) of
subsection (b) of that section).
SEC. 4. PROHIBITIONS.
(a) In General.--It shall be unlawful for any commercial user--
(1) to manufacture, sell, or contract to sell, any full-
size crib or nonfull-size crib that is unsafe for any infant
using it; or
(2) to sell, contract to sell or resell, lease, sublet, or
otherwise place in the stream of commerce, any full-size or
nonfull-size crib that is not new and that is unsafe for any
infant using the crib.
(b) Lodgings.--It shall be unlawful for any hotel, motel, or
similar transient lodging facility to offer or provide for use or
otherwise place in the stream of commerce, on or after the effective
date of this Act, any full-size crib or nonfull-size crib that is
unsafe for any infant using it.
SEC. 5. CRIB STANDARDS.
A crib shall be presumed to be unsafe under this Act if it does not
conform to all of the following:
(1) Part 1508 (commencing with section 1508.1) of title 16
of the Code of Federal Regulations.
(2) Part 1509 (commencing with section 1509.1) of title 16
of the Code of Federal Regulations.
(3) Part 1303 (commencing with section 1303.1) of title 16
of the Code of Federal Regulations.
(4) American Society for Testing Materials Voluntary
Standard F.406.
(5) American Society for Testing Materials Voluntary
Standards F966.
(6) American Society for Testing Materials Voluntary
Standards F1169.
(7) American Society for Testing Materials Voluntary
Standards F1822.
(8) Any regulations or standards that are adopted in order
to amend or supplement the regulations described in paragraphs
(1) through (7).
SEC. 6. EXCEPTIONS.
This Act shall not apply to a full-size crib or nonfull-size crib
that is not intended for use by an infant, including a toy or display
item, if at the time it is manufactured, made subject to a contract to
sell or resell, leased, subletted, or otherwise placed in the stream of
commerce, as applicable, it is accompanied by a notice to be furnished
by each commercial user declaring that the crib is not intended to be
used for an infant and is dangerous to use for an infant.
SEC. 7. ENFORCEMENT.
(a) Civil Penalty.--Any commercial user, hotel, motel, or similar
transient lodging facility that knowingly violates section 4 is subject
to a civil penalty not exceeding $1,000.
(b) Injunction.--Any person may bring an action in a district court
of the United States against any commercial user, hotel, motel, or
similar transient lodging facility to enjoin any act or omission that
violates section 4, and for reasonable attorneys fees and costs
incurred in bringing the action.
SEC. 8. REMEDIES.
Penalties or other remedies available under this Act are in
addition to any other fines, penalties, remedies, or procedures under
any other provision of law.
SEC. 9. EFFECTIVE DATE.
This Act shall become effective 90 days after the date of its
enactment. | Infant Crib Safety Act - Makes it unlawful for any commercial user to: (1) manufacture, sell, or contract to sell any full-size or nonfull-size crib which is unsafe for any infant; or (2) sell, contract to sell or resell, lease, sublet, or otherwise place in the stream of commerce any such crib which is not new and is unsafe for any infant. Makes it unlawful for any lodging facility to offer or provide such an unsafe crib. Presumes as unsafe a crib which does not conform to specified standards in the Code of Federal Regulations and the American Society for Testing Materials Voluntary Standards, unless labeled as dangerous for an infant and not intended to be used for one.Authorizes a fine and injunction against violators of this Act. | <s>[INST]SECTION 1. SHORT TITLE.
This Act may be cited as the ``Infant Crib Safety Act''.
SEC. 2. FINDINGS; PURPOSE.
(a) Findings.--Congress makes the following findings:
(1) The disability and death of infants resulting from
injuries sustained in crib incidents are a serious threat to
the public health, welfare, and safety of people of this
country.
(2) The design and construction of a baby crib must ensure
that it is safe to leave an infant unattended for extended
periods of time. A parent or caregiver has a right to believe
that the crib in use is a safe place to leave an infant.
(3) Each year more than 12,000 children ages 2 and under
are injured in cribs seriously enough to require hospital
treatment.
(4) Each year at least 50 children ages 2 and under die
from injuries sustained in cribs.
(5) The United States Consumer Product Safety Commission
estimates that the cost to society resulting from deaths due to
cribs is at least $225,000,000 per year.
(6) Secondhand, hand-me-down, and heirloom cribs pose a
special problem. There are nearly 4 million infants born in
this country each year, but only one million new cribs sold. As
many as 2 out of 4 infants are placed in secondhand, hand-me-
down, or heirloom cribs.
(7) Most crib deaths occur in secondhand, hand-me-down, or
heirloom cribs.
(8) Existing State and Federal legislation is inadequate to
deal with the hazard presented by secondhand, hand-me-down, or
heirloom cribs.
(9) Prohibiting the contracting to sell, resell, lease,
sublease of unsafe cribs that are not new, or otherwise place
in the stream of commerce unsafe secondhand, hand-me-down, or
heirloom cribs, will prevent injuries and deaths caused by
cribs.
(b) Purpose.--The purpose of this Act is to prevent the occurrence
of injuries and deaths to infants as a result of unsafe cribs by making
it illegal--
(1) to manufacture, sell, or contract to sell any crib that
is unsafe for any infant using it; or
(2) to resell, lease, sublet, or otherwise place in the
stream of commerce, after the effective date of this Act, any
unsafe crib, particularly any unsafe secondhand, hand-me-down,
or heirloom crib.
SEC. 3. DEFINITIONS.
As used in this Act:
(1) Commercial user.--The term ``commercial user'' means
any person--
(A) who manufactures, sells, or contracts to sell
full-size cribs or nonfull-size cribs; or
(B) who--
(i) deals in full-size or nonfull-size
cribs that are not new or who otherwise by
one's occupation holds oneself out as having
knowledge or skill peculiar to full-size cribs
or nonfull-size cribs, including child care
facilities and family child care homes; or
(ii) is in the business of contracting to
sell or resell, lease, sublet, or otherwise
placing in the stream of commerce full-size
cribs or nonfull-size cribs that are not new.
(2) Crib.--The term ``crib'' means a full-size crib or
nonfull-size crib.
(3) Full-size crib.--The term ``full-size crib'' means a
full-size baby crib as defined in section 1508.1 of title 16 of
the Code of Federal Regulations.
(4) Infant.--The term ``infant'' means any person less than
35 inches tall or less than 2 years of age.
(5) Nonfull-size crib.--The term ``nonfull-size crib''
means a nonfull-size baby crib as defined in section 1509.2(b)
of title 16 of the Code of Federal Regulations (including a
portable crib and a crib-pen described in paragraph (2) of
subsection (b) of that section).
SEC. 4. PROHIBITIONS.
(a) In General.--It shall be unlawful for any commercial user--
(1) to manufacture, sell, or contract to sell, any full-
size crib or nonfull-size crib that is unsafe for any infant
using it; or
(2) to sell, contract to sell or resell, lease, sublet, or
otherwise place in the stream of commerce, any full-size or
nonfull-size crib that is not new and that is unsafe for any
infant using the crib.
(b) Lodgings.--It shall be unlawful for any hotel, motel, or
similar transient lodging facility to offer or provide for use or
otherwise place in the stream of commerce, on or after the effective
date of this Act, any full-size crib or nonfull-size crib that is
unsafe for any infant using it.
SEC. 5. CRIB STANDARDS.
A crib shall be presumed to be unsafe under this Act if it does not
conform to all of the following:
(1) Part 1508 (commencing with section 1508.1) of title 16
of the Code of Federal Regulations.
(2) Part 1509 (commencing with section 1509.1) of title 16
of the Code of Federal Regulations.
(3) Part 1303 (commencing with section 1303.1) of title 16
of the Code of Federal Regulations.
(4) American Society for Testing Materials Voluntary
Standard F.406.
(5) American Society for Testing Materials Voluntary
Standards F966.
(6) American Society for Testing Materials Voluntary
Standards F1169.
(7) American Society for Testing Materials Voluntary
Standards F1822.
(8) Any regulations or standards that are adopted in order
to amend or supplement the regulations described in paragraphs
(1) through (7).
SEC. 6. EXCEPTIONS.
This Act shall not apply to a full-size crib or nonfull-size crib
that is not intended for use by an infant, including a toy or display
item, if at the time it is manufactured, made subject to a contract to
sell or resell, leased, subletted, or otherwise placed in the stream of
commerce, as applicable, it is accompanied by a notice to be furnished
by each commercial user declaring that the crib is not intended to be
used for an infant and is dangerous to use for an infant.
SEC. 7. ENFORCEMENT.
(a) Civil Penalty.--Any commercial user, hotel, motel, or similar
transient lodging facility that knowingly violates section 4 is subject
to a civil penalty not exceeding $1,000.
(b) Injunction.--Any person may bring an action in a district court
of the United States against any commercial user, hotel, motel, or
similar transient lodging facility to enjoin any act or omission that
violates section 4, and for reasonable attorneys fees and costs
incurred in bringing the action.
SEC. 8. REMEDIES.
Penalties or other remedies available under this Act are in
addition to any other fines, penalties, remedies, or procedures under
any other provision of law.
SEC. 9. EFFECTIVE DATE.
This Act shall become effective 90 days after the date of its
enactment.[/INST]Infant Crib Safety Act - Makes it unlawful for any commercial user to: (1) manufacture, sell, or contract to sell any full-size or nonfull-size crib which is unsafe for any infant; or (2) sell, contract to sell or resell, lease, sublet, or otherwise place in the stream of commerce any such crib which is not new and is unsafe for any infant. Makes it unlawful for any lodging facility to offer or provide such an unsafe crib. Presumes as unsafe a crib which does not conform to specified standards in the Code of Federal Regulations and the American Society for Testing Materials Voluntary Standards, unless labeled as dangerous for an infant and not intended to be used for one.Authorizes a fine and injunction against violators of this Act.</s> |
little is known about the history of the universe at redshifts @xmath7 , corresponding to @xmath8 years after the big bang , and only recently have astrophysicists begun to seriously investigate this crucial post - recombination era . at @xmath9
, the photons of the cosmic microwave background ( cmb ) shifted into the infrared , and the universe entered what has been termed the `` dark ages '' ( rees 1999 ) .
we know that the universe was reionized again before a redshift of @xmath10 from the absence of gunn - peterson absorption in the spectra of high redshift quasars .
one of the grand challenges in modern cosmology is to determine when the universe was lit up again by the first luminous objects ( the so - called population iii ) which were responsible for reionizing and reheating the intergalactic medium ( haiman & loeb 1997 ; ferrara 1998 ) .
the very first generation of stars must have formed out of probably unmagnetized , pure h / he gas , since heavy elements can only be produced in the interior of stars .
these characteristics render the primordial star formation problem very different from the present - day case , and lead to a significant simplification of the relevant physics ( larson 1998 ; loeb 1998 ) . to determine the characteristic mass scale of the population iii stars , and to constrain their initial mass function ( imf ) , one has to study the collapse and fragmentation of metal - free gas .
this problem has been addressed by a number of authors ( e.g. , yoneyama 1972 ; hutchins 1976 ; carlberg 1981 ; kashlinsky & rees 1983 ; palla , salpeter , & stahler 1983 ; silk 1983 ; haiman , thoul , & loeb 1996 ; uehara et al .
1996 ; tegmark et al .
1997 ; omukai & nishi 1998 ; nakamura & umemura 1999 ) . recently
, three - dimensional cosmological simulations have reached sufficient resolution on very small scales to approach the population iii star formation problem ( anninos & norman 1996 ; ostriker & gnedin 1996 ; abel et al .
1998a ) .
complementary to these last studies , we explore the fragmentation of primordial gas under a variety of initial conditions .
our method allows us to follow the evolution of the fragments for a few dynamical times , and to include the physics of competitive accretion .
these capabilities are crucial for the investigation of the resulting mass spectrum . a more detailed exposition of our code , together with further results of our exploratory survey , will be presented in a forthcoming publication ( bromm , coppi , & larson 1999 ) . in this letter , we focus on one representative experiment which addresses the key question : _ how does the fragmentation of the first collapsing gas clouds proceed in a hierarchical ( bottom up ) scenario of structure formation ? _
our code is based on a version of treesph ( hernquist & katz 1989 ) which combines the smoothed particle hydrodynamics ( sph ) method ( e.g. , monaghan 1992 ) with a hierarchical ( tree ) gravity solver . to study primordial gas ,
we have made a number of additions .
most importantly , radiative cooling due to hydrogen molecules has been taken into account . in the absence of metals ,
h@xmath11 is the main coolant below @xmath12 k , the typical temperature range in collapsing population iii objects .
we implement the h@xmath11 cooling function given by galli & palla ( 1998 ) . at temperatures approaching @xmath13 k , cooling due to lines of atomic hydrogen
dominates ( katz & gunn 1991 ) .
the efficiency of h@xmath11 cooling is very sensitive to the h@xmath11 abundance .
therefore , it is necessary to compute the nonequilibrium evolution of the primordial chemistry .
we take into account the six species h , h@xmath14 , h@xmath15 , h@xmath11 , h@xmath16 , and e@xmath15 .
helium is neglected , since the temperatures in our application are low enough ( @xmath17 k ) to render the he species almost inert .
reaction rates are taken from haiman et al .
in addition , we have included 3-body reactions which become important at high density ( @xmath18 @xmath5 ) , and can convert the gas almost completely into molecular form ( palla et al . 1983 ) .
the chemistry network is solved by the approximate backwards differencing formula ( bdf ) method ( anninos et al .
1997 ) .
we have devised an algorithm to merge sph particles in high density regions to overcome the otherwise prohibitive timestep limitation , as enforced by the courant stability criterion ( bate , bonnell , & price 1995 ) . to follow the simulation for a few dynamical times , we allow sph particles to merge into more massive ones , provided they exceed a pre - determined density threshold , typically @xmath19 @xmath5 .
more details of the merging algorithm will be given in bromm et al .
within a hierarchical cosmogony , the very first stars are expected to form out of @xmath20 peaks in the random field of primordial density fluctuations .
the early ( linear ) evolution of such a peak , assumed to be an isolated and roughly spherical overdensity , can be described by the top - hat model ( e.g. , padmanabhan 1993 ) .
we use the top - hat approximation to specify the initial dark matter ( dm ) configuration , where we choose the background universe to be described by the critical einstein - de sitter solution with density parameters : @xmath21 , @xmath22 , and hubble constant @xmath23 km s@xmath24 mpc@xmath24)=0.5 . in this paper
, we investigate the fate of a @xmath25 peak of total mass @xmath1 , corresponding to @xmath26 in baryons which is close to the cosmological jeans mass ( couchman & rees 1986 ) . on this mass scale , the standard cold dark matter ( cdm ) scenario predicts a present - day r.m.s .
overdensity of @xmath27 , with a normalization @xmath28 on the @xmath29mpc scale .
then , one can estimate the redshift of collapse ( or virialization ) from : @xmath30 , leading to @xmath2 .
our simulation is initialized at @xmath31 , by performing the following steps .
the collisionless dm particles are placed on a cubical cartesian grid , and are then perturbed according to a given power spectrum @xmath32 , by applying the zeldovich approximation ( zeldovich 1970 ) which also allows to self - consistently assign initial velocities .
the power - law index is set to @xmath33 which is the asymptotic small - scale behavior in the standard cdm model ( peebles 1993 ) .
the amplitude @xmath34 is adjusted , so that the fundamental mode ( i.e. , the smallest contributing wavenumber @xmath35 ) , has an initial mean square overdensity which grows to @xmath36 at collapse .
next , particles within a ( proper ) radius of @xmath37 150 pc are selected for the simulation .
the resulting number of dm particles is @xmath38 .
finally , the particles are set into rigid rotation and are endowed with a uniform hubble expansion ( see also katz 1991 ) .
angular momentum is added by assuming a spin - parameter @xmath39 , where @xmath40 , @xmath41 , and @xmath42 are the total angular momentum , energy , and mass , respectively .
the collisional sph particles ( @xmath43 in this simulation ) are randomly placed to approximate a uniform initial density .
the random sampling inevitably introduces shot - noise .
the dm particles were set up on a regular grid specifically to avoid the unphysical shot - noise distribution which could mask the desired physical power spectrum . for the gas , however , the presence of the shot noise is not a big problem , since the gas mass is initially smaller than the jeans mass .
therefore , sound waves will efficiently wipe out all initial density disturbances .
the sph particles are endowed with the same hubble expansion and rigid rotation as the dm ones . since @xmath44 , heating , cooling , and photoreactions due to the cmb can be safely neglected here . for the chemical abundances and the gas temperature
, we adopt the initial values ( see tegmark et al .
1997 ) : @xmath45 , @xmath46 , and @xmath47 k , where @xmath48 , @xmath49 are the initial free electron and h@xmath11 abundances , respectively .
the use of a more realistic rate for the photodissociation of h@xmath16 predicts a lower initial h@xmath11 abundance , typically @xmath50 .
the evolution of a simulation initialized with such a lower value , however , quickly converges to the case presented in this paper . from turnaround ( @xmath51 ) to the moment of collapse ( @xmath52 ) , both the dm and the gas are freely falling . in response to the initially imprinted @xmath53 noise ,
the dm develops marked substructure .
this happens in a hierarchical fashion , where smaller clumps form first , and rapidly merge into larger aggregations .
the gas initially falls together with the dm , heating up adiabatically , @xmath54 for @xmath55 , until the temperature reaches the virial value of @xmath56 5000 k which is determined by the depth of the dm potential well .
the virialized gas is able to cool efficiently , and the temperature decreases again with continuing compression down to a few 100 k. at first , the gas is not able to condense onto the shallow dm potential wells , and its mass distribution remains smooth . in the course of the collapse , however , the baryonic jeans mass decreases enough to eventually allow the gas to fall into the deepening dm troughs .
this gravitational `` head - start '' is important because it determines where fragmentation occurs first , resulting in the most massive gas clumps .
briefly after collapse , all the substructure in the dm has been wiped out in the process of violent relaxation ( lynden - bell 1967 ) which is very effective in quickly establishing virial equilibrium on the dynamical timescale of the dm halo ( @xmath57 years ) . before
having been wiped out , however , the dm substructure has left its imprint on the gas , determining the morphology of the incipient disk .
the dm reaches an equilibrium configuration with a core radius of @xmath58 10 pc and an approximately isothermal density profile ( @xmath59 ) further out .
the central gas disk is horizontally supported by rotation . in the presence of a dm halo , one expects a contraction by a factor of @xmath60 for rotational support .
the dimension of the disk , as shown in figure 2 , is in good accordance with this prediction .
vertically , the disk is roughly pressure supported with a scale height of @xmath61 2 pc , where @xmath62 2 km / s is the sound speed , and @xmath63 the gas surface density .
the resulting disk has a very filamentary and knotty structure with typical densities of @xmath64 @xmath5 and temperatures of @xmath65 k , corresponding to a jeans mass of @xmath3 .
we next discuss the fragmentation of these filamentary features . the gas which makes up the filaments is jeans unstable since @xmath66 , where the free - fall time is @xmath67 , and the sound - crossing time @xmath68 .
@xmath69 15 pc is the radius of the disk . in figure 1 ,
the free - fall time is compared to the sound - crossing time and to the cooling time , @xmath70 . here , @xmath71 is the fractional h@xmath11 abundance , and @xmath40 the cooling rate ( in erg s@xmath24 @xmath72 ) . for densities @xmath73 @xmath5 , the gas becomes jeans unstable .
the onset of instability roughly coincides with the condition that @xmath74 .
the value @xmath75 @xmath5 is also the critical density for the rotational - vibrational levels of h@xmath11 being populated according to local thermodynamic equilibrium ( lte ) .
the first regions to undergo runaway collapse lead to the formation of dense ( @xmath4 @xmath5 ) gas clumps of mass @xmath76 .
the dynamical state of a typical clump can be described by the ratios @xmath77 , and @xmath78 , where @xmath79 , @xmath80 , @xmath81 are the thermal , rotational , and gravitational energies of the clump .
the further evolution of the disk consists of a complex history of new clumps forming , and old ones continually accreting gas and occasionally merging with other clumps .
the outcome of this evolution is shown in figure 2 , corresponding to the situation at @xmath82 .
the disk - like structure has fragmented into 13 clumps , ranging in mass from 220 to @xmath6 . at this stage
, @xmath5850% of the total gas mass has been incorporated into high density clumps .
this fraction is unrealistically high due to the homologous nature of the top - hat collapse where all particles reach the center at the same time .
abel et al .
( 1998a ) , on the other hand , estimate this fraction to be @xmath588% .
this value is more realistic , since these authors consider an overdensity which is initially already centrally concentrated , leading to a collapse which is spread out in time . since the larger clumps tend to retain their individuality , the final evolutionary state of the disk is expected to be a small cluster of isolated clumps .
figure 3 summarizes the thermodynamic state of the gas together with the chemical abundances .
when a region undergoes runaway collapse , particles are drawn from the quasi - stationary `` reservoir '' at @xmath64 @xmath5 which corresponds to the filamentary gas , and swiftly move to higher densities at roughly constant temperature ( fig .
3c ) . at a density of @xmath83@xmath5 ,
sph particles are merged into more massive ones , as described in 2 . at higher densities
, the jeans mass would decrease below the resolution limit ( @xmath84 ; bate & burkert 1997 ) of our simulation ( fig .
3d ) . in order to reliably follow the evolution of the gas to even higher densities , a larger number of sph particles would be needed . in this case
, one would expect the gas density to increase up to the point where the now fully molecular gas becomes opaque , and subsequently behaves adiabatically again .
the present study , however , has the purpose of following the evolution of many gas clumps for a few dynamical times .
therefore , merging at some point is inevitable .
we have discussed the evolution of a primordial star forming region in the context of the standard cdm model for structure formation . in the early stages of the collapse , the morphology of the dm substructure imprints a pattern onto the initially completely smooth gas which determines where gas fragmentation is to occur first .
therefore , the initial power spectrum of the dm fluctuations might be an important ingredient for primordial star formation . simultaneously with the virialization of the dm component ,
the gas dissipatively settles down into a compact central disk .
this disk has a very filamentary structure , and is jeans unstable which leads to fragmentation into clumps of initially @xmath85 .
these clumps grow in mass by both accreting surrounding gas , and by merging with other high - density clumps . at the end of this process
, a small number ( @xmath58 10 ) of these clumps have formed .
population iii stars , then , might have been quite massive , perhaps even ` very massive ' ( @xmath86 ) , if one assumes that a jeans mass clump does not undergo significant further fragmentation .
although subsequent fragmentation can not be excluded , this is expected to lead to the formation of a binary or a small multiple system , if experience from present - day star formation offers any guidance here ( larson 1998 ) .
our results agree well with those of abel , bryan , & norman ( 1998b ) who have applied the adaptive mesh refinement ( amr ) method to the problem .
these authors find a dense core of order a few times @xmath87 , which continues to accrete mass and shows no sign of further subfragmentation .
clearly , high resolution studies of the further clump evolution are necessary , including a treatment of opacity effects ( see omukai & nishi 1998 ) .
we are presently engaged in doing so and will present our findings in a future publication .
the effects of cooling due to hd molecules ( galli & palla 1998 ) , and of the presence of the cmb on the h@xmath11 level populations ( capuzzo - dolcetta , di fazio , & palla 1991 ) , were not included in our work , and both could affect the estimate of the jeans mass .
test calculations indicate that the effect of hd cooling may not significantly change our results , but a more complete treatment will be incorporated in subsequent work .
abel , t. , anninos , p. , norman , m. l. , & zhang , y. 1998a , , 508 , 518 abel , t. , bryan , g. l. , & norman , m. l. 1998b , preprint , ( astro - ph/9810215 ) anninos , p. , & norman , m. l. 1996 , , 460 , 556 anninos , p. , zhang , y. , abel , t. , & norman , m. l. 1997 , newa , 2 , 209 bate , m. r. , bonnell , i. a. , & price , n. m. 1995 , mnras , 277 , 362 bate , m. r. , & burkert , a. 1997 , mnras , 288 , 1060 bromm , v. , coppi , p. s. , & larson , r. b. 1999 , in preparation capuzzo - dolcetta , r. , di fazio , a. , & palla , f. 1991 , a&as , 88 , 451 carlberg , r. g. 1981 , mnras , 197 , 1021 couchman , h. m. p. , & rees , m. j. 1986 , mnras , 221 , 53 ferrara , a. 1998 , , 499 , l17 galli , d. , & palla , f. 1998 , a&a , 335 , 403 haiman , z. , thoul , a. a. , & loeb , a. 1996 , , 464 , 523 haiman , z. , & loeb , a. 1997 , , 483 , 21 hernquist , l. , & katz , n. 1989 , , 70 , 419 hutchins , j. b. 1976 , , 205 , 103 kashlinsky , a. , & rees , m. j. 1983 , mnras , 205 , 955 katz , n. 1991 , , 368 , 325 katz , n. , & gunn , j. e. 1991 , , 377 , 365 larson , r. b. 1998 , mnras , 301 , 569 loeb , a. 1998 , in asp conf . ser . 133 , science with the next generation space telescope , ed .
e. smith & a. koratkar ( san francisco : asp ) , 73 lynden - bell , d. 1967 , mnras , 136 , 101 monaghan , j. j. 1992 , ara&a , 30 , 543 nakamura , f. , & umemura , m. 1999 , , 515 , 239 omukai , k. , & nishi , r. 1998 , , 508 , 141 ostriker , j. p. , & gnedin , n. y. 1996 , , 472 , l63 padmanabhan , t. 1993 , structure formation in the universe ( cambridge : cambridge univ . press ) , 273 palla , f. , salpeter , e. e. , & stahler , s. w. 1983 , , 271 , 632 peebles , p. j. e. 1993 , principles of physical cosmology ( princeton : princeton univ .
press ) , 625 rees , m. j. 1999 , in aip conf .
470 , after the dark ages : when galaxies were young ( the universe at @xmath88 ) , ed .
s. s. holt & e. smith ( woodbury : aip ) , 13 silk , j. 1983 , mnras , 205 , 705 tegmark , m. , silk , j. , rees , m. j. , blanchard , a. , abel , t. , & palla , f. 1997 , , 474 , 1 uehara , h. , susa , h. , nishi , r. , yamada , m. , & nakamura , t. 1996 , , 473 , l95 yoneyama , t. 1972 , pasj , 24 , 87 zeldovich , y. b. 1970 , a&a , 5 , 84 | in order to constrain the initial mass function ( imf ) of the first generation of stars ( population iii ) , we investigate the fragmentation properties of metal - free gas in the context of a hierarchical model of structure formation .
we investigate the evolution of an isolated 3 @xmath0 peak of mass @xmath1 which collapses at @xmath2 using smoothed particle hydrodynamics .
we find that the gas dissipatively settles into a rotationally supported disk which has a very filamentary morphology .
the gas in these filaments is jeans unstable with @xmath3 .
fragmentation leads to the formation of high density ( @xmath4 @xmath5 ) clumps which subsequently grow in mass by accreting surrounding gas and by merging with other clumps up to masses of @xmath6 .
this suggests that the very first stars were rather massive .
we explore the complex dynamics of the merging and tidal disruption of these clumps by following their evolution over a few dynamical times . | <s>[INST]little is known about the history of the universe at redshifts @xmath7 , corresponding to @xmath8 years after the big bang , and only recently have astrophysicists begun to seriously investigate this crucial post - recombination era . at @xmath9
, the photons of the cosmic microwave background ( cmb ) shifted into the infrared , and the universe entered what has been termed the `` dark ages '' ( rees 1999 ) .
we know that the universe was reionized again before a redshift of @xmath10 from the absence of gunn - peterson absorption in the spectra of high redshift quasars .
one of the grand challenges in modern cosmology is to determine when the universe was lit up again by the first luminous objects ( the so - called population iii ) which were responsible for reionizing and reheating the intergalactic medium ( haiman & loeb 1997 ; ferrara 1998 ) .
the very first generation of stars must have formed out of probably unmagnetized , pure h / he gas , since heavy elements can only be produced in the interior of stars .
these characteristics render the primordial star formation problem very different from the present - day case , and lead to a significant simplification of the relevant physics ( larson 1998 ; loeb 1998 ) . to determine the characteristic mass scale of the population iii stars , and to constrain their initial mass function ( imf ) , one has to study the collapse and fragmentation of metal - free gas .
this problem has been addressed by a number of authors ( e.g. , yoneyama 1972 ; hutchins 1976 ; carlberg 1981 ; kashlinsky & rees 1983 ; palla , salpeter , & stahler 1983 ; silk 1983 ; haiman , thoul , & loeb 1996 ; uehara et al .
1996 ; tegmark et al .
1997 ; omukai & nishi 1998 ; nakamura & umemura 1999 ) . recently
, three - dimensional cosmological simulations have reached sufficient resolution on very small scales to approach the population iii star formation problem ( anninos & norman 1996 ; ostriker & gnedin 1996 ; abel et al .
1998a ) .
complementary to these last studies , we explore the fragmentation of primordial gas under a variety of initial conditions .
our method allows us to follow the evolution of the fragments for a few dynamical times , and to include the physics of competitive accretion .
these capabilities are crucial for the investigation of the resulting mass spectrum . a more detailed exposition of our code , together with further results of our exploratory survey , will be presented in a forthcoming publication ( bromm , coppi , & larson 1999 ) . in this letter , we focus on one representative experiment which addresses the key question : _ how does the fragmentation of the first collapsing gas clouds proceed in a hierarchical ( bottom up ) scenario of structure formation ? _
our code is based on a version of treesph ( hernquist & katz 1989 ) which combines the smoothed particle hydrodynamics ( sph ) method ( e.g. , monaghan 1992 ) with a hierarchical ( tree ) gravity solver . to study primordial gas ,
we have made a number of additions .
most importantly , radiative cooling due to hydrogen molecules has been taken into account . in the absence of metals ,
h@xmath11 is the main coolant below @xmath12 k , the typical temperature range in collapsing population iii objects .
we implement the h@xmath11 cooling function given by galli & palla ( 1998 ) . at temperatures approaching @xmath13 k , cooling due to lines of atomic hydrogen
dominates ( katz & gunn 1991 ) .
the efficiency of h@xmath11 cooling is very sensitive to the h@xmath11 abundance .
therefore , it is necessary to compute the nonequilibrium evolution of the primordial chemistry .
we take into account the six species h , h@xmath14 , h@xmath15 , h@xmath11 , h@xmath16 , and e@xmath15 .
helium is neglected , since the temperatures in our application are low enough ( @xmath17 k ) to render the he species almost inert .
reaction rates are taken from haiman et al .
in addition , we have included 3-body reactions which become important at high density ( @xmath18 @xmath5 ) , and can convert the gas almost completely into molecular form ( palla et al . 1983 ) .
the chemistry network is solved by the approximate backwards differencing formula ( bdf ) method ( anninos et al .
1997 ) .
we have devised an algorithm to merge sph particles in high density regions to overcome the otherwise prohibitive timestep limitation , as enforced by the courant stability criterion ( bate , bonnell , & price 1995 ) . to follow the simulation for a few dynamical times , we allow sph particles to merge into more massive ones , provided they exceed a pre - determined density threshold , typically @xmath19 @xmath5 .
more details of the merging algorithm will be given in bromm et al .
within a hierarchical cosmogony , the very first stars are expected to form out of @xmath20 peaks in the random field of primordial density fluctuations .
the early ( linear ) evolution of such a peak , assumed to be an isolated and roughly spherical overdensity , can be described by the top - hat model ( e.g. , padmanabhan 1993 ) .
we use the top - hat approximation to specify the initial dark matter ( dm ) configuration , where we choose the background universe to be described by the critical einstein - de sitter solution with density parameters : @xmath21 , @xmath22 , and hubble constant @xmath23 km s@xmath24 mpc@xmath24)=0.5 . in this paper
, we investigate the fate of a @xmath25 peak of total mass @xmath1 , corresponding to @xmath26 in baryons which is close to the cosmological jeans mass ( couchman & rees 1986 ) . on this mass scale , the standard cold dark matter ( cdm ) scenario predicts a present - day r.m.s .
overdensity of @xmath27 , with a normalization @xmath28 on the @xmath29mpc scale .
then , one can estimate the redshift of collapse ( or virialization ) from : @xmath30 , leading to @xmath2 .
our simulation is initialized at @xmath31 , by performing the following steps .
the collisionless dm particles are placed on a cubical cartesian grid , and are then perturbed according to a given power spectrum @xmath32 , by applying the zeldovich approximation ( zeldovich 1970 ) which also allows to self - consistently assign initial velocities .
the power - law index is set to @xmath33 which is the asymptotic small - scale behavior in the standard cdm model ( peebles 1993 ) .
the amplitude @xmath34 is adjusted , so that the fundamental mode ( i.e. , the smallest contributing wavenumber @xmath35 ) , has an initial mean square overdensity which grows to @xmath36 at collapse .
next , particles within a ( proper ) radius of @xmath37 150 pc are selected for the simulation .
the resulting number of dm particles is @xmath38 .
finally , the particles are set into rigid rotation and are endowed with a uniform hubble expansion ( see also katz 1991 ) .
angular momentum is added by assuming a spin - parameter @xmath39 , where @xmath40 , @xmath41 , and @xmath42 are the total angular momentum , energy , and mass , respectively .
the collisional sph particles ( @xmath43 in this simulation ) are randomly placed to approximate a uniform initial density .
the random sampling inevitably introduces shot - noise .
the dm particles were set up on a regular grid specifically to avoid the unphysical shot - noise distribution which could mask the desired physical power spectrum . for the gas , however , the presence of the shot noise is not a big problem , since the gas mass is initially smaller than the jeans mass .
therefore , sound waves will efficiently wipe out all initial density disturbances .
the sph particles are endowed with the same hubble expansion and rigid rotation as the dm ones . since @xmath44 , heating , cooling , and photoreactions due to the cmb can be safely neglected here . for the chemical abundances and the gas temperature
, we adopt the initial values ( see tegmark et al .
1997 ) : @xmath45 , @xmath46 , and @xmath47 k , where @xmath48 , @xmath49 are the initial free electron and h@xmath11 abundances , respectively .
the use of a more realistic rate for the photodissociation of h@xmath16 predicts a lower initial h@xmath11 abundance , typically @xmath50 .
the evolution of a simulation initialized with such a lower value , however , quickly converges to the case presented in this paper . from turnaround ( @xmath51 ) to the moment of collapse ( @xmath52 ) , both the dm and the gas are freely falling . in response to the initially imprinted @xmath53 noise ,
the dm develops marked substructure .
this happens in a hierarchical fashion , where smaller clumps form first , and rapidly merge into larger aggregations .
the gas initially falls together with the dm , heating up adiabatically , @xmath54 for @xmath55 , until the temperature reaches the virial value of @xmath56 5000 k which is determined by the depth of the dm potential well .
the virialized gas is able to cool efficiently , and the temperature decreases again with continuing compression down to a few 100 k. at first , the gas is not able to condense onto the shallow dm potential wells , and its mass distribution remains smooth . in the course of the collapse , however , the baryonic jeans mass decreases enough to eventually allow the gas to fall into the deepening dm troughs .
this gravitational `` head - start '' is important because it determines where fragmentation occurs first , resulting in the most massive gas clumps .
briefly after collapse , all the substructure in the dm has been wiped out in the process of violent relaxation ( lynden - bell 1967 ) which is very effective in quickly establishing virial equilibrium on the dynamical timescale of the dm halo ( @xmath57 years ) . before
having been wiped out , however , the dm substructure has left its imprint on the gas , determining the morphology of the incipient disk .
the dm reaches an equilibrium configuration with a core radius of @xmath58 10 pc and an approximately isothermal density profile ( @xmath59 ) further out .
the central gas disk is horizontally supported by rotation . in the presence of a dm halo , one expects a contraction by a factor of @xmath60 for rotational support .
the dimension of the disk , as shown in figure 2 , is in good accordance with this prediction .
vertically , the disk is roughly pressure supported with a scale height of @xmath61 2 pc , where @xmath62 2 km / s is the sound speed , and @xmath63 the gas surface density .
the resulting disk has a very filamentary and knotty structure with typical densities of @xmath64 @xmath5 and temperatures of @xmath65 k , corresponding to a jeans mass of @xmath3 .
we next discuss the fragmentation of these filamentary features . the gas which makes up the filaments is jeans unstable since @xmath66 , where the free - fall time is @xmath67 , and the sound - crossing time @xmath68 .
@xmath69 15 pc is the radius of the disk . in figure 1 ,
the free - fall time is compared to the sound - crossing time and to the cooling time , @xmath70 . here , @xmath71 is the fractional h@xmath11 abundance , and @xmath40 the cooling rate ( in erg s@xmath24 @xmath72 ) . for densities @xmath73 @xmath5 , the gas becomes jeans unstable .
the onset of instability roughly coincides with the condition that @xmath74 .
the value @xmath75 @xmath5 is also the critical density for the rotational - vibrational levels of h@xmath11 being populated according to local thermodynamic equilibrium ( lte ) .
the first regions to undergo runaway collapse lead to the formation of dense ( @xmath4 @xmath5 ) gas clumps of mass @xmath76 .
the dynamical state of a typical clump can be described by the ratios @xmath77 , and @xmath78 , where @xmath79 , @xmath80 , @xmath81 are the thermal , rotational , and gravitational energies of the clump .
the further evolution of the disk consists of a complex history of new clumps forming , and old ones continually accreting gas and occasionally merging with other clumps .
the outcome of this evolution is shown in figure 2 , corresponding to the situation at @xmath82 .
the disk - like structure has fragmented into 13 clumps , ranging in mass from 220 to @xmath6 . at this stage
, @xmath5850% of the total gas mass has been incorporated into high density clumps .
this fraction is unrealistically high due to the homologous nature of the top - hat collapse where all particles reach the center at the same time .
abel et al .
( 1998a ) , on the other hand , estimate this fraction to be @xmath588% .
this value is more realistic , since these authors consider an overdensity which is initially already centrally concentrated , leading to a collapse which is spread out in time . since the larger clumps tend to retain their individuality , the final evolutionary state of the disk is expected to be a small cluster of isolated clumps .
figure 3 summarizes the thermodynamic state of the gas together with the chemical abundances .
when a region undergoes runaway collapse , particles are drawn from the quasi - stationary `` reservoir '' at @xmath64 @xmath5 which corresponds to the filamentary gas , and swiftly move to higher densities at roughly constant temperature ( fig .
3c ) . at a density of @xmath83@xmath5 ,
sph particles are merged into more massive ones , as described in 2 . at higher densities
, the jeans mass would decrease below the resolution limit ( @xmath84 ; bate & burkert 1997 ) of our simulation ( fig .
3d ) . in order to reliably follow the evolution of the gas to even higher densities , a larger number of sph particles would be needed . in this case
, one would expect the gas density to increase up to the point where the now fully molecular gas becomes opaque , and subsequently behaves adiabatically again .
the present study , however , has the purpose of following the evolution of many gas clumps for a few dynamical times .
therefore , merging at some point is inevitable .
we have discussed the evolution of a primordial star forming region in the context of the standard cdm model for structure formation . in the early stages of the collapse , the morphology of the dm substructure imprints a pattern onto the initially completely smooth gas which determines where gas fragmentation is to occur first .
therefore , the initial power spectrum of the dm fluctuations might be an important ingredient for primordial star formation . simultaneously with the virialization of the dm component ,
the gas dissipatively settles down into a compact central disk .
this disk has a very filamentary structure , and is jeans unstable which leads to fragmentation into clumps of initially @xmath85 .
these clumps grow in mass by both accreting surrounding gas , and by merging with other high - density clumps . at the end of this process
, a small number ( @xmath58 10 ) of these clumps have formed .
population iii stars , then , might have been quite massive , perhaps even ` very massive ' ( @xmath86 ) , if one assumes that a jeans mass clump does not undergo significant further fragmentation .
although subsequent fragmentation can not be excluded , this is expected to lead to the formation of a binary or a small multiple system , if experience from present - day star formation offers any guidance here ( larson 1998 ) .
our results agree well with those of abel , bryan , & norman ( 1998b ) who have applied the adaptive mesh refinement ( amr ) method to the problem .
these authors find a dense core of order a few times @xmath87 , which continues to accrete mass and shows no sign of further subfragmentation .
clearly , high resolution studies of the further clump evolution are necessary , including a treatment of opacity effects ( see omukai & nishi 1998 ) .
we are presently engaged in doing so and will present our findings in a future publication .
the effects of cooling due to hd molecules ( galli & palla 1998 ) , and of the presence of the cmb on the h@xmath11 level populations ( capuzzo - dolcetta , di fazio , & palla 1991 ) , were not included in our work , and both could affect the estimate of the jeans mass .
test calculations indicate that the effect of hd cooling may not significantly change our results , but a more complete treatment will be incorporated in subsequent work .
abel , t. , anninos , p. , norman , m. l. , & zhang , y. 1998a , , 508 , 518 abel , t. , bryan , g. l. , & norman , m. l. 1998b , preprint , ( astro - ph/9810215 ) anninos , p. , & norman , m. l. 1996 , , 460 , 556 anninos , p. , zhang , y. , abel , t. , & norman , m. l. 1997 , newa , 2 , 209 bate , m. r. , bonnell , i. a. , & price , n. m. 1995 , mnras , 277 , 362 bate , m. r. , & burkert , a. 1997 , mnras , 288 , 1060 bromm , v. , coppi , p. s. , & larson , r. b. 1999 , in preparation capuzzo - dolcetta , r. , di fazio , a. , & palla , f. 1991 , a&as , 88 , 451 carlberg , r. g. 1981 , mnras , 197 , 1021 couchman , h. m. p. , & rees , m. j. 1986 , mnras , 221 , 53 ferrara , a. 1998 , , 499 , l17 galli , d. , & palla , f. 1998 , a&a , 335 , 403 haiman , z. , thoul , a. a. , & loeb , a. 1996 , , 464 , 523 haiman , z. , & loeb , a. 1997 , , 483 , 21 hernquist , l. , & katz , n. 1989 , , 70 , 419 hutchins , j. b. 1976 , , 205 , 103 kashlinsky , a. , & rees , m. j. 1983 , mnras , 205 , 955 katz , n. 1991 , , 368 , 325 katz , n. , & gunn , j. e. 1991 , , 377 , 365 larson , r. b. 1998 , mnras , 301 , 569 loeb , a. 1998 , in asp conf . ser . 133 , science with the next generation space telescope , ed .
e. smith & a. koratkar ( san francisco : asp ) , 73 lynden - bell , d. 1967 , mnras , 136 , 101 monaghan , j. j. 1992 , ara&a , 30 , 543 nakamura , f. , & umemura , m. 1999 , , 515 , 239 omukai , k. , & nishi , r. 1998 , , 508 , 141 ostriker , j. p. , & gnedin , n. y. 1996 , , 472 , l63 padmanabhan , t. 1993 , structure formation in the universe ( cambridge : cambridge univ . press ) , 273 palla , f. , salpeter , e. e. , & stahler , s. w. 1983 , , 271 , 632 peebles , p. j. e. 1993 , principles of physical cosmology ( princeton : princeton univ .
press ) , 625 rees , m. j. 1999 , in aip conf .
470 , after the dark ages : when galaxies were young ( the universe at @xmath88 ) , ed .
s. s. holt & e. smith ( woodbury : aip ) , 13 silk , j. 1983 , mnras , 205 , 705 tegmark , m. , silk , j. , rees , m. j. , blanchard , a. , abel , t. , & palla , f. 1997 , , 474 , 1 uehara , h. , susa , h. , nishi , r. , yamada , m. , & nakamura , t. 1996 , , 473 , l95 yoneyama , t. 1972 , pasj , 24 , 87 zeldovich , y. b. 1970 , a&a , 5 , 84[/INST] in order to constrain the initial mass function ( imf ) of the first generation of stars ( population iii ) , we investigate the fragmentation properties of metal - free gas in the context of a hierarchical model of structure formation .
we investigate the evolution of an isolated 3 @xmath0 peak of mass @xmath1 which collapses at @xmath2 using smoothed particle hydrodynamics .
we find that the gas dissipatively settles into a rotationally supported disk which has a very filamentary morphology .
the gas in these filaments is jeans unstable with @xmath3 .
fragmentation leads to the formation of high density ( @xmath4 @xmath5 ) clumps which subsequently grow in mass by accreting surrounding gas and by merging with other clumps up to masses of @xmath6 .
this suggests that the very first stars were rather massive .
we explore the complex dynamics of the merging and tidal disruption of these clumps by following their evolution over a few dynamical times . </s> |
widely separated time - scales occur in many radio - frequency ( rf ) circuits such as mixers , oscillators , plls , etc . , making the analysis with standard numerical methods difficult and costly .
low frequency or baseband signals and high frequency carrier signals often occur in the same circuit , enforcing very small time - steps over a long time - period for the computation of the numerical solution .
the occurrence of widely separated time - scales is also referred to as a multi - scale or multi - rate problem , where classical numerical techniques require prohibitively long run - times . a method to circumvent this bottleneck
is to reformulate the ordinary circuit equations , which are differentieal algebraic equations ( daes ) , as a system of partial daes ( multi - rate pdae ) .
the method was first presented in @xcite , specialized to compute steady states.the technique was adapted to the transient simulation of driven circuits with a - priori known frequencies in @xcite .
a generalization for circuits with a - priori unknown or time - varying frequencies was developed in @xcite .
this approach opened the door to multi - rate techniques with frequency modulated signal sources or autonomous circuits such as oscillators with a priori unknown fundamental frequency @xcite . here ,
we present a new approach for the computation of a not a - priori known , time - varying frequency , which is driven by the requirement to have a smooth multi - rate solution , crucial for the efficiency of the computation .
we consider circuit equations in the charge / flux oriented modified nodal analysis ( mna ) formulation , which yields a mathematical model in the form of a system of differential - algebraic equations ( daes ) : @xmath0 here @xmath1 is the vector of node potentials and specific branch voltages and @xmath2 is the vector of charges and fluxes .
the vector @xmath3 comprises static contributions , while @xmath4 contains the contributions of independent sources . to separate different
time scales the problem is reformulated as a multi - rate pdae ( cf .
@xcite ) , i.e. , @xmath5 if the new source term is chosen , such that @xmath6 where @xmath7 , then a solution @xmath8 of ( [ multirate ] ) determines a family @xmath9 of solutions for @xmath10 by @xmath11 although the formulation ( [ multirate ] ) is valid for any circuit , it offers a more efficient solution only for certain types of problems .
this is the case if @xmath12 is periodic in @xmath13 and smooth with respect to @xmath14 . then , a semi - discretization with respect to @xmath14 can be done resulting in a relative small number of periodic boundary problems in @xmath13 for only a few discretization points @xmath15 . in the sequel we will consider ( [ multirate ] ) with periodicity conditions in @xmath13 , i.e. , @xmath16 and suitable initial conditions @xmath17 . here
@xmath18 is an arbitrary but fixed period length , which results in a scaling of @xmath12 and @xmath19 as we will see in the next section
. note that for a given initial value for the original circuit equations ( [ eq_mna_charge ] ) the multi - rate formulation ( [ multirate ] ) is not unique .
first it does not correspond to a single problem , but to a family of problems as described in ( [ singlerate ] ) .
this usually permits some freedom in the choice of the multi - rate source term @xmath20 and for the initial conditions .
furthermore , @xmath19 can , in principle , be chosen arbitrarily , but influences on the other hand , which choice of @xmath20 satisfies ( [ char_source ] ) . in the sequel
, we want to study how the above freedom can be used to facilitate an efficient numerical solution of ( [ multirate ] ) .
the smoothness of @xmath12 is essential for the efficiency of classical solvers .
that is , the freedom we have for the formulation of ( [ multirate ] ) should be used to make the solution as smooth as possible .
it can be easily verified that @xmath19 can be any positive function , if the source term @xmath20 is chosen to satisfy ( [ char_source ] ) .
therefore , we will first investigate , what effect different selections of @xmath19 have .
let @xmath21 and @xmath22 be two choices . if @xmath23 and @xmath24 both satisfy ( [ character ] ) , then it is obvious that @xmath25 where @xmath26 .
that is , for a fixed @xmath14 changing @xmath27 results in a phase shift of @xmath12 .
a corresponding phase shift for the source term has to be performed in order to satisfy ( [ char_source ] ) .
the following lemma describes how @xmath19 affects the smoothness of @xmath12 .
[ smoothmr ] let @xmath28 for any @xmath29 .
if @xmath30 for @xmath31 $ ] , then @xmath32 where @xmath33 is the unique solution of @xmath34 following ( [ character ] ) we have @xmath35 by the mean value theorem for integration we obtain @xmath36 thus , @xmath37 and ( [ smoothx ] ) follows from ( [ smoothxhat ] ) by ( [ character ] ) .
lemma [ smoothmr ] states that we can only expect smoothness of @xmath12 in @xmath14 if @xmath38 is nearly @xmath33-periodic in a neighborhood of @xmath14 . since typical multi - rate signals behave locally like a periodic signal , i.e. , @xmath39 as long as @xmath13 is close to some @xmath40
that is , there should be a choice of @xmath19 such that @xmath41 and @xmath42 do not differ much for sufficiently small @xmath43 .
this leads to the additional condition @xmath44 in order to determine @xmath19 .
a similar condition is used in @xcite ) . the difference to our approach is in the discretization of the problem .
while pulch derives a phase condition from the minimization condition , we will discretize the minimization condition directly , which will lead to a smaller linear system to be solved in the algorithm . furthermore
, we are using a rothe method for the discretization of the pdae , which allows a completely adaptive solution .
a different approach is suggested in @xcite , where @xmath12 is replaced by @xmath45 in ( [ min_cond ] ) .
although this seems the proper condition for an efficient discretization of the derivative in @xmath14 in the multi - rate pdae ( [ multirate ] ) , another problem occurs here . using an implicit multistep method for the discretization in @xmath14
, we need a predictor ( as initial guess for newton s method ) , which is usually based on the solution of the previous time step . here , a condition on @xmath12 as in ( [ min_cond ] ) occurs naturally .
a condition on @xmath45 covers only contributions of the signal which are already smoothed ( by capacitances or inductances ) , and might not provide a sufficient initial guess .
it turns out that condition ( [ min_cond ] ) yields the expected result for amplitude and frequency modulation of a periodic signal , i.e. , for typical multirate rf signals .
[ mr_modulated ] assume @xmath46 with @xmath47 is a solution of _ ( [ singlerate ] ) _ with non - trivial @xmath48 and @xmath49 .
the solution of the corresponding multi - rate problem _ ( [ multirate ] ) _ satisfies _ ( [ min_cond ] ) _ if and only if @xmath50 and @xmath51 . according to ( [ character ] ) and ( [ omega2 ] ) we can write the multi - rate solution as @xmath52 , where @xmath53 vanishes if and only if @xmath50 . taking the derivative with respect to @xmath14 we
obtain @xmath54 note , that due to periodicity of @xmath55 we have @xmath56 thus , the expression in ( [ min_cond ] ) , which has to be minimized becomes @xmath57 obviously the expression becomes minimal if @xmath58 , @xmath59 $ ] . from ( [ omega2 ] )
we see that @xmath60 and the statement is proven .
applying the approach to more general problems , permits to consider @xmath61 as a generalization of the instantaneous frequency of the multi - rate problem , if ( [ min_cond ] ) is satisfied .
for the numerical solution of the multi - rate problem we have to discretize the mpdae s ( [ multirate ] ) together with the smoothness condition ( [ min_cond ] ) .
the following section presents a new approach for the numerical solution of the multi - rate problem with unknown frequency parameter .
we discretize ( [ multirate ] ) with respect to @xmath14 by a rothe method using a linear multi step method and obtain @xmath62 complemented by the periodicity condition @xmath63 . here
we have to determine an approximation @xmath64 of @xmath65 from known , approximative solutions @xmath66 at previous time steps @xmath67 .
examples are the trapezoidal rule with @xmath69 , @xmath70 and @xmath71 or gear - bdf of order @xmath72 with @xmath73 and suitable @xmath74 .
that is , @xmath75 is the solution of a periodic boundary value problem for the daes given in ( [ rothe ] ) . assuming that the @xmath67 , @xmath76 and @xmath66 are known and fixed for @xmath77 we define @xmath78 & + ~\sum_{i=1}^s\bigg\ { \alpha^k_i q\big(x_{k - i}(t)\big ) + \beta^k_i \left(\omega_{k - i}\,\frac{d}{dt}q\big(x_{k - i}(t)\big ) + g\big(x_{k - i}(t)\big)-\hat{s}\big(\tau_{k - i},t\big)\right)\bigg\},\end{aligned}\ ] ] as well as @xmath79 .
then ( [ rothe ] ) becomes the periodic boundary value problem @xmath80 furthermore , @xmath81 is an approximation for @xmath82 , which has to be determined during the computation ( if not known in advance ) . since the midpoint rule states for a suitable choice of @xmath83 that @xmath84 we replace condition ( [ min_cond ] ) by @xmath85 i.e. , we aim to minimize the change of @xmath64 from one time step to the next , which corresponds well to the original goal .
if we have a smooth envelope , we may be able to choose the step sizes @xmath86 much larger than the period @xmath87 .
that means the number of time steps will become much smaller compared to the number of oscillations of the carrier signal .
this can lead to an essential gain in computation time compared to transient analysis , since the computation cost for one period is comparable to one envelope time step .
the periodic problem ( [ envelope ] ) can be solved by a collocation or galerkin method , where @xmath64 is expanded in a periodic basis @xmath88 ( as a fourier , b - spline , or wavelet basis ) and tested at collocation points or integrated against test functions ( see e.g. @xcite ) .
this leads to a nonlinear system @xmath89 of equations for the coefficients @xmath90 of the basis expansion @xmath91 and the unknown frequency parameter @xmath92 . here ,
condition ( [ min_cond2 ] ) is replaced by a condition on the expansion coefficients , namely @xmath93 this means , that we are still minimizing the distance of @xmath64 and @xmath94 , although with respect to a slightly modified measure . the nonlinear system ( [ nonlinear ] )
is solved by a modified newton s method .
the linearization of the problem yields the under - determined system @xmath95 with the right hand site @xmath96 , the jacobian @xmath97 , and @xmath98 .
furthermore , @xmath99 and @xmath100 are the updates in the newton iteration @xmath101 with an initial guess chosen as @xmath102 and @xmath103 . to find a solution satisfying ( [ min_cond3 ] ) we rewrite ( [ newton_ud ] ) as @xmath104 where @xmath105 and @xmath106 are computed by solving the corresponding linear systems .
this needs a lu - decomposition of @xmath107 and two forward - backward substitution , i.e. , the computational costs are only slightly higher as for @xmath19 fixed in advance .
possible higher step sizes and faster convergence of newton s method justify this extra cost if a good choice for @xmath19 is not available in advance . in the @xmath108-th newton step @xmath109 we determine the newton correction , which satisfies ( [ min_cond3 ] ) as follows .
we want @xmath110 to be minimal .
obviously the minimum is attained for @xmath111
the method has been tested on several circuits .
we show results from the multi - rate simulation of a phase locked loop ( pll ) with a frequency modulated input signal .
the phase of the output signal is synchronized with the phase of the input `` reference '' signal .
this is achieved , by comparing the phases of the `` reference '' signal and the output or `` feedback '' signal in a phase detector .
the result is then filtered , in order to stabilize the behavior of the pll , and fed to a voltage controlled oscillator ( vco ) whose frequency depends on the ( filtered ) phase difference .
the output is fed back ( possibly through a frequency divider ) to the phase detector .
if the pll is locked , the phases of reference and feedback signal are synchronized .
thus both signal will have ( almost ) the same local frequency .
we have tested a pll ( containing 145 mosfets and 80 unknowns ) with a frequency modulated sinusoidal signal with frequency 222khz .
the baseband signal is also sinusoidal with frequency 200hz and frequency deviation 200hz .
we have chosen this example , since it was particular challenging , due to its size , but also due its digital - like behavior , which requires an efficient adaptive representation of the solution , as well as a very accurate estimate of the frequency parameter @xmath19 .
although the baseband signal is known to us after locking of the pll , this information is not provided to the algorithm .
this permits a verification of the @xmath19 determined by our algorithm . before the locking of the pll the optimal @xmath19
is not known to us , and the estimate of the algorithm proved essential for this part of the simulation to be successful .
, scaledwidth=60.0% ] due to the chosen circuit design most of the signals show a digital behavior such that the solution can not efficiently be expanded by a fourier basis .
thus , using the harmonic balance method is not suited for the solution of the problem , in particular since the use of a frequency divider results in a wide frequency range of the solution .
therefore , the periodic problem is solved by an adaptive spline wavelet method described in @xcite .
the quality of the estimate of @xmath19 is essential for the efficiency of the method , because this results in a good initial guess for the solution and the spline grid in newton s method . in figure [ pllcontrol ] ( left )
one can see the control signal for the vco ( the filtered output of the phase detector ) , which controls the frequency of the oscillator .
note , that after the locking phase at the beginning the envelope corresponds to the baseband signal , while the carrier signal is due to the filtering almost constant .
figure [ pllcontrol ] ( right ) shows the digital feedback signal .
note that @xmath19 was chosen to satisfy the condition ( [ min_cond3 ] ) .
the plot of @xmath19 in figure [ pllomega ] fits almost perfectly the baseband signal , after the pll is locked . in the light of lemma [ mr_modulated ] ,
the graphs in figures [ pllcontrol ] and [ pllomega ] show indeed a frequency modulated box shaped signal . the optimal choice of @xmath19 results in high smoothness with respect to @xmath14 .
this allows to do the shown envelope simulation using only 74 envelope time steps , while a corresponding transient analysis would contain 3100 oscillations .
the wavelet envelope simulation of this circuit was done in 7min . however , a comparable transient simulation on the same simulator needed 33hours .
we have presented a new method for an accurate estimate of an unknown frequency parameter in multi - rate envelope simulations , which permits an efficient simulation even for challenging problems .
k. bittner and e. dautbegovic ( 2012_a _ ) , adaptive wavelet - based method for simulation of electronic circuits , in _ scientific computing in electrical engineering 2010 _ ( b. michielsen and j .- r .
poirier , eds ) , mathematics in industry , springer , berlin heidelberg , pp . 321 328 .
k. bittner and e. dautbegovic ( 2012_b _ ) , wavelets algorithm for circuit simulation , in _ progress in industrial mathematics at ecmi 2010 _ ( m. gnther , a. bartel , m. brunk , s. schps and m. striebel , eds ) , mathematics in industry , springer , berlin heidelberg , pp . 5 11 . h. g. brachtendorf ( 1997 ) , on the relation of certain classes of ordinary differential algebraic equations with partial differential algebraic equations , technical report 1131g0 - 971114 - 19tm , bell - laboratories .
h. g. brachtendorf ( 2001 ) , ` theorie und analyse von autonomen und quasiperiodisch angeregten elektrischen netzwerken .
eine algorithmisch orientierte betrachtung ' , universitt bremen .
abilitationsschrift .
s. houben ( 2004 ) , simulating multi - tone free - running oscillators with optimal sweep following , in _ scientific computing in electrical engineering 2010 _ ( w. schilders , e. ter maten and s. houben , eds ) , mathematics in industry , springer , berlin , pp . 240 247 . e. ngoya and r. larchevque ( 1996 ) , envelope transient analysis : a new method for the transient and steady state analysis of microwave communication circuit and systems , in _ proc .
ieee mtt - s int .
microwave symp .
_ , san francisco , pp . 13651368 . | * purpose rf circuits often possess a multi - rate behavior .
slow changing baseband signals and fast oscillating carrier signals often occur in the same circuit .
frequency modulated signals pose a particular challenge .
* * design / methodology / approach the ordinary circuit differential equations ( odes ) are first rewritten by a system of ( multi - rate ) partial differential equations ( mpdes ) in order to decouple the different time scales . for an efficient simulation
we need an optimal choice of a frequency dependent parameter .
this is achieved by an additional smoothness condition .
* * finding by incorporating the smoothness condition into the discretization , we obtain a nonlinear system of equations complemented by a minimization constraint
. this problem is solved by a modified newton method , which needs only little extra computational effort .
the method is tested on a phase locked loop with a frequency modulated input signal .
* * originality / value a new optimal frequency sweep method was introduced , which will permit a very efficient simulation of multi - rate circuits . * rf circuit simulation , multi - rate simulation , envelope simulation .
* paper type : * research paper | <s>[INST]widely separated time - scales occur in many radio - frequency ( rf ) circuits such as mixers , oscillators , plls , etc . , making the analysis with standard numerical methods difficult and costly .
low frequency or baseband signals and high frequency carrier signals often occur in the same circuit , enforcing very small time - steps over a long time - period for the computation of the numerical solution .
the occurrence of widely separated time - scales is also referred to as a multi - scale or multi - rate problem , where classical numerical techniques require prohibitively long run - times . a method to circumvent this bottleneck
is to reformulate the ordinary circuit equations , which are differentieal algebraic equations ( daes ) , as a system of partial daes ( multi - rate pdae ) .
the method was first presented in @xcite , specialized to compute steady states.the technique was adapted to the transient simulation of driven circuits with a - priori known frequencies in @xcite .
a generalization for circuits with a - priori unknown or time - varying frequencies was developed in @xcite .
this approach opened the door to multi - rate techniques with frequency modulated signal sources or autonomous circuits such as oscillators with a priori unknown fundamental frequency @xcite . here ,
we present a new approach for the computation of a not a - priori known , time - varying frequency , which is driven by the requirement to have a smooth multi - rate solution , crucial for the efficiency of the computation .
we consider circuit equations in the charge / flux oriented modified nodal analysis ( mna ) formulation , which yields a mathematical model in the form of a system of differential - algebraic equations ( daes ) : @xmath0 here @xmath1 is the vector of node potentials and specific branch voltages and @xmath2 is the vector of charges and fluxes .
the vector @xmath3 comprises static contributions , while @xmath4 contains the contributions of independent sources . to separate different
time scales the problem is reformulated as a multi - rate pdae ( cf .
@xcite ) , i.e. , @xmath5 if the new source term is chosen , such that @xmath6 where @xmath7 , then a solution @xmath8 of ( [ multirate ] ) determines a family @xmath9 of solutions for @xmath10 by @xmath11 although the formulation ( [ multirate ] ) is valid for any circuit , it offers a more efficient solution only for certain types of problems .
this is the case if @xmath12 is periodic in @xmath13 and smooth with respect to @xmath14 . then , a semi - discretization with respect to @xmath14 can be done resulting in a relative small number of periodic boundary problems in @xmath13 for only a few discretization points @xmath15 . in the sequel we will consider ( [ multirate ] ) with periodicity conditions in @xmath13 , i.e. , @xmath16 and suitable initial conditions @xmath17 . here
@xmath18 is an arbitrary but fixed period length , which results in a scaling of @xmath12 and @xmath19 as we will see in the next section
. note that for a given initial value for the original circuit equations ( [ eq_mna_charge ] ) the multi - rate formulation ( [ multirate ] ) is not unique .
first it does not correspond to a single problem , but to a family of problems as described in ( [ singlerate ] ) .
this usually permits some freedom in the choice of the multi - rate source term @xmath20 and for the initial conditions .
furthermore , @xmath19 can , in principle , be chosen arbitrarily , but influences on the other hand , which choice of @xmath20 satisfies ( [ char_source ] ) . in the sequel
, we want to study how the above freedom can be used to facilitate an efficient numerical solution of ( [ multirate ] ) .
the smoothness of @xmath12 is essential for the efficiency of classical solvers .
that is , the freedom we have for the formulation of ( [ multirate ] ) should be used to make the solution as smooth as possible .
it can be easily verified that @xmath19 can be any positive function , if the source term @xmath20 is chosen to satisfy ( [ char_source ] ) .
therefore , we will first investigate , what effect different selections of @xmath19 have .
let @xmath21 and @xmath22 be two choices . if @xmath23 and @xmath24 both satisfy ( [ character ] ) , then it is obvious that @xmath25 where @xmath26 .
that is , for a fixed @xmath14 changing @xmath27 results in a phase shift of @xmath12 .
a corresponding phase shift for the source term has to be performed in order to satisfy ( [ char_source ] ) .
the following lemma describes how @xmath19 affects the smoothness of @xmath12 .
[ smoothmr ] let @xmath28 for any @xmath29 .
if @xmath30 for @xmath31 $ ] , then @xmath32 where @xmath33 is the unique solution of @xmath34 following ( [ character ] ) we have @xmath35 by the mean value theorem for integration we obtain @xmath36 thus , @xmath37 and ( [ smoothx ] ) follows from ( [ smoothxhat ] ) by ( [ character ] ) .
lemma [ smoothmr ] states that we can only expect smoothness of @xmath12 in @xmath14 if @xmath38 is nearly @xmath33-periodic in a neighborhood of @xmath14 . since typical multi - rate signals behave locally like a periodic signal , i.e. , @xmath39 as long as @xmath13 is close to some @xmath40
that is , there should be a choice of @xmath19 such that @xmath41 and @xmath42 do not differ much for sufficiently small @xmath43 .
this leads to the additional condition @xmath44 in order to determine @xmath19 .
a similar condition is used in @xcite ) . the difference to our approach is in the discretization of the problem .
while pulch derives a phase condition from the minimization condition , we will discretize the minimization condition directly , which will lead to a smaller linear system to be solved in the algorithm . furthermore
, we are using a rothe method for the discretization of the pdae , which allows a completely adaptive solution .
a different approach is suggested in @xcite , where @xmath12 is replaced by @xmath45 in ( [ min_cond ] ) .
although this seems the proper condition for an efficient discretization of the derivative in @xmath14 in the multi - rate pdae ( [ multirate ] ) , another problem occurs here . using an implicit multistep method for the discretization in @xmath14
, we need a predictor ( as initial guess for newton s method ) , which is usually based on the solution of the previous time step . here , a condition on @xmath12 as in ( [ min_cond ] ) occurs naturally .
a condition on @xmath45 covers only contributions of the signal which are already smoothed ( by capacitances or inductances ) , and might not provide a sufficient initial guess .
it turns out that condition ( [ min_cond ] ) yields the expected result for amplitude and frequency modulation of a periodic signal , i.e. , for typical multirate rf signals .
[ mr_modulated ] assume @xmath46 with @xmath47 is a solution of _ ( [ singlerate ] ) _ with non - trivial @xmath48 and @xmath49 .
the solution of the corresponding multi - rate problem _ ( [ multirate ] ) _ satisfies _ ( [ min_cond ] ) _ if and only if @xmath50 and @xmath51 . according to ( [ character ] ) and ( [ omega2 ] ) we can write the multi - rate solution as @xmath52 , where @xmath53 vanishes if and only if @xmath50 . taking the derivative with respect to @xmath14 we
obtain @xmath54 note , that due to periodicity of @xmath55 we have @xmath56 thus , the expression in ( [ min_cond ] ) , which has to be minimized becomes @xmath57 obviously the expression becomes minimal if @xmath58 , @xmath59 $ ] . from ( [ omega2 ] )
we see that @xmath60 and the statement is proven .
applying the approach to more general problems , permits to consider @xmath61 as a generalization of the instantaneous frequency of the multi - rate problem , if ( [ min_cond ] ) is satisfied .
for the numerical solution of the multi - rate problem we have to discretize the mpdae s ( [ multirate ] ) together with the smoothness condition ( [ min_cond ] ) .
the following section presents a new approach for the numerical solution of the multi - rate problem with unknown frequency parameter .
we discretize ( [ multirate ] ) with respect to @xmath14 by a rothe method using a linear multi step method and obtain @xmath62 complemented by the periodicity condition @xmath63 . here
we have to determine an approximation @xmath64 of @xmath65 from known , approximative solutions @xmath66 at previous time steps @xmath67 .
examples are the trapezoidal rule with @xmath69 , @xmath70 and @xmath71 or gear - bdf of order @xmath72 with @xmath73 and suitable @xmath74 .
that is , @xmath75 is the solution of a periodic boundary value problem for the daes given in ( [ rothe ] ) . assuming that the @xmath67 , @xmath76 and @xmath66 are known and fixed for @xmath77 we define @xmath78 & + ~\sum_{i=1}^s\bigg\ { \alpha^k_i q\big(x_{k - i}(t)\big ) + \beta^k_i \left(\omega_{k - i}\,\frac{d}{dt}q\big(x_{k - i}(t)\big ) + g\big(x_{k - i}(t)\big)-\hat{s}\big(\tau_{k - i},t\big)\right)\bigg\},\end{aligned}\ ] ] as well as @xmath79 .
then ( [ rothe ] ) becomes the periodic boundary value problem @xmath80 furthermore , @xmath81 is an approximation for @xmath82 , which has to be determined during the computation ( if not known in advance ) . since the midpoint rule states for a suitable choice of @xmath83 that @xmath84 we replace condition ( [ min_cond ] ) by @xmath85 i.e. , we aim to minimize the change of @xmath64 from one time step to the next , which corresponds well to the original goal .
if we have a smooth envelope , we may be able to choose the step sizes @xmath86 much larger than the period @xmath87 .
that means the number of time steps will become much smaller compared to the number of oscillations of the carrier signal .
this can lead to an essential gain in computation time compared to transient analysis , since the computation cost for one period is comparable to one envelope time step .
the periodic problem ( [ envelope ] ) can be solved by a collocation or galerkin method , where @xmath64 is expanded in a periodic basis @xmath88 ( as a fourier , b - spline , or wavelet basis ) and tested at collocation points or integrated against test functions ( see e.g. @xcite ) .
this leads to a nonlinear system @xmath89 of equations for the coefficients @xmath90 of the basis expansion @xmath91 and the unknown frequency parameter @xmath92 . here ,
condition ( [ min_cond2 ] ) is replaced by a condition on the expansion coefficients , namely @xmath93 this means , that we are still minimizing the distance of @xmath64 and @xmath94 , although with respect to a slightly modified measure . the nonlinear system ( [ nonlinear ] )
is solved by a modified newton s method .
the linearization of the problem yields the under - determined system @xmath95 with the right hand site @xmath96 , the jacobian @xmath97 , and @xmath98 .
furthermore , @xmath99 and @xmath100 are the updates in the newton iteration @xmath101 with an initial guess chosen as @xmath102 and @xmath103 . to find a solution satisfying ( [ min_cond3 ] ) we rewrite ( [ newton_ud ] ) as @xmath104 where @xmath105 and @xmath106 are computed by solving the corresponding linear systems .
this needs a lu - decomposition of @xmath107 and two forward - backward substitution , i.e. , the computational costs are only slightly higher as for @xmath19 fixed in advance .
possible higher step sizes and faster convergence of newton s method justify this extra cost if a good choice for @xmath19 is not available in advance . in the @xmath108-th newton step @xmath109 we determine the newton correction , which satisfies ( [ min_cond3 ] ) as follows .
we want @xmath110 to be minimal .
obviously the minimum is attained for @xmath111
the method has been tested on several circuits .
we show results from the multi - rate simulation of a phase locked loop ( pll ) with a frequency modulated input signal .
the phase of the output signal is synchronized with the phase of the input `` reference '' signal .
this is achieved , by comparing the phases of the `` reference '' signal and the output or `` feedback '' signal in a phase detector .
the result is then filtered , in order to stabilize the behavior of the pll , and fed to a voltage controlled oscillator ( vco ) whose frequency depends on the ( filtered ) phase difference .
the output is fed back ( possibly through a frequency divider ) to the phase detector .
if the pll is locked , the phases of reference and feedback signal are synchronized .
thus both signal will have ( almost ) the same local frequency .
we have tested a pll ( containing 145 mosfets and 80 unknowns ) with a frequency modulated sinusoidal signal with frequency 222khz .
the baseband signal is also sinusoidal with frequency 200hz and frequency deviation 200hz .
we have chosen this example , since it was particular challenging , due to its size , but also due its digital - like behavior , which requires an efficient adaptive representation of the solution , as well as a very accurate estimate of the frequency parameter @xmath19 .
although the baseband signal is known to us after locking of the pll , this information is not provided to the algorithm .
this permits a verification of the @xmath19 determined by our algorithm . before the locking of the pll the optimal @xmath19
is not known to us , and the estimate of the algorithm proved essential for this part of the simulation to be successful .
, scaledwidth=60.0% ] due to the chosen circuit design most of the signals show a digital behavior such that the solution can not efficiently be expanded by a fourier basis .
thus , using the harmonic balance method is not suited for the solution of the problem , in particular since the use of a frequency divider results in a wide frequency range of the solution .
therefore , the periodic problem is solved by an adaptive spline wavelet method described in @xcite .
the quality of the estimate of @xmath19 is essential for the efficiency of the method , because this results in a good initial guess for the solution and the spline grid in newton s method . in figure [ pllcontrol ] ( left )
one can see the control signal for the vco ( the filtered output of the phase detector ) , which controls the frequency of the oscillator .
note , that after the locking phase at the beginning the envelope corresponds to the baseband signal , while the carrier signal is due to the filtering almost constant .
figure [ pllcontrol ] ( right ) shows the digital feedback signal .
note that @xmath19 was chosen to satisfy the condition ( [ min_cond3 ] ) .
the plot of @xmath19 in figure [ pllomega ] fits almost perfectly the baseband signal , after the pll is locked . in the light of lemma [ mr_modulated ] ,
the graphs in figures [ pllcontrol ] and [ pllomega ] show indeed a frequency modulated box shaped signal . the optimal choice of @xmath19 results in high smoothness with respect to @xmath14 .
this allows to do the shown envelope simulation using only 74 envelope time steps , while a corresponding transient analysis would contain 3100 oscillations .
the wavelet envelope simulation of this circuit was done in 7min . however , a comparable transient simulation on the same simulator needed 33hours .
we have presented a new method for an accurate estimate of an unknown frequency parameter in multi - rate envelope simulations , which permits an efficient simulation even for challenging problems .
k. bittner and e. dautbegovic ( 2012_a _ ) , adaptive wavelet - based method for simulation of electronic circuits , in _ scientific computing in electrical engineering 2010 _ ( b. michielsen and j .- r .
poirier , eds ) , mathematics in industry , springer , berlin heidelberg , pp . 321 328 .
k. bittner and e. dautbegovic ( 2012_b _ ) , wavelets algorithm for circuit simulation , in _ progress in industrial mathematics at ecmi 2010 _ ( m. gnther , a. bartel , m. brunk , s. schps and m. striebel , eds ) , mathematics in industry , springer , berlin heidelberg , pp . 5 11 . h. g. brachtendorf ( 1997 ) , on the relation of certain classes of ordinary differential algebraic equations with partial differential algebraic equations , technical report 1131g0 - 971114 - 19tm , bell - laboratories .
h. g. brachtendorf ( 2001 ) , ` theorie und analyse von autonomen und quasiperiodisch angeregten elektrischen netzwerken .
eine algorithmisch orientierte betrachtung ' , universitt bremen .
abilitationsschrift .
s. houben ( 2004 ) , simulating multi - tone free - running oscillators with optimal sweep following , in _ scientific computing in electrical engineering 2010 _ ( w. schilders , e. ter maten and s. houben , eds ) , mathematics in industry , springer , berlin , pp . 240 247 . e. ngoya and r. larchevque ( 1996 ) , envelope transient analysis : a new method for the transient and steady state analysis of microwave communication circuit and systems , in _ proc .
ieee mtt - s int .
microwave symp .
_ , san francisco , pp . 13651368 .[/INST] * purpose rf circuits often possess a multi - rate behavior .
slow changing baseband signals and fast oscillating carrier signals often occur in the same circuit .
frequency modulated signals pose a particular challenge .
* * design / methodology / approach the ordinary circuit differential equations ( odes ) are first rewritten by a system of ( multi - rate ) partial differential equations ( mpdes ) in order to decouple the different time scales . for an efficient simulation
we need an optimal choice of a frequency dependent parameter .
this is achieved by an additional smoothness condition .
* * finding by incorporating the smoothness condition into the discretization , we obtain a nonlinear system of equations complemented by a minimization constraint
. this problem is solved by a modified newton method , which needs only little extra computational effort .
the method is tested on a phase locked loop with a frequency modulated input signal .
* * originality / value a new optimal frequency sweep method was introduced , which will permit a very efficient simulation of multi - rate circuits . * rf circuit simulation , multi - rate simulation , envelope simulation .
* paper type : * research paper </s> |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Start Healthy Act of 2012''.
SEC. 2. MEDICAID ASSISTANCE FOR UNINSURED NEWBORNS.
(a) Mandatory Coverage of Certain Newborns.--Section
1902(a)(10)(A)(i) of the Social Security Act (42 U.S.C.
1396a(a)(10)(A)(i)) is amended--
(1) by striking ``or'' at the end of subclause (VIII);
(2) by adding ``or'' at the end of subclause (IX); and
(3) by adding at the end the following:
``(X) who are qualified newborns
(as defined in subsection
(e)(16)(A));''.
(b) Deemed Eligibility for Newborns.--Section 1902(e) of such Act
(42 U.S.C. 1396a(e)) is amended by adding at the end the following:
``(16) Deemed eligibility for qualified newborns.--
``(A) Qualified newborn defined.--For purposes of
this section, the term `qualified newborn' means a
child who--
``(i) is born in the United States;
``(ii) is under 1 year of age;
``(iii) is not a child who is deemed
eligible under paragraph (4); and
``(iv) for periods--
``(I) before January 1, 2014, is
not eligible for creditable coverage
under section 2701(c) of the Public
Health Service Act (42 U.S.C.
300gg(c)), as in effect before January
1, 2014, but applied without regard to
subparagraphs (D) and (F) of paragraph
(1) of such section; or
``(II) on or after such date, is
not eligible for minimum essential
coverage, as defined in section
5000A(f)(1) of the Internal Revenue
Code of 1986, but applied without
regard to subparagraph (A)(ii) of such
section.
``(B) Deemed eligibility.--Subject to subparagraph
(C), a child that a State reasonably believes is a
qualified newborn (and thus eligible for medical
assistance under subsection (a)(10)(A)(i)(X)) on the
date of such child's birth shall be deemed to have
applied for medical assistance and to have been found
eligible for such assistance under such plan on the
date of such birth and to remain eligible for such
assistance until such child is one year of age, unless
a State determines that a child is not eligible for
such medical assistance through a redetermination under
subparagraph (D).
``(C) Exception for other coverage.--
``(i) In general.--If, during the period of
eligibility under subparagraph (A), the State
determines that the child is enrolled in a type
of coverage described in subparagraph (A)(iv),
the State may terminate medical assistance for
such child under subsection (a)(10)(A)(i)(X).
``(ii) Limitation.--A State that determines
that a child is eligible for such coverage, but
not enrolled in such coverage, may not
terminate such medical assistance for such
child until such child is enrolled in such
coverage.
``(D) Redeterminations of eligibility.--
``(i) In general.--Subject to clause (ii)
and subparagraph (C)(ii), the State shall
redetermine a child's eligibility for medical
assistance under subsection (a)(10)(A)(i)(X)
not later than 180 days after the date of the
child's birth.
``(ii) Limitation.--If an application is
required for a redetermination under clause
(i), and such application is not received by
the State, and the State reasonably believes
that the child for which such application was
required continues to be a qualified newborn,
the State may not discontinue such child's
eligibility for medical assistance under
subsection (a)(10)(A)(i)(X) on the basis of
such missing application.
``(iii) Reduced fmap for failure to do
timely determination.--The increased Federal
medical assistance percentage provided under
the third sentence of section 1905(b) with
respect to individuals eligible for medical
assistance under section 1902(a)(10)(A)(i)(X)
shall not apply with respect to a child,
beginning 180 days after the date of the
child's birth, for whom a determination is not
made on a timely basis under clause (i), unless
the limitation under clause (ii) applies to
such child.''.
(c) 100 Percent Matching Rate for Temporary Coverage of Certain
Newborns.--
(1) In general.--The third sentence of section 1905(b) of
such Act (42 U.S.C. 1396d(b)) is amended by inserting before
the period at the end the following: ``and, subject to section
1902(e)(16)(E)(iii), for medical assistance for individuals in
one of the 50 States or the District of Columbia eligible for
such assistance under section 1902(a)(10)(A)(i)(X)''.
(2) Application to territories.--Section 1108(g)(4) of such
Act (42 U.S.C. 1308(g)(4)) is amended by adding at the end the
following: ``Payment for medical assistance for an individual
eligible for assistance under section 1902(a)(10)(A)(i)(X)
shall not be taken into account in applying subsection (f) (as
increased in accordance with paragraphs (1), (2), (3), and (4)
of this subsection).''
(d) Conforming Amendment.--Section 1903(f)(4) of such Act (42
U.S.C. 1396b(f)(4)) is amended by inserting ``1902(a)(10)(A)(i)(X),''
after ``1902(a)(10)(A)(i)(VIII),''.
(e) Technical Amendments.--Section 1902(e) of such Act (42 U.S.C.
1396a(e)) is amended by redesignating the paragraph (14) relating to
exclusion of compensation for participation in a clinical trial for
testing of treatments for a rare disease or condition, as added by
section 3 of the Improving Access to Clinical Trials Act of 2009, as
paragraph (15). Such redesignation shall not be construed to affect the
application of section (3)(e) of the Improving Access to Clinical
Trials Act of 2009 to such paragraph.
(f) Effective Date.--
(1) In general.--The amendments made by this section shall
apply to individuals born on or after the day that is 6 months
after the date of the enactment of this Act.
(2) Delay permitted for state plan amendment.--In the case
of a State plan for medical assistance under title XIX of the
Social Security Act which the Secretary of Health and Human
Services determines requires State legislation (other than
legislation appropriating funds) in order for the plan to meet
the additional requirements imposed by the amendments made by
this section, the State plan shall not be regarded as failing
to comply with the requirements of such title solely on the
basis of its failure to meet these additional requirements
before the first day of the first calendar quarter beginning
after the close of the first regular session of the State
legislature that begins after the date of enactment of this
Act. For purposes of the previous sentence, in the case of a
State that has a 2-year legislative session, each year of such
session shall be deemed to be a separate regular session of the
State legislature. | Start Healthy Act of 2012 - Amends title XIX (Medicaid) of the Social Security Act to provide: (1) mandatory coverage of qualified (uninsured) newborns, and (2) 100% federal medical assistance percentage (FMAP) for temporary coverage of such newborns. | <s>[INST]SECTION 1. SHORT TITLE.
This Act may be cited as the ``Start Healthy Act of 2012''.
SEC. 2. MEDICAID ASSISTANCE FOR UNINSURED NEWBORNS.
(a) Mandatory Coverage of Certain Newborns.--Section
1902(a)(10)(A)(i) of the Social Security Act (42 U.S.C.
1396a(a)(10)(A)(i)) is amended--
(1) by striking ``or'' at the end of subclause (VIII);
(2) by adding ``or'' at the end of subclause (IX); and
(3) by adding at the end the following:
``(X) who are qualified newborns
(as defined in subsection
(e)(16)(A));''.
(b) Deemed Eligibility for Newborns.--Section 1902(e) of such Act
(42 U.S.C. 1396a(e)) is amended by adding at the end the following:
``(16) Deemed eligibility for qualified newborns.--
``(A) Qualified newborn defined.--For purposes of
this section, the term `qualified newborn' means a
child who--
``(i) is born in the United States;
``(ii) is under 1 year of age;
``(iii) is not a child who is deemed
eligible under paragraph (4); and
``(iv) for periods--
``(I) before January 1, 2014, is
not eligible for creditable coverage
under section 2701(c) of the Public
Health Service Act (42 U.S.C.
300gg(c)), as in effect before January
1, 2014, but applied without regard to
subparagraphs (D) and (F) of paragraph
(1) of such section; or
``(II) on or after such date, is
not eligible for minimum essential
coverage, as defined in section
5000A(f)(1) of the Internal Revenue
Code of 1986, but applied without
regard to subparagraph (A)(ii) of such
section.
``(B) Deemed eligibility.--Subject to subparagraph
(C), a child that a State reasonably believes is a
qualified newborn (and thus eligible for medical
assistance under subsection (a)(10)(A)(i)(X)) on the
date of such child's birth shall be deemed to have
applied for medical assistance and to have been found
eligible for such assistance under such plan on the
date of such birth and to remain eligible for such
assistance until such child is one year of age, unless
a State determines that a child is not eligible for
such medical assistance through a redetermination under
subparagraph (D).
``(C) Exception for other coverage.--
``(i) In general.--If, during the period of
eligibility under subparagraph (A), the State
determines that the child is enrolled in a type
of coverage described in subparagraph (A)(iv),
the State may terminate medical assistance for
such child under subsection (a)(10)(A)(i)(X).
``(ii) Limitation.--A State that determines
that a child is eligible for such coverage, but
not enrolled in such coverage, may not
terminate such medical assistance for such
child until such child is enrolled in such
coverage.
``(D) Redeterminations of eligibility.--
``(i) In general.--Subject to clause (ii)
and subparagraph (C)(ii), the State shall
redetermine a child's eligibility for medical
assistance under subsection (a)(10)(A)(i)(X)
not later than 180 days after the date of the
child's birth.
``(ii) Limitation.--If an application is
required for a redetermination under clause
(i), and such application is not received by
the State, and the State reasonably believes
that the child for which such application was
required continues to be a qualified newborn,
the State may not discontinue such child's
eligibility for medical assistance under
subsection (a)(10)(A)(i)(X) on the basis of
such missing application.
``(iii) Reduced fmap for failure to do
timely determination.--The increased Federal
medical assistance percentage provided under
the third sentence of section 1905(b) with
respect to individuals eligible for medical
assistance under section 1902(a)(10)(A)(i)(X)
shall not apply with respect to a child,
beginning 180 days after the date of the
child's birth, for whom a determination is not
made on a timely basis under clause (i), unless
the limitation under clause (ii) applies to
such child.''.
(c) 100 Percent Matching Rate for Temporary Coverage of Certain
Newborns.--
(1) In general.--The third sentence of section 1905(b) of
such Act (42 U.S.C. 1396d(b)) is amended by inserting before
the period at the end the following: ``and, subject to section
1902(e)(16)(E)(iii), for medical assistance for individuals in
one of the 50 States or the District of Columbia eligible for
such assistance under section 1902(a)(10)(A)(i)(X)''.
(2) Application to territories.--Section 1108(g)(4) of such
Act (42 U.S.C. 1308(g)(4)) is amended by adding at the end the
following: ``Payment for medical assistance for an individual
eligible for assistance under section 1902(a)(10)(A)(i)(X)
shall not be taken into account in applying subsection (f) (as
increased in accordance with paragraphs (1), (2), (3), and (4)
of this subsection).''
(d) Conforming Amendment.--Section 1903(f)(4) of such Act (42
U.S.C. 1396b(f)(4)) is amended by inserting ``1902(a)(10)(A)(i)(X),''
after ``1902(a)(10)(A)(i)(VIII),''.
(e) Technical Amendments.--Section 1902(e) of such Act (42 U.S.C.
1396a(e)) is amended by redesignating the paragraph (14) relating to
exclusion of compensation for participation in a clinical trial for
testing of treatments for a rare disease or condition, as added by
section 3 of the Improving Access to Clinical Trials Act of 2009, as
paragraph (15). Such redesignation shall not be construed to affect the
application of section (3)(e) of the Improving Access to Clinical
Trials Act of 2009 to such paragraph.
(f) Effective Date.--
(1) In general.--The amendments made by this section shall
apply to individuals born on or after the day that is 6 months
after the date of the enactment of this Act.
(2) Delay permitted for state plan amendment.--In the case
of a State plan for medical assistance under title XIX of the
Social Security Act which the Secretary of Health and Human
Services determines requires State legislation (other than
legislation appropriating funds) in order for the plan to meet
the additional requirements imposed by the amendments made by
this section, the State plan shall not be regarded as failing
to comply with the requirements of such title solely on the
basis of its failure to meet these additional requirements
before the first day of the first calendar quarter beginning
after the close of the first regular session of the State
legislature that begins after the date of enactment of this
Act. For purposes of the previous sentence, in the case of a
State that has a 2-year legislative session, each year of such
session shall be deemed to be a separate regular session of the
State legislature.[/INST]Start Healthy Act of 2012 - Amends title XIX (Medicaid) of the Social Security Act to provide: (1) mandatory coverage of qualified (uninsured) newborns, and (2) 100% federal medical assistance percentage (FMAP) for temporary coverage of such newborns.</s> |
with the start of the lhc as a main source of motivation , jet physics has seen a tremendous development over the last couple of years .
a significant amount of effort has been placed in trying to define jets in an optimal way for new physics searches . just to mention a few examples ,
this includes the introduction of new jet algorithms @xcite , new techniques to clean the underlying event ( ue ) contribution to the jets @xcite , or a large series of sub - jet techniques aimed at tagging boosted objects @xcite . an aspect that has been slightly less investigated is the values that one should use for the parameters inherent to a jet definition .
a noticeable example is the case of the `` radius '' of a jet , often denoted by @xmath0 , common to all the standard jet definitions used in hadronic collisions .
it has been noticed @xcite that if one wants to optimise the kinematic reconstruction of dijet events at the lhc , it is mandatory to adapt the radius of the jet when varying the scale of the process and the type of partons involved in the reconstruction . with the appearance of new techniques ,
new parameters are added and one might expect the corresponding multi - dimensional optimisation to become more and more involved .
there is therefore a risk that a poor choice of parameters for the definition of jets counteracts the positive effect of these new refinements . in this paper
we thus want to take an alternative , complementary , approach and , instead of adding a new procedure with its own parameters , study how it is possible to fix one parameter in an optimal way given the properties of the events we want to reconstruct .
in other words , we shall remove one free parameter by determining it analytically from the scales in the process we shall look at . practically , we shall focus on the determination of the most natural parameter , the radius @xmath0 , for the reconstruction of a massive colour - neutral object decaying into two jets , as done within a monte carlo approach in @xcite . in that case , we want to choose @xmath0 large enough to catch the perturbative qcd radiation , but not too large to avoid an excessive contamination from the ue .
our approach thus goes along the same line as @xcite , except that we shall extend the discussion to include extra features requested by the fact that we are looking at a peaked distribution and wish to obtain a more precise determination of @xmath0 .
contrarily to the case of @xcite , where an attempt was made to adapt dynamically the size of the jet with its hardness by replacing the size parameter with a dimensionful scale varying with the process under consideration , we shall determine a unique value for @xmath0 from the hard scale of the event and the scale of the ue , _ i.e._not introducing any alternative parameter .
the paper is organised as follow : in section [ sec : process ] we describe the process we will study as well as the details on how we proceed with the event analysis .
we also describe in that section our strategy for the analytic computation of the optimal radius @xmath1 .
we then proceed with the computation of @xmath1itself .
section [ sec : pqcd ] concentrates on the situation at the partonic level , where only perturbative radiation has to be taken into account ; while in section [ sec : ue ] we add to the picture the contamination due to the ue . in both cases , we shall compare our results with what we obtain from monte - carlo studies , as in @xcite .
finally , in section [ sec : subtraction ] , we shall discuss the extraction of the optimal jet radius for situations where we perform an underlying event background subtraction .
as in @xcite , we shall study the hard processes @xmath2 and @xmath3 , where the ( fictitious ) @xmath4 and @xmath5 are made very narrow .
the main advantage of such simple processes is that one can easily study the definition of jets at a given scale , by varying the mass @xmath6 of the colourless resonance .
it also allows one to study the differences between quark and gluon jets , and to test the validity of our computations with monte - carlo simulations .
the procedure for the event analysis is straightforward : we cluster the events with a given jet definition , select the two highest-@xmath7 jets and reconstruct the heavy object from them . in monte - carlo studies , the events were generated either with pythia @xcite ( tune dwt ) or with herwig and @xmath8 events , which does not make any difference in the discussions throughout this paper . ]
@xcite with the default jimmy tune for the ue .
we have required that the jets satisfy @xmath9 gev and @xmath10 , and we have further imposed that the two hardest jets , the ones used to reconstruct the heavy object , are close enough in rapidity , @xmath11 ( so that the transverse momentum of the jets remains close to @xmath12 ) . the quantification of the performance of a given jet definition is also borrowed from @xcite : we define @xmath13 as the width of the smallest mass window that contains a fraction @xmath14 of the reconstructed objects was defined as a fraction of the generated objects rather than a fraction of the reconstructed ones . though the former is practically more reliable , choosing the later does not affect @xmath1 in practice and simplifies considerably the analytic computation . ] . with that definition , a smaller @xmath15 would correspond to a narrower peak and thus a better reconstruction quality . finding the optimal @xmath0 , @xmath1 ,
is therefore equivalent to finding the minimum of @xmath15 , seen as a function of @xmath0 .
our task in this paper is to perform an analytic computation of the spectrum of the reconstructed mass peak @xmath16 , or @xmath17 with @xmath18 , the difference between the reconstructed and the nominal mass . by integrating that spectrum
, we can compute the probability @xmath19 for the difference @xmath20to be between @xmath21 and @xmath22 .
if we write the quality measure as @xmath23 , where @xmath24 and @xmath25 are the lower and upper end of the mass window defining @xmath15 , it is a straightforward exercise to show that it can be computed from the analytic spectrum by solving @xmath26 repeating this for different values of @xmath0 , one can then compute @xmath27 , the value of @xmath0 for which the quality measure is minimal .
we shall use @xmath28 .
as far as the analytic computation itself is concerned , there are three physical contributions that will affect the width of the reconstructed peak : final - state radiation , initial - state radiation and the ue .
the first two are perturbative ; while final - state radiation leads to losses by emissions out of the jet , initial - state radiation adds extra , unwanted , radiation inside the jet . already at the purely partonic level , there is thus an optimal radius . at this stage ,
the mass spectrum will depend on the mass of the reconstructed object , @xmath6 , and whether it decays into quarks or gluons since , perturbatively , gluons radiate more than quarks . the third contamination , the underlying event , is softer .
like the initial - state radiation , it tends to move the reconstructed mass towards larger values by clustering soft particles into the jet .
the amount of contamination involves another scale : the density of ue ( per unit area ) @xmath29 .
the most important source of dispersion in the mass spectrum comes from the fact that @xmath29 varies from an event to another . in the next two sections , we first concentrate on the purely perturbative behaviour , then include the effect of the ue . but
before getting our hands dirty , there is one additional point that needs to be discussed : the fact that we should also expect some effect due to hadronisation . actually , for the purposes of this paper , hadronisation plays a limited role . in theory
@xcite , it leads to a loss that increases like @xmath30 at small @xmath0 , to be compared with a @xmath31 for the perturbative component , and so should dominate the small-@xmath0 behaviour .
however , the normalisation is such that for practical values of @xmath0 the perturbative contribution dominates , and the effect of hadronisation on the value of @xmath1remains negligible .
a final comment concerns the jet algorithm that we shall consider : we will mostly focus on the anti-@xmath32 algorithm @xcite as its behaviour is simpler . in section [ sec : full_algs ]
we shall discuss the case of the cambridge / aachen @xcite and cambridge / aachen with filtering @xcite algorithms .
the part of the spectrum that is the most naturally computed is the pure perturbative qcd contribution .
this is equivalent to concentrating on partonic events . in that case
, two types of contribution can affect the reconstruction of the jet momentum : final - state radiation outside of the jet which leads to an underestimation of the jet momentum , and in - jet initial - state radiation yielding an over - estimation of the momentum . in this section
, we shall thus compute the pure partonic spectrum .
we do this at the one - gluon - emission ( oge ) level . since we are interested in the behaviour of the spectrum close to the mass peak , we are dominated by the @xmath33 singularity directly coming from the soft divergence of qcd . in that region , to get an integrable spectrum around the mass peak ,
it is also important to resum the @xmath34 contributions to all orders , which we shall do assuming a sudakov - like exponentiation , neglecting non - global logarithms @xcite .
for the clarity of the computation , we first deal with the soft approximation , where we only keep the @xmath33 part of the gluon emission .
we then introduce the sub - leading corrections coming from the pdf in the initial state which can have non - negligible effects , especially in the case of gluon resonances at large mass . because of longitudinal boost invariance
, we can assume that the heavy object is produced at @xmath35 .
furthermore , because of our cut @xmath36 on the dijets , we shall assume that the decay products are at the same rapidity .
the correction due to the finiteness of @xmath37 can be computed but has very little effect ( at most a few percent ) .
since the calculation for a nonzero @xmath37 cut becomes rather technical , we shall keep things simple and assume @xmath38 . at the lowest order of perturbation theory , the incoming ( @xmath39 ) and outgoing ( @xmath40 ) partons
thus have the following momenta @xmath41 we shall consider the emission of an extra soft gluon : @xmath42 with @xmath43 .
the probability for such an emission to happen is given by the antenna formula @xmath44 for an emission from the initial state , and a similar expression with @xmath45 replaced by @xmath46 for final - state radiation .
the pre - factor @xmath47 is a colour factor which should be equal to @xmath48 for an emission from a quark line and @xmath49 for an emission from a gluon line .
note that in the case of a single soft emission , the gluon is caught if and only if it is at a geometric distance smaller than @xmath0 from one of the two `` leading '' partons in the final state @xcite or cambridge / aachen , with or without filtering , as well as for the siscone @xcite algorithm ( at least in the @xmath43 limit ) . ] .
if we denote by @xmath50 the difference , @xmath51 , between the reconstructed mass and the nominal one , initial - state radiation will lead to an overestimation of the jet mass with @xmath52 whenever the additional gluon is radiated inside the jet , while final - state radiation outside the jet will lead to an underestimation of the mass with @xmath53 . integrating over the rapidity and azimuth of the emitted gluon and using ( [ eq : antenna ] ) , we find @xmath54 for the initial - state radiation spectrum , and @xmath55 for final - state radiation , with @xmath56 & & \\[-3 mm ] a_f(r ) & = & 2 \pi \log(2/r ) - \frac{\pi}{72 } r^4 + { \cal o}(r^8)\nonumber\end{aligned}\ ] ] capturing the geometric factors and the @xmath0 dependence .
one recognises the typical expected behaviour : the contamination due to initial - state radiation is proportional to the jet area , _
i.e._to @xmath57 , while the logarithmic behaviour at small @xmath0 of the final - state radiation is the trace of the collinear divergence in qcd . in both cases
, the @xmath58 behaviour corresponds to the soft divergence of qcd .
note that the coefficient of the final - state radiation @xmath59 has been expanded in series of @xmath0 .
the logarithmic behaviour at small @xmath0 corresponds to the leading collinear term as computed in @xcite but we have kept enough terms in the expansion to have a correct description over the whole @xmath0 range . in particular , the numerator in the argument of the logarithm will play a mandatory role to allow the best radius to go above 1 , which is the case in the purely perturbative spectrum and , more generally , for large - mass gluon resonances .
it is also important to discuss the choice of scale @xmath60 for @xmath61 . when using equation ( [ eq : antenna ] ) , the argument of the coupling is , for initial and final - state radiation respectively , @xmath62 & & \\[-3 mm ] \mu_f^2 & \!=\ ! & 2 \frac{(k_1.k)(k_2.k)}{(k_1.k_2)}\,=\,\frac{z^2m^2}{4}\left[\cosh^2(y)-\cos^2(\phi)\right].\nonumber\end{aligned}\ ] ] assuming that emissions close to the edge of the jet are dominant , we will use the following simplified approximation : @xmath63 as we are interested in the behaviour of the mass spectrum in the vicinity of the peak , the last thing we need to consider is the virtual corrections and the higher - order terms that diverge as @xmath64 in that region . in principle , this would depend on the jet algorithm under consideration and an exact computation would involve non - global logarithms @xcite . in practice , we shall adopt a simpler approach and assume that the one - gluon - emission result exponentiates .
this is equivalent to the introduction of a sudakov factor @xmath65 where the integration is performed up to @xmath66 , corresponding to @xmath67 at @xmath35 .
this is an arbitrary choice though a different one would only introduce corrections beyond the level of precision we are working at . using equations ( [ eq : pqcd_barespectrum_i ] ) , ( [ eq : pqcd_barespectrum_f ] ) , ( [ eq : couplingscales ] ) and
( [ eq : sudakov ] ) we find @xmath68^{k_{i , f}-1},\ ] ] with @xmath69 we note that as long as @xmath70 is smaller than 1 , the spectrum goes to 0 when @xmath50 tends to @xmath71 .
alternatively , we could regularise the landau pole in the expression for @xmath61 but we have noticed no significant effect in our conclusions when doing so . , governing the behaviour of the initial or final - state qcd spectrum as a function of @xmath0 for different masses .
the left plot covers the case of quark jets for which we use @xmath72 , and the right plot is for gluon jets for which @xmath73 . ] together with the spectrum , we will also need the total probability for the reconstructed mass to be within a certain range , _ i.e._the integrated spectrum .
denoting by @xmath19 the probability for @xmath74 to be between @xmath21 and @xmath22 , we easily find @xmath75^{k_{i , f}}\ ] ] corresponding to the spectrum ( [ eq : spectrum_pqcd_rc ] ) .
note that in this computation , we have assume that the spectrum is cut at the landau pole , corresponding to @xmath76 . before proceeding with a more involved computation ,
it is important to comment on the limit of validity of this perturbative computation . from equations ( [ eq : pqcd_barespectrum_i ] ) , ( [ eq : pqcd_barespectrum_f ] ) and ( [ eq : pqcd_geomcoefs ] ) , one might expect higher - order corrections to be important when @xmath77 becomes of order 1 . fixing the scale in the coupling to @xmath12 for the sake of the argument , we have plotted that quantity on fig .
[ fig : coefs ] for various cases of interest . in the case of quark - jets , both @xmath78 and @xmath79 remain smaller than 1 .
the case of gluon jets is more interesting ; we see that the coefficient for final - state radiation goes above one at small @xmath0 . in the case of a small - mass resonance
, this can happen for values of @xmath0 as large as 0.5 . as a rule of thumb , we can thus say that , in the case of a small - mass resonance decaying to gluon jets , our perturbative computation would only be valid for @xmath80 .
it is particularly interesting to relate that to the observation made in @xcite that in this precise case of small - mass resonances decaying into gluons , we observed a disappearance of the peak in the reconstructed mass spectrum for small values of @xmath0 .
though this was happening at slightly smaller values of @xmath0 ( around @xmath81 ) , the present computation provides an explanation of this effect : when @xmath82 grows above 1 , the peak in the final - state radiation spectrum is no longer around @xmath83 and the mass peak disappears .
we shall come back to this point later in section [ sec : full_mc ] .
note also that , from fig . [
fig : coefs ] , one can have a feeling of what the optimal radius will be for parton - level events .
indeed , one can expect that , for @xmath84 , the spectrum will be nearly symmetric around the nominal mass ( _ i.e._around @xmath83 ) , that is @xmath85 . for both quarks and gluons and for all masses , this means that one should expect @xmath86 .
we will see later on that this is indeed relatively close to what we shall obtain but that pdf effects , computed in the next section , induce some departure from that situation . in order to get a better description of the variety of processes we consider over the whole kinematic range
, we shall see that it is important to take into account the effect of the pdf on initial - state radiation .
this addresses the fact that the emission of an initial - state gluon imposes to take the parton distribution functions at a larger momentum fraction @xmath87 .
this should therefore introduce an additional suppression , more important at large mass and for gluon - jets than for quark jets .
let us consider the production of a heavy particle at a fixed rapidity @xmath88 .
the leading - order cross section is easily obtained : @xmath89 where the index @xmath90 represents the colour of the colliding partons , @xmath91 is the pdf implicitly taken at a scale @xmath6 , and @xmath92 is the centre - of - mass energy of the collision .
this expression also comes with the kinematic constraint @xmath93 .
we should now add to that process an extra parton emitted at a rapidity @xmath94 .
for our purpose of computing the initial - state radiation contamination to a jet , we can safely make the simplifying assumption that the rapidity of the gluon is the same as the rapidity of the `` leading '' parton , _
i.e. _ , @xmath95 . by doing so , we decouple the effects of the pdf from the effects of the jet clustering .
the latter will be reinserted later on by multiplying our results by the geometric factor @xmath96 .
we thus have @xmath97 in that expression , @xmath98 is the longitudinal fraction of @xmath99 carried by the parton entering the collision satisfying @xmath100 . if we rewrite it in terms of the longitudinal momentum of the emitted parton ( measured w.r.t .
the momentum of the beam ) @xmath101 , one gets after a bit of algebra @xmath102 keeping the kinematic conventions introduced in the previous section , the longitudinal fraction @xmath103 can be rewritten in terms of the transverse momentum @xmath104 of the parton as @xmath105 which finally implies @xmath106 with the kinematic constraint @xmath107 in the limit of small @xmath50 , _ i.e._neglecting the @xmath50 offset in the pdf , one gets @xmath108 which is exactly the result we have obtained in the soft limit up to the geometric factor and @xmath109 where the gluon is emitted in one of the two jets . ] @xmath110 that we will need to reintroduce at the end of the computation . to simplify the discussion , we shall assume that the pdfs take the form @xmath111 the coefficients @xmath112 and @xmath113 will depend on the type of parton and the scale @xmath6 but we shall assume a unique value for @xmath114 . at this level , we could proceed by integrating over the rapidity @xmath88 .
this is feasible analytically with the choice of pdf but it leads to a gauss hypergeometric function in @xmath115 for which the sudakov factor can not be computed analytically .
we will therefore carry on with the computation at a fixed rapidity @xmath88 .
taking into account the emissions from both partons entering the collisions , normalising to the @xmath116 cross - section and reinserting the geometric factor , one obtains @xmath117,\ ] ] where we have introduced @xmath118 and @xmath119 , and it is understood that the terms in the squared brackets are restricted to the appropriate phase space _ i.e._@xmath120 , respectively for each term . in order to compute the sudakov form factor analytically , we shall make the approximation that the exponents @xmath113 are integers ( in practice , we shall use @xmath121 and @xmath122 for ( anti-)quark and gluon - jets respectively ) , and expand the small-@xmath87 power behaviour to first order in @xmath50 : @xmath123 using @xmath124 the fact that @xmath113 is an integer allows one to see as a polynomial in @xmath50 .
we can then easily compute the sudakov factor using the following fundamental integrals : @xmath125 - { \rm ei}\left[p\,\log({\ensuremath{\delta m}\xspace}/\lambda_i)\right]\right\},\end{aligned}\ ] ] where @xmath126 is the exponential integral . with these simplifying assumptions ,
the final perturbative spectrum for initial - state radiation can be written as @xmath127 with the integrated probability @xmath128^{k_i } \,\exp\left[-k_i\sum_{k=1}^{\beta_a+1 } \mu_k \ , { \cal e}_k \left(\frac{\lambda_i}{m}\right)^k\right],\ ] ] and the coefficients @xmath129,\\ \nu_{-1 } & = & \nu_{\beta_a+1 } = 0,\\ { \cal{e}}_k & = & { \rm ei}\left[k\,\log(m/(2\lambda_i))\right ] - { \rm ei}\left[k\,\log({\ensuremath{\delta m}\xspace}/\lambda_i)\right].\label{eq : suduptom2}\end{aligned}\ ] ] note that to obtain ( [ eq : suduptom2 ] ) , we have to integrate @xmath50 up to @xmath12 , which is strictly valid only when @xmath130 , but similar results can easily be derived at forward rapidities . dijet system at a nominal mass of 100 gev while the right plot is for the gluonic case at 2 tev . in both cases ,
the anti-@xmath32 algorithm with a radius of 1 has been used for the clustering . ]
we want to conclude this section by a comparison of the predictions we obtain for the optimal radius from our analytical studies and from monte - carlo approaches .
when dealing with the analytic result , we shall use the initial and final - state results computed in the previous sections in the two different situations for which we have analytic results : the soft limit with a running - coupling approximation , eqs . and , and the `` full '' spectrum where we also include the pdf effects in the initial - state radiation , eq . .
the total perturbative qcd spectrum is the convolution of the initial and final - state pieces which , in practice , will be carried numerically .
we shall use @xmath131 mev and @xmath132 to compute the running of the qcd coupling , and , for the pdf effects in the initial - state - radiation spectrum , we shall adopt @xmath133 , @xmath121 and @xmath122 , and assume @xmath35 , where we have checked that most of the massive objects in the monte carlo sample were produced . the quality measure is computed from the spectrum using . for the parton - level spectrum .
the ( red ) dashed curve corresponds to our analytic computation in the soft limit while the ( blue ) solid one includes pdf effects . the ( green ) triangles and ( cyan ) circles show the monte - carlo simulations for pythia and herwig respectively .
as for fig .
[ fig : parton_hist ] , the left plot is for a @xmath134 dijet system at a nominal mass of 100 gev while the right plot is for the gluonic case with @xmath135 tev . ] we start our comparison directly with the spectrum for the reconstructed dijet mass , as shown on fig .
[ fig : parton_hist ] for quark jets , @xmath136 gev and gluon jets , @xmath135 tev .
generally speaking , the agreement between our analytic computation and herwig is good , even very good for the 100 gev quark - jet case .
note that this agreement is always better in the region of the peak , where the soft - gluon emissions approximation we are working with is supposed to hold .
similarly the small differences in the tail at small and large @xmath137 are beyond the scope of our approximation . in both the quark and gluon - jet cases , we see that the inclusion of pdf effects , reducing the initial - state radiation , significantly improves the description , especially in the case of large - mass gluon jets , where we are sensitive to fast - falling gluon distributions at large @xmath87 . extracted from parton - level pythia ( green triangles ) and herwig ( cyan circles ) simulations .
the left plot shows the case of a resonance decaying into @xmath134 jets while the right plot has gluon jets . ]
next , we turn to the computation of the quality measure , presented in fig . [
fig : parton_quality ] .
after properly taking into account the pdf effects , our computation agrees in shape with the monte - carlo results . for the normalisation
, we are closer to the herwig simulation in the case of quark jets , while we better agree with pythia simulations for gluon jets .
since our analytic computation is identical in both cases , it it somehow hard to find an explanation for those differences .
finally , let us concentrate on the values of @xmath1extracted from the previous examples .
this is shown on fig .
[ fig : parton ] for quark jets ( left panel ) and gluon jets ( right panel ) .
despite the apparent normalisation issue between pythia and herwig observed on fig .
[ fig : parton_quality ] , the fact that they agree on the shape of the quality means that they yield very similar extracted optimal radii .
if we turn to the analytic computation , we first see that in the soft approximation , the optimal radius is independent on the process under consideration with @xmath138 regardless of the mass or the parton type . in practice , this is due to the fact that the quality measure is a complicated function of @xmath139 involving _ e.g._their derivatives which are different at @xmath140 . ] .
the reduction of the initial - state radiation due to the pdf effects has a sizeable effect on the extracted optimal radius in such a way that , at the end of the day , our analytic extraction of @xmath1 in the `` full '' model reproduces very well the monte - carlo simulations with an error @xmath141 0.1 .
one of the most important effects when clustering jets at hadronic colliders is the presence of the underlying event ( ue ) coming from multiple interaction and beam remnants .
this tends to produce a fairly uniform soft radiation of a few gev per unit area that contaminates the jets and affects their momentum reconstruction . in this section
, we therefore study the effects of this ue on the mass spectrum we have computed from perturbative qcd in the previous section .
if we work within the assumption that the ue is uniform in rapidity and azimuth , the average @xmath7 contamination to each jet will be @xmath142 where @xmath143 is the ( active ) area of the jet @xcite and @xmath29 the ue density per unit area .
for a given event , this contamination is affected by two kinds of fluctuations : first , the fluctuations of the background itself which go like @xmath144 , with @xmath145 the background fluctuations per unit area .
then , keeping in mind the possibility to discuss our results for different jet algorithms than the anti-@xmath32 algorithm , the active area of a jet is in general known to fluctuate , with an average value proportional to @xmath57 that increases with @xmath7 in a different way for each jet algorithm . for a given background density @xmath29 ,
let us denote by @xmath146 the probability distribution for a jet @xmath147 to receive a contamination @xmath148 from the ue .
for a jet of area @xmath149 , this distribution has an average of @xmath150 and a dispersion @xmath151 .
we therefore also have to introduce @xmath152 the distribution , of average @xmath153 and dispersion @xmath154 of the area divided by @xmath57 , of the jet @xmath147 .
if the two jets were perfect circles of radius @xmath0 , one could easily compute that the offset on the reconstructed mass would be @xmath155 , up to corrections proportional to @xmath156 , where @xmath157 is the modified bessel function of the first kind . for generic jets
we shall then use @xmath158 where @xmath159 and @xmath160 are the transverse momenta of the background contamination of our dijets .
on top of that , when we consider an event sample , the values of @xmath29 and @xmath145 will fluctuate from one event to another . for the event - by - event fluctuations of the background densities
, we shall assume a distribution @xmath161 , of average @xmath162 and dispersion @xmath163 .
for the intra - event fluctuations ( per unit area ) @xmath145 we shall simply assume that they remain proportional .
] to @xmath29 , _
i.e. _ , @xmath164 . given the event - by - event @xmath29 distribution @xmath161 , the intra - event fluctuations , @xmath165 and the area distribution @xmath152 , the ue spectrum can be inferred from ( [ eq : dmfromue ] ) @xmath166 without knowing exactly that distribution , we can compute its average and dispersion in terms of the properties of the fundamental distributions : @xmath167\,2 \pi r^2 \bar{a}\,{\left\langle \rho \right\rangle},\nonumber\\ \sigma_{{\ensuremath{\delta m}\xspace}}^2 & = & \int { \rm d}{\ensuremath{\delta m}\xspace}\,({\ensuremath{\delta m}\xspace}-{\left\langle { \ensuremath{\delta m}\xspace}\right\rangle})^2 \,\frac{{\rm d}p_{\rm ue}}{{\rm d}{\ensuremath{\delta m}\xspace}}\label{eq : uedisp}\\ & = & \left[\frac{2i_1(r)}{r}\right]^2 \left [ 4 \bar{a}^2 ( \pi r^2)^2 \sigma_\rho^2 + 2 ( \pi r^2)^2 \left({\left\langle \rho \right\rangle}^2+\sigma_\rho^2\right ) \sigma_a^2 + 2 \bar{a } ( \pi r^2 ) \left({\left\langle \rho \right\rangle}^2+\sigma_\rho^2\right ) \mu^2 \right].\nonumber\end{aligned}\ ] ] the average is consistent with what one would naively expect , and the dispersion is a combination of the three separate sources of dispersion we are including : event - by - event fluctuations in @xmath29 ( the first term ) , area fluctuations ( the second term ) and intra - event fluctuations ( the third term ) .
as expected , the first two are proportional to the area of the jet _ i.e._to @xmath57 , while the intra - event fluctuations are proportional to its square root .
so , instead of modelling the various distributions separately and perform the integrations in , we shall directly model the total ue spectrum and adjust its parameters to reproduce the total average and dispersion . more specifically
, we shall assume @xmath168 the parameters @xmath169 and @xmath170 can be adjusted to reproduce the average ( [ eq : ueavg ] ) and dispersion ( [ eq : uedisp ] ) of the ue distribution .
one finds @xmath171 this choice has the advantage over a gaussian distribution that it remains positive .
our strategy is rather straightforward : as we did when combining the initial - state and final - state radiation spectra , we shall convolute the perturbative qcd spectrum , discussed in section [ sec : pqcd_mc ] , with the ue spectrum . for each mass and parton - type ,
we wish to compare our results with the monte - carlo studies @xcite . for the perturbative qcd part of the spectrum , we use the convolution already discussed in section [ sec : pqcd_mc ] and consider the same models : the pure soft approximation and the spectrum including pdf effects in the initial - state .
the result is itself convoluted with the underlying - event distribution for which we still have to determine the parameters appearing in eqs .
( [ eq : ueavg ] ) and ( [ eq : uedisp ] ) .
the area properties @xmath153 and @xmath154 have been calculated , together with their scaling violations in @xcite .
the properties of the background are computed directly from the monte - carlo event sample using fastjet @xcite and the method advocated in @xcite and @xcite : each event is first clustered with the cambridge / aachen algorithm with @xmath172 ; @xmath29 and @xmath145 are then estimated from the jets that are within a rapidity strip of 1 unit around the hardest dijet system , excluding the two hardest jets in the event .
the average properties @xmath162 , @xmath60 and @xmath163 can then be easily extracted from the complete event sample . for completeness
, we give a table of the values we have obtained in appendix [ app : ueprops ] . with that method , we are able to compute the mass spectrum , and thus the quality measure , at a given mass and with a given parton type and ue characteristics .
we then extract @xmath1by searching the minimum of the quality measure by steps of 0.01 in @xmath0 . and the anti-@xmath32 algorithm . ] for quark dijets at 100 gev ( left panel ) and gluon dijets at 2 tev ( right panel ) .
the triangles and solid lines correspond to the pythia simulations while the circles and dashed lines correspond to herwig simulations . ] but for herwig simulations . ] as for the parton - level case , we shall compare our computations with the monte carlo simulations from pythia ( tune dwt ) and herwig ( with default jimmy tune ) as the details of the underlying event can differ .
we shall again proceed in three steps : first consider the histograms , then the quality measures and finally the optimal radius . for simplicity , we shall focus on the anti-@xmath32 algorithm for which @xmath173 and @xmath174 .
let us start with the histograms , figure [ fig : ue_hist ] , where we illustrate our description of the spectrum for the quark dijets at small mass and gluon dijets at large mass . in both cases ,
our analytic histogram correctly reproduces the behaviour observed with herwig .
we note however that our analytic computation slightly underestimating the ue in the peak region in the case of quark jets at small nominal mass , is a bit more pronounced . ] @xmath6 .
if we then move to the case of the quality measure , figure [ fig : ue_quality ] , we see that , given the differences we have already observed at the parton level ( see figure [ fig : parton_quality ] ) , the addition of the underlying event gives a reasonable description of the monte - carlo results , especially the shape of the quality at large @xmath0 .
note that only the curves corresponding to the model including the pdf effects are shown on figure [ fig : ue_quality ] for clarity reasons .
finally , the extracted optimal radius is presented on figures [ fig : ue_pythia ] and [ fig : ue_herwig ] for pythia and herwig simulations respectively , as a function of the mass for both quark and gluon jets .
generally speaking we obtain a good description of the monte - carlo results .
we see once again that the inclusion of the pdf effects significantly improves the description of the optimal radius for gluon jets at large mass , as expected .
we slightly underestimate the optimal radius in the case of gluon jets at large mass , but we have to notice that this is the regime on which it matters the least as in that region the minimum in the quality measure is rather flat .
we thus see that our complete analytic model , the solid ( blue ) curve on figures [ fig : ue_pythia ] and [ fig : ue_herwig ] , corresponding to our analytic pqcd computation including pdf effects , eq .
( [ eq : isrfull ] ) , convoluted with our model of the underlying event , eq .
( [ eq : spectue ] ) , gives a good extraction of the optimal radius @xmath1 .
results , the dashed ( green ) lines and the circles show c / a results , and the dotted ( red ) lines and the triangles correspond to c / a with filtering . ] now that we have checked the agreement between our analytic computations and monte - carlo simulations for the simpler case of the anti-@xmath32 algorithm , let us briefly discuss other possible jet algorithms . in this section , we shall apply our analytic computations to the case of the cambridge / aachen ( c / a ) as well as to the cambridge / aachen algorithm supplemented by a filter ( c / a+filt ) . while the former usually leads to quality measurements close to what is obtained in the anti-@xmath32 case , the latter produces narrower peaks with an optimal radius slightly larger than the one obtained from c / a without filtering . for simplicity
, we shall follow what has been done in @xcite and use @xmath175 and @xmath176 for the parameters of the filter , _
i.e. _ , recluster each jet with c / a and a radius of half the original one and keep the two hardest subjets , discarding the softer ones .
the analytic computation goes exactly as in the case of the anti-@xmath32 algorithm .
the only thing that will change in our approach is the inclusion of the area contribution in the ue distribution .
the expressions for the area are computed analytically , as in @xcite , up to order @xmath61 : @xmath177,\\ \sigma_a^2 & = & \sigma_{0,{\rm jd}}^2 + s_{{\rm jd}}^2\,\frac{c_a}{\beta_0\pi}\log\left[\frac{\alpha_s(q_{0,{\rm jd}}^{(a)})}{\alpha_s(rp_t)}\right],\end{aligned}\ ] ] where the coefficient @xmath178 , @xmath179 , @xmath180 and @xmath92 are computed in perturbation theory and have been calculated , c / a and siscone algorithms . ] in @xcite , while the scales @xmath181 are of non - perturbative origin and have been determined in @xcite from a fit to herwig simulations . in our case , we shall use @xmath182 together with the following values for the coefficients : @xmath183 to avoid multiplying the figures , we just show , see figure [ fig : algs_pythia ] , the final result of the extracted optimal radius as a function of the mass for the three algorithms under consideration , compared to pythia simulations .
we see that , in agreement with the monte carlo , the differences between anti-@xmath32 and cambridge / aachen are very small and thus our analytic approach reproduces the expected behaviour correctly . for the case of the c / a algorithm with filtering
, we obtain a good description in the case of quark dijet systems but systematically underestimate the optimal radius , by about 0.1 - 0.2 , in the case of gluon jets .
we believe that this is due to the fact that we should also introduce some dependence on the algorithm at the level of the perturbative spectrum . in our soft - gluon approximation all
the algorithm will have the same initial and final - state radiation spectra .
however , with a more complete treatment , _ e.g._including non - global logarithms as in @xcite , differences will start appearing .
another effect comes from the combination of the initial and final - state radiation spectra : the simple convolution we have used is reasonable in the case of the anti-@xmath32 algorithm where the shape of the jet is not affected by the radiation , but more subtle phenomena will appear for more complex algorithms , especially in the filtered case where , in some geometric regions , the capture of isr gluons can be affected by internal gluon radiation in the jet .
all these effects are beyond the reach of the present analysis .
as expected from the previous discussion , discrepancies are more pronounced in the case of gluon jets at large mass , where perturbative radiation dominated the spectrum .
our computation nevertheless gives reasonable results at the end of the day , given also that for gluon dijets at larger mass , the minimum in the quality measure is less pronounced than in other situations .
finally , let us mention that the case of the @xmath32 algorithm @xcite is also very close to what we obtain for the anti-@xmath32 and c / a algorithm , hence well reproduced by our calculation .
for the siscone algorithm , differences in the perturbative spectrum also appear when the radiated gluon is not soft , we therefore postpone that case for a further study . to some extent , the present calculation can be seen as an extended version of what has been done in @xcite , where the authors compute the average @xmath7 shift of a jet due to final - state radiation , hadronisation and the ue .
the approach we pursue in this paper is however much more complete in the sense that we obtain the full spectrum instead of just the average value . as a consequence
, we can extract the width of the peak really as the dispersion in the spectrum , while in @xcite the width is approximated by @xmath184 _
i.e._the total dispersion is approximated by the sum of each independent average squared .
the individual contributions are found to be @xcite @xmath185 with @xmath186 gev for @xmath187 gev and @xmath188 & & \\[-3 mm ] l_g & = & \left(2 \log(2)-\frac{43}{96}\right ) c_a + \frac{7}{48}n_ft_r . \nonumber\end{aligned}\ ] ] the optimal radius is then obtained by minimising w.r.t . @xmath0 . in practice ,
we have used @xmath189 , @xmath132 , @xmath131 mev and computed the qcd coupling at the scale @xmath190 . instead of using a fixed value for @xmath191 as in @xcite
, we have used the fact that it is related to the average background density , @xmath162 , through ( see section [ sec : full ] ) @xmath192 and used the values extracted from the monte carlo event samples and already used in section [ sec : full ] for @xmath162 . the extracted value of @xmath1is shown on fig .
[ fig : dms ] in the case of pythia simulations , for the anti-@xmath32 algorithm .
the results are compared with the monte carlo results and with our complete analytic calculation .
we see that the simpler approach of @xcite manages to extract the correct value for @xmath1at small mass but fails to reproduce the observed behaviour at larger mass , and this for both quark and gluon jets .
the reason for this failure is rather hard to pinpoint : it can come , _
e.g. _ , from the crudeness of the approximation ( [ eq : dmsdisp ] ) , the lack of an initial - state radiation contribution and the corresponding pdf effects , or the description of the underlying event in terms of the average density @xmath162 instead of its fluctuations @xmath163 .
the last point we wish to discuss is the situation where we perform background subtraction using jet areas @xcite , as advocated in @xcite .
the idea behind ue subtraction is to get rid of the shift due to the ue density contaminating the mass reconstruction .
since subtraction is performed on each single event , one hopes to get rid of the fluctuations of the background density across the events , hence obtaining a narrower peak . in this respect , all we should be left with is the background fluctuations inside an event which have a linear dependence on @xmath0 rather than the quadratic one computed in the unsubtracted case .
this is a much smaller effect and one thus expect the quality measure to be better ( _ i.e._smaller ) than in the unsubtracted case as well as the optimal radius to be larger . in practice
, one would thus naively convolute the perturbative spectrum computed in section [ sec : pqcd ] with a subtracted ue spectrum taking into account these intra - event fluctuations . doing that would actually lead to a quality much better than what is observed in monte - carlo studies and to a systematic over - estimation of @xmath1 . the additional effect that is mandatory to take into account is the fact that subtraction is performed using an estimated value for the background density @xmath193 which can differ from the exact value of @xmath29 for that event .
this results in some smearing effect left over from the unsubtracted spectrum . because of this , the computation of the subtracted ue spectrum turns out to be more involved than the corresponding unsubtracted case computed in section [ sec : full ] , mostly because one also would have to consider the distribution probability for @xmath193 .
the properties of the estimated value of @xmath29 have actually recently been discussed at length in @xcite , where we learn that the estimation of the background density using a median - based approach suffers from two sources of bias : one of soft origin , related to the fact that the median of a set of pure - ue jets may differ from its average ; and a contamination from radiation coming from the hard jets .
if we call @xmath29 and @xmath145 the average ue density and its fluctuations for one given event , and define @xmath194 as the relative error in the estimation of @xmath29 , the average and dispersion of @xmath195 are @xcite @xmath196 where , as in section [ sec : full ] we used @xmath197 , and the coefficients are @xmath198 and @xmath199 with @xmath200 in the previous set of equations , @xmath201 is a pure number extracted in @xcite , @xmath202 is the jet radius used to estimate the background properties , @xmath203 is the total area of the range we are using to estimate the background , @xmath181 is a soft cut - off that we fixed to 1 gev , and @xmath204 is the hard scale that we naturally took equal to @xmath12 .
these properties constrain the distribution of @xmath195 , that we shall denote by @xmath205 , as a function of @xmath60 .
since the intra - event fluctuations will play a substantial role in this ue - subtracted situation , we shall also consider a distribution for them .
for simplicity , we shall parametrise the distribution in terms of @xmath60 rather than in terms of @xmath145 as background estimations are naturally expressed in that variable .
we therefore introduce @xmath206 , of average @xmath207 and dispersion @xmath208 . in the course of the computation
below , we shall encounter higher cumulants for this distribution . to keep things simple
, we shall work with the gaussian assumption .
we have checked that this choice does not affect the resulting @xmath1 . ] _
i.e._@xmath209 , @xmath210 .
the values of @xmath207 and @xmath208 can again be extracted from the monte - carlo samples . with this at hand ,
we proceed , as in section [ sec : full ] , by computing the mass shift for a given configuration and deducing its average and dispersion . for given values of @xmath29 , @xmath60 , @xmath211 , jet areas @xmath212 and jet ue contaminations @xmath148 , the offset in the reconstructed mass after subtraction is @xmath213 \left[p_{t,1}+p_{t,2}-\pi r^2 ( a_1+a_2)(1+\delta)\rho\right],\ ] ] where the last term is the subtracted piece . after a slightly lengthy computation we reach .
the only additional approximation is the replacement of @xmath145 by @xmath214 in @xmath215 ( eq . ( [ eq : nh ] ) ) , which only introduces subleading corrections . ]
@xmath216\,2 \pi r^2 \bar{a}\,{\left\langle \rho \right\rangle } \left\lbrack -d_1{\left\langle \mu \right\rangle}+d_2({\left\langle \mu \right\rangle}^2+\sigma_\mu^2)\right\rbrack,\label{eq : ueavgsub}\\ \sigma_{{\ensuremath{\delta m}\xspace}}^2 & = & \left[\frac{2i_1(r)}{r}\right]^2 \left ( \left\{\left[2\pi r^2 \bar{a}+2(\pi r^2)^2\sigma_a^2(d_1 ^ 2+s_d^2)+4(\pi r^2 \bar{a})^2 s_d^2\right]({\left\langle \rho \right\rangle}^2+\sigma_\rho^2)\right.\right.\nonumber\\[-5 mm ] & & \phantom{\left[\frac{2i_1(r)}{r}\right]^2 ( ) } \left.+4(\pi r^2\bar{a})^2d_1 ^ 2\sigma_\rho^2\right\}({\left\langle \mu \right\rangle}^2+\sigma_\mu^2)\nonumber\\[-5 mm ] & & \phantom{\left[\frac{2i_1(r)}{r}\right]^2 } \left .
+ \left[2(\pi r^2)^2\sigma_a^2({\left\langle \rho \right\rangle}^2+\sigma_\rho^2)+4 ( \pi r^2 \bar{a})^2\sigma_\rho^2\right]\left(d_2 ^ 2{\left\langle \mu^4 \right\rangle}-2d_1d_2{\left\langle \mu^3 \right\rangle}\right)\right.\nonumber\\[-5 mm ] & & \phantom{\left[\frac{2i_1(r)}{r}\right]^2 } \left .
+ \ , 4 ( \pi r^2 \bar{a})^2 { \left\langle \rho \right\rangle}^2\left[2 d_2 ^ 2\sigma_\mu^2+(2d_2{\left\langle \mu \right\rangle}-d_1)^2\right]\sigma_\mu^2\right).\label{eq : uedispsub}\end{aligned}\ ] ] once we have these expressions , the last step is to parametrise the subtracted ue spectrum . since subtraction can produce negative values for @xmath20 , we can not use .
the technique we shall adopt is to keep the same distribution using the unsubtracted average together with the dispersion we have just computed , and then to shift the complete distribution in order to reproduce the subtracted average @xmath20 . in practice , this gives @xmath217 where the parameters @xmath169 , @xmath21 and @xmath170 are given by @xmath218 with @xmath219 and @xmath220 given by eqs . and , and @xmath221 by eq .
. finally , it is interesting to notice that in the case of a perfect estimation of the background density @xmath222 , _
i.e._@xmath223 , one recovers @xmath224 ^ 2 \ , 2\pi r^2 \bar{a}({\left\langle \rho \right\rangle}^2+\sigma_\rho^2)({\left\langle \mu \right\rangle}^2+\sigma_\mu^2)\end{aligned}\ ] ] _ i.e._no average shift and a ( squared ) dispersion that is proportional to the area ( linearly ) and to @xmath225 . as for the previous cases we have analysed
, we shall perform a comparison of our analytic predictions with monte carlo simulations for the ue - subtracted case .
the method goes exactly as before , so we just highlight the main steps and present our results for the optimal radius @xmath1and stay with the anti-@xmath32 algorithm . for the analytic part of the computation
, the perturbative qcd spectrum is convoluted with the subtracted ue spectrum calculated in the previous section . concerning the parameters of the latter ,
all background properties , @xmath162 , @xmath226 , @xmath207 and @xmath208 are extracted directly from the monte - carlo data sample and the estimation of the background density was performed using the cambridge / aachen algorithm with a radius of 0.6 .
we have kept all the jets within one unit of rapidity around the hardest dijet , excluding the two hardest jets in the event , giving a total area @xmath227 .
it is interesting to notice that when background subtraction is performed , the final results will slightly depend on the details of how @xmath29 is estimated , through the coefficients @xmath228 , @xmath229 and @xmath230 in our analytic approach . extending the range , _ i.e._increasing its area @xmath203 , would decrease the bias in the estimation of @xmath29 , but in that case , there would be a risk that the background would not be uniform over the range ( _ e.g._vary with rapidity ) .
following @xcite , we could therefore also try to optimise the choice of range and jet definition used for estimating @xmath29 . the computed value of @xmath1is shown on fig .
[ fig : subtract ] in the case of pythia simulations . for an easier comparison ,
we show both the subtracted and unsubtracted results .
for the analytic calculation , we observe a value of @xmath1larger in the subtracted case by about 0.04 in the case of quark - jets and by about 0.08 in the case of gluon - jets .
all these values are in good agreement with what is observed in the monte - carlo simulations .
throughout this paper we have investigated analytically the optimisation of the radius @xmath0 one uses with a jet algorithm to reconstruct dijet resonances .
we have already learnt @xcite that carefully choosing the jet radius can lead to significant improvement of the reconstructed signal and we find it valuable to supplement previous monte - carlo studies with an analytic understanding of these dijet reconstructions .
our approach has been to calculate the reconstructed dijet mass spectrum .
this was done by convoluting fundamental pieces : the perturbative qcd radiation in the initial and final state , and the contamination due to the underlying event . for the perturbative part
, we have worked in the soft - gluon emission approximation , a choice motivated by the fact that we are mostly interested in the behaviour in the vicinity of the mass peak . in the case of the initial - state radiation spectrum , we have also included pdf effects that can have a non - negligible impact , especially in the case of gluon jets and at large dijet mass .
for the ue description , we have modelled it in such a way as to reproduce the observed properties of the background . from the reconstructed mass spectrum
, we can compute a quality measure and extract an optimal radius , following the method outlined in @xcite .
our analytic results have been considered and compared with monte - carlo simulations in various cases .
we have started with parton - level events , where we can test our analytic computation of the perturbative spectrum ; then we have focused on full hadronic events including the underlying event ; and , finally , we have considered the situation with a jet - area - based background subtraction @xcite .
we have mostly considered the case of the anti-@xmath32 algorithm but have also considered other options . generally speaking , we can say that we obtain a good description of the monte - carlo results , especially when including the pdf effects in initial - state radiation .
the optimal radius @xmath1computed analytically is in most cases less than 0.1 away from the monte - carlo expectation .
the comparison at a more basic level , the quality measure or even the mass spectrum , also shows a good agreement .
most of the deviations between our analytic results and monte carlo simulations can probably be traced back to what we observe at the partonic level .
though our analytic computation reproduces nicely the monte - carlo simulations , we have observed some deviations in section [ sec : pqcd_mc ] .
it is interesting to notice that the differences between our description and the monte - carlo results is usually of the same order as the differences obtained between pythia and herwig .
these differences propagate to the situation where the ue is included .
the one case where our analytic results deviate a bit more from the monte - carlo simulations is the case of the cambridge / aachen algorithm supplemented by a filter ( see section [ sec : full_algs ] ) , for events including the ue , while our description remains good for the anti-@xmath32 and the cambridge / aachen algorithm without any filter .
we think that a better description goes beyond the reach of the present analysis , _
e.g._already at the partonic level , a simple convolution between the initial and final - state spectra may be too simplistic when filtering is applied .
let us also notice that our description of the ue allows us to treat successfully both the case where the ue is subtracted and the case where it is not .
our approach includes all the effects that contribute to the dispersion of the reconstructed mass : mostly background fluctuations from one event to another , intra - event fluctuations and area fluctuations .
it is interesting to notice that in the case of subtracted ue , it was also mandatory to take into account the fact that the estimated background can differ from its `` true '' value .
this leads to a significant additional contribution to the dispersion . using the analytic computations from @xcite
led to good results for the extracted @xmath1 .
if one wishes to improve the present description , additional effects have to be included in the analytic computation : relaxing the soft - gluon - emission approximation , obtaining sub - leading logarithmic corrections , performing a better resummation of the soft virtual corrections than a simple sudakov factor , _ e.g._using non - global logarithms , and including hadronisation corrections .
however , we have seen that the description we can achieve with our simple approach is already satisfactory without having to introduce these corrections .
it is nevertheless important to remember their existence as they might become relevant in more specific situations , like the case of filtering where we have observed that we start to reach the limits of our simple approach .
some effects , like subleading logarithmic corrections , may even be simpler to compute analytically than to implement in a monte carlo .
another point that we have not investigated and that might be interesting in a future study is the case of the rapidity dependence of @xmath1 .
as we have seen in section [ sec : pdf ] , pdf effects introduce a dependence on the rapidity at which the heavy object is produced @xcite and it might be interesting to see how @xmath1varies with that rapidity . also , all the computations we have performed were for a complete event - set .
a next major step would be to optimise the radius on an event - by - event basis .
this is much more complicated as the previous approach would then only give access to an average dispersion for a single event and the additional dispersion arising when combining the whole set of events would be much harder to handle .
we therefore also leave that step to future studies .
the question of knowing which jet algorithm should be preferred has already triggered many discussions both on the theoretical and on the experimental side , and more complex jet definitions introducing more parameters have often been proposed to improve jet reconstruction .
the present work , together with @xcite , can be seen as opening a new direction of improvement : analytically optimising the parameters in the jet definitions . considering a single parameter ,
the jet radius , for a simple process , dijet reconstructions , is a first step in that direction . gaining analytic control on the parameters entering jet definitions
can be extremely valuable .
this is especially true when new parameters are introduced : being able to predict them can avoid often costly determinations based on monte - carlo simulations or rough empirical choices .
the application of the techniques developed in this paper to other parameters and more general processes would therefore be very interesting .
i am extremely grateful to gavin salam for many useful suggestions and comments at every step of this work .
i also thank lorenzo magnea for a careful reading of the manuscript .
finally , i thank the brookhaven national laboratory for support when this work was initiated and the lpthe ( university of paris 6 ) where parts of this work has been done .
.background properties needed to parametrise the ue distribution .
values are given for quark and gluon jets as well as for pythia and herwig+jimmy simulations .
all dimensionful numbers are expressed in gev . [ cols=">,^,^,^,^,^,^,^,^,^,^,^,^ " , ] for the sake of completeness , we briefly mention in this appendix the values of the background properties that are necessary to fix the ue spectrum .
these will differ between quark and gluon jets and between pythia 6.4 ( tune dwt ) and herwig 6.51 ( with default jimmy tune ) .
all the values used in our analytic computation are summarised in table [ tab : ueprops ] .
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we also compare our results with previous monte - carlo studies . | <s>[INST]with the start of the lhc as a main source of motivation , jet physics has seen a tremendous development over the last couple of years .
a significant amount of effort has been placed in trying to define jets in an optimal way for new physics searches . just to mention a few examples ,
this includes the introduction of new jet algorithms @xcite , new techniques to clean the underlying event ( ue ) contribution to the jets @xcite , or a large series of sub - jet techniques aimed at tagging boosted objects @xcite . an aspect that has been slightly less investigated is the values that one should use for the parameters inherent to a jet definition .
a noticeable example is the case of the `` radius '' of a jet , often denoted by @xmath0 , common to all the standard jet definitions used in hadronic collisions .
it has been noticed @xcite that if one wants to optimise the kinematic reconstruction of dijet events at the lhc , it is mandatory to adapt the radius of the jet when varying the scale of the process and the type of partons involved in the reconstruction . with the appearance of new techniques ,
new parameters are added and one might expect the corresponding multi - dimensional optimisation to become more and more involved .
there is therefore a risk that a poor choice of parameters for the definition of jets counteracts the positive effect of these new refinements . in this paper
we thus want to take an alternative , complementary , approach and , instead of adding a new procedure with its own parameters , study how it is possible to fix one parameter in an optimal way given the properties of the events we want to reconstruct .
in other words , we shall remove one free parameter by determining it analytically from the scales in the process we shall look at . practically , we shall focus on the determination of the most natural parameter , the radius @xmath0 , for the reconstruction of a massive colour - neutral object decaying into two jets , as done within a monte carlo approach in @xcite . in that case , we want to choose @xmath0 large enough to catch the perturbative qcd radiation , but not too large to avoid an excessive contamination from the ue .
our approach thus goes along the same line as @xcite , except that we shall extend the discussion to include extra features requested by the fact that we are looking at a peaked distribution and wish to obtain a more precise determination of @xmath0 .
contrarily to the case of @xcite , where an attempt was made to adapt dynamically the size of the jet with its hardness by replacing the size parameter with a dimensionful scale varying with the process under consideration , we shall determine a unique value for @xmath0 from the hard scale of the event and the scale of the ue , _ i.e._not introducing any alternative parameter .
the paper is organised as follow : in section [ sec : process ] we describe the process we will study as well as the details on how we proceed with the event analysis .
we also describe in that section our strategy for the analytic computation of the optimal radius @xmath1 .
we then proceed with the computation of @xmath1itself .
section [ sec : pqcd ] concentrates on the situation at the partonic level , where only perturbative radiation has to be taken into account ; while in section [ sec : ue ] we add to the picture the contamination due to the ue . in both cases , we shall compare our results with what we obtain from monte - carlo studies , as in @xcite .
finally , in section [ sec : subtraction ] , we shall discuss the extraction of the optimal jet radius for situations where we perform an underlying event background subtraction .
as in @xcite , we shall study the hard processes @xmath2 and @xmath3 , where the ( fictitious ) @xmath4 and @xmath5 are made very narrow .
the main advantage of such simple processes is that one can easily study the definition of jets at a given scale , by varying the mass @xmath6 of the colourless resonance .
it also allows one to study the differences between quark and gluon jets , and to test the validity of our computations with monte - carlo simulations .
the procedure for the event analysis is straightforward : we cluster the events with a given jet definition , select the two highest-@xmath7 jets and reconstruct the heavy object from them . in monte - carlo studies , the events were generated either with pythia @xcite ( tune dwt ) or with herwig and @xmath8 events , which does not make any difference in the discussions throughout this paper . ]
@xcite with the default jimmy tune for the ue .
we have required that the jets satisfy @xmath9 gev and @xmath10 , and we have further imposed that the two hardest jets , the ones used to reconstruct the heavy object , are close enough in rapidity , @xmath11 ( so that the transverse momentum of the jets remains close to @xmath12 ) . the quantification of the performance of a given jet definition is also borrowed from @xcite : we define @xmath13 as the width of the smallest mass window that contains a fraction @xmath14 of the reconstructed objects was defined as a fraction of the generated objects rather than a fraction of the reconstructed ones . though the former is practically more reliable , choosing the later does not affect @xmath1 in practice and simplifies considerably the analytic computation . ] . with that definition , a smaller @xmath15 would correspond to a narrower peak and thus a better reconstruction quality . finding the optimal @xmath0 , @xmath1 ,
is therefore equivalent to finding the minimum of @xmath15 , seen as a function of @xmath0 .
our task in this paper is to perform an analytic computation of the spectrum of the reconstructed mass peak @xmath16 , or @xmath17 with @xmath18 , the difference between the reconstructed and the nominal mass . by integrating that spectrum
, we can compute the probability @xmath19 for the difference @xmath20to be between @xmath21 and @xmath22 .
if we write the quality measure as @xmath23 , where @xmath24 and @xmath25 are the lower and upper end of the mass window defining @xmath15 , it is a straightforward exercise to show that it can be computed from the analytic spectrum by solving @xmath26 repeating this for different values of @xmath0 , one can then compute @xmath27 , the value of @xmath0 for which the quality measure is minimal .
we shall use @xmath28 .
as far as the analytic computation itself is concerned , there are three physical contributions that will affect the width of the reconstructed peak : final - state radiation , initial - state radiation and the ue .
the first two are perturbative ; while final - state radiation leads to losses by emissions out of the jet , initial - state radiation adds extra , unwanted , radiation inside the jet . already at the purely partonic level , there is thus an optimal radius . at this stage ,
the mass spectrum will depend on the mass of the reconstructed object , @xmath6 , and whether it decays into quarks or gluons since , perturbatively , gluons radiate more than quarks . the third contamination , the underlying event , is softer .
like the initial - state radiation , it tends to move the reconstructed mass towards larger values by clustering soft particles into the jet .
the amount of contamination involves another scale : the density of ue ( per unit area ) @xmath29 .
the most important source of dispersion in the mass spectrum comes from the fact that @xmath29 varies from an event to another . in the next two sections , we first concentrate on the purely perturbative behaviour , then include the effect of the ue . but
before getting our hands dirty , there is one additional point that needs to be discussed : the fact that we should also expect some effect due to hadronisation . actually , for the purposes of this paper , hadronisation plays a limited role . in theory
@xcite , it leads to a loss that increases like @xmath30 at small @xmath0 , to be compared with a @xmath31 for the perturbative component , and so should dominate the small-@xmath0 behaviour .
however , the normalisation is such that for practical values of @xmath0 the perturbative contribution dominates , and the effect of hadronisation on the value of @xmath1remains negligible .
a final comment concerns the jet algorithm that we shall consider : we will mostly focus on the anti-@xmath32 algorithm @xcite as its behaviour is simpler . in section [ sec : full_algs ]
we shall discuss the case of the cambridge / aachen @xcite and cambridge / aachen with filtering @xcite algorithms .
the part of the spectrum that is the most naturally computed is the pure perturbative qcd contribution .
this is equivalent to concentrating on partonic events . in that case
, two types of contribution can affect the reconstruction of the jet momentum : final - state radiation outside of the jet which leads to an underestimation of the jet momentum , and in - jet initial - state radiation yielding an over - estimation of the momentum . in this section
, we shall thus compute the pure partonic spectrum .
we do this at the one - gluon - emission ( oge ) level . since we are interested in the behaviour of the spectrum close to the mass peak , we are dominated by the @xmath33 singularity directly coming from the soft divergence of qcd . in that region , to get an integrable spectrum around the mass peak ,
it is also important to resum the @xmath34 contributions to all orders , which we shall do assuming a sudakov - like exponentiation , neglecting non - global logarithms @xcite .
for the clarity of the computation , we first deal with the soft approximation , where we only keep the @xmath33 part of the gluon emission .
we then introduce the sub - leading corrections coming from the pdf in the initial state which can have non - negligible effects , especially in the case of gluon resonances at large mass . because of longitudinal boost invariance
, we can assume that the heavy object is produced at @xmath35 .
furthermore , because of our cut @xmath36 on the dijets , we shall assume that the decay products are at the same rapidity .
the correction due to the finiteness of @xmath37 can be computed but has very little effect ( at most a few percent ) .
since the calculation for a nonzero @xmath37 cut becomes rather technical , we shall keep things simple and assume @xmath38 . at the lowest order of perturbation theory , the incoming ( @xmath39 ) and outgoing ( @xmath40 ) partons
thus have the following momenta @xmath41 we shall consider the emission of an extra soft gluon : @xmath42 with @xmath43 .
the probability for such an emission to happen is given by the antenna formula @xmath44 for an emission from the initial state , and a similar expression with @xmath45 replaced by @xmath46 for final - state radiation .
the pre - factor @xmath47 is a colour factor which should be equal to @xmath48 for an emission from a quark line and @xmath49 for an emission from a gluon line .
note that in the case of a single soft emission , the gluon is caught if and only if it is at a geometric distance smaller than @xmath0 from one of the two `` leading '' partons in the final state @xcite or cambridge / aachen , with or without filtering , as well as for the siscone @xcite algorithm ( at least in the @xmath43 limit ) . ] .
if we denote by @xmath50 the difference , @xmath51 , between the reconstructed mass and the nominal one , initial - state radiation will lead to an overestimation of the jet mass with @xmath52 whenever the additional gluon is radiated inside the jet , while final - state radiation outside the jet will lead to an underestimation of the mass with @xmath53 . integrating over the rapidity and azimuth of the emitted gluon and using ( [ eq : antenna ] ) , we find @xmath54 for the initial - state radiation spectrum , and @xmath55 for final - state radiation , with @xmath56 & & \\[-3 mm ] a_f(r ) & = & 2 \pi \log(2/r ) - \frac{\pi}{72 } r^4 + { \cal o}(r^8)\nonumber\end{aligned}\ ] ] capturing the geometric factors and the @xmath0 dependence .
one recognises the typical expected behaviour : the contamination due to initial - state radiation is proportional to the jet area , _
i.e._to @xmath57 , while the logarithmic behaviour at small @xmath0 of the final - state radiation is the trace of the collinear divergence in qcd . in both cases
, the @xmath58 behaviour corresponds to the soft divergence of qcd .
note that the coefficient of the final - state radiation @xmath59 has been expanded in series of @xmath0 .
the logarithmic behaviour at small @xmath0 corresponds to the leading collinear term as computed in @xcite but we have kept enough terms in the expansion to have a correct description over the whole @xmath0 range . in particular , the numerator in the argument of the logarithm will play a mandatory role to allow the best radius to go above 1 , which is the case in the purely perturbative spectrum and , more generally , for large - mass gluon resonances .
it is also important to discuss the choice of scale @xmath60 for @xmath61 . when using equation ( [ eq : antenna ] ) , the argument of the coupling is , for initial and final - state radiation respectively , @xmath62 & & \\[-3 mm ] \mu_f^2 & \!=\ ! & 2 \frac{(k_1.k)(k_2.k)}{(k_1.k_2)}\,=\,\frac{z^2m^2}{4}\left[\cosh^2(y)-\cos^2(\phi)\right].\nonumber\end{aligned}\ ] ] assuming that emissions close to the edge of the jet are dominant , we will use the following simplified approximation : @xmath63 as we are interested in the behaviour of the mass spectrum in the vicinity of the peak , the last thing we need to consider is the virtual corrections and the higher - order terms that diverge as @xmath64 in that region . in principle , this would depend on the jet algorithm under consideration and an exact computation would involve non - global logarithms @xcite . in practice , we shall adopt a simpler approach and assume that the one - gluon - emission result exponentiates .
this is equivalent to the introduction of a sudakov factor @xmath65 where the integration is performed up to @xmath66 , corresponding to @xmath67 at @xmath35 .
this is an arbitrary choice though a different one would only introduce corrections beyond the level of precision we are working at . using equations ( [ eq : pqcd_barespectrum_i ] ) , ( [ eq : pqcd_barespectrum_f ] ) , ( [ eq : couplingscales ] ) and
( [ eq : sudakov ] ) we find @xmath68^{k_{i , f}-1},\ ] ] with @xmath69 we note that as long as @xmath70 is smaller than 1 , the spectrum goes to 0 when @xmath50 tends to @xmath71 .
alternatively , we could regularise the landau pole in the expression for @xmath61 but we have noticed no significant effect in our conclusions when doing so . , governing the behaviour of the initial or final - state qcd spectrum as a function of @xmath0 for different masses .
the left plot covers the case of quark jets for which we use @xmath72 , and the right plot is for gluon jets for which @xmath73 . ] together with the spectrum , we will also need the total probability for the reconstructed mass to be within a certain range , _ i.e._the integrated spectrum .
denoting by @xmath19 the probability for @xmath74 to be between @xmath21 and @xmath22 , we easily find @xmath75^{k_{i , f}}\ ] ] corresponding to the spectrum ( [ eq : spectrum_pqcd_rc ] ) .
note that in this computation , we have assume that the spectrum is cut at the landau pole , corresponding to @xmath76 . before proceeding with a more involved computation ,
it is important to comment on the limit of validity of this perturbative computation . from equations ( [ eq : pqcd_barespectrum_i ] ) , ( [ eq : pqcd_barespectrum_f ] ) and ( [ eq : pqcd_geomcoefs ] ) , one might expect higher - order corrections to be important when @xmath77 becomes of order 1 . fixing the scale in the coupling to @xmath12 for the sake of the argument , we have plotted that quantity on fig .
[ fig : coefs ] for various cases of interest . in the case of quark - jets , both @xmath78 and @xmath79 remain smaller than 1 .
the case of gluon jets is more interesting ; we see that the coefficient for final - state radiation goes above one at small @xmath0 . in the case of a small - mass resonance
, this can happen for values of @xmath0 as large as 0.5 . as a rule of thumb , we can thus say that , in the case of a small - mass resonance decaying to gluon jets , our perturbative computation would only be valid for @xmath80 .
it is particularly interesting to relate that to the observation made in @xcite that in this precise case of small - mass resonances decaying into gluons , we observed a disappearance of the peak in the reconstructed mass spectrum for small values of @xmath0 .
though this was happening at slightly smaller values of @xmath0 ( around @xmath81 ) , the present computation provides an explanation of this effect : when @xmath82 grows above 1 , the peak in the final - state radiation spectrum is no longer around @xmath83 and the mass peak disappears .
we shall come back to this point later in section [ sec : full_mc ] .
note also that , from fig . [
fig : coefs ] , one can have a feeling of what the optimal radius will be for parton - level events .
indeed , one can expect that , for @xmath84 , the spectrum will be nearly symmetric around the nominal mass ( _ i.e._around @xmath83 ) , that is @xmath85 . for both quarks and gluons and for all masses , this means that one should expect @xmath86 .
we will see later on that this is indeed relatively close to what we shall obtain but that pdf effects , computed in the next section , induce some departure from that situation . in order to get a better description of the variety of processes we consider over the whole kinematic range
, we shall see that it is important to take into account the effect of the pdf on initial - state radiation .
this addresses the fact that the emission of an initial - state gluon imposes to take the parton distribution functions at a larger momentum fraction @xmath87 .
this should therefore introduce an additional suppression , more important at large mass and for gluon - jets than for quark jets .
let us consider the production of a heavy particle at a fixed rapidity @xmath88 .
the leading - order cross section is easily obtained : @xmath89 where the index @xmath90 represents the colour of the colliding partons , @xmath91 is the pdf implicitly taken at a scale @xmath6 , and @xmath92 is the centre - of - mass energy of the collision .
this expression also comes with the kinematic constraint @xmath93 .
we should now add to that process an extra parton emitted at a rapidity @xmath94 .
for our purpose of computing the initial - state radiation contamination to a jet , we can safely make the simplifying assumption that the rapidity of the gluon is the same as the rapidity of the `` leading '' parton , _
i.e. _ , @xmath95 . by doing so , we decouple the effects of the pdf from the effects of the jet clustering .
the latter will be reinserted later on by multiplying our results by the geometric factor @xmath96 .
we thus have @xmath97 in that expression , @xmath98 is the longitudinal fraction of @xmath99 carried by the parton entering the collision satisfying @xmath100 . if we rewrite it in terms of the longitudinal momentum of the emitted parton ( measured w.r.t .
the momentum of the beam ) @xmath101 , one gets after a bit of algebra @xmath102 keeping the kinematic conventions introduced in the previous section , the longitudinal fraction @xmath103 can be rewritten in terms of the transverse momentum @xmath104 of the parton as @xmath105 which finally implies @xmath106 with the kinematic constraint @xmath107 in the limit of small @xmath50 , _ i.e._neglecting the @xmath50 offset in the pdf , one gets @xmath108 which is exactly the result we have obtained in the soft limit up to the geometric factor and @xmath109 where the gluon is emitted in one of the two jets . ] @xmath110 that we will need to reintroduce at the end of the computation . to simplify the discussion , we shall assume that the pdfs take the form @xmath111 the coefficients @xmath112 and @xmath113 will depend on the type of parton and the scale @xmath6 but we shall assume a unique value for @xmath114 . at this level , we could proceed by integrating over the rapidity @xmath88 .
this is feasible analytically with the choice of pdf but it leads to a gauss hypergeometric function in @xmath115 for which the sudakov factor can not be computed analytically .
we will therefore carry on with the computation at a fixed rapidity @xmath88 .
taking into account the emissions from both partons entering the collisions , normalising to the @xmath116 cross - section and reinserting the geometric factor , one obtains @xmath117,\ ] ] where we have introduced @xmath118 and @xmath119 , and it is understood that the terms in the squared brackets are restricted to the appropriate phase space _ i.e._@xmath120 , respectively for each term . in order to compute the sudakov form factor analytically , we shall make the approximation that the exponents @xmath113 are integers ( in practice , we shall use @xmath121 and @xmath122 for ( anti-)quark and gluon - jets respectively ) , and expand the small-@xmath87 power behaviour to first order in @xmath50 : @xmath123 using @xmath124 the fact that @xmath113 is an integer allows one to see as a polynomial in @xmath50 .
we can then easily compute the sudakov factor using the following fundamental integrals : @xmath125 - { \rm ei}\left[p\,\log({\ensuremath{\delta m}\xspace}/\lambda_i)\right]\right\},\end{aligned}\ ] ] where @xmath126 is the exponential integral . with these simplifying assumptions ,
the final perturbative spectrum for initial - state radiation can be written as @xmath127 with the integrated probability @xmath128^{k_i } \,\exp\left[-k_i\sum_{k=1}^{\beta_a+1 } \mu_k \ , { \cal e}_k \left(\frac{\lambda_i}{m}\right)^k\right],\ ] ] and the coefficients @xmath129,\\ \nu_{-1 } & = & \nu_{\beta_a+1 } = 0,\\ { \cal{e}}_k & = & { \rm ei}\left[k\,\log(m/(2\lambda_i))\right ] - { \rm ei}\left[k\,\log({\ensuremath{\delta m}\xspace}/\lambda_i)\right].\label{eq : suduptom2}\end{aligned}\ ] ] note that to obtain ( [ eq : suduptom2 ] ) , we have to integrate @xmath50 up to @xmath12 , which is strictly valid only when @xmath130 , but similar results can easily be derived at forward rapidities . dijet system at a nominal mass of 100 gev while the right plot is for the gluonic case at 2 tev . in both cases ,
the anti-@xmath32 algorithm with a radius of 1 has been used for the clustering . ]
we want to conclude this section by a comparison of the predictions we obtain for the optimal radius from our analytical studies and from monte - carlo approaches .
when dealing with the analytic result , we shall use the initial and final - state results computed in the previous sections in the two different situations for which we have analytic results : the soft limit with a running - coupling approximation , eqs . and , and the `` full '' spectrum where we also include the pdf effects in the initial - state radiation , eq . .
the total perturbative qcd spectrum is the convolution of the initial and final - state pieces which , in practice , will be carried numerically .
we shall use @xmath131 mev and @xmath132 to compute the running of the qcd coupling , and , for the pdf effects in the initial - state - radiation spectrum , we shall adopt @xmath133 , @xmath121 and @xmath122 , and assume @xmath35 , where we have checked that most of the massive objects in the monte carlo sample were produced . the quality measure is computed from the spectrum using . for the parton - level spectrum .
the ( red ) dashed curve corresponds to our analytic computation in the soft limit while the ( blue ) solid one includes pdf effects . the ( green ) triangles and ( cyan ) circles show the monte - carlo simulations for pythia and herwig respectively .
as for fig .
[ fig : parton_hist ] , the left plot is for a @xmath134 dijet system at a nominal mass of 100 gev while the right plot is for the gluonic case with @xmath135 tev . ] we start our comparison directly with the spectrum for the reconstructed dijet mass , as shown on fig .
[ fig : parton_hist ] for quark jets , @xmath136 gev and gluon jets , @xmath135 tev .
generally speaking , the agreement between our analytic computation and herwig is good , even very good for the 100 gev quark - jet case .
note that this agreement is always better in the region of the peak , where the soft - gluon emissions approximation we are working with is supposed to hold .
similarly the small differences in the tail at small and large @xmath137 are beyond the scope of our approximation . in both the quark and gluon - jet cases , we see that the inclusion of pdf effects , reducing the initial - state radiation , significantly improves the description , especially in the case of large - mass gluon jets , where we are sensitive to fast - falling gluon distributions at large @xmath87 . extracted from parton - level pythia ( green triangles ) and herwig ( cyan circles ) simulations .
the left plot shows the case of a resonance decaying into @xmath134 jets while the right plot has gluon jets . ]
next , we turn to the computation of the quality measure , presented in fig . [
fig : parton_quality ] .
after properly taking into account the pdf effects , our computation agrees in shape with the monte - carlo results . for the normalisation
, we are closer to the herwig simulation in the case of quark jets , while we better agree with pythia simulations for gluon jets .
since our analytic computation is identical in both cases , it it somehow hard to find an explanation for those differences .
finally , let us concentrate on the values of @xmath1extracted from the previous examples .
this is shown on fig .
[ fig : parton ] for quark jets ( left panel ) and gluon jets ( right panel ) .
despite the apparent normalisation issue between pythia and herwig observed on fig .
[ fig : parton_quality ] , the fact that they agree on the shape of the quality means that they yield very similar extracted optimal radii .
if we turn to the analytic computation , we first see that in the soft approximation , the optimal radius is independent on the process under consideration with @xmath138 regardless of the mass or the parton type . in practice , this is due to the fact that the quality measure is a complicated function of @xmath139 involving _ e.g._their derivatives which are different at @xmath140 . ] .
the reduction of the initial - state radiation due to the pdf effects has a sizeable effect on the extracted optimal radius in such a way that , at the end of the day , our analytic extraction of @xmath1 in the `` full '' model reproduces very well the monte - carlo simulations with an error @xmath141 0.1 .
one of the most important effects when clustering jets at hadronic colliders is the presence of the underlying event ( ue ) coming from multiple interaction and beam remnants .
this tends to produce a fairly uniform soft radiation of a few gev per unit area that contaminates the jets and affects their momentum reconstruction . in this section
, we therefore study the effects of this ue on the mass spectrum we have computed from perturbative qcd in the previous section .
if we work within the assumption that the ue is uniform in rapidity and azimuth , the average @xmath7 contamination to each jet will be @xmath142 where @xmath143 is the ( active ) area of the jet @xcite and @xmath29 the ue density per unit area .
for a given event , this contamination is affected by two kinds of fluctuations : first , the fluctuations of the background itself which go like @xmath144 , with @xmath145 the background fluctuations per unit area .
then , keeping in mind the possibility to discuss our results for different jet algorithms than the anti-@xmath32 algorithm , the active area of a jet is in general known to fluctuate , with an average value proportional to @xmath57 that increases with @xmath7 in a different way for each jet algorithm . for a given background density @xmath29 ,
let us denote by @xmath146 the probability distribution for a jet @xmath147 to receive a contamination @xmath148 from the ue .
for a jet of area @xmath149 , this distribution has an average of @xmath150 and a dispersion @xmath151 .
we therefore also have to introduce @xmath152 the distribution , of average @xmath153 and dispersion @xmath154 of the area divided by @xmath57 , of the jet @xmath147 .
if the two jets were perfect circles of radius @xmath0 , one could easily compute that the offset on the reconstructed mass would be @xmath155 , up to corrections proportional to @xmath156 , where @xmath157 is the modified bessel function of the first kind . for generic jets
we shall then use @xmath158 where @xmath159 and @xmath160 are the transverse momenta of the background contamination of our dijets .
on top of that , when we consider an event sample , the values of @xmath29 and @xmath145 will fluctuate from one event to another . for the event - by - event fluctuations of the background densities
, we shall assume a distribution @xmath161 , of average @xmath162 and dispersion @xmath163 .
for the intra - event fluctuations ( per unit area ) @xmath145 we shall simply assume that they remain proportional .
] to @xmath29 , _
i.e. _ , @xmath164 . given the event - by - event @xmath29 distribution @xmath161 , the intra - event fluctuations , @xmath165 and the area distribution @xmath152 , the ue spectrum can be inferred from ( [ eq : dmfromue ] ) @xmath166 without knowing exactly that distribution , we can compute its average and dispersion in terms of the properties of the fundamental distributions : @xmath167\,2 \pi r^2 \bar{a}\,{\left\langle \rho \right\rangle},\nonumber\\ \sigma_{{\ensuremath{\delta m}\xspace}}^2 & = & \int { \rm d}{\ensuremath{\delta m}\xspace}\,({\ensuremath{\delta m}\xspace}-{\left\langle { \ensuremath{\delta m}\xspace}\right\rangle})^2 \,\frac{{\rm d}p_{\rm ue}}{{\rm d}{\ensuremath{\delta m}\xspace}}\label{eq : uedisp}\\ & = & \left[\frac{2i_1(r)}{r}\right]^2 \left [ 4 \bar{a}^2 ( \pi r^2)^2 \sigma_\rho^2 + 2 ( \pi r^2)^2 \left({\left\langle \rho \right\rangle}^2+\sigma_\rho^2\right ) \sigma_a^2 + 2 \bar{a } ( \pi r^2 ) \left({\left\langle \rho \right\rangle}^2+\sigma_\rho^2\right ) \mu^2 \right].\nonumber\end{aligned}\ ] ] the average is consistent with what one would naively expect , and the dispersion is a combination of the three separate sources of dispersion we are including : event - by - event fluctuations in @xmath29 ( the first term ) , area fluctuations ( the second term ) and intra - event fluctuations ( the third term ) .
as expected , the first two are proportional to the area of the jet _ i.e._to @xmath57 , while the intra - event fluctuations are proportional to its square root .
so , instead of modelling the various distributions separately and perform the integrations in , we shall directly model the total ue spectrum and adjust its parameters to reproduce the total average and dispersion . more specifically
, we shall assume @xmath168 the parameters @xmath169 and @xmath170 can be adjusted to reproduce the average ( [ eq : ueavg ] ) and dispersion ( [ eq : uedisp ] ) of the ue distribution .
one finds @xmath171 this choice has the advantage over a gaussian distribution that it remains positive .
our strategy is rather straightforward : as we did when combining the initial - state and final - state radiation spectra , we shall convolute the perturbative qcd spectrum , discussed in section [ sec : pqcd_mc ] , with the ue spectrum . for each mass and parton - type ,
we wish to compare our results with the monte - carlo studies @xcite . for the perturbative qcd part of the spectrum , we use the convolution already discussed in section [ sec : pqcd_mc ] and consider the same models : the pure soft approximation and the spectrum including pdf effects in the initial - state .
the result is itself convoluted with the underlying - event distribution for which we still have to determine the parameters appearing in eqs .
( [ eq : ueavg ] ) and ( [ eq : uedisp ] ) .
the area properties @xmath153 and @xmath154 have been calculated , together with their scaling violations in @xcite .
the properties of the background are computed directly from the monte - carlo event sample using fastjet @xcite and the method advocated in @xcite and @xcite : each event is first clustered with the cambridge / aachen algorithm with @xmath172 ; @xmath29 and @xmath145 are then estimated from the jets that are within a rapidity strip of 1 unit around the hardest dijet system , excluding the two hardest jets in the event .
the average properties @xmath162 , @xmath60 and @xmath163 can then be easily extracted from the complete event sample . for completeness
, we give a table of the values we have obtained in appendix [ app : ueprops ] . with that method , we are able to compute the mass spectrum , and thus the quality measure , at a given mass and with a given parton type and ue characteristics .
we then extract @xmath1by searching the minimum of the quality measure by steps of 0.01 in @xmath0 . and the anti-@xmath32 algorithm . ] for quark dijets at 100 gev ( left panel ) and gluon dijets at 2 tev ( right panel ) .
the triangles and solid lines correspond to the pythia simulations while the circles and dashed lines correspond to herwig simulations . ] but for herwig simulations . ] as for the parton - level case , we shall compare our computations with the monte carlo simulations from pythia ( tune dwt ) and herwig ( with default jimmy tune ) as the details of the underlying event can differ .
we shall again proceed in three steps : first consider the histograms , then the quality measures and finally the optimal radius . for simplicity , we shall focus on the anti-@xmath32 algorithm for which @xmath173 and @xmath174 .
let us start with the histograms , figure [ fig : ue_hist ] , where we illustrate our description of the spectrum for the quark dijets at small mass and gluon dijets at large mass . in both cases ,
our analytic histogram correctly reproduces the behaviour observed with herwig .
we note however that our analytic computation slightly underestimating the ue in the peak region in the case of quark jets at small nominal mass , is a bit more pronounced . ] @xmath6 .
if we then move to the case of the quality measure , figure [ fig : ue_quality ] , we see that , given the differences we have already observed at the parton level ( see figure [ fig : parton_quality ] ) , the addition of the underlying event gives a reasonable description of the monte - carlo results , especially the shape of the quality at large @xmath0 .
note that only the curves corresponding to the model including the pdf effects are shown on figure [ fig : ue_quality ] for clarity reasons .
finally , the extracted optimal radius is presented on figures [ fig : ue_pythia ] and [ fig : ue_herwig ] for pythia and herwig simulations respectively , as a function of the mass for both quark and gluon jets .
generally speaking we obtain a good description of the monte - carlo results .
we see once again that the inclusion of the pdf effects significantly improves the description of the optimal radius for gluon jets at large mass , as expected .
we slightly underestimate the optimal radius in the case of gluon jets at large mass , but we have to notice that this is the regime on which it matters the least as in that region the minimum in the quality measure is rather flat .
we thus see that our complete analytic model , the solid ( blue ) curve on figures [ fig : ue_pythia ] and [ fig : ue_herwig ] , corresponding to our analytic pqcd computation including pdf effects , eq .
( [ eq : isrfull ] ) , convoluted with our model of the underlying event , eq .
( [ eq : spectue ] ) , gives a good extraction of the optimal radius @xmath1 .
results , the dashed ( green ) lines and the circles show c / a results , and the dotted ( red ) lines and the triangles correspond to c / a with filtering . ] now that we have checked the agreement between our analytic computations and monte - carlo simulations for the simpler case of the anti-@xmath32 algorithm , let us briefly discuss other possible jet algorithms . in this section , we shall apply our analytic computations to the case of the cambridge / aachen ( c / a ) as well as to the cambridge / aachen algorithm supplemented by a filter ( c / a+filt ) . while the former usually leads to quality measurements close to what is obtained in the anti-@xmath32 case , the latter produces narrower peaks with an optimal radius slightly larger than the one obtained from c / a without filtering . for simplicity
, we shall follow what has been done in @xcite and use @xmath175 and @xmath176 for the parameters of the filter , _
i.e. _ , recluster each jet with c / a and a radius of half the original one and keep the two hardest subjets , discarding the softer ones .
the analytic computation goes exactly as in the case of the anti-@xmath32 algorithm .
the only thing that will change in our approach is the inclusion of the area contribution in the ue distribution .
the expressions for the area are computed analytically , as in @xcite , up to order @xmath61 : @xmath177,\\ \sigma_a^2 & = & \sigma_{0,{\rm jd}}^2 + s_{{\rm jd}}^2\,\frac{c_a}{\beta_0\pi}\log\left[\frac{\alpha_s(q_{0,{\rm jd}}^{(a)})}{\alpha_s(rp_t)}\right],\end{aligned}\ ] ] where the coefficient @xmath178 , @xmath179 , @xmath180 and @xmath92 are computed in perturbation theory and have been calculated , c / a and siscone algorithms . ] in @xcite , while the scales @xmath181 are of non - perturbative origin and have been determined in @xcite from a fit to herwig simulations . in our case , we shall use @xmath182 together with the following values for the coefficients : @xmath183 to avoid multiplying the figures , we just show , see figure [ fig : algs_pythia ] , the final result of the extracted optimal radius as a function of the mass for the three algorithms under consideration , compared to pythia simulations .
we see that , in agreement with the monte carlo , the differences between anti-@xmath32 and cambridge / aachen are very small and thus our analytic approach reproduces the expected behaviour correctly . for the case of the c / a algorithm with filtering
, we obtain a good description in the case of quark dijet systems but systematically underestimate the optimal radius , by about 0.1 - 0.2 , in the case of gluon jets .
we believe that this is due to the fact that we should also introduce some dependence on the algorithm at the level of the perturbative spectrum . in our soft - gluon approximation all
the algorithm will have the same initial and final - state radiation spectra .
however , with a more complete treatment , _ e.g._including non - global logarithms as in @xcite , differences will start appearing .
another effect comes from the combination of the initial and final - state radiation spectra : the simple convolution we have used is reasonable in the case of the anti-@xmath32 algorithm where the shape of the jet is not affected by the radiation , but more subtle phenomena will appear for more complex algorithms , especially in the filtered case where , in some geometric regions , the capture of isr gluons can be affected by internal gluon radiation in the jet .
all these effects are beyond the reach of the present analysis .
as expected from the previous discussion , discrepancies are more pronounced in the case of gluon jets at large mass , where perturbative radiation dominated the spectrum .
our computation nevertheless gives reasonable results at the end of the day , given also that for gluon dijets at larger mass , the minimum in the quality measure is less pronounced than in other situations .
finally , let us mention that the case of the @xmath32 algorithm @xcite is also very close to what we obtain for the anti-@xmath32 and c / a algorithm , hence well reproduced by our calculation .
for the siscone algorithm , differences in the perturbative spectrum also appear when the radiated gluon is not soft , we therefore postpone that case for a further study . to some extent , the present calculation can be seen as an extended version of what has been done in @xcite , where the authors compute the average @xmath7 shift of a jet due to final - state radiation , hadronisation and the ue .
the approach we pursue in this paper is however much more complete in the sense that we obtain the full spectrum instead of just the average value . as a consequence
, we can extract the width of the peak really as the dispersion in the spectrum , while in @xcite the width is approximated by @xmath184 _
i.e._the total dispersion is approximated by the sum of each independent average squared .
the individual contributions are found to be @xcite @xmath185 with @xmath186 gev for @xmath187 gev and @xmath188 & & \\[-3 mm ] l_g & = & \left(2 \log(2)-\frac{43}{96}\right ) c_a + \frac{7}{48}n_ft_r . \nonumber\end{aligned}\ ] ] the optimal radius is then obtained by minimising w.r.t . @xmath0 . in practice ,
we have used @xmath189 , @xmath132 , @xmath131 mev and computed the qcd coupling at the scale @xmath190 . instead of using a fixed value for @xmath191 as in @xcite
, we have used the fact that it is related to the average background density , @xmath162 , through ( see section [ sec : full ] ) @xmath192 and used the values extracted from the monte carlo event samples and already used in section [ sec : full ] for @xmath162 . the extracted value of @xmath1is shown on fig .
[ fig : dms ] in the case of pythia simulations , for the anti-@xmath32 algorithm .
the results are compared with the monte carlo results and with our complete analytic calculation .
we see that the simpler approach of @xcite manages to extract the correct value for @xmath1at small mass but fails to reproduce the observed behaviour at larger mass , and this for both quark and gluon jets .
the reason for this failure is rather hard to pinpoint : it can come , _
e.g. _ , from the crudeness of the approximation ( [ eq : dmsdisp ] ) , the lack of an initial - state radiation contribution and the corresponding pdf effects , or the description of the underlying event in terms of the average density @xmath162 instead of its fluctuations @xmath163 .
the last point we wish to discuss is the situation where we perform background subtraction using jet areas @xcite , as advocated in @xcite .
the idea behind ue subtraction is to get rid of the shift due to the ue density contaminating the mass reconstruction .
since subtraction is performed on each single event , one hopes to get rid of the fluctuations of the background density across the events , hence obtaining a narrower peak . in this respect , all we should be left with is the background fluctuations inside an event which have a linear dependence on @xmath0 rather than the quadratic one computed in the unsubtracted case .
this is a much smaller effect and one thus expect the quality measure to be better ( _ i.e._smaller ) than in the unsubtracted case as well as the optimal radius to be larger . in practice
, one would thus naively convolute the perturbative spectrum computed in section [ sec : pqcd ] with a subtracted ue spectrum taking into account these intra - event fluctuations . doing that would actually lead to a quality much better than what is observed in monte - carlo studies and to a systematic over - estimation of @xmath1 . the additional effect that is mandatory to take into account is the fact that subtraction is performed using an estimated value for the background density @xmath193 which can differ from the exact value of @xmath29 for that event .
this results in some smearing effect left over from the unsubtracted spectrum . because of this , the computation of the subtracted ue spectrum turns out to be more involved than the corresponding unsubtracted case computed in section [ sec : full ] , mostly because one also would have to consider the distribution probability for @xmath193 .
the properties of the estimated value of @xmath29 have actually recently been discussed at length in @xcite , where we learn that the estimation of the background density using a median - based approach suffers from two sources of bias : one of soft origin , related to the fact that the median of a set of pure - ue jets may differ from its average ; and a contamination from radiation coming from the hard jets .
if we call @xmath29 and @xmath145 the average ue density and its fluctuations for one given event , and define @xmath194 as the relative error in the estimation of @xmath29 , the average and dispersion of @xmath195 are @xcite @xmath196 where , as in section [ sec : full ] we used @xmath197 , and the coefficients are @xmath198 and @xmath199 with @xmath200 in the previous set of equations , @xmath201 is a pure number extracted in @xcite , @xmath202 is the jet radius used to estimate the background properties , @xmath203 is the total area of the range we are using to estimate the background , @xmath181 is a soft cut - off that we fixed to 1 gev , and @xmath204 is the hard scale that we naturally took equal to @xmath12 .
these properties constrain the distribution of @xmath195 , that we shall denote by @xmath205 , as a function of @xmath60 .
since the intra - event fluctuations will play a substantial role in this ue - subtracted situation , we shall also consider a distribution for them .
for simplicity , we shall parametrise the distribution in terms of @xmath60 rather than in terms of @xmath145 as background estimations are naturally expressed in that variable .
we therefore introduce @xmath206 , of average @xmath207 and dispersion @xmath208 . in the course of the computation
below , we shall encounter higher cumulants for this distribution . to keep things simple
, we shall work with the gaussian assumption .
we have checked that this choice does not affect the resulting @xmath1 . ] _
i.e._@xmath209 , @xmath210 .
the values of @xmath207 and @xmath208 can again be extracted from the monte - carlo samples . with this at hand ,
we proceed , as in section [ sec : full ] , by computing the mass shift for a given configuration and deducing its average and dispersion . for given values of @xmath29 , @xmath60 , @xmath211 , jet areas @xmath212 and jet ue contaminations @xmath148 , the offset in the reconstructed mass after subtraction is @xmath213 \left[p_{t,1}+p_{t,2}-\pi r^2 ( a_1+a_2)(1+\delta)\rho\right],\ ] ] where the last term is the subtracted piece . after a slightly lengthy computation we reach .
the only additional approximation is the replacement of @xmath145 by @xmath214 in @xmath215 ( eq . ( [ eq : nh ] ) ) , which only introduces subleading corrections . ]
@xmath216\,2 \pi r^2 \bar{a}\,{\left\langle \rho \right\rangle } \left\lbrack -d_1{\left\langle \mu \right\rangle}+d_2({\left\langle \mu \right\rangle}^2+\sigma_\mu^2)\right\rbrack,\label{eq : ueavgsub}\\ \sigma_{{\ensuremath{\delta m}\xspace}}^2 & = & \left[\frac{2i_1(r)}{r}\right]^2 \left ( \left\{\left[2\pi r^2 \bar{a}+2(\pi r^2)^2\sigma_a^2(d_1 ^ 2+s_d^2)+4(\pi r^2 \bar{a})^2 s_d^2\right]({\left\langle \rho \right\rangle}^2+\sigma_\rho^2)\right.\right.\nonumber\\[-5 mm ] & & \phantom{\left[\frac{2i_1(r)}{r}\right]^2 ( ) } \left.+4(\pi r^2\bar{a})^2d_1 ^ 2\sigma_\rho^2\right\}({\left\langle \mu \right\rangle}^2+\sigma_\mu^2)\nonumber\\[-5 mm ] & & \phantom{\left[\frac{2i_1(r)}{r}\right]^2 } \left .
+ \left[2(\pi r^2)^2\sigma_a^2({\left\langle \rho \right\rangle}^2+\sigma_\rho^2)+4 ( \pi r^2 \bar{a})^2\sigma_\rho^2\right]\left(d_2 ^ 2{\left\langle \mu^4 \right\rangle}-2d_1d_2{\left\langle \mu^3 \right\rangle}\right)\right.\nonumber\\[-5 mm ] & & \phantom{\left[\frac{2i_1(r)}{r}\right]^2 } \left .
+ \ , 4 ( \pi r^2 \bar{a})^2 { \left\langle \rho \right\rangle}^2\left[2 d_2 ^ 2\sigma_\mu^2+(2d_2{\left\langle \mu \right\rangle}-d_1)^2\right]\sigma_\mu^2\right).\label{eq : uedispsub}\end{aligned}\ ] ] once we have these expressions , the last step is to parametrise the subtracted ue spectrum . since subtraction can produce negative values for @xmath20 , we can not use .
the technique we shall adopt is to keep the same distribution using the unsubtracted average together with the dispersion we have just computed , and then to shift the complete distribution in order to reproduce the subtracted average @xmath20 . in practice , this gives @xmath217 where the parameters @xmath169 , @xmath21 and @xmath170 are given by @xmath218 with @xmath219 and @xmath220 given by eqs . and , and @xmath221 by eq .
. finally , it is interesting to notice that in the case of a perfect estimation of the background density @xmath222 , _
i.e._@xmath223 , one recovers @xmath224 ^ 2 \ , 2\pi r^2 \bar{a}({\left\langle \rho \right\rangle}^2+\sigma_\rho^2)({\left\langle \mu \right\rangle}^2+\sigma_\mu^2)\end{aligned}\ ] ] _ i.e._no average shift and a ( squared ) dispersion that is proportional to the area ( linearly ) and to @xmath225 . as for the previous cases we have analysed
, we shall perform a comparison of our analytic predictions with monte carlo simulations for the ue - subtracted case .
the method goes exactly as before , so we just highlight the main steps and present our results for the optimal radius @xmath1and stay with the anti-@xmath32 algorithm . for the analytic part of the computation
, the perturbative qcd spectrum is convoluted with the subtracted ue spectrum calculated in the previous section . concerning the parameters of the latter ,
all background properties , @xmath162 , @xmath226 , @xmath207 and @xmath208 are extracted directly from the monte - carlo data sample and the estimation of the background density was performed using the cambridge / aachen algorithm with a radius of 0.6 .
we have kept all the jets within one unit of rapidity around the hardest dijet , excluding the two hardest jets in the event , giving a total area @xmath227 .
it is interesting to notice that when background subtraction is performed , the final results will slightly depend on the details of how @xmath29 is estimated , through the coefficients @xmath228 , @xmath229 and @xmath230 in our analytic approach . extending the range , _ i.e._increasing its area @xmath203 , would decrease the bias in the estimation of @xmath29 , but in that case , there would be a risk that the background would not be uniform over the range ( _ e.g._vary with rapidity ) .
following @xcite , we could therefore also try to optimise the choice of range and jet definition used for estimating @xmath29 . the computed value of @xmath1is shown on fig .
[ fig : subtract ] in the case of pythia simulations . for an easier comparison ,
we show both the subtracted and unsubtracted results .
for the analytic calculation , we observe a value of @xmath1larger in the subtracted case by about 0.04 in the case of quark - jets and by about 0.08 in the case of gluon - jets .
all these values are in good agreement with what is observed in the monte - carlo simulations .
throughout this paper we have investigated analytically the optimisation of the radius @xmath0 one uses with a jet algorithm to reconstruct dijet resonances .
we have already learnt @xcite that carefully choosing the jet radius can lead to significant improvement of the reconstructed signal and we find it valuable to supplement previous monte - carlo studies with an analytic understanding of these dijet reconstructions .
our approach has been to calculate the reconstructed dijet mass spectrum .
this was done by convoluting fundamental pieces : the perturbative qcd radiation in the initial and final state , and the contamination due to the underlying event . for the perturbative part
, we have worked in the soft - gluon emission approximation , a choice motivated by the fact that we are mostly interested in the behaviour in the vicinity of the mass peak . in the case of the initial - state radiation spectrum , we have also included pdf effects that can have a non - negligible impact , especially in the case of gluon jets and at large dijet mass .
for the ue description , we have modelled it in such a way as to reproduce the observed properties of the background . from the reconstructed mass spectrum
, we can compute a quality measure and extract an optimal radius , following the method outlined in @xcite .
our analytic results have been considered and compared with monte - carlo simulations in various cases .
we have started with parton - level events , where we can test our analytic computation of the perturbative spectrum ; then we have focused on full hadronic events including the underlying event ; and , finally , we have considered the situation with a jet - area - based background subtraction @xcite .
we have mostly considered the case of the anti-@xmath32 algorithm but have also considered other options . generally speaking , we can say that we obtain a good description of the monte - carlo results , especially when including the pdf effects in initial - state radiation .
the optimal radius @xmath1computed analytically is in most cases less than 0.1 away from the monte - carlo expectation .
the comparison at a more basic level , the quality measure or even the mass spectrum , also shows a good agreement .
most of the deviations between our analytic results and monte carlo simulations can probably be traced back to what we observe at the partonic level .
though our analytic computation reproduces nicely the monte - carlo simulations , we have observed some deviations in section [ sec : pqcd_mc ] .
it is interesting to notice that the differences between our description and the monte - carlo results is usually of the same order as the differences obtained between pythia and herwig .
these differences propagate to the situation where the ue is included .
the one case where our analytic results deviate a bit more from the monte - carlo simulations is the case of the cambridge / aachen algorithm supplemented by a filter ( see section [ sec : full_algs ] ) , for events including the ue , while our description remains good for the anti-@xmath32 and the cambridge / aachen algorithm without any filter .
we think that a better description goes beyond the reach of the present analysis , _
e.g._already at the partonic level , a simple convolution between the initial and final - state spectra may be too simplistic when filtering is applied .
let us also notice that our description of the ue allows us to treat successfully both the case where the ue is subtracted and the case where it is not .
our approach includes all the effects that contribute to the dispersion of the reconstructed mass : mostly background fluctuations from one event to another , intra - event fluctuations and area fluctuations .
it is interesting to notice that in the case of subtracted ue , it was also mandatory to take into account the fact that the estimated background can differ from its `` true '' value .
this leads to a significant additional contribution to the dispersion . using the analytic computations from @xcite
led to good results for the extracted @xmath1 .
if one wishes to improve the present description , additional effects have to be included in the analytic computation : relaxing the soft - gluon - emission approximation , obtaining sub - leading logarithmic corrections , performing a better resummation of the soft virtual corrections than a simple sudakov factor , _ e.g._using non - global logarithms , and including hadronisation corrections .
however , we have seen that the description we can achieve with our simple approach is already satisfactory without having to introduce these corrections .
it is nevertheless important to remember their existence as they might become relevant in more specific situations , like the case of filtering where we have observed that we start to reach the limits of our simple approach .
some effects , like subleading logarithmic corrections , may even be simpler to compute analytically than to implement in a monte carlo .
another point that we have not investigated and that might be interesting in a future study is the case of the rapidity dependence of @xmath1 .
as we have seen in section [ sec : pdf ] , pdf effects introduce a dependence on the rapidity at which the heavy object is produced @xcite and it might be interesting to see how @xmath1varies with that rapidity . also , all the computations we have performed were for a complete event - set .
a next major step would be to optimise the radius on an event - by - event basis .
this is much more complicated as the previous approach would then only give access to an average dispersion for a single event and the additional dispersion arising when combining the whole set of events would be much harder to handle .
we therefore also leave that step to future studies .
the question of knowing which jet algorithm should be preferred has already triggered many discussions both on the theoretical and on the experimental side , and more complex jet definitions introducing more parameters have often been proposed to improve jet reconstruction .
the present work , together with @xcite , can be seen as opening a new direction of improvement : analytically optimising the parameters in the jet definitions . considering a single parameter ,
the jet radius , for a simple process , dijet reconstructions , is a first step in that direction . gaining analytic control on the parameters entering jet definitions
can be extremely valuable .
this is especially true when new parameters are introduced : being able to predict them can avoid often costly determinations based on monte - carlo simulations or rough empirical choices .
the application of the techniques developed in this paper to other parameters and more general processes would therefore be very interesting .
i am extremely grateful to gavin salam for many useful suggestions and comments at every step of this work .
i also thank lorenzo magnea for a careful reading of the manuscript .
finally , i thank the brookhaven national laboratory for support when this work was initiated and the lpthe ( university of paris 6 ) where parts of this work has been done .
.background properties needed to parametrise the ue distribution .
values are given for quark and gluon jets as well as for pythia and herwig+jimmy simulations .
all dimensionful numbers are expressed in gev . [ cols=">,^,^,^,^,^,^,^,^,^,^,^,^ " , ] for the sake of completeness , we briefly mention in this appendix the values of the background properties that are necessary to fix the ue spectrum .
these will differ between quark and gluon jets and between pythia 6.4 ( tune dwt ) and herwig 6.51 ( with default jimmy tune ) .
all the values used in our analytic computation are summarised in table [ tab : ueprops ] .
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SECTION 1. SHORT TITLE; TABLE OF CONTENTS.
(a) Short Title.--This Act may be cited as the ``Unemployment
Insurance Solvency Act of 2011''.
(b) Table of Contents.--The table of contents of this Act is as
follows:
Sec. 1. Short title; table of contents.
Sec. 2. Extension of assistance for States with advances.
Sec. 3. Reduction in the rate of employer taxes.
Sec. 4. Modifications of employer credit reductions.
Sec. 5. Increase in the taxable wage base.
Sec. 6. Voluntary State agreements to abate principal on Federal loans.
Sec. 7. Rewards and incentives for solvent States and employers in
those States.
SEC. 2. EXTENSION OF ASSISTANCE FOR STATES WITH ADVANCES.
(a) In General.--Section 1202(b)(10)(A) of the Social Security Act
(42 U.S.C. 1322(b)(10)(A)) is amended by striking ``2010'' and
inserting ``2012'' in the matter preceding clause (i).
(b) Effective Date.--The amendment made by this section shall take
effect as if included in the enactment of section 2004 of the
Assistance for Unemployed Workers and Struggling Families Act (Public
Law 111-5; 123 Stat. 443).
SEC. 3. REDUCTION IN THE RATE OF EMPLOYER TAXES.
(a) In General.--Section 3301 of the Internal Revenue Code of 1986
is amended--
(1) in paragraph (1), by striking ``2010 and the first 6
months of calendar year 2011'' and inserting ``2013''; and
(2) in paragraph (2), by striking ``6.0 percent in the case
of the remainder of calendar year 2011'' and inserting ``5.78
percent in the case of calendar year 2014''.
(b) Effective Date.--The amendments made by this section shall take
effect on the earlier of--
(1) the date of the enactment of this Act; or
(2) July 1, 2011.
SEC. 4. MODIFICATIONS OF EMPLOYER CREDIT REDUCTIONS.
(a) Limit on Total Credits.--Section 3302(c) of the Internal
Revenue Code of 1986 is amended--
(1) in paragraph (1), by striking ``90 percent of the tax
against which such credits are allowable'' and inserting ``an
amount equal to 5.4 percent of the total wages (as defined in
section 3306(b)) paid by such taxpayer during the calendar year
with respect to employment (as defined in section 3306(c))'';
and
(2) in paragraph (2)--
(A) by striking subparagraphs (B) and (C) and the
flush matter following subparagraph (C);
(B) by striking ``(2) If'' and inserting ``(2)(A)
If'';
(C) by striking ``(A)(i) in'' and inserting ``(i)
in'';
(D) in clause (i) of subparagraph (A), as
redesignated by subparagraph (C), by striking ``5
percent of the tax imposed by section 3301 with respect
to the wages paid by such taxpayer during such taxable
year which are attributable to such State'' and
inserting ``an amount equal to 0.3 percent of the total
wages (as defined in section 3306(b)) paid by such
taxpayer during the calendar year with respect to
employment (as defined in section 3306(c))'';
(E) in clause (ii) of subparagraph (A)--
(i) by moving such clause 2 ems to the
left;
(ii) by striking ``5 percent, for each such
succeeding taxable year, of the tax imposed by
section 3301 with respect to the wages paid by
such taxpayer during such taxable year which
are attributable to such State;'' and inserting
``an amount equal to 0.3 percent of the total
wages (as defined in section 3306(b)) paid by
such taxpayer during the calendar year with
respect to employment (as defined in section
3306(c)), for each succeeding taxable year;'';
and
(iii) by striking the semicolon at the end
and inserting a period; and
(F) by adding at the end the following new
subparagraph:
``(B) The provisions of subparagraph (A) shall be applied
with respect to the taxable year beginning January 1, 2011, or
any succeeding taxable year by deeming January 1, 2013, to be
the first January 1 occurring after January 1, 2010. For
purposes of subparagraph (A), consecutive taxable years in the
period commencing January 1, 2013, shall be determined as if
the taxable year which begins on January 1, 2013, were the
taxable year immediately succeeding the taxable year which
began on January 1, 2010. No taxpayer shall be subject to
credit reductions under this paragraph for taxable years
beginning January 1, 2011, and January 1, 2012.''.
(b) Definitions and Special Rules.--Section 3302(d) of the Internal
Revenue Code of 1986 is amended--
(1) by striking paragraphs (1), (4), (5), (6), and (7); and
(2) by redesignating paragraphs (2) and (3) as paragraphs
(1) and (2), respectively.
(c) Effective Date.--The amendments made by this section shall take
effect as if enacted on January 1, 2011.
SEC. 5. INCREASE IN THE TAXABLE WAGE BASE.
(a) In General.--Section 3306 of the Internal Revenue Code of 1986
is amended--
(1) in subsection (b), by striking ``$7,000'' both places
it appears and inserting ``the applicable wage base amount (as
defined in subsection (v)(1))''; and
(2) by adding at the end the following new subsection:
``(v) Applicable Wage Base Amount.--
``(1) In general.--For purposes of subsection (b)(1), the
term `applicable wage base amount' means--
``(A) for a calendar year before calendar year
2014, $7,000;
``(B) for calendar year 2014, $15,000; and
``(C) for calendar years beginning on or after
January 1, 2015, the amount determined under paragraph
(2).
``(2) Amount for calendar year 2015 and thereafter.--
``(A) Amount.--
``(i) In general.--For purposes of
paragraph (1)(C), the amount determined under
this paragraph for a calendar year is an amount
equal to the product of--
``(I) the amount of average wage
growth for the year (as determined in
accordance with subparagraph (B)); and
``(II) the applicable wage base
amount for the preceding calendar year.
``(ii) Rounding.--If the amount determined
under clause (i) is not a multiple of $100,
such amount shall be rounded to the next higher
multiple of $100.
``(B) Average wage growth.--
``(i) In general.--For purposes of
subparagraph (A), the amount of annual wage
growth for a calendar year shall be determined
by dividing the average annual wage in the
United States for the 12-month period ending on
the June 30 of the preceding calendar year by
the average annual wage in the United States
for the 12-month period ending on the second
prior June 30, and rounding such ratio to the
fifth decimal place.
``(ii) Average annual wage.--For purposes
of clause (i), using data from the Quarterly
Census of Employment and Wages (or a successor
program), the average annual wage for a 12-
month period shall be determined by dividing
the total covered wages subject to
contributions under all State unemployment
compensation laws for such period by the
average covered employment subject to
contributions under all State unemployment
compensation laws for such period, and rounding
the result to the nearest whole dollar.''.
(b) Effective Date.--The amendments made by this section shall take
effect on the date of the enactment of this Act.
SEC. 6. VOLUNTARY STATE AGREEMENTS TO ABATE PRINCIPAL ON FEDERAL LOANS.
(a) In General.--Section 1203 of the Social Security Act (42 U.S.C.
1323) is amended--
(1) by inserting ``(a) Advances.--'' after ``1203''; and
(2) by adding at the end the following new subsection:
``(b) Voluntary Abatement Agreements.--
``(1) In general.--The governor of any State that has
outstanding repayable advances from the Federal unemployment
account pursuant to subsection (a) may apply to the Secretary
of Labor to enter into a voluntary principal abatement
agreement.
``(2) Contents of application.--An application described in
paragraph (1) shall include a plan that, based upon reasonable
economic projections, describes how the State will, within a
reasonable period of time--
``(A) repay the outstanding principal on its
remaining advance to the Federal unemployment account,
less the amount of the principal abatement pursuant to
paragraph (4); and
``(B) restore the solvency of the State's account
in the Unemployment Trust Fund to an average high cost
multiple of 1.0, as calculated and defined by the
United States Department of Labor.
``(3) Requirement for plan.--A plan described in paragraph
(2) shall be premised on the existing unemployment compensation
law of the State and may take into consideration the enactment
of any changes in law scheduled to become effective during the
life of the plan.
``(4) Agreement.--Upon review of the application and
satisfaction that the State's plan will meet the repayment and
solvency goals described in paragraph (2), the Secretary of
Labor may enter into a principal abatement agreement with the
State. Such an agreement shall be for a period of no more than
7 years.
``(5) Calculation.--Under any voluntary abatement agreement
under this subsection, the amount of principal abatement shall
be calculated as follows:
``(A) The State's repayable advances as of the date
of the enactment of this subsection or December 31,
2011, whichever is earlier, shall be multiplied by a
loan forgiveness multiplier.
``(B) The State's loan forgiveness multiplier shall
be calculated on the same basis as the temporary
increase of Medicaid FMAP under section 5001(c)(2)(A)
of division B of the American Recovery and Reinvestment
Act of 2009, using the State's additional FMAP tier as
of December 31, 2010. In the case of a State that meets
the criteria described in--
``(i) clause (i) of such section
5001(c)(2)(A), the loan multiplier shall be
0.2;
``(ii) clause (ii) of such section
5001(c)(2)(A), the loan multiplier shall be
0.4; and
``(iii) clause (iii) of such section
5001(c)(2)(A), the loan multiplier shall be
0.6.
``(C) The annual amount of principal abatement
shall equal one-seventh of the total amount of
principal abatement.
``(6) Certification.--Under any voluntary abatement
agreement under this subsection, the State shall certify that
during the period of the agreement--
``(A) the method governing the computation of
regular unemployment compensation under the State law
of the State will not be modified in a manner such that
the average weekly benefit amount of regular
unemployment compensation which will be payable during
the period of the agreement will be less than the
average weekly benefit amount of regular unemployment
compensation which would have otherwise been payable
under the State law as in effect on the date of the
enactment of this subsection;
``(B) State law will not be modified in a manner
such that any unemployed individual who would be
eligible for regular unemployment compensation under
the State law in effect on such date of enactment would
be ineligible for regular unemployment compensation
during the period of the agreement or would be subject
to any disqualification during the period of the
agreement that the individual would not have been
subject to under the State law in effect on such date
of enactment;
``(C) State law will not be modified in a manner
such that the maximum amount of regular unemployment
compensation that any unemployed individual would be
eligible to receive in a benefit year during the period
of the agreement will be less than the maximum amount
of regular unemployment compensation that the
individual would have been eligible to receive during a
benefit year under the State law in effect on such date
of enactment; and
``(D) upon a determination by the Secretary of
Labor that the State has modified State law in a manner
inconsistent with the certification described in the
preceding provisions of this paragraph or has failed to
comply with any certifications required by this
paragraph, the State shall be liable for any principal
previously abated under the agreement.
``(7) Transfer.--Under a voluntary abatement agreement
under this subsection, a transfer of the annual amount of the
principal abatement shall be made to the State's account in the
Unemployment Trust Fund on December 31st of the year in which
the agreement is executed so long as the State has complied
with the terms of the agreement. For each subsequent year that
the Secretary of Labor certifies that the State is in
compliance with the terms of the agreement, the annual amount
of the State's principal abatement will be credited to its
outstanding loan balance. If the loan balance reaches zero
while the State still has a remaining principal abatement
amount, the remaining amount shall be made as a positive
balance transfer to the State's account in the Unemployment
Trust Fund.
``(8) Regulations.--The Secretary of Labor shall promulgate
such regulations as are necessary to implement this subsection.
Such regulations shall include--
``(A) standards prescribing a reasonable period of
time for a State plan to reach a solvency level equal
to an average high cost multiple of 1.0, taking into
account the economic conditions and level of insolvency
of the State; and
``(B) guidelines for insuring progress toward
solvency for States with agreements that include plans
that require more than 7 years to reach an average high
cost multiple of 1.0.''.
(b) Effective Date.--The amendments made by this section shall take
effect on the date of the enactment of this Act.
SEC. 7. REWARDS AND INCENTIVES FOR SOLVENT STATES AND EMPLOYERS IN
THOSE STATES.
(a) Increased Interest for Solvent States.--
(1) In general.--Section 904(e) of the Social Security Act
(42 U.S.C. 1104(e)) is amended by adding at the end the
following new flush sentences:
``The separate book account for each State agency shall be augmented by
0.5 percent over the rate of interest provided in subsection (b) when
the State maintains reserves in the account that equal or exceed an
average high cost multiple of 1.0 as defined by the Secretary of Labor
as of December 31st of the preceding year. The State may apply the
additional funds to support State administration pursuant to the
requirements in section 903(c).''.
(b) Lower Rate of Tax for Solvent States.--
(1) In general.--Section 3301 of the Internal Revenue Code
of 1986, as amended by section 3, is amended by adding at the
end the following new sentence: ``For the second 6-month period
of 2011 or for each calendar year thereafter, in the case of a
State that maintains reserves in the State's separate book
account that equal or exceed an average high cost multiple of
1.0 as of December 31st of the year preceding the period or
year involved, paragraph (1) shall be applied for such period
or year in the State by substituting `6.0 percent' for `6.2
percent' or, as the case may be, paragraph (2) shall be applied
for such period or year in the State by substituting `5.68
percent' for `5.78 percent'.''.
(2) Effective date.--The amendment made by this subsection
shall take effect on the earlier of--
(A) the date of the enactment of this Act; or
(B) July 1, 2011. | Unemployment Insurance Solvency Act of 2011 - Amends title XII of the Social Security Act (Advances to State Unemployment Funds) to: (1) extend through December 31, 2012, the waiver granted to states for payment of interest on advances made from the federal unemployment account in the Unemployment Trust Fund; and (2) authorize the governor of any state that has outstanding repayable advances from the federal unemployment account to apply to the Secretary of Labor to enter into a voluntary principal abatement agreement.
Amends the Internal Revenue Code to: (1) extend the 6.2% employment tax rate for employers through 2013 and impose a reduced 5.78% rate in 2014, (2) modify the rate applicable to the limit on the credit allowed to employers for the federal unemployment tax, and (3) increase the taxable wage base for the federal unemployment tax to $15,000 in 2014.
Amends title IX of the Social Security Act (Miscellaneous Provisions Relating to Employment Security) to increase the rate of interest payable on unemployment compensation reserves and lower the rate of the employment tax for employers in states whose unemployment compensation fund remains solvent. | <s>[INST]SECTION 1. SHORT TITLE; TABLE OF CONTENTS.
(a) Short Title.--This Act may be cited as the ``Unemployment
Insurance Solvency Act of 2011''.
(b) Table of Contents.--The table of contents of this Act is as
follows:
Sec. 1. Short title; table of contents.
Sec. 2. Extension of assistance for States with advances.
Sec. 3. Reduction in the rate of employer taxes.
Sec. 4. Modifications of employer credit reductions.
Sec. 5. Increase in the taxable wage base.
Sec. 6. Voluntary State agreements to abate principal on Federal loans.
Sec. 7. Rewards and incentives for solvent States and employers in
those States.
SEC. 2. EXTENSION OF ASSISTANCE FOR STATES WITH ADVANCES.
(a) In General.--Section 1202(b)(10)(A) of the Social Security Act
(42 U.S.C. 1322(b)(10)(A)) is amended by striking ``2010'' and
inserting ``2012'' in the matter preceding clause (i).
(b) Effective Date.--The amendment made by this section shall take
effect as if included in the enactment of section 2004 of the
Assistance for Unemployed Workers and Struggling Families Act (Public
Law 111-5; 123 Stat. 443).
SEC. 3. REDUCTION IN THE RATE OF EMPLOYER TAXES.
(a) In General.--Section 3301 of the Internal Revenue Code of 1986
is amended--
(1) in paragraph (1), by striking ``2010 and the first 6
months of calendar year 2011'' and inserting ``2013''; and
(2) in paragraph (2), by striking ``6.0 percent in the case
of the remainder of calendar year 2011'' and inserting ``5.78
percent in the case of calendar year 2014''.
(b) Effective Date.--The amendments made by this section shall take
effect on the earlier of--
(1) the date of the enactment of this Act; or
(2) July 1, 2011.
SEC. 4. MODIFICATIONS OF EMPLOYER CREDIT REDUCTIONS.
(a) Limit on Total Credits.--Section 3302(c) of the Internal
Revenue Code of 1986 is amended--
(1) in paragraph (1), by striking ``90 percent of the tax
against which such credits are allowable'' and inserting ``an
amount equal to 5.4 percent of the total wages (as defined in
section 3306(b)) paid by such taxpayer during the calendar year
with respect to employment (as defined in section 3306(c))'';
and
(2) in paragraph (2)--
(A) by striking subparagraphs (B) and (C) and the
flush matter following subparagraph (C);
(B) by striking ``(2) If'' and inserting ``(2)(A)
If'';
(C) by striking ``(A)(i) in'' and inserting ``(i)
in'';
(D) in clause (i) of subparagraph (A), as
redesignated by subparagraph (C), by striking ``5
percent of the tax imposed by section 3301 with respect
to the wages paid by such taxpayer during such taxable
year which are attributable to such State'' and
inserting ``an amount equal to 0.3 percent of the total
wages (as defined in section 3306(b)) paid by such
taxpayer during the calendar year with respect to
employment (as defined in section 3306(c))'';
(E) in clause (ii) of subparagraph (A)--
(i) by moving such clause 2 ems to the
left;
(ii) by striking ``5 percent, for each such
succeeding taxable year, of the tax imposed by
section 3301 with respect to the wages paid by
such taxpayer during such taxable year which
are attributable to such State;'' and inserting
``an amount equal to 0.3 percent of the total
wages (as defined in section 3306(b)) paid by
such taxpayer during the calendar year with
respect to employment (as defined in section
3306(c)), for each succeeding taxable year;'';
and
(iii) by striking the semicolon at the end
and inserting a period; and
(F) by adding at the end the following new
subparagraph:
``(B) The provisions of subparagraph (A) shall be applied
with respect to the taxable year beginning January 1, 2011, or
any succeeding taxable year by deeming January 1, 2013, to be
the first January 1 occurring after January 1, 2010. For
purposes of subparagraph (A), consecutive taxable years in the
period commencing January 1, 2013, shall be determined as if
the taxable year which begins on January 1, 2013, were the
taxable year immediately succeeding the taxable year which
began on January 1, 2010. No taxpayer shall be subject to
credit reductions under this paragraph for taxable years
beginning January 1, 2011, and January 1, 2012.''.
(b) Definitions and Special Rules.--Section 3302(d) of the Internal
Revenue Code of 1986 is amended--
(1) by striking paragraphs (1), (4), (5), (6), and (7); and
(2) by redesignating paragraphs (2) and (3) as paragraphs
(1) and (2), respectively.
(c) Effective Date.--The amendments made by this section shall take
effect as if enacted on January 1, 2011.
SEC. 5. INCREASE IN THE TAXABLE WAGE BASE.
(a) In General.--Section 3306 of the Internal Revenue Code of 1986
is amended--
(1) in subsection (b), by striking ``$7,000'' both places
it appears and inserting ``the applicable wage base amount (as
defined in subsection (v)(1))''; and
(2) by adding at the end the following new subsection:
``(v) Applicable Wage Base Amount.--
``(1) In general.--For purposes of subsection (b)(1), the
term `applicable wage base amount' means--
``(A) for a calendar year before calendar year
2014, $7,000;
``(B) for calendar year 2014, $15,000; and
``(C) for calendar years beginning on or after
January 1, 2015, the amount determined under paragraph
(2).
``(2) Amount for calendar year 2015 and thereafter.--
``(A) Amount.--
``(i) In general.--For purposes of
paragraph (1)(C), the amount determined under
this paragraph for a calendar year is an amount
equal to the product of--
``(I) the amount of average wage
growth for the year (as determined in
accordance with subparagraph (B)); and
``(II) the applicable wage base
amount for the preceding calendar year.
``(ii) Rounding.--If the amount determined
under clause (i) is not a multiple of $100,
such amount shall be rounded to the next higher
multiple of $100.
``(B) Average wage growth.--
``(i) In general.--For purposes of
subparagraph (A), the amount of annual wage
growth for a calendar year shall be determined
by dividing the average annual wage in the
United States for the 12-month period ending on
the June 30 of the preceding calendar year by
the average annual wage in the United States
for the 12-month period ending on the second
prior June 30, and rounding such ratio to the
fifth decimal place.
``(ii) Average annual wage.--For purposes
of clause (i), using data from the Quarterly
Census of Employment and Wages (or a successor
program), the average annual wage for a 12-
month period shall be determined by dividing
the total covered wages subject to
contributions under all State unemployment
compensation laws for such period by the
average covered employment subject to
contributions under all State unemployment
compensation laws for such period, and rounding
the result to the nearest whole dollar.''.
(b) Effective Date.--The amendments made by this section shall take
effect on the date of the enactment of this Act.
SEC. 6. VOLUNTARY STATE AGREEMENTS TO ABATE PRINCIPAL ON FEDERAL LOANS.
(a) In General.--Section 1203 of the Social Security Act (42 U.S.C.
1323) is amended--
(1) by inserting ``(a) Advances.--'' after ``1203''; and
(2) by adding at the end the following new subsection:
``(b) Voluntary Abatement Agreements.--
``(1) In general.--The governor of any State that has
outstanding repayable advances from the Federal unemployment
account pursuant to subsection (a) may apply to the Secretary
of Labor to enter into a voluntary principal abatement
agreement.
``(2) Contents of application.--An application described in
paragraph (1) shall include a plan that, based upon reasonable
economic projections, describes how the State will, within a
reasonable period of time--
``(A) repay the outstanding principal on its
remaining advance to the Federal unemployment account,
less the amount of the principal abatement pursuant to
paragraph (4); and
``(B) restore the solvency of the State's account
in the Unemployment Trust Fund to an average high cost
multiple of 1.0, as calculated and defined by the
United States Department of Labor.
``(3) Requirement for plan.--A plan described in paragraph
(2) shall be premised on the existing unemployment compensation
law of the State and may take into consideration the enactment
of any changes in law scheduled to become effective during the
life of the plan.
``(4) Agreement.--Upon review of the application and
satisfaction that the State's plan will meet the repayment and
solvency goals described in paragraph (2), the Secretary of
Labor may enter into a principal abatement agreement with the
State. Such an agreement shall be for a period of no more than
7 years.
``(5) Calculation.--Under any voluntary abatement agreement
under this subsection, the amount of principal abatement shall
be calculated as follows:
``(A) The State's repayable advances as of the date
of the enactment of this subsection or December 31,
2011, whichever is earlier, shall be multiplied by a
loan forgiveness multiplier.
``(B) The State's loan forgiveness multiplier shall
be calculated on the same basis as the temporary
increase of Medicaid FMAP under section 5001(c)(2)(A)
of division B of the American Recovery and Reinvestment
Act of 2009, using the State's additional FMAP tier as
of December 31, 2010. In the case of a State that meets
the criteria described in--
``(i) clause (i) of such section
5001(c)(2)(A), the loan multiplier shall be
0.2;
``(ii) clause (ii) of such section
5001(c)(2)(A), the loan multiplier shall be
0.4; and
``(iii) clause (iii) of such section
5001(c)(2)(A), the loan multiplier shall be
0.6.
``(C) The annual amount of principal abatement
shall equal one-seventh of the total amount of
principal abatement.
``(6) Certification.--Under any voluntary abatement
agreement under this subsection, the State shall certify that
during the period of the agreement--
``(A) the method governing the computation of
regular unemployment compensation under the State law
of the State will not be modified in a manner such that
the average weekly benefit amount of regular
unemployment compensation which will be payable during
the period of the agreement will be less than the
average weekly benefit amount of regular unemployment
compensation which would have otherwise been payable
under the State law as in effect on the date of the
enactment of this subsection;
``(B) State law will not be modified in a manner
such that any unemployed individual who would be
eligible for regular unemployment compensation under
the State law in effect on such date of enactment would
be ineligible for regular unemployment compensation
during the period of the agreement or would be subject
to any disqualification during the period of the
agreement that the individual would not have been
subject to under the State law in effect on such date
of enactment;
``(C) State law will not be modified in a manner
such that the maximum amount of regular unemployment
compensation that any unemployed individual would be
eligible to receive in a benefit year during the period
of the agreement will be less than the maximum amount
of regular unemployment compensation that the
individual would have been eligible to receive during a
benefit year under the State law in effect on such date
of enactment; and
``(D) upon a determination by the Secretary of
Labor that the State has modified State law in a manner
inconsistent with the certification described in the
preceding provisions of this paragraph or has failed to
comply with any certifications required by this
paragraph, the State shall be liable for any principal
previously abated under the agreement.
``(7) Transfer.--Under a voluntary abatement agreement
under this subsection, a transfer of the annual amount of the
principal abatement shall be made to the State's account in the
Unemployment Trust Fund on December 31st of the year in which
the agreement is executed so long as the State has complied
with the terms of the agreement. For each subsequent year that
the Secretary of Labor certifies that the State is in
compliance with the terms of the agreement, the annual amount
of the State's principal abatement will be credited to its
outstanding loan balance. If the loan balance reaches zero
while the State still has a remaining principal abatement
amount, the remaining amount shall be made as a positive
balance transfer to the State's account in the Unemployment
Trust Fund.
``(8) Regulations.--The Secretary of Labor shall promulgate
such regulations as are necessary to implement this subsection.
Such regulations shall include--
``(A) standards prescribing a reasonable period of
time for a State plan to reach a solvency level equal
to an average high cost multiple of 1.0, taking into
account the economic conditions and level of insolvency
of the State; and
``(B) guidelines for insuring progress toward
solvency for States with agreements that include plans
that require more than 7 years to reach an average high
cost multiple of 1.0.''.
(b) Effective Date.--The amendments made by this section shall take
effect on the date of the enactment of this Act.
SEC. 7. REWARDS AND INCENTIVES FOR SOLVENT STATES AND EMPLOYERS IN
THOSE STATES.
(a) Increased Interest for Solvent States.--
(1) In general.--Section 904(e) of the Social Security Act
(42 U.S.C. 1104(e)) is amended by adding at the end the
following new flush sentences:
``The separate book account for each State agency shall be augmented by
0.5 percent over the rate of interest provided in subsection (b) when
the State maintains reserves in the account that equal or exceed an
average high cost multiple of 1.0 as defined by the Secretary of Labor
as of December 31st of the preceding year. The State may apply the
additional funds to support State administration pursuant to the
requirements in section 903(c).''.
(b) Lower Rate of Tax for Solvent States.--
(1) In general.--Section 3301 of the Internal Revenue Code
of 1986, as amended by section 3, is amended by adding at the
end the following new sentence: ``For the second 6-month period
of 2011 or for each calendar year thereafter, in the case of a
State that maintains reserves in the State's separate book
account that equal or exceed an average high cost multiple of
1.0 as of December 31st of the year preceding the period or
year involved, paragraph (1) shall be applied for such period
or year in the State by substituting `6.0 percent' for `6.2
percent' or, as the case may be, paragraph (2) shall be applied
for such period or year in the State by substituting `5.68
percent' for `5.78 percent'.''.
(2) Effective date.--The amendment made by this subsection
shall take effect on the earlier of--
(A) the date of the enactment of this Act; or
(B) July 1, 2011.[/INST]Unemployment Insurance Solvency Act of 2011 - Amends title XII of the Social Security Act (Advances to State Unemployment Funds) to: (1) extend through December 31, 2012, the waiver granted to states for payment of interest on advances made from the federal unemployment account in the Unemployment Trust Fund; and (2) authorize the governor of any state that has outstanding repayable advances from the federal unemployment account to apply to the Secretary of Labor to enter into a voluntary principal abatement agreement.
Amends the Internal Revenue Code to: (1) extend the 6.2% employment tax rate for employers through 2013 and impose a reduced 5.78% rate in 2014, (2) modify the rate applicable to the limit on the credit allowed to employers for the federal unemployment tax, and (3) increase the taxable wage base for the federal unemployment tax to $15,000 in 2014.
Amends title IX of the Social Security Act (Miscellaneous Provisions Relating to Employment Security) to increase the rate of interest payable on unemployment compensation reserves and lower the rate of the employment tax for employers in states whose unemployment compensation fund remains solvent.</s> |
in february 2011 , data on all referrals from the primary health care ( phc ) to the shc in northern norway in the time period 1 january 2007 until 31 december 2010 was accessed .
the data was retrospectively analysed and a comparative study focusing the sami - speaking municipalities ( sami group ) and a control group ( non - sami group ) was performed .
the number of inhabitants in each group was calculated according to data from statistics norway ( www.ssb.no ) .
all referrals were recorded with the following information : patient 's place of living ( municipality ) , gender , age - group and address of referral ( hospital trust ) .
many norwegian municipalities have sami settlers , but only 8 municipalities have been included in the administration area of the sami language law .
the latter were selected as the sami municipalities ( sami group ) in this study .
the coastal municipalities of northern norway have generally few sami people and 11 of them were chosen as the control group .
they were selected based on rural location , distance to hospital and a similar population in size , ratio between gender and age as the sami - speaking municipalities .
the names of the municipalities in the administration area of the sami language law written in sami language ( when employed ) and norwegian were : deatnu tana , unjrga nesseby , porsanger porsngu porsanki , krsjohka karasjok , guovdageaidnu kautokeino , givuotna kfjord , stvuona lavangen and divtasvuona tysfjord .
the municipalities included in the control group ( non - sami group ) were : ldingen , bjarky , lebesby , gamvik , msy , salangen , btsfjord , berlevg , nordkapp , hasvik and vard . despite both vard and honningsvg ( in nordkapp municipality )
are registered as norwegian towns , we argue that the number of inhabitants ( about 2,000 in each town ) and their location support the classification as rural areas .
the mean number of inhabitants during study period ( 20072010 ) was 18,840 ( 51.2% ) and 17,987 ( 48.8% ) in the sami and non - sami group , respectively .
details are shown in table i. the female / male ratio was 0.94 and 0.95 in the sami and the control group , respectively .
the map of northern norway and the sami and non - sami - speaking municipalities .
the number of inhabitants in sami and non - sami groups during study period the 2010 figures were not available .
individual patient referral data was imported from the patient administrative system ( pas ) in all hospital trusts in northern norway and the microsoft excel 2002 version was employed for the final database .
the data was depersonalized and made anonymous before exportation to the centre for clinical documentation and evaluation ( skde ) at the nnrha trust .
characteristics of the municipalities in terms of population , age groups and gender were derived from statistics norway ( www.ssb.no ) . statistical package for social science ( spss ) version 16.0
the comparison between groups ( sami and non - sami ) with regard to frequency of referrals were based on age adjusted rates ( number of referrals 20072010/population 20072010 * 1,000 ) .
one way analysis of variance ( anova ) was employed for the comparison between groups with regard to the primary endpoint ( referral rate during study period ) .
the study was performed as a retrospective analysis of referral rate for the 2 municipality groups . as a quality of care analysis ,
no approval from the regional committee for medical and health research ethics ( rek ) was necessary .
all tests were carried out 2-sided . the referral ratio ( rr ) for each municipality
was adjusted for age differences ( rra ) and calculated employing the following formula :
ria = number of referrals in age group in municipality y all referrals in municipality ynumber of referrals in age group in northern norwayall referrals in northern norway
individual patient referral data was imported from the patient administrative system ( pas ) in all hospital trusts in northern norway and the microsoft excel 2002 version was employed for the final database .
the data was depersonalized and made anonymous before exportation to the centre for clinical documentation and evaluation ( skde ) at the nnrha trust .
characteristics of the municipalities in terms of population , age groups and gender were derived from statistics norway ( www.ssb.no ) .
statistical package for social science ( spss ) version 16.0 was employed for statistical analysis .
the comparison between groups ( sami and non - sami ) with regard to frequency of referrals were based on age adjusted rates ( number of referrals 20072010/population 20072010 * 1,000 ) .
one way analysis of variance ( anova ) was employed for the comparison between groups with regard to the primary endpoint ( referral rate during study period ) .
the study was performed as a retrospective analysis of referral rate for the 2 municipality groups . as a quality of care analysis ,
no approval from the regional committee for medical and health research ethics ( rek ) was necessary .
all tests were carried out 2-sided . the referral ratio ( rr ) for each municipality
was adjusted for age differences ( rra ) and calculated employing the following formula :
ria = number of referrals in age group in municipality y all referrals in municipality ynumber of referrals in age group in northern norwayall referrals in northern norway
during the 4 years study period , a total of 504,292 referrals were sent from the phc to the shc in northern norway .
nine per cent ( 45,634 referrals ) of them were related to inhabitants in the sami and the control group of municipalities .
the referrals were similarly distributed between study groups ( sami 23,093 referrals 50.6% , non - sami group 22,541 referrals
details are shown in table ii . whereas there was a slightly dominance of males in the population ,
females constituted 57.7% ( 13.325 referrals ) and 57.2% ( 12.904 referrals ) of the referrals in the sami and non - sami group , respectively . correcting for population differences ,
the referral rate was lower among sami and the mean annual total referral rate per 1,000 inhabitants ( adjusted for gender and age ) was 280 and 305 , respectively .
the annual number of referrals according to gender and sami and non - sami speaking municipalities the gender and age adjusted referral rate per 1,000 inhabitants in the sami and non - sami speaking municipalities .
the range is within the municipalities in the 2 groups about 70% of all referrals were seen in the age group 1666 years , and most frequently in the age group 1649 years .
2 . the age adjusted referral rate of the sami population and the control group was 1.14 and 1.17 times that of the population of northern norway .
the difference from the north norway mean figure ( 1.00 ) was observed in the population below 67 years of age .
details are shown in table iv . whereas the referral rate was slightly lower in the sami group , the most striking finding was large inter - municipal variations in both groups .
a factor of 2 was observed between the municipality with the lowest and highest figure ( lavangen vs. kautokeino and bjarky vs. btsfjord ) in both groups .
the 2 ( karasjok and kautokeino ) most sami populated municipalities were in both ends of the scale .
the percentage of referrals in each age group . the mean age and gender adjusted reference ratio ( northern norway=1.0 ) in the time period 20072010 in all municipalities .
the referral ratio according to age intervals in the sami and non - sami speaking municipalities in the time period 20072010 .
the figures of northern norway in total was employed as 1.0 two - thirds of the referrals were sent to the finnmark hospital trust and one - third to the university hospital of north norway trust .
there were very few referrals to the southern located hospital trust ( helgeland hospital trust ) .
this strongly indicates that gps in both municipality groups were loyal to their local hospital trust when referring patients . the percentage of referrals related to the 4 hospital trusts in northern norway .
the age adjusted referral rate in the sami population and the control group was 1.14 and 1.17 times that of the total population of northern norway .
the difference from north norwegians in general was observed in the population below 67 years of age .
gps in both municipality groups were loyal to their local hospital trust as almost all patients were referred to the finnmark and university hospital trusts . despite the sami municipalities employed the sami language , the share of sami people or the percentage having sami as their mother tongue was not known in the sami or the control group .
however , a gallup poll back in october 2000 asked people in finnmark if they could speak sami and included 5 municipalities from the sami group and 8 from our control group .
this result supports our classification of the 2 groups as sami and non - sami .
we had access to all somatic referrals from the primary health care in northern norway during study period .
consequently , an excellent overview on the macro level concerning referrals and referral index was possible .
however , we had no data with regard to psychiatric diseases . furthermore , any sub - classification of the somatic referrals was not possible due to various clinical and departmental structures within the hospital trusts .
sami - speaking municipalities was therefore selected as a surrogate . whereas we revealed no difference between groups , several studies ( 813 )
mukadam and colleagues ( 8) documented that minority ethnic elders presented later to uk dementia services than others .
langford et al . ( 9 ) revealed that compared with whites , blacks and hispanics were less likely to have heard of a clinical trial . a british study ( 10 ) , reported similarly that awareness of breast and cervical cancer screening was high in the white and low in ethnic minority groups . among us
stroke survivors , levine and colleagues ( 11 ) documented mexican americans and blacks reporting worse access to physician care and medications than whites . in a review analysis
( 12 ) the authors concluded white children more likely to undergo tympanostomy tube insertion compared to black or hispanic children .
mcgarvey and colleagues ( 13 ) analysed residents living in appalachian countries in virginia and concluded that they did not receive adequate health care , even those with health insurance .
with regard to emergency and intensive care , race and ethnicity does not seem to have any influence on access to care ( 14,15 ) . focusing psychiatric diseases , unequal access for minority groups has been revealed ( 16,17 ) .
( 16 ) observed in texas us that depressed white students were more likely than depressed minority youth to report having received treatment for depression .
similarly , cooper and colleagues ( 17 ) observed in 3 english cities an increased risk of self - harm among young black females , but fewer of them received psychiatric care .
lakso and colleagues ( 18 ) documented that persistently worried patients after a gp consultation reported more anxiety than others and expected more often further medical examinations . knowing that most sami have a different native language and culture that may cause threshold , counter , queue and cultural challenges when assessing the health care ( 2 ) , we anticipated more anxiety and a raised number of referrals from this study group , but no difference was revealed .
this may be due to variations in gp practices and health care infrastructure in the municipalities ( 1,1921 ) .
dijk and co - workers ( 1 ) revealed that gp practices performing more minor surgery interventions had a lower referral rate for patients with a laceration / cut and those with a sebaceous cyst .
however , no difference was observed with regard to gp consultations for benign neoplasm skin / nevus . a female majority ( 58% ) with regard to referrals
stoves and colleagues ( 19 ) explored an electronic consultation between shc and gps as an alternative to hospital referral for patients with chronic kidney disease in uk .
another strategy has been the improvement of collaboration across organisational boarders by a focus on the referral process ( 20 ) . in this strategy ,
heimly ( 20 ) argue for the implementation of gps in part time positions as practice consultants in hospitals .
the authors argue that this has been fundamental for the improvement of understanding of each other 's needs and the work processes between collaborating actors .
increased competition between gps and access to low level specialised care can influence on referral index .
tjerbo ( 22 ) analysed this topic and the tests revealed that increased competition reduces the use of ambulatory care , while the effects on the use of in - patient services was unaffected .
srensen and co - workers ( 23 ) analysed the expenditures related to gp services and run a multilevel analysis of 2,123 gps within 15 danish counties .
they concluded that 38% of health care expenditures were associated with gp practices and referrals to specialised care were the main source of variation in gp initiated expenditures .
consequently , they concluded reforms aiming to reduce gp initiated expenditures should focus on general practice access to low level specialised care .
kvaerner and helgaker ( 24 ) analysed otitis media referrals and concluded that gps without speciality , availability to practicing specialist and heavy work load all increased referral . based on their findings
, they suggested that learning groups contribute to update knowledge in primary care and fewer referrals to specialists .
a slightly lower referral index in the sami group could be explained by a lower risk of cancer among the sami ( 25 ) .
when contracting a cancer , they experienced the same service of radiotherapy as the control group ( 25 ) .
in the future , hopefully more data on subgroup level will be available and further analysis should be performed .
the significant inter - municipality variations with regard to referral index within both study groups call for future studies identifying and clarifying possible explanations .
this study documents that people living in sami - speaking municipalities are not more or less commonly referred to the somatic specialist health care than comparable municipalities within northern norway .
the strategic goal of equal availability to shc for all inhabitants in the region has been successful .
the authors declare no conflict of interest and financial support came from the northern norway regional health authority . | objectivesthe sami people constitute the indigenous people in northern norway . the objective of this study was to clarify whether they have a similar supply of somatic specialist health care ( shc ) as others.methodsthe referrals from general practitioners ( gps ) in the primary health care ( phc ) in the administration area of the sami language law ( 8 municipalities ) were matched with a control group of 11 municipalities .
population data was accessed from statistics norway and the time period 20072010 was analysed .
the main outcome was the number of referrals per 1,000 inhabitants according to age group , gender and place of living.results504,292 referrals in northern norway were indentified and the sami and control group constituted 23,093 and 22,541 referrals , respectively .
the major findings were a similar referral ratio ( rr ) ( 1.14 and 1.17 ) ( p = 0.624 ) and women more commonly referred ( female / male ratio 1.45 and 1.41 ) in both groups .
gps in both groups were loyal to their local hospital trust.conclusioninhabitants in sami - speaking municipalities in northern norway have a similar supply of shc services as controls .
inter - municipal variation was significant in both groups . | <s>[INST]in february 2011 , data on all referrals from the primary health care ( phc ) to the shc in northern norway in the time period 1 january 2007 until 31 december 2010 was accessed .
the data was retrospectively analysed and a comparative study focusing the sami - speaking municipalities ( sami group ) and a control group ( non - sami group ) was performed .
the number of inhabitants in each group was calculated according to data from statistics norway ( www.ssb.no ) .
all referrals were recorded with the following information : patient 's place of living ( municipality ) , gender , age - group and address of referral ( hospital trust ) .
many norwegian municipalities have sami settlers , but only 8 municipalities have been included in the administration area of the sami language law .
the latter were selected as the sami municipalities ( sami group ) in this study .
the coastal municipalities of northern norway have generally few sami people and 11 of them were chosen as the control group .
they were selected based on rural location , distance to hospital and a similar population in size , ratio between gender and age as the sami - speaking municipalities .
the names of the municipalities in the administration area of the sami language law written in sami language ( when employed ) and norwegian were : deatnu tana , unjrga nesseby , porsanger porsngu porsanki , krsjohka karasjok , guovdageaidnu kautokeino , givuotna kfjord , stvuona lavangen and divtasvuona tysfjord .
the municipalities included in the control group ( non - sami group ) were : ldingen , bjarky , lebesby , gamvik , msy , salangen , btsfjord , berlevg , nordkapp , hasvik and vard . despite both vard and honningsvg ( in nordkapp municipality )
are registered as norwegian towns , we argue that the number of inhabitants ( about 2,000 in each town ) and their location support the classification as rural areas .
the mean number of inhabitants during study period ( 20072010 ) was 18,840 ( 51.2% ) and 17,987 ( 48.8% ) in the sami and non - sami group , respectively .
details are shown in table i. the female / male ratio was 0.94 and 0.95 in the sami and the control group , respectively .
the map of northern norway and the sami and non - sami - speaking municipalities .
the number of inhabitants in sami and non - sami groups during study period the 2010 figures were not available .
individual patient referral data was imported from the patient administrative system ( pas ) in all hospital trusts in northern norway and the microsoft excel 2002 version was employed for the final database .
the data was depersonalized and made anonymous before exportation to the centre for clinical documentation and evaluation ( skde ) at the nnrha trust .
characteristics of the municipalities in terms of population , age groups and gender were derived from statistics norway ( www.ssb.no ) . statistical package for social science ( spss ) version 16.0
the comparison between groups ( sami and non - sami ) with regard to frequency of referrals were based on age adjusted rates ( number of referrals 20072010/population 20072010 * 1,000 ) .
one way analysis of variance ( anova ) was employed for the comparison between groups with regard to the primary endpoint ( referral rate during study period ) .
the study was performed as a retrospective analysis of referral rate for the 2 municipality groups . as a quality of care analysis ,
no approval from the regional committee for medical and health research ethics ( rek ) was necessary .
all tests were carried out 2-sided . the referral ratio ( rr ) for each municipality
was adjusted for age differences ( rra ) and calculated employing the following formula :
ria = number of referrals in age group in municipality y all referrals in municipality ynumber of referrals in age group in northern norwayall referrals in northern norway
individual patient referral data was imported from the patient administrative system ( pas ) in all hospital trusts in northern norway and the microsoft excel 2002 version was employed for the final database .
the data was depersonalized and made anonymous before exportation to the centre for clinical documentation and evaluation ( skde ) at the nnrha trust .
characteristics of the municipalities in terms of population , age groups and gender were derived from statistics norway ( www.ssb.no ) .
statistical package for social science ( spss ) version 16.0 was employed for statistical analysis .
the comparison between groups ( sami and non - sami ) with regard to frequency of referrals were based on age adjusted rates ( number of referrals 20072010/population 20072010 * 1,000 ) .
one way analysis of variance ( anova ) was employed for the comparison between groups with regard to the primary endpoint ( referral rate during study period ) .
the study was performed as a retrospective analysis of referral rate for the 2 municipality groups . as a quality of care analysis ,
no approval from the regional committee for medical and health research ethics ( rek ) was necessary .
all tests were carried out 2-sided . the referral ratio ( rr ) for each municipality
was adjusted for age differences ( rra ) and calculated employing the following formula :
ria = number of referrals in age group in municipality y all referrals in municipality ynumber of referrals in age group in northern norwayall referrals in northern norway
during the 4 years study period , a total of 504,292 referrals were sent from the phc to the shc in northern norway .
nine per cent ( 45,634 referrals ) of them were related to inhabitants in the sami and the control group of municipalities .
the referrals were similarly distributed between study groups ( sami 23,093 referrals 50.6% , non - sami group 22,541 referrals
details are shown in table ii . whereas there was a slightly dominance of males in the population ,
females constituted 57.7% ( 13.325 referrals ) and 57.2% ( 12.904 referrals ) of the referrals in the sami and non - sami group , respectively . correcting for population differences ,
the referral rate was lower among sami and the mean annual total referral rate per 1,000 inhabitants ( adjusted for gender and age ) was 280 and 305 , respectively .
the annual number of referrals according to gender and sami and non - sami speaking municipalities the gender and age adjusted referral rate per 1,000 inhabitants in the sami and non - sami speaking municipalities .
the range is within the municipalities in the 2 groups about 70% of all referrals were seen in the age group 1666 years , and most frequently in the age group 1649 years .
2 . the age adjusted referral rate of the sami population and the control group was 1.14 and 1.17 times that of the population of northern norway .
the difference from the north norway mean figure ( 1.00 ) was observed in the population below 67 years of age .
details are shown in table iv . whereas the referral rate was slightly lower in the sami group , the most striking finding was large inter - municipal variations in both groups .
a factor of 2 was observed between the municipality with the lowest and highest figure ( lavangen vs. kautokeino and bjarky vs. btsfjord ) in both groups .
the 2 ( karasjok and kautokeino ) most sami populated municipalities were in both ends of the scale .
the percentage of referrals in each age group . the mean age and gender adjusted reference ratio ( northern norway=1.0 ) in the time period 20072010 in all municipalities .
the referral ratio according to age intervals in the sami and non - sami speaking municipalities in the time period 20072010 .
the figures of northern norway in total was employed as 1.0 two - thirds of the referrals were sent to the finnmark hospital trust and one - third to the university hospital of north norway trust .
there were very few referrals to the southern located hospital trust ( helgeland hospital trust ) .
this strongly indicates that gps in both municipality groups were loyal to their local hospital trust when referring patients . the percentage of referrals related to the 4 hospital trusts in northern norway .
the age adjusted referral rate in the sami population and the control group was 1.14 and 1.17 times that of the total population of northern norway .
the difference from north norwegians in general was observed in the population below 67 years of age .
gps in both municipality groups were loyal to their local hospital trust as almost all patients were referred to the finnmark and university hospital trusts . despite the sami municipalities employed the sami language , the share of sami people or the percentage having sami as their mother tongue was not known in the sami or the control group .
however , a gallup poll back in october 2000 asked people in finnmark if they could speak sami and included 5 municipalities from the sami group and 8 from our control group .
this result supports our classification of the 2 groups as sami and non - sami .
we had access to all somatic referrals from the primary health care in northern norway during study period .
consequently , an excellent overview on the macro level concerning referrals and referral index was possible .
however , we had no data with regard to psychiatric diseases . furthermore , any sub - classification of the somatic referrals was not possible due to various clinical and departmental structures within the hospital trusts .
sami - speaking municipalities was therefore selected as a surrogate . whereas we revealed no difference between groups , several studies ( 813 )
mukadam and colleagues ( 8) documented that minority ethnic elders presented later to uk dementia services than others .
langford et al . ( 9 ) revealed that compared with whites , blacks and hispanics were less likely to have heard of a clinical trial . a british study ( 10 ) , reported similarly that awareness of breast and cervical cancer screening was high in the white and low in ethnic minority groups . among us
stroke survivors , levine and colleagues ( 11 ) documented mexican americans and blacks reporting worse access to physician care and medications than whites . in a review analysis
( 12 ) the authors concluded white children more likely to undergo tympanostomy tube insertion compared to black or hispanic children .
mcgarvey and colleagues ( 13 ) analysed residents living in appalachian countries in virginia and concluded that they did not receive adequate health care , even those with health insurance .
with regard to emergency and intensive care , race and ethnicity does not seem to have any influence on access to care ( 14,15 ) . focusing psychiatric diseases , unequal access for minority groups has been revealed ( 16,17 ) .
( 16 ) observed in texas us that depressed white students were more likely than depressed minority youth to report having received treatment for depression .
similarly , cooper and colleagues ( 17 ) observed in 3 english cities an increased risk of self - harm among young black females , but fewer of them received psychiatric care .
lakso and colleagues ( 18 ) documented that persistently worried patients after a gp consultation reported more anxiety than others and expected more often further medical examinations . knowing that most sami have a different native language and culture that may cause threshold , counter , queue and cultural challenges when assessing the health care ( 2 ) , we anticipated more anxiety and a raised number of referrals from this study group , but no difference was revealed .
this may be due to variations in gp practices and health care infrastructure in the municipalities ( 1,1921 ) .
dijk and co - workers ( 1 ) revealed that gp practices performing more minor surgery interventions had a lower referral rate for patients with a laceration / cut and those with a sebaceous cyst .
however , no difference was observed with regard to gp consultations for benign neoplasm skin / nevus . a female majority ( 58% ) with regard to referrals
stoves and colleagues ( 19 ) explored an electronic consultation between shc and gps as an alternative to hospital referral for patients with chronic kidney disease in uk .
another strategy has been the improvement of collaboration across organisational boarders by a focus on the referral process ( 20 ) . in this strategy ,
heimly ( 20 ) argue for the implementation of gps in part time positions as practice consultants in hospitals .
the authors argue that this has been fundamental for the improvement of understanding of each other 's needs and the work processes between collaborating actors .
increased competition between gps and access to low level specialised care can influence on referral index .
tjerbo ( 22 ) analysed this topic and the tests revealed that increased competition reduces the use of ambulatory care , while the effects on the use of in - patient services was unaffected .
srensen and co - workers ( 23 ) analysed the expenditures related to gp services and run a multilevel analysis of 2,123 gps within 15 danish counties .
they concluded that 38% of health care expenditures were associated with gp practices and referrals to specialised care were the main source of variation in gp initiated expenditures .
consequently , they concluded reforms aiming to reduce gp initiated expenditures should focus on general practice access to low level specialised care .
kvaerner and helgaker ( 24 ) analysed otitis media referrals and concluded that gps without speciality , availability to practicing specialist and heavy work load all increased referral . based on their findings
, they suggested that learning groups contribute to update knowledge in primary care and fewer referrals to specialists .
a slightly lower referral index in the sami group could be explained by a lower risk of cancer among the sami ( 25 ) .
when contracting a cancer , they experienced the same service of radiotherapy as the control group ( 25 ) .
in the future , hopefully more data on subgroup level will be available and further analysis should be performed .
the significant inter - municipality variations with regard to referral index within both study groups call for future studies identifying and clarifying possible explanations .
this study documents that people living in sami - speaking municipalities are not more or less commonly referred to the somatic specialist health care than comparable municipalities within northern norway .
the strategic goal of equal availability to shc for all inhabitants in the region has been successful .
the authors declare no conflict of interest and financial support came from the northern norway regional health authority .[/INST]objectivesthe sami people constitute the indigenous people in northern norway . the objective of this study was to clarify whether they have a similar supply of somatic specialist health care ( shc ) as others.methodsthe referrals from general practitioners ( gps ) in the primary health care ( phc ) in the administration area of the sami language law ( 8 municipalities ) were matched with a control group of 11 municipalities .
population data was accessed from statistics norway and the time period 20072010 was analysed .
the main outcome was the number of referrals per 1,000 inhabitants according to age group , gender and place of living.results504,292 referrals in northern norway were indentified and the sami and control group constituted 23,093 and 22,541 referrals , respectively .
the major findings were a similar referral ratio ( rr ) ( 1.14 and 1.17 ) ( p = 0.624 ) and women more commonly referred ( female / male ratio 1.45 and 1.41 ) in both groups .
gps in both groups were loyal to their local hospital trust.conclusioninhabitants in sami - speaking municipalities in northern norway have a similar supply of shc services as controls .
inter - municipal variation was significant in both groups .</s> |
the ` merger ' hypothesis , postulating that elliptical galaxies form by spiral galaxy mergers , was first proposed by toomre & toomre ( 1972 ) .
this scenario has gained new impetus over the last few years by both numerical simulations ( e.g. barnes 1992 ; hernquist 1992 ; mihos & hernquist 1996 ) and observational studies , suggesting that the properties of merger remnants are consistent with those of ellipticals ( e.g. toomre 1977 ; schweizer et al .
1990 ; casoli et al .
1991 ; schweizer & seitzer 1992 ; hibbard & van gorkom 1996 ; georgakakis , forbes & norris 2000 ) .
however , one of the long standing drawbacks of the ` merger ' hypothesis is the excess globular clusters ( gcs ) per unit starlight around ellipticals compared to spirals ( van den bergh 1984 ) . to overcome this problem schweizer ( 1987 ) and
ashman & zepf ( 1992 ) suggested that the starburst activity usually experienced during gas - rich mergers will form new gcs and thus increase their number compared to their progenitors .
indeed , there is accumulating observational evidence supporting this scenario in on - going mergers ( e.g. lutz 1991 ; whitmore et al . 1993 ; whitmore & schweizer 1995 ; schweizer 1996 ; miller et al .
1997 ; zepf et al .
1999 ; forbes & hau 2000 ) .
however , the situation in ellitpical galaxies ( the eventual product of mergers ) is less clear .
although many ellipticals have been observed to have bimodal colour distributions , when examined in detail their gc properties do not match those from the merger picture ( forbes et al .
outstanding questions include whether the newly formed gcs survive and whether the final gc system resembles that of typical ( old ) ellipticals .
probing the gc properties in intermediate age merger - remnants ( 15gyrs ) may be of key importance for addressing these issues . indeed
, such young ellipticals may provide the link between on - going mergers and relaxed ellipticals .
for example , a sample of merger remnants spanning a range of ages will allow study of the chronological development of the system s specific frequency ( measuring the number of globular clusters per unit starlight ) in comparison with that of evolved ellipticals .
young ellipticals are also expected to have two distinct gc populations with different colour and magnitude distributions . by exploiting these differences one can attempt to age - date the newly formed gcs , which in turn can be compared to the time since the gaseous merger .
indeed , studies of the dynamically young proto - ellipticals ngc1700 and ngc3610 have shown the presence of bimodality in their colour distributions ( whitmore et al .
1997 ; brown et al . 2000 ) .
also the age of the new gcs , although model dependent , is found to be similar to estimates for the galaxy age based on spectroscopic or dynamical arguments . in this paper
we study the globular cluster system of the elliptical galaxy ngc6702 .
lauer ( 1985 ) found a dust lane in the centre of ngc6702 indicating a recent gaseous merger event .
this galaxy is also relatively luminous at far - infrared wavelengths compared to other elliptical galaxies , with @xmath6 ( wiklind et al .
terlevich & forbes ( 2000 ) have estimated a spectroscopic age and metallicity of about 2gyrs and @xmath7=+0.5}$ ] respectively for ngc6702 suggesting that it is a young elliptical .
the main observational properties of ngc6702 are given in table [ tab_0 ] . additionally , according to the ned database the nearest galaxy projected on the sky that is either brighter or no more than 2 magnitudes fainter , than ngc6702 is ngc6703 at a projected distance of 10arcmin .
however , as ngc6702 has a recession velocity of @xmath8 and ngc6703 has @xmath9 they are actually separated by some 30mpc assuming no peculiar motions .
the nearest galaxy with a similar recession velocity is ngc6711 ( @xmath10 ) with a separation of @xmath11arcmin or over 2mpc .
other galaxies listed by ned are more than 2 magnitudes fainter than ngc6702 .
thus ngc6702 is an example of an isolated elliptical galaxy with no comparable galaxies within 2mpc .
such galaxies are fairly rare and hence their evolutionary history is of some interest . in particular , ellipticals in low density environments are interesting within the hierarchical merger framework as they are expected to have assembled much more recently than their cluster counterparts ( kauffmann & charlot 1998 ) . any merger would be expected to have occurred in the more recent past and involved progenitors that have largely processed gas into stars . in section [ sec_obs ]
the observations , data reduction and the isophotal properties of ngc6702 are presented .
section [ sec_sel ] describes the candidate gc selection , while section [ sec_res ] presents our results which are discussed in section [ sec_disc ] .
finally , section [ sec_conc ] summarises our conclusions . throughout this paper
we adopt @xmath12 . [ cols="^,^,^,^,^,^,^,^,^,^ " , ]
broad - band imaging of ngc6702 in the @xmath0 , @xmath1 and @xmath2 filters was carried out at the keck - ii telescope on 1999 august 17 , using the the low resolution imaging spectrometer ( lris ; oke et al .
the lris instrument , equipped with a tek @xmath13 ccd , is mounted on the cassegrain focus providing a @xmath14 imaging scale and a @xmath15 field of view .
the total exposure time in the @xmath0 , @xmath1 and @xmath2 filters was 3600 , 1800 , and 1200sec respectively , segregated into three separate integrations of 1200 , 600 and 400sec respectively .
the seeing at the time of the observations varied between 0.8 to 1arcsec .
the data were reduced following standard procedures , using iraf tasks .
the reduced images are found to be flat to better than @xmath16 .
the final @xmath1-band image of ngc6702 is shown in figure [ fig_image ] .
photometric calibration was performed using standard stars from landolt ( 1992 ) .
the photometric accuracy , estimated using these standard stars , is @xmath17mag in all three bands .
we adopt a galactic extinction in the ngc6702 direction of @xmath18 , taken from burstein & heiles ( 1984 ) . assuming a standard reddening curve ( savage & mathis 1979 ) , we correct each magnitude for galactic extinction using the values @xmath19 , @xmath20 and @xmath21mag . the @xmath0-band surface brightness profile , @xmath22 , of ngc6702 is plotted in figure [ fig_prof ] .
this has been determined by fitting ellipses to the galaxy intensity profile using the isophote task within stsdas . during the ellipse fitting process
the centre of the galaxy was kept fixed and a @xmath23 clipping algorithm was employed .
also , bright objects as well as the central saturated parts of the galaxy , were masked out .
the position angle ( pa ) and ellipticity ( @xmath24 ) were fitted at each radius , until s / n constraints terminated the fitting process at low surface brightness . for ngc6702 this occurs at an equivalent radius @xmath25 ( @xmath26 , where @xmath27 is the semi - major axis ) . beyond
that radius the position angle and ellipticity were kept constant .
the sky level was determined using the method described by goudfrooij et al .
( 1994 ) .
although the isophotes of elliptical galaxies are well approximated by ellipses , deviations at the few per cent level are common .
such deviations are often quantified by the 4th sine and cosine amplitudes ( s4 and c4 respectively ) of the fourier transform of the galaxy intensity at a given radius .
the standard interpretation of the residual c4 terms is that they indicate either the presence of a weak underlying disk if positive or boxiness if negative .
however , it has been emphasised that both c4 and s4 terms should be considered when estimating the isophotal shape of galaxies ( franx et al .
1989 ; peletier et al . 1990 ; goodfrooij et al .
for example , the presence of a disk , bar or ring with a significant position angle twist relative to the elliptical galaxy semi - major axis is expected to give both positive and negative c4 and/or s4 terms , depending on its orientation .
consequently , in the case of such projection effects we expect s4 terms to be significant .
figure [ fig_prof1 ] plots the ellipticity , position angle as well as c4 and s4 terms as a function of radius for ngc6702 in the @xmath0-band .
similar trends are apparent for the @xmath1 and @xmath2-bands .
the c4 term is negative at small galactocentric distances , indicating boxiness , i.e. excess light at 45@xmath28 relative to the semi - major axis .
this is partly due to the presence of the dust lane in the core of ngc6702 ( lauer 1985 ) lying perpendicular to the semi - major axis and extending out to @xmath29 .
the s4 term is also non - zero within the same range of @xmath30 , albeit with a smaller amplitude .
masking out the dust lane reduces the amplitude of both the c4 and s4 terms .
these terms are also non - zero ( s4 positive and c4 negative ) at @xmath31 indicating boxiness . at larger distances ( @xmath32 )
both the c4 and s4 deviate significantly from the elliptical symmetry , but this is likely to be an artifact arising from the low s / n at these radii . to detect sources superimposed on ngc6702 we subtract the galaxy light profile using a median filter technique .
firstly , the reduced image for each filter is smoothed using a median rectangular filter with a size of 40 pixels .
the smoothed image is then subtracted from the original frame and the resulting image is subsequently used for source extraction and photometry .
the sources in the reduced frames were extracted using the sextractor package ( version 2.1.0 ; bertin & arnouts 1996 ) .
the main input parameters are the detection threshold , given as a multiple of the sky variance ( @xmath33 ) and the minimum area in pixels for an object to be extracted .
after considerable experimentation , we adopted a threshold of 2.5@xmath34 and a minimum area of 1015pixels ( @xmath350.50.7arcsec@xmath36 ) .
this choice of values minimises the number of spurious detections , while ensuring that faint objects are successfully extracted .
a total of 1455 , 1456 and 1494 sources were extracted form the @xmath0 , @xmath1 and @xmath2 frames respectively .
the photometric catalogues generated for each waveband were then matched , resulting in a total of 939 common detections in all three filters , @xmath0 , @xmath1 and @xmath2 .
this source list is referred to as the matched catalogue . using this catalogue we performed photometry using the phot task .
after a curve of growth analysis on several sources an aperture of 8 pixels radius was employed with the background estimated from an annulus of 15 to 20 pixels around each source . for unresolved sources the 8 pixels radius aperture magnitude is close to total .
the completeness limit in a given filter is estimated by adding artificial point sources of different magnitudes to the original image , using mkobjects task .
then we attempt to recover the artificial objects using sextractor package , with the same parameter settings as with those adopted for the real data .
a total of 1500 point sources were added to a given filter frame . to avoid overcrowding the frame ,
artificial sources are added in groups of 150 and the process is repeated 10 times .
the results are presented in figure [ fig_complete ] , plotting the fraction of recovered objects as a function of magnitude in the @xmath0 , @xmath1 and @xmath2 filters respectively .
the @xmath37 completeness limits in the @xmath0 , @xmath1 and @xmath2 filters are found to be @xmath38 , @xmath39 and @xmath40mag respectively
. the mean photometric error at these magnitude limits is @xmath41mag for all three filters .
we have also investigated variations of the completeness limits due to the increased background close to the galaxy centre . a method similar to that described above
was adopted , with artificial point sources being added within successive elliptical rings centred on ngc6702 and having the same mean ellipticity and position angle as the galaxy ( @xmath42 , pa=145@xmath43 ) .
the effect of galaxy background was found to be small except for @xmath44 .
however , this is close to the saturated region of the ccd images which is masked out in our analysis .
therefore , the lower sensitivity close to the galaxy center will not affect the results from this study .
globular cluster candidates are selected from the matched catalogue on the basis of their expected range in colour and magnitude . in particular
, the full range of possible globular cluster metallicities is @xmath45}<+1.0 $ ] . using the colour metallicity relation of couture et al .
( 1990 ) and kissler - patig et al .
( 1998 ) , the above mentioned metallicity interval corresponds to @xmath46 and @xmath47 .
figures [ fig_bv_bi ] and [ fig_bv_vi ] plot the @xmath48 and @xmath49 colours against @xmath50 respectively , for the objects in the matched catalogue .
the horizontal lines in these figures represent the above mentioned @xmath48 and @xmath49 colour cutoffs .
also shown are the regions of the parameter space occupied by the galactic gcs ( harris 1996 ; corrected for galactic reddening ) .
the accepted range of @xmath50 colour for globular cluster selection is chosen to span the @xmath50 colour range of the galactic gcs . additionally , using the population synthesis models of worthey ( 1994 ) we find that the @xmath48 , @xmath49 and @xmath50 colours of a stellar population of a given age get redder with increasing metallicity in the direction indicated by the arrows in figures [ fig_bv_bi ] and [ fig_bv_vi ] .
globular cluster candidates are selected on the basis of their photometric colours if they lie within the regions indicated in figures [ fig_bv_bi ] and [ fig_bv_vi ] , adopting a @xmath51 uncertainty on each colour given by the phot software .
a total of 374 candidate gcs are selected .
these objects are then visually inspected to discard resolved sources , likely to be galaxies , and sources lying near hot pixels .
the final list consists of 205 candidate gcs .
although visual inspection is not an objective method for identifying point sources , we believe that to the first approximation we successfully eliminate background galaxies from the gc catalogue .
this is demonstrated in figure [ fig_svsm ] plotting an estimator of the spatial extent of a source as a function of @xmath2-band magnitude .
the size of a source is estimated by the difference between the @xmath2-band magnitude measured within 3 and 8arcsec radius apertures .
it is clear from figure [ fig_svsm ] that visually classified resolved sources are separated from point - like objects , particularly at bright magnitudes . at fainter magnitudes ( @xmath52mag ) , however , the visual classification scheme becomes more uncertain .
also note that point sources brighter than @xmath53mag are likely to have saturated cores .
additionally , we apply a bright magnitude cutoff set to @xmath3mag brighter than the most luminous milky way gc ( @xmath54-cen ; @xmath55mag ) , shifted to the distance of ngc6702 .
this is because ngc6702 has a young stellar component , with an estimated spectroscopic age of @xmath56gyrs ( terlevich & forbes 2000 ) .
therefore , ngc6702 may possess a number of young metal
rich gcs , expected to be significantly brighter than the old metal poor gcs . for example , the worthey ( 1994 ) models predict a 2.0gyrs old stellar population to be brighter by as much as 1.5mag in the @xmath2-band compared to an old metal poor stellar population ( 15gyrs , @xmath57=-1.5 $ ] ) assumed to be representative of the milky way gcs .
the bright magnitude cutoffs are thus set to @xmath58 , @xmath59 and @xmath60mag .
sources brighter than this are almost certainly stars . in the rest of the paper , unless otherwise stated , we consider gcs brighter than the @xmath37 completeness limit for point sources . therefore , the magnitude range of the candidate gc sample is @xmath61 , @xmath62 and @xmath63mag .
the colour and magnitude selected and visually inspected sample comprises a total of 151 gc candidates .
it should be noted that including gcs brighter than the @xmath64 completeness limit for point sources does not change any of our conclusions .
figure [ fig_cm ] shows the colour - magnitude diagram of all the colour selected and visually inspected gc candidates before applying any magnitude cuts .
objects have a wide range of colours but there is some evidence for two concentrations at @xmath65 and @xmath66mag .
this will be further discussed in section [ sec_res ] .
although we attempt to minimise the fraction of foreground stars and background galaxies in the final gc sample , it is likely that a number of contaminating sources are also selected . the number counts and colour distribution of foreground stars are estimated using the model developed by bahcall & soneira ( 1980 ) . in this model
the galaxy consists of both a disk and a spheroid component from which the distribution of stars in the @xmath0 and @xmath1-bands as well as the @xmath50 colour distribution are calculated .
to predict both the star counts in the @xmath2-band and the @xmath48 and @xmath49 colour distributions we use the empirical tight relation between the @xmath50 and @xmath49 colours for stars ( bessel 1990 ) .
we predict about 120 stars within the field of view in the magnitude range @xmath67 , @xmath68 and @xmath69mag .
however , the colour selection ( assuming a @xmath51 uncertainty of 0.2mags ) eliminates the majority of stars from the final catalogue .
indeed , the model of bahcall & soneira ( 1980 ) , after both magnitude and colour selection , predicts a total of about @xmath70 stars in the final gc sample ( total of 151 sources ) .
therefore , the star contamination is about @xmath71 . to quantify the contamination of the final gc sample by background galaxies we should first estimate the completeness limits for galaxies at different wavebands . since galaxies are resolved sources , their completeness limit is expected to be at brighter magnitudes to that of point sources ( e.g. gcs in ngc6702 ) .
figure [ fig_bcounts ] plots the number counts for all the sources detected in our @xmath0-band frame ( total of 1455 ) .
also shown is the star count prediction from the model of bahcall & soneira ( 1980 ) .
the difference between the total observed source counts and the predicted star counts in a given magnitude bin estimates , to the first approximation , the number of background galaxies detected in our field ( here we ignore the contribution from gcs to the counts ) .
also shown in figure [ fig_bcounts ] are the @xmath0-band galaxy counts from metcalfe et al .
( 1991 , 1995 ) .
it is clear that the predicted galaxy counts in our field are in good agreement with those from metcalfe et al .
( 1991 , 1995 ) to the magnitude @xmath72 and then decline due to incompleteness .
we estimate our @xmath0-band galaxy catalogue to be about @xmath73 and @xmath74 complete at @xmath75 and @xmath76mag respectively .
figures [ fig_vcounts ] and [ fig_icounts ] are similar to figure [ fig_bcounts ] for the @xmath1 and @xmath2-bands respectively . from these figures , we estimate our @xmath1 and @xmath2-band galaxy catalogues to be @xmath73 complete at @xmath77 and @xmath78mag respectively . ignoring gcs
when calculating the number of galaxies within the field of view at @xmath0 , @xmath1 and @xmath2bands , overestimates the galaxy numbers at faint magnitudes .
the above mentioned completeness limits are conservative estimates . to quantify the contamination of the gc sample due to background galaxies we use the multiwavelength ( @xmath79 ) faint galaxy catalogue of lilly , cowie & gardner ( 1991 ) complete to @xmath80 .
the ab system is defined as @xmath81 , where @xmath82 is the flux cgs units .
the transformations from the ab system are : @xmath83 , @xmath84 and @xmath85 ( lilly , cowie & gardner 1991 ) . using this galaxy sample
we predict a total of @xmath86 galaxies with @xmath87 , @xmath88 and @xmath89mag after converting to our magnitude system and scaling to the area of the lris field of view ( @xmath90arcmin@xmath36 ) . taking into account the galaxy incompleteness of our sample , estimated from figures [ fig_bcounts][fig_icounts ] ,
we predict a total of @xmath91 galaxies within the above mentioned magnitude limits .
colour selection , using the aperture colours of lilly , cowie & gardner ( 1991 ) and assuming a @xmath51 uncertainty of 0.2mags , reduces the number of contaminating background galaxies in our candidate gc sample to @xmath92 . however , as demonstrated in figure [ fig_svsm ] , visual inspection is efficient in removing extended sources from the sample especially at bright magnitudes .
indeed , a total of @xmath93 resolved sources with @xmath94 , @xmath95 and @xmath96mag have been identified , leaving about @xmath97 unidentified galaxies within the final gc sample .
this corresponds to a contamination of the gc candidate catalogue ( total of 151 ) by galaxies of @xmath98 .
we stress that this fraction is an upper limit . in particular , we simulated galaxy bulges following @xmath99law profile , with absolute luminosity and effective radius of @xmath100=21.0mag and @xmath101kpc respectively , typical of @xmath102 ellipticals .
we found that only half of them are detected to the limit @xmath103mag and this fraction drops to @xmath104 at @xmath105mag .
moreover , disk - dominated galaxies will be missed by the detection algorithm at even brighter magnitudes .
these surface brightness effects are likely to be significantly less severe in the deep surveys used to determine the galaxy counts at faint magnitudes .
indeed these surveys have effective exposure times as much as 10 times longer than those used here and are therefore , specifically designed to detect sources at faint magnitudes .
since bulges and compact galaxies account for less than @xmath106 of the galaxy population at faint magnitude limits ( elson & santiago 1996 ) , we anticipate the galaxy contamination of our final candidate gc sample to be much less than @xmath107 .
the @xmath48 colour distribution for the final gc sample is plotted in figure [ fig_hist_bi ] .
there is evidence for bimodality with the peaks of the distribution at @xmath108 and @xmath109 . indeed the kmm statistical test ( ashman et al .
1994 ) rejects the single gaussian model at a confidence level better than @xmath110 , giving peaks at @xmath111 and 2.16 respectively .
it should be noted that this result is obtained after clipping objects with @xmath112mag , likely to be background galaxies ( 3 out of 151 ; see figure [ fig_hist_bi1 ] ) .
however , this is not expected to artificially increase the likelihood of the two gaussian fit . in particular ,
ashman et al . ( 1994 ) argue that clipping of the data before applying the kmm test is sometimes desirable to remove background contamination .
also shown in figure [ fig_hist_bi ] is the reddening corrected colour distribution of galactic gcs that comprise old metal poor gcs .
the blue peak of ngc6702 gcs lies close to the milky way gc distribution .
figure [ fig_hist_bi1 ] compares the candidate gc @xmath48 colour distribution with the colours of contaminating stars and galaxies ( after being selected on the basis of their magnitudes and colours ) predicted in the previous section .
it is clear that foreground stars do not significantly modify the observed candidate gc colour distribution .
background galaxies , however , have a larger effect on the observed colour distribution , having colours similar to those of the red gc peak .
nevertheless , the fraction of contaminating galaxies within the sample is expected to be sufficiently small that it will not significantly modify the position of the peaks of the gc colour distribution .
we further investigate this by subtracting the predicted galaxy colour distribution from that of the gc candidates in figure [ fig_hist_bi1 ] .
the kmm statistical test is then applied to the resulting distribution .
a single gaussian model is rejected at a confidence level better than @xmath110 , while the peaks of the bimodal distribution are at @xmath113 and 2.27mag respectively . although both peaks are redder than those recovered using the full candidate gc colour distribution , the difference is sufficiently small that does not alter any of our conclusions .
figure [ fig_hist_vi ] plots the @xmath49 colour histogram of both the ngc6702 gc candidates and the galactic gcs .
there is no strong evidence for bimodality , with the kmm test finding no improvement of the two - group fit over a single gaussian .
this seems surprising since the @xmath48 colour distribution shows clear evidence for bimodality .
it is likely that the absence of bimodality in figure [ fig_hist_vi ] is due to the smaller wavelength baseline of @xmath49 compared to the @xmath48 colour , providing less metallicity leverage .
the expected difference between the peaks in @xmath49 is smaller ( i.e. @xmath114mag ; see next section ) than that in the @xmath48 histogram and therefore random photometric errors can more easily smear out any bimodality .
contamination of the gc candidate sample by stars and galaxies may also affect the significance of the detection of bimodality in the @xmath49 colour distribution .
this is demonstrated in figure [ fig_hist_vi1 ] , plotting the @xmath49 colour distribution of contaminating stars and galaxies ( after being selected on the basis of their magnitudes and colours ) . to constrain the age and metallicity of ngc6702 gc system
we employ a method similar to that developed by whitmore et al .
( 1997 ) that uses the colour - magnitude relation of gcs .
the basic assumptions of the method are discussed in detail by whitmore et al .
( 1997 ) . in brief
, it is assumed that the gcs comprise two distinct sub - populations of different age and metallicity but with the same initial mass functions .
an additional assumption is that both sub - populations have similar numbers of gcs .
the older population is taken to have properties similar to those of the milky way gcs and therefore consists of old ( 15gyrs ) metal poor ( @xmath7=-1.5}$ ] ) gcs .
the younger population is formed at a later stage of the evolution of the galaxy , through either a merger event ( e.g. ashman & zepf 1992 ) or a secondary _ in situ _ star - formation burst ( forbes et al .
the young gcs , assumed to be metal
rich , are initially bluer than the old metal poor ones but become redder after about 12gyrs .
similarly , the newly formed gcs are much brighter than the pre - existing metal poor population but become fainter at later stages as they evolve passively .
therefore , the difference between the colours and magnitudes of the two gc populations can be used to constrain the age of the new gcs . here
we employ the models of worthey ( 1994 ) to predict the colour and magnitude difference of a young gc population relative to an old ( 15gyrs ) metal poor ( @xmath7=-1.5}$ ] ) population .
the predicted colours of this old stellar population are @xmath115 and @xmath116 .
the model predictions for the @xmath48 colour against both @xmath0 and @xmath2 magnitudes are shown in figures [ fig_worthy_b ] and [ fig_worthy_i ] respectively .
for ngc6702 the difference @xmath117 between the colours of the two gc populations is taken as the difference between the peaks of the bimodal @xmath48 distribution in figure [ fig_hist_bi ] .
the blue peak in that figure is assumed to correspond to the old metal
poor population .
this is a reasonable assumption since the blue peak overlaps with the milky way gcs fairly well .
the peak colour difference from the kmm statistical test is @xmath118 , where the error is estimated assuming an uncertainty of 0.07mag in defining the peaks of the bimodal distribution .
the @xmath0 and @xmath2-band magnitude difference , @xmath119 and @xmath120 , between the two gc populations is estimated following the method of whitmore et al .
( 1997 ) by taking the offset between the 10th brightest cluster of the blue and red subpopulations .
the blue and red subpopulations are defined to have colours in the range @xmath121 and @xmath122 respectively .
the uncertainties in @xmath123 and @xmath120 are estimating using the bootstrap resampling technique .
we find @xmath124 and @xmath125 , i.e. the young gcs are brighter than the old ones .
the results are shown in figures [ fig_worthy_b ] and [ fig_worthy_i ] , and suggest that ngc6702 gcs have solar to supersolar metallicity and an age in the range 2 - 5 gyrs .
also we note that despite the errorbars , in both figures the data point lies close to the age of 3gyrs and [ fe / h]=0.5 model prediction .
moreover , although there are uncertainties in the calculation of the age of the newly formed gcs , our estimate is in fair agreement with the galaxy s spectroscopically estimated age and metallicity of @xmath3gyrs and @xmath7\approx0.5}$ ] respectively ( terlevich & forbes 2000 ) . to assess the sensitivity of the age and metallicity estimates to the adopted single stellar population model of worthey
, we repeat our calculations using the models developed by bruzual & charlot ( 1996 ) and vazdekis et al . ( 1996 ) with a salpeter imf .
both models predict an age of about 2gyrs for the recently formed gc population .
the predicted metallicity of @xmath7>0.5}$ ] is higher than that from the worthey model .
despite , the discrepancies , it is clear that all three models used here predict that the blue gcs sub - population is relatively young with a supersolar metallicity . additionally , assuming an age of 3gyrs and [ fe / h]=0.5 for the red gcs , the worthey ( 1994 ) models predict a @xmath49 colour difference between the two gc subpopulations of @xmath114mag .
as discussed in the previous section such a small colour difference is difficult to detect with the present dataset .
we study the surface density profile , @xmath126 , of the ngc6702 gcs using all the sources detected in the @xmath0-band to @xmath127mag ( total of 1237 ) , the @xmath37 completeness limit for point sources .
we use the @xmath0-band detections instead of the colour selected gc sample because the selection criteria ( i.e. completeness limits ) are easier to quantify and do not depend on the gc colours .
the sample is binned into elliptical rings centred on ngc6702 and having the same mean ellipticity and position angle as the galaxy ( @xmath42 , pa=@xmath128 ) .
the counts in each bin are corrected for geometric incompleteness due to foreground saturated stars , bad columns and the limited size of the field of view . additionally , we mask out the central saturated part of ngc6702 for radii @xmath129 .
the correction for magnitude incompleteness to the counts in individual bins was found to be small ( @xmath130 ) and was ignored .
the density profile is plotted in figure [ fig_den_prof](a ) .
the background surface density level , @xmath131 , was determined by combining the counts within the outermost three bins lying at @xmath132 ( corresponding to galactocentric distances @xmath133kpc ) where the density profile reaches a constant level .
we find @xmath134 ( assuming poisson statistics ) or @xmath135 sources over the lris field of view of 31.2arcmin@xmath36 ( after applying geometrical corrections ) .
the total number of objects to @xmath127mag is 1237 and therefore the number of candidate gc is estimated to be 123@xmath13656 ( poisson statistics ) . in section [ sec_sel ]
we found a total of 151 candidate gcs , selected on the basis of their colours and magnitudes in the range @xmath61mag .
this is in fair agreement with the number of candidate gcs estimated here .
figure [ fig_den_prof](b ) shows the candidate gc density profile , estimated by statistically subtracting the constant background surface density level from the density profile of all the sources detected on the @xmath0-band frame to @xmath127mag . assuming a power law density profile of the form @xmath137 for the candidate gcs , we find @xmath138 .
this slope for the gc system of ngc6702 is consistent with that for other galaxies of a similar magnitude ( forbes et al .
1997 ) . also shown in figure [ fig_den_prof](b ) is the @xmath0-band surface brightness profile of ngc6702 .
it is clear that the starlight of ngc6702 drops more steeply than the gc density profile as is often seen in other galaxies ( harris 1991 ; durrell et al .
this is often attributed to further dissipative collapse of the host galaxy after the older gcs had formed and before the halo stars formed ( e.g. harris 1986 ) .
the radial distributions of the red and blue subpopulations of the gc candidates selected on the basis of their colours and magnitudes have also been investigated and have been found to be consistent within the uncertainties .
the globular cluster specific frequency @xmath139 is defined ( harris 1991 ) @xmath140 where @xmath141 is the total number of globular clusters in the galaxy and @xmath142 is the host galaxy absolute @xmath1-band luminosity . to calculate @xmath141
we assume that the @xmath0-band luminosity function of ngc6702 gcs is a gaussian with the same parameters as that of the milky way gcs ( @xmath143mag and @xmath144 ) .
we note that differences in the peak @xmath0-band magnitude of the blue and red gc subpopulation luminosity function are small ( see section [ sec_age ] ) . at the distance of ngc6702 @xmath145
corresponds to @xmath0=27.5mag .
previously , we found that the number of gcs to the limiting magnitude @xmath0=26mag is 123@xmath13656 . therefore integrating over the entire area of the luminosity function
we find @xmath146 .
this implies @xmath147 , assuming @xmath148mag for ngc6702 .
it is an interesting exercise to predict the evolution of @xmath149 with time to investigate whether ngc6702 will resemble normal ellipticals within a few gyrs . for this calculation
we assume that the total number of gcs is conserved and that the change in @xmath149 is due to passive evolution of the host galaxy .
furthermore , we assume that during the most recent major star - formation event , that took place about 2gyrs ago , @xmath104 of the ngc6702 mass ( see section [ sec_disc ] below ) has been converted into metal rich ( [ fe / h]=+0.5 ) stars .
after 10gyrs this new stellar population will fade in the @xmath1-band by @xmath150mag ( worthey 1994 ) , corresponding to @xmath151 .
harris , harris & mclaughlin ( 1998 ) found a mean of @xmath152 for large ellipticals in the virgo , fornax and the ngc5846 group ( excluding cd galaxies ) .
however , exclusion of bright cluster galaxies ( bcgs ) results in a mean @xmath153 , in better agreement , although somewhat larger , with the estimated @xmath5 for ngc6702 after 10gyrs .
however , the estimated @xmath139 evolution is sensitive to the galaxy mass fraction involved in the most recent major star - formation event , which in turn is uncertain and difficult to constraint .
we calculate an upper limit for the ngc6702 @xmath139 after 10gyrs by assuming the extreme scenario where as much as @xmath64 of the galaxy mass has been turned into stars .
we estimate a fading of @xmath154mag ( worthey 1994 ) within 10gyrs , corresponding to an upper limit of @xmath155 .
therefore , we conclude that the ngc6702 @xmath139 , although lower than that of bright cluster ellipticals , it is likely to be similar to that of ` normal ' ( old ) present - day ellipticals ( excluding bcgs ) within the next 10gyrs . the calculations above are also consistent with suggestions that galaxy interactions and mergers although unable to account for large @xmath149 galaxies , may explain the low values of @xmath156 in relatively isolated ellipticals ( elmegreen 1999 ) .
lrr & ngc6702 & ngc1700 + type & e3 & e4 + m@xmath157 ( mag ) & 21.9 & 21.5 + environment & field & group + @xmath158 & 0.21 & 0.38 + spectroscopic & & + age@xmath36 ( gyr ) & 2 & 2.3 + @xmath7}^{2}$ ] & 0.5 & @xmath1590.5 + @xmath160}^{2}$ ] & 0.12 & 0.13 + fundamental plane & & + residual@xmath161 & 0.20 & 0.37 + @xmath162 & @xmath163 & @xmath164 + + + + + a comparison between the properties of ngc6702 and the group proto - elliptical ngc1700 ( brown et al .
2000 ; whitmore et al .
1997 ) , is shown in table 2 .
it is clear that there are quite a few similarities between the two galaxies .
both of them have similar optical luminosities and deviate from the fundamental plane in the sense of having younger ages on average ( forbes , ponman & brown 1998 ) .
this is confirmed by their central spectroscopic ages of @xmath1652gyrs ( terlevich & forbes 2000 ) .
the central stars appear to be of high metallicity ( [ fe / h ] @xmath1650.5 ) with supersolar [ mg / fe ] abundance .
supersolar abundances have been the source of much debate in the literature but probably indicate either a rapid star formation time - scale or an imf skewed towards massive stars . both galaxies have radial velocity to velocity dispersion ratios , @xmath166 , indicating that they are anisotropic rotators .
bender et al .
( 1992 ) have suggested that the last major merger for anisotropic galaxies involved relatively little gas , i.e. the progenitors were largely stellar . in the case of ngc6702 and ngc1700 there
must have been sufficient gas to support the central starburst and associated cluster formation .
the similarities above also suggest a similar formation mechanism for these galaxies .
moreover , our analysis above indicates the presence of two gc populations in ngc6702 with different metallicities and ages .
it is an interesting exercise to estimate the formation efficiency of the young ( red ; @xmath167 ) gc subpopulation , assuming they formed during the most recent star - formation burst , and compare it to that of stars formed in the same burst .
a robust estimator of the gc formation efficiency is the ratio of the total gc mass to the total baryonic galaxy mass . for this calculation
we assume a typical gc mass of @xmath168 ( harris , harris & mclaughlin 1998 ) and a mass to light ratio for ngc6702 @xmath169 , typical to that of ellipticals ( faber & gallagher 1979 ; binney & tremaine 1987 ) . we have identified a total of 88 red gcs ( @xmath170 ) to the limit @xmath171mag , assumed to be the newly formed metal
rich gcs of ngc6702 .
we adopt a gaussian luminosity function for this gc subpopulation with parameters similar to those used in section [ sec_sn ] ( @xmath143mag and @xmath144 ) .
this is a reasonable assumption , since the blue and red gc subpopulations of ngc6702 in section [ sec_age ] have a similar @xmath0-band magnitude distribution within few tenths of a magnitude .
integrating over the entire luminosity function , assuming a completeness limit for our sample @xmath171mag , we estimate a total of 970 red gcs .
thus , the total mass of the red gcs is @xmath172 .
the total baryonic mass in stars of ngc6702 , estimated using its @xmath1-band luminosity and the assumed mass to light ratio , is found to be @xmath173 .
therefore , we estimate that @xmath174 of the ngc6702 mass has been turned into gcs during the most recent star - formation event , which is lower compared to recent estimates for the gc formation efficiency of 0.25% ( harris , harris & mclaughlin 1998 ; mclaughlin 1999 ) .
it should be noted that this calculation assumes that the estimated baryonic mass in stars represents the total mass of the system , i.e. most of initial gas has been used for star - formation .
elmegreen et al .
( 1999 ) , argue that gcs represent about @xmath175 of the total galaxy star - formation .
therefore , for the gc formation efficiency of @xmath174 we expect that @xmath176 of the total ngc6702 mass has turned into field stars ( not in bound clusters ) during the most recent star - formation event .
is our estimate of the mass in new stars ( i.e. 8% of the total ) consistent with the spectral line indices in the central r@xmath177/8 region ( gonzalez et al .
1993 ) ? if we assume that the new stars formed with a metallicity of [ fe / h]=0.5 , and that the old stars ( representing 92% of the central stellar mass ) have solar metallicity and an age of 15gyrs , then the new stars would have to be slightly younger than 1gyr old .
assuming a time since the starburst of @xmath3gyrs and applying that to the new stars , their mass fraction would have to be increased to @xmath178 .
furthermore , if the galaxy reveals evidence for a young stellar population outside of the central region this will also point towards a large mass fraction ( see also trager 1997 ) .
clearly there are large uncertainties involved in the above arguments , but there is some agreement between the mass fraction of young stars estimated independently using spectroscopic line indices and the properties of the ngc6702 gc system .
moreover , it seems clear that a large fraction of new stars formed in ngc6702 a few gyrs ago . in the merger context
, it implies a high gas fraction for the progenitors and hence a highly dissipational event .
this is contrary to the claims of bender et al .
( 1992 ) that anisotropic galaxies ( such as ngc6702 and ngc1700 ) formed by largely _
dissipationless _ mergers .
next , we compare the fraction of galaxy starlight in newly formed dense clusters relative to that of young field stars . to do that we add the luminosities of the red gcs ( total of 88 ; @xmath179 ) and then divide by the luminosity of the _ young _ stellar population of ngc6702 .
we note that estimating the total gc luminosity by extrapolating to the gc luminosity function will not modify our results , since the main contribution to the luminosity is from bright systems .
therefore , adding the red gc luminosities is a simple approximation that is sufficient for the purposes of the present study .
additionally , in our calculation we assume that @xmath104 by mass of the ngc6702 stars are young ( 2gyrs ) and metal rich ( [ fe / h]=0.5 ) , while the remaining @xmath180 of the mass is in old ( 15gyrs ) metal poor ( [ fe / h]=1.5 ) stars . using the mass to light ratios of the above stellar populations predicted by the models of worthey ( 1994 ) we estimate that @xmath181 of the total ngc6702 @xmath0-band light originates in newly formed stars , i.e. @xmath182 .
consequently , we estimate @xmath183 , i.e. @xmath184 of the young star @xmath0-band luminosity originates in bound clusters formed during the most recent star - formation event .
this is much lower than the estimates in recent mergers which have shown that as much as @xmath106 of the blue galaxy light originates from gcs ( zepf et al .
1999 ; meurer 1995 ) . however , the main contribution to the integrated starlight in bound clusters in these systems is from young luminous clusters , the nature of which is under debate .
in particular , it is still unclear whether these objects are proto - globular clusters that will evolve into _ bona - fide _ gcs ( brodie et al .
1998 ) or are luminous open clusters that will be destroyed by dynamical evolution ( van den bergh 1995 ) . indeed ,
in older merger remants , like ngc7252 , the fraction of light in bound clusters is somewhat lower than @xmath106 ( zepf et al .
moreover , van den bergh ( 1994 ) noted that gcs account for about @xmath184 of the total halo luminosity of both the milky way and the lmc , in good agreement with our estimate for ngc6702 .
clearly , the young elliptical galaxy ngc6702 ( and also ngc1700 ) is at an interesting evolutionary stage for further study of its gc system .
direct measurement of individual gc metallicities with 8 - 10 m class telescopes would confirm ( or refute ) the inferred supersolar metallicities for the new gcs and hence their age estimates .
we note that the magnitude differences @xmath119 and @xmath120 in section [ sec_age ] , used to constrain the gc age and metallicity , are hard to define and would benefit from deeper imaging .
deeper imaging studies would also help determine the gc luminosity function ( e.g. gaussian or power law ) to explore possible destruction mechanisms and would allow a detailed study of the radial distribution of the gc subpopulations .
we have carried out @xmath0 , @xmath1 and @xmath2-band photometric observations of the elliptical galaxy ngc6702 to explore its gc system .
the gc candidates are selected on the basis of their colour , magnitude and morphology .
we find strong evidence that the @xmath48 colour distribution of gc candidates is bimodal with the blue peak having a colour similar to that of the old metal poor galactic gcs .
assuming that the blue gc subpopulation is indeed old and metal poor , we estimate that the red gcs have an age of 25gyrs and super - solar metallicity . despite the large uncertainties ,
this is in reasonable agreement with the spectroscopically estimated age and metallcity of about 2gyrs and 0.5 respectively for the galaxy .
thus the red gcs in ngc6702 are consistent with having formed during the most recent starburst , likely to have been triggered by a merger or an accretion event , a few gyrs earlier .
additionally , we find a specific frequency for the ngc6702 gc system of @xmath147 .
we predict that passive evolution of the ngc6702 stellar population formed during the most recent star - formation event will increase the ngc6702 specific frequency to @xmath185 within 10gyrs , in reasonable agreement with the mean for present - day ellipticals , excluding the largest cluster ellipticals . finally , using the ngc6702 gc properties and making reasonable assumptions about the gc formation efficiency , we estimate the mass fraction of newly formed stars during the most recent star - formation event . we find reasonable agreement with
the mass fraction estimated using stellar population synthesis models to interpret the line indices of the underlying galaxy starlight .
we thank soeren larsen and richard brown for useful comments and suggestions .
part of this research was funded by nato collaborative research grant crg 971552 .
the data presented herein were obtained at the w.m .
keck observatory , which is operated as a scientific partnership among the california institute of technology , the university of california and the national aeronautics and space administration .
the observatory was made possible by the generous financial support of the w.m .
keck foundation .
this research has made use of the nasa / ipac extragalactic database ( ned ) , which is operated by the jet propulsion laboratory , caltech , under contract with the national aeronautics and space administration . | we study the globular cluster ( gc ) system of the dust - lane elliptical galaxy ngc6702 , using @xmath0 , @xmath1 and @xmath2-band photometric observations carried out at the keck telescope .
this galaxy has a spectroscopic age of @xmath3gyrs suggesting recent star - formation .
we find strong evidence for a bimodal gc colour distribution , with the blue peak having a colour similar to that of the galactic halo gcs .
assuming that the blue gcs are indeed old and metal poor , we estimate an age of 25gyrs and supersolar metallicity for the red gc subpopulation . despite the large uncertainties ,
this is in reasonable agreement with the spectroscopic galaxy age .
additionally , we estimate a specific frequency of @xmath4 for ngc6702 .
we predict that passive evolution of ngc6702 will further increase its specific frequency to @xmath5 within 10gyrs , in closer agreement to that of typical present - day ellipticals .
we also discuss evidence that the merger / accretion event that took place a few gyrs ago involved a high gas fraction .
globular clusters : general galaxies : individual : ngc 6702 galaxies : star clusters . | <s>[INST]the ` merger ' hypothesis , postulating that elliptical galaxies form by spiral galaxy mergers , was first proposed by toomre & toomre ( 1972 ) .
this scenario has gained new impetus over the last few years by both numerical simulations ( e.g. barnes 1992 ; hernquist 1992 ; mihos & hernquist 1996 ) and observational studies , suggesting that the properties of merger remnants are consistent with those of ellipticals ( e.g. toomre 1977 ; schweizer et al .
1990 ; casoli et al .
1991 ; schweizer & seitzer 1992 ; hibbard & van gorkom 1996 ; georgakakis , forbes & norris 2000 ) .
however , one of the long standing drawbacks of the ` merger ' hypothesis is the excess globular clusters ( gcs ) per unit starlight around ellipticals compared to spirals ( van den bergh 1984 ) . to overcome this problem schweizer ( 1987 ) and
ashman & zepf ( 1992 ) suggested that the starburst activity usually experienced during gas - rich mergers will form new gcs and thus increase their number compared to their progenitors .
indeed , there is accumulating observational evidence supporting this scenario in on - going mergers ( e.g. lutz 1991 ; whitmore et al . 1993 ; whitmore & schweizer 1995 ; schweizer 1996 ; miller et al .
1997 ; zepf et al .
1999 ; forbes & hau 2000 ) .
however , the situation in ellitpical galaxies ( the eventual product of mergers ) is less clear .
although many ellipticals have been observed to have bimodal colour distributions , when examined in detail their gc properties do not match those from the merger picture ( forbes et al .
outstanding questions include whether the newly formed gcs survive and whether the final gc system resembles that of typical ( old ) ellipticals .
probing the gc properties in intermediate age merger - remnants ( 15gyrs ) may be of key importance for addressing these issues . indeed
, such young ellipticals may provide the link between on - going mergers and relaxed ellipticals .
for example , a sample of merger remnants spanning a range of ages will allow study of the chronological development of the system s specific frequency ( measuring the number of globular clusters per unit starlight ) in comparison with that of evolved ellipticals .
young ellipticals are also expected to have two distinct gc populations with different colour and magnitude distributions . by exploiting these differences one can attempt to age - date the newly formed gcs , which in turn can be compared to the time since the gaseous merger .
indeed , studies of the dynamically young proto - ellipticals ngc1700 and ngc3610 have shown the presence of bimodality in their colour distributions ( whitmore et al .
1997 ; brown et al . 2000 ) .
also the age of the new gcs , although model dependent , is found to be similar to estimates for the galaxy age based on spectroscopic or dynamical arguments . in this paper
we study the globular cluster system of the elliptical galaxy ngc6702 .
lauer ( 1985 ) found a dust lane in the centre of ngc6702 indicating a recent gaseous merger event .
this galaxy is also relatively luminous at far - infrared wavelengths compared to other elliptical galaxies , with @xmath6 ( wiklind et al .
terlevich & forbes ( 2000 ) have estimated a spectroscopic age and metallicity of about 2gyrs and @xmath7=+0.5}$ ] respectively for ngc6702 suggesting that it is a young elliptical .
the main observational properties of ngc6702 are given in table [ tab_0 ] . additionally , according to the ned database the nearest galaxy projected on the sky that is either brighter or no more than 2 magnitudes fainter , than ngc6702 is ngc6703 at a projected distance of 10arcmin .
however , as ngc6702 has a recession velocity of @xmath8 and ngc6703 has @xmath9 they are actually separated by some 30mpc assuming no peculiar motions .
the nearest galaxy with a similar recession velocity is ngc6711 ( @xmath10 ) with a separation of @xmath11arcmin or over 2mpc .
other galaxies listed by ned are more than 2 magnitudes fainter than ngc6702 .
thus ngc6702 is an example of an isolated elliptical galaxy with no comparable galaxies within 2mpc .
such galaxies are fairly rare and hence their evolutionary history is of some interest . in particular , ellipticals in low density environments are interesting within the hierarchical merger framework as they are expected to have assembled much more recently than their cluster counterparts ( kauffmann & charlot 1998 ) . any merger would be expected to have occurred in the more recent past and involved progenitors that have largely processed gas into stars . in section [ sec_obs ]
the observations , data reduction and the isophotal properties of ngc6702 are presented .
section [ sec_sel ] describes the candidate gc selection , while section [ sec_res ] presents our results which are discussed in section [ sec_disc ] .
finally , section [ sec_conc ] summarises our conclusions . throughout this paper
we adopt @xmath12 . [ cols="^,^,^,^,^,^,^,^,^,^ " , ]
broad - band imaging of ngc6702 in the @xmath0 , @xmath1 and @xmath2 filters was carried out at the keck - ii telescope on 1999 august 17 , using the the low resolution imaging spectrometer ( lris ; oke et al .
the lris instrument , equipped with a tek @xmath13 ccd , is mounted on the cassegrain focus providing a @xmath14 imaging scale and a @xmath15 field of view .
the total exposure time in the @xmath0 , @xmath1 and @xmath2 filters was 3600 , 1800 , and 1200sec respectively , segregated into three separate integrations of 1200 , 600 and 400sec respectively .
the seeing at the time of the observations varied between 0.8 to 1arcsec .
the data were reduced following standard procedures , using iraf tasks .
the reduced images are found to be flat to better than @xmath16 .
the final @xmath1-band image of ngc6702 is shown in figure [ fig_image ] .
photometric calibration was performed using standard stars from landolt ( 1992 ) .
the photometric accuracy , estimated using these standard stars , is @xmath17mag in all three bands .
we adopt a galactic extinction in the ngc6702 direction of @xmath18 , taken from burstein & heiles ( 1984 ) . assuming a standard reddening curve ( savage & mathis 1979 ) , we correct each magnitude for galactic extinction using the values @xmath19 , @xmath20 and @xmath21mag . the @xmath0-band surface brightness profile , @xmath22 , of ngc6702 is plotted in figure [ fig_prof ] .
this has been determined by fitting ellipses to the galaxy intensity profile using the isophote task within stsdas . during the ellipse fitting process
the centre of the galaxy was kept fixed and a @xmath23 clipping algorithm was employed .
also , bright objects as well as the central saturated parts of the galaxy , were masked out .
the position angle ( pa ) and ellipticity ( @xmath24 ) were fitted at each radius , until s / n constraints terminated the fitting process at low surface brightness . for ngc6702 this occurs at an equivalent radius @xmath25 ( @xmath26 , where @xmath27 is the semi - major axis ) . beyond
that radius the position angle and ellipticity were kept constant .
the sky level was determined using the method described by goudfrooij et al .
( 1994 ) .
although the isophotes of elliptical galaxies are well approximated by ellipses , deviations at the few per cent level are common .
such deviations are often quantified by the 4th sine and cosine amplitudes ( s4 and c4 respectively ) of the fourier transform of the galaxy intensity at a given radius .
the standard interpretation of the residual c4 terms is that they indicate either the presence of a weak underlying disk if positive or boxiness if negative .
however , it has been emphasised that both c4 and s4 terms should be considered when estimating the isophotal shape of galaxies ( franx et al .
1989 ; peletier et al . 1990 ; goodfrooij et al .
for example , the presence of a disk , bar or ring with a significant position angle twist relative to the elliptical galaxy semi - major axis is expected to give both positive and negative c4 and/or s4 terms , depending on its orientation .
consequently , in the case of such projection effects we expect s4 terms to be significant .
figure [ fig_prof1 ] plots the ellipticity , position angle as well as c4 and s4 terms as a function of radius for ngc6702 in the @xmath0-band .
similar trends are apparent for the @xmath1 and @xmath2-bands .
the c4 term is negative at small galactocentric distances , indicating boxiness , i.e. excess light at 45@xmath28 relative to the semi - major axis .
this is partly due to the presence of the dust lane in the core of ngc6702 ( lauer 1985 ) lying perpendicular to the semi - major axis and extending out to @xmath29 .
the s4 term is also non - zero within the same range of @xmath30 , albeit with a smaller amplitude .
masking out the dust lane reduces the amplitude of both the c4 and s4 terms .
these terms are also non - zero ( s4 positive and c4 negative ) at @xmath31 indicating boxiness . at larger distances ( @xmath32 )
both the c4 and s4 deviate significantly from the elliptical symmetry , but this is likely to be an artifact arising from the low s / n at these radii . to detect sources superimposed on ngc6702 we subtract the galaxy light profile using a median filter technique .
firstly , the reduced image for each filter is smoothed using a median rectangular filter with a size of 40 pixels .
the smoothed image is then subtracted from the original frame and the resulting image is subsequently used for source extraction and photometry .
the sources in the reduced frames were extracted using the sextractor package ( version 2.1.0 ; bertin & arnouts 1996 ) .
the main input parameters are the detection threshold , given as a multiple of the sky variance ( @xmath33 ) and the minimum area in pixels for an object to be extracted .
after considerable experimentation , we adopted a threshold of 2.5@xmath34 and a minimum area of 1015pixels ( @xmath350.50.7arcsec@xmath36 ) .
this choice of values minimises the number of spurious detections , while ensuring that faint objects are successfully extracted .
a total of 1455 , 1456 and 1494 sources were extracted form the @xmath0 , @xmath1 and @xmath2 frames respectively .
the photometric catalogues generated for each waveband were then matched , resulting in a total of 939 common detections in all three filters , @xmath0 , @xmath1 and @xmath2 .
this source list is referred to as the matched catalogue . using this catalogue we performed photometry using the phot task .
after a curve of growth analysis on several sources an aperture of 8 pixels radius was employed with the background estimated from an annulus of 15 to 20 pixels around each source . for unresolved sources the 8 pixels radius aperture magnitude is close to total .
the completeness limit in a given filter is estimated by adding artificial point sources of different magnitudes to the original image , using mkobjects task .
then we attempt to recover the artificial objects using sextractor package , with the same parameter settings as with those adopted for the real data .
a total of 1500 point sources were added to a given filter frame . to avoid overcrowding the frame ,
artificial sources are added in groups of 150 and the process is repeated 10 times .
the results are presented in figure [ fig_complete ] , plotting the fraction of recovered objects as a function of magnitude in the @xmath0 , @xmath1 and @xmath2 filters respectively .
the @xmath37 completeness limits in the @xmath0 , @xmath1 and @xmath2 filters are found to be @xmath38 , @xmath39 and @xmath40mag respectively
. the mean photometric error at these magnitude limits is @xmath41mag for all three filters .
we have also investigated variations of the completeness limits due to the increased background close to the galaxy centre . a method similar to that described above
was adopted , with artificial point sources being added within successive elliptical rings centred on ngc6702 and having the same mean ellipticity and position angle as the galaxy ( @xmath42 , pa=145@xmath43 ) .
the effect of galaxy background was found to be small except for @xmath44 .
however , this is close to the saturated region of the ccd images which is masked out in our analysis .
therefore , the lower sensitivity close to the galaxy center will not affect the results from this study .
globular cluster candidates are selected from the matched catalogue on the basis of their expected range in colour and magnitude . in particular
, the full range of possible globular cluster metallicities is @xmath45}<+1.0 $ ] . using the colour metallicity relation of couture et al .
( 1990 ) and kissler - patig et al .
( 1998 ) , the above mentioned metallicity interval corresponds to @xmath46 and @xmath47 .
figures [ fig_bv_bi ] and [ fig_bv_vi ] plot the @xmath48 and @xmath49 colours against @xmath50 respectively , for the objects in the matched catalogue .
the horizontal lines in these figures represent the above mentioned @xmath48 and @xmath49 colour cutoffs .
also shown are the regions of the parameter space occupied by the galactic gcs ( harris 1996 ; corrected for galactic reddening ) .
the accepted range of @xmath50 colour for globular cluster selection is chosen to span the @xmath50 colour range of the galactic gcs . additionally , using the population synthesis models of worthey ( 1994 ) we find that the @xmath48 , @xmath49 and @xmath50 colours of a stellar population of a given age get redder with increasing metallicity in the direction indicated by the arrows in figures [ fig_bv_bi ] and [ fig_bv_vi ] .
globular cluster candidates are selected on the basis of their photometric colours if they lie within the regions indicated in figures [ fig_bv_bi ] and [ fig_bv_vi ] , adopting a @xmath51 uncertainty on each colour given by the phot software .
a total of 374 candidate gcs are selected .
these objects are then visually inspected to discard resolved sources , likely to be galaxies , and sources lying near hot pixels .
the final list consists of 205 candidate gcs .
although visual inspection is not an objective method for identifying point sources , we believe that to the first approximation we successfully eliminate background galaxies from the gc catalogue .
this is demonstrated in figure [ fig_svsm ] plotting an estimator of the spatial extent of a source as a function of @xmath2-band magnitude .
the size of a source is estimated by the difference between the @xmath2-band magnitude measured within 3 and 8arcsec radius apertures .
it is clear from figure [ fig_svsm ] that visually classified resolved sources are separated from point - like objects , particularly at bright magnitudes . at fainter magnitudes ( @xmath52mag ) , however , the visual classification scheme becomes more uncertain .
also note that point sources brighter than @xmath53mag are likely to have saturated cores .
additionally , we apply a bright magnitude cutoff set to @xmath3mag brighter than the most luminous milky way gc ( @xmath54-cen ; @xmath55mag ) , shifted to the distance of ngc6702 .
this is because ngc6702 has a young stellar component , with an estimated spectroscopic age of @xmath56gyrs ( terlevich & forbes 2000 ) .
therefore , ngc6702 may possess a number of young metal
rich gcs , expected to be significantly brighter than the old metal poor gcs . for example , the worthey ( 1994 ) models predict a 2.0gyrs old stellar population to be brighter by as much as 1.5mag in the @xmath2-band compared to an old metal poor stellar population ( 15gyrs , @xmath57=-1.5 $ ] ) assumed to be representative of the milky way gcs .
the bright magnitude cutoffs are thus set to @xmath58 , @xmath59 and @xmath60mag .
sources brighter than this are almost certainly stars . in the rest of the paper , unless otherwise stated , we consider gcs brighter than the @xmath37 completeness limit for point sources . therefore , the magnitude range of the candidate gc sample is @xmath61 , @xmath62 and @xmath63mag .
the colour and magnitude selected and visually inspected sample comprises a total of 151 gc candidates .
it should be noted that including gcs brighter than the @xmath64 completeness limit for point sources does not change any of our conclusions .
figure [ fig_cm ] shows the colour - magnitude diagram of all the colour selected and visually inspected gc candidates before applying any magnitude cuts .
objects have a wide range of colours but there is some evidence for two concentrations at @xmath65 and @xmath66mag .
this will be further discussed in section [ sec_res ] .
although we attempt to minimise the fraction of foreground stars and background galaxies in the final gc sample , it is likely that a number of contaminating sources are also selected . the number counts and colour distribution of foreground stars are estimated using the model developed by bahcall & soneira ( 1980 ) . in this model
the galaxy consists of both a disk and a spheroid component from which the distribution of stars in the @xmath0 and @xmath1-bands as well as the @xmath50 colour distribution are calculated .
to predict both the star counts in the @xmath2-band and the @xmath48 and @xmath49 colour distributions we use the empirical tight relation between the @xmath50 and @xmath49 colours for stars ( bessel 1990 ) .
we predict about 120 stars within the field of view in the magnitude range @xmath67 , @xmath68 and @xmath69mag .
however , the colour selection ( assuming a @xmath51 uncertainty of 0.2mags ) eliminates the majority of stars from the final catalogue .
indeed , the model of bahcall & soneira ( 1980 ) , after both magnitude and colour selection , predicts a total of about @xmath70 stars in the final gc sample ( total of 151 sources ) .
therefore , the star contamination is about @xmath71 . to quantify the contamination of the final gc sample by background galaxies we should first estimate the completeness limits for galaxies at different wavebands . since galaxies are resolved sources , their completeness limit is expected to be at brighter magnitudes to that of point sources ( e.g. gcs in ngc6702 ) .
figure [ fig_bcounts ] plots the number counts for all the sources detected in our @xmath0-band frame ( total of 1455 ) .
also shown is the star count prediction from the model of bahcall & soneira ( 1980 ) .
the difference between the total observed source counts and the predicted star counts in a given magnitude bin estimates , to the first approximation , the number of background galaxies detected in our field ( here we ignore the contribution from gcs to the counts ) .
also shown in figure [ fig_bcounts ] are the @xmath0-band galaxy counts from metcalfe et al .
( 1991 , 1995 ) .
it is clear that the predicted galaxy counts in our field are in good agreement with those from metcalfe et al .
( 1991 , 1995 ) to the magnitude @xmath72 and then decline due to incompleteness .
we estimate our @xmath0-band galaxy catalogue to be about @xmath73 and @xmath74 complete at @xmath75 and @xmath76mag respectively .
figures [ fig_vcounts ] and [ fig_icounts ] are similar to figure [ fig_bcounts ] for the @xmath1 and @xmath2-bands respectively . from these figures , we estimate our @xmath1 and @xmath2-band galaxy catalogues to be @xmath73 complete at @xmath77 and @xmath78mag respectively . ignoring gcs
when calculating the number of galaxies within the field of view at @xmath0 , @xmath1 and @xmath2bands , overestimates the galaxy numbers at faint magnitudes .
the above mentioned completeness limits are conservative estimates . to quantify the contamination of the gc sample due to background galaxies we use the multiwavelength ( @xmath79 ) faint galaxy catalogue of lilly , cowie & gardner ( 1991 ) complete to @xmath80 .
the ab system is defined as @xmath81 , where @xmath82 is the flux cgs units .
the transformations from the ab system are : @xmath83 , @xmath84 and @xmath85 ( lilly , cowie & gardner 1991 ) . using this galaxy sample
we predict a total of @xmath86 galaxies with @xmath87 , @xmath88 and @xmath89mag after converting to our magnitude system and scaling to the area of the lris field of view ( @xmath90arcmin@xmath36 ) . taking into account the galaxy incompleteness of our sample , estimated from figures [ fig_bcounts][fig_icounts ] ,
we predict a total of @xmath91 galaxies within the above mentioned magnitude limits .
colour selection , using the aperture colours of lilly , cowie & gardner ( 1991 ) and assuming a @xmath51 uncertainty of 0.2mags , reduces the number of contaminating background galaxies in our candidate gc sample to @xmath92 . however , as demonstrated in figure [ fig_svsm ] , visual inspection is efficient in removing extended sources from the sample especially at bright magnitudes .
indeed , a total of @xmath93 resolved sources with @xmath94 , @xmath95 and @xmath96mag have been identified , leaving about @xmath97 unidentified galaxies within the final gc sample .
this corresponds to a contamination of the gc candidate catalogue ( total of 151 ) by galaxies of @xmath98 .
we stress that this fraction is an upper limit . in particular , we simulated galaxy bulges following @xmath99law profile , with absolute luminosity and effective radius of @xmath100=21.0mag and @xmath101kpc respectively , typical of @xmath102 ellipticals .
we found that only half of them are detected to the limit @xmath103mag and this fraction drops to @xmath104 at @xmath105mag .
moreover , disk - dominated galaxies will be missed by the detection algorithm at even brighter magnitudes .
these surface brightness effects are likely to be significantly less severe in the deep surveys used to determine the galaxy counts at faint magnitudes .
indeed these surveys have effective exposure times as much as 10 times longer than those used here and are therefore , specifically designed to detect sources at faint magnitudes .
since bulges and compact galaxies account for less than @xmath106 of the galaxy population at faint magnitude limits ( elson & santiago 1996 ) , we anticipate the galaxy contamination of our final candidate gc sample to be much less than @xmath107 .
the @xmath48 colour distribution for the final gc sample is plotted in figure [ fig_hist_bi ] .
there is evidence for bimodality with the peaks of the distribution at @xmath108 and @xmath109 . indeed the kmm statistical test ( ashman et al .
1994 ) rejects the single gaussian model at a confidence level better than @xmath110 , giving peaks at @xmath111 and 2.16 respectively .
it should be noted that this result is obtained after clipping objects with @xmath112mag , likely to be background galaxies ( 3 out of 151 ; see figure [ fig_hist_bi1 ] ) .
however , this is not expected to artificially increase the likelihood of the two gaussian fit . in particular ,
ashman et al . ( 1994 ) argue that clipping of the data before applying the kmm test is sometimes desirable to remove background contamination .
also shown in figure [ fig_hist_bi ] is the reddening corrected colour distribution of galactic gcs that comprise old metal poor gcs .
the blue peak of ngc6702 gcs lies close to the milky way gc distribution .
figure [ fig_hist_bi1 ] compares the candidate gc @xmath48 colour distribution with the colours of contaminating stars and galaxies ( after being selected on the basis of their magnitudes and colours ) predicted in the previous section .
it is clear that foreground stars do not significantly modify the observed candidate gc colour distribution .
background galaxies , however , have a larger effect on the observed colour distribution , having colours similar to those of the red gc peak .
nevertheless , the fraction of contaminating galaxies within the sample is expected to be sufficiently small that it will not significantly modify the position of the peaks of the gc colour distribution .
we further investigate this by subtracting the predicted galaxy colour distribution from that of the gc candidates in figure [ fig_hist_bi1 ] .
the kmm statistical test is then applied to the resulting distribution .
a single gaussian model is rejected at a confidence level better than @xmath110 , while the peaks of the bimodal distribution are at @xmath113 and 2.27mag respectively . although both peaks are redder than those recovered using the full candidate gc colour distribution , the difference is sufficiently small that does not alter any of our conclusions .
figure [ fig_hist_vi ] plots the @xmath49 colour histogram of both the ngc6702 gc candidates and the galactic gcs .
there is no strong evidence for bimodality , with the kmm test finding no improvement of the two - group fit over a single gaussian .
this seems surprising since the @xmath48 colour distribution shows clear evidence for bimodality .
it is likely that the absence of bimodality in figure [ fig_hist_vi ] is due to the smaller wavelength baseline of @xmath49 compared to the @xmath48 colour , providing less metallicity leverage .
the expected difference between the peaks in @xmath49 is smaller ( i.e. @xmath114mag ; see next section ) than that in the @xmath48 histogram and therefore random photometric errors can more easily smear out any bimodality .
contamination of the gc candidate sample by stars and galaxies may also affect the significance of the detection of bimodality in the @xmath49 colour distribution .
this is demonstrated in figure [ fig_hist_vi1 ] , plotting the @xmath49 colour distribution of contaminating stars and galaxies ( after being selected on the basis of their magnitudes and colours ) . to constrain the age and metallicity of ngc6702 gc system
we employ a method similar to that developed by whitmore et al .
( 1997 ) that uses the colour - magnitude relation of gcs .
the basic assumptions of the method are discussed in detail by whitmore et al .
( 1997 ) . in brief
, it is assumed that the gcs comprise two distinct sub - populations of different age and metallicity but with the same initial mass functions .
an additional assumption is that both sub - populations have similar numbers of gcs .
the older population is taken to have properties similar to those of the milky way gcs and therefore consists of old ( 15gyrs ) metal poor ( @xmath7=-1.5}$ ] ) gcs .
the younger population is formed at a later stage of the evolution of the galaxy , through either a merger event ( e.g. ashman & zepf 1992 ) or a secondary _ in situ _ star - formation burst ( forbes et al .
the young gcs , assumed to be metal
rich , are initially bluer than the old metal poor ones but become redder after about 12gyrs .
similarly , the newly formed gcs are much brighter than the pre - existing metal poor population but become fainter at later stages as they evolve passively .
therefore , the difference between the colours and magnitudes of the two gc populations can be used to constrain the age of the new gcs . here
we employ the models of worthey ( 1994 ) to predict the colour and magnitude difference of a young gc population relative to an old ( 15gyrs ) metal poor ( @xmath7=-1.5}$ ] ) population .
the predicted colours of this old stellar population are @xmath115 and @xmath116 .
the model predictions for the @xmath48 colour against both @xmath0 and @xmath2 magnitudes are shown in figures [ fig_worthy_b ] and [ fig_worthy_i ] respectively .
for ngc6702 the difference @xmath117 between the colours of the two gc populations is taken as the difference between the peaks of the bimodal @xmath48 distribution in figure [ fig_hist_bi ] .
the blue peak in that figure is assumed to correspond to the old metal
poor population .
this is a reasonable assumption since the blue peak overlaps with the milky way gcs fairly well .
the peak colour difference from the kmm statistical test is @xmath118 , where the error is estimated assuming an uncertainty of 0.07mag in defining the peaks of the bimodal distribution .
the @xmath0 and @xmath2-band magnitude difference , @xmath119 and @xmath120 , between the two gc populations is estimated following the method of whitmore et al .
( 1997 ) by taking the offset between the 10th brightest cluster of the blue and red subpopulations .
the blue and red subpopulations are defined to have colours in the range @xmath121 and @xmath122 respectively .
the uncertainties in @xmath123 and @xmath120 are estimating using the bootstrap resampling technique .
we find @xmath124 and @xmath125 , i.e. the young gcs are brighter than the old ones .
the results are shown in figures [ fig_worthy_b ] and [ fig_worthy_i ] , and suggest that ngc6702 gcs have solar to supersolar metallicity and an age in the range 2 - 5 gyrs .
also we note that despite the errorbars , in both figures the data point lies close to the age of 3gyrs and [ fe / h]=0.5 model prediction .
moreover , although there are uncertainties in the calculation of the age of the newly formed gcs , our estimate is in fair agreement with the galaxy s spectroscopically estimated age and metallicity of @xmath3gyrs and @xmath7\approx0.5}$ ] respectively ( terlevich & forbes 2000 ) . to assess the sensitivity of the age and metallicity estimates to the adopted single stellar population model of worthey
, we repeat our calculations using the models developed by bruzual & charlot ( 1996 ) and vazdekis et al . ( 1996 ) with a salpeter imf .
both models predict an age of about 2gyrs for the recently formed gc population .
the predicted metallicity of @xmath7>0.5}$ ] is higher than that from the worthey model .
despite , the discrepancies , it is clear that all three models used here predict that the blue gcs sub - population is relatively young with a supersolar metallicity . additionally , assuming an age of 3gyrs and [ fe / h]=0.5 for the red gcs , the worthey ( 1994 ) models predict a @xmath49 colour difference between the two gc subpopulations of @xmath114mag .
as discussed in the previous section such a small colour difference is difficult to detect with the present dataset .
we study the surface density profile , @xmath126 , of the ngc6702 gcs using all the sources detected in the @xmath0-band to @xmath127mag ( total of 1237 ) , the @xmath37 completeness limit for point sources .
we use the @xmath0-band detections instead of the colour selected gc sample because the selection criteria ( i.e. completeness limits ) are easier to quantify and do not depend on the gc colours .
the sample is binned into elliptical rings centred on ngc6702 and having the same mean ellipticity and position angle as the galaxy ( @xmath42 , pa=@xmath128 ) .
the counts in each bin are corrected for geometric incompleteness due to foreground saturated stars , bad columns and the limited size of the field of view . additionally , we mask out the central saturated part of ngc6702 for radii @xmath129 .
the correction for magnitude incompleteness to the counts in individual bins was found to be small ( @xmath130 ) and was ignored .
the density profile is plotted in figure [ fig_den_prof](a ) .
the background surface density level , @xmath131 , was determined by combining the counts within the outermost three bins lying at @xmath132 ( corresponding to galactocentric distances @xmath133kpc ) where the density profile reaches a constant level .
we find @xmath134 ( assuming poisson statistics ) or @xmath135 sources over the lris field of view of 31.2arcmin@xmath36 ( after applying geometrical corrections ) .
the total number of objects to @xmath127mag is 1237 and therefore the number of candidate gc is estimated to be 123@xmath13656 ( poisson statistics ) . in section [ sec_sel ]
we found a total of 151 candidate gcs , selected on the basis of their colours and magnitudes in the range @xmath61mag .
this is in fair agreement with the number of candidate gcs estimated here .
figure [ fig_den_prof](b ) shows the candidate gc density profile , estimated by statistically subtracting the constant background surface density level from the density profile of all the sources detected on the @xmath0-band frame to @xmath127mag . assuming a power law density profile of the form @xmath137 for the candidate gcs , we find @xmath138 .
this slope for the gc system of ngc6702 is consistent with that for other galaxies of a similar magnitude ( forbes et al .
1997 ) . also shown in figure [ fig_den_prof](b ) is the @xmath0-band surface brightness profile of ngc6702 .
it is clear that the starlight of ngc6702 drops more steeply than the gc density profile as is often seen in other galaxies ( harris 1991 ; durrell et al .
this is often attributed to further dissipative collapse of the host galaxy after the older gcs had formed and before the halo stars formed ( e.g. harris 1986 ) .
the radial distributions of the red and blue subpopulations of the gc candidates selected on the basis of their colours and magnitudes have also been investigated and have been found to be consistent within the uncertainties .
the globular cluster specific frequency @xmath139 is defined ( harris 1991 ) @xmath140 where @xmath141 is the total number of globular clusters in the galaxy and @xmath142 is the host galaxy absolute @xmath1-band luminosity . to calculate @xmath141
we assume that the @xmath0-band luminosity function of ngc6702 gcs is a gaussian with the same parameters as that of the milky way gcs ( @xmath143mag and @xmath144 ) .
we note that differences in the peak @xmath0-band magnitude of the blue and red gc subpopulation luminosity function are small ( see section [ sec_age ] ) . at the distance of ngc6702 @xmath145
corresponds to @xmath0=27.5mag .
previously , we found that the number of gcs to the limiting magnitude @xmath0=26mag is 123@xmath13656 . therefore integrating over the entire area of the luminosity function
we find @xmath146 .
this implies @xmath147 , assuming @xmath148mag for ngc6702 .
it is an interesting exercise to predict the evolution of @xmath149 with time to investigate whether ngc6702 will resemble normal ellipticals within a few gyrs . for this calculation
we assume that the total number of gcs is conserved and that the change in @xmath149 is due to passive evolution of the host galaxy .
furthermore , we assume that during the most recent major star - formation event , that took place about 2gyrs ago , @xmath104 of the ngc6702 mass ( see section [ sec_disc ] below ) has been converted into metal rich ( [ fe / h]=+0.5 ) stars .
after 10gyrs this new stellar population will fade in the @xmath1-band by @xmath150mag ( worthey 1994 ) , corresponding to @xmath151 .
harris , harris & mclaughlin ( 1998 ) found a mean of @xmath152 for large ellipticals in the virgo , fornax and the ngc5846 group ( excluding cd galaxies ) .
however , exclusion of bright cluster galaxies ( bcgs ) results in a mean @xmath153 , in better agreement , although somewhat larger , with the estimated @xmath5 for ngc6702 after 10gyrs .
however , the estimated @xmath139 evolution is sensitive to the galaxy mass fraction involved in the most recent major star - formation event , which in turn is uncertain and difficult to constraint .
we calculate an upper limit for the ngc6702 @xmath139 after 10gyrs by assuming the extreme scenario where as much as @xmath64 of the galaxy mass has been turned into stars .
we estimate a fading of @xmath154mag ( worthey 1994 ) within 10gyrs , corresponding to an upper limit of @xmath155 .
therefore , we conclude that the ngc6702 @xmath139 , although lower than that of bright cluster ellipticals , it is likely to be similar to that of ` normal ' ( old ) present - day ellipticals ( excluding bcgs ) within the next 10gyrs . the calculations above are also consistent with suggestions that galaxy interactions and mergers although unable to account for large @xmath149 galaxies , may explain the low values of @xmath156 in relatively isolated ellipticals ( elmegreen 1999 ) .
lrr & ngc6702 & ngc1700 + type & e3 & e4 + m@xmath157 ( mag ) & 21.9 & 21.5 + environment & field & group + @xmath158 & 0.21 & 0.38 + spectroscopic & & + age@xmath36 ( gyr ) & 2 & 2.3 + @xmath7}^{2}$ ] & 0.5 & @xmath1590.5 + @xmath160}^{2}$ ] & 0.12 & 0.13 + fundamental plane & & + residual@xmath161 & 0.20 & 0.37 + @xmath162 & @xmath163 & @xmath164 + + + + + a comparison between the properties of ngc6702 and the group proto - elliptical ngc1700 ( brown et al .
2000 ; whitmore et al .
1997 ) , is shown in table 2 .
it is clear that there are quite a few similarities between the two galaxies .
both of them have similar optical luminosities and deviate from the fundamental plane in the sense of having younger ages on average ( forbes , ponman & brown 1998 ) .
this is confirmed by their central spectroscopic ages of @xmath1652gyrs ( terlevich & forbes 2000 ) .
the central stars appear to be of high metallicity ( [ fe / h ] @xmath1650.5 ) with supersolar [ mg / fe ] abundance .
supersolar abundances have been the source of much debate in the literature but probably indicate either a rapid star formation time - scale or an imf skewed towards massive stars . both galaxies have radial velocity to velocity dispersion ratios , @xmath166 , indicating that they are anisotropic rotators .
bender et al .
( 1992 ) have suggested that the last major merger for anisotropic galaxies involved relatively little gas , i.e. the progenitors were largely stellar . in the case of ngc6702 and ngc1700 there
must have been sufficient gas to support the central starburst and associated cluster formation .
the similarities above also suggest a similar formation mechanism for these galaxies .
moreover , our analysis above indicates the presence of two gc populations in ngc6702 with different metallicities and ages .
it is an interesting exercise to estimate the formation efficiency of the young ( red ; @xmath167 ) gc subpopulation , assuming they formed during the most recent star - formation burst , and compare it to that of stars formed in the same burst .
a robust estimator of the gc formation efficiency is the ratio of the total gc mass to the total baryonic galaxy mass . for this calculation
we assume a typical gc mass of @xmath168 ( harris , harris & mclaughlin 1998 ) and a mass to light ratio for ngc6702 @xmath169 , typical to that of ellipticals ( faber & gallagher 1979 ; binney & tremaine 1987 ) . we have identified a total of 88 red gcs ( @xmath170 ) to the limit @xmath171mag , assumed to be the newly formed metal
rich gcs of ngc6702 .
we adopt a gaussian luminosity function for this gc subpopulation with parameters similar to those used in section [ sec_sn ] ( @xmath143mag and @xmath144 ) .
this is a reasonable assumption , since the blue and red gc subpopulations of ngc6702 in section [ sec_age ] have a similar @xmath0-band magnitude distribution within few tenths of a magnitude .
integrating over the entire luminosity function , assuming a completeness limit for our sample @xmath171mag , we estimate a total of 970 red gcs .
thus , the total mass of the red gcs is @xmath172 .
the total baryonic mass in stars of ngc6702 , estimated using its @xmath1-band luminosity and the assumed mass to light ratio , is found to be @xmath173 .
therefore , we estimate that @xmath174 of the ngc6702 mass has been turned into gcs during the most recent star - formation event , which is lower compared to recent estimates for the gc formation efficiency of 0.25% ( harris , harris & mclaughlin 1998 ; mclaughlin 1999 ) .
it should be noted that this calculation assumes that the estimated baryonic mass in stars represents the total mass of the system , i.e. most of initial gas has been used for star - formation .
elmegreen et al .
( 1999 ) , argue that gcs represent about @xmath175 of the total galaxy star - formation .
therefore , for the gc formation efficiency of @xmath174 we expect that @xmath176 of the total ngc6702 mass has turned into field stars ( not in bound clusters ) during the most recent star - formation event .
is our estimate of the mass in new stars ( i.e. 8% of the total ) consistent with the spectral line indices in the central r@xmath177/8 region ( gonzalez et al .
1993 ) ? if we assume that the new stars formed with a metallicity of [ fe / h]=0.5 , and that the old stars ( representing 92% of the central stellar mass ) have solar metallicity and an age of 15gyrs , then the new stars would have to be slightly younger than 1gyr old .
assuming a time since the starburst of @xmath3gyrs and applying that to the new stars , their mass fraction would have to be increased to @xmath178 .
furthermore , if the galaxy reveals evidence for a young stellar population outside of the central region this will also point towards a large mass fraction ( see also trager 1997 ) .
clearly there are large uncertainties involved in the above arguments , but there is some agreement between the mass fraction of young stars estimated independently using spectroscopic line indices and the properties of the ngc6702 gc system .
moreover , it seems clear that a large fraction of new stars formed in ngc6702 a few gyrs ago . in the merger context
, it implies a high gas fraction for the progenitors and hence a highly dissipational event .
this is contrary to the claims of bender et al .
( 1992 ) that anisotropic galaxies ( such as ngc6702 and ngc1700 ) formed by largely _
dissipationless _ mergers .
next , we compare the fraction of galaxy starlight in newly formed dense clusters relative to that of young field stars . to do that we add the luminosities of the red gcs ( total of 88 ; @xmath179 ) and then divide by the luminosity of the _ young _ stellar population of ngc6702 .
we note that estimating the total gc luminosity by extrapolating to the gc luminosity function will not modify our results , since the main contribution to the luminosity is from bright systems .
therefore , adding the red gc luminosities is a simple approximation that is sufficient for the purposes of the present study .
additionally , in our calculation we assume that @xmath104 by mass of the ngc6702 stars are young ( 2gyrs ) and metal rich ( [ fe / h]=0.5 ) , while the remaining @xmath180 of the mass is in old ( 15gyrs ) metal poor ( [ fe / h]=1.5 ) stars . using the mass to light ratios of the above stellar populations predicted by the models of worthey ( 1994 ) we estimate that @xmath181 of the total ngc6702 @xmath0-band light originates in newly formed stars , i.e. @xmath182 .
consequently , we estimate @xmath183 , i.e. @xmath184 of the young star @xmath0-band luminosity originates in bound clusters formed during the most recent star - formation event .
this is much lower than the estimates in recent mergers which have shown that as much as @xmath106 of the blue galaxy light originates from gcs ( zepf et al .
1999 ; meurer 1995 ) . however , the main contribution to the integrated starlight in bound clusters in these systems is from young luminous clusters , the nature of which is under debate .
in particular , it is still unclear whether these objects are proto - globular clusters that will evolve into _ bona - fide _ gcs ( brodie et al .
1998 ) or are luminous open clusters that will be destroyed by dynamical evolution ( van den bergh 1995 ) . indeed ,
in older merger remants , like ngc7252 , the fraction of light in bound clusters is somewhat lower than @xmath106 ( zepf et al .
moreover , van den bergh ( 1994 ) noted that gcs account for about @xmath184 of the total halo luminosity of both the milky way and the lmc , in good agreement with our estimate for ngc6702 .
clearly , the young elliptical galaxy ngc6702 ( and also ngc1700 ) is at an interesting evolutionary stage for further study of its gc system .
direct measurement of individual gc metallicities with 8 - 10 m class telescopes would confirm ( or refute ) the inferred supersolar metallicities for the new gcs and hence their age estimates .
we note that the magnitude differences @xmath119 and @xmath120 in section [ sec_age ] , used to constrain the gc age and metallicity , are hard to define and would benefit from deeper imaging .
deeper imaging studies would also help determine the gc luminosity function ( e.g. gaussian or power law ) to explore possible destruction mechanisms and would allow a detailed study of the radial distribution of the gc subpopulations .
we have carried out @xmath0 , @xmath1 and @xmath2-band photometric observations of the elliptical galaxy ngc6702 to explore its gc system .
the gc candidates are selected on the basis of their colour , magnitude and morphology .
we find strong evidence that the @xmath48 colour distribution of gc candidates is bimodal with the blue peak having a colour similar to that of the old metal poor galactic gcs .
assuming that the blue gc subpopulation is indeed old and metal poor , we estimate that the red gcs have an age of 25gyrs and super - solar metallicity . despite the large uncertainties ,
this is in reasonable agreement with the spectroscopically estimated age and metallcity of about 2gyrs and 0.5 respectively for the galaxy .
thus the red gcs in ngc6702 are consistent with having formed during the most recent starburst , likely to have been triggered by a merger or an accretion event , a few gyrs earlier .
additionally , we find a specific frequency for the ngc6702 gc system of @xmath147 .
we predict that passive evolution of the ngc6702 stellar population formed during the most recent star - formation event will increase the ngc6702 specific frequency to @xmath185 within 10gyrs , in reasonable agreement with the mean for present - day ellipticals , excluding the largest cluster ellipticals . finally , using the ngc6702 gc properties and making reasonable assumptions about the gc formation efficiency , we estimate the mass fraction of newly formed stars during the most recent star - formation event . we find reasonable agreement with
the mass fraction estimated using stellar population synthesis models to interpret the line indices of the underlying galaxy starlight .
we thank soeren larsen and richard brown for useful comments and suggestions .
part of this research was funded by nato collaborative research grant crg 971552 .
the data presented herein were obtained at the w.m .
keck observatory , which is operated as a scientific partnership among the california institute of technology , the university of california and the national aeronautics and space administration .
the observatory was made possible by the generous financial support of the w.m .
keck foundation .
this research has made use of the nasa / ipac extragalactic database ( ned ) , which is operated by the jet propulsion laboratory , caltech , under contract with the national aeronautics and space administration .[/INST] we study the globular cluster ( gc ) system of the dust - lane elliptical galaxy ngc6702 , using @xmath0 , @xmath1 and @xmath2-band photometric observations carried out at the keck telescope .
this galaxy has a spectroscopic age of @xmath3gyrs suggesting recent star - formation .
we find strong evidence for a bimodal gc colour distribution , with the blue peak having a colour similar to that of the galactic halo gcs .
assuming that the blue gcs are indeed old and metal poor , we estimate an age of 25gyrs and supersolar metallicity for the red gc subpopulation . despite the large uncertainties ,
this is in reasonable agreement with the spectroscopic galaxy age .
additionally , we estimate a specific frequency of @xmath4 for ngc6702 .
we predict that passive evolution of ngc6702 will further increase its specific frequency to @xmath5 within 10gyrs , in closer agreement to that of typical present - day ellipticals .
we also discuss evidence that the merger / accretion event that took place a few gyrs ago involved a high gas fraction .
globular clusters : general galaxies : individual : ngc 6702 galaxies : star clusters . </s> |
gender determination in damaged and mutilated dead bodies or from skeletal remains constitutes the foremost step for identifying in medico - legal examination . matching specific features
detected on the dead bodies with data recorded during the life of an individual is an important aspect in forensics , and can be performed by fingerprint analysis , deoxyribonucleic acid matching , anthropological methods , radiological methods and other techniques which can facilitate age and sex identification .
determination of gender is done through various body parts , the skull , the pelvis , the long bones with an epiphysis and a metaphysis in skeletons , the mastoid process , the foramen magnum and the paranasal sinuses . in explosions , warfare , and other mass disasters like aircraft crashes ,
the skull and other bones are badly disfigured , however it has been reported that maxillary sinuses remain intact .
maxillary sinuses are two spaces , which are filled with air , located in the maxillary bone and can be in various sizes and shapes .
the apex of the sinuses can extend into the zygomatic process and can occupy the zygomatic bone .
the floor formed by the alveolar process , the first , the second and the third molars and the roots of the canines may elevate the sinuses or may perforate their floor . sinus radiography has been used for identification of remains and determination of sex and ancestry . computed tomography ( ct ) scans are excellent imaging modality used to evaluate the signal - nasal cavities .
they provide an accurate assessment of the paranasal sinuses , craniofacial bones , as well as the extent of pneumatization of the sinuses .
sexual dimorphism refers to the systemic difference in the form ( either in shape or size ) between individuals of different sexes in the same species .
based on this background , this study was done to estimate different dimensions of the maxillary sinuses to determine gender of an individual and sexual dimorphism .
a total of 30 patients including 17 male and 13 female , visiting the outpatient department of the mamata general hospital , khammam , andhra pradesh were included as the study subjects .
the dimensions of right and left maxillary sinuses of 30 subjects from plain ct were measured using syngo software .
( syngo.via 3d software ) the following measurements were performed by radiologists :
the right and left side height of the maxillary sinus ( height - maximal craniocaudal diameter ) [ figure 1]the right and left side depth of the maxillary sinus ( depth - anterioposterior diameter ) [ figure 2]the right and left side width of the maxillary sinus ( width - maximal width ) [ figure 3]the height measurement of the maxillary sinus was performed on coronal images , whereas measurements of the depth and width were performed on axial images .
the right and left side height of the maxillary sinus ( height - maximal craniocaudal diameter ) [ figure 1 ] the right and left side depth of the maxillary sinus ( depth - anterioposterior diameter ) [ figure 2 ] the right and left side width of the maxillary sinus ( width - maximal width ) [ figure 3 ] the height measurement of the maxillary sinus was performed on coronal images , whereas measurements of the depth and width were performed on axial images .
axial computed tomography image showing : ( a ) right side height ( maximal craniocaudal diameter ) of maxillary sinus .
( b ) left side height ( maximal craniocaudal diameter ) of maxillary sinus coronal computed tomography image showing : ( c ) right side depth ( anterioposterior diameter ) of maxillary sinus .
( d ) left side depth ( anterioposterior diameter ) of maxillary sinus coronal computed tomography image showing : ( e ) right side width ( maximal width ) of maxillary sinus .
( f ) left side width ( maximal width ) of maxillary sinus as all three - dimensions of the maxillary sinus were measured , the volume of each maxillary sinus was also calculated using the following equation .
after measuring all dimensions statistical analysis was performed by mann - whitney u - test .
percentage of dimorphism = { ( xm /xf ) 1 } 100 xm : mean male maxillary sinus dimension xf : mean female maxillary sinus dimension .
the mean values of the right side maxillary sinus height , length , width , and volume for males is 4 , 3.76 , 2.63 , and 39.93 , respectively , and in case of females it was 3.09 , 3.12 , 2.23 , and 21.53 .
sex determination using height , length , width and volume of the maxillary sinus on the right side showed statistically significant results with p = 0.00001 , 0.00001 , 0.00701 , and 0.00001 [ table 1 and figure 4 ] .
comparison of males and females with respect to height , length , width and volume in right side of maxillary sinus by mann - whitney u - test comparison of males and females with respect to height , length and width in right side of maxillary sinus the mean values of left side maxillary sinus height , length , width and volume for males is 3.93 , 3.73 , 2.53 , and 37.64 , respectively , and in case of females it was 3.07 , 3.12 , 2.20 , and 21.10 .
sex determination using height , length , width , and volume of the maxillary sinus on the left side also showed statistically significant results with p = 0.00001 , 0.00001 , 0.0110 , and 0.00001 [ table 2 and figure 5 ] .
comparison of males and females with respect to height , length , width and volume in left side of maxillary sinus by mann - whitney u - test comparison of males and females with respect to height , length and width in left side of maxillary sinus the sexual dimorphism of maxillary sinus right side height , length , width , and volume showed the percentages of 29.44% , 20.51% , 17.937 , and 85.46% , respectively [ table 3 ] .
percentage of dimorphism of right side the sexual dimorphism of maxillary sinus left side height , length , width , and volume showed the percentages of 28.01% , 19.5512% , 15 , and 78.38% , respectively [ table 4 ] .
a forensic study is very important in the identification of sex especially when the body of the deceased has been destroyed as a result of physical injury due to weapons , fire or strong chemicals .
this becomes more difficult if the bones are compromised by physical insults such as explosive or violence . in that case ,
in addition to the maxillary sinus , sexual dimorphism can also be done using other skeletal structures such as foramen magnum , occipital bone and frontal bone . in a study done about the gender determination from the foramen magnum
anteroposterior diameter and transverse diameter were higher in male skulls than females ( 34.04 vs. 31.72 and 28.63 vs. 26.59 ) . in another study gender determination
they concluded that frontal and occipital bones can be used as important key bones for understanding the calvarial phenotypic description and sexual dimorphism . in the present study , the dimensions and volume of maxillary sinuses of right and left side were notably larger in males compared with females .
they showed statistically significant values with a higher percentage of sexual dimorphism in the case of volume with 85.46% for the right side and 78.38% for the left side .
kawarai et al . in 1999 did a study on volume quantification of healthy paranasal cavities by three dimensional ct imaging in 20 japanese subjects and confirmed that paranasal sinuses were individually and on the whole , apparently larger in case of males than females .
fernandes and sahlstrand - johnson et al . stated that the mean value of the maxillary sinus volume was significantly larger in males than in females .
in addition to this , fernandes , found that the european crania had significantly larger maxillary sinus volume than zulu crania . in case of egyptians
cephalocaudal and size of the left maxillary sinuses are a useful feature in gender determination .
teke et al . in 2007 studied width , length and the height of the maxillary sinus in 127 adult patients by ct and observed that the measurements of the maxillary sinuses of males are larger than those of females .
accordingly uthman et al . , maxillary sinus height was the best discriminate parameter that could be used to study sexual dimorphism with overall accuracy of 71.6% .
study concluded that maxillary sinus dimension measurements , especially the right height , are valuable in studying the sexual dimorphism with overall accuracy 69.9% .
the height , length , width and volume of maxillary sinuses on each side were determined .
the results showed the measurements and volume of maxillary sinus of males were slightly more compared with females .
the result of the present study showed that the maxillary sinus exhibits anatomic variability between the genders .
maxillary sinus dimensions , especially the right side volume are valuable in studying sexual dimorphism and the ct images could provide adequate measurements for maxillary sinus . | background : individual identification is a subtle concept and often one of the most important priorities in mass disasters , road accidents , air crashes , fires , and even in the investigation of criminal cases . matching specific features detected on the cadaver with data recorded during the life of an individual is an important aspect in forensics , and can be performed by fingerprint analysis , deoxyribonucleic acid matching , anthropological methods , radiological methods and other techniques which can facilitate age and sex identification .
sinus radiography is one such method that has been used for determination of the sex of an individual .
hence , an attempt is being made to use the different dimensions of the maxillary sinus in the determination of sex using coronal and axial sections of plain computed tomography ( ct ) scan.materials and methods : a total of 30 patients including 17 male and 13 female , visiting the outpatient department of the mamata general hospital were included as the study subjects .
the dimensions of right and left maxillary sinuses of 30 subjects from plain ct were measured using syngo software and statistical analysis was done.results:sex determination using height , length , width , and volume of the maxillary sinus on both sides showed statistically significant results with a higher percentage of sexual dimorphism in the case of volume.conclusion:volume of the right maxillary sinus can be used as accurate diagnostic parameter for sex determination . | <s>[INST]gender determination in damaged and mutilated dead bodies or from skeletal remains constitutes the foremost step for identifying in medico - legal examination . matching specific features
detected on the dead bodies with data recorded during the life of an individual is an important aspect in forensics , and can be performed by fingerprint analysis , deoxyribonucleic acid matching , anthropological methods , radiological methods and other techniques which can facilitate age and sex identification .
determination of gender is done through various body parts , the skull , the pelvis , the long bones with an epiphysis and a metaphysis in skeletons , the mastoid process , the foramen magnum and the paranasal sinuses . in explosions , warfare , and other mass disasters like aircraft crashes ,
the skull and other bones are badly disfigured , however it has been reported that maxillary sinuses remain intact .
maxillary sinuses are two spaces , which are filled with air , located in the maxillary bone and can be in various sizes and shapes .
the apex of the sinuses can extend into the zygomatic process and can occupy the zygomatic bone .
the floor formed by the alveolar process , the first , the second and the third molars and the roots of the canines may elevate the sinuses or may perforate their floor . sinus radiography has been used for identification of remains and determination of sex and ancestry . computed tomography ( ct ) scans are excellent imaging modality used to evaluate the signal - nasal cavities .
they provide an accurate assessment of the paranasal sinuses , craniofacial bones , as well as the extent of pneumatization of the sinuses .
sexual dimorphism refers to the systemic difference in the form ( either in shape or size ) between individuals of different sexes in the same species .
based on this background , this study was done to estimate different dimensions of the maxillary sinuses to determine gender of an individual and sexual dimorphism .
a total of 30 patients including 17 male and 13 female , visiting the outpatient department of the mamata general hospital , khammam , andhra pradesh were included as the study subjects .
the dimensions of right and left maxillary sinuses of 30 subjects from plain ct were measured using syngo software .
( syngo.via 3d software ) the following measurements were performed by radiologists :
the right and left side height of the maxillary sinus ( height - maximal craniocaudal diameter ) [ figure 1]the right and left side depth of the maxillary sinus ( depth - anterioposterior diameter ) [ figure 2]the right and left side width of the maxillary sinus ( width - maximal width ) [ figure 3]the height measurement of the maxillary sinus was performed on coronal images , whereas measurements of the depth and width were performed on axial images .
the right and left side height of the maxillary sinus ( height - maximal craniocaudal diameter ) [ figure 1 ] the right and left side depth of the maxillary sinus ( depth - anterioposterior diameter ) [ figure 2 ] the right and left side width of the maxillary sinus ( width - maximal width ) [ figure 3 ] the height measurement of the maxillary sinus was performed on coronal images , whereas measurements of the depth and width were performed on axial images .
axial computed tomography image showing : ( a ) right side height ( maximal craniocaudal diameter ) of maxillary sinus .
( b ) left side height ( maximal craniocaudal diameter ) of maxillary sinus coronal computed tomography image showing : ( c ) right side depth ( anterioposterior diameter ) of maxillary sinus .
( d ) left side depth ( anterioposterior diameter ) of maxillary sinus coronal computed tomography image showing : ( e ) right side width ( maximal width ) of maxillary sinus .
( f ) left side width ( maximal width ) of maxillary sinus as all three - dimensions of the maxillary sinus were measured , the volume of each maxillary sinus was also calculated using the following equation .
after measuring all dimensions statistical analysis was performed by mann - whitney u - test .
percentage of dimorphism = { ( xm /xf ) 1 } 100 xm : mean male maxillary sinus dimension xf : mean female maxillary sinus dimension .
the mean values of the right side maxillary sinus height , length , width , and volume for males is 4 , 3.76 , 2.63 , and 39.93 , respectively , and in case of females it was 3.09 , 3.12 , 2.23 , and 21.53 .
sex determination using height , length , width and volume of the maxillary sinus on the right side showed statistically significant results with p = 0.00001 , 0.00001 , 0.00701 , and 0.00001 [ table 1 and figure 4 ] .
comparison of males and females with respect to height , length , width and volume in right side of maxillary sinus by mann - whitney u - test comparison of males and females with respect to height , length and width in right side of maxillary sinus the mean values of left side maxillary sinus height , length , width and volume for males is 3.93 , 3.73 , 2.53 , and 37.64 , respectively , and in case of females it was 3.07 , 3.12 , 2.20 , and 21.10 .
sex determination using height , length , width , and volume of the maxillary sinus on the left side also showed statistically significant results with p = 0.00001 , 0.00001 , 0.0110 , and 0.00001 [ table 2 and figure 5 ] .
comparison of males and females with respect to height , length , width and volume in left side of maxillary sinus by mann - whitney u - test comparison of males and females with respect to height , length and width in left side of maxillary sinus the sexual dimorphism of maxillary sinus right side height , length , width , and volume showed the percentages of 29.44% , 20.51% , 17.937 , and 85.46% , respectively [ table 3 ] .
percentage of dimorphism of right side the sexual dimorphism of maxillary sinus left side height , length , width , and volume showed the percentages of 28.01% , 19.5512% , 15 , and 78.38% , respectively [ table 4 ] .
a forensic study is very important in the identification of sex especially when the body of the deceased has been destroyed as a result of physical injury due to weapons , fire or strong chemicals .
this becomes more difficult if the bones are compromised by physical insults such as explosive or violence . in that case ,
in addition to the maxillary sinus , sexual dimorphism can also be done using other skeletal structures such as foramen magnum , occipital bone and frontal bone . in a study done about the gender determination from the foramen magnum
anteroposterior diameter and transverse diameter were higher in male skulls than females ( 34.04 vs. 31.72 and 28.63 vs. 26.59 ) . in another study gender determination
they concluded that frontal and occipital bones can be used as important key bones for understanding the calvarial phenotypic description and sexual dimorphism . in the present study , the dimensions and volume of maxillary sinuses of right and left side were notably larger in males compared with females .
they showed statistically significant values with a higher percentage of sexual dimorphism in the case of volume with 85.46% for the right side and 78.38% for the left side .
kawarai et al . in 1999 did a study on volume quantification of healthy paranasal cavities by three dimensional ct imaging in 20 japanese subjects and confirmed that paranasal sinuses were individually and on the whole , apparently larger in case of males than females .
fernandes and sahlstrand - johnson et al . stated that the mean value of the maxillary sinus volume was significantly larger in males than in females .
in addition to this , fernandes , found that the european crania had significantly larger maxillary sinus volume than zulu crania . in case of egyptians
cephalocaudal and size of the left maxillary sinuses are a useful feature in gender determination .
teke et al . in 2007 studied width , length and the height of the maxillary sinus in 127 adult patients by ct and observed that the measurements of the maxillary sinuses of males are larger than those of females .
accordingly uthman et al . , maxillary sinus height was the best discriminate parameter that could be used to study sexual dimorphism with overall accuracy of 71.6% .
study concluded that maxillary sinus dimension measurements , especially the right height , are valuable in studying the sexual dimorphism with overall accuracy 69.9% .
the height , length , width and volume of maxillary sinuses on each side were determined .
the results showed the measurements and volume of maxillary sinus of males were slightly more compared with females .
the result of the present study showed that the maxillary sinus exhibits anatomic variability between the genders .
maxillary sinus dimensions , especially the right side volume are valuable in studying sexual dimorphism and the ct images could provide adequate measurements for maxillary sinus .[/INST]background : individual identification is a subtle concept and often one of the most important priorities in mass disasters , road accidents , air crashes , fires , and even in the investigation of criminal cases . matching specific features detected on the cadaver with data recorded during the life of an individual is an important aspect in forensics , and can be performed by fingerprint analysis , deoxyribonucleic acid matching , anthropological methods , radiological methods and other techniques which can facilitate age and sex identification .
sinus radiography is one such method that has been used for determination of the sex of an individual .
hence , an attempt is being made to use the different dimensions of the maxillary sinus in the determination of sex using coronal and axial sections of plain computed tomography ( ct ) scan.materials and methods : a total of 30 patients including 17 male and 13 female , visiting the outpatient department of the mamata general hospital were included as the study subjects .
the dimensions of right and left maxillary sinuses of 30 subjects from plain ct were measured using syngo software and statistical analysis was done.results:sex determination using height , length , width , and volume of the maxillary sinus on both sides showed statistically significant results with a higher percentage of sexual dimorphism in the case of volume.conclusion:volume of the right maxillary sinus can be used as accurate diagnostic parameter for sex determination .</s> |
trinification @xcite refers to unified theories based on the gauge group @xmath1 , with gauge coupling equality imposed at a high scale , typically by a discrete symmetry that cyclically permutes the gauge group labels @xmath2 , @xmath3 , and @xmath4 .
the higgs fields responsible for breaking @xmath5 to the standard model gauge group appear in the @xmath6-dimensional representation , @xmath7 the component fields @xmath8 transform as @xmath9 , @xmath10 s under the pair of gauge groups @xmath11 , @xmath12 , and @xmath13 , respectively . the theory thus specified has a simple moose representation , shown in fig . [ fig1 ] , with the component fields @xmath8 serving as the ` links ' that connect neighboring gauge group ` sites ' .
this structure is reminiscent of a deconstructed higher - dimensional theory @xcite , aside from the fact that the link fields in eq .
( [ eq : higgs27 ] ) do not have the same purpose as in deconstruction , namely , to break chains of replicated gauge groups down to their diagonal subgroup .
nevertheless , the structure of fig . [ fig2 ] suggests a natural generalization to trinified theories in which the group factors @xmath2 , @xmath3 , and @xmath4 are replicated @xmath14 times .
we discuss this generalization in section [ sec : generalized ] .
these theories also have a simple moose representation , and a gauge spectrum that can be interpreted via deconstruction .
in particular , we will see that the gauge sector of the theory is a four - dimensional analog of the 5d trinified theory of ref .
@xcite , in which gauge symmetry breaking effects are localized entirely on a boundary .
such 5d theories have interesting properties @xcite , such as the logarithmic running of the gauge coupling difference @xmath15 , for @xmath16 , and a delay in the scale of unification above @xmath17 gev , the value obtained in the minimal supersymmetric standard model ( mssm ) .
the construction of purely four - dimensional theories with such properties is clearly worthy of pursuit , and has lead to interesting results in the case of su(5 ) @xcite and so(10 ) @xcite unification .
the present work complements this body of literature by introducing a new class of 4d unified theories that are closely related to the deconstruction of 5d trinified guts .
that said , it will not be the purpose of this paper to present a literal deconstruction of the theories discussed in ref .
rather , we proceed from a mostly 4d perspective and develop models that are viable and economical .
for example , in determining the embedding of matter fields in the theory , we do nt follow the prescription of deconstruction at all , so that our 4d theory as a whole can not be mapped to a local 5d theory in the continuum limit .
the higher - dimensional flavor of gauge unification is nonetheless retained leading to a new and interesting class of 4d unified theories .
our paper is organized as follows . in section [ sec : generalized ] , we review conventional trinification and define a generalization to @xmath0 replicated su(3 ) groups . in section [ sec : spectrum ] , we study the gauge boson spectrum of the model , for arbitrary values of the localized symmetry - breaking vacuum expectation values ( vevs ) . in section [ sec : unification ] , we apply these results to study gauge coupling unification in this class of models . in section [ sec : matter ] , we describe how one may successfully include matter and light higgs fields , so the low - energy particle content is the same as in the mssm . in section [ sec : conc ] , we summarize our results and suggest directions for future study .
3.3 in conventional trinified theories @xcite are based on the gauge group @xmath18 , where @xmath19 indicates a semidirect product .
the @xmath20 symmetry cyclically permutes the gauge group labels @xmath2 , @xmath3 and @xmath4 , ensuring a single unified coupling at the gut scale .
the breaking of @xmath5 to the standard model gauge group requires a higgs field in the @xmath21-dimensional representation , @xmath22 where the numbers shown represent the su(3)@xmath23 , su(3)@xmath24 and su(3)@xmath25 representations , respectively .
at least one such field must develop the vacuum expectation value , @xmath26 the presence of vevs only in the third row assures that su(2)@xmath24 remains unbroken , while nonvanishing @xmath27 and @xmath28 entries leave a single unbroken u(1 ) factor , generated by a linear combination of the diagonal generators of su(3)@xmath24 and su(3)@xmath25 . identifying this with hypercharge @xmath29 , one finds , @xmath30 note that su(3)@xmath31su(3)@xmath25 symmetry allows one to rotate away the vev @xmath32 in eq .
( [ eq : thevevs ] ) .
therefore , it is usually assumed that at least two @xmath6 higgs fields with vacuum expectation values in the desired entries are present in the theory .
we will return to this issue in sec .
[ sec : matter ] .
one can verify that this construction yields the standard gut - scale prediction for the weak mixing angle @xmath33 .
let us focus on the structure of the gauge and unified - symmetry - breaking sectors of the theory .
a conventional trinified theory can be represented by the moose diagram shown in fig .
[ fig1 ] . for the sake of simplicity we display only a single higgs @xmath6 .
the moose representation makes it clear that the @xmath6 is anomaly - free , which is relevant for the higgs representations since we assume supersymmetry .
the @xmath20 symmetry is encoded in the symmetry of the moose under rotations by @xmath34 . 3.3 in
now consider the generalization of this moose to @xmath0 gauge groups , as shown in fig .
each link field transforms as a @xmath35 under consecutive su(3 ) groups , reading around the moose diagram clockwise .
we assume that a generic link has vev @xmath36 where @xmath37 or @xmath4 .
this breaks a chain of su(3 ) factors , namely su(3)@xmath38 for @xmath39 , down to its diagonal subgroup .
the diagonal subgroups are precisely su(3)@xmath40su(3)@xmath31su(3)@xmath25 of conventional ( @xmath41 ) trinified theories .
the three links which are not generic are identified with the links of the @xmath41 theory and have the corresponding expectation values . in particular , the links @xmath42 and @xmath43 have no vevs and serve to truncate a linear moose that contains unbroken su(3)@xmath23 .
if the link @xmath44 also had no vev , we could make an analogous statement for su(3)@xmath24 and su(3)@xmath25 ; we assume , however , that this link has precisely the expectation value necessary to break su(3)@xmath45su(3)@xmath25 down to the electroweak gauge group of the standard model .
thus , the total effect of the link vevs is to break @xmath46 below the scales @xmath47 , @xmath48 and @xmath32 . at this point , we have said nothing about the values of the @xmath0 gauge couplings . to maintain gauge unification ,
we assume that the theory defined by fig .
[ fig2 ] is restricted by a @xmath20 symmetry that sets equal three sets of @xmath14 gauge couplings each , @xmath49 thus , we see that the moose in fig .
[ fig2 ] is also symmetric under rotations by @xmath34 , like the @xmath41 theory .
unification is maintained as in the @xmath41 theory since the couplings of the diagonal subgroups are given by @xmath50 for @xmath37 or @xmath4 .
note that the vev of the @xmath51 link breaks both su(3)@xmath52 and the cyclic symmetry of the moose .
it is important to note that we are agnostic as to whether the @xmath20 symmetry is a symmetry of the full theory , including the fermion representations , or is only an accidental symmetry of the gauge sector .
the latter could be the case if , for example , all of the gauge couplings are equal at a high scale due to the dynamics of a more complete , high - energy theory .
we will remain open to both possibilities in our subsequent model building . in the theory we have described thus far ,
the special links between @xmath53-@xmath54 , @xmath55-@xmath56 and @xmath57-@xmath58 contribute to the low - energy particle content of the theory . on the other hand
, we wish only to have two light higgs doublets together with the matter content of the mssm .
how we may arrange for this is discussed in sec .
[ sec : matter ] .
we first , however , address the less model - dependent issue of gauge unification , assuming that the low - energy matter and higgs content is that of the mssm .
let us begin by discussing the spectrum of the @xmath59 gauge multiplets , for @xmath60 .
this portion of the theory is a linear moose with @xmath14 unbroken su(3 ) factors .
the contribution to the gauge boson mass matrix from a link spanning the @xmath61 and @xmath62 site is given by @xmath63,\ ] ] ( with @xmath64 ) leading to the @xmath65 mass squared matrix @xmath66 here we take all su(3 ) gauge couplings to be equal , and adopt this simplifying assumption henceforth .
the mass spectrum given by eq .
( [ eq : cspec ] ) is that of a deconstructed 5d su(3 ) gauge theory , and is well known @xcite , @xmath67 where @xmath68 is the lattice spacing .
the @xmath3 and @xmath4 sectors of the moose are more interesting due to the presence of the nontrivial vev at the @xmath53-@xmath54 link .
let us define the @xmath69 gauge field as the @xmath70-component column vector @xmath71 \,\,\ , , \,\,\,\,\ ,
j = n+1-i \,\,\ , , \,\,\,\,\ , i=1\ldots n\ , .
\label{eq : basis}\ ] ] if one were to excise the @xmath72 sector of the circular moose in fig .
[ fig2 ] , and to bend it about the special link at @xmath53-@xmath54 , one would obtain a linear moose with @xmath14 sites , corresponding to gauge fields @xmath73 in eq .
( [ eq : basis ] ) .
the symmetry breaking effects of the special link are confined to the @xmath74 lattice site .
thus , we will be able to interpret our result as a deconstructed 5d theory with bulk su(3)@xmath31su(3)@xmath25 gauge symmetry broken at a boundary .
since the @xmath3-@xmath3 and @xmath4-@xmath4 link fields give identical contributions to the su(3)@xmath24 and su(3)@xmath25 gauge boson mass matrices , respectively , we may express the mass matrix for the @xmath73 as @xmath75 where each entry represents a @xmath76 matrix in @xmath72 space . only the boundary contribution @xmath77 has a nontrivial structure in this space all others are proportional to an implicit identity matrix .
the form of @xmath77 is precisely that of the @xmath72 gauge boson mass squared matrix in a conventional , @xmath41 trinified theory .
let @xmath78 be the @xmath70-dimensional unitary matrix which diagonalizes @xmath77 : @xmath79 then the @xmath80 entry of eq .
( [ eq : lrspec ] ) may be diagonalized without affecting any of the others by letting @xmath81 , where @xmath82 is the unitary matrix @xmath83 since each @xmath70-dimensional sub - block is now - diagonalized , we end up with @xmath70 decoupled mass matrices , corresponding to the eigenvalues @xmath84 of @xmath77 : @xmath85 four of the eigenvalues of @xmath77 are zero , corresponding to the unbroken su(2)@xmath86u(1)@xmath87 gauge bosons , while the remaining @xmath88 are superheavy . for the massless states ( @xmath89 ) , eq .
( [ eq : simplerm ] ) reduces to eq .
( [ eq : cspec ] ) , as one would expect , and the mass spectrum is given by eq .
( [ eq : mspecsm ] ) .
the massive gauge fields are more interesting . in this case , @xmath90 is nonvanishing and is of the order @xmath91 .
we can find the mass spectrum in the @xmath92 case by exploiting a mechanical analogy .
consider the system of masses @xmath93 and springs shown in fig .
[ fig3]a .
5 in the equation of motion for the @xmath69 block is given by @xmath94 where @xmath95 has precisely the form of eq .
( [ eq : simplerm ] ) , with the identifications @xmath96 and @xmath97 . the squared frequencies of the normal modes of this mechanical system are precisely the eigenvalues of @xmath95 .
notice that as @xmath98 is made large ( _ i.e. _ the massive gauge bosons of the last site in the moose are decoupled ) , the @xmath74 block in our spring system effectively becomes a fixed wall .
we then obtain an @xmath99 mass matrix of the same form as eq .
( [ eq : simplerm ] ) with @xmath100 .
this is exactly what we expect for the massive gauge modes when the @xmath74 site has a smaller gauge symmetry than the other sites in the moose ( see for example , ref .
@xcite . ) the eigenvalues of @xmath95 may be found by considering the translationally invariant system shown in fig .
[ fig3]b , and imposing boundary conditions that mimic the dynamics of the first and @xmath74 block of the system of interest .
let @xmath101 represent the displacement of the @xmath69 block about its equilibrium position , where @xmath102 is the inter - block spacing .
the fact that the first block has no spring to the left is equivalent to the boundary condition @xmath103 in the translationally invariant system . on the other hand ,
the effect of the spring with larger spring constant @xmath98 to the right of the @xmath74 block is replicated by the condition @xmath104 ) = -(\eta - 1 ) \ , \psi(an ) \,\,\ , .
\label{eq : bcright}\ ] ] in other words , in the infinite system , one requires that the @xmath105 block moves so that the force on the @xmath74 block is indistinguishable from that of a stiffer spring connected to a wall .
we may thus consider a normal mode solution to the infinite system of the form @xmath106 and determine the wave numbers @xmath107 allowed by these boundary conditions .
we find that @xmath108 values of @xmath107 are determined by the transcendental equation @xmath109 leading to the eigenvalues @xmath110 here , @xmath111 represents the squared frequencies of the normal mode solutions in the mechanical system , and @xmath108 gauge boson squared masses in the problem of interest .
the @xmath74 gauge boson mass , however , is not given by eqs .
( [ eq : telight ] ) and ( [ eq : mslight ] ) .
the reason is that we have assumed that @xmath107 is real ; complex @xmath107 is perfectly consistent with the translation invariance of the infinite system ( see , for example , ref .
taking @xmath112 , one finds another solution : @xmath113 with @xmath114 it is not hard to verify that eqs ( [ eq : telight ] ) , ( [ eq : mslight ] ) , ( [ eq : teheavy ] ) and ( [ eq : msheavy ] ) are correct .
for example , a two - by - two matrix with @xmath115 and @xmath116 , has eigenvalues @xmath117 .
the corresponding solutions to eqs .
( [ eq : telight ] ) and ( [ eq : teheavy ] ) are @xmath118 and @xmath119 , which yield precisely the same results via eqs .
( [ eq : mslight ] ) and ( [ eq : msheavy ] ) . the parameter @xmath90 allows us to interpolate between a number of familiar limits .
for example , the choice @xmath120 yields the mass matrix for a gauge boson distributed among @xmath14 sites that receives no mass contribution from the @xmath105 link field .
this is the case , for example , for the massive @xmath121 and @xmath29 bosons in an su(5 ) moose with @xmath122 sites , in which the gauge symmetry of the last site is taken to be su(3)@xmath40su(2)@xmath86u(1)@xmath87 . in this case , eq .
( [ eq : telight ] ) reduces to @xmath123)=0\ ] ] which is solved by @xmath124 this is consistent with the results of ref .
@xcite , which presents the spectrum of a deconstructed 5d su(5 ) theory with unified symmetry broken explicitly at an orbifold fixed point .
since we generally assume that @xmath125 , and hence that @xmath126 , a more relevant limit is the one in which @xmath127 .
as we described earlier , this corresponds to a physical system in which the @xmath74 block has effectively become fixed . in this case , eq .
( [ eq : telight ] ) reduces to @xmath128)=0\ ] ] which is solved by @xmath129 as we expect , this result is simply eq .
( [ eq : exone ] ) with the replacement @xmath130 . for large values of @xmath14 ,
the expression for @xmath93 is approximately @xmath131 where we have identified the compactification scale @xmath132 .
this is shifted relative to the gauge bosons with zero modes , which have the spectrum @xmath133 in the same limit .
this is exactly the behavior we expect in the higgsless theory @xcite , obtained when when takes the boundary vevs @xmath134 .
thus , the present work demonstrates how one may obtain a four - dimensional analog for the 5d higgsless trinified model described in ref .
@xcite . with eqs .
( [ eq : mspecsm ] ) , ( [ eq : telight ] ) , ( [ eq : mslight ] ) , ( [ eq : teheavy ] ) , and ( [ eq : msheavy ] ) in hand , we have all the information we need to take into account the effect of finite boundary vevs on the gauge boson mass spectrum .
we will use this result in our study of gauge unification in the following section .
aside from the @xmath135 vector supermultiplets that we expect at each massive kk level of the deconstructed theory @xcite , we assume that the only other fields relevant for unification are the light matter and higgs fields of the mssm .
we justify this assumption in sec .
[ sec : matter ] , where we demonstrate how this can be arranged .
we will find it convenient to express our results in terms of the differences @xmath136 where @xmath137 is the renormalization scale . since the theory of interest to us here represents a deconstructed version of the 5d trinified theory of ref .
@xcite , the basic quantities of interest in studying gauge unification at the one loop level have the same form : @xmath138 @xmath139 @xmath140 here , @xmath141 and @xmath142 represent the mass levels corresponding to gauge fields with and without zero modes , respectively .
these expressions are valid for @xmath143 , which we assume to be the lightest gauge field kk excitation ( recall that as @xmath127 , @xmath144 ) .
the unification scale @xmath145 is identified with the scale at which the moose is reduced to the diagonal subgroup su(3)@xmath40su(3)@xmath31su(3)@xmath25 ; this is usually taken to be @xmath146 , the scale of the heaviest kk excitation .
thus we require @xmath147 which determines the unification scale in terms of @xmath0 and @xmath90 . for arbitrary @xmath90 , eq .
( [ eq : ucond ] ) can be solved numerically ; for example , with @xmath148 and @xmath149 , one finds that @xmath150 is @xmath151 gev , as is shown in fig .
[ fig4 ] .
4 in the changes in slope of @xmath152 and @xmath153 above @xmath154 correspond to vector multiplet mass thresholds .
the one kink present above the unification scale corresponds to the mass threshold that decouples in the @xmath155 limit .
one finds that the quality of unification in this example is given by @xmath156 note that the unification scale is above @xmath17 gev , the unification scale of conventional supersymmetric theories .
since we are interested in @xmath157 , we will analyze the general case as an expansion in @xmath158 .
the results we present below may be derived by taking into account the following simplifications , @xmath159 and @xmath160 which are valid if the renormalization scale is above all but the last mass threshold @xmath161 ( _ i.e. _ , the kink above the unification point shown in fig . [ fig4 ] is not included in the sums ) .
then it follows that @xmath162 which clarifies the previously noted delay in unification by showing the scaling in @xmath14 and the weak dependence on @xmath90 , for @xmath90 large .
one may also use eqs .
( [ eq : sumzero ] ) and ( [ eq : sumh ] ) to obtain a general expression for the quality of unification ( _ e.g. _ eq .
( [ eq : n6uq ] ) ) .
one finds , @xmath163 where @xmath164 the function @xmath165 ranges approximately from @xmath166 to @xmath167 , for large @xmath90 , assuring reasonably accurate unification .
3.5 in we now show how one may construct tri - n - ified theories with the low - energy particle content of the mssm .
our first example assumes that the @xmath20 symmetry applies to the theory as a whole , including the fermion representations , which makes achieving the desired low - energy theory nontrivial .
let us consider a viable model for the next - to - minimal case of @xmath168 .
we would first like to arrange for precisely two higgs doublet fields in the low - energy spectrum .
we follow the approach of ref .
@xcite and consider doublets living within @xmath6 and @xmath169 representations of the diagonal subgroup , and an additional higgs field in the @xmath170-dimensional representation , to arrange for doublet - triplet splitting .
the higgs @xmath6 consists of the ` special ' links in the original circular moose , namely , the links between the sites @xmath53-@xmath171 , @xmath57-@xmath172 , and @xmath55-@xmath173 . the main purpose of these links was to cancel anomalies , and to provide for the breaking of the diagonal gauge group at a boundary .
we add the @xmath169 as shown by the dashed lines in fig .
[ fig5 ] . notice that to avoid anomalies , we have added spectator fields ; for example , the @xmath174 component requires three spectators with quantum numbers @xmath175 , for @xmath176 and three with quantum numbers @xmath177 .
the links that acquire diagonal vevs generate mass terms for these spectators , @xmath178 where the @xmath179 are coupling constants .
while the spectators are present at the unification scale , they do not alter the renormalization group analysis presented in the previous section . with both @xmath6 and @xmath169 higgs fields present in the theory
, we can arrange for heavy masses for all the color - triplet components .
doublet - triplet splitting may be obtained by adding the higgs representation @xmath180 .
notice that the representation @xmath181 is anomaly free , so we do not require any additional spectator fields .
we assume that only the @xmath182 component of the @xmath170 and the @xmath183 of the @xmath169 acquire gut - breaking vacuum expectation values , which again localizes the breaking of the diagonal subgroup to the @xmath53-@xmath171 link .
these new vevs contribute to the the matrix @xmath77 in eq .
( [ eq : lrspec ] ) , but otherwise do not alter the discussion of section [ sec : unification ] .
in addition , appropriate vevs in the @xmath170 and the @xmath169 prevent one from eliminating the desired symmetry - breaking effect of eq .
( [ eq : thevevs ] ) via a gauge transformation . calling the @xmath169 higgs @xmath184 ,
the superpotential terms relevant to doublet - triplet splitting are given by @xmath185 as described in ref .
@xcite , a vev of the form @xmath186 allows one to make a doublet component of @xmath187 and a doublet component of @xmath188 light , provided that @xmath189 .
the light components , which we identify as the two higgs doublets of the mssm are localized at the @xmath53-@xmath171 link .
note that the down - type higgs doublet lives within the @xmath169 representation , which does not have a direct yukawa coupling with matter fields transforming in the @xmath21 .
however , @xmath190 transforms as a @xmath6 , where @xmath191 is an ultraviolet cutoff .
this combination provides for down - type higgs yukawa couplings via higher - dimension operators , suppressed relative to the up - type couplings by a factor of @xmath192 .
we now must arrange for the embedding of three generations of matter fields , so that there are adequate couplings to the light , localized higgs doublets .
a possible configuration is shown in fig .
[ fig6 ] . 3.0 in here we have chosen to embed the matter fields so that the moose remains invariant under @xmath34 rotations .
one could argue , therefore , that the @xmath20 symmetry forces the existence of three generations in this model .
since the light higgs doublets are only present on the @xmath53-@xmath171 link , while the generations are delocalized we expect that yukawa couplings originate via higher - dimension operators , suppressed by powers of @xmath193 . for the model to be successful , these suppression factors must not be so great that we are prevented from achieving phenomenologically viable yukawa textures .
let us identify the matter @xmath6
s by the sites that they connect , _
e.g. _ , @xmath194 transforms under the subset of gauge groups ( @xmath172,@xmath53,@xmath171 ) .
then we identify the three generations as follows : @xmath195 given this choice , we see , for example , that the third generation yukawa couplings are not suppressed , @xmath196 while a purely second generation coupling @xmath197 involves a suppression factor of order @xmath198 .
one therefore finds that the entries of the up quark yukawa matrix involve suppression factors summarized by @xmath199 where we have defined @xmath200 ; the down sector suppression factors are one power of @xmath192 higher .
the tightest constraint on the size of these parameters comes from the strange quark yukawa coupling , which requires that @xmath201 .
provided that this is satisfied , one may choose coupling matrices @xmath202 and @xmath203 to obtain the additional flavor suppression required to produce yukawa textures that are phenomenologically viable ( for example , compare to those found in ref .
the reader can check that the same is true in the charged lepton sector as well .
in addition , the @xmath6 s of matter fields contain exotic particle content that becomes heavy in minimal trinified theories due to the su(3)@xmath204-breaking vevs of the @xmath53-@xmath171 link .
the same happens here , though there is some suppression due to the delocalization of the matter multiplets .
since a generic link field transforms as @xmath205 , and it is possible to arrange @xmath206 , by elementary su(3 ) group theory , one has the necessary building blocks to reproduce _ any _ mass operator of the @xmath41 theory at some order in @xmath207 .
note that the exotic fields in the @xmath21 form complete su(5 ) multiplets @xcite , so they can appear below the unification scale without substantially altering the conclusions of section [ sec : unification ] . while the previous model can accommodate the flavor structure of the standard model , it is not clear whether successful models can be constructed for larger @xmath14 .
the assumption of the unbroken @xmath20 symmetry would force different generations to be widely separated if the number of sites is large .
let us consider the possibility that the unified boundary condition on the gauge couplings has a dynamical origin and is not due to symmetry .
equivalently , we may assume that the @xmath20 symmetry is an accidental symmetry of the gauge and higgs sector , but not of the matter fields .
then we may place all three generations on a single set of gauge sites , namely , @xmath208-@xmath53-@xmath171 , for some @xmath61 . in this case , no suppression factors appear in the yukawa couplings , and the origin of the fermion mass hierarchy is completely decoupled from the physics of unification .
while we keep the arrangement of higgs fields the same , we can add an additional three pairs of @xmath209 and @xmath210 spectator fields at each new gauge site ; in this way , all spectators will acquire gut - scale masses by coupling in pairs via an intermediate link field .
for either the @xmath2 , @xmath3 or @xmath4-sector spectators , these interactions have the form @xmath211 using this construction , we can study models with many more gauge sites .
the only limitation on the size of @xmath14 comes from the assumption that the su(3 ) gauge couplings @xmath212 remain perturbative . for the case of identical gauge couplings ,
@xmath212 is related to the gauge coupling of the diagonal subgroup , @xmath213 , by @xmath214 using our earlier renormalization group analysis , one finds numerically that the constraint @xmath215 translates to @xmath216
we have considered a natural generalization of trinification to theories with @xmath0 gauge groups .
we have showed that the gauge and higgs sector of the theory can be interpreted as a deconstructed version of a 5d trinified theory with unified symmetry broken at a boundary ; we have studied the gauge spectrum in the deconstructed theory for arbitrary boundary higgs vevs . as in the 5d theory ,
the differences in inverse gauge couplings evolve logarithmically , and one finds successful unification at a scale higher than in the 4d mssm .
since the unification scale grows as @xmath217 , unification may be delayed to @xmath218 gev before the gauge coupling of the replicated su(3 ) factors becomes nonperturbative .
this might be compared to the result in the 5d theory , @xmath219 gev , which is the point at which the 5d planck scale and the unification scale coincide @xcite .
we have also considered ways in which the light matter and higgs content of the mssm could be embedded in the ( rather large ) unified group .
we first showed how doublet - triplet splitting could be arranged , via fine tuning , leaving light higgs doublets localized between two gauge sites in the original moose .
the point here is not to solve the doublet - triplet splitting problem , but to present a viable zeroth - order framework in which such questions can be studied . with all symmetry breaking localized
, we then considered the embedding of matter fields . assuming first that the unified boundary condition on the gauge couplings arises from a @xmath20 symmetry that rotates the moose by @xmath34 , one obtains symmetrical embeddings of the fermion multiplets within the moose ( _ c.f .
_ , fig .
[ fig6 ] ) .
although these have no strict extra - dimensional interpretation , we have , roughly speaking , delocalized the fermion multiplets while keeping all the symmetry - breaking and light higgs fields at one point .
we show for relatively small moose , one can arrange for sufficient overlaps via higher - dimension operators involving the link fields to account for fermion masses and inter - generational mixing . for larger
moose , we assume instead that the unified boundary condition on the gauge couplings is simply present ( or alternately , the @xmath20 symmetry is an accidental symmetry of only the gauge and higgs sectors ) so that matter can be embedded asymmetrically .
then the overlap between matter fields and light higgs fields can be made maximal and no restriction follows on the size of the moose .
alternatively , such models provide the freedom to adjust matter - matter and matter - higgs overlaps in a way that can account in part for the flavor hierarchies of the standard model .
this is one advantage of the models introduced here over minimal trinified scenarios . aside from demonstrating how one may deconstruct the 5d trinified theory described in ref .
@xcite , we have arrived at at class of 4d theories that are interesting in their own right .
this is not a surprise , as the same is true of deconstructed 5d theories based on su(5 ) symmetry that have been studied in the literature @xcite .
the present work therefore provides a new framework for future study of a range of familiar issues , including the implementation of solutions to the doublet - triplet splitting problem , proton decay phenomenology , the origin of flavor via combined unified and horizontal symmetries , construction of explicit symmetry breaking sectors , _
etc_. models based on the idea of nonsupersymmetric triplicated trinification @xcite may also be worthy of study in this context .
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d * 62 * , 016009 ( 2000 ) [ arxiv : hep - ph/0002044 ] ; phys .
b * 474 * , 170 ( 2000 ) [ arxiv : hep - ph/9910392 ] . | we consider a natural generalization of trinification to theories with @xmath0 su(3 ) gauge groups .
these theories have a simple moose representation and a gauge boson spectrum that can be interpreted via the deconstruction of a 5d theory with unified symmetry broken on a boundary .
although the matter and higgs sectors of the theory have no simple extra - dimensional analog , gauge unification retains features characteristic of the 5d theory .
we determine possible assignments of the matter and higgs fields to unified multiplets and present theories that are viable alternatives to minimal trinified guts . | <s>[INST]trinification @xcite refers to unified theories based on the gauge group @xmath1 , with gauge coupling equality imposed at a high scale , typically by a discrete symmetry that cyclically permutes the gauge group labels @xmath2 , @xmath3 , and @xmath4 .
the higgs fields responsible for breaking @xmath5 to the standard model gauge group appear in the @xmath6-dimensional representation , @xmath7 the component fields @xmath8 transform as @xmath9 , @xmath10 s under the pair of gauge groups @xmath11 , @xmath12 , and @xmath13 , respectively . the theory thus specified has a simple moose representation , shown in fig . [ fig1 ] , with the component fields @xmath8 serving as the ` links ' that connect neighboring gauge group ` sites ' .
this structure is reminiscent of a deconstructed higher - dimensional theory @xcite , aside from the fact that the link fields in eq .
( [ eq : higgs27 ] ) do not have the same purpose as in deconstruction , namely , to break chains of replicated gauge groups down to their diagonal subgroup .
nevertheless , the structure of fig . [ fig2 ] suggests a natural generalization to trinified theories in which the group factors @xmath2 , @xmath3 , and @xmath4 are replicated @xmath14 times .
we discuss this generalization in section [ sec : generalized ] .
these theories also have a simple moose representation , and a gauge spectrum that can be interpreted via deconstruction .
in particular , we will see that the gauge sector of the theory is a four - dimensional analog of the 5d trinified theory of ref .
@xcite , in which gauge symmetry breaking effects are localized entirely on a boundary .
such 5d theories have interesting properties @xcite , such as the logarithmic running of the gauge coupling difference @xmath15 , for @xmath16 , and a delay in the scale of unification above @xmath17 gev , the value obtained in the minimal supersymmetric standard model ( mssm ) .
the construction of purely four - dimensional theories with such properties is clearly worthy of pursuit , and has lead to interesting results in the case of su(5 ) @xcite and so(10 ) @xcite unification .
the present work complements this body of literature by introducing a new class of 4d unified theories that are closely related to the deconstruction of 5d trinified guts .
that said , it will not be the purpose of this paper to present a literal deconstruction of the theories discussed in ref .
rather , we proceed from a mostly 4d perspective and develop models that are viable and economical .
for example , in determining the embedding of matter fields in the theory , we do nt follow the prescription of deconstruction at all , so that our 4d theory as a whole can not be mapped to a local 5d theory in the continuum limit .
the higher - dimensional flavor of gauge unification is nonetheless retained leading to a new and interesting class of 4d unified theories .
our paper is organized as follows . in section [ sec : generalized ] , we review conventional trinification and define a generalization to @xmath0 replicated su(3 ) groups . in section [ sec : spectrum ] , we study the gauge boson spectrum of the model , for arbitrary values of the localized symmetry - breaking vacuum expectation values ( vevs ) . in section [ sec : unification ] , we apply these results to study gauge coupling unification in this class of models . in section [ sec : matter ] , we describe how one may successfully include matter and light higgs fields , so the low - energy particle content is the same as in the mssm . in section [ sec : conc ] , we summarize our results and suggest directions for future study .
3.3 in conventional trinified theories @xcite are based on the gauge group @xmath18 , where @xmath19 indicates a semidirect product .
the @xmath20 symmetry cyclically permutes the gauge group labels @xmath2 , @xmath3 and @xmath4 , ensuring a single unified coupling at the gut scale .
the breaking of @xmath5 to the standard model gauge group requires a higgs field in the @xmath21-dimensional representation , @xmath22 where the numbers shown represent the su(3)@xmath23 , su(3)@xmath24 and su(3)@xmath25 representations , respectively .
at least one such field must develop the vacuum expectation value , @xmath26 the presence of vevs only in the third row assures that su(2)@xmath24 remains unbroken , while nonvanishing @xmath27 and @xmath28 entries leave a single unbroken u(1 ) factor , generated by a linear combination of the diagonal generators of su(3)@xmath24 and su(3)@xmath25 . identifying this with hypercharge @xmath29 , one finds , @xmath30 note that su(3)@xmath31su(3)@xmath25 symmetry allows one to rotate away the vev @xmath32 in eq .
( [ eq : thevevs ] ) .
therefore , it is usually assumed that at least two @xmath6 higgs fields with vacuum expectation values in the desired entries are present in the theory .
we will return to this issue in sec .
[ sec : matter ] .
one can verify that this construction yields the standard gut - scale prediction for the weak mixing angle @xmath33 .
let us focus on the structure of the gauge and unified - symmetry - breaking sectors of the theory .
a conventional trinified theory can be represented by the moose diagram shown in fig .
[ fig1 ] . for the sake of simplicity we display only a single higgs @xmath6 .
the moose representation makes it clear that the @xmath6 is anomaly - free , which is relevant for the higgs representations since we assume supersymmetry .
the @xmath20 symmetry is encoded in the symmetry of the moose under rotations by @xmath34 . 3.3 in
now consider the generalization of this moose to @xmath0 gauge groups , as shown in fig .
each link field transforms as a @xmath35 under consecutive su(3 ) groups , reading around the moose diagram clockwise .
we assume that a generic link has vev @xmath36 where @xmath37 or @xmath4 .
this breaks a chain of su(3 ) factors , namely su(3)@xmath38 for @xmath39 , down to its diagonal subgroup .
the diagonal subgroups are precisely su(3)@xmath40su(3)@xmath31su(3)@xmath25 of conventional ( @xmath41 ) trinified theories .
the three links which are not generic are identified with the links of the @xmath41 theory and have the corresponding expectation values . in particular , the links @xmath42 and @xmath43 have no vevs and serve to truncate a linear moose that contains unbroken su(3)@xmath23 .
if the link @xmath44 also had no vev , we could make an analogous statement for su(3)@xmath24 and su(3)@xmath25 ; we assume , however , that this link has precisely the expectation value necessary to break su(3)@xmath45su(3)@xmath25 down to the electroweak gauge group of the standard model .
thus , the total effect of the link vevs is to break @xmath46 below the scales @xmath47 , @xmath48 and @xmath32 . at this point , we have said nothing about the values of the @xmath0 gauge couplings . to maintain gauge unification ,
we assume that the theory defined by fig .
[ fig2 ] is restricted by a @xmath20 symmetry that sets equal three sets of @xmath14 gauge couplings each , @xmath49 thus , we see that the moose in fig .
[ fig2 ] is also symmetric under rotations by @xmath34 , like the @xmath41 theory .
unification is maintained as in the @xmath41 theory since the couplings of the diagonal subgroups are given by @xmath50 for @xmath37 or @xmath4 .
note that the vev of the @xmath51 link breaks both su(3)@xmath52 and the cyclic symmetry of the moose .
it is important to note that we are agnostic as to whether the @xmath20 symmetry is a symmetry of the full theory , including the fermion representations , or is only an accidental symmetry of the gauge sector .
the latter could be the case if , for example , all of the gauge couplings are equal at a high scale due to the dynamics of a more complete , high - energy theory .
we will remain open to both possibilities in our subsequent model building . in the theory we have described thus far ,
the special links between @xmath53-@xmath54 , @xmath55-@xmath56 and @xmath57-@xmath58 contribute to the low - energy particle content of the theory . on the other hand
, we wish only to have two light higgs doublets together with the matter content of the mssm .
how we may arrange for this is discussed in sec .
[ sec : matter ] .
we first , however , address the less model - dependent issue of gauge unification , assuming that the low - energy matter and higgs content is that of the mssm .
let us begin by discussing the spectrum of the @xmath59 gauge multiplets , for @xmath60 .
this portion of the theory is a linear moose with @xmath14 unbroken su(3 ) factors .
the contribution to the gauge boson mass matrix from a link spanning the @xmath61 and @xmath62 site is given by @xmath63,\ ] ] ( with @xmath64 ) leading to the @xmath65 mass squared matrix @xmath66 here we take all su(3 ) gauge couplings to be equal , and adopt this simplifying assumption henceforth .
the mass spectrum given by eq .
( [ eq : cspec ] ) is that of a deconstructed 5d su(3 ) gauge theory , and is well known @xcite , @xmath67 where @xmath68 is the lattice spacing .
the @xmath3 and @xmath4 sectors of the moose are more interesting due to the presence of the nontrivial vev at the @xmath53-@xmath54 link .
let us define the @xmath69 gauge field as the @xmath70-component column vector @xmath71 \,\,\ , , \,\,\,\,\ ,
j = n+1-i \,\,\ , , \,\,\,\,\ , i=1\ldots n\ , .
\label{eq : basis}\ ] ] if one were to excise the @xmath72 sector of the circular moose in fig .
[ fig2 ] , and to bend it about the special link at @xmath53-@xmath54 , one would obtain a linear moose with @xmath14 sites , corresponding to gauge fields @xmath73 in eq .
( [ eq : basis ] ) .
the symmetry breaking effects of the special link are confined to the @xmath74 lattice site .
thus , we will be able to interpret our result as a deconstructed 5d theory with bulk su(3)@xmath31su(3)@xmath25 gauge symmetry broken at a boundary .
since the @xmath3-@xmath3 and @xmath4-@xmath4 link fields give identical contributions to the su(3)@xmath24 and su(3)@xmath25 gauge boson mass matrices , respectively , we may express the mass matrix for the @xmath73 as @xmath75 where each entry represents a @xmath76 matrix in @xmath72 space . only the boundary contribution @xmath77 has a nontrivial structure in this space all others are proportional to an implicit identity matrix .
the form of @xmath77 is precisely that of the @xmath72 gauge boson mass squared matrix in a conventional , @xmath41 trinified theory .
let @xmath78 be the @xmath70-dimensional unitary matrix which diagonalizes @xmath77 : @xmath79 then the @xmath80 entry of eq .
( [ eq : lrspec ] ) may be diagonalized without affecting any of the others by letting @xmath81 , where @xmath82 is the unitary matrix @xmath83 since each @xmath70-dimensional sub - block is now - diagonalized , we end up with @xmath70 decoupled mass matrices , corresponding to the eigenvalues @xmath84 of @xmath77 : @xmath85 four of the eigenvalues of @xmath77 are zero , corresponding to the unbroken su(2)@xmath86u(1)@xmath87 gauge bosons , while the remaining @xmath88 are superheavy . for the massless states ( @xmath89 ) , eq .
( [ eq : simplerm ] ) reduces to eq .
( [ eq : cspec ] ) , as one would expect , and the mass spectrum is given by eq .
( [ eq : mspecsm ] ) .
the massive gauge fields are more interesting . in this case , @xmath90 is nonvanishing and is of the order @xmath91 .
we can find the mass spectrum in the @xmath92 case by exploiting a mechanical analogy .
consider the system of masses @xmath93 and springs shown in fig .
[ fig3]a .
5 in the equation of motion for the @xmath69 block is given by @xmath94 where @xmath95 has precisely the form of eq .
( [ eq : simplerm ] ) , with the identifications @xmath96 and @xmath97 . the squared frequencies of the normal modes of this mechanical system are precisely the eigenvalues of @xmath95 .
notice that as @xmath98 is made large ( _ i.e. _ the massive gauge bosons of the last site in the moose are decoupled ) , the @xmath74 block in our spring system effectively becomes a fixed wall .
we then obtain an @xmath99 mass matrix of the same form as eq .
( [ eq : simplerm ] ) with @xmath100 .
this is exactly what we expect for the massive gauge modes when the @xmath74 site has a smaller gauge symmetry than the other sites in the moose ( see for example , ref .
@xcite . ) the eigenvalues of @xmath95 may be found by considering the translationally invariant system shown in fig .
[ fig3]b , and imposing boundary conditions that mimic the dynamics of the first and @xmath74 block of the system of interest .
let @xmath101 represent the displacement of the @xmath69 block about its equilibrium position , where @xmath102 is the inter - block spacing .
the fact that the first block has no spring to the left is equivalent to the boundary condition @xmath103 in the translationally invariant system . on the other hand ,
the effect of the spring with larger spring constant @xmath98 to the right of the @xmath74 block is replicated by the condition @xmath104 ) = -(\eta - 1 ) \ , \psi(an ) \,\,\ , .
\label{eq : bcright}\ ] ] in other words , in the infinite system , one requires that the @xmath105 block moves so that the force on the @xmath74 block is indistinguishable from that of a stiffer spring connected to a wall .
we may thus consider a normal mode solution to the infinite system of the form @xmath106 and determine the wave numbers @xmath107 allowed by these boundary conditions .
we find that @xmath108 values of @xmath107 are determined by the transcendental equation @xmath109 leading to the eigenvalues @xmath110 here , @xmath111 represents the squared frequencies of the normal mode solutions in the mechanical system , and @xmath108 gauge boson squared masses in the problem of interest .
the @xmath74 gauge boson mass , however , is not given by eqs .
( [ eq : telight ] ) and ( [ eq : mslight ] ) .
the reason is that we have assumed that @xmath107 is real ; complex @xmath107 is perfectly consistent with the translation invariance of the infinite system ( see , for example , ref .
taking @xmath112 , one finds another solution : @xmath113 with @xmath114 it is not hard to verify that eqs ( [ eq : telight ] ) , ( [ eq : mslight ] ) , ( [ eq : teheavy ] ) and ( [ eq : msheavy ] ) are correct .
for example , a two - by - two matrix with @xmath115 and @xmath116 , has eigenvalues @xmath117 .
the corresponding solutions to eqs .
( [ eq : telight ] ) and ( [ eq : teheavy ] ) are @xmath118 and @xmath119 , which yield precisely the same results via eqs .
( [ eq : mslight ] ) and ( [ eq : msheavy ] ) . the parameter @xmath90 allows us to interpolate between a number of familiar limits .
for example , the choice @xmath120 yields the mass matrix for a gauge boson distributed among @xmath14 sites that receives no mass contribution from the @xmath105 link field .
this is the case , for example , for the massive @xmath121 and @xmath29 bosons in an su(5 ) moose with @xmath122 sites , in which the gauge symmetry of the last site is taken to be su(3)@xmath40su(2)@xmath86u(1)@xmath87 . in this case , eq .
( [ eq : telight ] ) reduces to @xmath123)=0\ ] ] which is solved by @xmath124 this is consistent with the results of ref .
@xcite , which presents the spectrum of a deconstructed 5d su(5 ) theory with unified symmetry broken explicitly at an orbifold fixed point .
since we generally assume that @xmath125 , and hence that @xmath126 , a more relevant limit is the one in which @xmath127 .
as we described earlier , this corresponds to a physical system in which the @xmath74 block has effectively become fixed . in this case , eq .
( [ eq : telight ] ) reduces to @xmath128)=0\ ] ] which is solved by @xmath129 as we expect , this result is simply eq .
( [ eq : exone ] ) with the replacement @xmath130 . for large values of @xmath14 ,
the expression for @xmath93 is approximately @xmath131 where we have identified the compactification scale @xmath132 .
this is shifted relative to the gauge bosons with zero modes , which have the spectrum @xmath133 in the same limit .
this is exactly the behavior we expect in the higgsless theory @xcite , obtained when when takes the boundary vevs @xmath134 .
thus , the present work demonstrates how one may obtain a four - dimensional analog for the 5d higgsless trinified model described in ref .
@xcite . with eqs .
( [ eq : mspecsm ] ) , ( [ eq : telight ] ) , ( [ eq : mslight ] ) , ( [ eq : teheavy ] ) , and ( [ eq : msheavy ] ) in hand , we have all the information we need to take into account the effect of finite boundary vevs on the gauge boson mass spectrum .
we will use this result in our study of gauge unification in the following section .
aside from the @xmath135 vector supermultiplets that we expect at each massive kk level of the deconstructed theory @xcite , we assume that the only other fields relevant for unification are the light matter and higgs fields of the mssm .
we justify this assumption in sec .
[ sec : matter ] , where we demonstrate how this can be arranged .
we will find it convenient to express our results in terms of the differences @xmath136 where @xmath137 is the renormalization scale . since the theory of interest to us here represents a deconstructed version of the 5d trinified theory of ref .
@xcite , the basic quantities of interest in studying gauge unification at the one loop level have the same form : @xmath138 @xmath139 @xmath140 here , @xmath141 and @xmath142 represent the mass levels corresponding to gauge fields with and without zero modes , respectively .
these expressions are valid for @xmath143 , which we assume to be the lightest gauge field kk excitation ( recall that as @xmath127 , @xmath144 ) .
the unification scale @xmath145 is identified with the scale at which the moose is reduced to the diagonal subgroup su(3)@xmath40su(3)@xmath31su(3)@xmath25 ; this is usually taken to be @xmath146 , the scale of the heaviest kk excitation .
thus we require @xmath147 which determines the unification scale in terms of @xmath0 and @xmath90 . for arbitrary @xmath90 , eq .
( [ eq : ucond ] ) can be solved numerically ; for example , with @xmath148 and @xmath149 , one finds that @xmath150 is @xmath151 gev , as is shown in fig .
[ fig4 ] .
4 in the changes in slope of @xmath152 and @xmath153 above @xmath154 correspond to vector multiplet mass thresholds .
the one kink present above the unification scale corresponds to the mass threshold that decouples in the @xmath155 limit .
one finds that the quality of unification in this example is given by @xmath156 note that the unification scale is above @xmath17 gev , the unification scale of conventional supersymmetric theories .
since we are interested in @xmath157 , we will analyze the general case as an expansion in @xmath158 .
the results we present below may be derived by taking into account the following simplifications , @xmath159 and @xmath160 which are valid if the renormalization scale is above all but the last mass threshold @xmath161 ( _ i.e. _ , the kink above the unification point shown in fig . [ fig4 ] is not included in the sums ) .
then it follows that @xmath162 which clarifies the previously noted delay in unification by showing the scaling in @xmath14 and the weak dependence on @xmath90 , for @xmath90 large .
one may also use eqs .
( [ eq : sumzero ] ) and ( [ eq : sumh ] ) to obtain a general expression for the quality of unification ( _ e.g. _ eq .
( [ eq : n6uq ] ) ) .
one finds , @xmath163 where @xmath164 the function @xmath165 ranges approximately from @xmath166 to @xmath167 , for large @xmath90 , assuring reasonably accurate unification .
3.5 in we now show how one may construct tri - n - ified theories with the low - energy particle content of the mssm .
our first example assumes that the @xmath20 symmetry applies to the theory as a whole , including the fermion representations , which makes achieving the desired low - energy theory nontrivial .
let us consider a viable model for the next - to - minimal case of @xmath168 .
we would first like to arrange for precisely two higgs doublet fields in the low - energy spectrum .
we follow the approach of ref .
@xcite and consider doublets living within @xmath6 and @xmath169 representations of the diagonal subgroup , and an additional higgs field in the @xmath170-dimensional representation , to arrange for doublet - triplet splitting .
the higgs @xmath6 consists of the ` special ' links in the original circular moose , namely , the links between the sites @xmath53-@xmath171 , @xmath57-@xmath172 , and @xmath55-@xmath173 . the main purpose of these links was to cancel anomalies , and to provide for the breaking of the diagonal gauge group at a boundary .
we add the @xmath169 as shown by the dashed lines in fig .
[ fig5 ] . notice that to avoid anomalies , we have added spectator fields ; for example , the @xmath174 component requires three spectators with quantum numbers @xmath175 , for @xmath176 and three with quantum numbers @xmath177 .
the links that acquire diagonal vevs generate mass terms for these spectators , @xmath178 where the @xmath179 are coupling constants .
while the spectators are present at the unification scale , they do not alter the renormalization group analysis presented in the previous section . with both @xmath6 and @xmath169 higgs fields present in the theory
, we can arrange for heavy masses for all the color - triplet components .
doublet - triplet splitting may be obtained by adding the higgs representation @xmath180 .
notice that the representation @xmath181 is anomaly free , so we do not require any additional spectator fields .
we assume that only the @xmath182 component of the @xmath170 and the @xmath183 of the @xmath169 acquire gut - breaking vacuum expectation values , which again localizes the breaking of the diagonal subgroup to the @xmath53-@xmath171 link .
these new vevs contribute to the the matrix @xmath77 in eq .
( [ eq : lrspec ] ) , but otherwise do not alter the discussion of section [ sec : unification ] .
in addition , appropriate vevs in the @xmath170 and the @xmath169 prevent one from eliminating the desired symmetry - breaking effect of eq .
( [ eq : thevevs ] ) via a gauge transformation . calling the @xmath169 higgs @xmath184 ,
the superpotential terms relevant to doublet - triplet splitting are given by @xmath185 as described in ref .
@xcite , a vev of the form @xmath186 allows one to make a doublet component of @xmath187 and a doublet component of @xmath188 light , provided that @xmath189 .
the light components , which we identify as the two higgs doublets of the mssm are localized at the @xmath53-@xmath171 link .
note that the down - type higgs doublet lives within the @xmath169 representation , which does not have a direct yukawa coupling with matter fields transforming in the @xmath21 .
however , @xmath190 transforms as a @xmath6 , where @xmath191 is an ultraviolet cutoff .
this combination provides for down - type higgs yukawa couplings via higher - dimension operators , suppressed relative to the up - type couplings by a factor of @xmath192 .
we now must arrange for the embedding of three generations of matter fields , so that there are adequate couplings to the light , localized higgs doublets .
a possible configuration is shown in fig .
[ fig6 ] . 3.0 in here we have chosen to embed the matter fields so that the moose remains invariant under @xmath34 rotations .
one could argue , therefore , that the @xmath20 symmetry forces the existence of three generations in this model .
since the light higgs doublets are only present on the @xmath53-@xmath171 link , while the generations are delocalized we expect that yukawa couplings originate via higher - dimension operators , suppressed by powers of @xmath193 . for the model to be successful , these suppression factors must not be so great that we are prevented from achieving phenomenologically viable yukawa textures .
let us identify the matter @xmath6
s by the sites that they connect , _
e.g. _ , @xmath194 transforms under the subset of gauge groups ( @xmath172,@xmath53,@xmath171 ) .
then we identify the three generations as follows : @xmath195 given this choice , we see , for example , that the third generation yukawa couplings are not suppressed , @xmath196 while a purely second generation coupling @xmath197 involves a suppression factor of order @xmath198 .
one therefore finds that the entries of the up quark yukawa matrix involve suppression factors summarized by @xmath199 where we have defined @xmath200 ; the down sector suppression factors are one power of @xmath192 higher .
the tightest constraint on the size of these parameters comes from the strange quark yukawa coupling , which requires that @xmath201 .
provided that this is satisfied , one may choose coupling matrices @xmath202 and @xmath203 to obtain the additional flavor suppression required to produce yukawa textures that are phenomenologically viable ( for example , compare to those found in ref .
the reader can check that the same is true in the charged lepton sector as well .
in addition , the @xmath6 s of matter fields contain exotic particle content that becomes heavy in minimal trinified theories due to the su(3)@xmath204-breaking vevs of the @xmath53-@xmath171 link .
the same happens here , though there is some suppression due to the delocalization of the matter multiplets .
since a generic link field transforms as @xmath205 , and it is possible to arrange @xmath206 , by elementary su(3 ) group theory , one has the necessary building blocks to reproduce _ any _ mass operator of the @xmath41 theory at some order in @xmath207 .
note that the exotic fields in the @xmath21 form complete su(5 ) multiplets @xcite , so they can appear below the unification scale without substantially altering the conclusions of section [ sec : unification ] . while the previous model can accommodate the flavor structure of the standard model , it is not clear whether successful models can be constructed for larger @xmath14 .
the assumption of the unbroken @xmath20 symmetry would force different generations to be widely separated if the number of sites is large .
let us consider the possibility that the unified boundary condition on the gauge couplings has a dynamical origin and is not due to symmetry .
equivalently , we may assume that the @xmath20 symmetry is an accidental symmetry of the gauge and higgs sector , but not of the matter fields .
then we may place all three generations on a single set of gauge sites , namely , @xmath208-@xmath53-@xmath171 , for some @xmath61 . in this case , no suppression factors appear in the yukawa couplings , and the origin of the fermion mass hierarchy is completely decoupled from the physics of unification .
while we keep the arrangement of higgs fields the same , we can add an additional three pairs of @xmath209 and @xmath210 spectator fields at each new gauge site ; in this way , all spectators will acquire gut - scale masses by coupling in pairs via an intermediate link field .
for either the @xmath2 , @xmath3 or @xmath4-sector spectators , these interactions have the form @xmath211 using this construction , we can study models with many more gauge sites .
the only limitation on the size of @xmath14 comes from the assumption that the su(3 ) gauge couplings @xmath212 remain perturbative . for the case of identical gauge couplings ,
@xmath212 is related to the gauge coupling of the diagonal subgroup , @xmath213 , by @xmath214 using our earlier renormalization group analysis , one finds numerically that the constraint @xmath215 translates to @xmath216
we have considered a natural generalization of trinification to theories with @xmath0 gauge groups .
we have showed that the gauge and higgs sector of the theory can be interpreted as a deconstructed version of a 5d trinified theory with unified symmetry broken at a boundary ; we have studied the gauge spectrum in the deconstructed theory for arbitrary boundary higgs vevs . as in the 5d theory ,
the differences in inverse gauge couplings evolve logarithmically , and one finds successful unification at a scale higher than in the 4d mssm .
since the unification scale grows as @xmath217 , unification may be delayed to @xmath218 gev before the gauge coupling of the replicated su(3 ) factors becomes nonperturbative .
this might be compared to the result in the 5d theory , @xmath219 gev , which is the point at which the 5d planck scale and the unification scale coincide @xcite .
we have also considered ways in which the light matter and higgs content of the mssm could be embedded in the ( rather large ) unified group .
we first showed how doublet - triplet splitting could be arranged , via fine tuning , leaving light higgs doublets localized between two gauge sites in the original moose .
the point here is not to solve the doublet - triplet splitting problem , but to present a viable zeroth - order framework in which such questions can be studied . with all symmetry breaking localized
, we then considered the embedding of matter fields . assuming first that the unified boundary condition on the gauge couplings arises from a @xmath20 symmetry that rotates the moose by @xmath34 , one obtains symmetrical embeddings of the fermion multiplets within the moose ( _ c.f .
_ , fig .
[ fig6 ] ) .
although these have no strict extra - dimensional interpretation , we have , roughly speaking , delocalized the fermion multiplets while keeping all the symmetry - breaking and light higgs fields at one point .
we show for relatively small moose , one can arrange for sufficient overlaps via higher - dimension operators involving the link fields to account for fermion masses and inter - generational mixing . for larger
moose , we assume instead that the unified boundary condition on the gauge couplings is simply present ( or alternately , the @xmath20 symmetry is an accidental symmetry of only the gauge and higgs sectors ) so that matter can be embedded asymmetrically .
then the overlap between matter fields and light higgs fields can be made maximal and no restriction follows on the size of the moose .
alternatively , such models provide the freedom to adjust matter - matter and matter - higgs overlaps in a way that can account in part for the flavor hierarchies of the standard model .
this is one advantage of the models introduced here over minimal trinified scenarios . aside from demonstrating how one may deconstruct the 5d trinified theory described in ref .
@xcite , we have arrived at at class of 4d theories that are interesting in their own right .
this is not a surprise , as the same is true of deconstructed 5d theories based on su(5 ) symmetry that have been studied in the literature @xcite .
the present work therefore provides a new framework for future study of a range of familiar issues , including the implementation of solutions to the doublet - triplet splitting problem , proton decay phenomenology , the origin of flavor via combined unified and horizontal symmetries , construction of explicit symmetry breaking sectors , _
etc_. models based on the idea of nonsupersymmetric triplicated trinification @xcite may also be worthy of study in this context .
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b * 474 * , 170 ( 2000 ) [ arxiv : hep - ph/9910392 ] .[/INST] we consider a natural generalization of trinification to theories with @xmath0 su(3 ) gauge groups .
these theories have a simple moose representation and a gauge boson spectrum that can be interpreted via the deconstruction of a 5d theory with unified symmetry broken on a boundary .
although the matter and higgs sectors of the theory have no simple extra - dimensional analog , gauge unification retains features characteristic of the 5d theory .
we determine possible assignments of the matter and higgs fields to unified multiplets and present theories that are viable alternatives to minimal trinified guts . </s> |
let @xmath0 be a unital complex banach algebra . a linear mapping @xmath1 from a subspace @xmath2 into another unital complex banach algebra @xmath3
is called _ spectrally bounded _ if there is a constant @xmath4 such that @xmath5 for all @xmath6 . here , and in what follows , @xmath7 stands for the spectral radius of a banach algebra element @xmath8 .
this concept evolved in banach algebra theory , and especially automatic continuity , over time in the 1970 s and 1980 s but the terminology was only introduced in @xcite , together with its companions _ spectrally infinitesimal _ : @xmath9 ; _ spectrally contractive _ : @xmath10 ; and _ spectrally isometric _ : @xmath11 for all @xmath8 .
it follows from @xcite , see also @xcite , lemma a , that the separating space of every surjective / @xmath12 on a closed subspace @xmath13 is contained in the radical of @xmath3 ; thus @xmath12 is bounded if @xmath3 is semisimple .
this was used by aupetit in @xcite to give a new proof of johnson s uniqueness - of - the - complete - norm - topology theorem ; cf .
also @xcite .
it was further exploited in @xcite to investigate continuity properties of lie epimorphisms .
a systematic study of /s was begun in @xcite , with its main results published in @xcite and @xcite . since then , the interest in the topic has steadily grown and by now there is a sizeable literature on a variety of aspects . the present paper s aim is to discuss several of the open problems on /s along with some new results that should make it clear why these questions are natural and important .
section [ sec : auto - cont ] is devoted to a recapitulation of probably the most important and deepest problem on /s , the non - commutative singer wermer conjecture .
no substantial progress seems to have been made on this over the last few years .
a standard method to reduce a more sophisticated problem in banach algebra theory to a simpler one is to use quotients .
when dealing with operators between banach algebras , we , of course , need invariant ideals to perform this . in section [ sec : quotients ] we discuss the interplay between properties of a ( / ) operator and the operator it induces on suitable quotient banach algebras in a fairly general setting and recover recent results for operators preserving the essential spectral radius on @xmath14 in @xcite .
the identity element plays a distinguished role for /s .
suppose that @xmath15 is a surjective / between unital s @xmath0 and @xmath3 .
since @xmath12 restricted to the centre @xmath16 of @xmath0 is a * -isomorphism onto the centre @xmath17 of @xmath3 ( @xcite , proposition 2.3 ) , @xmath18 is a central unitary in @xmath3 .
therefore , whenever we study a / @xmath12 , we can without loss of generality assume that @xmath12 is unital ( i.e. , @xmath19 ) ; see the proof of @xcite , corollary 2.6 . for a general
/ , the situation changes and for this reason we shall pay attention in section [ sec : value - at - one ] to the relevance of the value @xmath18 .
as it turns out , if the domain algebra is sufficiently ` infinite ' , then @xmath18 must be a central invertible element in @xmath3 . as a consequence ,
we are able to extend the main results in @xcite and @xcite to the non - unital setting ( theorem [ thm : nonunital - spbdd ] below ) .
the special case @xmath20 , @xmath21 for hilbert spaces @xmath22 and @xmath23 was studied previously in @xcite . in @xcite
, we propose a non - selfadjoint version of kadison s classical theorem stating that every unital surjective isometry between unital s is a jordan * -isomorphism . in many cases , this conjecture ( see problem [ prob : spiom - conjecture ] below ) has been confirmed , however almost always under some strong assumption of ` infiniteness ' on the domain . in section [ sec : spec - isoms ] , we employ a reduction method developed in @xcite and @xcite to obtain a new result of a similar ilk ( theorem [ thm : no - tracial - states ] ) .
more importantly , perhaps , we propose a new route based on a description of /s in the presence of a trace to solve this open question at least in the setting of 1f / s ( corollary [ cor : type - twoone ] ) .
the _ separating space _ @xmath24 of an operator @xmath12 between normed spaces @xmath13 and @xmath25 is defined by @xmath26 and measures the degree of discontinuity of @xmath12 .
if @xmath13 and @xmath25 are banach spaces then @xmath12 is bounded if and only if @xmath27 , by the closed graph theorem . for a detailed discussion of the separating space see @xcite .
it follows from @xcite , see also @xcite and @xcite , that @xmath28 consists of quasinilpotent elements whenever @xmath1 is a / on a subspace @xmath13 of a banach algebra . in fact ,
@xmath29 for each @xmath6 and @xmath30 .
this , together with zemnek s characterisation of the jacobson radical @xmath31 of @xmath0 , entails the following result .
[ thm : aupetit - aut - cont ] let @xmath1 be a / on a closed subspace @xmath13 of a banach algebra onto a banach algebra @xmath3 . then @xmath32 . in particular ,
if @xmath3 is semisimple , then @xmath12 is bounded .
the above estimate on the spectral radii is used in @xcite to describe the continuity of surjective lie homomorphisms as follows .
[ thm : aut - cont - lie ] the separating space @xmath33 of a lie epimorphism @xmath34 between two banach algebras @xmath0 and @xmath3 is contained in @xmath35 , the centre modulo the radical .
the centre modulo the radical , @xmath35 , is the pre - image of the centre of @xmath36 under the canonical map @xmath37 and turns out to be the largest quasinilpotent lie ideal of @xmath3 . as a consequence , it is invariant under every lie epimorphism and thus the above result yields the following automatic continuity statement ( @xcite , corollary ) .
let @xmath38 be a lie epimorphism between the banach algebras @xmath0 and @xmath3 .
the induced lie epimorphism @xmath39 between the banach lie algebras @xmath40 and @xmath41 is continuous .
the centre modulo the radical also plays an important role in the automatic continuity of derivations on banach algebras .
it is an open question whether the separating space of each of the iterates @xmath42 , @xmath43 of a derivation @xmath44 on a banach algebra @xmath0 is contained in the radical of @xmath0 .
if this is the case , the following long - standing problem would have a positive answer .
[ prob : ncsw ] does @xmath45\in\mathcal{z}(a)$ ] for all @xmath46 imply that @xmath47 ? here ,
@xmath48 $ ] of course stands for the commutator @xmath49 .
if @xmath50 is replaced by the proper centre @xmath16 of @xmath0 , then problem [ prob : ncsw ] has an affirmative answer , due to a reduction technique developed in @xcite and marc thomas famous theorem @xcite .
the connection to /s is provided by the next result @xcite .
a derivation on a banach algebra @xmath0 is / if and only if it maps into @xmath31 . hence , problem [ prob : ncsw ] is equivalent to the following question .
* problem 1@xmath51 .
* does @xmath45\in\mathcal{z}(a)$ ] for all @xmath46 imply that @xmath52 is / ?
it appears that no progress on this question has been made in the last decade . for a fuller discussion
see @xcite and @xcite .
in the previous section , we exploited the concept of /s to study linear mappings satisfying some additional algebraic conditions , such as lie homomorphisms , derivations , etc .
another main direction of research has been on the question which algebraic properties can be derived from the assumption of spectral boundedness .
maybe the most prominent of these problems is the following one from @xcite . by a _
jordan epimorphism _ we will , of course , understand a surjective linear mapping preserving the jordan product @xmath53 .
[ prob : kaplansky ] let @xmath0 and @xmath3 be semisimple unital banach algebras .
suppose @xmath15 is unital , surjective and invertibility - preserving .
is @xmath12 necessarily a jordan epimorphism ?
note that a jordan epimorphism necessarily has all the properties assumed in problem [ prob : kaplansky ] and hence is bounded , by theorem [ thm : aupetit - aut - cont ] .
many contributions on kaplansky s problem have been made over the past decades but so far it eludes a final answer . from aupetit s substantial work on the question we only quote the following beautiful result in @xcite ; see also the references therein .
[ thm : aupetit - main ] let @xmath0 and @xmath3 be von neumann algebras .
then every unital surjective invertibility - preserving linear mapping @xmath15 is a jordan epimorphism . to the best of our knowledge ,
problem [ prob : kaplansky ] is still open even in the case when both domain and codomain are s ; cf .
also @xcite . the structural investigation of /s is partly motivated by the question to what extent the hypotheses in kaplansky s problem can be relaxed while retaining the same goal , to show that the mapping is a jordan homomorphism .
the relevance of the value at @xmath54 will be discussed in the next section . when considering the possibility of replacing `` invertibility - preserving '' by `` / '' we must keep in mind that ( a ) _ every _ bounded linear mapping defined on a commutative is / ( since spectral radius and norm coincide in spaces of the form @xmath55 ) ; ( b ) a finite trace on a is a spectral contraction , hence , already on the @xmath56 matrices there is a unital / onto @xmath57 which is not a jordan epimorphism . notwithstanding this
there are satisfactory results in the setting of ` very infinite ' s ; see sections [ sec : value - at - one ] and [ sec : spec - isoms ] .
many examples are known illustrating the fact that no strong results can be expected for non - surjective /s in general ; see , e.g. , @xcite .
we shall now study the situation when a / is merely surjective ` up to ' or ` modulo ' an ideal .
suppose @xmath58 and @xmath59 are proper closed ideals in the unital banach algebras @xmath0 and @xmath3 , respectively .
we say that a linear mapping @xmath15 is _ essentially / _
( more precisely , @xmath60-@xmath61-_essentially / _ ) if there is a constant @xmath4 such that @xmath62 for all @xmath46 .
we call @xmath12 _ surjective modulo _ @xmath61 if , for every @xmath63 , there is @xmath46 such such @xmath64 .
if @xmath65 , we can define the induced linear mapping @xmath66 by @xmath67 , @xmath46 .
the following proposition relates the properties of @xmath68 to those of @xmath12 .
[ prop : ess - spec - bdd ] let @xmath0 and @xmath3 be unital banach algebras .
suppose that @xmath60 and @xmath61 are proper closed ideals of @xmath0 and @xmath3 , respectively , such that @xmath69 is semisimple .
for a linear mapping @xmath15 the following conditions are equivalent . 1 .
@xmath12 is essentially spectrally bounded and surjective modulo @xmath61 ; 2 .
@xmath65 and @xmath68 is / and surjective .
( b)@xmath70(a ) under the assumption @xmath65 , @xmath68 is a well - defined linear mapping which is / if and only if @xmath12 is essentially / , by definition .
moreover , @xmath68 surjective precisely means that , for each @xmath63 , @xmath71 for some @xmath46 ; that is , @xmath12 is surjective modulo @xmath61 .
( a)@xmath70(b ) by the first paragraph in this proof , it suffices to show that @xmath65 .
take @xmath72 . by hypothesis , for each @xmath63 , there is @xmath73 such that @xmath74 .
let @xmath75 .
we have @xmath76 for some @xmath4 .
consequently , the subharmonic function @xmath77 is bounded on @xmath57 , hence constant .
it follows that @xmath78 for all @xmath63 from which we conclude that @xmath79 , by zemnek s characterisation of the radical .
as @xmath69 is semisimple , we obtain that @xmath80 as desired .
as an immediate consequence we have the following variant of the main result in @xcite .
[ cor : pure - infinite - quotient ] let @xmath15 be a unital linear mapping from a unital purely infinite @xmath0 with real rank zero into a unital banach algebra @xmath3 .
let @xmath59 be a proper closed ideal in @xmath3 such that @xmath69 is semisimple and suppose that , for some proper closed ideal @xmath58 of @xmath0 , the operator @xmath12 is @xmath60-@xmath61-essentially / and surjective modulo @xmath61 . then @xmath12 is a jordan epimorphism modulo @xmath61 .
by proposition [ prop : ess - spec - bdd ] , @xmath65 and the induced mapping @xmath66 is unital , / and surjective .
since @xmath81 is purely infinite and has real rank zero , corollary 2.5 in @xcite implies that @xmath68 is a jordan epimorphism ; hence , @xmath12 is a jordan epimorphism modulo @xmath61 .
in particular , if @xmath12 is even a spectral isometry modulo @xmath61 in the above situation , then @xmath68 provides a jordan isomorphism between the quotients @xmath81 and @xmath69 .
this was obtained in the special case @xmath82 and @xmath83 for an infinite dimensional hilbert space @xmath22 in @xcite , theorem 3.1 . in order to make use of quotients ,
invariant ideals are needed . in the setting of s , so - called glimm ideals offer themselves as good candidates , see section [ sec : spec - isoms ] below .
however , so far their invariance has only been established under additional hypotheses , for instance for / on von neumann algebras @xcite .
does every unital / from a unital onto another one leave each glimm ideal invariant ? the setting of s is favourable also because a / induces a / on every quotient ( @xcite , proposition 9 ) . in a more general
setting it is easy to see that a / induces a / quotient operator provided the domain algebra is an _
sr_-algebra ; cf . @xcite .
a surjective jordan homomorphism between unital algebras attains the value @xmath54 at @xmath54 . in this section
, we shall discuss the behaviour of an arbitrary / at @xmath54 to see how this affects the possible difference from a jordan homomorphism .
remembering that _ every _ bounded operator from a space @xmath55 is / , we have to be careful not to expect too much in a general setting .
the following observation follows directly from our earlier results .
[ prop : basic - fact ] let @xmath15 be a / from a unital @xmath0 onto a unital semisimple banach algebra @xmath3 . for every pair @xmath84 of mutually orthogonal properly infinite projections in @xmath0
we have @xmath85 by @xcite , corollary 3.2 , @xmath12 preserves elements of square zero .
by @xcite , proposition 2.1 , every element in the corners @xmath86 and @xmath87 can be written as a finite sum of elements of square zero ( in @xmath86 and @xmath87 , respectively ) , since both @xmath88 and @xmath89 are properly infinite .
the claim thus follows from lemma 3.3 in @xcite .
[ cor : t - of - one ] let @xmath15 be a / from a unital @xmath0 with real rank zero onto a unital semisimple banach algebra @xmath3 .
suppose that every non - zero projection in @xmath0 is properly infinite .
then @xmath18 is an invertible element in the centre of @xmath3 .
the basic idea of the argument has been used before in some special cases , see , e.g. , @xcite .
let @xmath90 be a non - trivial projection . applying the identity in proposition [ prop : basic - fact ] to @xmath91 and @xmath92 we obtain @xmath93 that is , @xmath94 . upon multiplying this identity first on the left , then on the right by @xmath95 and subtracting the resulting two identities we obtain @xmath96 for every ( non - trivial ) projection @xmath88 .
let @xmath97 be an orthogonal family of projections in @xmath0 . by applying ( [ eq : basic - fact ] ) inductively we find that @xmath98 . since @xmath0 has real rank zero , it follows that @xmath99 for all @xmath100 in a dense subset of @xmath101 and since @xmath12 is bounded , thus for all @xmath102 . as @xmath103 and @xmath104 for all selfadjoint @xmath105 , we conclude that @xmath18 commutes with @xmath106 for every @xmath46 .
the surjectivity of @xmath12 entails that @xmath18 commutes with every square of an element in @xmath3 but since @xmath107 for each @xmath63 , we finally obtain that @xmath18 belongs to the centre of @xmath3 .
going back to the first paragraph of the proof we therefore have @xmath108 for every projection @xmath90 . using the same argumentation as above and the fact that @xmath0 has real rank zero another time
we conclude that @xmath109 for all @xmath46 .
as @xmath12 is surjective , it follows that @xmath18 must be invertible .
whenever @xmath12 is a / such that @xmath18 is an invertible element in the centre of the codomain , the mapping @xmath110 defined by @xmath111 , @xmath46 is a unital / ; thus we can apply the results known in this situation .
[ thm : nonunital - spbdd ] let @xmath15 be a / from a unital @xmath0 onto a unital semisimple banach algebra @xmath3 .
suppose that 1 .
@xmath0 is a properly infinite von neumann algebra , or 2 .
@xmath0 is a purely infinite with real rank zero .
then there is a unique jordan epimorphism @xmath112 such that @xmath113 for all @xmath46 .
moreover , @xmath18 is a central invertible element in @xmath3 .
case ( ii ) is immediate from corollary [ cor : t - of - one ] , since every non - zero projection in a purely infinite is properly infinite .
thus we can define @xmath61 by @xmath114 , @xmath46 , which is a jordan epimorphism by @xcite , corollary 2.5 .
the case ( i ) will not only need the result in the unital case , @xcite , theorem 3.6 , in the same manner as just explained but also an elaboration of the projection techniques used in the main technical result to obtain the unital case , which is @xcite , proposition 3.4 .
note that , by the proof of corollary [ cor : t - of - one ] , it suffices to show that @xmath18 commutes with @xmath115 for every projection @xmath90 ; once this is verified , @xmath18 will be a central invertible element .
we shall use the same strategy as in proposition 3.4 of @xcite .
suppose first that both @xmath88 and @xmath116 are properly infinite .
then the assertion follows immediately from identity ( [ eq : basic - fact ] ) .
next suppose that @xmath88 is properly infinite but @xmath116 is not . by the halving lemma , there is a subprojection @xmath117 of @xmath88 such that @xmath118 , where @xmath119 denotes murray von neumann equivalence .
hence , all projections @xmath117 , @xmath120 , @xmath121 and @xmath122 are properly infinite , see the proof of @xcite , proposition 3.4 . by our first step
we thus have @xmath123 applying ( [ eq : basic - fact ] ) to @xmath117 and @xmath121 we have @xmath124 , wherefore @xmath18 commutes with @xmath115 .
suppose now that @xmath88 is infinite but not properly infinite .
then there is a non - trivial central projection @xmath125 in @xmath0 such that @xmath126 is properly infinite and @xmath127 is finite .
we need the following preliminary observation .
suppose that @xmath89 is a properly infinite projection in @xmath0 but @xmath128 is not .
choosing the subprojection @xmath117 of @xmath89 as in the last paragraph we have @xmath129 where the last two equality signs come from identity ( [ eq : basic - fact ] ) . multiplying this identity first on the left , then on the right by @xmath18 and subtracting the two identities we obtain @xmath130 by the previous paragraph .
to simplify our calculations we will now use the usual commutator notation @xmath48=xy - yx$ ] . since @xmath126 is a properly infinite projection , the preliminary observation yields @xmath131=0 $ ] . by the proof of @xcite , proposition 3.4 , the projection @xmath132 is properly infinite as well ; therefore , @xmath133=0 $ ] , too . as a result , @xmath134 & = [ ( t1)^2,tp]-[(t1)^2,t(zp ) ] = -\ , [ ( t1)^2,t(1-p)]\\ & = -\ , [ ( t1)^2,t(z(1-p))]-[(t1)^2,t((1-z)(1-p))]\\ & = -\ , [ ( t1)^2,tz]+[(t1)^2,t(zp)]=0 , \end{split}\ ] ] since every non - zero central projection in @xmath0 , in particular @xmath125 , is properly infinite and thus @xmath135=0 $ ] as well . from identity ( [ eq : basic - fact ] ) we have @xmath136 since @xmath137 is non - zero , hence properly infinite
. in particular , @xmath138 it follows that @xmath139 combining this with @xmath140=t1\,[t1,tw]+[t1,tw]\,t1=[t1,t1\,tw+tw\,t1]\qquad(w\in a)\ ] ] we find that @xmath141\\ & = [ t1,t(1-z)^2]+[t1,t((1-z)p)^2 ] - [ t1,(t1)\,t((1-z)p)+t((1-z)p)\,(t1)]\\ & = 0 + [ t1,t((1-z)p)^2 ] - [ ( t1)^2,t((1-z)p ) ] , \end{split}\ ] ] that is , @xmath142=[(t1)^2,t((1-z)p]$ ] .
the commutator on the right hand side is zero , as we saw above .
therefore , @xmath143=[t1,t(zp)^2]+[t1,t((1-z)p)^2]=0,\ ] ] where we used ( [ eq : basic - fact - central ] ) once again .
finally suppose that @xmath88 is finite .
then @xmath144 is infinite .
letting @xmath145 be the central projection such that @xmath146 is properly infinite and @xmath147 is finite , we recollect the necessary information from the arguments above . 1 . @xmath148=0 $ ] ; 2 .
@xmath149=[t1 , t((1-z')p')^2]=0 $ ] ; 3 .
@xmath150=[t1,t(z'p')^2]=0 $ ] .
consequently , @xmath151=[(t1)^2,t(z'p')]+[(t1)^2,t((1-z')p')]=0.\ ] ] as @xmath152 & = [ t1 , ( t1)^2]+[t1,(tp)^2]-[t1,(t1)\,(tp)+(tp)\,(t1)]\\ & = [ t1,(tp)^2]-[(t1)^2,tp]=[t1,(tp)^2]+[(t1)^2,t(1-p ) ] , \end{split}\ ] ] we conclude that @xmath153=[t1,(tp')^2]-[(t1)^2,tp']=0.\ ] ] this completes the argument that @xmath154=0 $ ] for every projection @xmath90 and , as explained above , this is sufficient to prove the result . evidently , all we need to assume on @xmath12 in the proof of the above theorem is that @xmath12 is surjective , bounded and preserves elements of square zero .
thus , the main result in @xcite , theorem 2.4 , extends appropriately to the non - unital setting . as pointed out above
, we can not expect a result like theorem [ thm : nonunital - spbdd ] for arbitrary s of real rank zero or even von neumann algebras .
however , in a more restricted setting the situation might change .
[ prob : tone - on - finite - factor ] let @xmath12 be a / defined on a finite von neumann factor ( onto a semisimple unital banach algebra @xmath3 )
. is @xmath18 a non - zero complex multiple of the identity in @xmath3 ?
generalising the classical banach stone theorem , kadison showed in @xcite that every unital surjective isometry @xmath12 between two unital s must be a jordan * -isomorphism .
in fact , he showed a stronger result in @xcite , theorem 2 , namely that it suffices that @xmath12 maps the selfadjoint part @xmath101 of @xmath0 isometrically onto the selfadjoint part @xmath155 of @xmath3 .
there are many interesting consequences of these results , all relating isometric properties to selfadjointness . as an example , we state and prove a variant of a theorem of chan ( @xcite , theorem 3 ) . since @xmath158 is a norm , @xmath12 is injective and it is clear that thus @xmath159 is numerical radius - preserving as well . as @xmath160 for all @xmath161 , by kadison
s theorem it suffices to show that @xmath162 .
let @xmath102 , @xmath163 .
write @xmath164 with @xmath165 .
suppose @xmath166 ; then there is @xmath167 and we may assume that @xmath168 . for each state
@xmath169 on @xmath3 and each @xmath43 , we have @xmath170 hence , for large @xmath171 , @xmath172 which is impossible as @xmath12 is numerical radius - preserving . therefore , @xmath173 and @xmath174 is selfadjoint .
kadison s theorem in one direction and an application of the russo
dye theorem in the other direction show that a unital surjective spectral isometry is selfadjoint ( i.e. , maps selfadjoint elements to selfadjoint elements ) if and only if it is an isometry , see @xcite , proposition 2.4 . these results and others , and the analogy to kaplansky
s question ( problem [ prob : kaplansky ] above ) , made us ask the following question which we indeed state as a conjecture in @xcite .
[ thm : no - tracial - states ] let @xmath15 be a unital spectral isometry from a unital @xmath0 with real rank zero and without tracial states such that @xmath175 is hausdorff and totally disconnected onto a unital @xmath3 .
then @xmath12 is a jordan isomorphism .
there are ( at least ) five structure spaces associated with a unital @xmath0 , which we will briefly discuss .
their relation can be depicted as follows .
@xmath176 the set @xmath177 of all irreducible representations of @xmath0 maps onto the set @xmath178 of all unitary equivalence classes of such representations .
since equivalent representations have the same kernel , there is a canonical surjection from @xmath178 onto @xmath175 , the set of all primitive ideals of @xmath0 .
the latter carries a natural topology , the jacobson topology , which can be pulled back to @xmath178 , and then to @xmath177 , to turn them into topological spaces in a canonical way . since @xmath16 is a commutative unital , @xmath179 allows several equivalent descriptions of which we choose the one via maximal ideals . for each maximal ideal @xmath180 of @xmath16 , the closed ideal @xmath181
is called a _ glimm ideal _ of @xmath0 . for each @xmath182
, @xmath183 gives the generating maximal ideal in @xmath16 back , wherefore there is a bijection between the two sets .
transporting the natural topology of @xmath179 over to @xmath184 thus turns the latter into a compact hausdorff space . from the other direction
, we can apply the _ complete regularisation map _
@xmath185 defined by @xmath186 and @xmath187 is the equivalence class with respect to this relation .
if @xmath60 is the glimm ideal given by @xmath188 then @xmath187 can be identified with @xmath189 . among the consequences of this
is @xmath190 , that is , the glimm ideals separate the points of @xmath0 .
it follows from the definition of the jacobson s topology that @xmath175 is t@xmath191 if and only if every primitive ideal is maximal . in a similar vein , @xmath175 is t@xmath192 , i.e. , hausdorff , if and only if every glimm ideal is maximal ( @xcite , lemma 9 ) .
in contrast to results like theorem [ thm : no - tracial - states ] , very little is known about the behaviour of / on s carrying a trace . in the remainder of this paper
we suggest a possible new route to tackle this situation . [
exam : spbdd - mnc ] let @xmath194 be a linear mapping . then @xmath12 is unital , surjective and / if and only if there are a jordan automorphism @xmath195 of @xmath196 and a non - zero complex number @xmath197 such that @xmath198 where @xmath199 denotes the normalised centre - valued trace on @xmath196
. evidently , the formula ( [ equa : canonical - form ] ) defines a unital mapping which is / , since the images under @xmath195 and @xmath199 commute .
moreover , @xmath12 is surjective : let @xmath200 and @xmath201 be such that @xmath202 . put @xmath203 and @xmath204 . then @xmath205 . setting @xmath206 we have @xmath207 conversely
, if @xmath12 is spectrally bounded , it leaves @xmath208 invariant , as this space is spanned by the nilpotent matrices and @xmath12 preserves nilpotency ( @xcite , lemma 3.1 ) . assuming that @xmath12 is surjective , it is in fact bijective and
hence remains injective when restricted to @xmath208 . since the latter is finite dimensional , @xmath209 is bijective from @xmath208 to @xmath208 .
by @xcite , there exist a jordan automorphism @xmath195 of @xmath210 and a non - zero complex number @xmath197 such that @xmath211 .
hence , for each @xmath212 , @xmath213 which is nothing but identity ( [ equa : canonical - form ] ) , if @xmath12 is unital . since @xmath214 is injective , by @xcite , proposition 4.2 , it is surjective as well . by the above description ( [ equa : canonical - form ] ) ,
@xmath211 for a jordan automorphism @xmath195 of @xmath210 and @xmath215 .
suppose first that @xmath216 and take @xmath217 with @xmath218 ; for instance , @xmath219 , where @xmath220 , @xmath221 denote the standard matrix units
. then @xmath222 on the other hand , @xmath12 preserves the peripheral spectrum , by proposition 4.7 in @xcite .
therefore @xmath223 , and the claim follows from ( [ equa : canonical - form ] ) . in the case
@xmath224 , note that identity ( [ equa : canonical - form ] ) entails that @xmath225 for all @xmath212 .
since @xmath12 always preserves one eigenvalue ( in the peripheral spectrum ) , it follows that @xmath12 preserves the entire spectrum and hence must be a jordan automorphism .
the case @xmath226 is trivial .
[ prob : spsiom - ii1f ] let @xmath0 be a 1f/ with normalised centre - valued trace @xmath199 .
let @xmath227 be a unital surjective /.
are there a jordan automorphism @xmath195 of @xmath0 and a non - zero complex number @xmath197 such that @xmath228 1 .
every jordan epimorphism @xmath229 is either multiplicative or anti - multiplicative , by a classical result due to herstein , as @xmath0 is simple , hence prime .
therefore its kernel is an ideal of @xmath0 .
since @xmath0 is simple , @xmath195 must be injective . 2 . by the remark just made together with the final part of the argument in example [ exam : spbdd - mnc ] it suffices to find a jordan epimorphism @xmath195 on @xmath0 such that @xmath211 for some non - zero @xmath230 .
it is easily seen that the representation ( [ equa : canonical - form - factor ] ) is unique .
suppose that @xmath231 are two representations of the / @xmath12 , where @xmath232 and both @xmath195 , @xmath233 are jordan automorphisms of @xmath0 .
it suffices to show that @xmath234 .
since @xmath235 and both @xmath195 and @xmath233 are spectral isometries , it follows that @xmath236 .
let @xmath90 be a projection with @xmath237 and put @xmath238 .
then @xmath239 .
as both @xmath195 and @xmath233 preserve the spectrum , it follows that @xmath240 and thus @xmath234 .
suppose the / @xmath227 can be written in the form ( [ equa : canonical - form - factor ] ) .
then @xmath211 for some non - zero @xmath230 .
since @xmath241 for all @xmath242 , it follows that @xmath243 .
let @xmath90 be a projection with @xmath237 .
then @xmath244 . as in example
[ exam : spisom - mnc ] , @xmath245 .
since @xmath12 preserves the peripheral spectrum , we conclude that @xmath223 . | we discuss several open problems on spectrally bounded operators , some new , some old , adding in a few new insights .
_ dedicated to professor rainer nagel on the occasion of his retirement . _ | <s>[INST]let @xmath0 be a unital complex banach algebra . a linear mapping @xmath1 from a subspace @xmath2 into another unital complex banach algebra @xmath3
is called _ spectrally bounded _ if there is a constant @xmath4 such that @xmath5 for all @xmath6 . here , and in what follows , @xmath7 stands for the spectral radius of a banach algebra element @xmath8 .
this concept evolved in banach algebra theory , and especially automatic continuity , over time in the 1970 s and 1980 s but the terminology was only introduced in @xcite , together with its companions _ spectrally infinitesimal _ : @xmath9 ; _ spectrally contractive _ : @xmath10 ; and _ spectrally isometric _ : @xmath11 for all @xmath8 .
it follows from @xcite , see also @xcite , lemma a , that the separating space of every surjective / @xmath12 on a closed subspace @xmath13 is contained in the radical of @xmath3 ; thus @xmath12 is bounded if @xmath3 is semisimple .
this was used by aupetit in @xcite to give a new proof of johnson s uniqueness - of - the - complete - norm - topology theorem ; cf .
also @xcite .
it was further exploited in @xcite to investigate continuity properties of lie epimorphisms .
a systematic study of /s was begun in @xcite , with its main results published in @xcite and @xcite . since then , the interest in the topic has steadily grown and by now there is a sizeable literature on a variety of aspects . the present paper s aim is to discuss several of the open problems on /s along with some new results that should make it clear why these questions are natural and important .
section [ sec : auto - cont ] is devoted to a recapitulation of probably the most important and deepest problem on /s , the non - commutative singer wermer conjecture .
no substantial progress seems to have been made on this over the last few years .
a standard method to reduce a more sophisticated problem in banach algebra theory to a simpler one is to use quotients .
when dealing with operators between banach algebras , we , of course , need invariant ideals to perform this . in section [ sec : quotients ] we discuss the interplay between properties of a ( / ) operator and the operator it induces on suitable quotient banach algebras in a fairly general setting and recover recent results for operators preserving the essential spectral radius on @xmath14 in @xcite .
the identity element plays a distinguished role for /s .
suppose that @xmath15 is a surjective / between unital s @xmath0 and @xmath3 .
since @xmath12 restricted to the centre @xmath16 of @xmath0 is a * -isomorphism onto the centre @xmath17 of @xmath3 ( @xcite , proposition 2.3 ) , @xmath18 is a central unitary in @xmath3 .
therefore , whenever we study a / @xmath12 , we can without loss of generality assume that @xmath12 is unital ( i.e. , @xmath19 ) ; see the proof of @xcite , corollary 2.6 . for a general
/ , the situation changes and for this reason we shall pay attention in section [ sec : value - at - one ] to the relevance of the value @xmath18 .
as it turns out , if the domain algebra is sufficiently ` infinite ' , then @xmath18 must be a central invertible element in @xmath3 . as a consequence ,
we are able to extend the main results in @xcite and @xcite to the non - unital setting ( theorem [ thm : nonunital - spbdd ] below ) .
the special case @xmath20 , @xmath21 for hilbert spaces @xmath22 and @xmath23 was studied previously in @xcite . in @xcite
, we propose a non - selfadjoint version of kadison s classical theorem stating that every unital surjective isometry between unital s is a jordan * -isomorphism . in many cases , this conjecture ( see problem [ prob : spiom - conjecture ] below ) has been confirmed , however almost always under some strong assumption of ` infiniteness ' on the domain . in section [ sec : spec - isoms ] , we employ a reduction method developed in @xcite and @xcite to obtain a new result of a similar ilk ( theorem [ thm : no - tracial - states ] ) .
more importantly , perhaps , we propose a new route based on a description of /s in the presence of a trace to solve this open question at least in the setting of 1f / s ( corollary [ cor : type - twoone ] ) .
the _ separating space _ @xmath24 of an operator @xmath12 between normed spaces @xmath13 and @xmath25 is defined by @xmath26 and measures the degree of discontinuity of @xmath12 .
if @xmath13 and @xmath25 are banach spaces then @xmath12 is bounded if and only if @xmath27 , by the closed graph theorem . for a detailed discussion of the separating space see @xcite .
it follows from @xcite , see also @xcite and @xcite , that @xmath28 consists of quasinilpotent elements whenever @xmath1 is a / on a subspace @xmath13 of a banach algebra . in fact ,
@xmath29 for each @xmath6 and @xmath30 .
this , together with zemnek s characterisation of the jacobson radical @xmath31 of @xmath0 , entails the following result .
[ thm : aupetit - aut - cont ] let @xmath1 be a / on a closed subspace @xmath13 of a banach algebra onto a banach algebra @xmath3 . then @xmath32 . in particular ,
if @xmath3 is semisimple , then @xmath12 is bounded .
the above estimate on the spectral radii is used in @xcite to describe the continuity of surjective lie homomorphisms as follows .
[ thm : aut - cont - lie ] the separating space @xmath33 of a lie epimorphism @xmath34 between two banach algebras @xmath0 and @xmath3 is contained in @xmath35 , the centre modulo the radical .
the centre modulo the radical , @xmath35 , is the pre - image of the centre of @xmath36 under the canonical map @xmath37 and turns out to be the largest quasinilpotent lie ideal of @xmath3 . as a consequence , it is invariant under every lie epimorphism and thus the above result yields the following automatic continuity statement ( @xcite , corollary ) .
let @xmath38 be a lie epimorphism between the banach algebras @xmath0 and @xmath3 .
the induced lie epimorphism @xmath39 between the banach lie algebras @xmath40 and @xmath41 is continuous .
the centre modulo the radical also plays an important role in the automatic continuity of derivations on banach algebras .
it is an open question whether the separating space of each of the iterates @xmath42 , @xmath43 of a derivation @xmath44 on a banach algebra @xmath0 is contained in the radical of @xmath0 .
if this is the case , the following long - standing problem would have a positive answer .
[ prob : ncsw ] does @xmath45\in\mathcal{z}(a)$ ] for all @xmath46 imply that @xmath47 ? here ,
@xmath48 $ ] of course stands for the commutator @xmath49 .
if @xmath50 is replaced by the proper centre @xmath16 of @xmath0 , then problem [ prob : ncsw ] has an affirmative answer , due to a reduction technique developed in @xcite and marc thomas famous theorem @xcite .
the connection to /s is provided by the next result @xcite .
a derivation on a banach algebra @xmath0 is / if and only if it maps into @xmath31 . hence , problem [ prob : ncsw ] is equivalent to the following question .
* problem 1@xmath51 .
* does @xmath45\in\mathcal{z}(a)$ ] for all @xmath46 imply that @xmath52 is / ?
it appears that no progress on this question has been made in the last decade . for a fuller discussion
see @xcite and @xcite .
in the previous section , we exploited the concept of /s to study linear mappings satisfying some additional algebraic conditions , such as lie homomorphisms , derivations , etc .
another main direction of research has been on the question which algebraic properties can be derived from the assumption of spectral boundedness .
maybe the most prominent of these problems is the following one from @xcite . by a _
jordan epimorphism _ we will , of course , understand a surjective linear mapping preserving the jordan product @xmath53 .
[ prob : kaplansky ] let @xmath0 and @xmath3 be semisimple unital banach algebras .
suppose @xmath15 is unital , surjective and invertibility - preserving .
is @xmath12 necessarily a jordan epimorphism ?
note that a jordan epimorphism necessarily has all the properties assumed in problem [ prob : kaplansky ] and hence is bounded , by theorem [ thm : aupetit - aut - cont ] .
many contributions on kaplansky s problem have been made over the past decades but so far it eludes a final answer . from aupetit s substantial work on the question we only quote the following beautiful result in @xcite ; see also the references therein .
[ thm : aupetit - main ] let @xmath0 and @xmath3 be von neumann algebras .
then every unital surjective invertibility - preserving linear mapping @xmath15 is a jordan epimorphism . to the best of our knowledge ,
problem [ prob : kaplansky ] is still open even in the case when both domain and codomain are s ; cf .
also @xcite . the structural investigation of /s is partly motivated by the question to what extent the hypotheses in kaplansky s problem can be relaxed while retaining the same goal , to show that the mapping is a jordan homomorphism .
the relevance of the value at @xmath54 will be discussed in the next section . when considering the possibility of replacing `` invertibility - preserving '' by `` / '' we must keep in mind that ( a ) _ every _ bounded linear mapping defined on a commutative is / ( since spectral radius and norm coincide in spaces of the form @xmath55 ) ; ( b ) a finite trace on a is a spectral contraction , hence , already on the @xmath56 matrices there is a unital / onto @xmath57 which is not a jordan epimorphism . notwithstanding this
there are satisfactory results in the setting of ` very infinite ' s ; see sections [ sec : value - at - one ] and [ sec : spec - isoms ] .
many examples are known illustrating the fact that no strong results can be expected for non - surjective /s in general ; see , e.g. , @xcite .
we shall now study the situation when a / is merely surjective ` up to ' or ` modulo ' an ideal .
suppose @xmath58 and @xmath59 are proper closed ideals in the unital banach algebras @xmath0 and @xmath3 , respectively .
we say that a linear mapping @xmath15 is _ essentially / _
( more precisely , @xmath60-@xmath61-_essentially / _ ) if there is a constant @xmath4 such that @xmath62 for all @xmath46 .
we call @xmath12 _ surjective modulo _ @xmath61 if , for every @xmath63 , there is @xmath46 such such @xmath64 .
if @xmath65 , we can define the induced linear mapping @xmath66 by @xmath67 , @xmath46 .
the following proposition relates the properties of @xmath68 to those of @xmath12 .
[ prop : ess - spec - bdd ] let @xmath0 and @xmath3 be unital banach algebras .
suppose that @xmath60 and @xmath61 are proper closed ideals of @xmath0 and @xmath3 , respectively , such that @xmath69 is semisimple .
for a linear mapping @xmath15 the following conditions are equivalent . 1 .
@xmath12 is essentially spectrally bounded and surjective modulo @xmath61 ; 2 .
@xmath65 and @xmath68 is / and surjective .
( b)@xmath70(a ) under the assumption @xmath65 , @xmath68 is a well - defined linear mapping which is / if and only if @xmath12 is essentially / , by definition .
moreover , @xmath68 surjective precisely means that , for each @xmath63 , @xmath71 for some @xmath46 ; that is , @xmath12 is surjective modulo @xmath61 .
( a)@xmath70(b ) by the first paragraph in this proof , it suffices to show that @xmath65 .
take @xmath72 . by hypothesis , for each @xmath63 , there is @xmath73 such that @xmath74 .
let @xmath75 .
we have @xmath76 for some @xmath4 .
consequently , the subharmonic function @xmath77 is bounded on @xmath57 , hence constant .
it follows that @xmath78 for all @xmath63 from which we conclude that @xmath79 , by zemnek s characterisation of the radical .
as @xmath69 is semisimple , we obtain that @xmath80 as desired .
as an immediate consequence we have the following variant of the main result in @xcite .
[ cor : pure - infinite - quotient ] let @xmath15 be a unital linear mapping from a unital purely infinite @xmath0 with real rank zero into a unital banach algebra @xmath3 .
let @xmath59 be a proper closed ideal in @xmath3 such that @xmath69 is semisimple and suppose that , for some proper closed ideal @xmath58 of @xmath0 , the operator @xmath12 is @xmath60-@xmath61-essentially / and surjective modulo @xmath61 . then @xmath12 is a jordan epimorphism modulo @xmath61 .
by proposition [ prop : ess - spec - bdd ] , @xmath65 and the induced mapping @xmath66 is unital , / and surjective .
since @xmath81 is purely infinite and has real rank zero , corollary 2.5 in @xcite implies that @xmath68 is a jordan epimorphism ; hence , @xmath12 is a jordan epimorphism modulo @xmath61 .
in particular , if @xmath12 is even a spectral isometry modulo @xmath61 in the above situation , then @xmath68 provides a jordan isomorphism between the quotients @xmath81 and @xmath69 .
this was obtained in the special case @xmath82 and @xmath83 for an infinite dimensional hilbert space @xmath22 in @xcite , theorem 3.1 . in order to make use of quotients ,
invariant ideals are needed . in the setting of s , so - called glimm ideals offer themselves as good candidates , see section [ sec : spec - isoms ] below .
however , so far their invariance has only been established under additional hypotheses , for instance for / on von neumann algebras @xcite .
does every unital / from a unital onto another one leave each glimm ideal invariant ? the setting of s is favourable also because a / induces a / on every quotient ( @xcite , proposition 9 ) . in a more general
setting it is easy to see that a / induces a / quotient operator provided the domain algebra is an _
sr_-algebra ; cf . @xcite .
a surjective jordan homomorphism between unital algebras attains the value @xmath54 at @xmath54 . in this section
, we shall discuss the behaviour of an arbitrary / at @xmath54 to see how this affects the possible difference from a jordan homomorphism .
remembering that _ every _ bounded operator from a space @xmath55 is / , we have to be careful not to expect too much in a general setting .
the following observation follows directly from our earlier results .
[ prop : basic - fact ] let @xmath15 be a / from a unital @xmath0 onto a unital semisimple banach algebra @xmath3 . for every pair @xmath84 of mutually orthogonal properly infinite projections in @xmath0
we have @xmath85 by @xcite , corollary 3.2 , @xmath12 preserves elements of square zero .
by @xcite , proposition 2.1 , every element in the corners @xmath86 and @xmath87 can be written as a finite sum of elements of square zero ( in @xmath86 and @xmath87 , respectively ) , since both @xmath88 and @xmath89 are properly infinite .
the claim thus follows from lemma 3.3 in @xcite .
[ cor : t - of - one ] let @xmath15 be a / from a unital @xmath0 with real rank zero onto a unital semisimple banach algebra @xmath3 .
suppose that every non - zero projection in @xmath0 is properly infinite .
then @xmath18 is an invertible element in the centre of @xmath3 .
the basic idea of the argument has been used before in some special cases , see , e.g. , @xcite .
let @xmath90 be a non - trivial projection . applying the identity in proposition [ prop : basic - fact ] to @xmath91 and @xmath92 we obtain @xmath93 that is , @xmath94 . upon multiplying this identity first on the left , then on the right by @xmath95 and subtracting the resulting two identities we obtain @xmath96 for every ( non - trivial ) projection @xmath88 .
let @xmath97 be an orthogonal family of projections in @xmath0 . by applying ( [ eq : basic - fact ] ) inductively we find that @xmath98 . since @xmath0 has real rank zero , it follows that @xmath99 for all @xmath100 in a dense subset of @xmath101 and since @xmath12 is bounded , thus for all @xmath102 . as @xmath103 and @xmath104 for all selfadjoint @xmath105 , we conclude that @xmath18 commutes with @xmath106 for every @xmath46 .
the surjectivity of @xmath12 entails that @xmath18 commutes with every square of an element in @xmath3 but since @xmath107 for each @xmath63 , we finally obtain that @xmath18 belongs to the centre of @xmath3 .
going back to the first paragraph of the proof we therefore have @xmath108 for every projection @xmath90 . using the same argumentation as above and the fact that @xmath0 has real rank zero another time
we conclude that @xmath109 for all @xmath46 .
as @xmath12 is surjective , it follows that @xmath18 must be invertible .
whenever @xmath12 is a / such that @xmath18 is an invertible element in the centre of the codomain , the mapping @xmath110 defined by @xmath111 , @xmath46 is a unital / ; thus we can apply the results known in this situation .
[ thm : nonunital - spbdd ] let @xmath15 be a / from a unital @xmath0 onto a unital semisimple banach algebra @xmath3 .
suppose that 1 .
@xmath0 is a properly infinite von neumann algebra , or 2 .
@xmath0 is a purely infinite with real rank zero .
then there is a unique jordan epimorphism @xmath112 such that @xmath113 for all @xmath46 .
moreover , @xmath18 is a central invertible element in @xmath3 .
case ( ii ) is immediate from corollary [ cor : t - of - one ] , since every non - zero projection in a purely infinite is properly infinite .
thus we can define @xmath61 by @xmath114 , @xmath46 , which is a jordan epimorphism by @xcite , corollary 2.5 .
the case ( i ) will not only need the result in the unital case , @xcite , theorem 3.6 , in the same manner as just explained but also an elaboration of the projection techniques used in the main technical result to obtain the unital case , which is @xcite , proposition 3.4 .
note that , by the proof of corollary [ cor : t - of - one ] , it suffices to show that @xmath18 commutes with @xmath115 for every projection @xmath90 ; once this is verified , @xmath18 will be a central invertible element .
we shall use the same strategy as in proposition 3.4 of @xcite .
suppose first that both @xmath88 and @xmath116 are properly infinite .
then the assertion follows immediately from identity ( [ eq : basic - fact ] ) .
next suppose that @xmath88 is properly infinite but @xmath116 is not . by the halving lemma , there is a subprojection @xmath117 of @xmath88 such that @xmath118 , where @xmath119 denotes murray von neumann equivalence .
hence , all projections @xmath117 , @xmath120 , @xmath121 and @xmath122 are properly infinite , see the proof of @xcite , proposition 3.4 . by our first step
we thus have @xmath123 applying ( [ eq : basic - fact ] ) to @xmath117 and @xmath121 we have @xmath124 , wherefore @xmath18 commutes with @xmath115 .
suppose now that @xmath88 is infinite but not properly infinite .
then there is a non - trivial central projection @xmath125 in @xmath0 such that @xmath126 is properly infinite and @xmath127 is finite .
we need the following preliminary observation .
suppose that @xmath89 is a properly infinite projection in @xmath0 but @xmath128 is not .
choosing the subprojection @xmath117 of @xmath89 as in the last paragraph we have @xmath129 where the last two equality signs come from identity ( [ eq : basic - fact ] ) . multiplying this identity first on the left , then on the right by @xmath18 and subtracting the two identities we obtain @xmath130 by the previous paragraph .
to simplify our calculations we will now use the usual commutator notation @xmath48=xy - yx$ ] . since @xmath126 is a properly infinite projection , the preliminary observation yields @xmath131=0 $ ] . by the proof of @xcite , proposition 3.4 , the projection @xmath132 is properly infinite as well ; therefore , @xmath133=0 $ ] , too . as a result , @xmath134 & = [ ( t1)^2,tp]-[(t1)^2,t(zp ) ] = -\ , [ ( t1)^2,t(1-p)]\\ & = -\ , [ ( t1)^2,t(z(1-p))]-[(t1)^2,t((1-z)(1-p))]\\ & = -\ , [ ( t1)^2,tz]+[(t1)^2,t(zp)]=0 , \end{split}\ ] ] since every non - zero central projection in @xmath0 , in particular @xmath125 , is properly infinite and thus @xmath135=0 $ ] as well . from identity ( [ eq : basic - fact ] ) we have @xmath136 since @xmath137 is non - zero , hence properly infinite
. in particular , @xmath138 it follows that @xmath139 combining this with @xmath140=t1\,[t1,tw]+[t1,tw]\,t1=[t1,t1\,tw+tw\,t1]\qquad(w\in a)\ ] ] we find that @xmath141\\ & = [ t1,t(1-z)^2]+[t1,t((1-z)p)^2 ] - [ t1,(t1)\,t((1-z)p)+t((1-z)p)\,(t1)]\\ & = 0 + [ t1,t((1-z)p)^2 ] - [ ( t1)^2,t((1-z)p ) ] , \end{split}\ ] ] that is , @xmath142=[(t1)^2,t((1-z)p]$ ] .
the commutator on the right hand side is zero , as we saw above .
therefore , @xmath143=[t1,t(zp)^2]+[t1,t((1-z)p)^2]=0,\ ] ] where we used ( [ eq : basic - fact - central ] ) once again .
finally suppose that @xmath88 is finite .
then @xmath144 is infinite .
letting @xmath145 be the central projection such that @xmath146 is properly infinite and @xmath147 is finite , we recollect the necessary information from the arguments above . 1 . @xmath148=0 $ ] ; 2 .
@xmath149=[t1 , t((1-z')p')^2]=0 $ ] ; 3 .
@xmath150=[t1,t(z'p')^2]=0 $ ] .
consequently , @xmath151=[(t1)^2,t(z'p')]+[(t1)^2,t((1-z')p')]=0.\ ] ] as @xmath152 & = [ t1 , ( t1)^2]+[t1,(tp)^2]-[t1,(t1)\,(tp)+(tp)\,(t1)]\\ & = [ t1,(tp)^2]-[(t1)^2,tp]=[t1,(tp)^2]+[(t1)^2,t(1-p ) ] , \end{split}\ ] ] we conclude that @xmath153=[t1,(tp')^2]-[(t1)^2,tp']=0.\ ] ] this completes the argument that @xmath154=0 $ ] for every projection @xmath90 and , as explained above , this is sufficient to prove the result . evidently , all we need to assume on @xmath12 in the proof of the above theorem is that @xmath12 is surjective , bounded and preserves elements of square zero .
thus , the main result in @xcite , theorem 2.4 , extends appropriately to the non - unital setting . as pointed out above
, we can not expect a result like theorem [ thm : nonunital - spbdd ] for arbitrary s of real rank zero or even von neumann algebras .
however , in a more restricted setting the situation might change .
[ prob : tone - on - finite - factor ] let @xmath12 be a / defined on a finite von neumann factor ( onto a semisimple unital banach algebra @xmath3 )
. is @xmath18 a non - zero complex multiple of the identity in @xmath3 ?
generalising the classical banach stone theorem , kadison showed in @xcite that every unital surjective isometry @xmath12 between two unital s must be a jordan * -isomorphism .
in fact , he showed a stronger result in @xcite , theorem 2 , namely that it suffices that @xmath12 maps the selfadjoint part @xmath101 of @xmath0 isometrically onto the selfadjoint part @xmath155 of @xmath3 .
there are many interesting consequences of these results , all relating isometric properties to selfadjointness . as an example , we state and prove a variant of a theorem of chan ( @xcite , theorem 3 ) . since @xmath158 is a norm , @xmath12 is injective and it is clear that thus @xmath159 is numerical radius - preserving as well . as @xmath160 for all @xmath161 , by kadison
s theorem it suffices to show that @xmath162 .
let @xmath102 , @xmath163 .
write @xmath164 with @xmath165 .
suppose @xmath166 ; then there is @xmath167 and we may assume that @xmath168 . for each state
@xmath169 on @xmath3 and each @xmath43 , we have @xmath170 hence , for large @xmath171 , @xmath172 which is impossible as @xmath12 is numerical radius - preserving . therefore , @xmath173 and @xmath174 is selfadjoint .
kadison s theorem in one direction and an application of the russo
dye theorem in the other direction show that a unital surjective spectral isometry is selfadjoint ( i.e. , maps selfadjoint elements to selfadjoint elements ) if and only if it is an isometry , see @xcite , proposition 2.4 . these results and others , and the analogy to kaplansky
s question ( problem [ prob : kaplansky ] above ) , made us ask the following question which we indeed state as a conjecture in @xcite .
[ thm : no - tracial - states ] let @xmath15 be a unital spectral isometry from a unital @xmath0 with real rank zero and without tracial states such that @xmath175 is hausdorff and totally disconnected onto a unital @xmath3 .
then @xmath12 is a jordan isomorphism .
there are ( at least ) five structure spaces associated with a unital @xmath0 , which we will briefly discuss .
their relation can be depicted as follows .
@xmath176 the set @xmath177 of all irreducible representations of @xmath0 maps onto the set @xmath178 of all unitary equivalence classes of such representations .
since equivalent representations have the same kernel , there is a canonical surjection from @xmath178 onto @xmath175 , the set of all primitive ideals of @xmath0 .
the latter carries a natural topology , the jacobson topology , which can be pulled back to @xmath178 , and then to @xmath177 , to turn them into topological spaces in a canonical way . since @xmath16 is a commutative unital , @xmath179 allows several equivalent descriptions of which we choose the one via maximal ideals . for each maximal ideal @xmath180 of @xmath16 , the closed ideal @xmath181
is called a _ glimm ideal _ of @xmath0 . for each @xmath182
, @xmath183 gives the generating maximal ideal in @xmath16 back , wherefore there is a bijection between the two sets .
transporting the natural topology of @xmath179 over to @xmath184 thus turns the latter into a compact hausdorff space . from the other direction
, we can apply the _ complete regularisation map _
@xmath185 defined by @xmath186 and @xmath187 is the equivalence class with respect to this relation .
if @xmath60 is the glimm ideal given by @xmath188 then @xmath187 can be identified with @xmath189 . among the consequences of this
is @xmath190 , that is , the glimm ideals separate the points of @xmath0 .
it follows from the definition of the jacobson s topology that @xmath175 is t@xmath191 if and only if every primitive ideal is maximal . in a similar vein , @xmath175 is t@xmath192 , i.e. , hausdorff , if and only if every glimm ideal is maximal ( @xcite , lemma 9 ) .
in contrast to results like theorem [ thm : no - tracial - states ] , very little is known about the behaviour of / on s carrying a trace . in the remainder of this paper
we suggest a possible new route to tackle this situation . [
exam : spbdd - mnc ] let @xmath194 be a linear mapping . then @xmath12 is unital , surjective and / if and only if there are a jordan automorphism @xmath195 of @xmath196 and a non - zero complex number @xmath197 such that @xmath198 where @xmath199 denotes the normalised centre - valued trace on @xmath196
. evidently , the formula ( [ equa : canonical - form ] ) defines a unital mapping which is / , since the images under @xmath195 and @xmath199 commute .
moreover , @xmath12 is surjective : let @xmath200 and @xmath201 be such that @xmath202 . put @xmath203 and @xmath204 . then @xmath205 . setting @xmath206 we have @xmath207 conversely
, if @xmath12 is spectrally bounded , it leaves @xmath208 invariant , as this space is spanned by the nilpotent matrices and @xmath12 preserves nilpotency ( @xcite , lemma 3.1 ) . assuming that @xmath12 is surjective , it is in fact bijective and
hence remains injective when restricted to @xmath208 . since the latter is finite dimensional , @xmath209 is bijective from @xmath208 to @xmath208 .
by @xcite , there exist a jordan automorphism @xmath195 of @xmath210 and a non - zero complex number @xmath197 such that @xmath211 .
hence , for each @xmath212 , @xmath213 which is nothing but identity ( [ equa : canonical - form ] ) , if @xmath12 is unital . since @xmath214 is injective , by @xcite , proposition 4.2 , it is surjective as well . by the above description ( [ equa : canonical - form ] ) ,
@xmath211 for a jordan automorphism @xmath195 of @xmath210 and @xmath215 .
suppose first that @xmath216 and take @xmath217 with @xmath218 ; for instance , @xmath219 , where @xmath220 , @xmath221 denote the standard matrix units
. then @xmath222 on the other hand , @xmath12 preserves the peripheral spectrum , by proposition 4.7 in @xcite .
therefore @xmath223 , and the claim follows from ( [ equa : canonical - form ] ) . in the case
@xmath224 , note that identity ( [ equa : canonical - form ] ) entails that @xmath225 for all @xmath212 .
since @xmath12 always preserves one eigenvalue ( in the peripheral spectrum ) , it follows that @xmath12 preserves the entire spectrum and hence must be a jordan automorphism .
the case @xmath226 is trivial .
[ prob : spsiom - ii1f ] let @xmath0 be a 1f/ with normalised centre - valued trace @xmath199 .
let @xmath227 be a unital surjective /.
are there a jordan automorphism @xmath195 of @xmath0 and a non - zero complex number @xmath197 such that @xmath228 1 .
every jordan epimorphism @xmath229 is either multiplicative or anti - multiplicative , by a classical result due to herstein , as @xmath0 is simple , hence prime .
therefore its kernel is an ideal of @xmath0 .
since @xmath0 is simple , @xmath195 must be injective . 2 . by the remark just made together with the final part of the argument in example [ exam : spbdd - mnc ] it suffices to find a jordan epimorphism @xmath195 on @xmath0 such that @xmath211 for some non - zero @xmath230 .
it is easily seen that the representation ( [ equa : canonical - form - factor ] ) is unique .
suppose that @xmath231 are two representations of the / @xmath12 , where @xmath232 and both @xmath195 , @xmath233 are jordan automorphisms of @xmath0 .
it suffices to show that @xmath234 .
since @xmath235 and both @xmath195 and @xmath233 are spectral isometries , it follows that @xmath236 .
let @xmath90 be a projection with @xmath237 and put @xmath238 .
then @xmath239 .
as both @xmath195 and @xmath233 preserve the spectrum , it follows that @xmath240 and thus @xmath234 .
suppose the / @xmath227 can be written in the form ( [ equa : canonical - form - factor ] ) .
then @xmath211 for some non - zero @xmath230 .
since @xmath241 for all @xmath242 , it follows that @xmath243 .
let @xmath90 be a projection with @xmath237 .
then @xmath244 . as in example
[ exam : spisom - mnc ] , @xmath245 .
since @xmath12 preserves the peripheral spectrum , we conclude that @xmath223 .[/INST] we discuss several open problems on spectrally bounded operators , some new , some old , adding in a few new insights .
_ dedicated to professor rainer nagel on the occasion of his retirement . _ </s> |
let @xmath0 be a symplectic 4-manifold with a lagrangian torus @xmath1 .
it was discovered by luttinger in @xcite that there is a family of surgeries along @xmath1 that produce symplectic @xmath2-manifolds .
this family is countable and indexed by the pairs @xmath3 , k)$ ] , where @xmath4 $ ] is an isotopy class of simple closed curves on @xmath1 and @xmath5 is an integer .
when @xmath6 and @xmath7 is the standard symplectic form @xmath8 , he also applied gromov s celebrated work in @xcite to show that , for any lagrangian torus @xmath1 , all the resulting symplectic manifolds are symplectomorphic to @xmath9 .
this does not occur in general ; a luttinger surgery often fails even to preserve homology . as a matter of fact
, many new exotic small manifolds are constructed via this surgery . in this note , we observe that the luttinger surgery preserves one basic invariant : [ kod ] the luttinger surgery preserves the symplectic kodaira dimension .
the symplectic kodaira dimension of a symplectic 4-manifold @xmath10 is defined by the products @xmath11 and @xmath12 $ ] , where @xmath13 is the symplectic canonical class ; if @xmath10 is minimal , then @xmath14 < 0\\ 0 & k_{\omega}^2=0\ and\ k_{\omega}\cdot [ \omega]=0 \\ 1 & k_{\omega}^2=0\ and\ k_{\omega}\cdot [ \omega]>0\\ 2 & k_{\omega}^2>0\ and\ k_{\omega}\cdot [ \omega ] > 0 \end{array}\right.\ ] ] for a general symplectic 4-manifold , the kodaira dimension is defined as the kodaira dimension of any of its minimal models . according to @xcite ,
@xmath15 is independent of the choice of symplectic form @xmath7 and hence is denoted by @xmath16 .
theorem [ kod ] is related to a question of auroux in @xcite ( see remarks [ omega ] and [ 44 ] ) .
furthermore , together with the elementary analysis of the homology change , the invariance of @xmath17 implies that [ int2 ] let @xmath0 be a symplectic 4-manifold with @xmath18 and @xmath19 be constructed from @xmath0 via a luttinger surgery .
then @xmath20 is symplectomorphic to @xmath10 . for minimal symplectic manifolds of kodaira dimension zero , i.e. , symplectic calabi - yau surfaces ,
we conclude that the luttinger surgery is a symplectic cy surgery .
moreover , together with the homology classification of such manifolds in @xcite , we have [ int3 ] suppose @xmath0 is a symplectic 4-manifold with @xmath21 and @xmath22 .
if @xmath19 is constructed from @xmath0 under a luttinger surgery , then @xmath23 and @xmath24 have the same integral homology type .
in fact , we conjecture that @xmath24 and @xmath23 in theorem [ int3 ] are diffeomorphic to each other . for symplectic cy surfaces with @xmath25 ,
the only known examples are torus bundles over torus .
we conjecture that they all can be obtained from @xmath26 via lutttinger surgeries ( conjecture [ torus ] ) .
theorems [ int2 ] and [ int3 ] provide topological constraints , phrased in terms of topological preferred framings ( see definition [ tprefer ] ) , on the existence of exotic lagrangian tori in such manifolds .
[ int4 ] let l be a lagrangian torus in @xmath0 .
if @xmath27 , or @xmath1 is null - homologous , @xmath21 and @xmath28 , then the lagrangian framing of @xmath1 is topological preferred . in particular ,
the invariant @xmath29 in @xcite vanishes whenever it is defined .
the organization of this paper is as follows . in section 2
, the construction of the luttinger surgery is reviewed .
we also discuss the lagrangian fibrations as the first application of this surgery . in section 3
, we establish the invariance of the symplectic kodaira dimension , which is the main result of this note . in section 4 , we prove theorems [ int2 ] and [ int3 ] . in section 5 , we apply these two theorems to derive constraints on framings of lagrangian tori in symplectic 4-manifolds with non - positive kodaira dimension . we are grateful to the referee for many useful suggestions which improve the exposition .
the first author would like to thank the following scholars for their insightful discussions and suggestions : anar akhmedov , inanc baykur , joel gomez , robert gompf , conan leung , weiwei wu and weiyi zhang .
the second author is grateful to the support of nsf .
in this section , we describe the luttinger surgery following @xcite .
applications to lagrangian fibrations are also discussed .
we assume all manifolds are oriented .
topologically , luttinger surgery is a framed torus surgery .
we start with a general description of framed torus surgeries .
let @xmath23 be a smooth 4-manifold and @xmath30 an embedded 2-torus with trivial normal bundle .
then let @xmath31 be a tubular neighborhood of @xmath1 .
if we assume @xmath32 is the complement of @xmath31 , @xmath33 and @xmath34 is a diffeomorphism , a new manifold @xmath24 can be constructed by cutting @xmath31 out of @xmath23 and gluing it back to @xmath35 along @xmath36 via @xmath37 : @xmath38 such surgery is called a @xmath39 @xmath40 .
it is often more explicit to describe this process via a framing of @xmath1 .
let @xmath23 , @xmath1 , @xmath31 and @xmath36 be given as above .
a diffeomorphism @xmath41 is called a framing of @xmath1 if @xmath42 .
let @xmath43 be the projection .
for any @xmath44 and @xmath45 , the lift @xmath46 of @xmath47 in @xmath36 is called a longitudinal curve of @xmath48 .
let @xmath49 be the induced map .
two framings @xmath50 are smoothly isotopic to each other if the map @xmath51 is homotopic to the identity map .
@xmath52 induces a @xmath53-bundle structure on @xmath36 .
a positive oriented fiber @xmath54 of @xmath36 is called a @xmath55 of @xmath1 . for @xmath24 in
, we will use @xmath56 to denote the torus @xmath57 .
notice that @xmath56 also inherits a framing @xmath58 and its meridian @xmath59 satisfies @xmath60=p[\mu]+k[\gamma_\varphi],\ ] ] in @xmath61 .
here @xmath62 is a longitudinal curve of @xmath48 and @xmath63 are coprime integers .
the diffeomorphism type of @xmath24 only depends on the class @xmath64 $ ] .
it is called a _ generalized logarithmic transform _ of @xmath23 along @xmath65 with multiplicity @xmath66 and auxiliary multiplicity @xmath5 , or of type @xmath67 ( see @xcite ) , and denoted as @xmath68 . for brevity
, we will call it a @xmath69-surgery .
if @xmath23 is a symplectic 4-manifold , weinstein s theorem states that there is a canonical framing for any lagrangian torus of @xmath23 .
let @xmath23 be a symplectic 4-manifoldand and @xmath1 a lagrangian torus of @xmath23 .
a framing @xmath48 of @xmath1 is called a lagrangian framing if @xmath70 is a lagrangian submanifold of @xmath23 for any @xmath71 .
topologically , a luttinger surgery is a @xmath72-surgery with respect to a lagrangian framing . in order to deal with the sympelctic structure , it is more convenient to use a square neighborhood rather than the disk neighborhood of @xmath1 as above . express the cotangent bundle @xmath73 as @xmath74 equipped with the canonical 2-form @xmath75 and let @xmath76 there exists a tubular neighborhood @xmath31 of @xmath1 and a symplectomorphism @xmath77 for small @xmath78 which satisfies @xmath79 in addition , given a simple closed curve @xmath47 on @xmath1
, we can choose the coordinates @xmath80 of @xmath81 such that @xmath82 let @xmath83 be an annular region and @xmath84 $ ] be a smooth increasing function such that @xmath85 for @xmath86 and @xmath87 for @xmath88 .
for any integer @xmath5 , we can define a diffeomorphism @xmath89 : @xmath90 observe that @xmath91 which follows from the relation @xmath92 for @xmath93 .
let @xmath94 and define @xmath95 via the following diagram @xmath96 then we can construct a new smooth manifold @xmath97 notice that , by , we have @xmath98 . thus @xmath24 carries a symplectic form @xmath99 induced by @xmath7 .
this process is called a _ luttinger surgery _ ( along the lagrangian torus @xmath1 ) . we know
that [ framing]@xcite any two lagrangian framings of a lagrangian torus are smoothly isotopic to each other .
hence the symplectomorphism type of @xmath100 only depends on the lagrangian isotopy class of @xmath1 , the isotopy class of @xmath47 in @xmath1 , and the integer @xmath5 .
therefore , @xmath101 is also denoted as @xmath102 .
it is worth mentioning that a luttinger surgery can be reversed .
let @xmath103 be the subsets @xmath104 and @xmath105 of @xmath24 .
we can apply the luttinger surgery to @xmath106 with coefficient @xmath107 to recover @xmath23 .
one natural source of lagrangian tori is smooth fibers of lagrangian fibrations .
let @xmath10 be a symplectic 4-manifold , and let @xmath108 be a 2-manifold ( with boundary or vertices ) .
a smooth map @xmath109 is called a lagrangian fibration if there exists an open dense subset @xmath110 such that @xmath111 is a compact lagrangian submanifold of @xmath23 for any @xmath112 .
@xmath23 is called lagrangian fibered if such a structure exists .
it is easy to see that any smooth fiber of a lagrangian fibration must be a torus .
moreover , we have [ fiber ] a luttinger surgery along a lagrangian fiber preserves the lagrangian fibration structure .
let @xmath113 be a lagrangian fibration and @xmath114 a generic fiber .
using notations from section 2.1 , it is shown in @xcite that there is a neighborhood @xmath115 of @xmath116 and @xmath117 with local charts @xmath77 and @xmath118 such that the diagram @xmath119 commutes . here
@xmath120 is the projection @xmath121 .
if @xmath122 is obtained by performing luttinger surgery along @xmath1 ( indexed by @xmath44 and @xmath123 ) , we can define a map @xmath124 as @xmath125 .
since @xmath126 , we have @xmath127 so @xmath128 is well - defined .
it is clear that @xmath128 is lagrangian and @xmath24 also possesses a lagrangian fibration structure .
lagrangian fibrations appear widely in toric geometry , integral systems and mirror symmetry .
we will discuss almost toric fibration introduced by symington in some detail .
an almost toric fibration of a symplectic 4-manifold @xmath0 is a lagrangian fibration @xmath113 with the following properties : for any critical point @xmath129 of @xmath130 , there exists a local coordinate @xmath131 near @xmath129 such that @xmath132 , @xmath133 , and @xmath130 has one of the forms @xmath134 an almost toric 4-manifold is a symplectic 4-manifold equipped with an almost toric fibration .
the base @xmath108 of an almost toric fibration has an affine structure with boundary and vertices . moreover , these three types of critical points project to vertices , edges and interior of @xmath108 respectively .
almost toric fibrations are classified by leung and symington : [ almost]@xcite let @xmath10 be a closed almost toric 4-manifold
. there are seven types of almost toric fibrations according to the homeomorphism type of the base @xmath108 . 1 .
@xmath135 or @xmath136 , @xmath108 is ( homeomorphic to ) a disk ; 2 . @xmath137 or @xmath138
, @xmath108 is a cylinder ; 3 . @xmath137 or @xmath138
, @xmath108 is a mbius band ; 4 .
the @xmath139 surface , @xmath108 is a sphere ; 5 . the enriques surface , @xmath108 is @xmath140 ; 6 .
a torus bundle over torus with monodromy @xmath141 @xmath108 is a torus ; 7 .
a torus bundle over the klein bottle with monodromy @xmath142 @xmath108 is a klein bottle .
an immediate consequence of this classification is the calculation of the symplectic kodaira dimension .
[ al ] if @xmath143 is an almost toric fibration , then @xmath144 .
moreover , @xmath21 if and only if the base @xmath108 is closed .
the effect of luttinger surgeries on almost toric fibrations is also easy to describe .
[ k3 ] suppose @xmath145 is an almost toric fibration and @xmath20 is obtained from @xmath0 by performing a luttinger surgery along a smooth fiber @xmath1 , then @xmath146 retains an almost toric fibration structure with the same base .
moreover , @xmath24 is diffeomorphic to @xmath23 if @xmath147 .
the first statement is given by lemma [ fiber ] . if @xmath147 , @xmath23 and @xmath24 are in one of the types ( 1)-(5 ) in theorem [ almost ] . in each of them ,
the list of manifolds are distinguished by the type of intersection forms and euler numbers .
so the second result for types ( 1)-(3 ) follows from proposition [ compare ] and the fact that homology classes of lagrangian tori in manifolds with @xmath148 are torsion .
it is clear for ( 4 ) and ( 5 ) from the classification .
propositions [ al ] and [ k3 ] provide examples of luttinger surgeries preserving the symplectic kodaira dimension . in the next section , we will show that it is true for any luttinger surgery .
in this section , we prove theorem [ kod ] . to proceed ,
we must first prove the invariance of minimality under luttinger surgery . a symplectic ( smooth ) @xmath149 class is a degree 2 homology class represented by an embedded symplectic ( smooth ) sphere with self - intersection @xmath149 .
a symplectic 4-manifold is called @xmath150 @xmath151
@xmath152 if it does not have any symplectic ( smooth ) @xmath149 class . the symplectic minimality is actually equivalent to smooth minimality .
[ minimality ] the luttinger surgery preserves the minimality .
since a luttinger surgery can be reversed and the reverse operation is also a luttinger surgery , it suffices to show that , if we start with a non - minimal symplectic 4-manifold , then after a luttinger surgery , the resulting symplectic manifold is still non - minimal .
but this is a direct consequence of the following fact in @xcite : [ disjoint ] given a lagrangian torus @xmath1 and a symplectic @xmath149 class , there is an embedded symplectic @xmath149 sphere in that class which is disjoint from @xmath1 .
now , we analyze the effect of luttinger surgery on the symplectic canonical class @xmath13 and the symplectic class @xmath153 $ ] .
recall that @xmath154 is an open submanifold of both @xmath23 and @xmath101 , and let @xmath155 and @xmath156 be the inclusions . to prepare for the following lemma
, we use the notations from section [ construction ] . for the sake of simplicity
, we will identify any object in @xmath23 with their image of @xmath48 and @xmath157 , @xmath158 will denote the coordinates of @xmath159 on @xmath154 and @xmath31 respectively .
[ thom ] there exists a 2-dimensional submanifold @xmath160 such that @xmath161)=pd(k_{\omega})\in h_2(x)$ ] and @xmath162)=pd(k_{\tilde{\omega}})\in h_2(\tilde{x})$ ] .
let @xmath163 be a @xmath7-tamed almost complex structure in @xmath23 which induces a complex structure on @xmath164 as @xmath165 assume @xmath166 $ ] is a continuous increasing function satisfying @xmath167 another almost complex structure @xmath168 in @xmath164 is defined as @xmath169 it is easy to check that @xmath168 is @xmath7-tamed and @xmath170 in @xmath171 .
let @xmath172 and @xmath173 be the canonical bundles of @xmath23 and @xmath24 , respectively , and let @xmath174 and @xmath175 denote the corresponding embeddings of zero sections . since @xmath176 is trivial on @xmath31 , we can find a global section @xmath177 of @xmath176 and a thom class @xmath178 such that @xmath179 in @xmath171 and @xmath180 in @xmath181 .
another nonzero @xmath182-form in @xmath31 is constructed as @xmath183 in @xmath171 , we have @xmath184 @xmath177 and @xmath185 give two local trivializations of @xmath186 with transition function @xmath187 .
since @xmath188 arg@xmath189 , we can normalize the frame of @xmath190 such that @xmath191 .
hence @xmath192 can be extended to @xmath193 via constant function and form a thom class @xmath194 satisfying 1 .
@xmath195 in @xmath196 .
@xmath194 is independent of the coordinates @xmath158 in @xmath190 . in particular , @xmath197 in @xmath198 .
it is clear that these 2-forms @xmath199 and @xmath200 are equivalent in @xmath154 and vanish in @xmath201 and @xmath202 respectively . using these representations ,
we can find a 2-submanifold @xmath203 supp@xmath204 which is poincar dual to @xmath13 in @xmath23 , and dual to @xmath205 in @xmath24 .
the main theorem can be proved now .
suppose @xmath24 is obtained from @xmath23 by applying a luttinger surgery along @xmath1 .
let us first consider the case in which @xmath23 is minimal . by proposition [ minimality ]
, @xmath206 is also minimal .
let @xmath207 and @xmath208 denote the canonical classes of @xmath23 and @xmath24 respectively .
by lemma [ thom ] , there exists a submanifold @xmath160 such that @xmath161)=pd(k_{\omega})$ ] and @xmath162)=pd ( k_{\tilde{\omega}})$ ] .
we also know that @xmath209 in @xmath154 .
so @xmath210 @xmath211 = \int_s\omega=\int_s\tilde{\omega}=k_{\tilde{\omega}}\cdot [ \tilde{\omega}]\ ] ] thus the kodaira dimensions of @xmath23 and @xmath24 coincide .
if @xmath23 is not minimal , we can blow down @xmath23 along symplectic @xmath149 spheres disjoint from @xmath1 to a minimal model .
these spheres are contained in @xmath154 and the same procedure can be applied to @xmath24 , so we can argue as above .
theorem [ kod ] can be used to distinguish non - diffeomorphic manifolds . in @xcite , several symplectic manifolds homeomorphic but not diffeomorphic to non - minimal rational surfaces
are constructed . with @xmath212 for the building blocks , it also easily follows from theorem [ kod ] that they are exotic .
[ omega ] 1 .
the main theorem is proved based on the invariance of @xmath213 $ ] and @xmath214 . actually , the class @xmath153 ^ 2 $ ] is also preserved since the volume is invariant under a luttinger surgery . theorem [ kod ] is expected , in light of auroux s question 2.6 in @xcite : + + _ let @xmath215 be two integral compact symplectic 4-manifolds with the smae @xmath216 , [ \omega]^2)$ ] .
is it always possible to obtain @xmath217 from @xmath218 by a sequence of luttinger surgeries ? _ + 2 .
it is well known that the dolgachev surfaces @xmath219 obtained by performing two logarithmic transforms with multiplicities @xmath220 to @xmath221 have @xmath222 .
so a generalized logarithmic transform may not preserve @xmath17 ( see a related discussion in @xcite ) .
in this section we apply theorem [ kod ] to study the effect of luttinger surgeries on symplectic 4-manifolds with @xmath223 .
we start by analyzing how homology changes under a general torus surgery .
suppose @xmath23 is a smooth 4-manifold and @xmath30 is an embedded 2-torus with trivial normal bundle .
moreover , @xmath224 are defined as in section [ construction ] . [ [ section ] ] to compare the homology of @xmath23 and @xmath24
, we need to compare both of them with the homology of @xmath35 .
the inclusion @xmath225 induces homomorphisms @xmath226 and @xmath227 in homology .
we often use @xmath228 to denote @xmath229 and @xmath230 to denote @xmath231 .
we also use @xmath232 to denote the dimension of any @xmath233-vector space @xmath234 .
the following lemma is a well know fact , for which we offer a geometric argument .
[ mul ] @xmath235\in \ker i_1 $ ] if and only if @xmath236\ne 0 $ ] in @xmath237 .
suppose @xmath238=0 $ ] in @xmath239 , i.e. @xmath240=0 $ ] in @xmath241 for some positive integer @xmath242 .
thus @xmath242 copies of @xmath54 bounds an oriented surface @xmath234 in @xmath35 . extend @xmath234 by @xmath242 normal disks inside the tubular neighborhood to obtain a closed oriented surface @xmath243 intersecting with @xmath1 at @xmath242 points with the same sign .
this implies in particular that @xmath236\ne 0 $ ] in @xmath237 .
conversely , suppose @xmath236\ne 0 $ ] in @xmath237 , then there exists a closed oriented surface @xmath108 in @xmath23 intersecting @xmath1 with nonzero algebraic intersection numbers , say @xmath242 .
we may assume that the intersection is transverse with @xmath244 positive intersection points and @xmath116 negative intersection points .
we can further assume that @xmath108 intersects the closure of @xmath31 at @xmath245 normal disks , @xmath244 of those having positive orientations , the remaining @xmath116 disks having negative orientations .
this implies that the complement of those disks in @xmath108 is an oriented surface in @xmath35 , whose boundary is homologous to @xmath246 , and thus @xmath238 $ ] is zero . when we consider the integral homology , lemma [ mul ] immediately implies [ mulz ] if @xmath236=0 $ ] in @xmath247 , then @xmath248 $ ] is a non - torsion class in @xmath249 .
consider the mayer - vietoris sequence @xmath250 where @xmath251 and @xmath252 with @xmath253 induced by inclusions .
[ meridian ] 1 .
@xmath254 and @xmath255 is surjective .
2 . @xmath256\neq 0\\ 2 & \hbox{if } i_1[\mu ] = 0 \end{array}\right.\ ] ] and @xmath257 is injective if and only if @xmath235\notin \ker i_1 $ ] .
3 . @xmath258>\ ] ] 4 .
if @xmath236=0\in h_2(x)$ ] , then @xmath259 is surjective . 1 .
it is clear that any class @xmath260 in @xmath261 can be represented by a 1-cycle @xmath262 disjoint from @xmath1 .
@xmath262 is also disjoint from @xmath36 if the neighborhood @xmath31 is small enough .
so @xmath263=0 $ ] .
@xmath264 implies that @xmath265 is surjective .
2 . we know
@xmath266 . since @xmath267>$ ] , @xmath268\neq 0 \\ < [ \mu ] > & \hbox{if } i_1[\mu ] = 0 \end{array}\right.\ ] ] and @xmath257 is injective if and only if @xmath238\neq 0 $ ] .
the rank of im@xmath269 is given from @xmath270im@xmath271 .
3 . the sequence induces a short exact sequence @xmath272 @xmath254 implies that @xmath273 because @xmath265 is surjective , we also have @xmath274 if @xmath275 , \gamma_1 , \gamma_2\}$ ] is a basis of @xmath61 , then @xmath276 , 0),(\gamma_1,\gamma_1 ) , ( \gamma_2,\gamma_2)>$ ] and @xmath277 . for @xmath278 , @xmath279 if and only if @xmath280im@xmath257 , or @xmath281 $ ] for some @xmath123
. so @xmath282>$ ] and @xmath283>\ ] ] 4 .
@xmath284=0\in h_2(x ) & \leftrightarrow & [ \mu]\neq 0\in h_1(y ) & ( \hbox{by lemma \ref{mul } } ) \\ & \leftrightarrow & \rho_1\hbox { injective } & ( \hbox{by part(2)})\\ & \leftrightarrow & \partial_2=0 & ( \hbox{exactness})\\ & \leftrightarrow & \nu_2\hbox { surjective } & ( \hbox{exactness } ) \end{array}\ ] ] since @xmath236=0 $ ] also implies @xmath285 , @xmath286 has to be surjective .
all the results hold if we replace @xmath23 , @xmath1 , @xmath54 by @xmath287 and @xmath288 .
now , we are ready to compare @xmath23 and @xmath24 .
lemma [ meridian ] , applied to torus surgeries , gives [ compare ] if @xmath24 is obtained from @xmath23 via a torus surgery , then 1
. @xmath291 , @xmath292 .
2 . @xmath293=0=i_1[\tilde \mu]$ or $ i_1[\mu]\neq 0 \neq i_1[\tilde \mu]$}\\ -1 & \hbox{if $ i_1[\mu]=0 $ and $ i_1[\tilde \mu]\ne 0$}\\ 1 & \hbox{if $ i_1[\mu]\ne 0 $ and $ i_1[\tilde \mu]= 0 $ } \end{array}\right . \ ] ] 3 .
@xmath294 and @xmath295 . 1 . obvious .
2 . since @xmath254
, we can conclude that @xmath296\neq 0 \\ b_1(y ) & \hbox{if } i_1[\mu ] = 0 .
\end{array}\right.\ ] ] the same is true for @xmath297 with @xmath238 $ ] replaced by @xmath298 $ ] .
the proof is finished by comparing @xmath299 and @xmath297 .
the first inequality is given by part ( 2 ) .
the second inequality follows from part ( 1 ) and the first inequality .
the next result concerns with the intersection forms .
[ comparez ] suppose @xmath23 and @xmath24 are defined as above . if @xmath236 $ ] is a torsion class in @xmath247 and the intersection form @xmath300 is odd , then @xmath301 is odd as well . in particular ,
if both @xmath236 $ ] and @xmath302 $ ] are torsion , then @xmath24 and @xmath23 have the same intersection form .
since @xmath300 is odd , there exists a closed oriented surface @xmath303 in @xmath23 such that @xmath304 is odd . by lemma [ meridian](4 ) , @xmath305\in \hbox{im}\nu_2'$ ] and @xmath303
can be chosen such that @xmath306 .
thus , @xmath303 is contained in @xmath24 , and hence , @xmath301 is also odd . by proposition [ k3 ] , if a symplectic manifold @xmath0 with @xmath27 has an almost toric structure @xmath308 and if we apply a luttinger surgery along a smooth fiber of @xmath130 , the new manifold @xmath19 is diffeomorphic to @xmath0 .
such phenomenon is still true for any 4-manifold with @xmath307 .
moreover , we have the stronger theorem [ int2 ] . proposition [ minimality ]
allows us to reduce to the case where @xmath0 is minimal .
we first show that @xmath101 is diffeomorphic to @xmath23 .
observe that the diffeomorphism types of minimal manifolds with @xmath307 are distinguished by their euler numbers and intersection forms .
since such manifolds have @xmath148 , the homology classes of lagrangian tori are torsion .
thus , both quantities are preserved by proposition [ compare ] and [ comparez ] . to show further that @xmath100 and @xmath0 are symplectomorphic to each other
, it is enough to show that @xmath7 is cohomologous to @xmath99 ( @xcite ) .
if @xmath23 is diffeomorpic to @xmath309 , the symplectic structure is determined by the volume @xmath153 ^ 2 $ ] , which is preserved by remark [ omega](1 ) .
when @xmath23 is ruled , @xmath310 is either generated by @xmath207 and the poincar dual to the homology class of a fiber @xmath311 , or by @xmath13 and @xmath153 $ ] .
hence the class of @xmath7 is determined by @xmath12 $ ] , @xmath153 ^ 2 $ ] and @xmath153(f)$ ] . as mentioned above ,
the first two quantities are preserved .
by @xcite the fiber sphere can be chosen to be disjoint from @xmath1 , so it follows that the last quantity is also preserved .
a symplectic cy surface is a symplectic 4-manifold with torsion canonical class , or equivalently , a minimal symplectic 4-manifold with @xmath312 . by theorem [ kod ] and proposition [ minimality ]
, we have [ cy1 ] a luttinger surgery is a symplectic cy surgery in dimension four .
there is a homological classification of symplectic cy surfaces in @xcite and @xcite .
[ cy2 ] a symplectic cy surface is an integral homology k3 , an integral homology enriques surface or a rational homology torus bundle over torus .
the following table lists possible rational homological invariants of symplectic cy surfaces @xcite : @xmath313 [ cols="^,^,^,^,^,^",options="header " , ] @xmath313 it follows from propositions [ compare ] , [ cy1 ] , theorem [ cy2 ] and the table above .
it is also speculated that a symplectic cy surface is diffeomorphic to the k3 surface , the enriques surface or a torus bundle over torus .
thus we make the following [ 00 ] if @xmath23 is a k3 surface , or an enriques surface , then under a luttinger surgery along any embedded lagrangian torus , @xmath101 is diffeomorphic to x. as for torus bundles over torus , we have [ torus ] any smooth oriented torus bundle @xmath23 over torus possesses a symplectic structure @xmath7 such that @xmath10 can be obtained by applying luttinger surgeries to @xmath314 . in the list of torus bundles over torus in @xcite ,
any manifold in classes ( a ) , ( b ) and ( d ) has a lagrangian bundle structure . for any such manifold ,
it is not hard to verify conjecture [ torus ] via luttinger surgery along lagrangian fibers . [
44 ] 1 .
conjectures [ 00 ] and [ torus ] are clearly related to question 2.6 in @xcite .
2 . there is another symplectic cy surgery in dimension six , the symplectic conifold transition .
if @xmath315 with @xmath316 contains disjoint lagrangian spheres @xmath317 with homology relations generated by @xmath318=0 $ ] with all @xmath319 , smith , thomas , yau ( @xcite ) construct from @xmath315 a new symplectic manifold @xmath320 with @xmath321 and smaller @xmath322 .
we notice that there is a parametrized luttinger surgery in higher dimension and believe it also should be a symplectic cy surgery .
this will be discussed elsewhere .
in this section , we will introduce topological preferred framings and compare them with the lagrangian framing for lagrangian tori in @xmath223 symplectic 4-manifolds .
suppose @xmath23 is a smooth 4-manifold and @xmath30 is an embedded 2-torus with trivial normal bundle .
recall that a framing is a diffeomorphism @xmath41 for a tubular neighborhood @xmath31 of @xmath1 such that @xmath42 and a longitudinal curve of @xmath48 is a lift @xmath323 of some simple closed curve @xmath44 in @xmath36 .
let @xmath324|\gamma_\varphi : \hbox { longitudinal curve of } \varphi>\ ] ] @xmath325 is a subgroup of @xmath326 and it induces a decomposition of @xmath326 : @xmath327>\oplus h_{1,\varphi}.\ ] ] conversely , any rank 2 subgroup @xmath328 of @xmath61 such that @xmath235 $ ] and @xmath328 generate @xmath61 corresponds to a framing of @xmath1 . in @xcite , luttinger introduced a version of topological preferred framings of lagrangian tori in @xmath329 .
it requires that @xmath325 is in the kernel of @xmath330 . on the other hand , fintushel and stern ( @xcite ) defined null - homologous framings for a null - homologous torus via @xmath331 ( seemingly , under the assumption that @xmath261 vanishes , though not explicitly mentioned ) .
[ tprefer ] suppose @xmath1 is null - homologous , i.e. , @xmath236=0 $ ] in @xmath247 . a framing @xmath48 is called a topological preferred framing if @xmath332\in \ker i_2^{\mathbb{z}}$ ] . here , @xmath333 is a longitudinal torus of @xmath48 given by @xmath70 , @xmath45 . in order to compare various preferred framings and the lagrangian framing , we need to investigate the relation of the maps @xmath336 and @xmath337 given by and .
let @xmath35 be a smooth oriented 4-manifold with boundary @xmath338 . 1 .
consider the exact sequence @xmath346 it induces a short exact sequence @xmath347 by lefschetz duality and universal coefficient theorem , @xmath348 and @xmath349 .
so implies that @xmath350 which is ( 1 ) .
2 . consider the dual pairing @xmath351 + because the maps @xmath336 and @xmath352 are induced by embedding and restriction , this pairing is natural , i.e. , for @xmath353 and @xmath354 , @xmath355 + there is an isomorphism of long exact sequences induced naturally by lefschetz and poincar dualities : @xmath356 & & \downarrow \cap [ y ] & & \downarrow \cap [ z ] & & \downarrow \cap [ y ] & \\ \cdots \stackrel{i_{3}}{\longrightarrow } & h_3(y ) & \stackrel{\delta_3}{\longrightarrow } & h_3(y , z ) & \stackrel{\partial_{2}}{\longrightarrow } & h_2(z ) & \stackrel{i_{2}}{\longrightarrow } & h_2(y ) & \stackrel{\delta_2}{\longrightarrow } \cdots \end{array}\ ] ] + using this diagram , the dual pairing induces the intersection pairing : @xmath357 + given @xmath358 , there exists @xmath359 such that @xmath360 .
let @xmath361 be the lefschetz dual of @xmath362 in @xmath363 .
for any @xmath364 , @xmath365 it shows that @xmath366 . from part ( 1 ) , @xmath367 so @xmath368 .
similar argument shows that @xmath344 .
3 . suppose @xmath369 , then @xmath370 and @xmath337 is the zero map by part ( 1 ) .
let @xmath371 be two nonisotopic embedded tori in @xmath36 intersecting in a curve @xmath262 transversely . since @xmath338 , @xmath372\cap [ t_2]=[c]\neq 0 $ ] in @xmath373 .
meanwhile , each @xmath374 bounds a 3-manifold @xmath375 in @xmath35 .
@xmath376 is a 2-cycle whose boundary is @xmath262 and @xmath377 $ ] is in the kernel of @xmath336 , which contradicts the assumption that @xmath336 is injective .
here is a geometric interpretation of this lemma .
assume @xmath378 is an integral class of @xmath335 and @xmath262 is a closed curve in @xmath36 such that @xmath377\cdot z_2\neq 0 $ ] in @xmath36 .
there exists a relative 3-cycle @xmath379 in @xmath380 such that @xmath381=z_2 $ ] .
in particular , we can assume that @xmath379 intersects @xmath36 transversely and @xmath382 intersects @xmath262 transversely at @xmath383 and @xmath384 in @xmath36 with positive and negative intersections respectively .
furthermore , we can give a collar structure @xmath385 near @xmath36 and assume @xmath386 .
if we push @xmath262 to @xmath387 in the interior of @xmath35 , then @xmath388 and @xmath379 intersect transversely at @xmath389 and @xmath390 with positive and negative intersections respectively .
hence @xmath391=i_1([c])$ ] and @xmath392\cdot [ w]=[c]\cdot [ \partial w]=p - n=[c]\cdot z_2\neq 0\ ] ] so @xmath377 $ ] can not be in @xmath334 . 1 .
part ( 1 ) of lemma [ kernel ] is still true in arbitrary dimension . if @xmath35 is a @xmath393-dimensional manifold with connected boundary @xmath36 and @xmath394 denotes the homomorphism induced by the inclusion @xmath395 , then @xmath396 for @xmath397 .
2 . part ( 3 ) of lemma [ kernel ] is pointed out by robert gompf . 1 .
let @xmath399 be the trivial knot in @xmath400 and @xmath401 .
the complement of the torus @xmath402 is @xmath403 if @xmath404 denote the isotopy classes of these two @xmath53 and @xmath405 , then @xmath406 , [ m ] , [ l]>$ ] and @xmath334 has rank 1 which is generated by @xmath407 $ ] . on the other hand ,
@xmath335 is generated by @xmath408 , [ l\times m]$ ] and has rank 2 . + in general , if @xmath409 is any knot in @xmath400 and @xmath303 is a seifert surface with boundary @xmath409 , we can define @xmath410 and @xmath411 as above and choose @xmath242 as the push - off of @xmath409 in @xmath303 .
then @xmath35 and @xmath412 have isomorphic homology groups and @xmath334 is still generated by @xmath242 , which bounds the surface @xmath303 .
similarly , @xmath335 has rank 2 and is generated by @xmath408 , [ l\times m]$ ] .
they bound @xmath413 and @xmath414 respectively . in @xcite ,
fintushel and stern use these manifolds as building blocks to define knot surgery in 4-manifolds .
+ in the next example , the results of lemma [ kernel ] are not obvious .
let @xmath415 be a ruled surface and the loop @xmath416 be a lift of a loop in @xmath417 .
we can construct a torus @xmath1 in @xmath23 as the product of @xmath47 and some circle @xmath116 in the fiber . if @xmath418 is a meridian of @xmath1 and @xmath419 is nontrivial in @xmath420 , it is easy to show that @xmath334 is generated by a push - off of @xmath116 . but @xmath335 is not obvious even when @xmath421 is the trivial bundle . by lemma [ kernel ] , we know that @xmath335 has rank 2 and is generated by @xmath422 $ ] and @xmath423 $ ] .
2 . let @xmath424 be the clifford torus embedded in the rational manifold @xmath425 .
the group @xmath373 is generated by @xmath426 , [ b]$ ] and the meridian @xmath235 $ ] .
it is easy to show that @xmath427 , [ b]>$ ] has rank 2 and @xmath428>$ ] .
+ in general , if @xmath23 is simply connected and @xmath30 is a torus with trivial normal bundle , then @xmath429 if and only if @xmath236=0 $ ] in @xmath237 .
if @xmath430 , it follows from lemma [ meridian ] that such surgery will not change the homology for any torus surgery .
@xmath444\in \ker i_2^{\mathbb{q}}\\ & \leftrightarrow & < [ l_{\varphi}]>\subset \ker i_2^{\mathbb{q}}\\ & \leftrightarrow & \mathbf{ann}(<[l_{\varphi}]>)\supset \mathbf{ann}(\ker i_2^{\mathbb{q}})\\ & \leftrightarrow & \ker i_1^{\mathbb{q}}\subset h_{1,\varphi}\otimes { \mathbb{q}}. \ \hbox{(lemma \ref{kernel})}\end{aligned}\ ] ] 1 .
since @xmath236=0 $ ] in @xmath247 , there exists a 3-chain @xmath379 such that @xmath446 .
we can assume that @xmath379 intersects @xmath36 transversely .
in fact , we can choose a framing @xmath41 such that @xmath447 , where @xmath448 .
then @xmath449 is a longitudinal torus of @xmath48 and @xmath450 is a relative 3-cycle of @xmath380 with @xmath451 .
so @xmath452\in \ker i_2^{\mathbb{z}}$ ] and @xmath48 is a topological preferred framing .
@xmath332\in \ker i_2^{\mathbb{z}}$ ] implies that @xmath453)\supset \mathbf{ann}_{\mathbb{z}}(\ker i_2^{\mathbb{z}})$ ] .
it is easy to observe that @xmath454>)=h_{1,\varphi}$ ] . by lemma [ zker ] , @xmath455)=h_{1,\varphi}.\ ] ] if @xmath236 $ ] is torsion in @xmath23 , proposition [ exist](1 ) may fail in two situations .
first , there may exist @xmath456 such that @xmath457 but @xmath458 for some nonzero integer @xmath5 .
so we can only define rational topological preferred framings .
second , @xmath235 $ ] and @xmath435 might not generate the group @xmath326 . in this case , rational topological preferred framings also do not exist . 1 . in knot theory
, the notion of preferred framings is similar to that of definition [ tprefer ] .
let @xmath459 be an integral homology 3-sphere and @xmath460 be a knot .
if @xmath328 is a tubular neighborhood of @xmath409 , a diffeomorphism @xmath461 satisfying @xmath462 is called a framing of @xmath409 .
furthermore , @xmath463 is called a preferred framing if @xmath464 is homologically trivial in @xmath465 . for any knot @xmath409 in @xmath459 ,
preferred framings exist and are unique up to isotopy ( @xcite ) .
it is easy to see from proposition [ exist ] that luttinger s definition coincides with definition [ tprefer ] when @xmath6 .
3 . in @xcite ,
an invariant @xmath466 is defined when @xmath236=0 $ ] and @xmath1 has a unique topological preferred framing @xmath467 .
assume @xmath468 is the lagrangian preferred framing .
then @xmath469 if and only if @xmath470 . otherwise , @xmath466 is the smallest positive integer @xmath5 such that @xmath471+[\gamma_\varphi]\in h_{1,\varphi_{lag}}$ ] for some @xmath472\in h_{1,\varphi_0}$ ] .
[ r1k ] suppose @xmath23 is a smooth 4-manifold and @xmath30 is a torus with trivial normal bundle such that @xmath236=0 $ ] in @xmath442 and @xmath48 is a framing of @xmath1 .
let @xmath474 be constructed from @xmath23 via @xmath473-surgery along @xmath475 . 1 .
if @xmath48 is a rational topological preferred framing of @xmath1 , then @xmath24 satisfies @xmath476 for any @xmath47 and @xmath5 .
if @xmath477 for any @xmath47 and @xmath5 , then @xmath48 is a rational topological preferred framing of @xmath1 . 1 . by lemma [ meridian](3 ) , we have @xmath478\neq 0 \\ r(h_1(y ) ) & \hbox{if } i_1[\mu]=0 . \end{array}\right.\ ] ] lemma [ mul ] implies that @xmath238\neq 0 $ ] in @xmath479 .
since @xmath48 is a rational topological preferred framing , proposition [ rexist ] implies that @xmath235+k[\gamma_\varphi]\notin \ker i_1 $ ] for any integer @xmath5 and @xmath472\in h_{1,\varphi}$ ] .
so @xmath480 if @xmath24 is given via @xmath72-surgery .
we first prove that any @xmath481 lies in @xmath325 .
let @xmath482+t[\gamma_\varphi]$ ] for some @xmath483 and @xmath44 ( recall that @xmath62 is a lift of @xmath47 ) . for @xmath484 , the meridian of @xmath56 in @xmath24 satisfies @xmath485=[\mu]+kt[\gamma_\varphi]=[\mu]+k(a - s[\mu])=(1-sk)[\mu]+ka\ ] ] so + @xmath486+ka ) > & $ ] ( by ) @xmath487 ) > & ( a\in \ker i_1^{\mathbb{z}})\\ & \cong & h_1(y;{\mathbb{z}})/<i_1^{\mathbb{z}}[\mu ] > \end{array}$ ] + because @xmath235 $ ] is essential in @xmath35 and @xmath5 is arbitrary , @xmath488 should be zero and @xmath489 . otherwise , @xmath261 has infinitely many torsion classes with different orders .
+ tensoring with @xmath233 , we have @xmath490 by proposition [ rexist ] , @xmath48 is a rational topological preferred framing .
[ 1k ] suppose @xmath261 has no torsion and @xmath1 is null - homologous .
then a framing @xmath48 of @xmath1 is a topological preferred framing if and only if @xmath477 for any @xmath474 obtained from @xmath23 via @xmath473-surgery .
assume @xmath48 is a topological preferred framing .
consider the 3-chain @xmath379 given in the proof of proposition [ exist ] .
it is clear that a meridian @xmath54 intersects @xmath379 at one point .
so @xmath248\cdot [ w]=\pm 1 $ ] and @xmath248 $ ] is a primitive class .
similarly , the simple closed curve @xmath288 has class @xmath235+k[\gamma_\varphi]$ ] and is homotopic to a curve intersecting @xmath379 at one point .
hence @xmath491 $ ] is also a primitive class for any @xmath492 .
since @xmath249 is a free abelian group , we have @xmath493>\cong h_1(y,{\mathbb{z}})/<i_1^{\mathbb{z}}[\tilde{\mu}]>$ ] .
so @xmath494 by lemma [ meridian](3 ) .
conversely , if @xmath494 for any @xmath24 , the proof of proposition [ r1k](2 ) shows that @xmath48 is a rational topological preferred framing .
the assumption that @xmath247 has no torsion implies that @xmath48 is actually a topological preferred framing .
the knot surgery in @xcite is an example of @xmath473-surgeries .
suppose @xmath495 , @xmath409 is a knot in @xmath400 and @xmath496 .
let @xmath54 be the meridian of @xmath1 , @xmath260 the longitude of the preferred framing of @xmath409 and @xmath497 .
then @xmath498>$ ] and @xmath499 , [ a\times b]>$ ] .
consider the framings @xmath500 of @xmath1 where @xmath501 is generated by @xmath502+[a]$ ] and @xmath503 $ ] .
it is clear that @xmath500 is a topological preferred framing of @xmath1 exactly when @xmath504 .
if @xmath409 is the trivial knot and @xmath4=p[\mu]+[a]$ ] , the resulting manifold of @xmath72-surgery is @xmath505 and @xmath506 . if @xmath507 , @xmath508 has rank @xmath509 for any @xmath510 , but the torsion subgroups vary . propositions [ 1k ] and [ r1k ] show that @xmath500 is not a rational topological preferred framing
actually , such framings do not exist for @xmath1 . here
we provide topological constraints on the isotopy classes of lagrangian tori in many symplectic manifolds with non - positive kodaira dimension .
in particular , they imply that the invariant @xmath466 of fintushel and stern ( remark [ lambda](3 ) ) is zero if the manifold has non - positive kodaira dimension and vanishing integral @xmath511 .
recall that the lagrangian framing for lagrangian tori is defined in section [ construction ] . 1 .
if @xmath247 is torsion free and @xmath1 is null - homologous , then the lagrangian framing of @xmath1 is a topological preferred framing .
if @xmath236 $ ] is torsion then the lagrangian framing of @xmath1 is a rational topological preferred framing .
since @xmath512 and @xmath247 has no torsion , @xmath1 is null - homologous . for any @xmath101 given from @xmath23 by applying luttinger surgery along @xmath1
, @xmath101 is diffeomorphic to @xmath23 by theorem [ int2 ] .
now the claim follows from proposition [ prefer ] . when @xmath1 is essential , @xmath235\in\ker i_1^{\mathbb{q}}$ ] by lemma [ mul ] .
if @xmath514 , there exists @xmath44 such that @xmath515)\neq 0 $ ] . in the manifold @xmath516 , the class @xmath64=[\mu]+[\gamma_\varphi]$ ] is nonzero in @xmath239 . by proposition
[ compare ] , @xmath517 , which contradicts theorem [ int3 ] .
so @xmath518 and @xmath1 is completely essential .
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four manifolds with non - positive kodaira dimension are also derived . | <s>[INST]let @xmath0 be a symplectic 4-manifold with a lagrangian torus @xmath1 .
it was discovered by luttinger in @xcite that there is a family of surgeries along @xmath1 that produce symplectic @xmath2-manifolds .
this family is countable and indexed by the pairs @xmath3 , k)$ ] , where @xmath4 $ ] is an isotopy class of simple closed curves on @xmath1 and @xmath5 is an integer .
when @xmath6 and @xmath7 is the standard symplectic form @xmath8 , he also applied gromov s celebrated work in @xcite to show that , for any lagrangian torus @xmath1 , all the resulting symplectic manifolds are symplectomorphic to @xmath9 .
this does not occur in general ; a luttinger surgery often fails even to preserve homology . as a matter of fact
, many new exotic small manifolds are constructed via this surgery . in this note , we observe that the luttinger surgery preserves one basic invariant : [ kod ] the luttinger surgery preserves the symplectic kodaira dimension .
the symplectic kodaira dimension of a symplectic 4-manifold @xmath10 is defined by the products @xmath11 and @xmath12 $ ] , where @xmath13 is the symplectic canonical class ; if @xmath10 is minimal , then @xmath14 < 0\\ 0 & k_{\omega}^2=0\ and\ k_{\omega}\cdot [ \omega]=0 \\ 1 & k_{\omega}^2=0\ and\ k_{\omega}\cdot [ \omega]>0\\ 2 & k_{\omega}^2>0\ and\ k_{\omega}\cdot [ \omega ] > 0 \end{array}\right.\ ] ] for a general symplectic 4-manifold , the kodaira dimension is defined as the kodaira dimension of any of its minimal models . according to @xcite ,
@xmath15 is independent of the choice of symplectic form @xmath7 and hence is denoted by @xmath16 .
theorem [ kod ] is related to a question of auroux in @xcite ( see remarks [ omega ] and [ 44 ] ) .
furthermore , together with the elementary analysis of the homology change , the invariance of @xmath17 implies that [ int2 ] let @xmath0 be a symplectic 4-manifold with @xmath18 and @xmath19 be constructed from @xmath0 via a luttinger surgery .
then @xmath20 is symplectomorphic to @xmath10 . for minimal symplectic manifolds of kodaira dimension zero , i.e. , symplectic calabi - yau surfaces ,
we conclude that the luttinger surgery is a symplectic cy surgery .
moreover , together with the homology classification of such manifolds in @xcite , we have [ int3 ] suppose @xmath0 is a symplectic 4-manifold with @xmath21 and @xmath22 .
if @xmath19 is constructed from @xmath0 under a luttinger surgery , then @xmath23 and @xmath24 have the same integral homology type .
in fact , we conjecture that @xmath24 and @xmath23 in theorem [ int3 ] are diffeomorphic to each other . for symplectic cy surfaces with @xmath25 ,
the only known examples are torus bundles over torus .
we conjecture that they all can be obtained from @xmath26 via lutttinger surgeries ( conjecture [ torus ] ) .
theorems [ int2 ] and [ int3 ] provide topological constraints , phrased in terms of topological preferred framings ( see definition [ tprefer ] ) , on the existence of exotic lagrangian tori in such manifolds .
[ int4 ] let l be a lagrangian torus in @xmath0 .
if @xmath27 , or @xmath1 is null - homologous , @xmath21 and @xmath28 , then the lagrangian framing of @xmath1 is topological preferred . in particular ,
the invariant @xmath29 in @xcite vanishes whenever it is defined .
the organization of this paper is as follows . in section 2
, the construction of the luttinger surgery is reviewed .
we also discuss the lagrangian fibrations as the first application of this surgery . in section 3
, we establish the invariance of the symplectic kodaira dimension , which is the main result of this note . in section 4 , we prove theorems [ int2 ] and [ int3 ] . in section 5 , we apply these two theorems to derive constraints on framings of lagrangian tori in symplectic 4-manifolds with non - positive kodaira dimension . we are grateful to the referee for many useful suggestions which improve the exposition .
the first author would like to thank the following scholars for their insightful discussions and suggestions : anar akhmedov , inanc baykur , joel gomez , robert gompf , conan leung , weiwei wu and weiyi zhang .
the second author is grateful to the support of nsf .
in this section , we describe the luttinger surgery following @xcite .
applications to lagrangian fibrations are also discussed .
we assume all manifolds are oriented .
topologically , luttinger surgery is a framed torus surgery .
we start with a general description of framed torus surgeries .
let @xmath23 be a smooth 4-manifold and @xmath30 an embedded 2-torus with trivial normal bundle .
then let @xmath31 be a tubular neighborhood of @xmath1 .
if we assume @xmath32 is the complement of @xmath31 , @xmath33 and @xmath34 is a diffeomorphism , a new manifold @xmath24 can be constructed by cutting @xmath31 out of @xmath23 and gluing it back to @xmath35 along @xmath36 via @xmath37 : @xmath38 such surgery is called a @xmath39 @xmath40 .
it is often more explicit to describe this process via a framing of @xmath1 .
let @xmath23 , @xmath1 , @xmath31 and @xmath36 be given as above .
a diffeomorphism @xmath41 is called a framing of @xmath1 if @xmath42 .
let @xmath43 be the projection .
for any @xmath44 and @xmath45 , the lift @xmath46 of @xmath47 in @xmath36 is called a longitudinal curve of @xmath48 .
let @xmath49 be the induced map .
two framings @xmath50 are smoothly isotopic to each other if the map @xmath51 is homotopic to the identity map .
@xmath52 induces a @xmath53-bundle structure on @xmath36 .
a positive oriented fiber @xmath54 of @xmath36 is called a @xmath55 of @xmath1 . for @xmath24 in
, we will use @xmath56 to denote the torus @xmath57 .
notice that @xmath56 also inherits a framing @xmath58 and its meridian @xmath59 satisfies @xmath60=p[\mu]+k[\gamma_\varphi],\ ] ] in @xmath61 .
here @xmath62 is a longitudinal curve of @xmath48 and @xmath63 are coprime integers .
the diffeomorphism type of @xmath24 only depends on the class @xmath64 $ ] .
it is called a _ generalized logarithmic transform _ of @xmath23 along @xmath65 with multiplicity @xmath66 and auxiliary multiplicity @xmath5 , or of type @xmath67 ( see @xcite ) , and denoted as @xmath68 . for brevity
, we will call it a @xmath69-surgery .
if @xmath23 is a symplectic 4-manifold , weinstein s theorem states that there is a canonical framing for any lagrangian torus of @xmath23 .
let @xmath23 be a symplectic 4-manifoldand and @xmath1 a lagrangian torus of @xmath23 .
a framing @xmath48 of @xmath1 is called a lagrangian framing if @xmath70 is a lagrangian submanifold of @xmath23 for any @xmath71 .
topologically , a luttinger surgery is a @xmath72-surgery with respect to a lagrangian framing . in order to deal with the sympelctic structure , it is more convenient to use a square neighborhood rather than the disk neighborhood of @xmath1 as above . express the cotangent bundle @xmath73 as @xmath74 equipped with the canonical 2-form @xmath75 and let @xmath76 there exists a tubular neighborhood @xmath31 of @xmath1 and a symplectomorphism @xmath77 for small @xmath78 which satisfies @xmath79 in addition , given a simple closed curve @xmath47 on @xmath1
, we can choose the coordinates @xmath80 of @xmath81 such that @xmath82 let @xmath83 be an annular region and @xmath84 $ ] be a smooth increasing function such that @xmath85 for @xmath86 and @xmath87 for @xmath88 .
for any integer @xmath5 , we can define a diffeomorphism @xmath89 : @xmath90 observe that @xmath91 which follows from the relation @xmath92 for @xmath93 .
let @xmath94 and define @xmath95 via the following diagram @xmath96 then we can construct a new smooth manifold @xmath97 notice that , by , we have @xmath98 . thus @xmath24 carries a symplectic form @xmath99 induced by @xmath7 .
this process is called a _ luttinger surgery _ ( along the lagrangian torus @xmath1 ) . we know
that [ framing]@xcite any two lagrangian framings of a lagrangian torus are smoothly isotopic to each other .
hence the symplectomorphism type of @xmath100 only depends on the lagrangian isotopy class of @xmath1 , the isotopy class of @xmath47 in @xmath1 , and the integer @xmath5 .
therefore , @xmath101 is also denoted as @xmath102 .
it is worth mentioning that a luttinger surgery can be reversed .
let @xmath103 be the subsets @xmath104 and @xmath105 of @xmath24 .
we can apply the luttinger surgery to @xmath106 with coefficient @xmath107 to recover @xmath23 .
one natural source of lagrangian tori is smooth fibers of lagrangian fibrations .
let @xmath10 be a symplectic 4-manifold , and let @xmath108 be a 2-manifold ( with boundary or vertices ) .
a smooth map @xmath109 is called a lagrangian fibration if there exists an open dense subset @xmath110 such that @xmath111 is a compact lagrangian submanifold of @xmath23 for any @xmath112 .
@xmath23 is called lagrangian fibered if such a structure exists .
it is easy to see that any smooth fiber of a lagrangian fibration must be a torus .
moreover , we have [ fiber ] a luttinger surgery along a lagrangian fiber preserves the lagrangian fibration structure .
let @xmath113 be a lagrangian fibration and @xmath114 a generic fiber .
using notations from section 2.1 , it is shown in @xcite that there is a neighborhood @xmath115 of @xmath116 and @xmath117 with local charts @xmath77 and @xmath118 such that the diagram @xmath119 commutes . here
@xmath120 is the projection @xmath121 .
if @xmath122 is obtained by performing luttinger surgery along @xmath1 ( indexed by @xmath44 and @xmath123 ) , we can define a map @xmath124 as @xmath125 .
since @xmath126 , we have @xmath127 so @xmath128 is well - defined .
it is clear that @xmath128 is lagrangian and @xmath24 also possesses a lagrangian fibration structure .
lagrangian fibrations appear widely in toric geometry , integral systems and mirror symmetry .
we will discuss almost toric fibration introduced by symington in some detail .
an almost toric fibration of a symplectic 4-manifold @xmath0 is a lagrangian fibration @xmath113 with the following properties : for any critical point @xmath129 of @xmath130 , there exists a local coordinate @xmath131 near @xmath129 such that @xmath132 , @xmath133 , and @xmath130 has one of the forms @xmath134 an almost toric 4-manifold is a symplectic 4-manifold equipped with an almost toric fibration .
the base @xmath108 of an almost toric fibration has an affine structure with boundary and vertices . moreover , these three types of critical points project to vertices , edges and interior of @xmath108 respectively .
almost toric fibrations are classified by leung and symington : [ almost]@xcite let @xmath10 be a closed almost toric 4-manifold
. there are seven types of almost toric fibrations according to the homeomorphism type of the base @xmath108 . 1 .
@xmath135 or @xmath136 , @xmath108 is ( homeomorphic to ) a disk ; 2 . @xmath137 or @xmath138
, @xmath108 is a cylinder ; 3 . @xmath137 or @xmath138
, @xmath108 is a mbius band ; 4 .
the @xmath139 surface , @xmath108 is a sphere ; 5 . the enriques surface , @xmath108 is @xmath140 ; 6 .
a torus bundle over torus with monodromy @xmath141 @xmath108 is a torus ; 7 .
a torus bundle over the klein bottle with monodromy @xmath142 @xmath108 is a klein bottle .
an immediate consequence of this classification is the calculation of the symplectic kodaira dimension .
[ al ] if @xmath143 is an almost toric fibration , then @xmath144 .
moreover , @xmath21 if and only if the base @xmath108 is closed .
the effect of luttinger surgeries on almost toric fibrations is also easy to describe .
[ k3 ] suppose @xmath145 is an almost toric fibration and @xmath20 is obtained from @xmath0 by performing a luttinger surgery along a smooth fiber @xmath1 , then @xmath146 retains an almost toric fibration structure with the same base .
moreover , @xmath24 is diffeomorphic to @xmath23 if @xmath147 .
the first statement is given by lemma [ fiber ] . if @xmath147 , @xmath23 and @xmath24 are in one of the types ( 1)-(5 ) in theorem [ almost ] . in each of them ,
the list of manifolds are distinguished by the type of intersection forms and euler numbers .
so the second result for types ( 1)-(3 ) follows from proposition [ compare ] and the fact that homology classes of lagrangian tori in manifolds with @xmath148 are torsion .
it is clear for ( 4 ) and ( 5 ) from the classification .
propositions [ al ] and [ k3 ] provide examples of luttinger surgeries preserving the symplectic kodaira dimension . in the next section , we will show that it is true for any luttinger surgery .
in this section , we prove theorem [ kod ] . to proceed ,
we must first prove the invariance of minimality under luttinger surgery . a symplectic ( smooth ) @xmath149 class is a degree 2 homology class represented by an embedded symplectic ( smooth ) sphere with self - intersection @xmath149 .
a symplectic 4-manifold is called @xmath150 @xmath151
@xmath152 if it does not have any symplectic ( smooth ) @xmath149 class . the symplectic minimality is actually equivalent to smooth minimality .
[ minimality ] the luttinger surgery preserves the minimality .
since a luttinger surgery can be reversed and the reverse operation is also a luttinger surgery , it suffices to show that , if we start with a non - minimal symplectic 4-manifold , then after a luttinger surgery , the resulting symplectic manifold is still non - minimal .
but this is a direct consequence of the following fact in @xcite : [ disjoint ] given a lagrangian torus @xmath1 and a symplectic @xmath149 class , there is an embedded symplectic @xmath149 sphere in that class which is disjoint from @xmath1 .
now , we analyze the effect of luttinger surgery on the symplectic canonical class @xmath13 and the symplectic class @xmath153 $ ] .
recall that @xmath154 is an open submanifold of both @xmath23 and @xmath101 , and let @xmath155 and @xmath156 be the inclusions . to prepare for the following lemma
, we use the notations from section [ construction ] . for the sake of simplicity
, we will identify any object in @xmath23 with their image of @xmath48 and @xmath157 , @xmath158 will denote the coordinates of @xmath159 on @xmath154 and @xmath31 respectively .
[ thom ] there exists a 2-dimensional submanifold @xmath160 such that @xmath161)=pd(k_{\omega})\in h_2(x)$ ] and @xmath162)=pd(k_{\tilde{\omega}})\in h_2(\tilde{x})$ ] .
let @xmath163 be a @xmath7-tamed almost complex structure in @xmath23 which induces a complex structure on @xmath164 as @xmath165 assume @xmath166 $ ] is a continuous increasing function satisfying @xmath167 another almost complex structure @xmath168 in @xmath164 is defined as @xmath169 it is easy to check that @xmath168 is @xmath7-tamed and @xmath170 in @xmath171 .
let @xmath172 and @xmath173 be the canonical bundles of @xmath23 and @xmath24 , respectively , and let @xmath174 and @xmath175 denote the corresponding embeddings of zero sections . since @xmath176 is trivial on @xmath31 , we can find a global section @xmath177 of @xmath176 and a thom class @xmath178 such that @xmath179 in @xmath171 and @xmath180 in @xmath181 .
another nonzero @xmath182-form in @xmath31 is constructed as @xmath183 in @xmath171 , we have @xmath184 @xmath177 and @xmath185 give two local trivializations of @xmath186 with transition function @xmath187 .
since @xmath188 arg@xmath189 , we can normalize the frame of @xmath190 such that @xmath191 .
hence @xmath192 can be extended to @xmath193 via constant function and form a thom class @xmath194 satisfying 1 .
@xmath195 in @xmath196 .
@xmath194 is independent of the coordinates @xmath158 in @xmath190 . in particular , @xmath197 in @xmath198 .
it is clear that these 2-forms @xmath199 and @xmath200 are equivalent in @xmath154 and vanish in @xmath201 and @xmath202 respectively . using these representations ,
we can find a 2-submanifold @xmath203 supp@xmath204 which is poincar dual to @xmath13 in @xmath23 , and dual to @xmath205 in @xmath24 .
the main theorem can be proved now .
suppose @xmath24 is obtained from @xmath23 by applying a luttinger surgery along @xmath1 .
let us first consider the case in which @xmath23 is minimal . by proposition [ minimality ]
, @xmath206 is also minimal .
let @xmath207 and @xmath208 denote the canonical classes of @xmath23 and @xmath24 respectively .
by lemma [ thom ] , there exists a submanifold @xmath160 such that @xmath161)=pd(k_{\omega})$ ] and @xmath162)=pd ( k_{\tilde{\omega}})$ ] .
we also know that @xmath209 in @xmath154 .
so @xmath210 @xmath211 = \int_s\omega=\int_s\tilde{\omega}=k_{\tilde{\omega}}\cdot [ \tilde{\omega}]\ ] ] thus the kodaira dimensions of @xmath23 and @xmath24 coincide .
if @xmath23 is not minimal , we can blow down @xmath23 along symplectic @xmath149 spheres disjoint from @xmath1 to a minimal model .
these spheres are contained in @xmath154 and the same procedure can be applied to @xmath24 , so we can argue as above .
theorem [ kod ] can be used to distinguish non - diffeomorphic manifolds . in @xcite , several symplectic manifolds homeomorphic but not diffeomorphic to non - minimal rational surfaces
are constructed . with @xmath212 for the building blocks , it also easily follows from theorem [ kod ] that they are exotic .
[ omega ] 1 .
the main theorem is proved based on the invariance of @xmath213 $ ] and @xmath214 . actually , the class @xmath153 ^ 2 $ ] is also preserved since the volume is invariant under a luttinger surgery . theorem [ kod ] is expected , in light of auroux s question 2.6 in @xcite : + + _ let @xmath215 be two integral compact symplectic 4-manifolds with the smae @xmath216 , [ \omega]^2)$ ] .
is it always possible to obtain @xmath217 from @xmath218 by a sequence of luttinger surgeries ? _ + 2 .
it is well known that the dolgachev surfaces @xmath219 obtained by performing two logarithmic transforms with multiplicities @xmath220 to @xmath221 have @xmath222 .
so a generalized logarithmic transform may not preserve @xmath17 ( see a related discussion in @xcite ) .
in this section we apply theorem [ kod ] to study the effect of luttinger surgeries on symplectic 4-manifolds with @xmath223 .
we start by analyzing how homology changes under a general torus surgery .
suppose @xmath23 is a smooth 4-manifold and @xmath30 is an embedded 2-torus with trivial normal bundle .
moreover , @xmath224 are defined as in section [ construction ] . [ [ section ] ] to compare the homology of @xmath23 and @xmath24
, we need to compare both of them with the homology of @xmath35 .
the inclusion @xmath225 induces homomorphisms @xmath226 and @xmath227 in homology .
we often use @xmath228 to denote @xmath229 and @xmath230 to denote @xmath231 .
we also use @xmath232 to denote the dimension of any @xmath233-vector space @xmath234 .
the following lemma is a well know fact , for which we offer a geometric argument .
[ mul ] @xmath235\in \ker i_1 $ ] if and only if @xmath236\ne 0 $ ] in @xmath237 .
suppose @xmath238=0 $ ] in @xmath239 , i.e. @xmath240=0 $ ] in @xmath241 for some positive integer @xmath242 .
thus @xmath242 copies of @xmath54 bounds an oriented surface @xmath234 in @xmath35 . extend @xmath234 by @xmath242 normal disks inside the tubular neighborhood to obtain a closed oriented surface @xmath243 intersecting with @xmath1 at @xmath242 points with the same sign .
this implies in particular that @xmath236\ne 0 $ ] in @xmath237 .
conversely , suppose @xmath236\ne 0 $ ] in @xmath237 , then there exists a closed oriented surface @xmath108 in @xmath23 intersecting @xmath1 with nonzero algebraic intersection numbers , say @xmath242 .
we may assume that the intersection is transverse with @xmath244 positive intersection points and @xmath116 negative intersection points .
we can further assume that @xmath108 intersects the closure of @xmath31 at @xmath245 normal disks , @xmath244 of those having positive orientations , the remaining @xmath116 disks having negative orientations .
this implies that the complement of those disks in @xmath108 is an oriented surface in @xmath35 , whose boundary is homologous to @xmath246 , and thus @xmath238 $ ] is zero . when we consider the integral homology , lemma [ mul ] immediately implies [ mulz ] if @xmath236=0 $ ] in @xmath247 , then @xmath248 $ ] is a non - torsion class in @xmath249 .
consider the mayer - vietoris sequence @xmath250 where @xmath251 and @xmath252 with @xmath253 induced by inclusions .
[ meridian ] 1 .
@xmath254 and @xmath255 is surjective .
2 . @xmath256\neq 0\\ 2 & \hbox{if } i_1[\mu ] = 0 \end{array}\right.\ ] ] and @xmath257 is injective if and only if @xmath235\notin \ker i_1 $ ] .
3 . @xmath258>\ ] ] 4 .
if @xmath236=0\in h_2(x)$ ] , then @xmath259 is surjective . 1 .
it is clear that any class @xmath260 in @xmath261 can be represented by a 1-cycle @xmath262 disjoint from @xmath1 .
@xmath262 is also disjoint from @xmath36 if the neighborhood @xmath31 is small enough .
so @xmath263=0 $ ] .
@xmath264 implies that @xmath265 is surjective .
2 . we know
@xmath266 . since @xmath267>$ ] , @xmath268\neq 0 \\ < [ \mu ] > & \hbox{if } i_1[\mu ] = 0 \end{array}\right.\ ] ] and @xmath257 is injective if and only if @xmath238\neq 0 $ ] .
the rank of im@xmath269 is given from @xmath270im@xmath271 .
3 . the sequence induces a short exact sequence @xmath272 @xmath254 implies that @xmath273 because @xmath265 is surjective , we also have @xmath274 if @xmath275 , \gamma_1 , \gamma_2\}$ ] is a basis of @xmath61 , then @xmath276 , 0),(\gamma_1,\gamma_1 ) , ( \gamma_2,\gamma_2)>$ ] and @xmath277 . for @xmath278 , @xmath279 if and only if @xmath280im@xmath257 , or @xmath281 $ ] for some @xmath123
. so @xmath282>$ ] and @xmath283>\ ] ] 4 .
@xmath284=0\in h_2(x ) & \leftrightarrow & [ \mu]\neq 0\in h_1(y ) & ( \hbox{by lemma \ref{mul } } ) \\ & \leftrightarrow & \rho_1\hbox { injective } & ( \hbox{by part(2)})\\ & \leftrightarrow & \partial_2=0 & ( \hbox{exactness})\\ & \leftrightarrow & \nu_2\hbox { surjective } & ( \hbox{exactness } ) \end{array}\ ] ] since @xmath236=0 $ ] also implies @xmath285 , @xmath286 has to be surjective .
all the results hold if we replace @xmath23 , @xmath1 , @xmath54 by @xmath287 and @xmath288 .
now , we are ready to compare @xmath23 and @xmath24 .
lemma [ meridian ] , applied to torus surgeries , gives [ compare ] if @xmath24 is obtained from @xmath23 via a torus surgery , then 1
. @xmath291 , @xmath292 .
2 . @xmath293=0=i_1[\tilde \mu]$ or $ i_1[\mu]\neq 0 \neq i_1[\tilde \mu]$}\\ -1 & \hbox{if $ i_1[\mu]=0 $ and $ i_1[\tilde \mu]\ne 0$}\\ 1 & \hbox{if $ i_1[\mu]\ne 0 $ and $ i_1[\tilde \mu]= 0 $ } \end{array}\right . \ ] ] 3 .
@xmath294 and @xmath295 . 1 . obvious .
2 . since @xmath254
, we can conclude that @xmath296\neq 0 \\ b_1(y ) & \hbox{if } i_1[\mu ] = 0 .
\end{array}\right.\ ] ] the same is true for @xmath297 with @xmath238 $ ] replaced by @xmath298 $ ] .
the proof is finished by comparing @xmath299 and @xmath297 .
the first inequality is given by part ( 2 ) .
the second inequality follows from part ( 1 ) and the first inequality .
the next result concerns with the intersection forms .
[ comparez ] suppose @xmath23 and @xmath24 are defined as above . if @xmath236 $ ] is a torsion class in @xmath247 and the intersection form @xmath300 is odd , then @xmath301 is odd as well . in particular ,
if both @xmath236 $ ] and @xmath302 $ ] are torsion , then @xmath24 and @xmath23 have the same intersection form .
since @xmath300 is odd , there exists a closed oriented surface @xmath303 in @xmath23 such that @xmath304 is odd . by lemma [ meridian](4 ) , @xmath305\in \hbox{im}\nu_2'$ ] and @xmath303
can be chosen such that @xmath306 .
thus , @xmath303 is contained in @xmath24 , and hence , @xmath301 is also odd . by proposition [ k3 ] , if a symplectic manifold @xmath0 with @xmath27 has an almost toric structure @xmath308 and if we apply a luttinger surgery along a smooth fiber of @xmath130 , the new manifold @xmath19 is diffeomorphic to @xmath0 .
such phenomenon is still true for any 4-manifold with @xmath307 .
moreover , we have the stronger theorem [ int2 ] . proposition [ minimality ]
allows us to reduce to the case where @xmath0 is minimal .
we first show that @xmath101 is diffeomorphic to @xmath23 .
observe that the diffeomorphism types of minimal manifolds with @xmath307 are distinguished by their euler numbers and intersection forms .
since such manifolds have @xmath148 , the homology classes of lagrangian tori are torsion .
thus , both quantities are preserved by proposition [ compare ] and [ comparez ] . to show further that @xmath100 and @xmath0 are symplectomorphic to each other
, it is enough to show that @xmath7 is cohomologous to @xmath99 ( @xcite ) .
if @xmath23 is diffeomorpic to @xmath309 , the symplectic structure is determined by the volume @xmath153 ^ 2 $ ] , which is preserved by remark [ omega](1 ) .
when @xmath23 is ruled , @xmath310 is either generated by @xmath207 and the poincar dual to the homology class of a fiber @xmath311 , or by @xmath13 and @xmath153 $ ] .
hence the class of @xmath7 is determined by @xmath12 $ ] , @xmath153 ^ 2 $ ] and @xmath153(f)$ ] . as mentioned above ,
the first two quantities are preserved .
by @xcite the fiber sphere can be chosen to be disjoint from @xmath1 , so it follows that the last quantity is also preserved .
a symplectic cy surface is a symplectic 4-manifold with torsion canonical class , or equivalently , a minimal symplectic 4-manifold with @xmath312 . by theorem [ kod ] and proposition [ minimality ]
, we have [ cy1 ] a luttinger surgery is a symplectic cy surgery in dimension four .
there is a homological classification of symplectic cy surfaces in @xcite and @xcite .
[ cy2 ] a symplectic cy surface is an integral homology k3 , an integral homology enriques surface or a rational homology torus bundle over torus .
the following table lists possible rational homological invariants of symplectic cy surfaces @xcite : @xmath313 [ cols="^,^,^,^,^,^",options="header " , ] @xmath313 it follows from propositions [ compare ] , [ cy1 ] , theorem [ cy2 ] and the table above .
it is also speculated that a symplectic cy surface is diffeomorphic to the k3 surface , the enriques surface or a torus bundle over torus .
thus we make the following [ 00 ] if @xmath23 is a k3 surface , or an enriques surface , then under a luttinger surgery along any embedded lagrangian torus , @xmath101 is diffeomorphic to x. as for torus bundles over torus , we have [ torus ] any smooth oriented torus bundle @xmath23 over torus possesses a symplectic structure @xmath7 such that @xmath10 can be obtained by applying luttinger surgeries to @xmath314 . in the list of torus bundles over torus in @xcite ,
any manifold in classes ( a ) , ( b ) and ( d ) has a lagrangian bundle structure . for any such manifold ,
it is not hard to verify conjecture [ torus ] via luttinger surgery along lagrangian fibers . [
44 ] 1 .
conjectures [ 00 ] and [ torus ] are clearly related to question 2.6 in @xcite .
2 . there is another symplectic cy surgery in dimension six , the symplectic conifold transition .
if @xmath315 with @xmath316 contains disjoint lagrangian spheres @xmath317 with homology relations generated by @xmath318=0 $ ] with all @xmath319 , smith , thomas , yau ( @xcite ) construct from @xmath315 a new symplectic manifold @xmath320 with @xmath321 and smaller @xmath322 .
we notice that there is a parametrized luttinger surgery in higher dimension and believe it also should be a symplectic cy surgery .
this will be discussed elsewhere .
in this section , we will introduce topological preferred framings and compare them with the lagrangian framing for lagrangian tori in @xmath223 symplectic 4-manifolds .
suppose @xmath23 is a smooth 4-manifold and @xmath30 is an embedded 2-torus with trivial normal bundle .
recall that a framing is a diffeomorphism @xmath41 for a tubular neighborhood @xmath31 of @xmath1 such that @xmath42 and a longitudinal curve of @xmath48 is a lift @xmath323 of some simple closed curve @xmath44 in @xmath36 .
let @xmath324|\gamma_\varphi : \hbox { longitudinal curve of } \varphi>\ ] ] @xmath325 is a subgroup of @xmath326 and it induces a decomposition of @xmath326 : @xmath327>\oplus h_{1,\varphi}.\ ] ] conversely , any rank 2 subgroup @xmath328 of @xmath61 such that @xmath235 $ ] and @xmath328 generate @xmath61 corresponds to a framing of @xmath1 . in @xcite , luttinger introduced a version of topological preferred framings of lagrangian tori in @xmath329 .
it requires that @xmath325 is in the kernel of @xmath330 . on the other hand , fintushel and stern ( @xcite ) defined null - homologous framings for a null - homologous torus via @xmath331 ( seemingly , under the assumption that @xmath261 vanishes , though not explicitly mentioned ) .
[ tprefer ] suppose @xmath1 is null - homologous , i.e. , @xmath236=0 $ ] in @xmath247 . a framing @xmath48 is called a topological preferred framing if @xmath332\in \ker i_2^{\mathbb{z}}$ ] . here , @xmath333 is a longitudinal torus of @xmath48 given by @xmath70 , @xmath45 . in order to compare various preferred framings and the lagrangian framing , we need to investigate the relation of the maps @xmath336 and @xmath337 given by and .
let @xmath35 be a smooth oriented 4-manifold with boundary @xmath338 . 1 .
consider the exact sequence @xmath346 it induces a short exact sequence @xmath347 by lefschetz duality and universal coefficient theorem , @xmath348 and @xmath349 .
so implies that @xmath350 which is ( 1 ) .
2 . consider the dual pairing @xmath351 + because the maps @xmath336 and @xmath352 are induced by embedding and restriction , this pairing is natural , i.e. , for @xmath353 and @xmath354 , @xmath355 + there is an isomorphism of long exact sequences induced naturally by lefschetz and poincar dualities : @xmath356 & & \downarrow \cap [ y ] & & \downarrow \cap [ z ] & & \downarrow \cap [ y ] & \\ \cdots \stackrel{i_{3}}{\longrightarrow } & h_3(y ) & \stackrel{\delta_3}{\longrightarrow } & h_3(y , z ) & \stackrel{\partial_{2}}{\longrightarrow } & h_2(z ) & \stackrel{i_{2}}{\longrightarrow } & h_2(y ) & \stackrel{\delta_2}{\longrightarrow } \cdots \end{array}\ ] ] + using this diagram , the dual pairing induces the intersection pairing : @xmath357 + given @xmath358 , there exists @xmath359 such that @xmath360 .
let @xmath361 be the lefschetz dual of @xmath362 in @xmath363 .
for any @xmath364 , @xmath365 it shows that @xmath366 . from part ( 1 ) , @xmath367 so @xmath368 .
similar argument shows that @xmath344 .
3 . suppose @xmath369 , then @xmath370 and @xmath337 is the zero map by part ( 1 ) .
let @xmath371 be two nonisotopic embedded tori in @xmath36 intersecting in a curve @xmath262 transversely . since @xmath338 , @xmath372\cap [ t_2]=[c]\neq 0 $ ] in @xmath373 .
meanwhile , each @xmath374 bounds a 3-manifold @xmath375 in @xmath35 .
@xmath376 is a 2-cycle whose boundary is @xmath262 and @xmath377 $ ] is in the kernel of @xmath336 , which contradicts the assumption that @xmath336 is injective .
here is a geometric interpretation of this lemma .
assume @xmath378 is an integral class of @xmath335 and @xmath262 is a closed curve in @xmath36 such that @xmath377\cdot z_2\neq 0 $ ] in @xmath36 .
there exists a relative 3-cycle @xmath379 in @xmath380 such that @xmath381=z_2 $ ] .
in particular , we can assume that @xmath379 intersects @xmath36 transversely and @xmath382 intersects @xmath262 transversely at @xmath383 and @xmath384 in @xmath36 with positive and negative intersections respectively .
furthermore , we can give a collar structure @xmath385 near @xmath36 and assume @xmath386 .
if we push @xmath262 to @xmath387 in the interior of @xmath35 , then @xmath388 and @xmath379 intersect transversely at @xmath389 and @xmath390 with positive and negative intersections respectively .
hence @xmath391=i_1([c])$ ] and @xmath392\cdot [ w]=[c]\cdot [ \partial w]=p - n=[c]\cdot z_2\neq 0\ ] ] so @xmath377 $ ] can not be in @xmath334 . 1 .
part ( 1 ) of lemma [ kernel ] is still true in arbitrary dimension . if @xmath35 is a @xmath393-dimensional manifold with connected boundary @xmath36 and @xmath394 denotes the homomorphism induced by the inclusion @xmath395 , then @xmath396 for @xmath397 .
2 . part ( 3 ) of lemma [ kernel ] is pointed out by robert gompf . 1 .
let @xmath399 be the trivial knot in @xmath400 and @xmath401 .
the complement of the torus @xmath402 is @xmath403 if @xmath404 denote the isotopy classes of these two @xmath53 and @xmath405 , then @xmath406 , [ m ] , [ l]>$ ] and @xmath334 has rank 1 which is generated by @xmath407 $ ] . on the other hand ,
@xmath335 is generated by @xmath408 , [ l\times m]$ ] and has rank 2 . + in general , if @xmath409 is any knot in @xmath400 and @xmath303 is a seifert surface with boundary @xmath409 , we can define @xmath410 and @xmath411 as above and choose @xmath242 as the push - off of @xmath409 in @xmath303 .
then @xmath35 and @xmath412 have isomorphic homology groups and @xmath334 is still generated by @xmath242 , which bounds the surface @xmath303 .
similarly , @xmath335 has rank 2 and is generated by @xmath408 , [ l\times m]$ ] .
they bound @xmath413 and @xmath414 respectively . in @xcite ,
fintushel and stern use these manifolds as building blocks to define knot surgery in 4-manifolds .
+ in the next example , the results of lemma [ kernel ] are not obvious .
let @xmath415 be a ruled surface and the loop @xmath416 be a lift of a loop in @xmath417 .
we can construct a torus @xmath1 in @xmath23 as the product of @xmath47 and some circle @xmath116 in the fiber . if @xmath418 is a meridian of @xmath1 and @xmath419 is nontrivial in @xmath420 , it is easy to show that @xmath334 is generated by a push - off of @xmath116 . but @xmath335 is not obvious even when @xmath421 is the trivial bundle . by lemma [ kernel ] , we know that @xmath335 has rank 2 and is generated by @xmath422 $ ] and @xmath423 $ ] .
2 . let @xmath424 be the clifford torus embedded in the rational manifold @xmath425 .
the group @xmath373 is generated by @xmath426 , [ b]$ ] and the meridian @xmath235 $ ] .
it is easy to show that @xmath427 , [ b]>$ ] has rank 2 and @xmath428>$ ] .
+ in general , if @xmath23 is simply connected and @xmath30 is a torus with trivial normal bundle , then @xmath429 if and only if @xmath236=0 $ ] in @xmath237 .
if @xmath430 , it follows from lemma [ meridian ] that such surgery will not change the homology for any torus surgery .
@xmath444\in \ker i_2^{\mathbb{q}}\\ & \leftrightarrow & < [ l_{\varphi}]>\subset \ker i_2^{\mathbb{q}}\\ & \leftrightarrow & \mathbf{ann}(<[l_{\varphi}]>)\supset \mathbf{ann}(\ker i_2^{\mathbb{q}})\\ & \leftrightarrow & \ker i_1^{\mathbb{q}}\subset h_{1,\varphi}\otimes { \mathbb{q}}. \ \hbox{(lemma \ref{kernel})}\end{aligned}\ ] ] 1 .
since @xmath236=0 $ ] in @xmath247 , there exists a 3-chain @xmath379 such that @xmath446 .
we can assume that @xmath379 intersects @xmath36 transversely .
in fact , we can choose a framing @xmath41 such that @xmath447 , where @xmath448 .
then @xmath449 is a longitudinal torus of @xmath48 and @xmath450 is a relative 3-cycle of @xmath380 with @xmath451 .
so @xmath452\in \ker i_2^{\mathbb{z}}$ ] and @xmath48 is a topological preferred framing .
@xmath332\in \ker i_2^{\mathbb{z}}$ ] implies that @xmath453)\supset \mathbf{ann}_{\mathbb{z}}(\ker i_2^{\mathbb{z}})$ ] .
it is easy to observe that @xmath454>)=h_{1,\varphi}$ ] . by lemma [ zker ] , @xmath455)=h_{1,\varphi}.\ ] ] if @xmath236 $ ] is torsion in @xmath23 , proposition [ exist](1 ) may fail in two situations .
first , there may exist @xmath456 such that @xmath457 but @xmath458 for some nonzero integer @xmath5 .
so we can only define rational topological preferred framings .
second , @xmath235 $ ] and @xmath435 might not generate the group @xmath326 . in this case , rational topological preferred framings also do not exist . 1 . in knot theory
, the notion of preferred framings is similar to that of definition [ tprefer ] .
let @xmath459 be an integral homology 3-sphere and @xmath460 be a knot .
if @xmath328 is a tubular neighborhood of @xmath409 , a diffeomorphism @xmath461 satisfying @xmath462 is called a framing of @xmath409 .
furthermore , @xmath463 is called a preferred framing if @xmath464 is homologically trivial in @xmath465 . for any knot @xmath409 in @xmath459 ,
preferred framings exist and are unique up to isotopy ( @xcite ) .
it is easy to see from proposition [ exist ] that luttinger s definition coincides with definition [ tprefer ] when @xmath6 .
3 . in @xcite ,
an invariant @xmath466 is defined when @xmath236=0 $ ] and @xmath1 has a unique topological preferred framing @xmath467 .
assume @xmath468 is the lagrangian preferred framing .
then @xmath469 if and only if @xmath470 . otherwise , @xmath466 is the smallest positive integer @xmath5 such that @xmath471+[\gamma_\varphi]\in h_{1,\varphi_{lag}}$ ] for some @xmath472\in h_{1,\varphi_0}$ ] .
[ r1k ] suppose @xmath23 is a smooth 4-manifold and @xmath30 is a torus with trivial normal bundle such that @xmath236=0 $ ] in @xmath442 and @xmath48 is a framing of @xmath1 .
let @xmath474 be constructed from @xmath23 via @xmath473-surgery along @xmath475 . 1 .
if @xmath48 is a rational topological preferred framing of @xmath1 , then @xmath24 satisfies @xmath476 for any @xmath47 and @xmath5 .
if @xmath477 for any @xmath47 and @xmath5 , then @xmath48 is a rational topological preferred framing of @xmath1 . 1 . by lemma [ meridian](3 ) , we have @xmath478\neq 0 \\ r(h_1(y ) ) & \hbox{if } i_1[\mu]=0 . \end{array}\right.\ ] ] lemma [ mul ] implies that @xmath238\neq 0 $ ] in @xmath479 .
since @xmath48 is a rational topological preferred framing , proposition [ rexist ] implies that @xmath235+k[\gamma_\varphi]\notin \ker i_1 $ ] for any integer @xmath5 and @xmath472\in h_{1,\varphi}$ ] .
so @xmath480 if @xmath24 is given via @xmath72-surgery .
we first prove that any @xmath481 lies in @xmath325 .
let @xmath482+t[\gamma_\varphi]$ ] for some @xmath483 and @xmath44 ( recall that @xmath62 is a lift of @xmath47 ) . for @xmath484 , the meridian of @xmath56 in @xmath24 satisfies @xmath485=[\mu]+kt[\gamma_\varphi]=[\mu]+k(a - s[\mu])=(1-sk)[\mu]+ka\ ] ] so + @xmath486+ka ) > & $ ] ( by ) @xmath487 ) > & ( a\in \ker i_1^{\mathbb{z}})\\ & \cong & h_1(y;{\mathbb{z}})/<i_1^{\mathbb{z}}[\mu ] > \end{array}$ ] + because @xmath235 $ ] is essential in @xmath35 and @xmath5 is arbitrary , @xmath488 should be zero and @xmath489 . otherwise , @xmath261 has infinitely many torsion classes with different orders .
+ tensoring with @xmath233 , we have @xmath490 by proposition [ rexist ] , @xmath48 is a rational topological preferred framing .
[ 1k ] suppose @xmath261 has no torsion and @xmath1 is null - homologous .
then a framing @xmath48 of @xmath1 is a topological preferred framing if and only if @xmath477 for any @xmath474 obtained from @xmath23 via @xmath473-surgery .
assume @xmath48 is a topological preferred framing .
consider the 3-chain @xmath379 given in the proof of proposition [ exist ] .
it is clear that a meridian @xmath54 intersects @xmath379 at one point .
so @xmath248\cdot [ w]=\pm 1 $ ] and @xmath248 $ ] is a primitive class .
similarly , the simple closed curve @xmath288 has class @xmath235+k[\gamma_\varphi]$ ] and is homotopic to a curve intersecting @xmath379 at one point .
hence @xmath491 $ ] is also a primitive class for any @xmath492 .
since @xmath249 is a free abelian group , we have @xmath493>\cong h_1(y,{\mathbb{z}})/<i_1^{\mathbb{z}}[\tilde{\mu}]>$ ] .
so @xmath494 by lemma [ meridian](3 ) .
conversely , if @xmath494 for any @xmath24 , the proof of proposition [ r1k](2 ) shows that @xmath48 is a rational topological preferred framing .
the assumption that @xmath247 has no torsion implies that @xmath48 is actually a topological preferred framing .
the knot surgery in @xcite is an example of @xmath473-surgeries .
suppose @xmath495 , @xmath409 is a knot in @xmath400 and @xmath496 .
let @xmath54 be the meridian of @xmath1 , @xmath260 the longitude of the preferred framing of @xmath409 and @xmath497 .
then @xmath498>$ ] and @xmath499 , [ a\times b]>$ ] .
consider the framings @xmath500 of @xmath1 where @xmath501 is generated by @xmath502+[a]$ ] and @xmath503 $ ] .
it is clear that @xmath500 is a topological preferred framing of @xmath1 exactly when @xmath504 .
if @xmath409 is the trivial knot and @xmath4=p[\mu]+[a]$ ] , the resulting manifold of @xmath72-surgery is @xmath505 and @xmath506 . if @xmath507 , @xmath508 has rank @xmath509 for any @xmath510 , but the torsion subgroups vary . propositions [ 1k ] and [ r1k ] show that @xmath500 is not a rational topological preferred framing
actually , such framings do not exist for @xmath1 . here
we provide topological constraints on the isotopy classes of lagrangian tori in many symplectic manifolds with non - positive kodaira dimension .
in particular , they imply that the invariant @xmath466 of fintushel and stern ( remark [ lambda](3 ) ) is zero if the manifold has non - positive kodaira dimension and vanishing integral @xmath511 .
recall that the lagrangian framing for lagrangian tori is defined in section [ construction ] . 1 .
if @xmath247 is torsion free and @xmath1 is null - homologous , then the lagrangian framing of @xmath1 is a topological preferred framing .
if @xmath236 $ ] is torsion then the lagrangian framing of @xmath1 is a rational topological preferred framing .
since @xmath512 and @xmath247 has no torsion , @xmath1 is null - homologous . for any @xmath101 given from @xmath23 by applying luttinger surgery along @xmath1
, @xmath101 is diffeomorphic to @xmath23 by theorem [ int2 ] .
now the claim follows from proposition [ prefer ] . when @xmath1 is essential , @xmath235\in\ker i_1^{\mathbb{q}}$ ] by lemma [ mul ] .
if @xmath514 , there exists @xmath44 such that @xmath515)\neq 0 $ ] . in the manifold @xmath516 , the class @xmath64=[\mu]+[\gamma_\varphi]$ ] is nonzero in @xmath239 . by proposition
[ compare ] , @xmath517 , which contradicts theorem [ int3 ] .
so @xmath518 and @xmath1 is completely essential .
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four manifolds with non - positive kodaira dimension are also derived . </s> |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``21st Century Teacher Training Act of
2001''.
SEC. 2. GRANTS FOR CLASSROOM-RELATED COMPUTER TRAINING FOR TEACHERS.
(a) In General.--The Secretary of Education, through the Office of
Educational Technology established under section 216 of the Department
of Education Organization Act (20 U.S.C. 3425), may award grants on a
competitive basis to local educational agencies (as defined in section
14101 of the Elementary and Secondary Education Act of 1965 (20 U.S.C.
8801)) to assist such agencies in providing intensive classroom-related
computer training for teachers.
(b) Minimum Grant Amount.--A grant awarded pursuant to subsection
(a) shall be for not less than $10,000,000.
(c) Requirements of Grant.--A grant awarded pursuant to subsection
(a) shall provide that--
(1) the grantee will enter into a contract with an
institution of higher education or another nonprofit
educational provider (hereafter in this section referred to as
the ``contractor'') under which the contractor will agree to
establish, operate, and provide the non-Federal share of the
cost of a teacher training program described in such
subsection;
(2) funds made available by the Secretary to the grantee
pursuant to any contract entered into under this section will
be used to pay the Federal share of the cost of establishing
and operating a teacher training program as provided in
paragraph (1); and
(3) the grantee will meet such other conditions and
standards as the Secretary determines to be necessary to assure
compliance with the provisions of this section and will provide
such technical assistance as may be necessary to carry out the
provisions of this section.
(d) Teacher Training Programs.--The teacher training programs
authorized in subsection (a)--
(1) shall be conducted during the school year and during
the summer months;
(2) shall train teachers who teach grades kindergarten
through college;
(3) shall select teachers to become members of a teacher
network whose members will conduct workshops for other teachers
employed by the local educational agency; and
(4) shall encourage teachers from all disciplines to
participate in such teacher training programs.
(e) Supplement and not Supplant.--Grants awarded pursuant to this
section shall be used to supplement and not supplant State and local
funds available for the purpose set forth in subsection (a).
SEC. 3. INCOME TAX CREDIT FOR TECHNOLOGY-RELATED PROFESSIONAL
DEVELOPMENT FOR TEACHERS.
(a) In General.--Subpart A of part IV of subchapter A of chapter 1
of the Internal Revenue Code of 1986 (relating to nonrefundable
personal credits) is amended by inserting after section 25A the
following new section:
``SEC. 25B. TECHNOLOGY-RELATED PROFESSIONAL DEVELOPMENT EXPENSES OF
TEACHERS.
``(a) Allowance of Credit.--In the case of an eligible teacher,
there shall be allowed as a credit against the tax imposed by this
chapter for the taxable year an amount equal to the qualified
technology-related expenses paid or incurred by the taxpayer during
such taxable year.
``(b) Maximum Credit.--The credit allowed by subsection (a) for any
taxable year shall not exceed $1,000 with respect to each eligible
teacher.
``(c) Eligible Teacher.--For purposes of this section, the term
`eligible teacher' means any individual--
``(1) who, at the time the expense is paid or incurred, is
a full-time teacher for any of grades K-12 in the United
States, or
``(2) who reasonably expects to be such a full-time teacher
for the academic year beginning in the taxable year in which
such expense is paid or incurred.
``(d) Qualified Technology-Related Expenses.--
``(1) In general.--For purposes of this section, the term
`qualified technology-related expenses' means expenses--
``(A) which would (but for subsection (e)) be
allowed as a deduction under this chapter by reason of
being related to teaching activities referred to in
subsection (c), and
``(B) which are for training in the use of
technology (including computers) in the classroom.
``(2) Computers included.--Such term includes the cost of
any computer or technology equipment (as defined in section
170(e)(6)(F)) if at least 50 percent of the use of which
(whether or not in the classroom) is related to teaching
activities as an eligible teacher.
``(e) Denial of Double Benefit.--No deduction shall be allowed
under this chapter for any expense for which a credit is allowed under
this section.
``(f) Election To Have Credit Not Apply.--A taxpayer may elect to
have this section not apply to any taxable year.''
(b) Clerical Amendment.--The table of sections for such subpart A
is amended by inserting after the item relating to section 25A the
following new item:
``Sec. 25B. Technology-related
professional development
expenses of teachers.''
(c) Effective Date.--The amendments made by this section shall
apply to taxable years beginning after the date of the enactment of
this Act.
SEC. 4. EXPANSION OF DEDUCTION FOR COMPUTER DONATIONS TO CHARITIES.
(a) Extension of Age of Eligible Computers.--Clause (ii) of section
170(e)(6)(B) of the Internal Revenue Code of 1986 (defining qualified
computer contribution) is amended by striking ``date'' the first place
it appears and all that follows and inserting the following:
``date--
``(I) the taxpayer acquired or
reacquired the property,
``(II) construction of the property
is substantially completed in the case
of property constructed by the taxpayer
for its own use in its trade or
business and which is not inventory
with respect to the taxpayer, or
``(III) the property was originally
sold, leased, or otherwise disposed of
by the taxpayer in the case of property
reacquired by the taxpayer.''.
(b) Reacquired Computers Eligible for Donation.--Clause (iii) of
section 170(e)(6)(B) of such Code (defining qualified computer
contribution) is amended by inserting ``, the person from whom the
donor reacquires the property,'' after ``the donor''.
(c) Effective Date.--The amendments made by this section shall
apply to contributions made in taxable years ending after the date of
the enactment of this Act.
SEC. 5. CREDIT FOR COMPUTER DONATIONS TO SCHOOLS AND PUBLIC LIBRARIES.
(a) In General.--Subpart D of part IV of subchapter A of chapter 1
of the Internal Revenue Code of 1986 (relating to business related
credits) is amended by adding at the end the following:
``SEC. 45E. CREDIT FOR COMPUTER DONATIONS TO SCHOOLS AND PUBLIC
LIBRARIES.
``(a) General Rule.--For purposes of section 38, the school and
public library computer donation credit determined under this section
is an amount equal to 30 percent of the qualified computer
contributions made by the taxpayer during the taxable year.
``(b) Increased Percentage for Contributions to Schools or Public
Libraries in Empowerment Zones, Enterprise Communities, and Indian
Reservations.--In the case of a qualified computer contribution to an
educational organization, public library, or entity located in an
empowerment zone or enterprise community designated under section 1391
or an Indian reservation (as defined in section 168(j)(6)), subsection
(a) shall be applied by substituting `50 percent' for `30 percent'.
``(c) Limitation.--No credit shall be allowed under subsection (a)
for the contribution of a computer (as defined in section
168(i)(2)(B)(ii)) if the computer software (as defined in section
197(e)(3)(B)) that serves as the operating system of such computer has
not been lawfully installed.
``(d) Qualified Computer Contribution.--For purposes of this
section, the term `qualified computer contribution' has the meaning
given such term by section 170(e)(6)(B).
``(e) Certain Rules Made Applicable.--For purposes of this section,
rules similar to the rules of paragraphs (1) and (2) of section 41(f)
shall apply.
``(f) Termination.--This section shall not apply to taxable years
beginning on or after the date which is 3 years after the date of the
enactment of the 21st Century Teacher Training Act of 2001.''
(b) Current Year Business Credit Calculation.--Section 38(b) of
such Code (relating to current year business credit) is amended by
striking ``plus'' at the end of paragraph (12), by striking the period
at the end of paragraph (13) and inserting ``, plus'', and by adding at
the end the following:
``(14) the school and public library computer donation
credit determined under section 45E(a).''.
(c) Disallowance of Deduction by Amount of Credit.--Section 280C of
such Code (relating to certain expenses for which credits are
allowable) is amended by adding at the end the following:
``(d) Credit for School and Public Library Computer Donations.--No
deduction shall be allowed for that portion of the qualified computer
contributions (as defined in section 170(e)(6)(B)) made during the
taxable year that is equal to the amount of credit determined for the
taxable year under section 45E(a). In the case of a corporation which
is a member of a controlled group of corporations (within the meaning
of section 52(a)) or a trade or business which is treated as being
under common control with other trades or businesses (within the
meaning of section 52(b)), this subsection shall be applied under rules
prescribed by the Secretary similar to the rules applicable under
subsections (a) and (b) of section 52.''
(d) Limitation on Carryback.--Subsection (d) of section 39 of such
Code (relating to carryback and carryforward of unused credits) is
amended by adding at the end the following:
``(10) No carryback of school and public library computer
donation credit before effective date.--No amount of unused
business credit available under section 45E may be carried back
to a taxable year beginning on or before the date of the
enactment of this paragraph.''.
(e) Clerical Amendment.--The table of sections for subpart D of
part IV of subchapter A of chapter 1 of such Code is amended by
inserting after the item relating to section 45D the following:
``Sec. 45E. Credit for computer donations
to schools and public
libraries.''
(f) Effective Date.--The amendments made by this section shall
apply to contributions made in taxable years beginning after the date
of the enactment of this Act. | 21st Century Teacher Training Act of 2001 - Authorizes the Secretary of Education, through the Office of Educational Technology, to award competitive grants to local educational agencies (LEAs) to provide programs of intensive classroom-related computer training for teachers. Requires grantees to enter into contracts with institutions of higher education or other nonprofit educational providers that will establish, operate, and provide the non-Federal share of the cost of such programs.Amends the Internal Revenue Code to establish a personal income tax credit of up to $1,000 for technology-related professional development expenses for eligible teachers. Establishes a business-related tax credit for donations of computers to schools and public libraries. | <s>[INST]SECTION 1. SHORT TITLE.
This Act may be cited as the ``21st Century Teacher Training Act of
2001''.
SEC. 2. GRANTS FOR CLASSROOM-RELATED COMPUTER TRAINING FOR TEACHERS.
(a) In General.--The Secretary of Education, through the Office of
Educational Technology established under section 216 of the Department
of Education Organization Act (20 U.S.C. 3425), may award grants on a
competitive basis to local educational agencies (as defined in section
14101 of the Elementary and Secondary Education Act of 1965 (20 U.S.C.
8801)) to assist such agencies in providing intensive classroom-related
computer training for teachers.
(b) Minimum Grant Amount.--A grant awarded pursuant to subsection
(a) shall be for not less than $10,000,000.
(c) Requirements of Grant.--A grant awarded pursuant to subsection
(a) shall provide that--
(1) the grantee will enter into a contract with an
institution of higher education or another nonprofit
educational provider (hereafter in this section referred to as
the ``contractor'') under which the contractor will agree to
establish, operate, and provide the non-Federal share of the
cost of a teacher training program described in such
subsection;
(2) funds made available by the Secretary to the grantee
pursuant to any contract entered into under this section will
be used to pay the Federal share of the cost of establishing
and operating a teacher training program as provided in
paragraph (1); and
(3) the grantee will meet such other conditions and
standards as the Secretary determines to be necessary to assure
compliance with the provisions of this section and will provide
such technical assistance as may be necessary to carry out the
provisions of this section.
(d) Teacher Training Programs.--The teacher training programs
authorized in subsection (a)--
(1) shall be conducted during the school year and during
the summer months;
(2) shall train teachers who teach grades kindergarten
through college;
(3) shall select teachers to become members of a teacher
network whose members will conduct workshops for other teachers
employed by the local educational agency; and
(4) shall encourage teachers from all disciplines to
participate in such teacher training programs.
(e) Supplement and not Supplant.--Grants awarded pursuant to this
section shall be used to supplement and not supplant State and local
funds available for the purpose set forth in subsection (a).
SEC. 3. INCOME TAX CREDIT FOR TECHNOLOGY-RELATED PROFESSIONAL
DEVELOPMENT FOR TEACHERS.
(a) In General.--Subpart A of part IV of subchapter A of chapter 1
of the Internal Revenue Code of 1986 (relating to nonrefundable
personal credits) is amended by inserting after section 25A the
following new section:
``SEC. 25B. TECHNOLOGY-RELATED PROFESSIONAL DEVELOPMENT EXPENSES OF
TEACHERS.
``(a) Allowance of Credit.--In the case of an eligible teacher,
there shall be allowed as a credit against the tax imposed by this
chapter for the taxable year an amount equal to the qualified
technology-related expenses paid or incurred by the taxpayer during
such taxable year.
``(b) Maximum Credit.--The credit allowed by subsection (a) for any
taxable year shall not exceed $1,000 with respect to each eligible
teacher.
``(c) Eligible Teacher.--For purposes of this section, the term
`eligible teacher' means any individual--
``(1) who, at the time the expense is paid or incurred, is
a full-time teacher for any of grades K-12 in the United
States, or
``(2) who reasonably expects to be such a full-time teacher
for the academic year beginning in the taxable year in which
such expense is paid or incurred.
``(d) Qualified Technology-Related Expenses.--
``(1) In general.--For purposes of this section, the term
`qualified technology-related expenses' means expenses--
``(A) which would (but for subsection (e)) be
allowed as a deduction under this chapter by reason of
being related to teaching activities referred to in
subsection (c), and
``(B) which are for training in the use of
technology (including computers) in the classroom.
``(2) Computers included.--Such term includes the cost of
any computer or technology equipment (as defined in section
170(e)(6)(F)) if at least 50 percent of the use of which
(whether or not in the classroom) is related to teaching
activities as an eligible teacher.
``(e) Denial of Double Benefit.--No deduction shall be allowed
under this chapter for any expense for which a credit is allowed under
this section.
``(f) Election To Have Credit Not Apply.--A taxpayer may elect to
have this section not apply to any taxable year.''
(b) Clerical Amendment.--The table of sections for such subpart A
is amended by inserting after the item relating to section 25A the
following new item:
``Sec. 25B. Technology-related
professional development
expenses of teachers.''
(c) Effective Date.--The amendments made by this section shall
apply to taxable years beginning after the date of the enactment of
this Act.
SEC. 4. EXPANSION OF DEDUCTION FOR COMPUTER DONATIONS TO CHARITIES.
(a) Extension of Age of Eligible Computers.--Clause (ii) of section
170(e)(6)(B) of the Internal Revenue Code of 1986 (defining qualified
computer contribution) is amended by striking ``date'' the first place
it appears and all that follows and inserting the following:
``date--
``(I) the taxpayer acquired or
reacquired the property,
``(II) construction of the property
is substantially completed in the case
of property constructed by the taxpayer
for its own use in its trade or
business and which is not inventory
with respect to the taxpayer, or
``(III) the property was originally
sold, leased, or otherwise disposed of
by the taxpayer in the case of property
reacquired by the taxpayer.''.
(b) Reacquired Computers Eligible for Donation.--Clause (iii) of
section 170(e)(6)(B) of such Code (defining qualified computer
contribution) is amended by inserting ``, the person from whom the
donor reacquires the property,'' after ``the donor''.
(c) Effective Date.--The amendments made by this section shall
apply to contributions made in taxable years ending after the date of
the enactment of this Act.
SEC. 5. CREDIT FOR COMPUTER DONATIONS TO SCHOOLS AND PUBLIC LIBRARIES.
(a) In General.--Subpart D of part IV of subchapter A of chapter 1
of the Internal Revenue Code of 1986 (relating to business related
credits) is amended by adding at the end the following:
``SEC. 45E. CREDIT FOR COMPUTER DONATIONS TO SCHOOLS AND PUBLIC
LIBRARIES.
``(a) General Rule.--For purposes of section 38, the school and
public library computer donation credit determined under this section
is an amount equal to 30 percent of the qualified computer
contributions made by the taxpayer during the taxable year.
``(b) Increased Percentage for Contributions to Schools or Public
Libraries in Empowerment Zones, Enterprise Communities, and Indian
Reservations.--In the case of a qualified computer contribution to an
educational organization, public library, or entity located in an
empowerment zone or enterprise community designated under section 1391
or an Indian reservation (as defined in section 168(j)(6)), subsection
(a) shall be applied by substituting `50 percent' for `30 percent'.
``(c) Limitation.--No credit shall be allowed under subsection (a)
for the contribution of a computer (as defined in section
168(i)(2)(B)(ii)) if the computer software (as defined in section
197(e)(3)(B)) that serves as the operating system of such computer has
not been lawfully installed.
``(d) Qualified Computer Contribution.--For purposes of this
section, the term `qualified computer contribution' has the meaning
given such term by section 170(e)(6)(B).
``(e) Certain Rules Made Applicable.--For purposes of this section,
rules similar to the rules of paragraphs (1) and (2) of section 41(f)
shall apply.
``(f) Termination.--This section shall not apply to taxable years
beginning on or after the date which is 3 years after the date of the
enactment of the 21st Century Teacher Training Act of 2001.''
(b) Current Year Business Credit Calculation.--Section 38(b) of
such Code (relating to current year business credit) is amended by
striking ``plus'' at the end of paragraph (12), by striking the period
at the end of paragraph (13) and inserting ``, plus'', and by adding at
the end the following:
``(14) the school and public library computer donation
credit determined under section 45E(a).''.
(c) Disallowance of Deduction by Amount of Credit.--Section 280C of
such Code (relating to certain expenses for which credits are
allowable) is amended by adding at the end the following:
``(d) Credit for School and Public Library Computer Donations.--No
deduction shall be allowed for that portion of the qualified computer
contributions (as defined in section 170(e)(6)(B)) made during the
taxable year that is equal to the amount of credit determined for the
taxable year under section 45E(a). In the case of a corporation which
is a member of a controlled group of corporations (within the meaning
of section 52(a)) or a trade or business which is treated as being
under common control with other trades or businesses (within the
meaning of section 52(b)), this subsection shall be applied under rules
prescribed by the Secretary similar to the rules applicable under
subsections (a) and (b) of section 52.''
(d) Limitation on Carryback.--Subsection (d) of section 39 of such
Code (relating to carryback and carryforward of unused credits) is
amended by adding at the end the following:
``(10) No carryback of school and public library computer
donation credit before effective date.--No amount of unused
business credit available under section 45E may be carried back
to a taxable year beginning on or before the date of the
enactment of this paragraph.''.
(e) Clerical Amendment.--The table of sections for subpart D of
part IV of subchapter A of chapter 1 of such Code is amended by
inserting after the item relating to section 45D the following:
``Sec. 45E. Credit for computer donations
to schools and public
libraries.''
(f) Effective Date.--The amendments made by this section shall
apply to contributions made in taxable years beginning after the date
of the enactment of this Act.[/INST]21st Century Teacher Training Act of 2001 - Authorizes the Secretary of Education, through the Office of Educational Technology, to award competitive grants to local educational agencies (LEAs) to provide programs of intensive classroom-related computer training for teachers. Requires grantees to enter into contracts with institutions of higher education or other nonprofit educational providers that will establish, operate, and provide the non-Federal share of the cost of such programs.Amends the Internal Revenue Code to establish a personal income tax credit of up to $1,000 for technology-related professional development expenses for eligible teachers. Establishes a business-related tax credit for donations of computers to schools and public libraries.</s> |
How the other half fear: Super-rich worry that their wealth is killing drive and ambition in their children
Survey looked at top fears of 4,500 of the world's wealthiest families
Found wealthiest worried about their fortunes killing children's drive
Fear ranked above worries over investments and marital breakdown
Sting said today that his children will not inherit any of his £180million
With millions of pounds in the bank, you might have thought the world's super-rich wouldn't have a care in the world.
But a new survey has revealed the top fears of the world's wealthiest people, and one of the most common is that their money is their children's ambition and drive to do well.
For the most successful - defined as those with fortunes of $10million (£5.9million) and above - worries about children's motivation came second only to worries about their own health.
Sting said his kids will not inherit his £180million fortune as the money will be an 'albatross around their necks'
According to the study, by law firm Withersworldwide, fears over children's ambition come above worries about investments failing, inability to provide for the family, and even divorce.
Among those with a fortune of less than $10million the fear still ranked highly, but came in fourth place, behind health troubles and worries over income.
The study found that, wealthy families have the most to fear from third generation family members when it comes to losing the family millions.
Sara Cormack, a partner at Wither's, said: 'If the first generation are wealth creators then the second generation tend to be wealth preservers, but it is the third generation that families are most worried about.
'If they have had everything put on a plate for them without seeing any of the hard graft that goes into creating that wealth, then they can lose track of how best to use that wealth and how ifficult it was to build up in the first place.'
Former Police lead singer and musician Sting has today said he will not be passing on any of his £180million fortune to his children because he wants them to earn their money themselves.
He said: ‘I told them there won’t be much money left because we are spending it! We have a lot of commitments. What comes in, we spend, and there isn’t much left.
Nigella Lawson previously said that not having to earn their own money 'ruins people' while Brooklyn Beckham was encouraged to get a job earning £2.68 an hour in a coffee shop by David and Victoria
‘I certainly don’t want to leave them trust funds that are albatrosses round their necks.
‘They have to work. All my kids know that and they rarely ask me for anything, which I really respect and appreciate.
‘Obviously, if they were in trouble I would help them, but I’ve never really had to do that. They have the work ethic that makes them want to succeed on their own merit.’
Celebrity chef Nigella Lawson also said that her children will not be passed any of her own fortune, adding that 'it ruins people not having to earn their own money.'
According to reports, Brooklyn Beckham recently got a job in a West London coffee shop earning £2.68 an hour after being encouraged to do it by parents David and Victoria, who are worth an estimated £165million.
The data, a rare insight into the minds of the world's most powerful, was based on surveys of more than 4,500 and interviews with 16 very wealthy families from Europe, Asia and North America.
Families interviewed said they were using charitable donations or setting up a new business to give the family a renewed sense of direction.
Some even said they had drawn up a family statement, similar to a business statement, in order to give the next generation a purpose and something to achieve.
||||| Why my children will not be inheriting my £180million fortune: Sting wants his sons and daughters to earn their way (and says he's spending all his money anyway)
As one of the world’s most successful rock stars, he has risen from an impoverished childhood to amass a huge fortune.
Now Sting has made it clear that his children will also have to earn their own way and should not expect to benefit from his £180 million earnings.
In a frank interview in today’s Mail on Sunday Event magazine, the former Police frontman said he expected his three sons and three daughters to work, and added that there would not be much left to inherit anyway.
Sting, 62, who still has more than 100 people on his payroll, said: ‘I told them there won’t be much money left because we are spending it! We have a lot of commitments. What comes in, we spend, and there isn’t much left.’
He added: ‘I certainly don’t want to leave them trust funds that are albatrosses round their necks.
‘They have to work. All my kids know that and they rarely ask me for anything, which I really respect and appreciate.
‘Obviously, if they were in trouble I would help them, but I’ve never really had to do that. They have the work ethic that makes them want to succeed on their own merit.’
Sting is not the only celebrity who expects their children to stand on their own feet.
Celebrity chef Nigella Lawson said a few years ago: ‘I am determined that my children should have no financial security. It ruins people not having to earn money.’
READ THE FULL INTERVIEW BELOW
Sting had to escape his family and abandon his North East roots. 'It was a pretty violent wrench. I didn't feel I belonged there and the family was pretty dysfunctional in many ways,' he said
It’s not exactly rock ’n’ roll, but the woman who really changed Sting’s life – sorry, Trudie – was the Queen Mother.
Young Gordon Sumner, dressed in his Sunday best almost 50 years ago, was mesmerised as her Rolls-Royce swished past the front door of his street in Wallsend, North Tyneside.
The Sumners were poor, working-class Geordies; his parents Audrey, a hairdresser, and Ernie, a milkman.
The Royal visitor was there to launch a ship built at the end of his street at the Swan Hunter shipyard. Sting’s grandfather had been a shipwright and the young Sumner was expected to go into a manual job, too.
'I've never hidden my age. I am a father and now a grandfather,' said Sting
The biggest vessels on the planet were hammered, welded and built there long before Gordon became Sting (named for wearing a black-and-yellow jersey, like a wasp).
‘The Queen Mum waved and looked at me, and I looked back at her and that was it,’ he says.
‘There and then I thought, I am going to be rich, famous, successful and drive a Rolls-Royce like her.’
He decided he would use his voice and guitar to get a big house in the country, great wealth and acclaim. And so it all came to pass.
Now aged 62, the rock star, eco-warrior, father of six and grandfather laughs as he tells of the inspiration for his aspiration, all courtesy of the House of Windsor.
This is just one of a torrent of revealing anecdotes in a candid and wide-ranging interview, in which he tells Event about his complicated family background, his politics, children, death, drugs, Botox, the secrets of his long and happy marriage – and why his children won’t be getting their hands on his fortune.
Today it’s his own childhood that’s playing on the mind of the boy from Wallsend who went on to buy seven homes across Britain, Italy and the U.S., sell more than 100 million records and earn an estimated £180 million.
Because to get all that, Sting tells me, he had to escape his family and abandon his North East roots.
‘It was a pretty violent wrench. I didn’t feel I belonged there and the family was pretty dysfunctional in many ways. My parents were not happy together.
'They loved their kids but it was a toxic environment. I needed to escape and I am glad I did.’
His mother was unfaithful, which eventually led to the breakdown of the marriage, and divorce.
Sting pursued his dream, which his father dismissed as delusional. And, at times, fame and fortune did look like fantasy, as Sting struggled through a series of jobs before finally becoming a teacher, his musical talents unrecognised.
'I demand a citizen's life - I really do. Walking the street; going to a bar on my own,' Sting said
He moved to London and began hurtling up and down the M1 to play gigs in pubs.
It was all small beer until 1979, when with his band, The Police, he exploded into the charts with Roxanne and everything changed.
And so the rest – five No 1 records with The Police, huge success as a solo artist, starring roles in movies, rainforest crusades, 16 Grammy awards and the most enduring marriage in rock ’n’ roll (not to mention fending off 1,000 questions about tantric sex) – is well-rehearsed history.
Less well known is the acutely personal inspiration for his latest project, a compulsively toe-tapping, heart-rending musical called The Last Ship.
The musical, which had its world premiere in Chicago last week, draws upon his early life growing up around the harsh shipyard docks. Sitting in his 20th-floor penthouse in a Chicago hotel after overseeing final preparations for The Last Ship’s maiden voyage, Sting talks with boyish wonder that his musical, four years in the making, is finally on stage. Next stop, Broadway.
‘The irony is that I’m going back to Wallsend, from where I had done everything in my power to escape,’ he says.
‘But we have to go back to where we came from and reassess, give thanks for it and honour it. I want to celebrate where I came from; that town, what they did, and the hardship.’
In The Last Ship, a young man runs away from home, returning 15 years later to discover he had fathered a child before he left, only to abandon his home town again, on a ship after the shipyard goes bust.
The songs, he says, came in a rush of inspiration following a period of writer’s block. He knew it should be a musical, and from the off knew that one of his oldest pals from the North East, Jimmy Nail, would star in it. (The actor and sometime musician is the one person on the planet who gets to call Sting Gordon.) The music is as addictive as his most potent songs – all are written by Sting – and after Broadway he would be happy to see it open in London.
'I am married to an extraordinary, gifted woman,' said Sting of wife Trudie Styler
The story draws on Sting’s ruptured relationship with his father.
‘A father’s love can sometimes be misconstrued,’ he says.
‘It can be about control; it comes from anxiety.
'A father wants to dictate to a son what he should or should not be doing. And to my father the ambition I had seemed like bulls***, pie in the sky. And he wasn’t wrong. I wanted to be a successful musician; the chances of that coming off were millions to one. He thought it was ridiculous. “Get a proper job!”
‘Once I had become successful he was proud of me, but he never really understood it.
'I passed the 11-plus to get into a grammar school with a scholarship but he had wanted me to go to a technical school. Engineering was what he knew and did.’
Sting’s aim was more fanciful.
‘I had some vague idea I wanted to study the classics, speak French and Latin.’
His goal was always to escape.
Such aspirations were more encouraged by his mother.
‘She initiated me in the dark arts of music and dreaming. She lived her life through me and encouraged me to do all the things my dad did not understand.
'Did I have to divorce my dad? As much as any son has to do so to individuate. You have to. It’s part of growing up. You have to leave the nest. Sometimes it’s painful. It is necessary.’
Sting did not attend either of his parents’ funerals, because he felt the inevitable media intrusion would be disrespectful, but he did pay his dad a final farewell as he lay dying of cancer.
As he sat beside him, Sting suddenly realised ‘with the jolt of an electrical shock’ that for all their differences, their hands were identical. “We have the same hands, Dad, look!” I was a child again, desperately trying to get his attention.’
Sting held his father’s hand next to his own, but little was said by these two strong Tyneside men. One sentence, however, stayed in Sting’s memory.
‘Aye, son, but you used yours better than I used mine.’
It was the first time Sting could recall ever hearing a compliment from his dad, or being acknowledged for what he had achieved.
His father, just 59, closed his eyes in exhaustion, Sting kissed him softly in the centre of his forehead and whispered that he was a good man and that he loved him. They never saw each other again.
On his children: 'They have this work ethic that makes them want to succeed on their own merit. People make assumptions, that they were born with a silver spoon in their mouth, but they have not been given a lot'
For years Sting felt unable to grieve properly for the loss of his parents.
He dedicated his 2005 memoir, Broken Music, to his parents but his new musical is obliquely a tribute as well. His voice lowers to just above a whisper as he recalls his dad. It is still a tender subject, 27 years after his death.
When I ask Sting when he last cried, there is a silence before he says: ‘Just now.’
And he clearly is moved. He does not do public tears. The musical ends with a funeral, a joyous and celebratory one, at sea, and he feels as if many wounds are being unconsciously healed, many unsaid words being heard.
‘Last night [at the theatre] I just thought back to my dad,’ he says, ‘and I think other members of the crew also did to theirs.’
Mortality is on Sting’s mind, as he is now three years shy of 65, but he says he is relaxed about growing old.
‘I’ve never hidden my age. I am a father and now a grandfather and I am proud of that [his youngest son, Giacomo, is 18 and his eldest, Joseph, 37].
‘I have a story still to tell and part of that is I am facing the end of my life.
'I have lived more of my life than is to come: that is an interesting place for an artist – more interesting than writing about your first girlfriend. It is kind of serious.
'I have lived more of my life than is to come: that is an interesting place for an artist - more interesting than writing about your first girlfriend. It is kind of serious,' said Sting
'In our 60s, how do we face this imponderable idea that we are not going to exist any more? We make art. We tell stories. We have to face it, to tell it. I am certainly not ready for death. Do I fear it? Well, I fear sudden death. I want to die consciously. I want to see the process. I suppose I already do.
'My eyesight is not as good as it used to be, nor my hearing. I am still extremely fit but have to work hard. But we decay. I love what Christopher Hitchens said about death – you have been asked to leave the party and the problem is the party will carry on without you. Very eloquent.
'But I am interested in the future. What will happen to the planet and us? I want to use every minute to enjoy it.’
While Sting outshone his parents, the challenge now for his own children is competing with the success he’s achieved through what he modestly calls his ‘singing and rhyming couplets’.
'I passed the 11-plus to get into a grammar school with a scholarship,' said Sting
‘My generation all assumed we would have a better standard of living. The one that we spawned cannot assume that.
'With my children there is great wealth, success – a great shadow over them – so it’s no picnic at all being my child. I discuss that with them; it’s tough for them.’
Sting does not believe they will inherit great riches.
‘I told them there won’t be much money left because we are spending it! We have a lot of commitments. What comes in we spend, and there isn’t much left.
'I certainly don’t want to leave them trust funds that are albatrosses round their necks. They have to work. All my kids know that and they rarely ask me for anything, which I really respect and appreciate.
'Obviously, if they were in trouble I would help them, but I’ve never really had to do that.
'They have this work ethic that makes them want to succeed on their own merit. People make assumptions, that they were born with a silver spoon in their mouth, but they have not been given a lot.’
Sting has more than 100 people on his payroll.
‘I keep a community of people going. My crew, my band, my staff... it’s a corporation!’ Who runs it? ‘Trudie! Well, a large aspect of it is Trudie, but I have a very good team of managers and lawyers. They all need paying, too.’
Selling the family home in London should raise some extra funds, then. The nine-bedroom townhouse, a stone’s throw from Buckingham Palace, is currently on the market for more than £15 million.
‘It’s just too big,’ he says. ‘The kids have all gone and there are just so many empty bedrooms. We’re just rattling around. But we are not leaving. I love England. I’m still English.’
Sting is not afraid to speak his mind and has stuck his neck out by campaigning for the decriminalisation of drugs. Does he really believe they help the creative process?
'Did I have to divorce my dad? As much as any son has to do so to individuate,' he said
‘I think if they’re used specifically as tools for a stated purpose. As in, “I’ll now smoke this joint and I’ll write a song... or I will write a piece of poetry.”
'Then I think it’s perfectly acceptable. But if you’re just taking stuff to get out of it, then you’ll just get out of it.
'If I’m feeling stuck on a lyric or an idea isn’t quite gelling, sometimes a puff of weed will free it up.
'I rarely smoke it socially. It’s a tool, just as a pen is. I’m not alone. Several artists have used drugs to make great art.
‘I certainly wouldn’t advocate that you have to take drugs to make art, but then you can’t nullify the work of The Beatles. They took LSD and they made fantastic albums.
'Miles Davies made the most extraordinary music on heroin.
'Some people can cope with it perfectly well. I’m not here to make rules, or even state that there should be any rules. Drugs are dangerous, without a doubt.
'At the same time they can be useful tools but they need to be thought about as tools.’
So where does he stand on the legalisation of drugs?
‘Legalising is a very complex issue. Decriminalisation is a first step, because I don’t think it [criminalisation] helps. I don’t think the social problems related to drugs are helped by the legal system or the police.
'Social problems and mental problems are best dealt with by psychiatrists.’
And what about when you see casualties of drugs, like Whitney Houston or Amy Winehouse?
‘There are laws in place right now and they haven’t protected Amy, they haven’t protected anyone. I tell my children to be extremely careful. Luckily, they’re not particularly prone to drug-taking, to my knowledge. But they’re smart and they’re careful.
‘The drug laws aren’t helping. We need a really honest debate in society. People will tend to want to make life richer. Life seems flat a lot of the time. Chemicals, alcohol, marijuana can help. It’s almost a spiritual need to re-enchant life.
'I think that people are disenchanted with modern living and the drug culture is an attempt to re-enchant the world. It can, and it can fail.’
Sting's childhood home in Wallsend on Tyneside
Sting has a ferocious fitness regime and a healthy diet. He drinks. He does not smoke. He has tried Botox twice, to relax a wrinkle on his forehead, but has no plans to try it again.
‘I don’t want to go down that path. I am not that vain.’
He has lived the rock ’n’ roll life to the full and is candid about it. In fact, he seems a man of few secrets. He emails a close coterie of friends on a regular basis and that almost acts as his diary.
Have there been failures? He hesitates. He divorced his first wife, the mother of his two eldest children, and his memoir hints of other sadnesses.
‘Relationships could have been better. No names. I’m still learning. When you’re young you make mistakes. But were they failures? It’s not a word I like.’
What has certainly worked is his marriage. He is passionate about Trudie.
‘I am married to an extraordinary, gifted woman who surprises me every day with her intelligence, her compassion and her talent.
'Above all else, I like her. She walks into a room and my world lights up. She is sunshine.
'I am very fortunate. I like what she says, the way she laughs. Her sense of humour.
'We share the same nostalgia, we come from the same working-class homes in the North of England. We remember the same TV shows, same commercials, same daft jokes that tickled us as kids.
‘We have a lot in common. Both of us went to grammar school. I was educated with kids like me but also lawyers’ and doctors’ sons learning eclectic things with sons of miners, every sort. It gave you a sense of the world, a bigger world.
‘But marriage is a daily negotiation, a daily compromise, a daily debate, a reassessment.
'I make all the big decisions, but luckily in the past 30 years there haven’t been any!
'I don’t want to jinx it by saying we have a secret formula. We appreciate our time together. I miss her when I am touring and we are apart.’
'I came up in an era of playing pubs for ten quid each and going back night after night,' he said. The Police exploded into the charts with Roxanne in 1979 and went on to have five No 1 records
When it comes to overnight stars like Justin Bieber, he says he’s glad he had to work from the ground up to get his rewards.
‘I came up in an era of playing pubs for ten quid each and going back night after night. I served on the shop floor. It builds a resilience and a toughness.
'If it had all been handed to me on a plate, I’m not sure I would appreciate it or have survived.
‘These days you can become an international superstar overnight with a video aged 18 or 19, but I don’t envy them.
'I don’t know how you cope with that without another life with which to compare it. I had a job, a mortgage and children. I was a tax worker! It’s not about fame – anyone who wants fame needs their head examined – it is about happiness.
‘But the shop floor I have described has disappeared. Pub rock became stadium rock, so there aren’t places for people to play. It’s hard for young musicians. You can make a killing, but it’s hard to make a living.’
Does he feel guilty about his wealth?
‘Why would I feel guilty? It’s not a useful emotion. I use my houses and love having them. I am grateful I have made money.
'I appreciate it because I spent much time without it. I use my money well. I am not a billionaire. I am very well off and I am certainly not complaining. I was not given it. I earned it through hard work and it was hard work. You try singing for two hours, getting on a plane every day. It’s hard, but I love it.’
Despite the fame, he tries to live as normal a life as possible.
‘I demand a citizen’s life – I really do. Walking the street; going to a bar on my own. But there is also a bit of the school master in me.’
When he was mobbed at the airport, he firmly told fans it was inappropriate to be chasing autographs when he was trying to get his luggage.
‘I want to be able to pick up my bags from the carousel and walk to the car. There are times when I don’t want or need attention.’
The Last Ship, which had its world premiere in Chicago last week, draws upon Sting's early life growing up around the harsh shipyard docks
Sting is not interested in party politics, but instead takes a philosophical view on events, including the war on terror.
‘It’s a very odd phrase this “war on terror”,’ he says. ‘Let’s try to understand it a bit before we declare war on it. I think most of our problems are a lack of consciousness about things, a low level of understanding of reality.
'For me, jihad is a metaphor – you are fighting your own demons in your own mind. The Promised Land is another metaphor. The Virgin Birth, Adam and Eve is a metaphor. They are beautiful metaphors but when you accept them as literally true then you are in very dangerous territory.
'This is happening in all religions. I don’t have a religion. They have a right to believe but they can’t foist that on everyone else. We are not blameless. We created Iraq, Jordan, Syria.
'We just drew arbitrary lines on a map to control resources and people, disregarding tribal affinities, and that is always going to cause problems. No belief or region has a monopoly on stupidity.’
And on that note it is time to head back to the theatre. He is happy to spend a 12-hour day making sure his new baby gets better and better.
‘The play continues to grow and it is exciting but there is still much to do. I’m utterly exhausted but seriously happy.’
The show must go on. It is a piece of musical theatre as compelling on the head, the heart – and the toe. Singing, rhyming couplets – and spending. It’s what Sting does.
| – Sting may be worth more than $306 million, but his six children will have to make their own way, he tells the Daily Mail's Sunday magazine. First of all, "I told them there won’t be much money left because we are spending it!" he explains. "We have a lot of commitments. What comes in, we spend, and there isn’t much left." But beyond that, he says, "I certainly don’t want to leave them trust funds that are albatrosses round their necks. They have to work. All my kids know that and they rarely ask me for anything, which I really respect and appreciate." He adds that he would help them if they were in trouble, but so far he hasn't really had to. "They have this work ethic that makes them want to succeed on their own merit," he says. "People make assumptions, that they were born with a silver spoon in their mouth, but they have not been given a lot." The revelation came as a new survey revealed that many of the ultra-wealthy worry that if they give their kids too much, it will ruin their ambition, the Mail notes. Anderson Cooper said earlier this year that's the reason he won't be inheriting any of his mom's $200 million fortune. | <s>[INST]How the other half fear: Super-rich worry that their wealth is killing drive and ambition in their children
Survey looked at top fears of 4,500 of the world's wealthiest families
Found wealthiest worried about their fortunes killing children's drive
Fear ranked above worries over investments and marital breakdown
Sting said today that his children will not inherit any of his £180million
With millions of pounds in the bank, you might have thought the world's super-rich wouldn't have a care in the world.
But a new survey has revealed the top fears of the world's wealthiest people, and one of the most common is that their money is their children's ambition and drive to do well.
For the most successful - defined as those with fortunes of $10million (£5.9million) and above - worries about children's motivation came second only to worries about their own health.
Sting said his kids will not inherit his £180million fortune as the money will be an 'albatross around their necks'
According to the study, by law firm Withersworldwide, fears over children's ambition come above worries about investments failing, inability to provide for the family, and even divorce.
Among those with a fortune of less than $10million the fear still ranked highly, but came in fourth place, behind health troubles and worries over income.
The study found that, wealthy families have the most to fear from third generation family members when it comes to losing the family millions.
Sara Cormack, a partner at Wither's, said: 'If the first generation are wealth creators then the second generation tend to be wealth preservers, but it is the third generation that families are most worried about.
'If they have had everything put on a plate for them without seeing any of the hard graft that goes into creating that wealth, then they can lose track of how best to use that wealth and how ifficult it was to build up in the first place.'
Former Police lead singer and musician Sting has today said he will not be passing on any of his £180million fortune to his children because he wants them to earn their money themselves.
He said: ‘I told them there won’t be much money left because we are spending it! We have a lot of commitments. What comes in, we spend, and there isn’t much left.
Nigella Lawson previously said that not having to earn their own money 'ruins people' while Brooklyn Beckham was encouraged to get a job earning £2.68 an hour in a coffee shop by David and Victoria
‘I certainly don’t want to leave them trust funds that are albatrosses round their necks.
‘They have to work. All my kids know that and they rarely ask me for anything, which I really respect and appreciate.
‘Obviously, if they were in trouble I would help them, but I’ve never really had to do that. They have the work ethic that makes them want to succeed on their own merit.’
Celebrity chef Nigella Lawson also said that her children will not be passed any of her own fortune, adding that 'it ruins people not having to earn their own money.'
According to reports, Brooklyn Beckham recently got a job in a West London coffee shop earning £2.68 an hour after being encouraged to do it by parents David and Victoria, who are worth an estimated £165million.
The data, a rare insight into the minds of the world's most powerful, was based on surveys of more than 4,500 and interviews with 16 very wealthy families from Europe, Asia and North America.
Families interviewed said they were using charitable donations or setting up a new business to give the family a renewed sense of direction.
Some even said they had drawn up a family statement, similar to a business statement, in order to give the next generation a purpose and something to achieve.
||||| Why my children will not be inheriting my £180million fortune: Sting wants his sons and daughters to earn their way (and says he's spending all his money anyway)
As one of the world’s most successful rock stars, he has risen from an impoverished childhood to amass a huge fortune.
Now Sting has made it clear that his children will also have to earn their own way and should not expect to benefit from his £180 million earnings.
In a frank interview in today’s Mail on Sunday Event magazine, the former Police frontman said he expected his three sons and three daughters to work, and added that there would not be much left to inherit anyway.
Sting, 62, who still has more than 100 people on his payroll, said: ‘I told them there won’t be much money left because we are spending it! We have a lot of commitments. What comes in, we spend, and there isn’t much left.’
He added: ‘I certainly don’t want to leave them trust funds that are albatrosses round their necks.
‘They have to work. All my kids know that and they rarely ask me for anything, which I really respect and appreciate.
‘Obviously, if they were in trouble I would help them, but I’ve never really had to do that. They have the work ethic that makes them want to succeed on their own merit.’
Sting is not the only celebrity who expects their children to stand on their own feet.
Celebrity chef Nigella Lawson said a few years ago: ‘I am determined that my children should have no financial security. It ruins people not having to earn money.’
READ THE FULL INTERVIEW BELOW
Sting had to escape his family and abandon his North East roots. 'It was a pretty violent wrench. I didn't feel I belonged there and the family was pretty dysfunctional in many ways,' he said
It’s not exactly rock ’n’ roll, but the woman who really changed Sting’s life – sorry, Trudie – was the Queen Mother.
Young Gordon Sumner, dressed in his Sunday best almost 50 years ago, was mesmerised as her Rolls-Royce swished past the front door of his street in Wallsend, North Tyneside.
The Sumners were poor, working-class Geordies; his parents Audrey, a hairdresser, and Ernie, a milkman.
The Royal visitor was there to launch a ship built at the end of his street at the Swan Hunter shipyard. Sting’s grandfather had been a shipwright and the young Sumner was expected to go into a manual job, too.
'I've never hidden my age. I am a father and now a grandfather,' said Sting
The biggest vessels on the planet were hammered, welded and built there long before Gordon became Sting (named for wearing a black-and-yellow jersey, like a wasp).
‘The Queen Mum waved and looked at me, and I looked back at her and that was it,’ he says.
‘There and then I thought, I am going to be rich, famous, successful and drive a Rolls-Royce like her.’
He decided he would use his voice and guitar to get a big house in the country, great wealth and acclaim. And so it all came to pass.
Now aged 62, the rock star, eco-warrior, father of six and grandfather laughs as he tells of the inspiration for his aspiration, all courtesy of the House of Windsor.
This is just one of a torrent of revealing anecdotes in a candid and wide-ranging interview, in which he tells Event about his complicated family background, his politics, children, death, drugs, Botox, the secrets of his long and happy marriage – and why his children won’t be getting their hands on his fortune.
Today it’s his own childhood that’s playing on the mind of the boy from Wallsend who went on to buy seven homes across Britain, Italy and the U.S., sell more than 100 million records and earn an estimated £180 million.
Because to get all that, Sting tells me, he had to escape his family and abandon his North East roots.
‘It was a pretty violent wrench. I didn’t feel I belonged there and the family was pretty dysfunctional in many ways. My parents were not happy together.
'They loved their kids but it was a toxic environment. I needed to escape and I am glad I did.’
His mother was unfaithful, which eventually led to the breakdown of the marriage, and divorce.
Sting pursued his dream, which his father dismissed as delusional. And, at times, fame and fortune did look like fantasy, as Sting struggled through a series of jobs before finally becoming a teacher, his musical talents unrecognised.
'I demand a citizen's life - I really do. Walking the street; going to a bar on my own,' Sting said
He moved to London and began hurtling up and down the M1 to play gigs in pubs.
It was all small beer until 1979, when with his band, The Police, he exploded into the charts with Roxanne and everything changed.
And so the rest – five No 1 records with The Police, huge success as a solo artist, starring roles in movies, rainforest crusades, 16 Grammy awards and the most enduring marriage in rock ’n’ roll (not to mention fending off 1,000 questions about tantric sex) – is well-rehearsed history.
Less well known is the acutely personal inspiration for his latest project, a compulsively toe-tapping, heart-rending musical called The Last Ship.
The musical, which had its world premiere in Chicago last week, draws upon his early life growing up around the harsh shipyard docks. Sitting in his 20th-floor penthouse in a Chicago hotel after overseeing final preparations for The Last Ship’s maiden voyage, Sting talks with boyish wonder that his musical, four years in the making, is finally on stage. Next stop, Broadway.
‘The irony is that I’m going back to Wallsend, from where I had done everything in my power to escape,’ he says.
‘But we have to go back to where we came from and reassess, give thanks for it and honour it. I want to celebrate where I came from; that town, what they did, and the hardship.’
In The Last Ship, a young man runs away from home, returning 15 years later to discover he had fathered a child before he left, only to abandon his home town again, on a ship after the shipyard goes bust.
The songs, he says, came in a rush of inspiration following a period of writer’s block. He knew it should be a musical, and from the off knew that one of his oldest pals from the North East, Jimmy Nail, would star in it. (The actor and sometime musician is the one person on the planet who gets to call Sting Gordon.) The music is as addictive as his most potent songs – all are written by Sting – and after Broadway he would be happy to see it open in London.
'I am married to an extraordinary, gifted woman,' said Sting of wife Trudie Styler
The story draws on Sting’s ruptured relationship with his father.
‘A father’s love can sometimes be misconstrued,’ he says.
‘It can be about control; it comes from anxiety.
'A father wants to dictate to a son what he should or should not be doing. And to my father the ambition I had seemed like bulls***, pie in the sky. And he wasn’t wrong. I wanted to be a successful musician; the chances of that coming off were millions to one. He thought it was ridiculous. “Get a proper job!”
‘Once I had become successful he was proud of me, but he never really understood it.
'I passed the 11-plus to get into a grammar school with a scholarship but he had wanted me to go to a technical school. Engineering was what he knew and did.’
Sting’s aim was more fanciful.
‘I had some vague idea I wanted to study the classics, speak French and Latin.’
His goal was always to escape.
Such aspirations were more encouraged by his mother.
‘She initiated me in the dark arts of music and dreaming. She lived her life through me and encouraged me to do all the things my dad did not understand.
'Did I have to divorce my dad? As much as any son has to do so to individuate. You have to. It’s part of growing up. You have to leave the nest. Sometimes it’s painful. It is necessary.’
Sting did not attend either of his parents’ funerals, because he felt the inevitable media intrusion would be disrespectful, but he did pay his dad a final farewell as he lay dying of cancer.
As he sat beside him, Sting suddenly realised ‘with the jolt of an electrical shock’ that for all their differences, their hands were identical. “We have the same hands, Dad, look!” I was a child again, desperately trying to get his attention.’
Sting held his father’s hand next to his own, but little was said by these two strong Tyneside men. One sentence, however, stayed in Sting’s memory.
‘Aye, son, but you used yours better than I used mine.’
It was the first time Sting could recall ever hearing a compliment from his dad, or being acknowledged for what he had achieved.
His father, just 59, closed his eyes in exhaustion, Sting kissed him softly in the centre of his forehead and whispered that he was a good man and that he loved him. They never saw each other again.
On his children: 'They have this work ethic that makes them want to succeed on their own merit. People make assumptions, that they were born with a silver spoon in their mouth, but they have not been given a lot'
For years Sting felt unable to grieve properly for the loss of his parents.
He dedicated his 2005 memoir, Broken Music, to his parents but his new musical is obliquely a tribute as well. His voice lowers to just above a whisper as he recalls his dad. It is still a tender subject, 27 years after his death.
When I ask Sting when he last cried, there is a silence before he says: ‘Just now.’
And he clearly is moved. He does not do public tears. The musical ends with a funeral, a joyous and celebratory one, at sea, and he feels as if many wounds are being unconsciously healed, many unsaid words being heard.
‘Last night [at the theatre] I just thought back to my dad,’ he says, ‘and I think other members of the crew also did to theirs.’
Mortality is on Sting’s mind, as he is now three years shy of 65, but he says he is relaxed about growing old.
‘I’ve never hidden my age. I am a father and now a grandfather and I am proud of that [his youngest son, Giacomo, is 18 and his eldest, Joseph, 37].
‘I have a story still to tell and part of that is I am facing the end of my life.
'I have lived more of my life than is to come: that is an interesting place for an artist – more interesting than writing about your first girlfriend. It is kind of serious.
'I have lived more of my life than is to come: that is an interesting place for an artist - more interesting than writing about your first girlfriend. It is kind of serious,' said Sting
'In our 60s, how do we face this imponderable idea that we are not going to exist any more? We make art. We tell stories. We have to face it, to tell it. I am certainly not ready for death. Do I fear it? Well, I fear sudden death. I want to die consciously. I want to see the process. I suppose I already do.
'My eyesight is not as good as it used to be, nor my hearing. I am still extremely fit but have to work hard. But we decay. I love what Christopher Hitchens said about death – you have been asked to leave the party and the problem is the party will carry on without you. Very eloquent.
'But I am interested in the future. What will happen to the planet and us? I want to use every minute to enjoy it.’
While Sting outshone his parents, the challenge now for his own children is competing with the success he’s achieved through what he modestly calls his ‘singing and rhyming couplets’.
'I passed the 11-plus to get into a grammar school with a scholarship,' said Sting
‘My generation all assumed we would have a better standard of living. The one that we spawned cannot assume that.
'With my children there is great wealth, success – a great shadow over them – so it’s no picnic at all being my child. I discuss that with them; it’s tough for them.’
Sting does not believe they will inherit great riches.
‘I told them there won’t be much money left because we are spending it! We have a lot of commitments. What comes in we spend, and there isn’t much left.
'I certainly don’t want to leave them trust funds that are albatrosses round their necks. They have to work. All my kids know that and they rarely ask me for anything, which I really respect and appreciate.
'Obviously, if they were in trouble I would help them, but I’ve never really had to do that.
'They have this work ethic that makes them want to succeed on their own merit. People make assumptions, that they were born with a silver spoon in their mouth, but they have not been given a lot.’
Sting has more than 100 people on his payroll.
‘I keep a community of people going. My crew, my band, my staff... it’s a corporation!’ Who runs it? ‘Trudie! Well, a large aspect of it is Trudie, but I have a very good team of managers and lawyers. They all need paying, too.’
Selling the family home in London should raise some extra funds, then. The nine-bedroom townhouse, a stone’s throw from Buckingham Palace, is currently on the market for more than £15 million.
‘It’s just too big,’ he says. ‘The kids have all gone and there are just so many empty bedrooms. We’re just rattling around. But we are not leaving. I love England. I’m still English.’
Sting is not afraid to speak his mind and has stuck his neck out by campaigning for the decriminalisation of drugs. Does he really believe they help the creative process?
'Did I have to divorce my dad? As much as any son has to do so to individuate,' he said
‘I think if they’re used specifically as tools for a stated purpose. As in, “I’ll now smoke this joint and I’ll write a song... or I will write a piece of poetry.”
'Then I think it’s perfectly acceptable. But if you’re just taking stuff to get out of it, then you’ll just get out of it.
'If I’m feeling stuck on a lyric or an idea isn’t quite gelling, sometimes a puff of weed will free it up.
'I rarely smoke it socially. It’s a tool, just as a pen is. I’m not alone. Several artists have used drugs to make great art.
‘I certainly wouldn’t advocate that you have to take drugs to make art, but then you can’t nullify the work of The Beatles. They took LSD and they made fantastic albums.
'Miles Davies made the most extraordinary music on heroin.
'Some people can cope with it perfectly well. I’m not here to make rules, or even state that there should be any rules. Drugs are dangerous, without a doubt.
'At the same time they can be useful tools but they need to be thought about as tools.’
So where does he stand on the legalisation of drugs?
‘Legalising is a very complex issue. Decriminalisation is a first step, because I don’t think it [criminalisation] helps. I don’t think the social problems related to drugs are helped by the legal system or the police.
'Social problems and mental problems are best dealt with by psychiatrists.’
And what about when you see casualties of drugs, like Whitney Houston or Amy Winehouse?
‘There are laws in place right now and they haven’t protected Amy, they haven’t protected anyone. I tell my children to be extremely careful. Luckily, they’re not particularly prone to drug-taking, to my knowledge. But they’re smart and they’re careful.
‘The drug laws aren’t helping. We need a really honest debate in society. People will tend to want to make life richer. Life seems flat a lot of the time. Chemicals, alcohol, marijuana can help. It’s almost a spiritual need to re-enchant life.
'I think that people are disenchanted with modern living and the drug culture is an attempt to re-enchant the world. It can, and it can fail.’
Sting's childhood home in Wallsend on Tyneside
Sting has a ferocious fitness regime and a healthy diet. He drinks. He does not smoke. He has tried Botox twice, to relax a wrinkle on his forehead, but has no plans to try it again.
‘I don’t want to go down that path. I am not that vain.’
He has lived the rock ’n’ roll life to the full and is candid about it. In fact, he seems a man of few secrets. He emails a close coterie of friends on a regular basis and that almost acts as his diary.
Have there been failures? He hesitates. He divorced his first wife, the mother of his two eldest children, and his memoir hints of other sadnesses.
‘Relationships could have been better. No names. I’m still learning. When you’re young you make mistakes. But were they failures? It’s not a word I like.’
What has certainly worked is his marriage. He is passionate about Trudie.
‘I am married to an extraordinary, gifted woman who surprises me every day with her intelligence, her compassion and her talent.
'Above all else, I like her. She walks into a room and my world lights up. She is sunshine.
'I am very fortunate. I like what she says, the way she laughs. Her sense of humour.
'We share the same nostalgia, we come from the same working-class homes in the North of England. We remember the same TV shows, same commercials, same daft jokes that tickled us as kids.
‘We have a lot in common. Both of us went to grammar school. I was educated with kids like me but also lawyers’ and doctors’ sons learning eclectic things with sons of miners, every sort. It gave you a sense of the world, a bigger world.
‘But marriage is a daily negotiation, a daily compromise, a daily debate, a reassessment.
'I make all the big decisions, but luckily in the past 30 years there haven’t been any!
'I don’t want to jinx it by saying we have a secret formula. We appreciate our time together. I miss her when I am touring and we are apart.’
'I came up in an era of playing pubs for ten quid each and going back night after night,' he said. The Police exploded into the charts with Roxanne in 1979 and went on to have five No 1 records
When it comes to overnight stars like Justin Bieber, he says he’s glad he had to work from the ground up to get his rewards.
‘I came up in an era of playing pubs for ten quid each and going back night after night. I served on the shop floor. It builds a resilience and a toughness.
'If it had all been handed to me on a plate, I’m not sure I would appreciate it or have survived.
‘These days you can become an international superstar overnight with a video aged 18 or 19, but I don’t envy them.
'I don’t know how you cope with that without another life with which to compare it. I had a job, a mortgage and children. I was a tax worker! It’s not about fame – anyone who wants fame needs their head examined – it is about happiness.
‘But the shop floor I have described has disappeared. Pub rock became stadium rock, so there aren’t places for people to play. It’s hard for young musicians. You can make a killing, but it’s hard to make a living.’
Does he feel guilty about his wealth?
‘Why would I feel guilty? It’s not a useful emotion. I use my houses and love having them. I am grateful I have made money.
'I appreciate it because I spent much time without it. I use my money well. I am not a billionaire. I am very well off and I am certainly not complaining. I was not given it. I earned it through hard work and it was hard work. You try singing for two hours, getting on a plane every day. It’s hard, but I love it.’
Despite the fame, he tries to live as normal a life as possible.
‘I demand a citizen’s life – I really do. Walking the street; going to a bar on my own. But there is also a bit of the school master in me.’
When he was mobbed at the airport, he firmly told fans it was inappropriate to be chasing autographs when he was trying to get his luggage.
‘I want to be able to pick up my bags from the carousel and walk to the car. There are times when I don’t want or need attention.’
The Last Ship, which had its world premiere in Chicago last week, draws upon Sting's early life growing up around the harsh shipyard docks
Sting is not interested in party politics, but instead takes a philosophical view on events, including the war on terror.
‘It’s a very odd phrase this “war on terror”,’ he says. ‘Let’s try to understand it a bit before we declare war on it. I think most of our problems are a lack of consciousness about things, a low level of understanding of reality.
'For me, jihad is a metaphor – you are fighting your own demons in your own mind. The Promised Land is another metaphor. The Virgin Birth, Adam and Eve is a metaphor. They are beautiful metaphors but when you accept them as literally true then you are in very dangerous territory.
'This is happening in all religions. I don’t have a religion. They have a right to believe but they can’t foist that on everyone else. We are not blameless. We created Iraq, Jordan, Syria.
'We just drew arbitrary lines on a map to control resources and people, disregarding tribal affinities, and that is always going to cause problems. No belief or region has a monopoly on stupidity.’
And on that note it is time to head back to the theatre. He is happy to spend a 12-hour day making sure his new baby gets better and better.
‘The play continues to grow and it is exciting but there is still much to do. I’m utterly exhausted but seriously happy.’
The show must go on. It is a piece of musical theatre as compelling on the head, the heart – and the toe. Singing, rhyming couplets – and spending. It’s what Sting does.
[/INST]– Sting may be worth more than $306 million, but his six children will have to make their own way, he tells the Daily Mail's Sunday magazine. First of all, "I told them there won’t be much money left because we are spending it!" he explains. "We have a lot of commitments. What comes in, we spend, and there isn’t much left." But beyond that, he says, "I certainly don’t want to leave them trust funds that are albatrosses round their necks. They have to work. All my kids know that and they rarely ask me for anything, which I really respect and appreciate." He adds that he would help them if they were in trouble, but so far he hasn't really had to. "They have this work ethic that makes them want to succeed on their own merit," he says. "People make assumptions, that they were born with a silver spoon in their mouth, but they have not been given a lot." The revelation came as a new survey revealed that many of the ultra-wealthy worry that if they give their kids too much, it will ruin their ambition, the Mail notes. Anderson Cooper said earlier this year that's the reason he won't be inheriting any of his mom's $200 million fortune.</s> |
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to approve
any regulatory action shall
take or fail to take, or threaten to take or fail to take,
recommend or direct that others take or fail to take, or
threaten to so recommend or direct,
approve the taking or failing to take, or threaten to so
approve,
such regulatory action because of any disclosure by a person
subject to the action, or by any other person, of information that the
person believed indicative of:
(A) violation or inconsistent application of any law, rule,
regulation, policy, or internal standard;
(B) arbitrary action or other abuse of authority;
(C) mismanagement;
(D) Waste or misallocation of resources;
(E) Inconsistent, discriminatory or
disproportionate enforcement;
(F) endangerment of public health or safety;
(G) personal favoritism; or
(H) coercion for partisan political purposes;
by any agency or its employees.
(2) An action shall be deemed to have been taken, not taken,
approved, or recommended because of the disclosure of information
within the meaning of subsection (b)(1) if the disclosure of
information was a contributing factor to the decision to take, not to
take, to approve, or to recommend.
SEC. 4. PROHIBITED REGULATORY PRACTICE AS A DEFENSE TO AGENCY ACTION.
(a) In any administrative or judicial action or proceeding, formal
or informal, by an agency to create, apply or enforce any obligation,
duty or liability under any law, rule or regulation against any person,
the person may assert as a defense that the agency or one or more
employees of the agency have engaged in a prohibited regulatory
practice with respect to the person or to a related entity in
connection with the action or proceeding.
(b) If the existence of a prohibited regulatory practice is
established, the person may be required to comply with the obligation,
duty or liability to the extent compliance is required of and enforced
against other persons similarly situated, but no penalty, fine,
damages, costs or other obligation except compliance shall be imposed
on the person.
SEC. 5. ENFORCEMENT.
(a) Any agency, and any employee of an agency, engaging in a
prohibited regulatory practice may be assessed a civil penalty of not
more than $25,000 for each such practice. In the case of a continuing
prohibited regulatory practice, each day that the practice continues
shall be deemed a separate practice.
(b) The President shall, by regulation, establish procedures
providing for the administrative enforcement of the requirements of
subsection (a) of this section.
SEC. 6. CITIZEN SUITS.
(a) Any person injured or threatened by a prohibited regulatory
practice may commence a civil action on his own behalf against any
person or agency alleged to have engaged in or threatened to engage in
such practice.
(b) Any action under subsection (a) of this section shall be
brought in the district court for any district in which the alleged
prohibited regulatory practice occurred or in which the alleged injury
occurred. The district court shall have jurisdiction, without regard to
the amount in controversy or the citizenship of the parties, to:
(1) restrain any agency or person who has engaged or is
engaging in any prohibited regulatory practice;
(2) order the cancellation or remission of any penalty,
fine, damages, or other monetary assessment that resulted from
a prohibited regulatory practice;
(3) order the rescission of any settlement that resulted
from a prohibited regulatory practice;
(4) order the issuance of any permit or license that has
been denied or delayed as a result of a prohibited regulatory
practice;
(5) order the agency and/or the employee engaging in a
prohibited regulatory practice to pay to the injured person
such damages as may be necessary to compensate the person for
any harm resulting from the practice, including damages for--
(A) injury to, deterioration of, or destruction of
real or personal property;
(B) loss of profits from idle or underutilized
resources, and from business forgone;
(C) costs incurred, including costs of compliance
where appropriate;
(D) loss in value of a business;
(E) reasonable legal, consulting and expert witness
fees; or
(F) payments to third parties;
(6) order the payment of punitive damages, in an amount not
to exceed $25,000 for each such prohibited regulatory practice,
provided that, in the case of a continuing prohibited
regulatory practice, each day that the practice continues shall
be deemed a separate practice.
SEC. 7. OFFICE OF THE SPECIAL COUNSEL.
(a) Any person who has reason to believe that any employee of any
agency has engaged in a prohibited regulatory practice may request the
Special Counsel established by section 1211 of title 5, United States
Code, to investigate.
(b) The Special Counsel shall have the same power to investigate
prohibited regulatory practices that it has to investigate prohibited
personnel practices pursuant to section 1212 of title 5, United States
Code. | Provides persons subject to regulatory action with protection against reprisal for disclosing agency waste, mismanagement, abuse of authority, or other prohibited regulatory practices. | <s>[INST]SECTION 1. PURPOSE.
The Federal regulatory system should be implemented consistent with
the principle that any person subject to Government regulation should
be protected against reprisal for disclosing information that the
person believes is indicative of--
(1) violation or inconsistent application of any law, rule,
regulation, policy, or internal standard;
(2) arbitrary action or other abuse of authority;
(3) mismanagement;
(4) waste or misallocation of resources;
(5) inconsistent, discriminatory or disproportionate
enforcement proceedings;
(6) endangerment of public health or safety;
(7) personal favoritism; and
(8) coercion for partisan political purposes;
by any agency or its employees.
SEC. 2. COVERAGE.
This Act shall apply to:
(1) Any agency of the Federal Government as defined in
section 551 of title 5, United States Code.
(2) Any agency of a State government that exercises
authority under Federal law, or that exercises authority under
State law establishing a program approved by a Federal agency
as a substitute for or supplement to a program established by
Federal law.
SEC. 3. PROHIBITED REGULATORY PRACTICES.
(a) For purposes of this title, ``prohibited regulatory practice''
means any action described in subsection (b) of this section.
(b)(1) No employee of an Agency who has authority--
to take or direct other employees to take,
to recommend, or
to approve
any regulatory action shall
take or fail to take, or threaten to take or fail to take,
recommend or direct that others take or fail to take, or
threaten to so recommend or direct,
approve the taking or failing to take, or threaten to so
approve,
such regulatory action because of any disclosure by a person
subject to the action, or by any other person, of information that the
person believed indicative of:
(A) violation or inconsistent application of any law, rule,
regulation, policy, or internal standard;
(B) arbitrary action or other abuse of authority;
(C) mismanagement;
(D) Waste or misallocation of resources;
(E) Inconsistent, discriminatory or
disproportionate enforcement;
(F) endangerment of public health or safety;
(G) personal favoritism; or
(H) coercion for partisan political purposes;
by any agency or its employees.
(2) An action shall be deemed to have been taken, not taken,
approved, or recommended because of the disclosure of information
within the meaning of subsection (b)(1) if the disclosure of
information was a contributing factor to the decision to take, not to
take, to approve, or to recommend.
SEC. 4. PROHIBITED REGULATORY PRACTICE AS A DEFENSE TO AGENCY ACTION.
(a) In any administrative or judicial action or proceeding, formal
or informal, by an agency to create, apply or enforce any obligation,
duty or liability under any law, rule or regulation against any person,
the person may assert as a defense that the agency or one or more
employees of the agency have engaged in a prohibited regulatory
practice with respect to the person or to a related entity in
connection with the action or proceeding.
(b) If the existence of a prohibited regulatory practice is
established, the person may be required to comply with the obligation,
duty or liability to the extent compliance is required of and enforced
against other persons similarly situated, but no penalty, fine,
damages, costs or other obligation except compliance shall be imposed
on the person.
SEC. 5. ENFORCEMENT.
(a) Any agency, and any employee of an agency, engaging in a
prohibited regulatory practice may be assessed a civil penalty of not
more than $25,000 for each such practice. In the case of a continuing
prohibited regulatory practice, each day that the practice continues
shall be deemed a separate practice.
(b) The President shall, by regulation, establish procedures
providing for the administrative enforcement of the requirements of
subsection (a) of this section.
SEC. 6. CITIZEN SUITS.
(a) Any person injured or threatened by a prohibited regulatory
practice may commence a civil action on his own behalf against any
person or agency alleged to have engaged in or threatened to engage in
such practice.
(b) Any action under subsection (a) of this section shall be
brought in the district court for any district in which the alleged
prohibited regulatory practice occurred or in which the alleged injury
occurred. The district court shall have jurisdiction, without regard to
the amount in controversy or the citizenship of the parties, to:
(1) restrain any agency or person who has engaged or is
engaging in any prohibited regulatory practice;
(2) order the cancellation or remission of any penalty,
fine, damages, or other monetary assessment that resulted from
a prohibited regulatory practice;
(3) order the rescission of any settlement that resulted
from a prohibited regulatory practice;
(4) order the issuance of any permit or license that has
been denied or delayed as a result of a prohibited regulatory
practice;
(5) order the agency and/or the employee engaging in a
prohibited regulatory practice to pay to the injured person
such damages as may be necessary to compensate the person for
any harm resulting from the practice, including damages for--
(A) injury to, deterioration of, or destruction of
real or personal property;
(B) loss of profits from idle or underutilized
resources, and from business forgone;
(C) costs incurred, including costs of compliance
where appropriate;
(D) loss in value of a business;
(E) reasonable legal, consulting and expert witness
fees; or
(F) payments to third parties;
(6) order the payment of punitive damages, in an amount not
to exceed $25,000 for each such prohibited regulatory practice,
provided that, in the case of a continuing prohibited
regulatory practice, each day that the practice continues shall
be deemed a separate practice.
SEC. 7. OFFICE OF THE SPECIAL COUNSEL.
(a) Any person who has reason to believe that any employee of any
agency has engaged in a prohibited regulatory practice may request the
Special Counsel established by section 1211 of title 5, United States
Code, to investigate.
(b) The Special Counsel shall have the same power to investigate
prohibited regulatory practices that it has to investigate prohibited
personnel practices pursuant to section 1212 of title 5, United States
Code.[/INST]Provides persons subject to regulatory action with protection against reprisal for disclosing agency waste, mismanagement, abuse of authority, or other prohibited regulatory practices.</s> |
David Mauricio Rivera (born September 16, 1965) is a Republican politician from Florida. He was a member of the U.S. House of Representatives for one term, representing parts of South Florida from 2011 to 2013. In 2012 he was named one of the most corrupt members of Congress by Citizens for Responsibility and Ethics in Washington.[1]
Early life, education, and early career [ edit ]
Rivera was born in New York City on September 16, 1965 and moved to Florida in 1974. He graduated from Miami Christian High School. He earned his Bachelor of Arts degree with honors in Political Science from Florida International University in 1986 and his MPA in 1994.[2]
After college, Rivera worked as Public Affairs Director for the Washington D.C.-based Valladares Foundation, an international human rights NGO. The organization was founded by U.S. Ambassador Armando Valladares, the former U.S. Ambassador to the United Nations Human Rights Commission. Then, he worked for the Office of Cuba Broadcasting managed by auspices of the U.S. State Department. He has also been an adjunct professor in the FIU School of Policy and Management. His articles on U.S.-Cuba relations have been published in The Miami Herald and El Nuevo Herald.
Florida House of Representatives [ edit ]
In 2002, he ran for Florida's 112th state house district. He defeated Ray Gonzalez in the Republican primary, 52–48%.[3] He won the general election unopposed. He won re-election unopposed in 2004, 2006, and 2008.
In addition to his legislative office, he has served the Republican Party as State Committeeman for the Republican Party of Florida and as the Executive Director for the Republican Party of Miami-Dade County.[4][5]
U.S. House of Representatives [ edit ]
Elections [ edit ]
2010
In January 2009, Rivera filed to run for the state senate seat being vacated by J. Alex Villalobos.[6] However, when neighboring U.S. Congressman Lincoln Diaz-Balart decided not to run for another term in 2010, his brother, U.S. Congressman Mario Diaz-Balart, opted to run for a new term in Lincoln's district rather than his current one. This created an opening in the seat and prompted Rivera to announce he would run for Florida's 25th congressional district on February 25, 2010. On August 24, he won the Republican primary with 63% of the vote.[7] On November 2, Rivera defeated Democratic nominee Joe Garcia 52%–43%.[8]
2012
Redistricting resulted in Rivera's district being renumbered as the 26th district. It lost its share of Collier County and picked up the Florida Keys, as well as portions of Miami-Dade County. While the old 25th leaned Republican, the new 26th is more of a swing district and is equally split between Democrats and Republicans. In a rematch from 2010, Garcia defeated Rivera 54%–43%.[9][10]
Committee assignments [ edit ]
Later career [ edit ]
In May 2014, Rivera announced he would run for Congress again.[11] He was defeated in the Republican primary, coming in fourth place with 7.5% of the vote.
In March 2016, David Rivera announced he would run for the open state house district 118, but lost to Democrat Robert Asencio by 53 votes.[12] In March 2017, Rivera announced he would run for the state house again in 2018, this time in neighboring district 105.[13]
See also [ edit ] ||||| It’s not easy policing the image of a member of Congress — especially when your boss is Rep. David Rivera, the Florida Republican freshman beset by so many public controversies that Majority Leader Eric Cantor declined to meet with him when he visited Miami last month.
So, on March 16 at 6:40 p.m., a Wikipedia editor with the handle “Lmveiga” decided to do some maintenance to Rivera’s Wikipedia page. First, Lmveiga removed a précis of the congressman’s legislative career, replacing it with a six-point list of “Rivera’s Legislative Accomplishments,” taken directly from his campaign website.
Text Size -
+
reset POLITICO 44
Then, Lmveiga removed the entire “controversies” section.
The deleted text included accusations that a David M. Rivera was named as the defendant in a domestic abuse case in 1994 (both the congressman and the victim have said he was not the defendant named.) The entry also included an allegation that Rivera was involved in a 2002 traffic accident with a truck that was moments from delivering fliers detailing the domestic abuse case. (Rivera said he was meeting the truck to pick up his own fliers.) The section also said Rivera amended his state financial disclosure forms after one of his primary listed sources of income, USAID, said it had no record of working with him. (Rivera said he had worked for subcontractors to whom he had promised anonymity.) And it said state law enforcement agencies were investigating $500,000 in payments to Rivera’s mother for work with a dog track for which Rivera, then a state lawmaker, had lobbied.
Wikipedia editors quickly restored the controversies section. And “Lmveiga” again deleted it.
Lmveiga is the twitter handle of Rivera’s press secretary, Leslie Veiga.
“My only interaction with Wikipedia editing, which has been personal interaction on my own personal time, has been to add factual, documented information and remove false, undocumented allegations,” Veiga said in response to an inquiry from POLITICO. “The information I added was well sourced and linked to legislation on the Florida House website that the congressman sponsored during his time in the state Legislature, as well as current information about his committee assignments and subcommittee assignments in the U.S. House.”
Wikipedia experts said Veiga has an uphill climb against the army of volunteer editors of the highly trafficked site, who will keep putting the controversies back into Rivera’s entry.
“You are never going to find success by trying to whitewash the details of the biography you don’t like,” said William Beutler, an enthusiast of the open-source encyclopedia who writes the blog The Wikipedian. Beutler has developed a “best practices” strategy for editing articles in which there might be a potential conflict of interest. “All Wikipedia aims to do is reflect what is public knowledge and has been widely reported, and [it] is a well of information about a public official’s career. Anything publicly reported about their career is fair game for a Wikipedia article,” he said.
That meant that for the Wikipedia editors, the links to the Miami Herald, St. Petersburg Times, CBS and POLITICO were enough of a citation to include in the entry.
Beutler said it’s not all that uncommon for staffers to edit congressional entries. On Capitol Hill, the habit of polishing an elected official’s online encyclopedia reference became a trend in 2006, after Reps. Marty Meehan, Gil Gutknecht and David Davis and Sens. Norm Coleman, Joe Biden, Tom Harkin and Dianne Feinstein were dinged when their staffers’ flattering alterations showed up in their bosses’ Wikipedia edit history. In early 2006, Wikinews, a news source linked to Wikipedia, investigated all edits coming from the House and Senate offices and found most Senate edits to be helpful. House edits were more difficult to trace.
During the 2008 election, Wikipedia’s online guardians often refereed, and sometimes waged, fierce battles over the pages of Barack Obama and Hillary Clinton — removing a photo depicting the current secretary of state as a walrus, for example, or references to the president as Kenyan-American. | – David Rivera’s been involved in a lot of controversies—so many that when Eric Cantor visited Miami last month, he refused to meet with him—but for a few minutes at a time, he’s had a clean slate on Wikipedia. Last month, Wikipedia editor “Lmveiga”—which is to say, Rivera’s press secretary, Leslie Veiga—went in and edited her boss's page, pasting in a list of “legislative accomplishments” straight from his campaign website, and deleting the entire “controversies” section, Politico reports. Among the allegations in that section: That Rivera was named the defendant in a 1994 domestic abuse case (something he and the victim both say isn’t true), that he got into a car crash with a truck carrying fliers about that case, and that state law enforcement agencies are investigating $500,000 that a dog track paid to Rivera's mother after he lobbied for it as a state legislator. Wikipedia quickly restored the section, which was well-sourced. Veiga deleted them again, but it was again quickly restored. The page has now been locked, with the controversy section intact—complete with a line about Veiga’s attempts to edit it. | <s>[INST]David Mauricio Rivera (born September 16, 1965) is a Republican politician from Florida. He was a member of the U.S. House of Representatives for one term, representing parts of South Florida from 2011 to 2013. In 2012 he was named one of the most corrupt members of Congress by Citizens for Responsibility and Ethics in Washington.[1]
Early life, education, and early career [ edit ]
Rivera was born in New York City on September 16, 1965 and moved to Florida in 1974. He graduated from Miami Christian High School. He earned his Bachelor of Arts degree with honors in Political Science from Florida International University in 1986 and his MPA in 1994.[2]
After college, Rivera worked as Public Affairs Director for the Washington D.C.-based Valladares Foundation, an international human rights NGO. The organization was founded by U.S. Ambassador Armando Valladares, the former U.S. Ambassador to the United Nations Human Rights Commission. Then, he worked for the Office of Cuba Broadcasting managed by auspices of the U.S. State Department. He has also been an adjunct professor in the FIU School of Policy and Management. His articles on U.S.-Cuba relations have been published in The Miami Herald and El Nuevo Herald.
Florida House of Representatives [ edit ]
In 2002, he ran for Florida's 112th state house district. He defeated Ray Gonzalez in the Republican primary, 52–48%.[3] He won the general election unopposed. He won re-election unopposed in 2004, 2006, and 2008.
In addition to his legislative office, he has served the Republican Party as State Committeeman for the Republican Party of Florida and as the Executive Director for the Republican Party of Miami-Dade County.[4][5]
U.S. House of Representatives [ edit ]
Elections [ edit ]
2010
In January 2009, Rivera filed to run for the state senate seat being vacated by J. Alex Villalobos.[6] However, when neighboring U.S. Congressman Lincoln Diaz-Balart decided not to run for another term in 2010, his brother, U.S. Congressman Mario Diaz-Balart, opted to run for a new term in Lincoln's district rather than his current one. This created an opening in the seat and prompted Rivera to announce he would run for Florida's 25th congressional district on February 25, 2010. On August 24, he won the Republican primary with 63% of the vote.[7] On November 2, Rivera defeated Democratic nominee Joe Garcia 52%–43%.[8]
2012
Redistricting resulted in Rivera's district being renumbered as the 26th district. It lost its share of Collier County and picked up the Florida Keys, as well as portions of Miami-Dade County. While the old 25th leaned Republican, the new 26th is more of a swing district and is equally split between Democrats and Republicans. In a rematch from 2010, Garcia defeated Rivera 54%–43%.[9][10]
Committee assignments [ edit ]
Later career [ edit ]
In May 2014, Rivera announced he would run for Congress again.[11] He was defeated in the Republican primary, coming in fourth place with 7.5% of the vote.
In March 2016, David Rivera announced he would run for the open state house district 118, but lost to Democrat Robert Asencio by 53 votes.[12] In March 2017, Rivera announced he would run for the state house again in 2018, this time in neighboring district 105.[13]
See also [ edit ] ||||| It’s not easy policing the image of a member of Congress — especially when your boss is Rep. David Rivera, the Florida Republican freshman beset by so many public controversies that Majority Leader Eric Cantor declined to meet with him when he visited Miami last month.
So, on March 16 at 6:40 p.m., a Wikipedia editor with the handle “Lmveiga” decided to do some maintenance to Rivera’s Wikipedia page. First, Lmveiga removed a précis of the congressman’s legislative career, replacing it with a six-point list of “Rivera’s Legislative Accomplishments,” taken directly from his campaign website.
Text Size -
+
reset POLITICO 44
Then, Lmveiga removed the entire “controversies” section.
The deleted text included accusations that a David M. Rivera was named as the defendant in a domestic abuse case in 1994 (both the congressman and the victim have said he was not the defendant named.) The entry also included an allegation that Rivera was involved in a 2002 traffic accident with a truck that was moments from delivering fliers detailing the domestic abuse case. (Rivera said he was meeting the truck to pick up his own fliers.) The section also said Rivera amended his state financial disclosure forms after one of his primary listed sources of income, USAID, said it had no record of working with him. (Rivera said he had worked for subcontractors to whom he had promised anonymity.) And it said state law enforcement agencies were investigating $500,000 in payments to Rivera’s mother for work with a dog track for which Rivera, then a state lawmaker, had lobbied.
Wikipedia editors quickly restored the controversies section. And “Lmveiga” again deleted it.
Lmveiga is the twitter handle of Rivera’s press secretary, Leslie Veiga.
“My only interaction with Wikipedia editing, which has been personal interaction on my own personal time, has been to add factual, documented information and remove false, undocumented allegations,” Veiga said in response to an inquiry from POLITICO. “The information I added was well sourced and linked to legislation on the Florida House website that the congressman sponsored during his time in the state Legislature, as well as current information about his committee assignments and subcommittee assignments in the U.S. House.”
Wikipedia experts said Veiga has an uphill climb against the army of volunteer editors of the highly trafficked site, who will keep putting the controversies back into Rivera’s entry.
“You are never going to find success by trying to whitewash the details of the biography you don’t like,” said William Beutler, an enthusiast of the open-source encyclopedia who writes the blog The Wikipedian. Beutler has developed a “best practices” strategy for editing articles in which there might be a potential conflict of interest. “All Wikipedia aims to do is reflect what is public knowledge and has been widely reported, and [it] is a well of information about a public official’s career. Anything publicly reported about their career is fair game for a Wikipedia article,” he said.
That meant that for the Wikipedia editors, the links to the Miami Herald, St. Petersburg Times, CBS and POLITICO were enough of a citation to include in the entry.
Beutler said it’s not all that uncommon for staffers to edit congressional entries. On Capitol Hill, the habit of polishing an elected official’s online encyclopedia reference became a trend in 2006, after Reps. Marty Meehan, Gil Gutknecht and David Davis and Sens. Norm Coleman, Joe Biden, Tom Harkin and Dianne Feinstein were dinged when their staffers’ flattering alterations showed up in their bosses’ Wikipedia edit history. In early 2006, Wikinews, a news source linked to Wikipedia, investigated all edits coming from the House and Senate offices and found most Senate edits to be helpful. House edits were more difficult to trace.
During the 2008 election, Wikipedia’s online guardians often refereed, and sometimes waged, fierce battles over the pages of Barack Obama and Hillary Clinton — removing a photo depicting the current secretary of state as a walrus, for example, or references to the president as Kenyan-American.[/INST]– David Rivera’s been involved in a lot of controversies—so many that when Eric Cantor visited Miami last month, he refused to meet with him—but for a few minutes at a time, he’s had a clean slate on Wikipedia. Last month, Wikipedia editor “Lmveiga”—which is to say, Rivera’s press secretary, Leslie Veiga—went in and edited her boss's page, pasting in a list of “legislative accomplishments” straight from his campaign website, and deleting the entire “controversies” section, Politico reports. Among the allegations in that section: That Rivera was named the defendant in a 1994 domestic abuse case (something he and the victim both say isn’t true), that he got into a car crash with a truck carrying fliers about that case, and that state law enforcement agencies are investigating $500,000 that a dog track paid to Rivera's mother after he lobbied for it as a state legislator. Wikipedia quickly restored the section, which was well-sourced. Veiga deleted them again, but it was again quickly restored. The page has now been locked, with the controversy section intact—complete with a line about Veiga’s attempts to edit it.</s> |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Capitol Visitor Center Authorization
Act of 1997''.
SEC. 2. ESTABLISHMENT OF CAPITOL VISITOR CENTER.
(a) In General.--The Architect of the Capitol, under the direction
of the United States Capitol Preservation Commission, is authorized--
(1) to plan, construct, furnish, and equip the Capitol
Visitor Center under the East Plaza of the United States
Capitol with associated improvements to the Capitol to provide
access thereto; and
(2) to reconstruct the East Plaza of the United States
Capitol and its environs to enhance its attractiveness, safety,
and security;
in a manner that preserves and maintains Olmstead's ``General Plan for
the Improvement of the United States Capitol Grounds'', 1874.
(b) Purposes.--The purposes of the Capitol Visitor Center shall
include--
(1) providing reception facilities, educational materials
and exhibits, information, amenities, a gift shop, and other
programs and facilities for members of the public visiting the
United States Capitol; and
(2) enhancing the security of the Capitol.
(c) Design.--Plans for construction of the Capitol Visitor Center
shall be substantially in accordance with the Final Design Report dated
November 10, 1995, submitted by the Architect of the Capitol to the
Committee on Transportation and Infrastructure of the House of
Representatives, the Committee on Rules and Administration of the
Senate, and the United States Capitol Preservation Commission, subject
to modifications approved by the Commission.
(d) Exhibits.--The informational and educational experience
afforded visitors to the Capitol Visitor Center, including all
exhibits, shall be the responsibility of the United States Capitol
Visitor Board under the direction of the United States Capitol
Preservation Commission, as approved by the House of Representatives
and the Senate. The Architect of the Capitol, the Clerk of the House of
Representatives, the Secretary of the Senate, the Sergeant at Arms of
the House of Representatives, and the Sergeant at Arms and Doorkeeper
of the Senate shall provide staff, support, and resources for the
installation, assembly, and maintenance of all exhibits and other
informational and educational fixtures and equipment. Exhibits and all
informational and educational materials shall be subject to section
7(b).
(e) Security Systems.--The design, installation, and maintenance of
security systems for the Capitol Visitor Center shall be the
responsibility of the Capitol Police Board in accordance with section
308 of the Legislative Branch Appropriations Act, 1996 (40 U.S.C. 212a-
4) and section 308 of the Legislative Branch Appropriations Act, 1997
(40 U.S.C. 212a-4a).
(f) Management.--After the opening of the Capitol Visitor Center to
the public, the Architect of the Capitol shall administer, maintain,
and improve the Capitol Visitor Center as part of the Capitol Building
and Grounds, subject to this Act and the oversight of the appropriate
officers and committees of the House of Representatives and the Senate.
(g) Definition of Project.--In this Act, the term ``project'' means
the activities and purposes set forth in subsections (a) through (f).
SEC. 3. UNITED STATES CAPITOL PRESERVATION COMMISSION; FINANCING PLAN;
SECURITY STUDY.
(a) Development of Project Implementation Capacity.--Not later than
30 days after the date of enactment of this Act, the United States
Capitol Preservation Commission shall meet at the call of either co-
chairman for the purpose of establishing a special committee of the
Commission to carry out the functions of the Commission in implementing
and overseeing the project.
(b) Financing Plan.--As soon as practicable after the date of
enactment of this Act, the United States Capitol Preservation
Commission shall develop a detailed plan for financing the project at
the lowest net cost to the Government. The financing plan shall provide
for--
(1) the acceptance of donations from public and private
sources to be used to minimize the use of or to repay any
appropriated or borrowed funds;
(2) the use of any revenues generated by the Capitol
Visitor Center to minimize the use of or to repay any
appropriated or borrowed funds and, to the extent available, to
pay the operating costs of the Capitol Visitor Center;
(3) the use of any other funds available for the
preservation and restoration of the Capitol; and
(4) only to the extent necessary, the use of appropriated
or borrowed funds.
The plan shall be submitted to Committees on Appropriations and House
Oversight of the House of Representatives and the Committees on
Appropriations and Rules and Administration of the Senate.
(c) Revolving Fund.--All funds described in subsection (b) shall be
deposited in the United States Capitol Visitor Center Revolving Fund,
which is hereby established in the Treasury. The Fund shall be managed
as provided in section 9602 of the Internal Revenue Code of 1986 and
shall be available, without fiscal year limitation, to carry out the
project, including--
(1) the reimbursement of appropriations accounts of the
Senate, the House of Representatives, and the Architect of the
Capitol for all costs associated with the operation of the
Capitol Visitor Center Gift Shop;
(2) the payment of costs of the continued conservation and
preservation of the Capitol Building; and
(3) the payment of costs of further acquisitions of fine
arts as approved by the Senate Commission on Art or the House
Fine Arts Board.
(d) Security Study.--The Capitol Police Board shall conduct a study
to assess security cost savings and other benefits resulting from the
construction and operation of the Capitol Visitor Center and shall
report the results of its study to the United States Capitol
Preservation Commission and to the Committees on Appropriations and
House Oversight of the House of Representatives and the Committees on
Appropriations and Rules and Administration of the Senate.
SEC. 4. CONSTRUCTION.
(a) Building Codes.--The project shall meet design standards
applicable under nationally recognized building codes, as determined by
the Architect of the Capitol. During construction, the Architect shall
conduct periodic inspections for the purpose of ensuring that such
standards are being met.
(b) Applicability of Certain Laws.--The project shall not be
subject to any Federal or State law (including law of the District of
Columbia) relating to taxes, building codes, studies, reports, permits,
or inspections.
SEC. 5. GIFTS.
(a) In General.--For the purposes of carrying out the project,
gifts or donations of services or property may be received, accepted,
held, and disposed of, subject to the provisions of the plan
promulgated under section 3.
(b) Treatment Under Tax Laws.--Any gift accepted in accordance with
the plan promulgated under section 3 shall be considered a gift to the
United States for the purposes of income, estate, and gift tax laws of
the United States.
SEC. 6. AUTHORITY TO CONTRACT.
Notwithstanding any other provision of law, the Architect of the
Capitol may establish competitive procedures for work on the project by
the use of prequalification standards and may award contracts on the
basis of contractor qualifications as well as price. Such procedures
and contract awards shall be final and conclusive upon all officers of
the Government.
SEC. 7. CAPITOL VISITOR BOARD.
(a) In General.--
(1) Authority of capitol visitor board.--The Capitol
Visitor Board, under the direction of the United States Capitol
Preservation Commission and subject to prior approval of the
House of Representatives and the Senate, shall establish the
Capitol Visitor Center operations, tour, exhibit and education
policies, including--
(A) establishing hours of operation, tour content,
and tour schedules;
(B) producing or selecting films, videos, exhibits,
publications, and other items of an educational nature;
and
(C) approving items for sale by the Capitol Visitor
Center gift shop.
(2) Consultation.--In carrying out this section, the
Capitol Visitor Board shall consult with the Historians of the
Senate and House of Representatives, the Senate Commission on
Art, the House Fine Arts Board, and any advisory board of the
United States Capitol Preservation Commission designated for
this purpose by the Commission.
(3) Other authorities not affected.--
(A) Security.--Nothing in this section affects the
authority of the Capitol Police Board with respect to
security of the Capitol, the Capitol Visitor Center, or their environs.
(B) Senate commission on art.--Nothing in this
section affects the authority of the Senate Commission
on Art with respect to the Old Senate Chamber and the
Old Supreme Court Chamber.
(b) Exhibits and Informational and Educational Material.--
(1) Exhibits.--Exhibits, including any audio, video, or
demonstrative presentations, shall illustrate the history and
the Constitutional role of the United States Congress and the
history, including art and architectural history, of the
Capitol.
(2) Informational and educational materials.--To assist
visitors, the Capitol Visitor Board shall publish or provide
for informational and educational materials for free
distribution to the public, in accordance with title 44, United
States Code. Materials provided for sale may be purchased
through approved procedures for the Capitol Visitor Center gift
shop and any revenues produced shall be deposited to the United
States Capitol Visitor Center Revolving Fund account as
approved by the United States Capitol Preservation Commission.
(c) Capitol Visitor Center Gift Shop.--
(1) Purpose.--The Capitol Visitor Center Board shall
establish and operate the Capitol Visitor Center Gift Shop in
accordance with policies approved by the United States Capitol
Preservation Commission and the appropriate oversight
committees of each House.
(2) Proceeds of sales or services.--All monies received
from sales or services of the Capitol Visitor Center Gift Shop
shall be deposited in the United States Capitol Visitor Center
Revolving Fund established by section 3(c) of this Act.
SEC. 8. AMENDMENTS RELATING TO THE UNITED STATES CAPITOL PRESERVATION
COMMISSION.
(a) Purposes.--Section 801(a) of the Arizona-Idaho Conservation Act
of 1988 (40 U.S.C. 188a(a)) is amended--
(1) by striking ``and'' at the end of paragraph (2); and
(2) by striking paragraph (3) and inserting the following:
``(3) carrying out functions assigned by the Capitol
Visitor Center Authorization Act of 1997; and
``(4) conducting other activities that directly facilitate,
encourage, or support the purposes specified in the preceding
paragraphs.''.
(b) Staff Support.--Section 801(e) Arizona-Idaho Conservation Act
of 1988 (40 U.S.C. 188a(e)) is amended by inserting ``Clerk of the
House of Representatives, the Secretary of the Senate, the Sergeant at
Arms of the House of Representatives, the Sergeant at Arms and
Doorkeeper of the Senate, the'' after ``The''.
(c) Delegation.--Section 801 of the Arizona-Idaho Conservation Act
of 1988 (40 U.S.C. 188a) is amended by adding at the end the following:
``(f) Delegation.--In addition to the special committee provided
for by section 3(a), the United States Capitol Preservation Commission
may delegate any functions to 1 or more special committees if the
membership of each such committee is drawn equally from the House of
Representatives and the Senate.''.
(d) Fund Transfers.--Section 803 of the Arizona-Idaho Conservation
Act of 1988 (40 U.S.C. 188a-2) is amended by adding at the end the
following:
``(f) Transfers.--Not later than 30 days after the date of
enactment of this Act, the balance in the account in excess of $250,000
shall be transferred to the fund established by section 3(c) of the
Capitol Visitor Center Authorization Act of 1997.''.
(e) Capitol Visitor Board.--
(1) Renaming.--Section 441 of the Legislative
Reorganization Act of 1970 (40 U.S.C. 851) is amended by
striking ``Capitol Guide Board'' each place it appears and
inserting ``Capitol Visitor Board''.
(2) Information.--Section 441(a) of the Legislative
Reorganization Act of 1970 (40 U.S.C. 851(a)) is amended by
inserting after ``Architect of the Capitol,'' the following:
``the Secretary of the Senate, the Clerk of the House of
Representatives,''.
SEC. 9. REPEAL.
(a) In General.--The provisions of title III of the National
Visitor Center Facilities Act of 1968 (40 U.S.C. 831) shall be repealed
to the extent that such provisions are inconsistent with the provisions
of this Act.
(b) Conforming Amendment.--Section 301 of the National Visitor
Center Facilities Act of 1968 (40 U.S.C. 831) is amended by striking
``the United States Capitol Historical Society,''. | Capitol Visitor Center Authorization Act of 1997 - Authorizes the Architect of the Capitol (AOC), under the direction of the U.S. Capitol Preservation Commission (Commission), to: (1) plan, construct, furnish and equip the Capitol Visitor Center (Center) under the East Plaza of the Capitol; and (2) reconstruct the East Plaza and its environs to enhance its attractiveness, safety, and security.
Requires the design of the Center to be substantially in accordance with the Final Design Report dated November 10, 1995, submitted by the AOC to specified congressional committees. Specifies entities responsible for Center exhibits, security systems, and management. Directs the Commission to: (1) establish a special committee to implement and oversee the Center project; and (2) develop and submit to specified congressional committees a detailed plan for financing the project at the lowest net cost to the Government. Establishes in the Treasury the United States Capitol Visitor Center Revolving Fund for the collection of deposits received under the financing plan. Directs the Capitol Police Board to study and report to specified congressional committees on the security cost savings and other cost benefits associated with the construction and operation of the Center.
Authorizes the AOC to establish competitive procedures for work to carry out the project by the use of prequalification standards, and to award contracts on the basis of contractor qualifications as well as price. States that such procedures and contract awards shall be final and conclusive upon all officers of the Government.
Directs the Capitol Visitor Center Board to: (1) establish Center operations, tour, exhibit, and education policies; and (2) establish and operate the Capitol Visitor Center Gift Shop.
Amends the Arizona-Idaho Conservation Act of 1988 to: (1) direct the Commission to carry out functions assigned under this Act; (2) provide increased Commission staff support from specified congressional offices; (3) authorize the Commission to delegate any of its functions to one or more special committees as long as membership of such committees is drawn equally from both Houses of Congress; and (4) provide fund transfer authority. Renames the Capitol Guide Board the Capitol Visitor Board.
Repeals provisions of title III of the National Visitor Center Facilities Act of 1968 to the extent that such provisions are inconsistent with the provisions of this Act. | <s>[INST]SECTION 1. SHORT TITLE.
This Act may be cited as the ``Capitol Visitor Center Authorization
Act of 1997''.
SEC. 2. ESTABLISHMENT OF CAPITOL VISITOR CENTER.
(a) In General.--The Architect of the Capitol, under the direction
of the United States Capitol Preservation Commission, is authorized--
(1) to plan, construct, furnish, and equip the Capitol
Visitor Center under the East Plaza of the United States
Capitol with associated improvements to the Capitol to provide
access thereto; and
(2) to reconstruct the East Plaza of the United States
Capitol and its environs to enhance its attractiveness, safety,
and security;
in a manner that preserves and maintains Olmstead's ``General Plan for
the Improvement of the United States Capitol Grounds'', 1874.
(b) Purposes.--The purposes of the Capitol Visitor Center shall
include--
(1) providing reception facilities, educational materials
and exhibits, information, amenities, a gift shop, and other
programs and facilities for members of the public visiting the
United States Capitol; and
(2) enhancing the security of the Capitol.
(c) Design.--Plans for construction of the Capitol Visitor Center
shall be substantially in accordance with the Final Design Report dated
November 10, 1995, submitted by the Architect of the Capitol to the
Committee on Transportation and Infrastructure of the House of
Representatives, the Committee on Rules and Administration of the
Senate, and the United States Capitol Preservation Commission, subject
to modifications approved by the Commission.
(d) Exhibits.--The informational and educational experience
afforded visitors to the Capitol Visitor Center, including all
exhibits, shall be the responsibility of the United States Capitol
Visitor Board under the direction of the United States Capitol
Preservation Commission, as approved by the House of Representatives
and the Senate. The Architect of the Capitol, the Clerk of the House of
Representatives, the Secretary of the Senate, the Sergeant at Arms of
the House of Representatives, and the Sergeant at Arms and Doorkeeper
of the Senate shall provide staff, support, and resources for the
installation, assembly, and maintenance of all exhibits and other
informational and educational fixtures and equipment. Exhibits and all
informational and educational materials shall be subject to section
7(b).
(e) Security Systems.--The design, installation, and maintenance of
security systems for the Capitol Visitor Center shall be the
responsibility of the Capitol Police Board in accordance with section
308 of the Legislative Branch Appropriations Act, 1996 (40 U.S.C. 212a-
4) and section 308 of the Legislative Branch Appropriations Act, 1997
(40 U.S.C. 212a-4a).
(f) Management.--After the opening of the Capitol Visitor Center to
the public, the Architect of the Capitol shall administer, maintain,
and improve the Capitol Visitor Center as part of the Capitol Building
and Grounds, subject to this Act and the oversight of the appropriate
officers and committees of the House of Representatives and the Senate.
(g) Definition of Project.--In this Act, the term ``project'' means
the activities and purposes set forth in subsections (a) through (f).
SEC. 3. UNITED STATES CAPITOL PRESERVATION COMMISSION; FINANCING PLAN;
SECURITY STUDY.
(a) Development of Project Implementation Capacity.--Not later than
30 days after the date of enactment of this Act, the United States
Capitol Preservation Commission shall meet at the call of either co-
chairman for the purpose of establishing a special committee of the
Commission to carry out the functions of the Commission in implementing
and overseeing the project.
(b) Financing Plan.--As soon as practicable after the date of
enactment of this Act, the United States Capitol Preservation
Commission shall develop a detailed plan for financing the project at
the lowest net cost to the Government. The financing plan shall provide
for--
(1) the acceptance of donations from public and private
sources to be used to minimize the use of or to repay any
appropriated or borrowed funds;
(2) the use of any revenues generated by the Capitol
Visitor Center to minimize the use of or to repay any
appropriated or borrowed funds and, to the extent available, to
pay the operating costs of the Capitol Visitor Center;
(3) the use of any other funds available for the
preservation and restoration of the Capitol; and
(4) only to the extent necessary, the use of appropriated
or borrowed funds.
The plan shall be submitted to Committees on Appropriations and House
Oversight of the House of Representatives and the Committees on
Appropriations and Rules and Administration of the Senate.
(c) Revolving Fund.--All funds described in subsection (b) shall be
deposited in the United States Capitol Visitor Center Revolving Fund,
which is hereby established in the Treasury. The Fund shall be managed
as provided in section 9602 of the Internal Revenue Code of 1986 and
shall be available, without fiscal year limitation, to carry out the
project, including--
(1) the reimbursement of appropriations accounts of the
Senate, the House of Representatives, and the Architect of the
Capitol for all costs associated with the operation of the
Capitol Visitor Center Gift Shop;
(2) the payment of costs of the continued conservation and
preservation of the Capitol Building; and
(3) the payment of costs of further acquisitions of fine
arts as approved by the Senate Commission on Art or the House
Fine Arts Board.
(d) Security Study.--The Capitol Police Board shall conduct a study
to assess security cost savings and other benefits resulting from the
construction and operation of the Capitol Visitor Center and shall
report the results of its study to the United States Capitol
Preservation Commission and to the Committees on Appropriations and
House Oversight of the House of Representatives and the Committees on
Appropriations and Rules and Administration of the Senate.
SEC. 4. CONSTRUCTION.
(a) Building Codes.--The project shall meet design standards
applicable under nationally recognized building codes, as determined by
the Architect of the Capitol. During construction, the Architect shall
conduct periodic inspections for the purpose of ensuring that such
standards are being met.
(b) Applicability of Certain Laws.--The project shall not be
subject to any Federal or State law (including law of the District of
Columbia) relating to taxes, building codes, studies, reports, permits,
or inspections.
SEC. 5. GIFTS.
(a) In General.--For the purposes of carrying out the project,
gifts or donations of services or property may be received, accepted,
held, and disposed of, subject to the provisions of the plan
promulgated under section 3.
(b) Treatment Under Tax Laws.--Any gift accepted in accordance with
the plan promulgated under section 3 shall be considered a gift to the
United States for the purposes of income, estate, and gift tax laws of
the United States.
SEC. 6. AUTHORITY TO CONTRACT.
Notwithstanding any other provision of law, the Architect of the
Capitol may establish competitive procedures for work on the project by
the use of prequalification standards and may award contracts on the
basis of contractor qualifications as well as price. Such procedures
and contract awards shall be final and conclusive upon all officers of
the Government.
SEC. 7. CAPITOL VISITOR BOARD.
(a) In General.--
(1) Authority of capitol visitor board.--The Capitol
Visitor Board, under the direction of the United States Capitol
Preservation Commission and subject to prior approval of the
House of Representatives and the Senate, shall establish the
Capitol Visitor Center operations, tour, exhibit and education
policies, including--
(A) establishing hours of operation, tour content,
and tour schedules;
(B) producing or selecting films, videos, exhibits,
publications, and other items of an educational nature;
and
(C) approving items for sale by the Capitol Visitor
Center gift shop.
(2) Consultation.--In carrying out this section, the
Capitol Visitor Board shall consult with the Historians of the
Senate and House of Representatives, the Senate Commission on
Art, the House Fine Arts Board, and any advisory board of the
United States Capitol Preservation Commission designated for
this purpose by the Commission.
(3) Other authorities not affected.--
(A) Security.--Nothing in this section affects the
authority of the Capitol Police Board with respect to
security of the Capitol, the Capitol Visitor Center, or their environs.
(B) Senate commission on art.--Nothing in this
section affects the authority of the Senate Commission
on Art with respect to the Old Senate Chamber and the
Old Supreme Court Chamber.
(b) Exhibits and Informational and Educational Material.--
(1) Exhibits.--Exhibits, including any audio, video, or
demonstrative presentations, shall illustrate the history and
the Constitutional role of the United States Congress and the
history, including art and architectural history, of the
Capitol.
(2) Informational and educational materials.--To assist
visitors, the Capitol Visitor Board shall publish or provide
for informational and educational materials for free
distribution to the public, in accordance with title 44, United
States Code. Materials provided for sale may be purchased
through approved procedures for the Capitol Visitor Center gift
shop and any revenues produced shall be deposited to the United
States Capitol Visitor Center Revolving Fund account as
approved by the United States Capitol Preservation Commission.
(c) Capitol Visitor Center Gift Shop.--
(1) Purpose.--The Capitol Visitor Center Board shall
establish and operate the Capitol Visitor Center Gift Shop in
accordance with policies approved by the United States Capitol
Preservation Commission and the appropriate oversight
committees of each House.
(2) Proceeds of sales or services.--All monies received
from sales or services of the Capitol Visitor Center Gift Shop
shall be deposited in the United States Capitol Visitor Center
Revolving Fund established by section 3(c) of this Act.
SEC. 8. AMENDMENTS RELATING TO THE UNITED STATES CAPITOL PRESERVATION
COMMISSION.
(a) Purposes.--Section 801(a) of the Arizona-Idaho Conservation Act
of 1988 (40 U.S.C. 188a(a)) is amended--
(1) by striking ``and'' at the end of paragraph (2); and
(2) by striking paragraph (3) and inserting the following:
``(3) carrying out functions assigned by the Capitol
Visitor Center Authorization Act of 1997; and
``(4) conducting other activities that directly facilitate,
encourage, or support the purposes specified in the preceding
paragraphs.''.
(b) Staff Support.--Section 801(e) Arizona-Idaho Conservation Act
of 1988 (40 U.S.C. 188a(e)) is amended by inserting ``Clerk of the
House of Representatives, the Secretary of the Senate, the Sergeant at
Arms of the House of Representatives, the Sergeant at Arms and
Doorkeeper of the Senate, the'' after ``The''.
(c) Delegation.--Section 801 of the Arizona-Idaho Conservation Act
of 1988 (40 U.S.C. 188a) is amended by adding at the end the following:
``(f) Delegation.--In addition to the special committee provided
for by section 3(a), the United States Capitol Preservation Commission
may delegate any functions to 1 or more special committees if the
membership of each such committee is drawn equally from the House of
Representatives and the Senate.''.
(d) Fund Transfers.--Section 803 of the Arizona-Idaho Conservation
Act of 1988 (40 U.S.C. 188a-2) is amended by adding at the end the
following:
``(f) Transfers.--Not later than 30 days after the date of
enactment of this Act, the balance in the account in excess of $250,000
shall be transferred to the fund established by section 3(c) of the
Capitol Visitor Center Authorization Act of 1997.''.
(e) Capitol Visitor Board.--
(1) Renaming.--Section 441 of the Legislative
Reorganization Act of 1970 (40 U.S.C. 851) is amended by
striking ``Capitol Guide Board'' each place it appears and
inserting ``Capitol Visitor Board''.
(2) Information.--Section 441(a) of the Legislative
Reorganization Act of 1970 (40 U.S.C. 851(a)) is amended by
inserting after ``Architect of the Capitol,'' the following:
``the Secretary of the Senate, the Clerk of the House of
Representatives,''.
SEC. 9. REPEAL.
(a) In General.--The provisions of title III of the National
Visitor Center Facilities Act of 1968 (40 U.S.C. 831) shall be repealed
to the extent that such provisions are inconsistent with the provisions
of this Act.
(b) Conforming Amendment.--Section 301 of the National Visitor
Center Facilities Act of 1968 (40 U.S.C. 831) is amended by striking
``the United States Capitol Historical Society,''.[/INST]Capitol Visitor Center Authorization Act of 1997 - Authorizes the Architect of the Capitol (AOC), under the direction of the U.S. Capitol Preservation Commission (Commission), to: (1) plan, construct, furnish and equip the Capitol Visitor Center (Center) under the East Plaza of the Capitol; and (2) reconstruct the East Plaza and its environs to enhance its attractiveness, safety, and security.
Requires the design of the Center to be substantially in accordance with the Final Design Report dated November 10, 1995, submitted by the AOC to specified congressional committees. Specifies entities responsible for Center exhibits, security systems, and management. Directs the Commission to: (1) establish a special committee to implement and oversee the Center project; and (2) develop and submit to specified congressional committees a detailed plan for financing the project at the lowest net cost to the Government. Establishes in the Treasury the United States Capitol Visitor Center Revolving Fund for the collection of deposits received under the financing plan. Directs the Capitol Police Board to study and report to specified congressional committees on the security cost savings and other cost benefits associated with the construction and operation of the Center.
Authorizes the AOC to establish competitive procedures for work to carry out the project by the use of prequalification standards, and to award contracts on the basis of contractor qualifications as well as price. States that such procedures and contract awards shall be final and conclusive upon all officers of the Government.
Directs the Capitol Visitor Center Board to: (1) establish Center operations, tour, exhibit, and education policies; and (2) establish and operate the Capitol Visitor Center Gift Shop.
Amends the Arizona-Idaho Conservation Act of 1988 to: (1) direct the Commission to carry out functions assigned under this Act; (2) provide increased Commission staff support from specified congressional offices; (3) authorize the Commission to delegate any of its functions to one or more special committees as long as membership of such committees is drawn equally from both Houses of Congress; and (4) provide fund transfer authority. Renames the Capitol Guide Board the Capitol Visitor Board.
Repeals provisions of title III of the National Visitor Center Facilities Act of 1968 to the extent that such provisions are inconsistent with the provisions of this Act.</s> |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Forest Service Flexible Partnerships
Act of 2017''.
SEC. 2. AUTHORIZATION FOR LEASE OF FOREST SERVICE SITES.
(a) Definitions.--In this Act:
(1) Administrative site.--
(A) In general.--The term ``administrative site''
means--
(i) any facility or improvement, including
curtilage, that was acquired or is used
specifically for purposes of administration of
the National Forest System;
(ii) any Federal land that--
(I) is associated with a facility
or improvement described in clause (i)
that was acquired or is used
specifically for purposes of
administration of Forest Service
activities; and
(II) underlies or abuts the
facility or improvement; and
(iii) for each fiscal year, not more than
10 isolated, undeveloped parcels of not more
than 40 acres each.
(B) Exclusions.--The term ``administrative site''
does not include--
(i) any land within a unit of the National
Forest System that is exclusively designated
for natural area or recreational purposes;
(ii) any land within--
(I) a component of the National
Wilderness Preservation System;
(II) a component of the National
Wild and Scenic Rivers System; or
(III) a National Monument; or
(iii) any Federal land that the Secretary
determines--
(I) is needed for resource
management purposes or to provide
access to other land or water; or
(II) would be in the public
interest not to lease.
(2) Facility or improvement.--The term ``facility or
improvement'' includes--
(A) a forest headquarters;
(B) a ranger station;
(C) a research station or laboratory;
(D) a dwelling;
(E) a warehouse;
(F) a scaling station;
(G) a fire-retardant mixing station;
(H) a fire-lookout station;
(I) a guard station;
(J) a storage facility;
(K) a telecommunication facility; and
(L) any other administrative installation for
conducting Forest Service activities.
(3) Market analysis.--The term ``market analysis'' means
the identification and study of the market for a particular
economic good or service.
(4) Secretary.--The term ``Secretary'' means the Secretary
of Agriculture.
(b) Authorization.--The Secretary may lease an administrative site
that is under the jurisdiction of the Secretary in accordance with this
Act.
(c) Identification of Eligible Sites.--A regional forester, in
consultation with forest supervisors in the region, may submit to the
Secretary a recommendation for administrative sites in the region that
the regional forester considers eligible for leasing under this Act.
(d) Consultation With Local Government and Public Notice.--Before
making an administrative site available for lease under this Act, the
Secretary shall--
(1) consult with local governmental officials of the
community, and governmental officials of the State, in which
the administrative site is located; and
(2) provide public notice of the proposed lease.
(e) Lease Requirements.--
(1) Size.--An administrative site or compound of
administrative sites under a single lease under this Act may
not exceed 40 acres.
(2) Configuration of administrative sites.--
(A) In general.--To facilitate the lease of an
administrative site under this Act, the Secretary may
configure the administrative site--
(i) to maximize the marketability of the
administrative site; and
(ii) to achieve management objectives.
(B) Separate treatment of facility or
improvement.--A facility or improvement on an
administrative site to be leased under this Act may be
severed from the land and leased under a separate lease
under this Act.
(3) Consideration.--
(A) In general.--A person to which a lease of an
administrative site is made under this Act shall
provide to the Secretary consideration described in
subparagraph (B) in an amount that is not less than the
market value of the administrative site, as determined
in accordance with subparagraph (C).
(B) Form of consideration.--The consideration
referred to in subparagraph (A) may be--
(i) cash;
(ii) in-kind, including--
(I) the construction of new
facilities or improvements, title to
which the lessee transfers to the
Secretary, for use by the Secretary;
(II) the maintenance, repair,
improvement, or restoration of existing
facilities or improvements; and
(III) other services relating to
activities that occur on the
administrative site as the Secretary
considers appropriate; or
(iii) any combination of the consideration
described in clauses (i) and (ii).
(C) Determination of market value.--
(i) In general.--The Secretary shall
determine the market value of an administrative
site to be leased under this Act--
(I) by conducting an appraisal in
accordance with--
(aa) the Uniform Appraisal
Standards for Federal Land
Acquisitions established in
accordance with the Uniform
Relocation Assistance and Real
Property Acquisition Policies
Act of 1970 (42 U.S.C. 4601 et
seq.); and
(bb) the Uniform Standards
of Professional Appraisal
Practice; or
(II) by competitive lease.
(ii) In-kind consideration.--The Secretary
shall determine the market value of any in-kind
consideration under subparagraph (B)(ii) by a
process determined by the Secretary to be
appropriate for the form of the in-kind
consideration.
(4) Conditions.--The lease of an administrative site under
this Act shall be subject to such conditions, including
bonding, as the Secretary determines to be appropriate.
(f) Relation to Other Laws.--
(1) Federal property disposal.--Chapter 5 of subtitle I of
title 40, United States Code, shall not apply to the lease of
an administrative site under this Act.
(2) Lead-based paint and asbestos abatement.--
(A) In general.--Notwithstanding any provision of
law relating to the mitigation or abatement of lead-
based paint or asbestos-containing building materials,
the Secretary shall not be required to mitigate or
abate lead-based paint or asbestos-containing building
materials with respect to an administrative site to be
leased under this Act.
(B) Procedures.--With respect to an administrative
site to be leased under this Act that has lead-based
paint or asbestos-containing building materials, the
Secretary shall--
(i) provide notice to the person to which
the administrative site will be leased of the
presence of the lead-based paint or asbestos-
containing building material; and
(ii) obtain written assurance from that
person that the person will comply with
applicable Federal, State, and local laws
relating to the management of lead-based paint
and asbestos-containing building materials.
(3) Environmental review.--The National Environmental
Policy Act of 1969 (42 U.S.C. 4321 et seq.) shall apply to the
lease of an administrative site under this Act, except that, in
any environmental review or analysis required under that Act
for the lease of an administrative site under this Act, the
Secretary shall be required only--
(A) to analyze the most reasonably foreseeable use
of the administrative site, as determined through a
market analysis;
(B) to determine whether to include any conditions
under subsection (e)(4); and
(C) to evaluate the alternative of not leasing the
administrative site in accordance with the National
Environmental Policy Act of 1969 (42 U.S.C. 4321 et
seq.).
(g) Use of Consideration.--Cash consideration for a lease of an
administrative site under this Act shall be available to the Secretary,
until expended and without further appropriation, to pay--
(1) any necessary and incidental costs incurred by the
Secretary in connection with--
(A) the acquisition, improvement, maintenance,
reconstruction, or construction of a facility or
improvement for the National Forest System; and
(B) the lease of an administrative site under this
Act; and
(2) reasonable commissions or fees for brokerage services
obtained in connection with the lease, subject to the
conditions that the Secretary--
(A) determines that the services are in the public
interest; and
(B) shall provide public notice of any brokerage
services contract entered into in connection with a
lease under this Act.
(h) Congressional Notifications.--
(1) Anticipated use of authority.--As part of the annual
budget justification documents provided to the Committee on
Appropriations of the House of Representatives and the
Committee on Appropriations of the Senate, the Secretary shall
include--
(A) a list of the anticipated leases to be made,
including the anticipated revenue that may be obtained,
under this Act;
(B) a description of the intended use of any
revenue obtained under a lease under this Act,
including a list of any projects that cost more than
$500,000; and
(C) a description of accomplishments during
previous years using the authority of the Secretary
under this Act.
(2) Changes to lease list.--If the Secretary desires to
lease an administrative site under this Act that is not
included on a list provided under paragraph (1)(A), the
Secretary shall submit to the congressional committees
described in paragraph (3) a notice of the proposed lease,
including the anticipated revenue that may be obtained from the
lease.
(3) Use of authority.--Not less frequently than once each
year, the Secretary shall submit to the Committee on
Agriculture, the Committee on Appropriations, and the Committee
on Natural Resources of the House of Representatives and the
Committee on Agriculture, Nutrition, and Forestry, the
Committee on Appropriations, and the Committee on Energy and
Natural Resources of the Senate a report describing each lease
made by the Secretary under this Act during the period covered
by the report.
(i) Expiration of Authority.--
(1) In general.--The authority of the Secretary to enter
into a lease agreement for an administrative site under this
Act expires on September 30, 2027.
(2) Effect on lease agreement.--Any lease agreement entered
into by the Secretary under this Act before the date of the
expiration of authority under paragraph (1) shall not be
affected by that expiration of authority. | Forest Service Flexible Partnerships Act of 2017 This bill authorizes the Department of Agriculture (USDA) to lease as an administrative site, for consideration that is at least the market value of the site: any facility or improvement that was acquired or is used for the administration of the National Forest System (NFS); any federal land associated with such a facility or improvement that was acquired or is used for the administration of Forest Service activities and underlies or abuts such facility or improvement; or per fiscal year, no more than 10 isolated, undeveloped parcels no larger than 40 acres each. The bill makes the National Environmental Policy Act of 1969 applicable to the leasing of administrative sites, subject to an exception. Cash consideration for an administrative site shall be available to USDA to pay: necessary and incidental costs incurred in acquiring, improving, maintaining, reconstructing, or constructing a facility or improvement for the NFS and the lease of such site; and reasonable commissions or fees for brokerage services obtained regarding the lease. | <s>[INST]SECTION 1. SHORT TITLE.
This Act may be cited as the ``Forest Service Flexible Partnerships
Act of 2017''.
SEC. 2. AUTHORIZATION FOR LEASE OF FOREST SERVICE SITES.
(a) Definitions.--In this Act:
(1) Administrative site.--
(A) In general.--The term ``administrative site''
means--
(i) any facility or improvement, including
curtilage, that was acquired or is used
specifically for purposes of administration of
the National Forest System;
(ii) any Federal land that--
(I) is associated with a facility
or improvement described in clause (i)
that was acquired or is used
specifically for purposes of
administration of Forest Service
activities; and
(II) underlies or abuts the
facility or improvement; and
(iii) for each fiscal year, not more than
10 isolated, undeveloped parcels of not more
than 40 acres each.
(B) Exclusions.--The term ``administrative site''
does not include--
(i) any land within a unit of the National
Forest System that is exclusively designated
for natural area or recreational purposes;
(ii) any land within--
(I) a component of the National
Wilderness Preservation System;
(II) a component of the National
Wild and Scenic Rivers System; or
(III) a National Monument; or
(iii) any Federal land that the Secretary
determines--
(I) is needed for resource
management purposes or to provide
access to other land or water; or
(II) would be in the public
interest not to lease.
(2) Facility or improvement.--The term ``facility or
improvement'' includes--
(A) a forest headquarters;
(B) a ranger station;
(C) a research station or laboratory;
(D) a dwelling;
(E) a warehouse;
(F) a scaling station;
(G) a fire-retardant mixing station;
(H) a fire-lookout station;
(I) a guard station;
(J) a storage facility;
(K) a telecommunication facility; and
(L) any other administrative installation for
conducting Forest Service activities.
(3) Market analysis.--The term ``market analysis'' means
the identification and study of the market for a particular
economic good or service.
(4) Secretary.--The term ``Secretary'' means the Secretary
of Agriculture.
(b) Authorization.--The Secretary may lease an administrative site
that is under the jurisdiction of the Secretary in accordance with this
Act.
(c) Identification of Eligible Sites.--A regional forester, in
consultation with forest supervisors in the region, may submit to the
Secretary a recommendation for administrative sites in the region that
the regional forester considers eligible for leasing under this Act.
(d) Consultation With Local Government and Public Notice.--Before
making an administrative site available for lease under this Act, the
Secretary shall--
(1) consult with local governmental officials of the
community, and governmental officials of the State, in which
the administrative site is located; and
(2) provide public notice of the proposed lease.
(e) Lease Requirements.--
(1) Size.--An administrative site or compound of
administrative sites under a single lease under this Act may
not exceed 40 acres.
(2) Configuration of administrative sites.--
(A) In general.--To facilitate the lease of an
administrative site under this Act, the Secretary may
configure the administrative site--
(i) to maximize the marketability of the
administrative site; and
(ii) to achieve management objectives.
(B) Separate treatment of facility or
improvement.--A facility or improvement on an
administrative site to be leased under this Act may be
severed from the land and leased under a separate lease
under this Act.
(3) Consideration.--
(A) In general.--A person to which a lease of an
administrative site is made under this Act shall
provide to the Secretary consideration described in
subparagraph (B) in an amount that is not less than the
market value of the administrative site, as determined
in accordance with subparagraph (C).
(B) Form of consideration.--The consideration
referred to in subparagraph (A) may be--
(i) cash;
(ii) in-kind, including--
(I) the construction of new
facilities or improvements, title to
which the lessee transfers to the
Secretary, for use by the Secretary;
(II) the maintenance, repair,
improvement, or restoration of existing
facilities or improvements; and
(III) other services relating to
activities that occur on the
administrative site as the Secretary
considers appropriate; or
(iii) any combination of the consideration
described in clauses (i) and (ii).
(C) Determination of market value.--
(i) In general.--The Secretary shall
determine the market value of an administrative
site to be leased under this Act--
(I) by conducting an appraisal in
accordance with--
(aa) the Uniform Appraisal
Standards for Federal Land
Acquisitions established in
accordance with the Uniform
Relocation Assistance and Real
Property Acquisition Policies
Act of 1970 (42 U.S.C. 4601 et
seq.); and
(bb) the Uniform Standards
of Professional Appraisal
Practice; or
(II) by competitive lease.
(ii) In-kind consideration.--The Secretary
shall determine the market value of any in-kind
consideration under subparagraph (B)(ii) by a
process determined by the Secretary to be
appropriate for the form of the in-kind
consideration.
(4) Conditions.--The lease of an administrative site under
this Act shall be subject to such conditions, including
bonding, as the Secretary determines to be appropriate.
(f) Relation to Other Laws.--
(1) Federal property disposal.--Chapter 5 of subtitle I of
title 40, United States Code, shall not apply to the lease of
an administrative site under this Act.
(2) Lead-based paint and asbestos abatement.--
(A) In general.--Notwithstanding any provision of
law relating to the mitigation or abatement of lead-
based paint or asbestos-containing building materials,
the Secretary shall not be required to mitigate or
abate lead-based paint or asbestos-containing building
materials with respect to an administrative site to be
leased under this Act.
(B) Procedures.--With respect to an administrative
site to be leased under this Act that has lead-based
paint or asbestos-containing building materials, the
Secretary shall--
(i) provide notice to the person to which
the administrative site will be leased of the
presence of the lead-based paint or asbestos-
containing building material; and
(ii) obtain written assurance from that
person that the person will comply with
applicable Federal, State, and local laws
relating to the management of lead-based paint
and asbestos-containing building materials.
(3) Environmental review.--The National Environmental
Policy Act of 1969 (42 U.S.C. 4321 et seq.) shall apply to the
lease of an administrative site under this Act, except that, in
any environmental review or analysis required under that Act
for the lease of an administrative site under this Act, the
Secretary shall be required only--
(A) to analyze the most reasonably foreseeable use
of the administrative site, as determined through a
market analysis;
(B) to determine whether to include any conditions
under subsection (e)(4); and
(C) to evaluate the alternative of not leasing the
administrative site in accordance with the National
Environmental Policy Act of 1969 (42 U.S.C. 4321 et
seq.).
(g) Use of Consideration.--Cash consideration for a lease of an
administrative site under this Act shall be available to the Secretary,
until expended and without further appropriation, to pay--
(1) any necessary and incidental costs incurred by the
Secretary in connection with--
(A) the acquisition, improvement, maintenance,
reconstruction, or construction of a facility or
improvement for the National Forest System; and
(B) the lease of an administrative site under this
Act; and
(2) reasonable commissions or fees for brokerage services
obtained in connection with the lease, subject to the
conditions that the Secretary--
(A) determines that the services are in the public
interest; and
(B) shall provide public notice of any brokerage
services contract entered into in connection with a
lease under this Act.
(h) Congressional Notifications.--
(1) Anticipated use of authority.--As part of the annual
budget justification documents provided to the Committee on
Appropriations of the House of Representatives and the
Committee on Appropriations of the Senate, the Secretary shall
include--
(A) a list of the anticipated leases to be made,
including the anticipated revenue that may be obtained,
under this Act;
(B) a description of the intended use of any
revenue obtained under a lease under this Act,
including a list of any projects that cost more than
$500,000; and
(C) a description of accomplishments during
previous years using the authority of the Secretary
under this Act.
(2) Changes to lease list.--If the Secretary desires to
lease an administrative site under this Act that is not
included on a list provided under paragraph (1)(A), the
Secretary shall submit to the congressional committees
described in paragraph (3) a notice of the proposed lease,
including the anticipated revenue that may be obtained from the
lease.
(3) Use of authority.--Not less frequently than once each
year, the Secretary shall submit to the Committee on
Agriculture, the Committee on Appropriations, and the Committee
on Natural Resources of the House of Representatives and the
Committee on Agriculture, Nutrition, and Forestry, the
Committee on Appropriations, and the Committee on Energy and
Natural Resources of the Senate a report describing each lease
made by the Secretary under this Act during the period covered
by the report.
(i) Expiration of Authority.--
(1) In general.--The authority of the Secretary to enter
into a lease agreement for an administrative site under this
Act expires on September 30, 2027.
(2) Effect on lease agreement.--Any lease agreement entered
into by the Secretary under this Act before the date of the
expiration of authority under paragraph (1) shall not be
affected by that expiration of authority.[/INST]Forest Service Flexible Partnerships Act of 2017 This bill authorizes the Department of Agriculture (USDA) to lease as an administrative site, for consideration that is at least the market value of the site: any facility or improvement that was acquired or is used for the administration of the National Forest System (NFS); any federal land associated with such a facility or improvement that was acquired or is used for the administration of Forest Service activities and underlies or abuts such facility or improvement; or per fiscal year, no more than 10 isolated, undeveloped parcels no larger than 40 acres each. The bill makes the National Environmental Policy Act of 1969 applicable to the leasing of administrative sites, subject to an exception. Cash consideration for an administrative site shall be available to USDA to pay: necessary and incidental costs incurred in acquiring, improving, maintaining, reconstructing, or constructing a facility or improvement for the NFS and the lease of such site; and reasonable commissions or fees for brokerage services obtained regarding the lease. </s> |
Jerry Seinfeld appeared on WFAN radio show Boomer & Carton on Thursday to talk football, but the conversation eventually turned to the Seinfeld reunion rumors that have emerged ever since he and Jason Alexander (better known as George Costanza) were seen outside the series’ iconic New York landmark Tom’s Restaurant earlier this month.
Seinfeld confirmed that the outing was indeed filmed, but not for a Super Bowl commercial or for an episode of his web series Comedians in Cars Getting Coffee. “It’s a secret project,” Seinfeld said, adding that it’s “short-ish” form, but longer than 60 seconds. He also revealed that other Seinfeld alumni were involved — including Larry David, who will not appear on camera — and that they shot at other locations besides Tom’s, though they didn’t film at Jerry’s apartment on Manhattan’s Upper West Side.
Unfortunately, Seinfeld — who is also rumored to be working on “a gigantic project” for Broadway with David — said the mystery Seinfeld reunion project won’t be a recurring series. “I think it’s one and done,” he noted.
But there is some good news: The project will be unveiled “very, very soon,” Seinfeld added. ||||| It's a Festivus miracle! The "Seinfeld" gang is getting back together.
When people spotted Jerry Seinfeld and former co-star Jason Alexander together, rumors of a reunion began to circulate, but others thought they were just filming an episode of Seinfeld's web series "Comedians In Cars Getting Coffee."
"It is not. But it is not not those things either," revealed Seinfeld on New York's "Boomer and Carton" radio show. "It's a secret project."
Here's what we squeezed from the interview:
· Alexander will plays George
· It's longer than 60 seconds
· Larry David is in on it
· Other Seinfeld characters are involved, making us believe it'll be the first true Seinfeld reunion.
Most importantly, Seinfeld said the project will be "one-and-done" and that we will all see it "very, very soon."
So what exactly is this secret-but-not-so-secret "Seinfeld" sort-of reunion? We have a few theories.
It's A Filmed Segment For The Super Bowl
Since every other New Yorker is complaining about the Super Bowl, why not Jerry and George?
Considering Seinfeld is a big sports fan both in real life and on the show, we'd be hard-pressed to think that the reunion has absolutely nothing to do with the fact that, for the first time ever, the Super Bowl is in (or close to) New York. If not a commercial, the reunion could be part of the pre-game festivities or the half-time show.
Maybe George has become the GM for the New York Jets after his run working with the Yankees? We can only hope Larry David finds some reason to come back to voice the ghost of George Steinbrenner.
'Seinfeld: The Later Years'
We'd love to think the project is a web series, but considering it's one-and-done and short-form (and that Julia-Louis Dreyfus is probably really busy with "Veep"), that's unlikely. More possible: it's a short about the gang's return to society after their prison sentence. They have plenty to catch up on; I mean really, what is the deal with Facebook, Twitter and Justin Bieber? And what is Newman up to now that the postal service is dying (spoiler: he works for Amazon)?
It's Nothing
"Seinfeld" was a show about nothing. Considering both Seinfeld and David are known for being a bit absurdist, maybe that's the biggest hint for this secret project: it's nothing. It's just the people from "Seinfeld" sitting around and talking in character, with no plot or purpose behind it.
It would probably still be better than the last episode. ||||| Jerry Seinfeld Says the Seinfeld Reunion Is Real
Seinfeld's coming back – but the details are more yada yada than concrete.Jerry Seinfeld confirmed a reunion of his eponymous '90s sitcom is happening – at least, sort of.The comedian, whose popular – and quotable – show about a quartet of narcissistic New Yorkers wrapped in 1998 after a nine-year run, gave away a few details about the project while appearing on a sports radio talk show Thursday, according to CBS New York Seinfeld, 59, was chatting about football on WFAN's Boomer and Carton when the hosts couldn't resist inquiring about the tantalizing photo that was taken of Seinfeld and Jason Alexander walking into Tom's Diner on Manhattan's Upper West Side (just as they had done so many times on the show).Seinfeld confirmed the duo weren't filming a commercial or an episode of "Comedians in Cars Getting Coffee" (his hit web series ), and once again referred to it as a " secret project .""I gave you more now than I’ve given anyone," Seinfeld told the still-baffled hosts. "I told you what it isn’t. And then I also told you that it isn’t not that, either."Not surprisingly, the hosts were unsatisfied with that response – and grilled the star for further details.He obliged (kind of), confirming a few nuggets, including that Alexander reprised his role as neurotic George Constanza while they filmed in the diner, that the project involves original co-creator Larry David and that more of the show's characters are also involved.Seinfeld called it a "short-ish"-form project, but that it's longer than 60 seconds and will go public "very very soon."Only don't get too excited, super fans: Seinfeld says the project is probably "one and done." | – Jerry Seinfeld confirmed today that he, Jason Alexander, and other members of the Seinfeld cast have worked on a "short-ish" project that will be seen "very, very soon," reports BuzzFeed. Seinfeld wouldn't divulge much, however, during his appearance on the Boomer & Carton radio show on WFAN this morning. He said it was neither a commercial nor an episode of his “Comedians in Cars Getting Coffee" series, before jokily adding that it's "not not those things, either." Whatever it is, he said it's probably "one and done," reports People. Seinfeld also confirmed that co-creator Larry David is involved, though he didn't say which of the other Seinfeld characters besides George Costanza were on board. The hosts grilled him (see and hear the questions and responses at CBS New York) because Seinfeld and Alexander were spotted filming at Tom's Restaurant, the hangout from the show. So what on earth? MTV speculates that it might be related to the Super Bowl in some way, given that the game is being played in New Jersey. That would at least explain the "very, very soon" part. | <s>[INST]Jerry Seinfeld appeared on WFAN radio show Boomer & Carton on Thursday to talk football, but the conversation eventually turned to the Seinfeld reunion rumors that have emerged ever since he and Jason Alexander (better known as George Costanza) were seen outside the series’ iconic New York landmark Tom’s Restaurant earlier this month.
Seinfeld confirmed that the outing was indeed filmed, but not for a Super Bowl commercial or for an episode of his web series Comedians in Cars Getting Coffee. “It’s a secret project,” Seinfeld said, adding that it’s “short-ish” form, but longer than 60 seconds. He also revealed that other Seinfeld alumni were involved — including Larry David, who will not appear on camera — and that they shot at other locations besides Tom’s, though they didn’t film at Jerry’s apartment on Manhattan’s Upper West Side.
Unfortunately, Seinfeld — who is also rumored to be working on “a gigantic project” for Broadway with David — said the mystery Seinfeld reunion project won’t be a recurring series. “I think it’s one and done,” he noted.
But there is some good news: The project will be unveiled “very, very soon,” Seinfeld added. ||||| It's a Festivus miracle! The "Seinfeld" gang is getting back together.
When people spotted Jerry Seinfeld and former co-star Jason Alexander together, rumors of a reunion began to circulate, but others thought they were just filming an episode of Seinfeld's web series "Comedians In Cars Getting Coffee."
"It is not. But it is not not those things either," revealed Seinfeld on New York's "Boomer and Carton" radio show. "It's a secret project."
Here's what we squeezed from the interview:
· Alexander will plays George
· It's longer than 60 seconds
· Larry David is in on it
· Other Seinfeld characters are involved, making us believe it'll be the first true Seinfeld reunion.
Most importantly, Seinfeld said the project will be "one-and-done" and that we will all see it "very, very soon."
So what exactly is this secret-but-not-so-secret "Seinfeld" sort-of reunion? We have a few theories.
It's A Filmed Segment For The Super Bowl
Since every other New Yorker is complaining about the Super Bowl, why not Jerry and George?
Considering Seinfeld is a big sports fan both in real life and on the show, we'd be hard-pressed to think that the reunion has absolutely nothing to do with the fact that, for the first time ever, the Super Bowl is in (or close to) New York. If not a commercial, the reunion could be part of the pre-game festivities or the half-time show.
Maybe George has become the GM for the New York Jets after his run working with the Yankees? We can only hope Larry David finds some reason to come back to voice the ghost of George Steinbrenner.
'Seinfeld: The Later Years'
We'd love to think the project is a web series, but considering it's one-and-done and short-form (and that Julia-Louis Dreyfus is probably really busy with "Veep"), that's unlikely. More possible: it's a short about the gang's return to society after their prison sentence. They have plenty to catch up on; I mean really, what is the deal with Facebook, Twitter and Justin Bieber? And what is Newman up to now that the postal service is dying (spoiler: he works for Amazon)?
It's Nothing
"Seinfeld" was a show about nothing. Considering both Seinfeld and David are known for being a bit absurdist, maybe that's the biggest hint for this secret project: it's nothing. It's just the people from "Seinfeld" sitting around and talking in character, with no plot or purpose behind it.
It would probably still be better than the last episode. ||||| Jerry Seinfeld Says the Seinfeld Reunion Is Real
Seinfeld's coming back – but the details are more yada yada than concrete.Jerry Seinfeld confirmed a reunion of his eponymous '90s sitcom is happening – at least, sort of.The comedian, whose popular – and quotable – show about a quartet of narcissistic New Yorkers wrapped in 1998 after a nine-year run, gave away a few details about the project while appearing on a sports radio talk show Thursday, according to CBS New York Seinfeld, 59, was chatting about football on WFAN's Boomer and Carton when the hosts couldn't resist inquiring about the tantalizing photo that was taken of Seinfeld and Jason Alexander walking into Tom's Diner on Manhattan's Upper West Side (just as they had done so many times on the show).Seinfeld confirmed the duo weren't filming a commercial or an episode of "Comedians in Cars Getting Coffee" (his hit web series ), and once again referred to it as a " secret project .""I gave you more now than I’ve given anyone," Seinfeld told the still-baffled hosts. "I told you what it isn’t. And then I also told you that it isn’t not that, either."Not surprisingly, the hosts were unsatisfied with that response – and grilled the star for further details.He obliged (kind of), confirming a few nuggets, including that Alexander reprised his role as neurotic George Constanza while they filmed in the diner, that the project involves original co-creator Larry David and that more of the show's characters are also involved.Seinfeld called it a "short-ish"-form project, but that it's longer than 60 seconds and will go public "very very soon."Only don't get too excited, super fans: Seinfeld says the project is probably "one and done."[/INST]– Jerry Seinfeld confirmed today that he, Jason Alexander, and other members of the Seinfeld cast have worked on a "short-ish" project that will be seen "very, very soon," reports BuzzFeed. Seinfeld wouldn't divulge much, however, during his appearance on the Boomer & Carton radio show on WFAN this morning. He said it was neither a commercial nor an episode of his “Comedians in Cars Getting Coffee" series, before jokily adding that it's "not not those things, either." Whatever it is, he said it's probably "one and done," reports People. Seinfeld also confirmed that co-creator Larry David is involved, though he didn't say which of the other Seinfeld characters besides George Costanza were on board. The hosts grilled him (see and hear the questions and responses at CBS New York) because Seinfeld and Alexander were spotted filming at Tom's Restaurant, the hangout from the show. So what on earth? MTV speculates that it might be related to the Super Bowl in some way, given that the game is being played in New Jersey. That would at least explain the "very, very soon" part.</s> |
lipomatosis of the gastrointestinal tract is a rare condition with a small number of cases .
the term lipomatosis describes focal proliferation of normal fat in the soft tissue including the mediastinum , kidneys , pelvis , or the intestine ( 1 ) .
intestinal lipomatosis is the infiltration of the submucosa by mature fat tissue without tumor formation ( 2 ) .
we are able to obtain higher quality images with the development of radiological imaging technologies .
pathologic conditions can be diagnosed and learned better with coronal and sagittal reformatted images of multidetector computed tomography ( mdct ) , a product of this technology . here
hepatosteatosis , gallbladder stones and bilateral renal cysts were detected on ultrasound examination . abdominal computed tomography ( ct ) examinaton
was performed with 64-row ct unit ( aquilion 64 , toshiba medical systems , tokyo , japan ) .
it revealed intramural fatty infiltration of the terminal ileum and ileocecal valve ( figure 1 ) .
the density of the lesions was between -70 and -90 hounsfield units ( hu ) .
luminal narrowing at these sites was the secondary finding , but the contrast passage was present .
a few number of millimetric diverticules were also present in the descending and sigmoid colon .
abnormal fatty tissue deposits in the intestine can be seen in the forms of single or multiple lipomas or diffuse adipose tissue infiltration of the submucosa without tumor formation .
lack of encapsulation differentiates it from lipoma ( 3 ) . the fatty tissue proliferation and deposition
is usually limited to the submucosal layer , but it may extend to the serosa and mesenteric fat . the cause of the fat deposition is not known ( 2 ) .
intestinal lipomatosis shows no sex predominance , and it occurs usually after the fourth decade of life ( 1 , 3 , 4 ) .
colon is the most common site ( % 65 - 75 ) and ileum is the second most common site in terms of lipoma ( 5 ) .
the most common manifestations are nonspecific abdominal pain , constipation , diarrhea and bleeding ( 3 , 6 , 7 ) .
abdominal pain was the only symptom in our patient , there was no gastrointestinal bleeding .
the ileocecal area may be affected by many pathologic conditions such as benign and malignant tumors , inflammatory processes ( appendicitis , diverticulitis , crohn disease ) , and infectious diseases .
intestinal lipomatosis is shown as well - defined homogeneous intramural hypodense areas with an attenuation between -80 and -120 hu ( 1 , 5 ) .
it can be differentiated from true lipoma , which appears as an asymmetric mass , whereas lipomatosis manifests as symmetric enlargement ( 5 , 8) . thumb - printing of fluid - containing bowels is seen in coronal magnetic resonance images . the same sign can also be seen in intestinal ischemia , but intestinal wall thickness is normal in lipomatosis ( 1 ) .
when it reaches big sizes and obstruction develops , surgical procedures may be necessary for treatment .
coronal and sagittal reformatted images are added and larger areas with thinner sections can be examined with mdct . it is the preferred diagnostic method for a rare , benign condition , such as intestinal lipomatosis , because it can differentiate fat tissue from other tissues . | intestinal lipomatosis also known as lipohyperplasia is a rare disease .
diffuse infiltration of the fatty tissue mainly in the submucosal layer is characteristic .
it is usually asymptomatic and found incidentally .
we report a case of lipomatosis in the terminal ileum and ileocecal valve .
multidetector computed tomography ( mdct ) with contrast enhancement showed fatty infiltration of the terminal ileum and ileocecal valve . | <s>[INST]lipomatosis of the gastrointestinal tract is a rare condition with a small number of cases .
the term lipomatosis describes focal proliferation of normal fat in the soft tissue including the mediastinum , kidneys , pelvis , or the intestine ( 1 ) .
intestinal lipomatosis is the infiltration of the submucosa by mature fat tissue without tumor formation ( 2 ) .
we are able to obtain higher quality images with the development of radiological imaging technologies .
pathologic conditions can be diagnosed and learned better with coronal and sagittal reformatted images of multidetector computed tomography ( mdct ) , a product of this technology . here
hepatosteatosis , gallbladder stones and bilateral renal cysts were detected on ultrasound examination . abdominal computed tomography ( ct ) examinaton
was performed with 64-row ct unit ( aquilion 64 , toshiba medical systems , tokyo , japan ) .
it revealed intramural fatty infiltration of the terminal ileum and ileocecal valve ( figure 1 ) .
the density of the lesions was between -70 and -90 hounsfield units ( hu ) .
luminal narrowing at these sites was the secondary finding , but the contrast passage was present .
a few number of millimetric diverticules were also present in the descending and sigmoid colon .
abnormal fatty tissue deposits in the intestine can be seen in the forms of single or multiple lipomas or diffuse adipose tissue infiltration of the submucosa without tumor formation .
lack of encapsulation differentiates it from lipoma ( 3 ) . the fatty tissue proliferation and deposition
is usually limited to the submucosal layer , but it may extend to the serosa and mesenteric fat . the cause of the fat deposition is not known ( 2 ) .
intestinal lipomatosis shows no sex predominance , and it occurs usually after the fourth decade of life ( 1 , 3 , 4 ) .
colon is the most common site ( % 65 - 75 ) and ileum is the second most common site in terms of lipoma ( 5 ) .
the most common manifestations are nonspecific abdominal pain , constipation , diarrhea and bleeding ( 3 , 6 , 7 ) .
abdominal pain was the only symptom in our patient , there was no gastrointestinal bleeding .
the ileocecal area may be affected by many pathologic conditions such as benign and malignant tumors , inflammatory processes ( appendicitis , diverticulitis , crohn disease ) , and infectious diseases .
intestinal lipomatosis is shown as well - defined homogeneous intramural hypodense areas with an attenuation between -80 and -120 hu ( 1 , 5 ) .
it can be differentiated from true lipoma , which appears as an asymmetric mass , whereas lipomatosis manifests as symmetric enlargement ( 5 , 8) . thumb - printing of fluid - containing bowels is seen in coronal magnetic resonance images . the same sign can also be seen in intestinal ischemia , but intestinal wall thickness is normal in lipomatosis ( 1 ) .
when it reaches big sizes and obstruction develops , surgical procedures may be necessary for treatment .
coronal and sagittal reformatted images are added and larger areas with thinner sections can be examined with mdct . it is the preferred diagnostic method for a rare , benign condition , such as intestinal lipomatosis , because it can differentiate fat tissue from other tissues .[/INST]intestinal lipomatosis also known as lipohyperplasia is a rare disease .
diffuse infiltration of the fatty tissue mainly in the submucosal layer is characteristic .
it is usually asymptomatic and found incidentally .
we report a case of lipomatosis in the terminal ileum and ileocecal valve .
multidetector computed tomography ( mdct ) with contrast enhancement showed fatty infiltration of the terminal ileum and ileocecal valve .</s> |
the german - british project geo600
@xcite is part of an international network of kilometre - scale michelson - type laser interferometers @xcite searching for gravitational wave ( gw ) signals at audio frequencies in a band of 10hz10khz . while at frequencies below a few hundred hertz the measurement sensitivity is , at the moment , still limited by seismic , thermal and technical noises , at higher frequencies photon shot noise constitutes the limiting factor ( for an extended review of quantum effects in gw interferometers , see @xcite ) .
currently , geo600 undergoes an upgrade program to geo - hf , aiming at a measurement sensitivity improvement by about an order of magnitude at high frequencies @xcite .
a gravitational wave signal is ` translated ' by the laser interferometer into a variation of the optical power at the signal output port .
a limit for the possible measurement accuracy is set by the poissonian distribution of the photon number arriving within a time interval at the interferometric photo detector .
laser gw interferometers are operated close to their _ dark fringe _ , which means that due to destructive interference almost no light leaves the signal port and all optical power
is reflected back to the laser .
however , zero - point ( vacuum ) fluctuations of the electro - magnetic field are coupled into the interferometer s signal port and generate a signal that is not distinguishable from a gw signal . a possibility to reduce this _ shot noise _ , as was first proposed by caves in @xcite , is the use of _ squeezed light _
such a light field has a non - classical noise distribution with a reduced uncertainty in one of the field quadratures , when compared to a vacuum state .
injected from the signal port , the squeezed state replaces the vacuum state , thereby directly reducing the interferometer s quantum noise . since the first observation of squeezed light in the 1980s @xcite ,
the degree of squeezing has been constantly improved @xcite , recently reaching a value of almost 13db @xcite . in the gw detection band ,
the generation of squeezing remained an unsolved problem for a long time .
it was not until 2004 that squeezing at audio frequencies down to 280hz could be generated for the first time @xcite , soon followed by the creation of a coherent control scheme @xcite that allowed the observation of frequency - independent squeezing over the entire earth - bound gravitational wave detection band from 10hz to 10khz @xcite .
the implementation of squeezed light was tested in a table - top michelson - type interferometer @xcite as well as in a suspended gw prototype detector @xcite .
finally , a squeezed - light laser for geo600 was constructed @xcite , first results of a squeezing - improved measurement sensitivity were recently published in @xcite . in this paper , a characterization of the squeezed - light laser is presented along with the current status of the implementation in geo600 .
figure [ figure1 ] shows a schematic of the optical layout of the squeezed - light laser . to maintain clarity ,
only the core components are shown .
altogether , the experiment consists of approximately 130 components which are situated on a 135 cm @xmath0 113 cm optical breadboard .
a detailled discussion of the single subsystems and of the employed control scheme is provided in reference @xcite .
the experiment is driven by a monolithic non - planar nd : yag ring laser ( npro ) of 2w single - mode output power at 1064 nm .
one part of this beam is frequency up - converted in a second - harmonic generator ( shg ) , which uses 7% mgo doped linbo@xmath1 as nonlinear @xmath2 medium .
this 532 nm _
pump beam _ is filtered by a mode - cleaning travelling - wave resonator ( not shown in fig .
[ figure1 ] ) .
thereby , high - frequency phase noise that has been shown to diminish the maximal degree of squeezing achievable @xcite , is attenuated .
subsequently , the pump beam is injected into the squeezed - light source that consists of a periodically poled potassium titanyl phosphate ( ppktp ) crystal placed in a standing - wave hemilithic cavity .
the usage in a gravitational wave detector requires a high long - term stability of the squeezing degree and consequently a high stability of the pump beam power .
the dependence of the degree of squeezing on the pump power value is discussed in detail in @xcite .
a mach - zehnder interferometer is employed to stabilize the pump beam intensity .
the scheme ensures the squeezing value to be stable on long - term timescales , first characterization results are presented in @xcite .
the generation of squeezed states at audio frequencies from 10hz to 10khz requires the implementation of a control scheme that avoids the introduction of technical laser noise to the squeezed vacuum state .
the basic idea is to remove all noisy fields that could by means of interference introduce noise to the squeezed field at the frequencies of interest @xcite .
the _ coherent control scheme _
@xcite employed uses two auxiliary optical frequencies that are provided by two additional npro laser sources .
the frequency of the auxiliary units is locked to the main laser that is in turn phase - locked to the geo600 master laser when operating the squeezed - light laser at the detector site . for characterization of the squeezed - light laser
, an on - board diagnostic homodyne detector is available .
a small fraction of the main 1064 nm beam , that is also filtered by a ring mode - cleaner , is used as a local oscillator ( lo ) beam .
the left part of figure [ figure2 ] shows squeezing and anti - squeezing values measured for different 532 nm pump powers .
the values are normalized to the noise level of a vacuum state that can be measured when the signal port of the diagnostic homodyne detector is blocked ( black trace ) .
it is worth noting that very low 532 nm pump powers are sufficient to produce a high degree of squeezing . at a power of 5mw ( corresponding to about 15mw intra - cavity power ) ,
the quantum noise was reduced by more than 3db , equivalent to a factor of two in noise power reduction .
the degree of squeezing reached a maximal value of 9.5db at a pump power of 45mw . this value is more than an order of magnitude below the pump power levels necessary to reach correspondent squeezing values with similar cavity designs using mgo : linbo@xmath1 as nonlinear medium @xcite .
to the best of our knowledge , the observed non - classical noise suppression of 9.5db sets a new benchmark for the degree of squeezing up to now reported at audio frequencies . in the right part of figure [ figure2 ] , the measured values ( taken at a frequency of 5khz )
are compared with the theoretical expectations .
the squeezed and anti - squeezed noise powers in decibel @xcite @xmath3 with the variances @xmath4 depend on the pump power @xmath5 as well as on optical loss . in this expression , _ a _ and _ s _ and the upper and lower signs denote the anti - squeezing and the squeezing , respectively , @xmath6 describes the total detection efficiency and @xmath7 is the opo threshold power . the normalized frequency @xmath8 that is a function of cavity parameters is not relevant for the presented discussion , since frequencies much smaller than the cavity linewidth are considered . + the different loss sources during the generation and detection proscesses are : * the escape efficiency @xmath9 of the squeezed - light resonator . here , @xmath10 is the power transmittance of the output coupling mirror and @xmath11 is the intra - cavity loss .
the total loss per round - trip , due to the non - perfect ar - coating of the crystal facet as well as to the residual power absorption of the nonlinear crystal , can be estimated to @xmath12 , thus resulting in @xmath13 . * the total propagation loss suffered by the squeezed field on the way from the squeezing resonator to the homodyne detector .
the critical components in this path are two polarizing beam splitters as well as a faraday rotator , while the contribution of the super - polished lenses is negligible . in an independent measurement
, the propagation efficiency was estimated to be @xmath14 . *
the fringe visibility @xmath15 at the homodyne detector , contributing quadratically , was measured to range between @xmath16 and @xmath17 . * the quantum efficiency of the homodyne photo diodes . to minimize this loss ,
custom - made high - efficiency diodes are used .
the diameter of the active area is @xmath18 m .
equivalent diodes have already been used in high - level squeezing experiments , as e.g. reported in @xcite , and have been estimated to have a quantum efficiency of @xmath19 . a consideration of all possible sources results in a total detection efficiency of .
this value corresponds very well to the measured squeezing and anti - squeezing levels , as shown in figure [ figure2 ] . from the measurements , an opo threshold power of @xmath20mw was estimated .
+ it is important to note that the homodyne detector is merely a diagnostic device which is by - passed when the squeezed - light laser is used in geo600 .
hence , the homodyne visibility loss is not relevant for a later operation and has to be corrected for .
thus , a total loss of merely 7% can be deduced .
the initial requirement formulated for the squeezed - light laser was a squeezing value of 10db .
when operated at a pump power of 35mw , more than 10db of squeezing are available for the injection into the dark geo600 port .
the advantage of this operation point is that with a corresponding anti - squeezing value of about 17db , the generated state is still relatively pure .
if the pump power is increased further , the gain in squeezing is marginal while the anti - squeezing increases rapidly , leading to an increased sensitivity to phase noise .
the highest squeezing value available is 11.3db ( with about 23db of anti - squeezing ) when using a pump power of 45mw .
the high squeezing factor was achieved over almost the entire frequency band of earth - bound instruments extending from 10hz up to 10khz @xcite .
the long - term stability of the device was discussed in @xcite .
altogether , this means that the requirements initially formulated for the geo600 squeezed light laser have been fully achieved .
a sketch of the squeezing - input stage at the geo600 detector site is shown in fig .
[ figure5 ] .
the squeezing injection scheme is realized through the combination of a faraday rotator ( fr ) and a polarizing beam splitter : the squeezed field is reflected at the pbs between the output mode - cleaner ( omc ) and the signal - recycling mirror ( msr ) , experiences a 45 degree polarization rotation passing the fr and another 45 degree rotation after having been reflected at the msr .
the total polarization rotation of 90 degrees allows the squeezed beam to be transmitted by the pbs together with the output beam of the interferometer ( carrying the gw signal ) and to arrive at the gw signal photo detector after a transmission through the omc .
the squeezed - light laser is situated on the so - called _ detection bench _ , an optical table located close to the vacuum chamber that contains the squeezing input pbs , the omc and the gw photo detector ( this vacuum chamber is referred to as _ tco - c _ in the following ) . at
the output of the squeezing breadboard , up to 11.3db of squeezing is available for injection into geo600 .
however , different loss sources appearing at various stages of the squeezed light injection have to be considered . in the end , they limit the maximal sensitivity improvement achievable with squeezed light . in the following ,
the optical losses experienced by the squeezed field are summarized , the individual contributions are illustrated in fig .
[ figure5 ] . *
the total loss on the squeezing breadboard is , as stated above , about 7% , taking into account an estimated escape efficiency of 95% and a propagation loss of 2% .
* during the implementation of squeezing , it was discovered that an additional faraday isolator was required to protect the interferometer from back - scattering as well as the squeezed - light source from a bright beam coming from the interferometer .
the additional faraday isolator adds 44db of isolation but contributes 4% to the propagation loss .
the total propagation loss on the detection bench is therefore about 5% . * the expected single - path propagation loss inside tco - c , due to imperfect ar coatings and absorption of the pbs
, the faraday rotator and the waveplate can be estimated to be about 3% . * 1%
is transmitted at one of the suspended steering mirrors ( bdo@xmath21 in fig .
[ figure5 ] ) for error signal generation ( this loss also contributes twice due to the double - path of the squeezed beam ) . *
a frequency - dependent loss is introduced by the signal - recycling cavity . while at frequencies outside the src linewidth it acts as a mirror , at low frequencies the squeezed field is coupled into the interferometer and experiences the intra - cavity loss .
figure [ figure6 ] shows the expected power reflectivity of the src for the squeezed field . for this , the finesse file of geo600 published in @xcite was used .
+ in the course of the geo - hf upgrade , the msr reflectivity was reduced from 98.1% to 90% . as far as the squeezed field is concerned , the higher bandwidth leads to a slightly increased loss value at khz - frequencies .
the expected effect is shown in the blue trace of fig .
[ figure6 ] . * the best mode - matching to the signal - recycling cavity and to the output mode - cleaner measured was about 94% .
* from the design parameters , the optical loss for a single transmission through the omc was estimated to be below 1% . during characterization
, however , a much higher value of about 10% was measured .
this loss could not be reduced further by cleaning and probably arises from a combination of imperfect optical surfaces and dielectric coatings deviating from the design specifications .
* before the geo - hf upgrade , a perkin elmer c30642 photo diode was used .
it was substituted by a custom - made high - efficiency photo diode , as already used in the diagnostic homodyne detector .
the diameter of the active area is 3 mm .
the quantum efficiency was measured to be 8% higher than for the perkin elmer pd and is expected to be similar to the @xmath18 m diodes used in previous squeezing experiments , namely about 99% . the total loss for the squeezing , being the sum of all contributions mentioned above , is therefore estimated to a value of 32% at khz - frequencies and up to 50% at frequencies much lower than the src linewidth .
with 220hz the latter is , however , already in the frequency range where the interferometer sensitivity is no longer limited by quantum noise .
figure [ figure7 ] shows the expected squeezing and anti - squeezing values for the squeezed - light laser operated with a pump power of 35mw .
traces ( a b ) refer to the squeezing and anti - squeezing measured at the diagnostic homodyne detector .
traces ( c d ) correct those values for the homodyne detector loss and therefore show the squeezing or anti - squeezing available for injection at the squeezing breadboard output .
traces ( e f ) finally give an estimation of the amount of squeezing or anti - squeezing present at the geo600 gw photo detector .
traces ( g h ) illustrate the effect of the msr exchange , leading to an increased src linewidth .
the long - term goal to be achieved with squeezed light injection is a desired reduction of the observatory noise by 6db at quantum - noise limited frequencies and a permanent squeezing contribution during the operation of geo - hf .
after the first successful enhancement of the observatory sensitivity by squeezed light , the achievement of both intents seems to be feasible in the near future . regarding the squeezing factor , the following loss sources need to be addressed : * the optical loss during beam propagation on the detection bench is mainly due to the currently used faraday isolator with a suboptimal performance in this respect as well as to polarization optics .
the use of a high - throughput faraday isolator identical to the one already used in the squeezed - light laser setup will allow a reduction of the propagation loss .
apart from the faraday isolator , merely super - polished optics with a high - performance ar - coating ( as used on the squeezing breadboard ) will be used , thereby reducing loss due to surface scattering and to residual ar - coating reflection . *
lenses with a super - polished surface and a low residual reflection at the ar coating ( as already used in the squeezed - light laser setup ) will be used inside tco - c . * up to now
, the largest single loss contribution arises from the transmission through the output mode - cleaner . in the future
, the omc optics will be exchanged . from the specifications of the single optics , the total transmission loss ( mainly due to coating and surface imperfections and to a 100ppm residual transmission of one of the mirrors for monitoring purposes )
was estimated to be below 1% .
an important issue to be addressed is the automatic alignment of the squeezed beam to the interferometer . without this control loop ,
the suspended interferometer optics , though locked with respect to each other , are free swinging with respect to the squeezed beam injection path .
this introduces a time - dependent , unknown effective loss for the squeezing injection .
the generation of auto - alignment error signals is currently under investigation .
in this paper , we presented a characterization of the geo600 squeezed - light laser .
the highest directly observed degree of squeezing is 9.5db , which constitutes the highest degree of squeezing reported so far at audio frequencies .
thus , more than 11db of squeezing is available for the injection into the signal port of geo600 .
furthermore , individual sources of optical loss experienced by the squeezed field in the course of generation , propagation in geo600 , and the final photo - electric detection at the output port were discussed .
the presented possibilities to reduce the total optical loss suggest an even stronger non - classical sensitivity improvement of geo600 by squeezed light to be feasible in the near future . this work has been supported by the international max planck research school ( imprs ) and the cluster of excellence quest ( centre for quantum engineering and space - time research ) .
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gottfried wilhelm leibniz universitt hannover _ phd thesis | in the course of the high - frequency upgrade of geo600 , its optical configuration was extended by a squeezed - light laser @xcite . recently ,
a non - classically enhanced measurement sensitivity of geo600 was reported @xcite . in this paper ,
a characterization of the squeezed - light laser is presented .
thereupon , the status of the integration into geo 600 is reviewed , focussing on the sources of optical loss limiting the shot noise reduction by squeezing at the moment . finally , the possibilities for a future loss reduction are discussed . | <s>[INST]the german - british project geo600
@xcite is part of an international network of kilometre - scale michelson - type laser interferometers @xcite searching for gravitational wave ( gw ) signals at audio frequencies in a band of 10hz10khz . while at frequencies below a few hundred hertz the measurement sensitivity is , at the moment , still limited by seismic , thermal and technical noises , at higher frequencies photon shot noise constitutes the limiting factor ( for an extended review of quantum effects in gw interferometers , see @xcite ) .
currently , geo600 undergoes an upgrade program to geo - hf , aiming at a measurement sensitivity improvement by about an order of magnitude at high frequencies @xcite .
a gravitational wave signal is ` translated ' by the laser interferometer into a variation of the optical power at the signal output port .
a limit for the possible measurement accuracy is set by the poissonian distribution of the photon number arriving within a time interval at the interferometric photo detector .
laser gw interferometers are operated close to their _ dark fringe _ , which means that due to destructive interference almost no light leaves the signal port and all optical power
is reflected back to the laser .
however , zero - point ( vacuum ) fluctuations of the electro - magnetic field are coupled into the interferometer s signal port and generate a signal that is not distinguishable from a gw signal . a possibility to reduce this _ shot noise _ , as was first proposed by caves in @xcite , is the use of _ squeezed light _
such a light field has a non - classical noise distribution with a reduced uncertainty in one of the field quadratures , when compared to a vacuum state .
injected from the signal port , the squeezed state replaces the vacuum state , thereby directly reducing the interferometer s quantum noise . since the first observation of squeezed light in the 1980s @xcite ,
the degree of squeezing has been constantly improved @xcite , recently reaching a value of almost 13db @xcite . in the gw detection band ,
the generation of squeezing remained an unsolved problem for a long time .
it was not until 2004 that squeezing at audio frequencies down to 280hz could be generated for the first time @xcite , soon followed by the creation of a coherent control scheme @xcite that allowed the observation of frequency - independent squeezing over the entire earth - bound gravitational wave detection band from 10hz to 10khz @xcite .
the implementation of squeezed light was tested in a table - top michelson - type interferometer @xcite as well as in a suspended gw prototype detector @xcite .
finally , a squeezed - light laser for geo600 was constructed @xcite , first results of a squeezing - improved measurement sensitivity were recently published in @xcite . in this paper , a characterization of the squeezed - light laser is presented along with the current status of the implementation in geo600 .
figure [ figure1 ] shows a schematic of the optical layout of the squeezed - light laser . to maintain clarity ,
only the core components are shown .
altogether , the experiment consists of approximately 130 components which are situated on a 135 cm @xmath0 113 cm optical breadboard .
a detailled discussion of the single subsystems and of the employed control scheme is provided in reference @xcite .
the experiment is driven by a monolithic non - planar nd : yag ring laser ( npro ) of 2w single - mode output power at 1064 nm .
one part of this beam is frequency up - converted in a second - harmonic generator ( shg ) , which uses 7% mgo doped linbo@xmath1 as nonlinear @xmath2 medium .
this 532 nm _
pump beam _ is filtered by a mode - cleaning travelling - wave resonator ( not shown in fig .
[ figure1 ] ) .
thereby , high - frequency phase noise that has been shown to diminish the maximal degree of squeezing achievable @xcite , is attenuated .
subsequently , the pump beam is injected into the squeezed - light source that consists of a periodically poled potassium titanyl phosphate ( ppktp ) crystal placed in a standing - wave hemilithic cavity .
the usage in a gravitational wave detector requires a high long - term stability of the squeezing degree and consequently a high stability of the pump beam power .
the dependence of the degree of squeezing on the pump power value is discussed in detail in @xcite .
a mach - zehnder interferometer is employed to stabilize the pump beam intensity .
the scheme ensures the squeezing value to be stable on long - term timescales , first characterization results are presented in @xcite .
the generation of squeezed states at audio frequencies from 10hz to 10khz requires the implementation of a control scheme that avoids the introduction of technical laser noise to the squeezed vacuum state .
the basic idea is to remove all noisy fields that could by means of interference introduce noise to the squeezed field at the frequencies of interest @xcite .
the _ coherent control scheme _
@xcite employed uses two auxiliary optical frequencies that are provided by two additional npro laser sources .
the frequency of the auxiliary units is locked to the main laser that is in turn phase - locked to the geo600 master laser when operating the squeezed - light laser at the detector site . for characterization of the squeezed - light laser
, an on - board diagnostic homodyne detector is available .
a small fraction of the main 1064 nm beam , that is also filtered by a ring mode - cleaner , is used as a local oscillator ( lo ) beam .
the left part of figure [ figure2 ] shows squeezing and anti - squeezing values measured for different 532 nm pump powers .
the values are normalized to the noise level of a vacuum state that can be measured when the signal port of the diagnostic homodyne detector is blocked ( black trace ) .
it is worth noting that very low 532 nm pump powers are sufficient to produce a high degree of squeezing . at a power of 5mw ( corresponding to about 15mw intra - cavity power ) ,
the quantum noise was reduced by more than 3db , equivalent to a factor of two in noise power reduction .
the degree of squeezing reached a maximal value of 9.5db at a pump power of 45mw . this value is more than an order of magnitude below the pump power levels necessary to reach correspondent squeezing values with similar cavity designs using mgo : linbo@xmath1 as nonlinear medium @xcite .
to the best of our knowledge , the observed non - classical noise suppression of 9.5db sets a new benchmark for the degree of squeezing up to now reported at audio frequencies . in the right part of figure [ figure2 ] , the measured values ( taken at a frequency of 5khz )
are compared with the theoretical expectations .
the squeezed and anti - squeezed noise powers in decibel @xcite @xmath3 with the variances @xmath4 depend on the pump power @xmath5 as well as on optical loss . in this expression , _ a _ and _ s _ and the upper and lower signs denote the anti - squeezing and the squeezing , respectively , @xmath6 describes the total detection efficiency and @xmath7 is the opo threshold power . the normalized frequency @xmath8 that is a function of cavity parameters is not relevant for the presented discussion , since frequencies much smaller than the cavity linewidth are considered . + the different loss sources during the generation and detection proscesses are : * the escape efficiency @xmath9 of the squeezed - light resonator . here , @xmath10 is the power transmittance of the output coupling mirror and @xmath11 is the intra - cavity loss .
the total loss per round - trip , due to the non - perfect ar - coating of the crystal facet as well as to the residual power absorption of the nonlinear crystal , can be estimated to @xmath12 , thus resulting in @xmath13 . * the total propagation loss suffered by the squeezed field on the way from the squeezing resonator to the homodyne detector .
the critical components in this path are two polarizing beam splitters as well as a faraday rotator , while the contribution of the super - polished lenses is negligible . in an independent measurement
, the propagation efficiency was estimated to be @xmath14 . *
the fringe visibility @xmath15 at the homodyne detector , contributing quadratically , was measured to range between @xmath16 and @xmath17 . * the quantum efficiency of the homodyne photo diodes . to minimize this loss ,
custom - made high - efficiency diodes are used .
the diameter of the active area is @xmath18 m .
equivalent diodes have already been used in high - level squeezing experiments , as e.g. reported in @xcite , and have been estimated to have a quantum efficiency of @xmath19 . a consideration of all possible sources results in a total detection efficiency of .
this value corresponds very well to the measured squeezing and anti - squeezing levels , as shown in figure [ figure2 ] . from the measurements , an opo threshold power of @xmath20mw was estimated .
+ it is important to note that the homodyne detector is merely a diagnostic device which is by - passed when the squeezed - light laser is used in geo600 .
hence , the homodyne visibility loss is not relevant for a later operation and has to be corrected for .
thus , a total loss of merely 7% can be deduced .
the initial requirement formulated for the squeezed - light laser was a squeezing value of 10db .
when operated at a pump power of 35mw , more than 10db of squeezing are available for the injection into the dark geo600 port .
the advantage of this operation point is that with a corresponding anti - squeezing value of about 17db , the generated state is still relatively pure .
if the pump power is increased further , the gain in squeezing is marginal while the anti - squeezing increases rapidly , leading to an increased sensitivity to phase noise .
the highest squeezing value available is 11.3db ( with about 23db of anti - squeezing ) when using a pump power of 45mw .
the high squeezing factor was achieved over almost the entire frequency band of earth - bound instruments extending from 10hz up to 10khz @xcite .
the long - term stability of the device was discussed in @xcite .
altogether , this means that the requirements initially formulated for the geo600 squeezed light laser have been fully achieved .
a sketch of the squeezing - input stage at the geo600 detector site is shown in fig .
[ figure5 ] .
the squeezing injection scheme is realized through the combination of a faraday rotator ( fr ) and a polarizing beam splitter : the squeezed field is reflected at the pbs between the output mode - cleaner ( omc ) and the signal - recycling mirror ( msr ) , experiences a 45 degree polarization rotation passing the fr and another 45 degree rotation after having been reflected at the msr .
the total polarization rotation of 90 degrees allows the squeezed beam to be transmitted by the pbs together with the output beam of the interferometer ( carrying the gw signal ) and to arrive at the gw signal photo detector after a transmission through the omc .
the squeezed - light laser is situated on the so - called _ detection bench _ , an optical table located close to the vacuum chamber that contains the squeezing input pbs , the omc and the gw photo detector ( this vacuum chamber is referred to as _ tco - c _ in the following ) . at
the output of the squeezing breadboard , up to 11.3db of squeezing is available for injection into geo600 .
however , different loss sources appearing at various stages of the squeezed light injection have to be considered . in the end , they limit the maximal sensitivity improvement achievable with squeezed light . in the following ,
the optical losses experienced by the squeezed field are summarized , the individual contributions are illustrated in fig .
[ figure5 ] . *
the total loss on the squeezing breadboard is , as stated above , about 7% , taking into account an estimated escape efficiency of 95% and a propagation loss of 2% .
* during the implementation of squeezing , it was discovered that an additional faraday isolator was required to protect the interferometer from back - scattering as well as the squeezed - light source from a bright beam coming from the interferometer .
the additional faraday isolator adds 44db of isolation but contributes 4% to the propagation loss .
the total propagation loss on the detection bench is therefore about 5% . * the expected single - path propagation loss inside tco - c , due to imperfect ar coatings and absorption of the pbs
, the faraday rotator and the waveplate can be estimated to be about 3% . * 1%
is transmitted at one of the suspended steering mirrors ( bdo@xmath21 in fig .
[ figure5 ] ) for error signal generation ( this loss also contributes twice due to the double - path of the squeezed beam ) . *
a frequency - dependent loss is introduced by the signal - recycling cavity . while at frequencies outside the src linewidth it acts as a mirror , at low frequencies the squeezed field is coupled into the interferometer and experiences the intra - cavity loss .
figure [ figure6 ] shows the expected power reflectivity of the src for the squeezed field . for this , the finesse file of geo600 published in @xcite was used .
+ in the course of the geo - hf upgrade , the msr reflectivity was reduced from 98.1% to 90% . as far as the squeezed field is concerned , the higher bandwidth leads to a slightly increased loss value at khz - frequencies .
the expected effect is shown in the blue trace of fig .
[ figure6 ] . * the best mode - matching to the signal - recycling cavity and to the output mode - cleaner measured was about 94% .
* from the design parameters , the optical loss for a single transmission through the omc was estimated to be below 1% . during characterization
, however , a much higher value of about 10% was measured .
this loss could not be reduced further by cleaning and probably arises from a combination of imperfect optical surfaces and dielectric coatings deviating from the design specifications .
* before the geo - hf upgrade , a perkin elmer c30642 photo diode was used .
it was substituted by a custom - made high - efficiency photo diode , as already used in the diagnostic homodyne detector .
the diameter of the active area is 3 mm .
the quantum efficiency was measured to be 8% higher than for the perkin elmer pd and is expected to be similar to the @xmath18 m diodes used in previous squeezing experiments , namely about 99% . the total loss for the squeezing , being the sum of all contributions mentioned above , is therefore estimated to a value of 32% at khz - frequencies and up to 50% at frequencies much lower than the src linewidth .
with 220hz the latter is , however , already in the frequency range where the interferometer sensitivity is no longer limited by quantum noise .
figure [ figure7 ] shows the expected squeezing and anti - squeezing values for the squeezed - light laser operated with a pump power of 35mw .
traces ( a b ) refer to the squeezing and anti - squeezing measured at the diagnostic homodyne detector .
traces ( c d ) correct those values for the homodyne detector loss and therefore show the squeezing or anti - squeezing available for injection at the squeezing breadboard output .
traces ( e f ) finally give an estimation of the amount of squeezing or anti - squeezing present at the geo600 gw photo detector .
traces ( g h ) illustrate the effect of the msr exchange , leading to an increased src linewidth .
the long - term goal to be achieved with squeezed light injection is a desired reduction of the observatory noise by 6db at quantum - noise limited frequencies and a permanent squeezing contribution during the operation of geo - hf .
after the first successful enhancement of the observatory sensitivity by squeezed light , the achievement of both intents seems to be feasible in the near future . regarding the squeezing factor , the following loss sources need to be addressed : * the optical loss during beam propagation on the detection bench is mainly due to the currently used faraday isolator with a suboptimal performance in this respect as well as to polarization optics .
the use of a high - throughput faraday isolator identical to the one already used in the squeezed - light laser setup will allow a reduction of the propagation loss .
apart from the faraday isolator , merely super - polished optics with a high - performance ar - coating ( as used on the squeezing breadboard ) will be used , thereby reducing loss due to surface scattering and to residual ar - coating reflection . *
lenses with a super - polished surface and a low residual reflection at the ar coating ( as already used in the squeezed - light laser setup ) will be used inside tco - c . * up to now
, the largest single loss contribution arises from the transmission through the output mode - cleaner . in the future
, the omc optics will be exchanged . from the specifications of the single optics , the total transmission loss ( mainly due to coating and surface imperfections and to a 100ppm residual transmission of one of the mirrors for monitoring purposes )
was estimated to be below 1% .
an important issue to be addressed is the automatic alignment of the squeezed beam to the interferometer . without this control loop ,
the suspended interferometer optics , though locked with respect to each other , are free swinging with respect to the squeezed beam injection path .
this introduces a time - dependent , unknown effective loss for the squeezing injection .
the generation of auto - alignment error signals is currently under investigation .
in this paper , we presented a characterization of the geo600 squeezed - light laser .
the highest directly observed degree of squeezing is 9.5db , which constitutes the highest degree of squeezing reported so far at audio frequencies .
thus , more than 11db of squeezing is available for the injection into the signal port of geo600 .
furthermore , individual sources of optical loss experienced by the squeezed field in the course of generation , propagation in geo600 , and the final photo - electric detection at the output port were discussed .
the presented possibilities to reduce the total optical loss suggest an even stronger non - classical sensitivity improvement of geo600 by squeezed light to be feasible in the near future . this work has been supported by the international max planck research school ( imprs ) and the cluster of excellence quest ( centre for quantum engineering and space - time research ) .
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gottfried wilhelm leibniz universitt hannover _ phd thesis[/INST] in the course of the high - frequency upgrade of geo600 , its optical configuration was extended by a squeezed - light laser @xcite . recently ,
a non - classically enhanced measurement sensitivity of geo600 was reported @xcite . in this paper ,
a characterization of the squeezed - light laser is presented .
thereupon , the status of the integration into geo 600 is reviewed , focussing on the sources of optical loss limiting the shot noise reduction by squeezing at the moment . finally , the possibilities for a future loss reduction are discussed . </s> |
primary cardiac lymphoma ( pcl ) is a very rare neoplasm originating in the heart . traditionally , pcl is defined as an extranodal lymphoma limited to the heart or pericardium .
however , some previous reports demonstrated pcl cases with extracardiac involvement.1,2,3 pcl occupies 1.3% of primary cardiac tumors and 0.5% of extranodal lymphomas.4 patients with pcl generally complain of nonspecific symptoms such as dyspnea , edema , and arrhythmia.5,6 treatment of pcl is variable because the optimal treatment strategy has not yet been established .
however , previous studies have shown that chemotherapy is the most effective therapy.5,7 in this report , we delineate a case of diffuse infiltrative type of pcl with spread to the mediastinum and cervical lymph nodes .
a 48-year - old man visiting the korea university ansan hospital presented with the symptoms of exertional dyspnea and cough .
chest radiography showed pleural effusion , pulmonary congestion , and cardiomegaly . in a transthoracic two - dimensional echocardiography , a large amount of pericardial effusion and diffuse cardiac wall thickening
we performed cardiac magnetic resonance imaging ( mri ) for differential diagnosis of myocardial infiltrative diseases such as cardiac amyloidosis .
however , there was no lymphadenopathy or a mass lesion in the mri images ( fig .
however , the myocardial biopsy showed myocyte hypertrophy , and the pericardial biopsy showed chronic inflammation with fibrosis and the congo red staining was negative
. we could not identify a definite cause of the pericardial effusion ; hence , the patient underwent conservative treatment and received outpatient follow - up .
chest computed tomography ( ct ) revealed an infiltrative soft tissue mass in the anterior mediastinum and diffuse thickening of all ventricular and atrial walls ( fig .
immunohistochemical staining was positive for cd45 , but owing to the lack of specimen tissue , we could not perform more tests .
clinically , we suspected a diagnosis of fibrosing mediastinitis , and glucocorticoids were used empirically .
we prescribed prednisolone 60 mg daily for 1 month , which was tapered to 15 mg per day within 5 months . after tapering of prednisolone
ten months later , the patient complained of a nontender mass on the right side of the neck ( fig .
immunohistochemistry demonstrated a large lymphoid neoplasm , which was positive for cd45 , cd79a , and cd20 .
finally , the patient was diagnosed with primary cardiac diffuse large b cell lymphoma ( dlbcl ) .
he commenced chemotherapy with rituximab and chop ( cyclophosphamide , doxorubicin , vincristine , and prednisolone ) .
after the second cycle of chemotherapy , we performed chest ct . in the chest ct , the infiltrative lesion , involving the myocardium and multiple lymph nodes ,
3b ) compared with the chest ct performed before the r - chop therapy ( fig .
3b ) . on the basis of this result , we are confident that the dlbcl originated in the heart and the final diagnosis was pcl . after 6 cycles of chemotherapy , chest ct and positron emission tomography scans were performed to assess the response to treatment .
he commenced radiation therapy ( total 40 gy ) for the cardiophrenic angle lymph nodes .
it is defined as an extranodal lymphoma limited to the heart or pericardium.4,5 histologically , diffuse large b cell type of non - hodgkin 's lymphoma is the most common of the pcls , and its incidence ranges from 60% to 81%.6,8,9 in previous reports , most of the cases showed a mass - like lesion.6 the right atrium is the most common site of invasion , followed by the right ventricle , left ventricle , and left atrium.7 patients commonly present with nonspecific , different symptoms ; and clinical findings such as dyspnea , arrhythmia , pericardial effusion , and congestive heart failure are observed.5,6 because of its nonspecific clinical manifestation , it is difficult to diagnose pcl .
imaging studies such as echocardiography , ct , and mri are helpful for the diagnosis of pcl . however , pathologic examination is the only way to obtain a definite diagnosis.10 chemotherapy is effective for treatment of any subtype of primary cardiac lymphoma .
a previous report demonstrated that rituximab in combination with the chop regimen has a good outcome in the dlbcl type of pcl.1,9,10 petric et al.5 stated that the median overall survival after diagnosis was 12 months . among the patients , the chemotherapy group had a longer overall survival up to 30 months.5
first , the pcl was observed as thickened myocardium without an intracardiac mass . to our knowledge , this is the second case report of a diffuse infiltrative pcl without an intracardiac mass.11 second , in this case , the dlbcl originated in the heart and delayed extracardiac involvement was noted .
two cases presented with an extracardiac metastasis at the first diagnosis.1,2 one case had a pcl involving only the heart at the primary diagnosis , but microscopic involvement of the lungs , peritoneal , and retroperitoneal adipose tissue was detected on autopsy.3 however , these cases did not clearly show delayed metastasis of the pcl to an extracardiac site .
our case clearly showed that the pcl had no extracardiac involvement initially but afterwards showed extracardiac involvement .
mediastinal lymph node biopsy was performed at the second admission , and lymphoma was suspected . however , because of insufficient specimens and refusal of the patient to undergo further testing , we could not confirm the diagnosis of lymphoma , and we administered steroids for a possible diagnosis of fibrosing mediastinitis . we think that the use of steroids led to an immunocompromised state , and this state may have contributed to the delayed extracardiac involvement .
it is well known that steroids have a lympholytic effect , and this effect probably caused a disturbance of the detection time from the symptom onset to the administration of proper treatment .
although this is only a hypothesis , clinicians should be aware of the possibility of delayed diagnosis of a pcl owing to the use of steroids .
despite these interesting points , this report had one large limitation . because we failed to confirm the diagnosis of pcl from previous cardiac and mediastinal biopsies , the tissues from the enlarged lymph node in the right neck were used to confirm the diagnosis of pcl .
although the biopsy was not performed at the primary site of lymphoma , given that the initial cardiac mri demonstrated diffuse cardiac infiltration without lymph node enlargements , it appears proper to diagnose pcl . in summary , we have reported a case of an infiltrative type of pcl without an intracardiac mass and with delayed extracardiac involvement . | primary cardiac lymphoma ( pcl ) is an extremely rare and fatal neoplasm of the heart .
traditionally , it is defined as lymphoma involving the heart or pericardium .
pcl has a poor prognosis because of the diagnostic difficulty and its location .
we present the case of a 48-year - old man who presented with pericardial effusion and diffuse cardiac wall thickening .
we first suspected infiltrative heart disease .
however , even after performing a biopsy , we could not establish an accurate diagnosis .
after 20 months , primary cardiac diffuse large b cell lymphoma ( dlbcl ) was diagnosed by cervical lymph node biopsy . in this case , after chemotherapy , the dlbcl lesions , including cardiac wall thickening , improved .
the treatment outcome suggests that the diagnosis was diffuse infiltrative pcl with delayed extracardiac involvement . | <s>[INST]primary cardiac lymphoma ( pcl ) is a very rare neoplasm originating in the heart . traditionally , pcl is defined as an extranodal lymphoma limited to the heart or pericardium .
however , some previous reports demonstrated pcl cases with extracardiac involvement.1,2,3 pcl occupies 1.3% of primary cardiac tumors and 0.5% of extranodal lymphomas.4 patients with pcl generally complain of nonspecific symptoms such as dyspnea , edema , and arrhythmia.5,6 treatment of pcl is variable because the optimal treatment strategy has not yet been established .
however , previous studies have shown that chemotherapy is the most effective therapy.5,7 in this report , we delineate a case of diffuse infiltrative type of pcl with spread to the mediastinum and cervical lymph nodes .
a 48-year - old man visiting the korea university ansan hospital presented with the symptoms of exertional dyspnea and cough .
chest radiography showed pleural effusion , pulmonary congestion , and cardiomegaly . in a transthoracic two - dimensional echocardiography , a large amount of pericardial effusion and diffuse cardiac wall thickening
we performed cardiac magnetic resonance imaging ( mri ) for differential diagnosis of myocardial infiltrative diseases such as cardiac amyloidosis .
however , there was no lymphadenopathy or a mass lesion in the mri images ( fig .
however , the myocardial biopsy showed myocyte hypertrophy , and the pericardial biopsy showed chronic inflammation with fibrosis and the congo red staining was negative
. we could not identify a definite cause of the pericardial effusion ; hence , the patient underwent conservative treatment and received outpatient follow - up .
chest computed tomography ( ct ) revealed an infiltrative soft tissue mass in the anterior mediastinum and diffuse thickening of all ventricular and atrial walls ( fig .
immunohistochemical staining was positive for cd45 , but owing to the lack of specimen tissue , we could not perform more tests .
clinically , we suspected a diagnosis of fibrosing mediastinitis , and glucocorticoids were used empirically .
we prescribed prednisolone 60 mg daily for 1 month , which was tapered to 15 mg per day within 5 months . after tapering of prednisolone
ten months later , the patient complained of a nontender mass on the right side of the neck ( fig .
immunohistochemistry demonstrated a large lymphoid neoplasm , which was positive for cd45 , cd79a , and cd20 .
finally , the patient was diagnosed with primary cardiac diffuse large b cell lymphoma ( dlbcl ) .
he commenced chemotherapy with rituximab and chop ( cyclophosphamide , doxorubicin , vincristine , and prednisolone ) .
after the second cycle of chemotherapy , we performed chest ct . in the chest ct , the infiltrative lesion , involving the myocardium and multiple lymph nodes ,
3b ) compared with the chest ct performed before the r - chop therapy ( fig .
3b ) . on the basis of this result , we are confident that the dlbcl originated in the heart and the final diagnosis was pcl . after 6 cycles of chemotherapy , chest ct and positron emission tomography scans were performed to assess the response to treatment .
he commenced radiation therapy ( total 40 gy ) for the cardiophrenic angle lymph nodes .
it is defined as an extranodal lymphoma limited to the heart or pericardium.4,5 histologically , diffuse large b cell type of non - hodgkin 's lymphoma is the most common of the pcls , and its incidence ranges from 60% to 81%.6,8,9 in previous reports , most of the cases showed a mass - like lesion.6 the right atrium is the most common site of invasion , followed by the right ventricle , left ventricle , and left atrium.7 patients commonly present with nonspecific , different symptoms ; and clinical findings such as dyspnea , arrhythmia , pericardial effusion , and congestive heart failure are observed.5,6 because of its nonspecific clinical manifestation , it is difficult to diagnose pcl .
imaging studies such as echocardiography , ct , and mri are helpful for the diagnosis of pcl . however , pathologic examination is the only way to obtain a definite diagnosis.10 chemotherapy is effective for treatment of any subtype of primary cardiac lymphoma .
a previous report demonstrated that rituximab in combination with the chop regimen has a good outcome in the dlbcl type of pcl.1,9,10 petric et al.5 stated that the median overall survival after diagnosis was 12 months . among the patients , the chemotherapy group had a longer overall survival up to 30 months.5
first , the pcl was observed as thickened myocardium without an intracardiac mass . to our knowledge , this is the second case report of a diffuse infiltrative pcl without an intracardiac mass.11 second , in this case , the dlbcl originated in the heart and delayed extracardiac involvement was noted .
two cases presented with an extracardiac metastasis at the first diagnosis.1,2 one case had a pcl involving only the heart at the primary diagnosis , but microscopic involvement of the lungs , peritoneal , and retroperitoneal adipose tissue was detected on autopsy.3 however , these cases did not clearly show delayed metastasis of the pcl to an extracardiac site .
our case clearly showed that the pcl had no extracardiac involvement initially but afterwards showed extracardiac involvement .
mediastinal lymph node biopsy was performed at the second admission , and lymphoma was suspected . however , because of insufficient specimens and refusal of the patient to undergo further testing , we could not confirm the diagnosis of lymphoma , and we administered steroids for a possible diagnosis of fibrosing mediastinitis . we think that the use of steroids led to an immunocompromised state , and this state may have contributed to the delayed extracardiac involvement .
it is well known that steroids have a lympholytic effect , and this effect probably caused a disturbance of the detection time from the symptom onset to the administration of proper treatment .
although this is only a hypothesis , clinicians should be aware of the possibility of delayed diagnosis of a pcl owing to the use of steroids .
despite these interesting points , this report had one large limitation . because we failed to confirm the diagnosis of pcl from previous cardiac and mediastinal biopsies , the tissues from the enlarged lymph node in the right neck were used to confirm the diagnosis of pcl .
although the biopsy was not performed at the primary site of lymphoma , given that the initial cardiac mri demonstrated diffuse cardiac infiltration without lymph node enlargements , it appears proper to diagnose pcl . in summary , we have reported a case of an infiltrative type of pcl without an intracardiac mass and with delayed extracardiac involvement .[/INST]primary cardiac lymphoma ( pcl ) is an extremely rare and fatal neoplasm of the heart .
traditionally , it is defined as lymphoma involving the heart or pericardium .
pcl has a poor prognosis because of the diagnostic difficulty and its location .
we present the case of a 48-year - old man who presented with pericardial effusion and diffuse cardiac wall thickening .
we first suspected infiltrative heart disease .
however , even after performing a biopsy , we could not establish an accurate diagnosis .
after 20 months , primary cardiac diffuse large b cell lymphoma ( dlbcl ) was diagnosed by cervical lymph node biopsy . in this case , after chemotherapy , the dlbcl lesions , including cardiac wall thickening , improved .
the treatment outcome suggests that the diagnosis was diffuse infiltrative pcl with delayed extracardiac involvement .</s> |
theories with weak scale supersymmetry represent the most complete and cherished vision of physics beyond the standard model .
their many successes include stabilization of the electroweak scale with respect to high - scale physics , improvement of the convergence of couplings necessary for grand unification , possible electroweak baryogenesis to explain the matter - anti - matter asymmetry of the universe , and ( with @xmath0 parity ) relatively mild contributions to precision electroweak data and a successful dark matter candidate .
however , none of those successes rest crucially on the minimal realization of the supersymmetric standard model @xcite .
in fact , there are features of the minimal supersymmetric standard model ( mssm ) which are somewhat at odds with the mssm as a completely natural theory of the electroweak scale . the @xmath1 or @xmath2 problem indicates that the supersymmetric @xmath1 term must be roughly of the same size as the supersymmetry - breaking parameters , and yet the mssm offers no explanation for why this should be the case .
the lightest higgs mass in the mssm is , at tree - level , less than the @xmath3 boson mass , and even including radiative corrections typically in conflict with the lep - ii bound @xcite .
the model survives based on large radiative corrections from scalar top quarks , but in turn this requires the stops to be so heavy that the higgs soft masses end up fine - tuned to the per - cent level .
perhaps the most disturbing feature of the mssm is the fact that if one naively assumes a general spectrum of supersymmetry - breaking parameters , it is simply ruled out .
if there are large mixings among the squarks and among the sleptons , flavor - violating processes such as @xmath4-@xmath5 mixing , @xmath6 , and others , can be enhanced by orders of magnitude with respect to standard model predictions , in obvious contradiction to experimental data .
the traditional solution ( of which gauge mediation is the prototype ) is to engineer supersymmetry breaking such that the soft - breaking mass parameters are highly flavor diagonal @xcite .
this controls flavor violation to an acceptable level at a given energy scale , but continues to be challenged by natural electroweak symmetry breaking , the higgs mass , and cosmology .
an alternative is to alter the low energy structure of the model such that the supersymmetric solution to the hierarchy problem is preserved , but flavor violation is ameliorated .
a recent elegant solution imposes a continuous @xmath0 symmetry @xcite , to form the minimal @xmath0-symmetric supersymmetric standard model ( mrssm ) @xcite .
this model invokes the @xmath0 symmetry to forbid the potentially flavor - violating left - right mixing @xmath7-terms , and to guarantee ( at least largely in light of anomaly - mediated contributions ) dirac gaugino masses .
this dirac nature often leads to an additional suppression in flavor - violating processes from gauginos running in the loops , which causes many contributions to scale with large gaugino mass as @xmath8 instead of the majorana scaling , @xmath9 @xcite .
the model has additional interesting features , such as uv finite scalar masses due to the super - soft feature of dirac gauginos @xcite , and additional matter content at the electroweak scale .
for example , if the gluino is a dirac particle , the two on - shell degrees of freedom from the gluon are not sufficient to construct a supersymmetric four - spinor .
to provide the two additional bosonic degrees of freedom , the mrssm adds a complex scalar partner .
an unbroken @xmath0 symmetry is also a generic feature of simple models of meta - stable supersymmetry breaking @xcite . in this article
we consider the phenomenology of the scalar partner of the dirac gluino , a color adjoint scalar the sgluon . as a colored particle , it couples to a gluon and
will have large pair - production rates at the tevatron and lhc .
it interacts with quarks at the one - loop level proportional to the quark masses .
thanks to the large mixing naturally expected in the mrssm s squark sector , it will readily decay into flavor violating channels .
previous studies have considered scalar color octets with either decays into missing energy @xcite , with electroweak as well as @xmath10 charges @xcite , or purely flavor diagonal couplings @xcite , which all lead to very different phenomena .
our work is organized as follows . in section [ sec : sgluons ] we show how sgluons arise in a model with dirac gluinos , examine their soft masses , and derive their interactions including the one - loop contribution to the @xmath11@xmath12@xmath13 and @xmath11@xmath14@xmath14 vertices . in section [ sec : fcnc ] we examine the flavor - violating effects mediated by sgluons and derive some mild constraints from @xmath4-@xmath15 mixing . in section
[ sec : search ] we discuss the production of a pair of sgluons through the strong interaction , and examine the decay of the pair into like - sign tops .
this distinctive signature provides bounds on the sgluon mass at the tevatron and will easily be discovered at the lhc for a wide range of masses .
we particularly focus on the proper treatment of the jet activity in such events .
scalar gluons are contained in a chiral superfield @xmath16 which is a color adjoint carrying @xmath0 charge zero .
the fermionic component @xmath17 is married through @xmath18term supersymmetry breaking to the ordinary gluino @xmath19 .
the lowest component @xmath20 is a complex color adjoint scalar .
supersymmetry breaking will generally split this into two real scalar states which are admixtures of the real and imaginary parts of @xmath11 .
we discuss the spectrum below .
kinetic terms for the sgluons are contained in canonical khler potential terms for @xmath21 , @xmath22 where @xmath23 is the vector superfield containing the gluon and the @xmath24 gauge indices are implied .
the kinetic terms include the coupling of the sgluon @xmath11 to the gluons from the covariant derivative , a @xmath11-@xmath25-@xmath26 coupling of strength @xmath27 required by supersymmetry , and @xmath18term contributions to the scalar potential that are of the form @xmath28-@xmath11-@xmath29-@xmath30 which will not be important for our purposes .
there are no renormalizable gauge invariant terms through which @xmath21 interacts with matter superfields in either the khler potential or in the super - potential , and the assumed @xmath0 symmetry is incompatible with @xmath31 or @xmath32 interactions in the super - potential .
thus , the tree - level supersymmetric interactions of @xmath11 are determined entirely by supersymmetric qcd , @xmath33 where @xmath34 is the usual covariant derivative for a color adjoint , @xmath35 is the ( four - component ) gluino , and @xmath36 are the structure constants of @xmath10 .
soft mass terms for the sgluons can arise from either @xmath37term ( @xmath38 ) or @xmath18term ( @xmath39 ) spurions of supersymmetry breaking , @xmath40 and also are generated by the term responsible for the dirac gluino mass @xcite , @xmath41 where @xmath42 is the usual superfield @xmath24 field strength .
this super - potential term , along with the usual mssm @xmath24 @xmath18-terms , lead to terms in the lagrangian , @xmath43 where @xmath44 is the dirac gluino mass , and @xmath45 are the generators of @xmath24 in the fundamental representation . replacing the @xmath10 auxiliary field @xmath46 through its equation of motion
leads to terms proportional to @xmath47 and @xmath48 as well as @xmath49 @xcite .
it also induces tri - linear interactions of @xmath11 with squarks , somewhat analogous to the @xmath7 terms in the usual mssm .
altogether , the supersymmetry - breaking lagrangian for @xmath11 reads @xmath50 where @xmath51 is a real parameter and @xmath52 may be complex .
the mass eigenstates are two real color adjoint scalars which can be labelled as @xmath53 and @xmath54 .
the mass - squared eigenvalues are given by , @xmath55 and clearly we must have @xmath56 or run the risk of a color - breaking vacuum . there will be a non - trivial mixing angle when @xmath52 is complex .
when we write @xmath52 in terms of its phase @xmath57 , the mass eigenstates are @xmath58 for simplicity we will assume @xmath59 and @xmath52 are real , and thus there is no non - trivial mixing from here on . in that case
both sgluons are either a pure scalar or a pure pseudoscalar , which is equivalent as long as we combine them with massless qcd , the theory relevant for lhc .
all tree - level interactions of the sgluon with standard model and mssm states we can read off @xmath60 and @xmath61 .
the coupling of two sgluon to gluons is simply a result of its adjoint color charge and arises from the kinetic term .
the coupling to two gluinos is the supersymmetric partner of the gluon couplings , while the couplings to two squarks arise from @xmath18 terms .
note in particular that the dirac gluino mass sets the size of the squark - squark - sgluon coupling .
feynman diagrams for sgluon interactions with quarks.,title="fig : " ] feynman diagrams for sgluon interactions with quarks.,title="fig : " ] if we insert the squark and gluino couplings to a sgluon shown in eq.([eq : susy_qcd ] ) and in eq.([eq : soft ] ) into one - loop diagrams , the sgluon will couple to quarks .
there are two feynman graphs responsible for this interaction induced by gluinos and squarks , shown in figure [ fig : qvertex ] . for each of the two sgluon states the effective action after electroweak symmetry breaking contains a dimension-4 operator of the form , @xmath62 + \text{h.c.}\ ] ] where @xmath63 and @xmath64 are quark flavor indices .
the couplings may be expressed as @xmath65 where @xmath66 is the relevant squark mixing parameter , @xmath67 are the quark masses , and the dimensionless @xmath68s are functions of the heavy sgluon , gluino , and the squark masses . their form is given in the appendix .
it is important to notice that in the mrssm these couplings come out automatically proportional to quark masses , which mitigates their contribution to flavor - violating observables .
in contrast , for example , the @xmath7 terms in the mssm have to be _ defined _ to appear proportionally with the quark masses , as @xmath69 , which is an additional assumption on the flavor structure of the general mssm . in the limit of degenerate squarks , this source of flavor violation in
the mrssm will switch off through a super - gim mechanism . in the limit of large squark , gluino , or sgluon masses
the quark - quark - sgluon coupling will be suppressed by @xmath70 , @xmath71 , or @xmath72 , respectively .
feynman diagrams for single sgluon interactions with gluons.,title="fig : " ] feynman diagrams for single sgluon interactions with gluons.,title="fig : " ] feynman diagrams for single sgluon interactions with gluons.,title="fig : " ] pairs of sgluons interact with one or two gluons as a consequence of the fact that the sgluons are adjoints of @xmath10 .
there is also a single sgluon - gluon - gluon interaction mediated by squarks , as shown in figure [ fig : gvertex ] .
the effective action contains a dimension - five operator generated at one loop @xmath73 where @xmath74 is the symmetric gauge - invariant combination of three @xmath10 adjoints and the dimensionless form factor @xmath75 is given in the appendix . a similar contribution mediated by gluinos vanishes at one loop , due to the symmetry structure of the ( asymmetric ) color factor and the ( symmetric ) loop contribution . in the limit of heavy squarks
the coupling @xmath75 will vanish proportionally to @xmath76 .
through its flavor - violating couplings to quarks , the sgluon can also mediate flavor - changing processes . at energies far below the sgluon mass ,
these interactions look like @xmath77 four fermion interactions . using the @xmath78-@xmath79 transition operators relevant for @xmath4-@xmath5 mixing we can illustrate the terms left behind when the sgluon is integrated out : @xmath80 + g^{sd}_r g^{sd}_l \left [ q^{sd}_3 + \widetilde{q}^{sd}_3 -\frac{1}{3 } q^{sd}_2 - \frac{1}{3 } \widetilde{q}^{sd}_2 \right ] \right\}\ ] ] where the @xmath81 are the four fermion interactions defined in ref .
@xcite . comparing to eq.([eq : qvertex ] ) we know that the couplings @xmath14 are proportional to @xmath82 , so the relevant parameters which will be constrained are @xmath83 .
analogous expressions describe @xmath84-@xmath79 , @xmath84-@xmath78 , and @xmath85-@xmath86 mixing .
we compute the coefficients of each of these operators and compare with the global fit by the ut@xmath87 collaboration @xcite to obtain bounds on the sgluon mass , for a given choice of gluino mass , average squark masses , and squark flavor mixing parameters @xmath82 . in fig .
[ fig : fcnc ] , we present the scale of the most constraining of the four fermion operators , expressed as the effective scale @xmath88 . since mixing effects will only raise the effective scale of the four fermion interactions , the curves are the minimum possible effective scales for a given choice of sgluon , gluino , and average squark masses . in other words ,
a realistic choice of mixing parameters will increase the effective scales which suppress the fcnc operators and thus result in less constraints from flavor violation mediated by sgluons .
we also show the bounds on the corresponding scales from ref .
bounds from @xmath89-@xmath90 and @xmath18-@xmath91 mixing are mild enough as to basically provide no constraint .
the @xmath4-@xmath15 mixing bound is more severe , but the plotted bound is on the imaginary part of @xmath92 , and thus can be avoided if there is no large @xmath93-violating phase in the down - strange squark mixing element . in any case ,
sgluon masses above 600 gev or so are compatible with measurement , regardless of mixing .
note also that the constraints on down - type mixing do not in any way preclude the sgluon flavor - violating decays into up - type quarks which we consider below . mixing ( 2 curves ) ,
@xmath18 mixing , @xmath4 mixing with @xmath94 tev and an average @xmath95 gev , and @xmath4 mixing with @xmath96 tev . dashed lines : current bounds on the operators ( bottom to top ) , @xmath97 , @xmath98 , @xmath99 , and @xmath100 ( imaginary part ) , obtained from the global fit .
[ fig : fcnc],width=264 ]
as discussed in section [ sec : sgluons ] , we expect the @xmath0symmetric supersymmetric theory to include a pair of sgluons whose mass is split by something of order the gluino mass .
there will thus be two sgluon states which we can search for at hadron colliders .
since the masses are not typically degenerate , the results in this section are presented for a single sgluon state , and apply equally to the lighter or the heavier sgluon . the couplings to quarks and single sgluon coupling to gluons will depend on the mixing between the two states , but tree level pair production of sgluons involves only the strong coupling , as these interactions are protected by @xmath24 gauge invariance .
the resulting pair cross sections thus only depend on the sgluon mass , similar to , for example , the case of scalar leptoquark pairs . ,
width=302 ] in figure [ fig : xsec ] , we present the leading order cross section for pair production of sgluons as a function of their mass at the tevatron and lhc @xcite . for masses around 250 gev , the production rate of the order of 200 fb at the tevatron would correspond to a few hundred sgluon pair events in the currently available cdf and dzero data , depending on the decays and triggers . as expected
, the production rate at the tevatron drops below the femtobarn level for sgluon masses around 400 gev , thanks to the limited center - of - mass energy and @xmath101wave suppression of the dominant subprocess @xmath102 . from a dedicated analysis
we could expect sgluon mass bounds similar to squark mass bounds in the limit of large gluino mass . at the lhc ,
the dominant subprocess is @xmath103 with large cross sections , falling from around 400 pb for masses around 250 gev to 2 fb for masses around 1.5 tev . for sgluon masses in the tev range ,
the lhc will rely on its sea - quark suppressed @xmath104 luminosity which leads to a rapid drop of the cross section above 1.8 tev . with an appreciable lhc luminosity these rates correspond to several hundred to a few million events available for analyses . for the lhc we also present the single production rate from gluon fusion @xcite , for two choices of squark and gluino masses . through the one - loop diagrams discussed in sec .
[ sec : sgluons ] there can be appreciable single sgluon production through @xmath105 , which can dominate for large sgluon masses because of the phase space suppression of the pair production and threshold effects . for small sgluon masses
the lhc is not energy limited , so the single production channel is suppressed by a loop factor @xmath106 squared .
the problem of single production will be challenging backgrounds discussed below .
the sgluon interaction with quarks typically results in a negligible single sgluon production rate , because the leading contribution is one loop and the suppression by the light quark masses .
sgluons can also be produced at the lhc in cascade decays involving squarks , through the soft breaking interaction of eq.([eq : soft ] ) .
production of pairs of heavier squarks can thus cascade down through sgluons into lighter squarks , leaving behind either light jets which reconstruct the sgluon mass , or events enriched with top quarks .
either of these possibilities is rather exotic from the point of view of the standard mssm , and we leave their detailed exploration for future work . branching ratios for sgluon decays into @xmath107 , @xmath108 , @xmath109 for @xmath110 and @xmath111 as a function of sgluon mass and for two choices of left - handed squark and gluino masses .
right - handed squark masses are set to @xmath112 of the left - handed squark masses .
we assume maximal up - squark mixing.,title="fig : " ] branching ratios for sgluon decays into @xmath107 , @xmath108 , @xmath109 for @xmath110 and @xmath111 as a function of sgluon mass and for two choices of left - handed squark and gluino masses .
right - handed squark masses are set to @xmath112 of the left - handed squark masses .
we assume maximal up - squark mixing.,title="fig : " ] if heavy enough , sgluons will decay at tree level into pairs of gluinos and/or squarks . if these decay channels are closed , the sgluon has to decay through its loop - induced couplings into quarks and gluons . in the case of decays into quarks ,
the @xmath11-@xmath12-@xmath113 interaction is proportional to the heavier of the two quark masses , so one can expect that decays including at least one top quark to dominate .
if the mixing in the up - type squark sector is large ( as is the point of the mrssm ) , we therefore expect large and comparable branching ratios into @xmath114 , @xmath115 , and @xmath116 .
the specifics of the branching ratios are a window into the details of the squark mixing matrices . in figure
[ fig : br ] we present the branching ratios as a function of the sgluon mass for two sets of average squark and gluino masses , and assuming maximal mixing in the up - squark sector . the mixed heavy
light quark decays can dominate the sgluon decays for small masses and decreases with larger sgluon masses . for the maximal mixing considered here ,
the decay into @xmath116 is roughly comparable to any single one of the heavy - light decays .
thus , combing channels together , the branching ratio into one top ( or anti - top ) and a light quark are a factor of a few times larger than that into a top pair . for heavier squarks the supersymmetric decay channels
are typically closed in the region accessible to the lhc . again , the decay to one heavy and one light quark typically dominates . at large sgluon masses
decays into gluons dominate because the @xmath11@xmath14@xmath14 coupling is a dimension five operator which grows with the invariant mass of the sgluon , the only scale in the process , while the decay to quarks will be suppressed by a relative factor @xmath117 .
when sgluons are pair - produced , each sgluon is as likely to decay into a top as an anti - top .
thus , half of the decays where both sgluons decay into a top and a light - quark initiated jet will have same sign tops ( @xmath118 or @xmath119 ) .
when both tops decay leptonically we have a final state containing two light jets and either @xmath120 or a @xmath121 ( where @xmath122 is an electron or muon ) - a striking signature of physics beyond the standard model that also arises in the context of models of top compositeness @xcite .
reference @xcite has considered a search for like - sign tops at the tevatron in the context of a model of maximal flavor violation .
the authors perform a sophisticated treatment of the backgrounds and the cdf detector efficiencies .
while the maximal flavor violation model signal is the result of a mixture of pair and single production of a neutral color singlet scalar @xmath123 which interacts moderately strongly with top and charm , the analysis only requires a pair of like sign leptons , a @xmath84-tagged jet , and missing energy .
thus , our signal events are expected to have a high efficiency with respect to the analysis cuts , and one could get a tevatron bound on the sgluon mass from a similar analysis . a single sgluon produced at the lhc can decay through its flavor - violating interactions into a single top quark and a light jet , similar in topology to the @xmath78-channel mode of single top production . even in the standard model ,
this mode is challenging at the lhc because of large backgrounds from @xmath116 and @xmath124-channel single top @xcite .
therefore , single sgluon production is unlikely to be phenomenologically relevant after considering qcd effects and backgrounds .
however , if the sgluon is heavy enough it may be possible to use the peak in the top plus light jet invariant mass to isolate a signal @xcite . , width=264 ] from the discussion above we are immediately lead to study in more detail sgluon pair production with a subsequent decay into two like - sign tops with leptonic decays . with sizeable production rates and branching ratios above 10%
the question remains if this channel survives the lhc triggers and acceptance cuts . in fig .
[ fig : signal ] we show the normalized transverse momentum distributions of all sgluon decay particles . for both sgluon masses of 300 and 600 gev the light - flavor jet and bottom transverse momenta peak above @xmath125 gev , which indicates that observing four jets and tagging two bottoms should not be a problem . for a 300 gev sgluon
the harder jet has a typical transverse momentum around @xmath126 gev .
similarly , the harder bottom can acquire @xmath127 gev .
for a heavier sgluon we see that the bottom distributions hardly change , since they are mostly determined by the top and @xmath128 masses .
the two light - flavor jets from the sgluon decay become significantly harder and peak around @xmath129 gev and 280 gev , respectively .
as we will see later , in particular for heavier sgluons the decay jet can be identified unambiguously even in the presence of qcd jets . on the lepton side of fig .
[ fig : signal ] we see that the harder lepton with a typical transverse momentum close to 100 gev guarantees the triggering of sgluon pair production
. moreover , such a large transverse momentum might be useful to distinguish the sgluon pairs from the standard model backgrounds , even in the same - sign lepton case .
the second lepton is comparably soft , and the missing transverse momentum peaking around 70 gev is unlikely to contribute to the smoking - gun signature . nevertheless , from the distributions in fig .
[ fig : signal ] we can see that triggering and acceptance cuts will not be a problem for the largely background - free like - sign tops signature .
moreover , both hard light - flavor decay jets as well as the relatively hard lepton spectrum should help to reconstruct the sgluon mass scale , which would allow us to gain information on the branching ratio and thereby on the flavor structure of the mrssm .
gev and @xmath130 on the parton level .
[ fig : jets],title="fig:",width=196 ] gev and @xmath130 on the parton level .
[ fig : jets],title="fig:",width=196 ] gev and @xmath130 on the parton level .
[ fig : jets],title="fig:",width=196 ] because the light - flavor decay jets from the sgluons are crucial for the analysis described above , we have to answer the question if this jet can be identified in the jet - rich lhc environment .
this question becomes even more relevant once we try to search for the opposite - sign lepton channel or attempt to determine the sgluon mass from hadronic top decays .
recently , there have been theoretical developments which allow us to simulate qcd jet radiation over the entire transverse momentum range of these additional jets and including high jet multiplicities .
we simulate additional qcd jets in the signal process @xmath131 using the madevent @xcite implementation of the mlm scheme . in particular because the sgluons in the final state provide a hard scale for the process we do not expect the mlm results to differ from a corresponding ckkw analysis @xcite .
in particular for heavier sgluon masses the qcd activity should be dominated by collinear parton - shower effects @xcite , but the mlm scheme now allows us to consistently treat top backgrounds and the sgluon signal for different masses . for this simulation
we avoid introducing a supersymmetric shower including sgluon splittings , which would be required to include final - state radiation . because of the lack of a collinear enhancement we know that final - state radiation will not contribute strongly to qcd jet radiation .
therefore , we only include initial - state radiation which is universal for different heavy new - physics states produced at the lhc . in fig .
[ fig : jets ] we show the number of qcd jets in sgluon pair events at the lhc .
apart from a crucial minimal jet separation of @xmath132 we apply only a varying transverse momentum cut of 30 , 50 and 100 gev on the radiated jets . in the left panel
we see that while top quarks most likely come with no additional jet from initial - state radiation , a 300 gev sgluon will most likely be accompanied by one and a 600 gev sgluon by two additional qcd jets .
this is an effect of the hard factorization scale in the process which determines the size and the maximum range of the collinear enhancement of initial - state radiation .
when we increase the minimum @xmath133 to 50 gev the typical number of additional jets drops by roughly one , but in particularly heavy states still come with zero , one , or two jets at roughly the same rate .
only the three additional jets channel is suppressed to the 10% level , where this quantitative result should be taken with a grain of salt without a tuned parton shower for the lhc .
finally , a cut of at least @xmath134 gev gets rid of additional jets in roughly two thirds of the events and allows us to use light - flavor decay jets in the analysis . .
the leading jets is shown as a solid line .
[ fig : merging],width=264 ] the normalized transverse momentum distributions for the radiated jets are shown in fig .
[ fig : merging ] .
the different areas under the curves for the four leading jets reflect the fact that only a fraction of events actually show such jets .
again , we see that from the top pairs to the 600 gev sgluons the situation changes qualitatively : in the bottom panel the curves for the leading and the sub - leading are similar , and as long as we stay below @xmath133 even a third qcd jet is very likely to appear . in a way
, the crossing point between the two hardest jet indicates a @xmath133 range below which we should not rely on qcd jets being rare or suppressed . in other words ,
50 gev jets should not be used as part of the signal unless we have a way to identify decay jets , while jets with @xmath134 gev are comparably safe .
of course , this insight is not new for example , careful squark and gluino analyses for the lhc have always been designed that way @xcite .
the good news of this qcd analysis is that jet activity will actually be helpful to distinguish sgluon pairs from @xmath108 backgrounds .
first , top pair events are quite unlikely to come with a qcd jet of @xmath134 gev , which we have seen in sec .
[ sec : lhc ] is typical for the signal s decay jets .
secondly , as long as we require @xmath134 gev for the decay jets , even a 600 gev sgluon will hardly come with such hard qcd jets .
in general , if we consider something like the total visible mass as an observable to distinguish the sgluon - pair signal from top pairs , fig . [
fig : jets ] shows that qcd radiation will improve this handle .
based on these results , we can estimate that for sgluon branching ratios into @xmath135 of order 10% , we can expect an lhc discovery reach of up to roughly @xmath136 tev .
the bad news is that for the reconstruction of the sgluon mass we could utilize the semileptonic sample . from fig .
[ fig : signal ] we can guess that the jet from the hadronic top decay should be comparable to the lepton spectrum , which does not guarantee that both of them even lie above @xmath137 gev , where the safe region would really only start at @xmath134 gev , as seen in fig .
[ fig : jets ] . reconstructing the sgluon including a hadronic top decay is unlikely to succeed in a realistic qcd environment . as mentioned above
, single sgluon production might rely on such a reconstruction for a side - bin analysis against the theoretically notorious single - top background , so qcd effects are unlikely to help with this problem .
the mrssm , with a continuous @xmath0 symmetry , is an interesting alternative to the mssm , which provides a novel solution to the tension between supersymmetry at the tev scale and measurements from the flavor sector .
a key feature of any @xmath0symmetric model is the promotion of gauginos to dirac fermions , which automatically implies the existence of an additional color - octet scalar with standard - model type @xmath0 charge , the sgluon .
sgluons necessarily have tree - level couplings to gluons , gluinos , and squarks , which further induce couplings to quarks and ( single sgluon coupling to ) gluons through loops .
sgluons have a large color charge and can be copiously produced at the lhc .
their decays can include squarks , gluinos , gluons , and quarks .
this last decay , through the large squark mixing which is the hallmark of the mrssm , can violate flavor , leading to large branching ratios into a top and a light quark .
pair production with a subsequent decay to light - sign top quarks appears to be the most promising search channel at the lhc .
we have computed the relevant lhc cross sections and branching ratios , with special focus on jet activity in this essentially background - free signature .
properly simulated qcd effects turn out to be helpful with regard to the sgluon pair analysis : additional jet radiation in the signal will typically create more hard jets , adding to the two hard decay jets from the sgluon pair . while the qcd jets are too soft to be mistaken for decay jets they create a generally harder signal event , while jet radiation for the already softer top - pair background makes this general feature even more prominent . in the light of this result
, a search for sgluon pairs with a @xmath108 final state might be feasible . for single sgluon production
the qcd - induced background uncertainty is potentially dangerous . the obvious way to tell apart signal and background would be to look for a peak in the top
jet invariant mass , with a hadronically decaying top quark .
however , qcd jet radiation can be expected to lead to a sizeable combinatorical background to the @xmath128 decay jets , which is worsened by the generically higher scale of the signal process .
the authors are grateful for conversations with beate heinemann , ben kilminster , charles plager , dave rainwater , and daniel whiteson . for the qcd simulations we are hugely grateful to johan alwall for teaching us madevent and jet merging .
we also would like to thank the aspen center for physics for providing such a stimulating environment which inspired this study .
we thank claude duhr and fabio maltoni for helping us implement the correct color structure for the @xmath11-@xmath11-@xmath14-@xmath14 vertex in madevent , which is not properly gauge invariant by default .
we are grateful to the authors of @xcite for detailed comparisons with part of our results and correcting a sign error in our original feynman rules .
our phenomenological results have not changed significantly .
research at argonne national laboratory is supported in part by the department of energy under contract de - ac02 - 06ch11357 .
in this appendix , we present the expressions for sgluon coupling to quarks and gluons induced at one loop . the results are presented in terms of the scalar integral functions of passarino and veltman @xcite , normalized such that the measure is @xmath138 .
the sgluon coupling to quark @xmath139 and anti - quark @xmath140 receives contributions from both right- and left - handed squarks . in the mrssm , right- and left - handed squarks do not mix with each other , so even with large squark mixing , they form two distinct sectors .
we are interested in two cases .
the first has @xmath141 , for which we can approximate , @xmath142 \notag \\ & - \frac{1}{n_c } \left [ b \left(m_i^2 ; { m_{\tilde{g } } } , { m_{\tilde{q}}}\right ) - b \left({m_g}^2 ; { m_{\tilde{q } } } , { m_{\tilde{q}}}\right ) + \left ( { m_{\tilde{g}}}^2 - { m_{\tilde{q}}}^2 \right ) c \left ( m_i^2 , 0 , { m_g}^2 ; { m_{\tilde{q } } } , { m_{\tilde{g } } } , { m_{\tilde{q}}}\right ) \right ] \big\}\end{aligned}\ ] ] where the left - handed squarks contribute . and , @xmath143 \notag \\ & - \frac{1}{n_c } \left [ b \left(m_i^2 ; { m_{\tilde{g } } } , { m_{\tilde{q}}}\right ) - b \left({m_g}^2 ; { m_{\tilde{q } } } , { m_{\tilde{q}}}\right ) + \left ( { m_{\tilde{g}}}^2 - { m_{\tilde{q}}}^2 \right ) c \left ( m_i^2 , 0 , { m_g}^2 ; { m_{\tilde{q } } } , { m_{\tilde{g } } } , { m_{\tilde{q}}}\right ) \right ] \big\}\end{aligned}\ ] ] where the right - handed squarks are running in the loops .
the chiral couplings are a consequence of eq.([eq : susy_qcd ] ) and will be different for different admixtures of @xmath11 and @xmath28 .
the @xmath144 multiply @xmath145 and thus can be neglected .
the second case has @xmath146 .
the relevant quantities are @xmath147 given by , @xmath148 \right . \notag \\ & \left
. - \frac{2}{n_c } \ ; \left [ b \left(m_i^2 ; { m_{\tilde{g } } } , { m_{\tilde{q}}}\right ) - b \left({m_g}^2 ; { m_{\tilde{q } } } , { m_{\tilde{q}}}\right ) - \left ( { m_{\tilde{g}}}^2 - { m_{\tilde{q}}}^2 + m_i^2 \right ) c \left ( m_i^2 , m_i^2 , { m_g}^2 ; { m_{\tilde{q } } } , { m_{\tilde{g } } } , { m_{\tilde{q}}}\right ) \right ] \right\}\end{aligned}\ ] ] where the right - handed squarks contribute to @xmath149 and vice - versa . the sgluon coupling to gluons for one squark flavor
is @xmath150 \label{eq : formfac}\ ] ] summed over all of the @xmath151 squark flavors . from the naive computation ,
the color factor of this coupling includes the antisymmetric @xmath36 as well as the symmetric @xmath152 .
however , due to the symmetry structure of eq.([eq : formfac ] ) only @xmath152 survives . for the same reason , the gluino loop contribution with its only color structure @xmath36 cancels completely .
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g. passarino and m. j. g. veltman , nucl .
b * 160 * , 151 ( 1979 ) .
s. y. choi , m. drees , j. kalinowski , j. m. kim , e. popenda and p. m. zerwas , arxiv:0812.3586 [ hep - ph ] . | scalar gluons or sgluons are color octet scalars without electroweak charges .
they occur in supersymmetric models of dirac gauginos as the scalar partners of the gluino and carry standard - model type @xmath0 charge .
this allows them to interact with ordinary matter and to be produced at the lhc , singly as well as in pairs .
sgluons dominantly decay into gluons , top pairs , and a top quark plus a light quark .
a pair of sgluons decaying into like - sign tops would provide a striking signature at the lhc . in our discussion of this channel we especially focus on the proper treatment of qcd jets . | <s>[INST]theories with weak scale supersymmetry represent the most complete and cherished vision of physics beyond the standard model .
their many successes include stabilization of the electroweak scale with respect to high - scale physics , improvement of the convergence of couplings necessary for grand unification , possible electroweak baryogenesis to explain the matter - anti - matter asymmetry of the universe , and ( with @xmath0 parity ) relatively mild contributions to precision electroweak data and a successful dark matter candidate .
however , none of those successes rest crucially on the minimal realization of the supersymmetric standard model @xcite .
in fact , there are features of the minimal supersymmetric standard model ( mssm ) which are somewhat at odds with the mssm as a completely natural theory of the electroweak scale . the @xmath1 or @xmath2 problem indicates that the supersymmetric @xmath1 term must be roughly of the same size as the supersymmetry - breaking parameters , and yet the mssm offers no explanation for why this should be the case .
the lightest higgs mass in the mssm is , at tree - level , less than the @xmath3 boson mass , and even including radiative corrections typically in conflict with the lep - ii bound @xcite .
the model survives based on large radiative corrections from scalar top quarks , but in turn this requires the stops to be so heavy that the higgs soft masses end up fine - tuned to the per - cent level .
perhaps the most disturbing feature of the mssm is the fact that if one naively assumes a general spectrum of supersymmetry - breaking parameters , it is simply ruled out .
if there are large mixings among the squarks and among the sleptons , flavor - violating processes such as @xmath4-@xmath5 mixing , @xmath6 , and others , can be enhanced by orders of magnitude with respect to standard model predictions , in obvious contradiction to experimental data .
the traditional solution ( of which gauge mediation is the prototype ) is to engineer supersymmetry breaking such that the soft - breaking mass parameters are highly flavor diagonal @xcite .
this controls flavor violation to an acceptable level at a given energy scale , but continues to be challenged by natural electroweak symmetry breaking , the higgs mass , and cosmology .
an alternative is to alter the low energy structure of the model such that the supersymmetric solution to the hierarchy problem is preserved , but flavor violation is ameliorated .
a recent elegant solution imposes a continuous @xmath0 symmetry @xcite , to form the minimal @xmath0-symmetric supersymmetric standard model ( mrssm ) @xcite .
this model invokes the @xmath0 symmetry to forbid the potentially flavor - violating left - right mixing @xmath7-terms , and to guarantee ( at least largely in light of anomaly - mediated contributions ) dirac gaugino masses .
this dirac nature often leads to an additional suppression in flavor - violating processes from gauginos running in the loops , which causes many contributions to scale with large gaugino mass as @xmath8 instead of the majorana scaling , @xmath9 @xcite .
the model has additional interesting features , such as uv finite scalar masses due to the super - soft feature of dirac gauginos @xcite , and additional matter content at the electroweak scale .
for example , if the gluino is a dirac particle , the two on - shell degrees of freedom from the gluon are not sufficient to construct a supersymmetric four - spinor .
to provide the two additional bosonic degrees of freedom , the mrssm adds a complex scalar partner .
an unbroken @xmath0 symmetry is also a generic feature of simple models of meta - stable supersymmetry breaking @xcite . in this article
we consider the phenomenology of the scalar partner of the dirac gluino , a color adjoint scalar the sgluon . as a colored particle , it couples to a gluon and
will have large pair - production rates at the tevatron and lhc .
it interacts with quarks at the one - loop level proportional to the quark masses .
thanks to the large mixing naturally expected in the mrssm s squark sector , it will readily decay into flavor violating channels .
previous studies have considered scalar color octets with either decays into missing energy @xcite , with electroweak as well as @xmath10 charges @xcite , or purely flavor diagonal couplings @xcite , which all lead to very different phenomena .
our work is organized as follows . in section [ sec : sgluons ] we show how sgluons arise in a model with dirac gluinos , examine their soft masses , and derive their interactions including the one - loop contribution to the @xmath11@xmath12@xmath13 and @xmath11@xmath14@xmath14 vertices . in section [ sec : fcnc ] we examine the flavor - violating effects mediated by sgluons and derive some mild constraints from @xmath4-@xmath15 mixing . in section
[ sec : search ] we discuss the production of a pair of sgluons through the strong interaction , and examine the decay of the pair into like - sign tops .
this distinctive signature provides bounds on the sgluon mass at the tevatron and will easily be discovered at the lhc for a wide range of masses .
we particularly focus on the proper treatment of the jet activity in such events .
scalar gluons are contained in a chiral superfield @xmath16 which is a color adjoint carrying @xmath0 charge zero .
the fermionic component @xmath17 is married through @xmath18term supersymmetry breaking to the ordinary gluino @xmath19 .
the lowest component @xmath20 is a complex color adjoint scalar .
supersymmetry breaking will generally split this into two real scalar states which are admixtures of the real and imaginary parts of @xmath11 .
we discuss the spectrum below .
kinetic terms for the sgluons are contained in canonical khler potential terms for @xmath21 , @xmath22 where @xmath23 is the vector superfield containing the gluon and the @xmath24 gauge indices are implied .
the kinetic terms include the coupling of the sgluon @xmath11 to the gluons from the covariant derivative , a @xmath11-@xmath25-@xmath26 coupling of strength @xmath27 required by supersymmetry , and @xmath18term contributions to the scalar potential that are of the form @xmath28-@xmath11-@xmath29-@xmath30 which will not be important for our purposes .
there are no renormalizable gauge invariant terms through which @xmath21 interacts with matter superfields in either the khler potential or in the super - potential , and the assumed @xmath0 symmetry is incompatible with @xmath31 or @xmath32 interactions in the super - potential .
thus , the tree - level supersymmetric interactions of @xmath11 are determined entirely by supersymmetric qcd , @xmath33 where @xmath34 is the usual covariant derivative for a color adjoint , @xmath35 is the ( four - component ) gluino , and @xmath36 are the structure constants of @xmath10 .
soft mass terms for the sgluons can arise from either @xmath37term ( @xmath38 ) or @xmath18term ( @xmath39 ) spurions of supersymmetry breaking , @xmath40 and also are generated by the term responsible for the dirac gluino mass @xcite , @xmath41 where @xmath42 is the usual superfield @xmath24 field strength .
this super - potential term , along with the usual mssm @xmath24 @xmath18-terms , lead to terms in the lagrangian , @xmath43 where @xmath44 is the dirac gluino mass , and @xmath45 are the generators of @xmath24 in the fundamental representation . replacing the @xmath10 auxiliary field @xmath46 through its equation of motion
leads to terms proportional to @xmath47 and @xmath48 as well as @xmath49 @xcite .
it also induces tri - linear interactions of @xmath11 with squarks , somewhat analogous to the @xmath7 terms in the usual mssm .
altogether , the supersymmetry - breaking lagrangian for @xmath11 reads @xmath50 where @xmath51 is a real parameter and @xmath52 may be complex .
the mass eigenstates are two real color adjoint scalars which can be labelled as @xmath53 and @xmath54 .
the mass - squared eigenvalues are given by , @xmath55 and clearly we must have @xmath56 or run the risk of a color - breaking vacuum . there will be a non - trivial mixing angle when @xmath52 is complex .
when we write @xmath52 in terms of its phase @xmath57 , the mass eigenstates are @xmath58 for simplicity we will assume @xmath59 and @xmath52 are real , and thus there is no non - trivial mixing from here on . in that case
both sgluons are either a pure scalar or a pure pseudoscalar , which is equivalent as long as we combine them with massless qcd , the theory relevant for lhc .
all tree - level interactions of the sgluon with standard model and mssm states we can read off @xmath60 and @xmath61 .
the coupling of two sgluon to gluons is simply a result of its adjoint color charge and arises from the kinetic term .
the coupling to two gluinos is the supersymmetric partner of the gluon couplings , while the couplings to two squarks arise from @xmath18 terms .
note in particular that the dirac gluino mass sets the size of the squark - squark - sgluon coupling .
feynman diagrams for sgluon interactions with quarks.,title="fig : " ] feynman diagrams for sgluon interactions with quarks.,title="fig : " ] if we insert the squark and gluino couplings to a sgluon shown in eq.([eq : susy_qcd ] ) and in eq.([eq : soft ] ) into one - loop diagrams , the sgluon will couple to quarks .
there are two feynman graphs responsible for this interaction induced by gluinos and squarks , shown in figure [ fig : qvertex ] . for each of the two sgluon states the effective action after electroweak symmetry breaking contains a dimension-4 operator of the form , @xmath62 + \text{h.c.}\ ] ] where @xmath63 and @xmath64 are quark flavor indices .
the couplings may be expressed as @xmath65 where @xmath66 is the relevant squark mixing parameter , @xmath67 are the quark masses , and the dimensionless @xmath68s are functions of the heavy sgluon , gluino , and the squark masses . their form is given in the appendix .
it is important to notice that in the mrssm these couplings come out automatically proportional to quark masses , which mitigates their contribution to flavor - violating observables .
in contrast , for example , the @xmath7 terms in the mssm have to be _ defined _ to appear proportionally with the quark masses , as @xmath69 , which is an additional assumption on the flavor structure of the general mssm . in the limit of degenerate squarks , this source of flavor violation in
the mrssm will switch off through a super - gim mechanism . in the limit of large squark , gluino , or sgluon masses
the quark - quark - sgluon coupling will be suppressed by @xmath70 , @xmath71 , or @xmath72 , respectively .
feynman diagrams for single sgluon interactions with gluons.,title="fig : " ] feynman diagrams for single sgluon interactions with gluons.,title="fig : " ] feynman diagrams for single sgluon interactions with gluons.,title="fig : " ] pairs of sgluons interact with one or two gluons as a consequence of the fact that the sgluons are adjoints of @xmath10 .
there is also a single sgluon - gluon - gluon interaction mediated by squarks , as shown in figure [ fig : gvertex ] .
the effective action contains a dimension - five operator generated at one loop @xmath73 where @xmath74 is the symmetric gauge - invariant combination of three @xmath10 adjoints and the dimensionless form factor @xmath75 is given in the appendix . a similar contribution mediated by gluinos vanishes at one loop , due to the symmetry structure of the ( asymmetric ) color factor and the ( symmetric ) loop contribution . in the limit of heavy squarks
the coupling @xmath75 will vanish proportionally to @xmath76 .
through its flavor - violating couplings to quarks , the sgluon can also mediate flavor - changing processes . at energies far below the sgluon mass ,
these interactions look like @xmath77 four fermion interactions . using the @xmath78-@xmath79 transition operators relevant for @xmath4-@xmath5 mixing we can illustrate the terms left behind when the sgluon is integrated out : @xmath80 + g^{sd}_r g^{sd}_l \left [ q^{sd}_3 + \widetilde{q}^{sd}_3 -\frac{1}{3 } q^{sd}_2 - \frac{1}{3 } \widetilde{q}^{sd}_2 \right ] \right\}\ ] ] where the @xmath81 are the four fermion interactions defined in ref .
@xcite . comparing to eq.([eq : qvertex ] ) we know that the couplings @xmath14 are proportional to @xmath82 , so the relevant parameters which will be constrained are @xmath83 .
analogous expressions describe @xmath84-@xmath79 , @xmath84-@xmath78 , and @xmath85-@xmath86 mixing .
we compute the coefficients of each of these operators and compare with the global fit by the ut@xmath87 collaboration @xcite to obtain bounds on the sgluon mass , for a given choice of gluino mass , average squark masses , and squark flavor mixing parameters @xmath82 . in fig .
[ fig : fcnc ] , we present the scale of the most constraining of the four fermion operators , expressed as the effective scale @xmath88 . since mixing effects will only raise the effective scale of the four fermion interactions , the curves are the minimum possible effective scales for a given choice of sgluon , gluino , and average squark masses . in other words ,
a realistic choice of mixing parameters will increase the effective scales which suppress the fcnc operators and thus result in less constraints from flavor violation mediated by sgluons .
we also show the bounds on the corresponding scales from ref .
bounds from @xmath89-@xmath90 and @xmath18-@xmath91 mixing are mild enough as to basically provide no constraint .
the @xmath4-@xmath15 mixing bound is more severe , but the plotted bound is on the imaginary part of @xmath92 , and thus can be avoided if there is no large @xmath93-violating phase in the down - strange squark mixing element . in any case ,
sgluon masses above 600 gev or so are compatible with measurement , regardless of mixing .
note also that the constraints on down - type mixing do not in any way preclude the sgluon flavor - violating decays into up - type quarks which we consider below . mixing ( 2 curves ) ,
@xmath18 mixing , @xmath4 mixing with @xmath94 tev and an average @xmath95 gev , and @xmath4 mixing with @xmath96 tev . dashed lines : current bounds on the operators ( bottom to top ) , @xmath97 , @xmath98 , @xmath99 , and @xmath100 ( imaginary part ) , obtained from the global fit .
[ fig : fcnc],width=264 ]
as discussed in section [ sec : sgluons ] , we expect the @xmath0symmetric supersymmetric theory to include a pair of sgluons whose mass is split by something of order the gluino mass .
there will thus be two sgluon states which we can search for at hadron colliders .
since the masses are not typically degenerate , the results in this section are presented for a single sgluon state , and apply equally to the lighter or the heavier sgluon . the couplings to quarks and single sgluon coupling to gluons will depend on the mixing between the two states , but tree level pair production of sgluons involves only the strong coupling , as these interactions are protected by @xmath24 gauge invariance .
the resulting pair cross sections thus only depend on the sgluon mass , similar to , for example , the case of scalar leptoquark pairs . ,
width=302 ] in figure [ fig : xsec ] , we present the leading order cross section for pair production of sgluons as a function of their mass at the tevatron and lhc @xcite . for masses around 250 gev , the production rate of the order of 200 fb at the tevatron would correspond to a few hundred sgluon pair events in the currently available cdf and dzero data , depending on the decays and triggers . as expected
, the production rate at the tevatron drops below the femtobarn level for sgluon masses around 400 gev , thanks to the limited center - of - mass energy and @xmath101wave suppression of the dominant subprocess @xmath102 . from a dedicated analysis
we could expect sgluon mass bounds similar to squark mass bounds in the limit of large gluino mass . at the lhc ,
the dominant subprocess is @xmath103 with large cross sections , falling from around 400 pb for masses around 250 gev to 2 fb for masses around 1.5 tev . for sgluon masses in the tev range ,
the lhc will rely on its sea - quark suppressed @xmath104 luminosity which leads to a rapid drop of the cross section above 1.8 tev . with an appreciable lhc luminosity these rates correspond to several hundred to a few million events available for analyses . for the lhc we also present the single production rate from gluon fusion @xcite , for two choices of squark and gluino masses . through the one - loop diagrams discussed in sec .
[ sec : sgluons ] there can be appreciable single sgluon production through @xmath105 , which can dominate for large sgluon masses because of the phase space suppression of the pair production and threshold effects . for small sgluon masses
the lhc is not energy limited , so the single production channel is suppressed by a loop factor @xmath106 squared .
the problem of single production will be challenging backgrounds discussed below .
the sgluon interaction with quarks typically results in a negligible single sgluon production rate , because the leading contribution is one loop and the suppression by the light quark masses .
sgluons can also be produced at the lhc in cascade decays involving squarks , through the soft breaking interaction of eq.([eq : soft ] ) .
production of pairs of heavier squarks can thus cascade down through sgluons into lighter squarks , leaving behind either light jets which reconstruct the sgluon mass , or events enriched with top quarks .
either of these possibilities is rather exotic from the point of view of the standard mssm , and we leave their detailed exploration for future work . branching ratios for sgluon decays into @xmath107 , @xmath108 , @xmath109 for @xmath110 and @xmath111 as a function of sgluon mass and for two choices of left - handed squark and gluino masses .
right - handed squark masses are set to @xmath112 of the left - handed squark masses .
we assume maximal up - squark mixing.,title="fig : " ] branching ratios for sgluon decays into @xmath107 , @xmath108 , @xmath109 for @xmath110 and @xmath111 as a function of sgluon mass and for two choices of left - handed squark and gluino masses .
right - handed squark masses are set to @xmath112 of the left - handed squark masses .
we assume maximal up - squark mixing.,title="fig : " ] if heavy enough , sgluons will decay at tree level into pairs of gluinos and/or squarks . if these decay channels are closed , the sgluon has to decay through its loop - induced couplings into quarks and gluons . in the case of decays into quarks ,
the @xmath11-@xmath12-@xmath113 interaction is proportional to the heavier of the two quark masses , so one can expect that decays including at least one top quark to dominate .
if the mixing in the up - type squark sector is large ( as is the point of the mrssm ) , we therefore expect large and comparable branching ratios into @xmath114 , @xmath115 , and @xmath116 .
the specifics of the branching ratios are a window into the details of the squark mixing matrices . in figure
[ fig : br ] we present the branching ratios as a function of the sgluon mass for two sets of average squark and gluino masses , and assuming maximal mixing in the up - squark sector . the mixed heavy
light quark decays can dominate the sgluon decays for small masses and decreases with larger sgluon masses . for the maximal mixing considered here ,
the decay into @xmath116 is roughly comparable to any single one of the heavy - light decays .
thus , combing channels together , the branching ratio into one top ( or anti - top ) and a light quark are a factor of a few times larger than that into a top pair . for heavier squarks the supersymmetric decay channels
are typically closed in the region accessible to the lhc . again , the decay to one heavy and one light quark typically dominates . at large sgluon masses
decays into gluons dominate because the @xmath11@xmath14@xmath14 coupling is a dimension five operator which grows with the invariant mass of the sgluon , the only scale in the process , while the decay to quarks will be suppressed by a relative factor @xmath117 .
when sgluons are pair - produced , each sgluon is as likely to decay into a top as an anti - top .
thus , half of the decays where both sgluons decay into a top and a light - quark initiated jet will have same sign tops ( @xmath118 or @xmath119 ) .
when both tops decay leptonically we have a final state containing two light jets and either @xmath120 or a @xmath121 ( where @xmath122 is an electron or muon ) - a striking signature of physics beyond the standard model that also arises in the context of models of top compositeness @xcite .
reference @xcite has considered a search for like - sign tops at the tevatron in the context of a model of maximal flavor violation .
the authors perform a sophisticated treatment of the backgrounds and the cdf detector efficiencies .
while the maximal flavor violation model signal is the result of a mixture of pair and single production of a neutral color singlet scalar @xmath123 which interacts moderately strongly with top and charm , the analysis only requires a pair of like sign leptons , a @xmath84-tagged jet , and missing energy .
thus , our signal events are expected to have a high efficiency with respect to the analysis cuts , and one could get a tevatron bound on the sgluon mass from a similar analysis . a single sgluon produced at the lhc can decay through its flavor - violating interactions into a single top quark and a light jet , similar in topology to the @xmath78-channel mode of single top production . even in the standard model ,
this mode is challenging at the lhc because of large backgrounds from @xmath116 and @xmath124-channel single top @xcite .
therefore , single sgluon production is unlikely to be phenomenologically relevant after considering qcd effects and backgrounds .
however , if the sgluon is heavy enough it may be possible to use the peak in the top plus light jet invariant mass to isolate a signal @xcite . , width=264 ] from the discussion above we are immediately lead to study in more detail sgluon pair production with a subsequent decay into two like - sign tops with leptonic decays . with sizeable production rates and branching ratios above 10%
the question remains if this channel survives the lhc triggers and acceptance cuts . in fig .
[ fig : signal ] we show the normalized transverse momentum distributions of all sgluon decay particles . for both sgluon masses of 300 and 600 gev the light - flavor jet and bottom transverse momenta peak above @xmath125 gev , which indicates that observing four jets and tagging two bottoms should not be a problem . for a 300 gev sgluon
the harder jet has a typical transverse momentum around @xmath126 gev .
similarly , the harder bottom can acquire @xmath127 gev .
for a heavier sgluon we see that the bottom distributions hardly change , since they are mostly determined by the top and @xmath128 masses .
the two light - flavor jets from the sgluon decay become significantly harder and peak around @xmath129 gev and 280 gev , respectively .
as we will see later , in particular for heavier sgluons the decay jet can be identified unambiguously even in the presence of qcd jets . on the lepton side of fig .
[ fig : signal ] we see that the harder lepton with a typical transverse momentum close to 100 gev guarantees the triggering of sgluon pair production
. moreover , such a large transverse momentum might be useful to distinguish the sgluon pairs from the standard model backgrounds , even in the same - sign lepton case .
the second lepton is comparably soft , and the missing transverse momentum peaking around 70 gev is unlikely to contribute to the smoking - gun signature . nevertheless , from the distributions in fig .
[ fig : signal ] we can see that triggering and acceptance cuts will not be a problem for the largely background - free like - sign tops signature .
moreover , both hard light - flavor decay jets as well as the relatively hard lepton spectrum should help to reconstruct the sgluon mass scale , which would allow us to gain information on the branching ratio and thereby on the flavor structure of the mrssm .
gev and @xmath130 on the parton level .
[ fig : jets],title="fig:",width=196 ] gev and @xmath130 on the parton level .
[ fig : jets],title="fig:",width=196 ] gev and @xmath130 on the parton level .
[ fig : jets],title="fig:",width=196 ] because the light - flavor decay jets from the sgluons are crucial for the analysis described above , we have to answer the question if this jet can be identified in the jet - rich lhc environment .
this question becomes even more relevant once we try to search for the opposite - sign lepton channel or attempt to determine the sgluon mass from hadronic top decays .
recently , there have been theoretical developments which allow us to simulate qcd jet radiation over the entire transverse momentum range of these additional jets and including high jet multiplicities .
we simulate additional qcd jets in the signal process @xmath131 using the madevent @xcite implementation of the mlm scheme . in particular because the sgluons in the final state provide a hard scale for the process we do not expect the mlm results to differ from a corresponding ckkw analysis @xcite .
in particular for heavier sgluon masses the qcd activity should be dominated by collinear parton - shower effects @xcite , but the mlm scheme now allows us to consistently treat top backgrounds and the sgluon signal for different masses . for this simulation
we avoid introducing a supersymmetric shower including sgluon splittings , which would be required to include final - state radiation . because of the lack of a collinear enhancement we know that final - state radiation will not contribute strongly to qcd jet radiation .
therefore , we only include initial - state radiation which is universal for different heavy new - physics states produced at the lhc . in fig .
[ fig : jets ] we show the number of qcd jets in sgluon pair events at the lhc .
apart from a crucial minimal jet separation of @xmath132 we apply only a varying transverse momentum cut of 30 , 50 and 100 gev on the radiated jets . in the left panel
we see that while top quarks most likely come with no additional jet from initial - state radiation , a 300 gev sgluon will most likely be accompanied by one and a 600 gev sgluon by two additional qcd jets .
this is an effect of the hard factorization scale in the process which determines the size and the maximum range of the collinear enhancement of initial - state radiation .
when we increase the minimum @xmath133 to 50 gev the typical number of additional jets drops by roughly one , but in particularly heavy states still come with zero , one , or two jets at roughly the same rate .
only the three additional jets channel is suppressed to the 10% level , where this quantitative result should be taken with a grain of salt without a tuned parton shower for the lhc .
finally , a cut of at least @xmath134 gev gets rid of additional jets in roughly two thirds of the events and allows us to use light - flavor decay jets in the analysis . .
the leading jets is shown as a solid line .
[ fig : merging],width=264 ] the normalized transverse momentum distributions for the radiated jets are shown in fig .
[ fig : merging ] .
the different areas under the curves for the four leading jets reflect the fact that only a fraction of events actually show such jets .
again , we see that from the top pairs to the 600 gev sgluons the situation changes qualitatively : in the bottom panel the curves for the leading and the sub - leading are similar , and as long as we stay below @xmath133 even a third qcd jet is very likely to appear . in a way
, the crossing point between the two hardest jet indicates a @xmath133 range below which we should not rely on qcd jets being rare or suppressed . in other words ,
50 gev jets should not be used as part of the signal unless we have a way to identify decay jets , while jets with @xmath134 gev are comparably safe .
of course , this insight is not new for example , careful squark and gluino analyses for the lhc have always been designed that way @xcite .
the good news of this qcd analysis is that jet activity will actually be helpful to distinguish sgluon pairs from @xmath108 backgrounds .
first , top pair events are quite unlikely to come with a qcd jet of @xmath134 gev , which we have seen in sec .
[ sec : lhc ] is typical for the signal s decay jets .
secondly , as long as we require @xmath134 gev for the decay jets , even a 600 gev sgluon will hardly come with such hard qcd jets .
in general , if we consider something like the total visible mass as an observable to distinguish the sgluon - pair signal from top pairs , fig . [
fig : jets ] shows that qcd radiation will improve this handle .
based on these results , we can estimate that for sgluon branching ratios into @xmath135 of order 10% , we can expect an lhc discovery reach of up to roughly @xmath136 tev .
the bad news is that for the reconstruction of the sgluon mass we could utilize the semileptonic sample . from fig .
[ fig : signal ] we can guess that the jet from the hadronic top decay should be comparable to the lepton spectrum , which does not guarantee that both of them even lie above @xmath137 gev , where the safe region would really only start at @xmath134 gev , as seen in fig .
[ fig : jets ] . reconstructing the sgluon including a hadronic top decay is unlikely to succeed in a realistic qcd environment . as mentioned above
, single sgluon production might rely on such a reconstruction for a side - bin analysis against the theoretically notorious single - top background , so qcd effects are unlikely to help with this problem .
the mrssm , with a continuous @xmath0 symmetry , is an interesting alternative to the mssm , which provides a novel solution to the tension between supersymmetry at the tev scale and measurements from the flavor sector .
a key feature of any @xmath0symmetric model is the promotion of gauginos to dirac fermions , which automatically implies the existence of an additional color - octet scalar with standard - model type @xmath0 charge , the sgluon .
sgluons necessarily have tree - level couplings to gluons , gluinos , and squarks , which further induce couplings to quarks and ( single sgluon coupling to ) gluons through loops .
sgluons have a large color charge and can be copiously produced at the lhc .
their decays can include squarks , gluinos , gluons , and quarks .
this last decay , through the large squark mixing which is the hallmark of the mrssm , can violate flavor , leading to large branching ratios into a top and a light quark .
pair production with a subsequent decay to light - sign top quarks appears to be the most promising search channel at the lhc .
we have computed the relevant lhc cross sections and branching ratios , with special focus on jet activity in this essentially background - free signature .
properly simulated qcd effects turn out to be helpful with regard to the sgluon pair analysis : additional jet radiation in the signal will typically create more hard jets , adding to the two hard decay jets from the sgluon pair . while the qcd jets are too soft to be mistaken for decay jets they create a generally harder signal event , while jet radiation for the already softer top - pair background makes this general feature even more prominent . in the light of this result
, a search for sgluon pairs with a @xmath108 final state might be feasible . for single sgluon production
the qcd - induced background uncertainty is potentially dangerous . the obvious way to tell apart signal and background would be to look for a peak in the top
jet invariant mass , with a hadronically decaying top quark .
however , qcd jet radiation can be expected to lead to a sizeable combinatorical background to the @xmath128 decay jets , which is worsened by the generically higher scale of the signal process .
the authors are grateful for conversations with beate heinemann , ben kilminster , charles plager , dave rainwater , and daniel whiteson . for the qcd simulations we are hugely grateful to johan alwall for teaching us madevent and jet merging .
we also would like to thank the aspen center for physics for providing such a stimulating environment which inspired this study .
we thank claude duhr and fabio maltoni for helping us implement the correct color structure for the @xmath11-@xmath11-@xmath14-@xmath14 vertex in madevent , which is not properly gauge invariant by default .
we are grateful to the authors of @xcite for detailed comparisons with part of our results and correcting a sign error in our original feynman rules .
our phenomenological results have not changed significantly .
research at argonne national laboratory is supported in part by the department of energy under contract de - ac02 - 06ch11357 .
in this appendix , we present the expressions for sgluon coupling to quarks and gluons induced at one loop . the results are presented in terms of the scalar integral functions of passarino and veltman @xcite , normalized such that the measure is @xmath138 .
the sgluon coupling to quark @xmath139 and anti - quark @xmath140 receives contributions from both right- and left - handed squarks . in the mrssm , right- and left - handed squarks do not mix with each other , so even with large squark mixing , they form two distinct sectors .
we are interested in two cases .
the first has @xmath141 , for which we can approximate , @xmath142 \notag \\ & - \frac{1}{n_c } \left [ b \left(m_i^2 ; { m_{\tilde{g } } } , { m_{\tilde{q}}}\right ) - b \left({m_g}^2 ; { m_{\tilde{q } } } , { m_{\tilde{q}}}\right ) + \left ( { m_{\tilde{g}}}^2 - { m_{\tilde{q}}}^2 \right ) c \left ( m_i^2 , 0 , { m_g}^2 ; { m_{\tilde{q } } } , { m_{\tilde{g } } } , { m_{\tilde{q}}}\right ) \right ] \big\}\end{aligned}\ ] ] where the left - handed squarks contribute . and , @xmath143 \notag \\ & - \frac{1}{n_c } \left [ b \left(m_i^2 ; { m_{\tilde{g } } } , { m_{\tilde{q}}}\right ) - b \left({m_g}^2 ; { m_{\tilde{q } } } , { m_{\tilde{q}}}\right ) + \left ( { m_{\tilde{g}}}^2 - { m_{\tilde{q}}}^2 \right ) c \left ( m_i^2 , 0 , { m_g}^2 ; { m_{\tilde{q } } } , { m_{\tilde{g } } } , { m_{\tilde{q}}}\right ) \right ] \big\}\end{aligned}\ ] ] where the right - handed squarks are running in the loops .
the chiral couplings are a consequence of eq.([eq : susy_qcd ] ) and will be different for different admixtures of @xmath11 and @xmath28 .
the @xmath144 multiply @xmath145 and thus can be neglected .
the second case has @xmath146 .
the relevant quantities are @xmath147 given by , @xmath148 \right . \notag \\ & \left
. - \frac{2}{n_c } \ ; \left [ b \left(m_i^2 ; { m_{\tilde{g } } } , { m_{\tilde{q}}}\right ) - b \left({m_g}^2 ; { m_{\tilde{q } } } , { m_{\tilde{q}}}\right ) - \left ( { m_{\tilde{g}}}^2 - { m_{\tilde{q}}}^2 + m_i^2 \right ) c \left ( m_i^2 , m_i^2 , { m_g}^2 ; { m_{\tilde{q } } } , { m_{\tilde{g } } } , { m_{\tilde{q}}}\right ) \right ] \right\}\end{aligned}\ ] ] where the right - handed squarks contribute to @xmath149 and vice - versa . the sgluon coupling to gluons for one squark flavor
is @xmath150 \label{eq : formfac}\ ] ] summed over all of the @xmath151 squark flavors . from the naive computation ,
the color factor of this coupling includes the antisymmetric @xmath36 as well as the symmetric @xmath152 .
however , due to the symmetry structure of eq.([eq : formfac ] ) only @xmath152 survives . for the same reason , the gluino loop contribution with its only color structure @xmath36 cancels completely .
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s. y. choi , m. drees , j. kalinowski , j. m. kim , e. popenda and p. m. zerwas , arxiv:0812.3586 [ hep - ph ] .[/INST] scalar gluons or sgluons are color octet scalars without electroweak charges .
they occur in supersymmetric models of dirac gauginos as the scalar partners of the gluino and carry standard - model type @xmath0 charge .
this allows them to interact with ordinary matter and to be produced at the lhc , singly as well as in pairs .
sgluons dominantly decay into gluons , top pairs , and a top quark plus a light quark .
a pair of sgluons decaying into like - sign tops would provide a striking signature at the lhc . in our discussion of this channel we especially focus on the proper treatment of qcd jets . </s> |
since the striking idea of _ white dwarf _ by chandrasekhar @xcite the study of general relativistic compact objects received a tremendous thrust to carry out research in the field of ultra - dense objects .
white dwarfs are composed of one of the densest forms of matter known , surpassed only by other compact stars such as neutron stars , quark stars / strange stars , boson stars , gravastars etc . in the compact stars the matter is found to be in stable ground state where the quarks are confined inside the hadrons .
if it is composed of the de - confined quarks then also a stable ground state of matter , known as ` strange matter ' , is achievable which provides a ` strange star ' @xcite . the main theoretical motivation for postulating the existence of strange stars was to explain the exotic phenomena of gamma ray bursts and soft gamma ray repeaters @xcite .
on the observational side , the rossi x - ray timing explorer has now confirmed that @xmath0 is one of the candidates for a strange star @xcite . as a start of the astrophysical objects of compact nature of the above kind
the theoretical investigation has been done by several researchers by using both analytical and numerical methods . however , the density distribution inside the compact stars need not be isotropic and homogeneous as proposed in the tov model . in the early seventies ruderman @xcite has investigated the stellar models and argued that the nuclear matter may have anisotropic features at least in certain very high density ranges ( @xmath1gm / c.c . ) , where the nuclear interaction must be treated relativistically .
later on bowers and liang @xcite gave emphasis on the importance of locally anisotropic equations of state for relativistic fluid spheres .
they showed that anisotropy might have non - negligible effects on such parameters like maximum equilibrium mass and surface redshift .
anisotropic matter distribution have been considered recently by several investigators as key feature in the configuration of compact stars ( with or without cosmological constant ) to model the objects physically more realistic @xcite . as one of the physical characteristics mak and harko
@xcite have calculated the mass - radius ratio or compactness factor for compact relativistic star however in the presence of cosmological constant . to study mass and radii of neutron star egeland @xcite incorporated the existence of cosmological constant proportionality depending on the density of vacuum .
kalam et al .
@xcite by using their model calculated mass - radius ratio for strange star @xmath2 of their model and found it as @xmath3 which satisfies buchdahl s limit and corresponds to the same mass - radius ratio for the observed strange star @xmath2 .
this physical aspect is very important because of the fact it helps to determine nature of the compact stars , its size , shape , matter contain and several other features . now to get more information ,
several studies have been done on charged or neutral fluid spheres with a spacetime geometry that admits a conformal symmetry , in the static as well as generalized non - static cases . in this line of conformal symmetry
we note that there are lots of works available in the literature @xcite .
however , we investigate in the present work a new anisotropic star admitting non - static conformal symmetry ( mathematical formalism is provided in detail in the next sec .
2 ) . under this background and motivation
we investigation in the present paper a model for relativistic compact star with anisotropy and find out exact spherically symmetric solutions which describe the interior of the dense star admitting non - static conformal symmetry .
the scheme of this study is as follows : we provide mathematical formalism for non - static conformal motion in sec . 2 whereas the einstein field equations for anisotropic stellar source are given in sec .
3 . the solutions and general features of the field equations under the dev - gleiser energy - density profile
have been found out in sec .
4 along with a special discussion on two prescriptions , in section 5 , viz .
( _ 5.1 _ ) the misner prescription , and ( _ 5.2 _ ) the dev - gleiser prescription are done to show that mass to size ratio clearly indicates that the model represents a quark / strange compact star . in sec .
6 we have made some concluding remarks .
now , we consider the interior of a star under conformal motion through non - static conformal killing vector as @xcite @xmath4 where @xmath5 represents the lie derivative operator , @xmath6 is the four vector along which the derivative is taken , @xmath7 is the conformal factor and @xmath8 are the metric potentials @xcite .
it is to be noted that for @xmath9 , the equation above yields the killing vector , whereas for @xmath10 corresponds to the homothetic vector .
so , in general for @xmath11 we obtain conformal vectors . in this manner
, one can perform a more general study of the spacetime geometry by using conformal killing vector .
the static spherically symmetric spacetime is given by the line element ( with @xmath12 in geometrized units ) @xcite @xmath13 where @xmath14 and @xmath15 are the metric potentials and functions of radial coordinate @xmath16 only .
the proposed charged fluid spacetime is mapped conformally onto itself along the direction @xmath6 . here following herrera et al .
@xcite we assume @xmath6 as non - static but @xmath7 to be static as follows : @xmath17 @xmath18 the above set of equations ( 1)-(4 ) give the following expressions @xcite for @xmath19 , @xmath20 , @xmath7 and @xmath21 : @xmath22 @xmath23 @xmath24 @xmath25 , \label{eq8}\ ] ] where @xmath26 , @xmath27 , @xmath28 and @xmath29 are arbitrary constants . according to maartens and maharaj @xcite one can set @xmath30 and @xmath31 so that by rescalling we can get @xmath32 @xmath33 @xmath34 @xmath35 . \label{eq12}\ ] ] however , one can note that the above considerations , i.e. @xmath30 and @xmath31 , do not loss any generality .
this is because the rescalling @xmath6 and @xmath7 in the following manner , @xmath36 and @xmath37 , leaves eq .
( 1 ) invariant .
in the present investigation we consider the most general energy - momentum tensor compatible with spherically symmetry in the following form : @xmath38 with @xmath39 , where @xmath40 is the matter density , @xmath41 and @xmath42 are radial and the transverse pressures of the fluid respectively . for the metric given in eq .
( [ eq2 ] ) , the einstein field equations are @xcite @xmath43+\frac{1}{r^{2}}=8\pi\rho , \label{eq14}\ ] ] @xmath44-\frac{1}{r^{2}}=8\pi p_{r } , \label{eq15}\ ] ] @xmath45=8\pi p_{t}. \label{eq16}\ ] ] imposing the conformal motion , one can write the stress energy components in terms of conformal function as follows : @xmath46 @xmath47 @xmath48 . \label{eq19}\ ] ]
now our task is to find out solutions for the above set of the modified einstein equation in terms of the conformal motion . however , to do so we would like to study the following case for specific energy density as proposed by dev and gleiser @xcite for stars with the energy density in the form @xmath49 where @xmath50 and @xmath51 are constants .
it is to be noted that the choice of the values for @xmath50 and @xmath51 is dictated by the physical configuration under consideration , e.g. @xmath52 and @xmath53 , corresponds to a relativistic fermi gas for ultradense cores of neutron stars @xcite whereas the values @xmath52 and @xmath54 represent a relativistic fermi gas with core immersed in a constant density background @xcite .
it can easily be observed from eq .
( [ eq - rho ] ) that for large @xmath16 the constant density term dominates ( @xmath55 ) so that the corresponding star can be modeled with shell - type feature surrounding the core . due to use of the above energy density , eq .
( [ eq17 ] ) will take the following form : @xmath56 solving this eq .
( [ eq20 ] ) , we get @xmath57 where @xmath58 is an integration constant . substituting the value of @xmath7 in eqs .
( [ eq18 ] ) and ( [ eq19 ] ) , expressions for radial and tangential pressures can be obtained as @xmath59 , \label{eq22}\ ] ] @xmath60 . \label{eq23}\ ] ] , with respect to the parameters @xmath50 and @xmath51 for a fixed radial distance @xmath61 km ] in figs . 2 - 3 we have shown the behaviour of radial and tangential pressures and whereas fig .
1 represents the @xmath62-dimensional presentation indicating the variation of radial pressure with respect to the parameters @xmath63 for a fixed radius .
all the curves are in accordance to the physical feasibility within the acceptable range .
let us now consider a simplest form of barotropic equation of state ( eos ) as @xmath64 , where @xmath65 are the eos parameters along radial and transverse directions . here at present as such we are not considering different forms of @xmath66 with it s possible space and time dependence as are available in the literature @xcite .
thus , the eos parameters @xmath66 can straightly be written in the following forms : @xmath67 , \label{eq24}\ ] ] @xmath68 . \label{eq25}\ ] ] in figs . 4 and 5 we plot variations of radial and transverse eos parameter with respect to radial distance .
in which radial eos represents expected nature with a decreasing pattern .
however , transverse eos parameter indicates that it lies between @xmath69 .
it is negative like exotic matter in nature , however , later we will see that all energy conditions are satisfied for real matter situation . for the model under consideration the measure of anisotropy in pressures can be obtained , from eqs .
( 23 ) and ( 24 ) , as follows : @xmath70 .
\label{eq28}\ ] ] it can be seen that the ` anisotropy ' will be directed outward when @xmath71 i.e. @xmath72 , and inward when @xmath73 i.e. @xmath74 .
this feature is obvious from fig .
( 5 ) of our model that a repulsive ` anisotropic ' force ( @xmath74 ) allows the construction of a more massive stellar distribution @xcite .
we now put and verify different energy conditions of the stellar configuration as follows : @xmath75 @xmath76 and @xmath77 .
it is seen that null energy condition ( nec ) , weak energy condition ( wec ) , strong energy condition ( sec ) and dominant energy condition ( dec ) i.e. all the energy conditions for our particular choices of the values of mass and radius are satisfied which can also be observed from fig . 7 .
are plotted for the specified range ] to search equilibrium situation of this anisotropic star under different forces , we write the generalized tolman - oppenheimer - volkoff ( tov ) equation as @xcite @xmath78 where @xmath79 is the effective gravitational mass inside a sphere of radius @xmath16 which can be derived from the tolmam - whittaker formula as @xmath80 the above equation explains the equilibrium conditions of the fluid sphere due to the following hydrostatic , anisotropic and gravitational forces : @xmath81,\label{eqn28}\ ] ] @xmath82,\label{eqn29}\ ] ] @xmath83,\label{eqn30}\end{aligned}\ ] ] , hydrostatics @xmath84 and anisotropy @xmath85 forces . ]
( 28 ) can be rewritten in the form @xmath86 the profiles of different forces @xmath87 , @xmath88 , @xmath89 are shown in fig .
the figure exposes that our model of anisotropic star is in static equilibrium under the gravitational @xmath90 , hydrostatics @xmath84 and anisotropic @xmath85 forces .
the velocity of sound should follow the condition @xmath91 for a physically realistic model @xcite .
we therefore calculate the radial and transverse sound speed for our anisotropic model as follows @xcite : @xmath92 , \label{eq26}\ ] ] @xmath93 .
\label{eq27}\ ] ] with respect to radial distance .
] let us check whether the sound speeds lie between @xmath94 and @xmath95 .
for this requirement we plot the sound speeds in figs . 8 and 9 .
it is observed that numerical values of these parameters satisfy the inequalities @xmath96 everywhere within the stellar object .
however , for radial sound velocity there is a prominent change over after attaining certain higher value which gradually goes down . since the transverse sound velocity is negative ( due to negative transverse pressure )
, we use numerical value .
as sound speeds lie between @xmath94 and @xmath95 , we should have @xmath97 as evident from fig . 10 .
now , one can go through a technique for stability check of local anisotropic matter distribution as available in the literature @xcite . this technique is known as the cracking concept of herrera and states that the region for which radial speed of sound is greater than the transverse speed is a potentially stable region . fig .
10 indicates that there is a change of sign for the term @xmath98 within the specific configuration and thus confirming that the model has a transition from unstable to stable configuration .
the present stellar model gradually gets stability with the increase of the radius .
however , in terms of the maximum allowable compactness ( mass - radius ratio ) for a fluid sphere as given by buchdahl @xcite , the stability issue will be discussed later on .
one can calculate the effective gravitational mass in terms of the energy density @xmath40 as @xmath99 .
\label{eq33}\ ] ] therefore , the compactness of the star is given by @xmath100.\label{eq35}\ ] ] the nature of variation of the above expression for compactness of the star can be seen in the fig . 9 which is gradually increasing .
we now define the surface redshift corresponding to the above compactness as @xmath101^{-1/2}=\left[1 - \left(a+br^2\right)\right]^{-1/2 } , \label{eq36}\ ] ] so that the surface redshift can be expressed as follows : @xmath102^{-\frac{1}{2 } } - 1 .
\label{eq36}\ ] ] with radial coordinate @xmath16 ] we plot surface redshift in fig .
likewise compactness factor @xmath104 this has also a behaviour of gradual increase .
this feature is also observed from the table 1 .
the maximum surface redshift for the present stellar configuration of radius @xmath105 km turns out to be @xmath106 ( see table 1 ) .
.calculation of masses and hence compactness factors for different values of constant @xmath51 with @xmath52 and @xmath107 km ( with the conversion @xmath108 ) [ cols="^,^,^,^,^,^,^,^,^",options="header " , ] [ table 1 ]
if we look at eq . ( 35 ) as well as eq .
( 36 ) then it will at once reveal that there are lots of information inherently hidden inside these two equations .
let us therefore examine the present model for the specified values of @xmath50 and @xmath51 , appearing in eq .
( 35 ) and eq .
( 36 ) , as follows : for the prescription of misner @xcite i.e. @xmath52 and @xmath53 , we get the effective gravitational mass as @xmath109 which numerically comes out to be @xmath110 so that the compactness factor becomes @xmath111 as can be seen from table 1 . here to estimate mass we have taken radius of the star @xmath107 km by solving @xmath112 at @xmath113 graphically from fig .
this therefore represents a relativistic fermi gas for ultradense cores of neutron stars as noticed in the ref .
@xcite .
increases with the increase of the parameter @xmath58 ] in this prescription @xcite , by substituting the values @xmath115 and @xmath54 one can get the expression for the effective gravitational mass as @xmath116 $ ] . for this case
we provide here a data sheet by choosing different values for @xmath51 ( for case a , @xmath117 whereas for case b , @xmath118 ) in table 1 .
this corresponds to a relativistic fermi gas with core immersed in a constant density background @xcite .
in the investigations we have observed some interesting points which are as follows : \(1 ) note that though transverse pressure is negative , however , all energy conditions are satisfied .
this indicates that matter distribution of the star is real i.e. star is comprising of normal matter .
\(2 ) it is observed that the transverse sound velocity is negative ( due to negative transverse pressure ) so that we use numerical value .
as sound speeds lie between @xmath94 and @xmath95 , we should have @xmath119 @xcite .
on the other hand , bhmer and harko @xcite argued that for an anisotropic star in the presence of a cosmological constant the surface redshift must obey the general restriction @xmath120 , which is consistent with the bound @xmath121 as obtained by ivanov @xcite .
therefore , for an anisotropic star without cosmological constant the above value @xmath122 seems to be within an acceptable range ( fig .
\(4 ) the radius of the star depends on the parameter @xmath58 , as appears in eq .
( 23 ) , with an increasing mode ( fig . 13 ) .
\(5 ) it is well known that the anisotropic factor @xmath123 should vanish at the origin .
however , in the present model the energy density under consideration has an infinite central density . according to misner and zapolsky @xcite
one may use it as an asymptotic solution with a cut - off density below which the eq .
( 27 ) will not valid .
\(6 ) in the present model , the stability of the matter distributions comprising of the anisotropic star has been attained .
we have come to conclude this by analyzing the tov equation which describes the equilibrium condition for matter distribution subject to the gravitational force ( @xmath87 ) , hydrostatic force ( @xmath88 ) and another force ( @xmath89 ) due to anisotropic pressure ( fig . 8) .
\(7 ) for an overall view of the present study and also to have a physically viable model we put here the data which are available on some compact stars , e.g. @xmath2 and @xmath124 and @xmath125 ( see table 1 of the ref .
the compactness factor @xmath104 for these stars are @xmath126 , @xmath127 and @xmath128 respectively . in comparison to these data
we can conclude that our model represents a star with moderate compactness and also indicates that the star might be a compact star of strange / quark type rather than neutron star .
this is because , in general , superdense stars with mass - size ratio exceeding @xmath129 are expected to be composed of strange matter @xcite . now according to buchdahl @xcite
, the maximum allowable compactness for a fluid sphere is given by @xmath130 .
our compactness values for the chosen model ( see table 1 ) within this acceptable range and hence provides a stable stellar configuration .
fr and sr wish to thank the authorities of the inter - university centre for astronomy and astrophysics , pune , india for providing the visiting associateship under which a part of this work was carried out . | we have proposed a model for relativistic compact star with anisotropy and analytically obtained exact spherically symmetric solutions describing the interior of the dense star admitting non - static conformal symmetry .
several features of the solutions including drawbacks of the model have been explored and discussed . for this purpose
we have provided the energy conditions , tov - equations and other physical requirements and thus thoroughly investigated stability , mass - radius relation and surface redshift of the model . it is observed that most of the features are well matched with the compact stars , like quark / strange stars . , , , general relativity ; noncommutative geometry ; compact stars | <s>[INST]since the striking idea of _ white dwarf _ by chandrasekhar @xcite the study of general relativistic compact objects received a tremendous thrust to carry out research in the field of ultra - dense objects .
white dwarfs are composed of one of the densest forms of matter known , surpassed only by other compact stars such as neutron stars , quark stars / strange stars , boson stars , gravastars etc . in the compact stars the matter is found to be in stable ground state where the quarks are confined inside the hadrons .
if it is composed of the de - confined quarks then also a stable ground state of matter , known as ` strange matter ' , is achievable which provides a ` strange star ' @xcite . the main theoretical motivation for postulating the existence of strange stars was to explain the exotic phenomena of gamma ray bursts and soft gamma ray repeaters @xcite .
on the observational side , the rossi x - ray timing explorer has now confirmed that @xmath0 is one of the candidates for a strange star @xcite . as a start of the astrophysical objects of compact nature of the above kind
the theoretical investigation has been done by several researchers by using both analytical and numerical methods . however , the density distribution inside the compact stars need not be isotropic and homogeneous as proposed in the tov model . in the early seventies ruderman @xcite has investigated the stellar models and argued that the nuclear matter may have anisotropic features at least in certain very high density ranges ( @xmath1gm / c.c . ) , where the nuclear interaction must be treated relativistically .
later on bowers and liang @xcite gave emphasis on the importance of locally anisotropic equations of state for relativistic fluid spheres .
they showed that anisotropy might have non - negligible effects on such parameters like maximum equilibrium mass and surface redshift .
anisotropic matter distribution have been considered recently by several investigators as key feature in the configuration of compact stars ( with or without cosmological constant ) to model the objects physically more realistic @xcite . as one of the physical characteristics mak and harko
@xcite have calculated the mass - radius ratio or compactness factor for compact relativistic star however in the presence of cosmological constant . to study mass and radii of neutron star egeland @xcite incorporated the existence of cosmological constant proportionality depending on the density of vacuum .
kalam et al .
@xcite by using their model calculated mass - radius ratio for strange star @xmath2 of their model and found it as @xmath3 which satisfies buchdahl s limit and corresponds to the same mass - radius ratio for the observed strange star @xmath2 .
this physical aspect is very important because of the fact it helps to determine nature of the compact stars , its size , shape , matter contain and several other features . now to get more information ,
several studies have been done on charged or neutral fluid spheres with a spacetime geometry that admits a conformal symmetry , in the static as well as generalized non - static cases . in this line of conformal symmetry
we note that there are lots of works available in the literature @xcite .
however , we investigate in the present work a new anisotropic star admitting non - static conformal symmetry ( mathematical formalism is provided in detail in the next sec .
2 ) . under this background and motivation
we investigation in the present paper a model for relativistic compact star with anisotropy and find out exact spherically symmetric solutions which describe the interior of the dense star admitting non - static conformal symmetry .
the scheme of this study is as follows : we provide mathematical formalism for non - static conformal motion in sec . 2 whereas the einstein field equations for anisotropic stellar source are given in sec .
3 . the solutions and general features of the field equations under the dev - gleiser energy - density profile
have been found out in sec .
4 along with a special discussion on two prescriptions , in section 5 , viz .
( _ 5.1 _ ) the misner prescription , and ( _ 5.2 _ ) the dev - gleiser prescription are done to show that mass to size ratio clearly indicates that the model represents a quark / strange compact star . in sec .
6 we have made some concluding remarks .
now , we consider the interior of a star under conformal motion through non - static conformal killing vector as @xcite @xmath4 where @xmath5 represents the lie derivative operator , @xmath6 is the four vector along which the derivative is taken , @xmath7 is the conformal factor and @xmath8 are the metric potentials @xcite .
it is to be noted that for @xmath9 , the equation above yields the killing vector , whereas for @xmath10 corresponds to the homothetic vector .
so , in general for @xmath11 we obtain conformal vectors . in this manner
, one can perform a more general study of the spacetime geometry by using conformal killing vector .
the static spherically symmetric spacetime is given by the line element ( with @xmath12 in geometrized units ) @xcite @xmath13 where @xmath14 and @xmath15 are the metric potentials and functions of radial coordinate @xmath16 only .
the proposed charged fluid spacetime is mapped conformally onto itself along the direction @xmath6 . here following herrera et al .
@xcite we assume @xmath6 as non - static but @xmath7 to be static as follows : @xmath17 @xmath18 the above set of equations ( 1)-(4 ) give the following expressions @xcite for @xmath19 , @xmath20 , @xmath7 and @xmath21 : @xmath22 @xmath23 @xmath24 @xmath25 , \label{eq8}\ ] ] where @xmath26 , @xmath27 , @xmath28 and @xmath29 are arbitrary constants . according to maartens and maharaj @xcite one can set @xmath30 and @xmath31 so that by rescalling we can get @xmath32 @xmath33 @xmath34 @xmath35 . \label{eq12}\ ] ] however , one can note that the above considerations , i.e. @xmath30 and @xmath31 , do not loss any generality .
this is because the rescalling @xmath6 and @xmath7 in the following manner , @xmath36 and @xmath37 , leaves eq .
( 1 ) invariant .
in the present investigation we consider the most general energy - momentum tensor compatible with spherically symmetry in the following form : @xmath38 with @xmath39 , where @xmath40 is the matter density , @xmath41 and @xmath42 are radial and the transverse pressures of the fluid respectively . for the metric given in eq .
( [ eq2 ] ) , the einstein field equations are @xcite @xmath43+\frac{1}{r^{2}}=8\pi\rho , \label{eq14}\ ] ] @xmath44-\frac{1}{r^{2}}=8\pi p_{r } , \label{eq15}\ ] ] @xmath45=8\pi p_{t}. \label{eq16}\ ] ] imposing the conformal motion , one can write the stress energy components in terms of conformal function as follows : @xmath46 @xmath47 @xmath48 . \label{eq19}\ ] ]
now our task is to find out solutions for the above set of the modified einstein equation in terms of the conformal motion . however , to do so we would like to study the following case for specific energy density as proposed by dev and gleiser @xcite for stars with the energy density in the form @xmath49 where @xmath50 and @xmath51 are constants .
it is to be noted that the choice of the values for @xmath50 and @xmath51 is dictated by the physical configuration under consideration , e.g. @xmath52 and @xmath53 , corresponds to a relativistic fermi gas for ultradense cores of neutron stars @xcite whereas the values @xmath52 and @xmath54 represent a relativistic fermi gas with core immersed in a constant density background @xcite .
it can easily be observed from eq .
( [ eq - rho ] ) that for large @xmath16 the constant density term dominates ( @xmath55 ) so that the corresponding star can be modeled with shell - type feature surrounding the core . due to use of the above energy density , eq .
( [ eq17 ] ) will take the following form : @xmath56 solving this eq .
( [ eq20 ] ) , we get @xmath57 where @xmath58 is an integration constant . substituting the value of @xmath7 in eqs .
( [ eq18 ] ) and ( [ eq19 ] ) , expressions for radial and tangential pressures can be obtained as @xmath59 , \label{eq22}\ ] ] @xmath60 . \label{eq23}\ ] ] , with respect to the parameters @xmath50 and @xmath51 for a fixed radial distance @xmath61 km ] in figs . 2 - 3 we have shown the behaviour of radial and tangential pressures and whereas fig .
1 represents the @xmath62-dimensional presentation indicating the variation of radial pressure with respect to the parameters @xmath63 for a fixed radius .
all the curves are in accordance to the physical feasibility within the acceptable range .
let us now consider a simplest form of barotropic equation of state ( eos ) as @xmath64 , where @xmath65 are the eos parameters along radial and transverse directions . here at present as such we are not considering different forms of @xmath66 with it s possible space and time dependence as are available in the literature @xcite .
thus , the eos parameters @xmath66 can straightly be written in the following forms : @xmath67 , \label{eq24}\ ] ] @xmath68 . \label{eq25}\ ] ] in figs . 4 and 5 we plot variations of radial and transverse eos parameter with respect to radial distance .
in which radial eos represents expected nature with a decreasing pattern .
however , transverse eos parameter indicates that it lies between @xmath69 .
it is negative like exotic matter in nature , however , later we will see that all energy conditions are satisfied for real matter situation . for the model under consideration the measure of anisotropy in pressures can be obtained , from eqs .
( 23 ) and ( 24 ) , as follows : @xmath70 .
\label{eq28}\ ] ] it can be seen that the ` anisotropy ' will be directed outward when @xmath71 i.e. @xmath72 , and inward when @xmath73 i.e. @xmath74 .
this feature is obvious from fig .
( 5 ) of our model that a repulsive ` anisotropic ' force ( @xmath74 ) allows the construction of a more massive stellar distribution @xcite .
we now put and verify different energy conditions of the stellar configuration as follows : @xmath75 @xmath76 and @xmath77 .
it is seen that null energy condition ( nec ) , weak energy condition ( wec ) , strong energy condition ( sec ) and dominant energy condition ( dec ) i.e. all the energy conditions for our particular choices of the values of mass and radius are satisfied which can also be observed from fig . 7 .
are plotted for the specified range ] to search equilibrium situation of this anisotropic star under different forces , we write the generalized tolman - oppenheimer - volkoff ( tov ) equation as @xcite @xmath78 where @xmath79 is the effective gravitational mass inside a sphere of radius @xmath16 which can be derived from the tolmam - whittaker formula as @xmath80 the above equation explains the equilibrium conditions of the fluid sphere due to the following hydrostatic , anisotropic and gravitational forces : @xmath81,\label{eqn28}\ ] ] @xmath82,\label{eqn29}\ ] ] @xmath83,\label{eqn30}\end{aligned}\ ] ] , hydrostatics @xmath84 and anisotropy @xmath85 forces . ]
( 28 ) can be rewritten in the form @xmath86 the profiles of different forces @xmath87 , @xmath88 , @xmath89 are shown in fig .
the figure exposes that our model of anisotropic star is in static equilibrium under the gravitational @xmath90 , hydrostatics @xmath84 and anisotropic @xmath85 forces .
the velocity of sound should follow the condition @xmath91 for a physically realistic model @xcite .
we therefore calculate the radial and transverse sound speed for our anisotropic model as follows @xcite : @xmath92 , \label{eq26}\ ] ] @xmath93 .
\label{eq27}\ ] ] with respect to radial distance .
] let us check whether the sound speeds lie between @xmath94 and @xmath95 .
for this requirement we plot the sound speeds in figs . 8 and 9 .
it is observed that numerical values of these parameters satisfy the inequalities @xmath96 everywhere within the stellar object .
however , for radial sound velocity there is a prominent change over after attaining certain higher value which gradually goes down . since the transverse sound velocity is negative ( due to negative transverse pressure )
, we use numerical value .
as sound speeds lie between @xmath94 and @xmath95 , we should have @xmath97 as evident from fig . 10 .
now , one can go through a technique for stability check of local anisotropic matter distribution as available in the literature @xcite . this technique is known as the cracking concept of herrera and states that the region for which radial speed of sound is greater than the transverse speed is a potentially stable region . fig .
10 indicates that there is a change of sign for the term @xmath98 within the specific configuration and thus confirming that the model has a transition from unstable to stable configuration .
the present stellar model gradually gets stability with the increase of the radius .
however , in terms of the maximum allowable compactness ( mass - radius ratio ) for a fluid sphere as given by buchdahl @xcite , the stability issue will be discussed later on .
one can calculate the effective gravitational mass in terms of the energy density @xmath40 as @xmath99 .
\label{eq33}\ ] ] therefore , the compactness of the star is given by @xmath100.\label{eq35}\ ] ] the nature of variation of the above expression for compactness of the star can be seen in the fig . 9 which is gradually increasing .
we now define the surface redshift corresponding to the above compactness as @xmath101^{-1/2}=\left[1 - \left(a+br^2\right)\right]^{-1/2 } , \label{eq36}\ ] ] so that the surface redshift can be expressed as follows : @xmath102^{-\frac{1}{2 } } - 1 .
\label{eq36}\ ] ] with radial coordinate @xmath16 ] we plot surface redshift in fig .
likewise compactness factor @xmath104 this has also a behaviour of gradual increase .
this feature is also observed from the table 1 .
the maximum surface redshift for the present stellar configuration of radius @xmath105 km turns out to be @xmath106 ( see table 1 ) .
.calculation of masses and hence compactness factors for different values of constant @xmath51 with @xmath52 and @xmath107 km ( with the conversion @xmath108 ) [ cols="^,^,^,^,^,^,^,^,^",options="header " , ] [ table 1 ]
if we look at eq . ( 35 ) as well as eq .
( 36 ) then it will at once reveal that there are lots of information inherently hidden inside these two equations .
let us therefore examine the present model for the specified values of @xmath50 and @xmath51 , appearing in eq .
( 35 ) and eq .
( 36 ) , as follows : for the prescription of misner @xcite i.e. @xmath52 and @xmath53 , we get the effective gravitational mass as @xmath109 which numerically comes out to be @xmath110 so that the compactness factor becomes @xmath111 as can be seen from table 1 . here to estimate mass we have taken radius of the star @xmath107 km by solving @xmath112 at @xmath113 graphically from fig .
this therefore represents a relativistic fermi gas for ultradense cores of neutron stars as noticed in the ref .
@xcite .
increases with the increase of the parameter @xmath58 ] in this prescription @xcite , by substituting the values @xmath115 and @xmath54 one can get the expression for the effective gravitational mass as @xmath116 $ ] . for this case
we provide here a data sheet by choosing different values for @xmath51 ( for case a , @xmath117 whereas for case b , @xmath118 ) in table 1 .
this corresponds to a relativistic fermi gas with core immersed in a constant density background @xcite .
in the investigations we have observed some interesting points which are as follows : \(1 ) note that though transverse pressure is negative , however , all energy conditions are satisfied .
this indicates that matter distribution of the star is real i.e. star is comprising of normal matter .
\(2 ) it is observed that the transverse sound velocity is negative ( due to negative transverse pressure ) so that we use numerical value .
as sound speeds lie between @xmath94 and @xmath95 , we should have @xmath119 @xcite .
on the other hand , bhmer and harko @xcite argued that for an anisotropic star in the presence of a cosmological constant the surface redshift must obey the general restriction @xmath120 , which is consistent with the bound @xmath121 as obtained by ivanov @xcite .
therefore , for an anisotropic star without cosmological constant the above value @xmath122 seems to be within an acceptable range ( fig .
\(4 ) the radius of the star depends on the parameter @xmath58 , as appears in eq .
( 23 ) , with an increasing mode ( fig . 13 ) .
\(5 ) it is well known that the anisotropic factor @xmath123 should vanish at the origin .
however , in the present model the energy density under consideration has an infinite central density . according to misner and zapolsky @xcite
one may use it as an asymptotic solution with a cut - off density below which the eq .
( 27 ) will not valid .
\(6 ) in the present model , the stability of the matter distributions comprising of the anisotropic star has been attained .
we have come to conclude this by analyzing the tov equation which describes the equilibrium condition for matter distribution subject to the gravitational force ( @xmath87 ) , hydrostatic force ( @xmath88 ) and another force ( @xmath89 ) due to anisotropic pressure ( fig . 8) .
\(7 ) for an overall view of the present study and also to have a physically viable model we put here the data which are available on some compact stars , e.g. @xmath2 and @xmath124 and @xmath125 ( see table 1 of the ref .
the compactness factor @xmath104 for these stars are @xmath126 , @xmath127 and @xmath128 respectively . in comparison to these data
we can conclude that our model represents a star with moderate compactness and also indicates that the star might be a compact star of strange / quark type rather than neutron star .
this is because , in general , superdense stars with mass - size ratio exceeding @xmath129 are expected to be composed of strange matter @xcite . now according to buchdahl @xcite
, the maximum allowable compactness for a fluid sphere is given by @xmath130 .
our compactness values for the chosen model ( see table 1 ) within this acceptable range and hence provides a stable stellar configuration .
fr and sr wish to thank the authorities of the inter - university centre for astronomy and astrophysics , pune , india for providing the visiting associateship under which a part of this work was carried out .[/INST] we have proposed a model for relativistic compact star with anisotropy and analytically obtained exact spherically symmetric solutions describing the interior of the dense star admitting non - static conformal symmetry .
several features of the solutions including drawbacks of the model have been explored and discussed . for this purpose
we have provided the energy conditions , tov - equations and other physical requirements and thus thoroughly investigated stability , mass - radius relation and surface redshift of the model . it is observed that most of the features are well matched with the compact stars , like quark / strange stars . , , , general relativity ; noncommutative geometry ; compact stars </s> |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Fairness in the Workplace Commission
Act''.
SEC. 2. FINDINGS.
The Congress finds the following:
(1) Workers are not achieving wage and benefit increases
commensurate with corporate profits and sustained economic
expansion. While the median wage for workers fell 8 percent in
real terms during the business cycle peaks from 1979 through
1996, after-tax corporate profit rates grew 66 percent.
(2) The wage gap between men and women has increased in the
last 4 years, reversing a 20 year trend in which that gap had
narrowed.
(3) Despite a significant degree of closing the education
gap between minority and white Americans, wage gaps between
these groups persist and for some minority groups have been
expanded.
(4) Over the period of 1979 through 1996, workers have
experienced a heightened sense of job insecurity due to
corporate downsizing, deregulation of key industries, new
technology, and foreign competition.
(5) The last decade has seen a growth in the use of part-
time and temporary workers.
(6) Insufficient research has been done to determine the
extent and the impact of the use of part-time workers and the
failure of wages, especially for female workers, to keep pace
with economic growth and corporate profits.
SEC. 3. ESTABLISHMENT.
(a) In General.--There is established the National Commission on
Fairness in the Workplace (hereafter in this Act referred to as the
``Commission'').
(b) Member Authority.--Any member or agent of the Commission may,
if authorized by the Commission, take any action which the Commission
is authorized to take by this Act.
(c) Chairperson, Vice Chairperson.--The Chairperson of the
Commission shall be designated by the President at the time of
appointment. The Vice Chairperson shall be elected by the members of
the Commission. The term of office of the Chairperson and the vice
Chairperson shall be the life of the Commission.
(d) Termination.--The Commission shall cease to exist upon the
expiration of 18 months after the date of the enactment of this Act.
SEC. 4. COMMISSION DUTY.
(a) In General.--The Commission shall examine--
(1) the growing corporate practice of providing wages and
benefit levels for part-time and temporary employees which are
lower than the wage and benefit levels provided to full-time
employees who perform essentially identical work;
(2) how the use of part-time and temporary employees has
affected wage and benefit levels, employee job insecurity, and
employee productivity;
(3) the reasons that workers' wages have not kept pace with
corporate profits and economic growth;
(4) the reasons for the widening median wage gap between
working men and working women; and
(5) the reasons for the consistent discrepancy in the
average wage of minority populations in comparison to the
average wage of white Americans.
At the conclusion of the examination, the Commission shall develop
policy options for the Congress to address the problems identified in
the examination.
(b) Scope.--The Commission shall conduct its examination with
respect to the States and Guam, the Commonwealth of Puerto Rico, the
Virgin Islands, American Samoa, and the Commonwealth of the Northern
Marianas Islands.
(c) Definition.--As used in section 2 and this section, the term
``minority populations'' means Blacks (not of Hispanic origin),
Hispanics, Asians, Pacific Islanders, American Indians, and Alaskan
natives.
SEC. 5. MEMBERSHIP.
(a) Appointment.--Within 60 days of the date of the enactment of
this Act, the Commission shall be composed of 14 members appointed as
follows:
(1) 6 members appointed by the President of which 2 shall
be from the executive branch and 4 representatives from either
labor, business management, or academia.
(2) 2 members appointed by the Majority Leader of the
Senate of which one shall be a member of the Senate and one
shall be from private life.
(3) 2 members appointed by the Minority Leader of the
Senate of which one shall be a member of the Senate and one
shall be from private life.
(4) 2 members appointed by the Speaker of the House of
Representatives of which one shall be a member of the House of
Representatives and one shall be from private life.
(5) 2 members appointed by the Minority Leader of the House
of Representatives of which one shall be a member of the House
of Representatives and one shall be from private life.
The Secretary of Labor shall be an ex-officio member of the Commission.
(b) Waiver of Limitation on Executive Schedule Positions.--
Appointments may be made under subsection (a) without regard to section
5311(b) of title 5, United States Code.
(c) Terms.--Each member shall be appointed for the life of the
Commission.
(d) Rates of pay.--
(1) In general.--Except as provided in paragraph (2),
members shall each be paid at a rate not to exceed the rate of
basic pay for GS-15 of the General Schedule for each day
(including travel time) during which they are engaged in the
actual performance of duties vested in the Commission.
(2) Prohibition of compensation of members and federal
employees.--Members of the Commission who are Members of the
Senate or the House of Representatives or full-time officers or
employees of the United States may not receive additional pay,
allowances, or benefits by reason of their service on the
Commission.
(3) Travel expenses.--Each member shall receive travel
expenses, including per diem in lieu of subsistence, in
accordance with sections 5702 and 5703 of title 5, United
States Code.
SEC. 6. GENERAL AUTHORITY OF THE COMMISSION.
(a) Hearings and Sessions.--The Commission may, for the purpose of
carrying out this Act, hold hearings, sit and act at times and places,
take testimony, and receive evidence as the Commission considers
appropriate. The Commission may administer oaths or affirmations to
witnesses appearing before it.
(b) Meetings.--The Commission shall meet monthly or at the call of
the chairperson or a majority of its members.
(c) Staff.--The Commission shall appoint a staff.
(d) Experts and Consultants.--Subject to rules prescribed by the
Commission, the Commission may procure temporary and intermittent
services under section 3109(b) of title 5, United States Code, but at
rates for individuals not to exceed the daily equivalent of the minimum
annual rate of basic pay payable for GS-15 of the General Schedule.
(e) Staff of Federal Agencies.--Upon request of the Commission, the
head of any Federal department or agency may detail, on a reimbursable
basis, any of the personnel of that department or agency to the
Commission to assist it in carrying out its duties under this Act.
(f) Obtaining Official Data.--The Commission may secure directly
from any department or agency of the United States information
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Commission, the head of that department or agency shall furnish that
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(g) Contract Authority.--The Commission may contract with and
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(h) Mails.--The Commission may use the United States mails in the
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(1) In general.--The Commission may issue subpoenas
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and the production of evidence may be required from any place
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(2) Failure to obey a subpoena.--If a person refuses to
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SEC. 7. REPORT.
The Commission shall report its findings and policy options
developed under section 4 to the Congress not later than 30 days after
the termination date of the Commission, together with its
recommendations for legislation and administrative actions the
Commission considers appropriate. | Fairness in the Workplace Commission Act - Establishes the National Commission on Fairness in the Workplace, which shall examine and report to the Congress on: (1) the growing corporate practice of providing wages and benefit levels for part-time and temporary employees which are lower than the wage and benefit levels provided to full-time employees who perform essentially identical work; (2) how the use of part-time and temporary employees has affected wage and benefit levels, employee job insecurity, and employee productivity; (3) the reasons that workers' wages have not kept pace with corporate profits and economic growth; (4) the reasons for the widening median wage gap between working men and working women; and (5) the reasons for the consistent discrepancy in the average wage of minority populations in comparison to the average wage of white Americans. Requires the Commission to develop policy options for the Congress to address the problems identified in the examination. | <s>[INST]SECTION 1. SHORT TITLE.
This Act may be cited as the ``Fairness in the Workplace Commission
Act''.
SEC. 2. FINDINGS.
The Congress finds the following:
(1) Workers are not achieving wage and benefit increases
commensurate with corporate profits and sustained economic
expansion. While the median wage for workers fell 8 percent in
real terms during the business cycle peaks from 1979 through
1996, after-tax corporate profit rates grew 66 percent.
(2) The wage gap between men and women has increased in the
last 4 years, reversing a 20 year trend in which that gap had
narrowed.
(3) Despite a significant degree of closing the education
gap between minority and white Americans, wage gaps between
these groups persist and for some minority groups have been
expanded.
(4) Over the period of 1979 through 1996, workers have
experienced a heightened sense of job insecurity due to
corporate downsizing, deregulation of key industries, new
technology, and foreign competition.
(5) The last decade has seen a growth in the use of part-
time and temporary workers.
(6) Insufficient research has been done to determine the
extent and the impact of the use of part-time workers and the
failure of wages, especially for female workers, to keep pace
with economic growth and corporate profits.
SEC. 3. ESTABLISHMENT.
(a) In General.--There is established the National Commission on
Fairness in the Workplace (hereafter in this Act referred to as the
``Commission'').
(b) Member Authority.--Any member or agent of the Commission may,
if authorized by the Commission, take any action which the Commission
is authorized to take by this Act.
(c) Chairperson, Vice Chairperson.--The Chairperson of the
Commission shall be designated by the President at the time of
appointment. The Vice Chairperson shall be elected by the members of
the Commission. The term of office of the Chairperson and the vice
Chairperson shall be the life of the Commission.
(d) Termination.--The Commission shall cease to exist upon the
expiration of 18 months after the date of the enactment of this Act.
SEC. 4. COMMISSION DUTY.
(a) In General.--The Commission shall examine--
(1) the growing corporate practice of providing wages and
benefit levels for part-time and temporary employees which are
lower than the wage and benefit levels provided to full-time
employees who perform essentially identical work;
(2) how the use of part-time and temporary employees has
affected wage and benefit levels, employee job insecurity, and
employee productivity;
(3) the reasons that workers' wages have not kept pace with
corporate profits and economic growth;
(4) the reasons for the widening median wage gap between
working men and working women; and
(5) the reasons for the consistent discrepancy in the
average wage of minority populations in comparison to the
average wage of white Americans.
At the conclusion of the examination, the Commission shall develop
policy options for the Congress to address the problems identified in
the examination.
(b) Scope.--The Commission shall conduct its examination with
respect to the States and Guam, the Commonwealth of Puerto Rico, the
Virgin Islands, American Samoa, and the Commonwealth of the Northern
Marianas Islands.
(c) Definition.--As used in section 2 and this section, the term
``minority populations'' means Blacks (not of Hispanic origin),
Hispanics, Asians, Pacific Islanders, American Indians, and Alaskan
natives.
SEC. 5. MEMBERSHIP.
(a) Appointment.--Within 60 days of the date of the enactment of
this Act, the Commission shall be composed of 14 members appointed as
follows:
(1) 6 members appointed by the President of which 2 shall
be from the executive branch and 4 representatives from either
labor, business management, or academia.
(2) 2 members appointed by the Majority Leader of the
Senate of which one shall be a member of the Senate and one
shall be from private life.
(3) 2 members appointed by the Minority Leader of the
Senate of which one shall be a member of the Senate and one
shall be from private life.
(4) 2 members appointed by the Speaker of the House of
Representatives of which one shall be a member of the House of
Representatives and one shall be from private life.
(5) 2 members appointed by the Minority Leader of the House
of Representatives of which one shall be a member of the House
of Representatives and one shall be from private life.
The Secretary of Labor shall be an ex-officio member of the Commission.
(b) Waiver of Limitation on Executive Schedule Positions.--
Appointments may be made under subsection (a) without regard to section
5311(b) of title 5, United States Code.
(c) Terms.--Each member shall be appointed for the life of the
Commission.
(d) Rates of pay.--
(1) In general.--Except as provided in paragraph (2),
members shall each be paid at a rate not to exceed the rate of
basic pay for GS-15 of the General Schedule for each day
(including travel time) during which they are engaged in the
actual performance of duties vested in the Commission.
(2) Prohibition of compensation of members and federal
employees.--Members of the Commission who are Members of the
Senate or the House of Representatives or full-time officers or
employees of the United States may not receive additional pay,
allowances, or benefits by reason of their service on the
Commission.
(3) Travel expenses.--Each member shall receive travel
expenses, including per diem in lieu of subsistence, in
accordance with sections 5702 and 5703 of title 5, United
States Code.
SEC. 6. GENERAL AUTHORITY OF THE COMMISSION.
(a) Hearings and Sessions.--The Commission may, for the purpose of
carrying out this Act, hold hearings, sit and act at times and places,
take testimony, and receive evidence as the Commission considers
appropriate. The Commission may administer oaths or affirmations to
witnesses appearing before it.
(b) Meetings.--The Commission shall meet monthly or at the call of
the chairperson or a majority of its members.
(c) Staff.--The Commission shall appoint a staff.
(d) Experts and Consultants.--Subject to rules prescribed by the
Commission, the Commission may procure temporary and intermittent
services under section 3109(b) of title 5, United States Code, but at
rates for individuals not to exceed the daily equivalent of the minimum
annual rate of basic pay payable for GS-15 of the General Schedule.
(e) Staff of Federal Agencies.--Upon request of the Commission, the
head of any Federal department or agency may detail, on a reimbursable
basis, any of the personnel of that department or agency to the
Commission to assist it in carrying out its duties under this Act.
(f) Obtaining Official Data.--The Commission may secure directly
from any department or agency of the United States information
necessary to enable it to carry out this Act. Upon request of the
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the dynamics and the storage and retrieval properties of multi - state attractor neural networks have been studied over some time now and numerous results are available ( see , e.g. , @xcite and references therein ) . the majority of the results obtained on the storage and retrieval properties concern sequential updating of the neurons .
recently , it has been realized that synchronous updating of the spins in disordered systems can lead to different physics @xcite-@xcite .
for example , for binary spins , it is known that the phase diagram of the sequential and synchronous little - hopfield neural network @xcite in the replica - symmetric approximation are different @xcite , whereas the phase diagrams of the sherrington - kirkpatrick model @xcite are the same @xcite .
for the three - state ising ferromagnet the same stationary solutions appear except for negative couplings , while for the blume - emery - griffiths ferromagnet the phase diagram for synchronous updating is much richer @xcite .
for the three - state ising neural network the possible different physics between sequential and synchronous updating has not yet been studied .
looking at the literature we see that using sequential updating the equilibrium properties of the @xmath0-ising model for the fully connected architecture have been studied in @xcite and @xcite making a replica symmetric ansatz .
the results for the extremely diluted architecture appeared in @xcite and have been extended later to the whole dilution range in @xcite .
the layered architecture with variable dilution has been examined recently @xcite .
nothing has been reported on the equilibrium properties for the recurrent architectures , however , when synchronous updating is used . on the other hand , concerning dynamics no calculations were done for the @xmath0-ising model with sequential updating . for synchronous updating the work of @xcite on the exactly solvable extremely diluted asymmetric little - hopfield model has been extended to the @xmath0-ising model in @xcite .
later on , the dynamics for the fully connected and the extremely diluted symmetric @xmath0-ising architecture have been solved in @xcite and , respectively , @xcite .
the latter studies make use of the so - called signal - to - noise analysis ( see , e.g. , @xcite for references on this method ) .
an extension to the whole dilution range , in analogy with @xcite has not yet been given .
the aim of this work is precisely to fill the gaps mentioned above with a report on the study of the @xmath1-ising network with synchronous updating and variable dilution and a detailed comparison of the results obtained with the ones for sequential updating .
first , the thermodynamic and retrieval properties are examined using replica symmetric mean - field theory .
capacity - temperature phase diagrams are derived for several values of the pattern activity and different gradations of dilution . apart from the appearance of cycles
the asymptotic behaviour is almost identical to the one for sequential updating .
the spin - glass region is visibly enhanced , while the retrieval region , however , is only marginally enhanced .
only the addition of self - couplings can enlarge the retrieval region substantially , especially in the case of strong dilution .
a calculaton of the information content shows that both for synchronous and sequential updating the three - state networks are robust against the interference of static noise coming from random dilution .
next , the dynamics of the model is studied using the generating function technique @xcite . as an illustration
some typical flow diagrams for the overlap order parameter are presented .
it is possible to extract the result for sequential updating from the one for synchronous updating . as in the hopfield model
@xcite one can argue that the signal - to - noise analysis used before in the literature is a short memory approximation correct up to the third time step . and
it can also be shown that the signal - to - noise analysis can be made exact .
the rest of the paper is organized as follows . in section 2
the three - state ising neural network with synchronous updating and variable dilution is introduced . section 3 reports on the replica symmetric mean field theory calculation of the free energy and the fixed - point equations for the relevant order parameters . in section 4
the phase diagrams and retrieval properties are discussed for arbitrary temperatures as a function of the gain parameter , the amount of dilution and the strength of the self - coupling .
section 5 discusses the dynamics for the model using the generating functional analysis and comments on the relation with the signal - to - noise analysis . in section 6
some concluding remarks are given .
finally , the appendix presents the explicit saddle - point equations .
consider a network of n neurons , @xmath2 , which can take values from the set @xmath3 . in this network
we want to store @xmath4 patterns , @xmath5 , @xmath6 and @xmath7 .
they are supposed to be independent identically distributed random variables ( i.i.d.r.v . ) with respect to @xmath8 and @xmath9 , drawn from a probability distribution given by @xmath10 with @xmath11 the pattern activity defined by the expectation value @xmath12 the neurons are updated synchronously according to the transition probability @xmath13= \prod_{i=1}^n\mbox{pr}\left(\sigma_i(t+1)=s\in \mathcal{s}|{\mbox{\boldmath $ \sigma'$}}(t ) \right ) \\
\label{three } & & \mbox{pr}\left(\sigma_i(t+1)=s\in\mathcal{s}|{\mbox{\boldmath $ \sigma'$}}(t ) \right)= \frac{\exp[-\beta \epsilon_i(s|{\mbox{\boldmath $ \sigma'$}}(t ) ) ] } { \displaystyle{\sum_{s \in\mathcal{s } } \exp[-\beta \epsilon_i(s|{\mbox{\boldmath $ \sigma'$}}(t ) ) ] } } \end{aligned}\ ] ] with @xmath14 the inverse temperature and @xmath15 an effective single site energy function given by @xcite @xmath16 \ , , \label{eq : energy}\ ] ] where @xmath17 is the gain parameter of the system suppressing or enhancing the zero state of the neurons .
the random local fields are defined by @xmath18 the couplings @xmath19 are taken to be of the form @xmath20 where the probability distribution of the @xmath21 is given by @xmath22 hence , they allow for a diluted architecture .
the @xmath23 are determined via the hebb rule @xmath24 in order for the model to satisfy detailed balance ( see , e.g . , @xcite )
, the dilution has to be symmetric ( @xmath25 ) . in the case of extreme dilution ,
when @xmath26 , the average number of connections per neuron , @xmath27 , is still infinite @xmath28 finally , we recall that the detailed balance property for synchronous updating is not destroyed by the presence of self - couplings , i.e. , couplings of the form @xmath29 . hence , we do allow for this type of couplings and redefine @xmath30 , with @xmath31 a parameter and @xmath32 the capacity .
the long - time behaviour is governed by the hamiltonian @xcite @xmath33)}\right ] } + b\sum_{i=1}^n\sigma_i^2 \ , .
\label{parqham}\ ] ] in addition , when evaluating traces over spins in the calculation of , e.g. , the partition function , one realizes that the system is equivalent to one with a hamiltonian involving a set of duplicate ising spins ( see , e.g. , @xcite ) , which can be written as @xmath34\ ] ] such that @xmath35= \underset{{\mbox{\boldmath $ \sigma$}}}{{\mbox{tr}}}\underset{{\mbox{\boldmath $ \tau$}}}{{\mbox{tr}}}\exp [ -\beta h({\mbox{\boldmath $ \sigma$ } } , { \mbox{\boldmath $ \tau$ } } ) ] $ ] .
it is well - known that the equilibrium behaviour can be fixed - points and/or cycles of period 2 , i.e. , @xmath36 . in the next section we study the thermodynamic and retrieval properties of this model starting from the free energy .
in order to calculate the free energy we use the replica method as applied to dilute systems @xcite,@xcite,@xcite-@xcite .
since this method is really standard by now , at least for sequential updating , we refrain from giving any detailed calculations but concentrate on the main results and the differences between sequential and synchronous updating . indeed , some complications arise due to the symmetry between the two types of spins in the hamiltonian . starting from the replicated partition function , performing the dilution average and the average over the condensed ( @xmath37 ) and non - condensed ( @xmath38 ) patterns we obtain for the replicated free energy density @xmath39 with @xmath40 the symbol
@xmath41 denotes the unit matrix in replica space and @xmath42 hereby the usual order parameters are introduced as replica matrices ( @xmath43 is the replica index ) with elements @xmath44 their conjugate variables are denoted with a hat .
the free energy should be interpreted as being extremised with respect to @xmath45 , @xmath46 , @xmath47 , @xmath48 and @xmath49 .
we remark that the corresponding result for sequential dynamics ( see , e.g. , @xcite ) is recovered by assuming @xmath50 and rescaling the temperature with a factor 2 .
furthermore , we notice that compared with sequential updating , the replicated free energy ( [ eq : qisingp : fe_n ] ) is more involved .
it is clear that a priori the matrices appearing in this expression are not necessarily symmetric .
as mentioned in the introduction it is known that synchronous updating can lead to two - cycles as stationary solutions .
results for the hopfield model @xcite and the blume - emery - griffiths model @xcite show that such cycles do not appear in the retrieval region of the corresponding phase diagrams .
therefore , cycles have been neglected in the replica calculation of the retrieval properties of these models . in analogy , for the three - state ising model discussed here we make a similar ansatz .
we neglect cycles in the sequel of the replica calculation and we assume that the two sets of spins behave in a completely symmetric way . consequently , @xmath51 , @xmath52 , and similarly for the conjugate variables .
the same symmetry applies to @xmath45 and @xmath53 .
the free energy then becomes @xmath54 with @xmath55 next , we take the replica symmetry ( rs ) ansatz @xmath56 and similarly for the conjugated variables . due to the non - cycle ansatz , we have in addition @xmath57 such that the rs free energy reads @xmath58 - \alpha c \frac{q}{1-\chi_r - \chi } \nonumber \\ & & \hspace{1 cm } - ( 1-c)\frac{\alpha \beta } { 2 } { \ensuremath{\left ( q_0 ^ 2 - 2 q^2 + r^2 \right ) } } + { \alpha \beta } { \ensuremath{\left ( \hat q_0 q_0 - 2 \hat{q_1 } q_1 + \hat{r } r \right ) } } \nonumber \\ & & \hspace{1 cm } + \alpha ( c - j_0 ) r - \frac{1}{\beta } { \ensuremath{\left\langle \int { { \mathcal d } z } \log \underset{{\sigma \tau}}{\mbox{tr}}\exp{\ensuremath{\left ( -\beta \tilde h(\sigma,\tau|z ) \right ) } } \right\rangle}}_\xi \ , \label{eq : qising : fe - par}\end{aligned}\ ] ] with the effective hamiltonian @xmath59 and @xmath60 the gaussian measure @xmath61 .
we have also defined the susceptibilities @xmath62 and their conjugate expressions @xmath63 the phase structure of the network is then determined by the solution of the following set of saddle - point equations @xmath64 where the average @xmath65 is defined with respect to the effective hamiltonian ( [ eq : qising : ham - par ] ) and @xmath66 \ , \label{saddlecon0 } \\ & & \hat \chi = ( 1-c ) \chi + c \frac{\chi}{(1-\chi_r)^2 - \chi^2 } \ , \label{saddlecon1 } \\ & & \hat \chi_r = ( 1-c ) \chi_r + c
\frac{1-\chi_r}{(1-\chi_r)^2 - \chi^2 } + ( j - c ) \ . \label{saddlecon}\end{aligned}\ ] ] compared with sequential updating @xcite we notice the extra equations for @xmath67 and @xmath68 expressing that @xmath69 and @xmath70 can be affected differently by thermal fluctuations and the fact that the equations for the conjugate parameters are different . in the appendix we present the explicit forms for ( [ eq : pising : sp : rs : mr])-([eq : pising : sp : rs : q01 ] ) .
first , we look at the special case of low loading ( @xmath71 ) . in that case
the effective hamiltonian ( [ eq : qising : ham - par ] ) simplifies to @xmath72 which practically means that the two spin variables occurring in the expression for the free energy ( [ eq : qising : fe - par ] ) become independent yielding @xmath73 as found before for other models @xcite .
consequently , the saddle point equations are the same for synchronous and sequential updating and both yield the same stationary states .
an explicit calculation shows that the low loading results correspond to those of the @xmath74-ising ferromagnet . for the relevant phase diagram
we refer to @xcite ( fig . 2 for @xmath75 ) .
next , we turn to finite loading and solve the saddle point equations ( [ eq : pising : sp : rs : mr])-([saddlecon ] ) numerically for arbitrary temperature @xmath76 .
we present the phase diagrams for some representative values of the parameters @xmath77 , @xmath17 and @xmath78 .
we focuss on uniformly distributed patterns ( @xmath79 ) .
results for sequential updating of the network are included for comparison .
phase diagram for the 3-ising network with @xmath80 , @xmath79 , @xmath81 ( a ) and @xmath82 ( b ) .
solid ( dotted ) lines present synchronous updating for @xmath83 ( @xmath84 ) .
dashed lines are for sequential updating .
the retrieval state is stable below the thick lines .
the spin glass state is stable at the left of the thin lines.,title="fig:",width=245,height=170 ] phase diagram for the 3-ising network with @xmath80 , @xmath79 , @xmath81 ( a ) and @xmath82 ( b ) .
solid ( dotted ) lines present synchronous updating for @xmath83 ( @xmath84 ) .
dashed lines are for sequential updating .
the retrieval state is stable below the thick lines .
the spin glass state is stable at the left of the thin lines.,title="fig:",width=245,height=170 ] in figure 1 we present the rs @xmath85 phase diagrams with ( @xmath86 ) and without ( @xmath83 ) self - coupling for the fully connectivity architecture ( @xmath80 ) and gain parameter @xmath81 and @xmath82 .
the retrieval transition is discontinuous in all cases . for a fixed @xmath76 ,
the retrieval capacity of the synchronously updated network with self - coupling is slightly larger than the one for the network without self - coupling , and both are slightly larger than the one for the sequentially updated network .
however , the enhancement stays marginal , also for growing self - coupling .
the spin glass transition is always continuous . for @xmath82 ,
contrary to @xmath81 , the spin glass phase is not stable at small @xmath87 . but the retrieval phase is stable .
this means that for @xmath82 , small @xmath87 and low @xmath76 the retrieval phase co - exists only with the paramagnetic phase , and not with the spin glass phase .
.,title="fig:",width=245,height=170 ] .,title="fig:",width=245,height=170 ] in figure 2 we show the rs phase diagrams for the symmetrically diluted networks with @xmath88 .
the other network parameters are kept identical to those in figure 1 .
the retrieval ( spin - glass ) transitions remain discontinuous ( continuous ) .
the enhancement of the retrieval capacity is again marginal for the network with synchronous updating and without self - coupling , compared to the one for sequential updating .
however , increasing the self - coupling shows a substantial improvement , except for @xmath71 . also the spin - glass region is visibly enlarged in that case .
the remark concerning the stability of the spin - glass phase for @xmath82 and low @xmath76 also applies to the diluted network , but with a small change : one remarks ( see the bottom left corner of figure 2 ( b ) ) that the spin - glass phase becomes stable at small @xmath87 and low @xmath76 , although there remains a region where only the retrieval and paramagnetic phases are stable .
finally , we notice a strong re - entrant behaviour in the retrieval region .
this is related to the replica - symmetric approximation and is also seen in the hopfield model @xcite .
consequently , we conjecture that the fact that for @xmath82 , e.g. , the maximal critical capacity for the network with self - coupling is larger compared to the one for the network without self - coupling , is an effect of this approximation . . the curves for the sequentially and synchronously updated network without self coupling coincide.,title="fig:",width=245,height=170 ] .
the curves for the sequentially and synchronously updated network without self coupling coincide.,title="fig:",width=245,height=170 ] the rs phase diagrams for the extremely diluted symmetric ( @xmath26 ) network are shown in figure 3 .
the other parameters are kept identical to those in figures 1 and 2 .
the results for sequential and synchronous updating without self - coupling coincide .
all transitions are continuous .
again , we notice a strong re - entrance behaviour in the retrieval region , in agreement with earlier results for this extremely diluted limit @xcite . increasing the self - coupling
makes the synchronously updated network more robust against temperature , although , as expected , it has no effect on the critical temperature at zero @xmath87 .
the re - entrance point is reached for the same value of @xmath87 . as a function of the loading capacity @xmath87 for the @xmath74-ising model with synchronous updating at @xmath89 with uniform patterns ( @xmath79 ) , two values of @xmath17 , with and without self - coupling and @xmath90 ( a ) and @xmath91 ( b).,title="fig:",width=226,height=170 ] as a function of the loading capacity @xmath87 for the @xmath74-ising model with synchronous updating at @xmath89 with uniform patterns ( @xmath79 ) , two values of @xmath17 , with and without self - coupling and @xmath90 ( a ) and @xmath91 ( b).,title="fig:",width=226,height=170 ] as a function of the loading capacity @xmath87 for the @xmath74-ising model with sequential updating , uniform patterns , @xmath82 , @xmath89 , and @xmath88 , @xmath92 and @xmath93 . ] finally
, we briefly study the robustness of these three - state networks against the interference of static noise coming from random dilution . in fig .
4 we show the information content of the model , being the product of the loading capacity and the mutual information @xcite , for synchronous updating and several amounts of dilution @xmath77 with and without self - coupling .
we see that for the fully connected network ( @xmath90 , left figure ) , the results for @xmath83 and @xmath86 do practically coincide , in agreement with fig . 1
. we remark that for b=0.2 , two solutions co - exist at small @xmath87 ( @xmath94 ) .
one of them corresponds to perfect retrieval , with @xmath95 , @xmath96 .
the corresponding information content is very close to that for @xmath82 . for the diluted network ( @xmath88 , right figure ) , in agreement with fig . 2
, self - coupling mostly leads to a higher information content for the optimal gain parameter @xmath82 .
( again , for @xmath81 there exist two solutions for small @xmath87 but the difference is very small and can hardly be seen on the scale of the figure . ) next , by comparing with fig . 5 for sequential updating ,
one notices that the results for sequential and synchronous updating ( without self - coupling ) are almost coincident . in all cases ,
we find that the quality of the retrieval properties is affected very little , unless the amount of dilution is high .
as mentioned in the introduction most studies in the literature on the dynamics of the @xmath0-ising model are based upon the signal - to - noise analysis . except for the extremely diluted asymmetric and layered architectures , which can be solved
exactly in closed form , the dynamics for the other architectures , only examined for synchronous updating , is obtained in the form of a recursive scheme .
recently , by a comparison with the generating functional analysis ( gfa ) , it has been found @xcite for the hopfield model that the application of this method in the study of the dynamics involves a short - memory approximation implying that the results are only exact up to the third time step , although they stay very accurate in the retrieval region for further time steps , but not so in the spin - glass region .
it has also been shown that the signal - to - noise analysis can be made exact , leading to the same results as the generating functional analysis . therefore , it is interesting to reconsider the dynamics for the @xmath1-state ising model using this generating functional technique , which was introduced in @xcite to the field of statistical mechanics and , by now , is part of many textbooks .
we closely follow the derivation in @xcite , extend it to variable dilution and indicate the differences for the model at hand . both sequential and synchronous updating
are discussed .
in fact , the discussion is made for general @xmath0 . since the method
itself has become rather standard , we restrict ourselves to a presentation of the main arguments .
the idea of the gfa approach to study dynamics @xcite is to look at the probability to find a certain microscopic path in time .
the basic tool to study the statistics of these paths is the generating functional @xmath97 = \sum_{{\mbox{\boldmath $ \sigma$}}(0 ) , \dots , { { \mbox{\boldmath $ \sigma$}}}(t ) } p[{{\mbox{\boldmath $ \sigma$}}}(0 ) , \dots , { { \mbox{\boldmath $ \sigma$}}}(t ) ] \ , \prod_{i=1}^n \prod_{t'=0}^t e^{-i \ , \psi_i(t ' ) \ , \sigma_i(t ' ) } \label{functional}\ ] ] with @xmath98 $ ] the probability to have a certain path in phase space @xmath99 = p[{{\mbox{\boldmath $ \sigma$}}(0 ) } ] \prod_{t'=0}^{t-1 } w[{{\mbox{\boldmath $ \sigma$}}}(t'+1)|{{\mbox{\boldmath $ \sigma$}}}(t')]\ ] ] and @xmath100 $ ] the transition probabilities from @xmath101 to @xmath102 .
synchronous updating is expressed by ( recall eq .
( [ three ] ) ) . @xmath103=
\prod_{i=1}^n\frac{\exp{\left(\beta\sigma_i(t'+1 ) \epsilon_i(\sigma_i(t'+1)|{\mbox{\boldmath $ \sigma$}}(t'))\right ) } } { \underset{\sigma}{\textrm{tr } } \exp{\left(\beta\sigma \epsilon_i(\sigma|{\mbox{\boldmath $ \sigma$}}(t ' ) ) \right)}}\ ] ] where @xmath104 now includes a time - dependent external field @xmath105 in order to define a response function @xmath106 + \theta_i(t')\,.\ ] ] one can find all the relevant order parameters , i.e. , the overlap @xmath107 , the correlation function @xmath108 and the response function @xmath109 , by calculating appropriate derivatives of the above functional ( [ functional ] ) and letting @xmath110 tend to zero afterwards @xmath111}{\delta\psi_i(t ) } \ , , \label{factora } \\
g(t , t ' ) & = & i \lim_{{\mbox{\boldmath $ { \psi}$}}\to0 } \frac{1}{n } \sum_{i } \frac{\delta^2 z[{\mbox{\boldmath $ { \psi}$}}]}{\delta\psi_i(t ) \delta\theta_i(t ' ) } \ , , \\ c(t , t ' ) & = & - \lim_{{\mbox{\boldmath $ { \psi}$}}\to0 } \frac{1}{n } \sum_{i } \frac{\delta^2 z[{\mbox{\boldmath $ { \psi}$}}]}{\delta\psi_i(t ) \delta\psi_i(t')}\,.\end{aligned}\ ] ] a difference with the little - hopfield model @xcite is the presence of the factor @xmath112 in ( [ factora ] ) .
first , due to the proper scaling of the couplings with this factor ( recall eq .
( [ couphebb ] ) ) the average over the non - condensed patterns does not introduce an extra factor .
secondly , in the saddle point , terms containing this extra factor vanish . as a consequence
, the factor @xmath112 does not appear explicitly in the expressions at all .
the only point to keep in mind is the occurrence of the term proportional to the factor @xmath17 in the dynamics ( recall eq .
( [ eq : energy ] ) ) .
another difference with respect to the treatment in @xcite is that one needs to average over the dilution .
this is done before averaging over the non - condensed patterns by using the fact that the diluted couplings @xmath113 are of order @xmath114 and that the @xmath115 .
noting that the distribution for the dilution eq .
( [ propdil ] ) is i.i.d.r.v . for @xmath116 and expanding the exponential containing the @xmath113 up to order @xmath117 makes this average then straightforward
. in the thermodynamic limit one expects the physics of the problem to be independent of the quenched disorder and , therefore , one is interested in derivatives of @xmath118}$ ] , whereby the overline denotes the average over this disorder , i.e. , over all pattern realizations .
this results in an effective single spin local field given by @xmath119 with @xmath120 temporally correlated noise with zero mean and correlation matrix @xmath121 and the retarded self - interactions @xmath122 the order parameters defined above can be written as @xmath123 the average over the effective path measure @xmath124 is given by @xmath125 where @xmath126 and with @xmath127 where @xmath128 . the average denoted by the double brackets in ( [ eq : ordergfa ] ) is over the condensed pattern and initial conditions .
the set of eqs .
( [ eq : h])-([selfmatrix ] ) and ( [ eq : noise : dist])-([eq : eta ] ) represent an exact dynamical scheme for the evolution of the network from which all relevant order parameters can be obtained at all time steps .
the order parameters are given by ( [ orderm])-([eq : ordergfa ] ) .
to acquire a more intuitive expression for the response function we note that also @xmath129 we remark that @xmath130 for @xmath131 and @xmath132 and that for all @xmath133 @xmath134 \right\rangle}}_\star \right\rangle\!\right\rangle\ ] ] where @xmath135 appearing in @xmath136 is given by ( [ eq : h ] ) . for sequential updating
we have to start from the stochastic process @xmath137\,p_s({\mbox{\boldmath $ \sigma$}}')\ ] ] with @xmath138 the probability to be in a state @xmath102 at time @xmath139 and @xmath140 $ ] given by @xmath141= \frac{1}{n}\sum_i\left\ { w_i({\mbox{\boldmath $ \sigma$}})\delta_{{\mbox{\boldmath $ \sigma$}},{\mbox{\boldmath $ \sigma$ } } ' } + w_i(f_i{\mbox{\boldmath $ \sigma$}})\delta_{{\mbox{\boldmath $ \sigma$}},g_i{\mbox{\boldmath $ \sigma$}}'}+ w_i(g_i{\mbox{\boldmath $ \sigma$}})\delta_{{\mbox{\boldmath $ \sigma$}},f_i{\mbox{\boldmath $ \sigma$}}'}\right\ } \,,\ ] ] with the shorthand @xmath142 and where @xmath143 and @xmath144 are cyclic spin - flip operators between the spin states .
each time step a randomly chosen spin is updated . in the thermodynamic limit the dynamics becomes continuous because the characteristic time scale is @xmath145 .
the standard procedure is then to update a random spin according to ( [ three ] ) and ( [ eq : energy ] ) with time intervals @xmath146 that are poisson distributed with mean @xmath145
. we can then write a continuous master equation in the thermodynamic limit @xmath147 in that case the effective path average reads @xmath148 _ { { \mbox{\boldmath $ \eta$}}}\ , \ ] ] where @xmath149 _ { { \mbox{\boldmath $ \eta$}}}$ ] is an average over the ( effective ) stochastic process conditioned to the noise @xmath150 generated by the dynamics ( [ conp ] ) and the distribution @xmath151 is gaussian with correlation matrix @xmath152 @xmath153 this result is very similar to the one for synchronous dynamics ( recall eq .
[ eq : eta ] ) .
the main reason is that one does not need the explicit form of the transition rates of the markovian process in order to derive the effective path average .
if only the initial conditions factorize over the site index @xmath8 then all sites become independent in the thermodynamic limit . in general , this is a characteristic feature of mean - field systems . specialising this discussion to three ising states
@xmath154 we have that for synchronous updating the trace in eq .
( [ eq : s|eta ] ) is given by @xmath155 for sequential updating the spin - flip operators in eq .
( [ put2 ] ) are defined by @xmath156 we have solved the dynamics numerically using the eissfeller - opper method @xcite .
the idea thereby is to replicate the system into @xmath157 copies of the effective spin and let each of them evolve independently in time according to their own stochastic path with its own noise variable .
averages over the effective path measure ( recall eqs .
( [ eq : noise : dist ] ) and ( [ eq : noise : distseq ] ) ) are replaced by averages over the ensemble of copies for large @xmath157 .
we have taken @xmath158 .
as a function of time using the eissfeller - opper algorithm with @xmath159 samples for the fully connected ( @xmath80 , top ) and diluted ( @xmath88 , bottom ) @xmath74-ising model with synchronous updating and uniform patterns ( @xmath79 ) for @xmath160 and @xmath83 .
the other model parameters are @xmath161 ( top left ) , @xmath162 ( top right ) , @xmath163 ( bottom left ) and @xmath164 ( bottom right ) . ,
title="fig:",width=226,height=170 ] as a function of time using the eissfeller - opper algorithm with @xmath159 samples for the fully connected ( @xmath80 , top ) and diluted ( @xmath88 , bottom ) @xmath74-ising model with synchronous updating and uniform patterns ( @xmath79 ) for @xmath160 and @xmath83 .
the other model parameters are @xmath161 ( top left ) , @xmath162 ( top right ) , @xmath163 ( bottom left ) and @xmath164 ( bottom right ) . , title="fig:",width=226,height=170 ]
+ as a function of time using the eissfeller - opper algorithm with @xmath159 samples for the fully connected ( @xmath80 , top ) and diluted ( @xmath88 , bottom ) @xmath74-ising model with synchronous updating and uniform patterns ( @xmath79 ) for @xmath160 and @xmath83 .
the other model parameters are @xmath161 ( top left ) , @xmath162 ( top right ) , @xmath163 ( bottom left ) and @xmath164 ( bottom right ) . ,
title="fig:",width=226,height=170 ] as a function of time using the eissfeller - opper algorithm with @xmath159 samples for the fully connected ( @xmath80 , top ) and diluted ( @xmath88 , bottom ) @xmath74-ising model with synchronous updating and uniform patterns ( @xmath79 ) for @xmath160 and @xmath83 .
the other model parameters are @xmath161 ( top left ) , @xmath162 ( top right ) , @xmath163 ( bottom left ) and @xmath164 ( bottom right ) .
, title="fig:",width=226,height=170 ] as an illustration we show some typical flow diagrams for the overlap order parameter in figure 6 for some fully connected ( @xmath80 , top figures ) and diluted ( @xmath88 , bottom figures ) models .
the model parameters are @xmath160 and @xmath161 ( top left ) , @xmath162 ( top right ) , @xmath163 ( bottom left ) and @xmath164 ( bottom right ) .
self - couplings are set to zero .
several remarks are in order .
all situations shown are in the retrieval phase of the corresponding phase diagrams figures 1 and 2 .
they all converge to the corresponding rs equilibrium results provided the initial overlap order parameter is large enough .
this gives us also an idea of the basins of attraction .
these basins are bigger for @xmath81 since the relevant model parameters are chosen deeper in the retrieval region , i.e. , closer to the line of thermodynamic stability .
for completeness we end this section on the discussion of the dynamics employing the gfa approach with a couple of remarks . first , this technique can also be applied to asymmetric dilution ( @xmath165 ) and we then get for the correlation matrix and retarded self - interactions @xmath166 with the asymmetry factor @xmath167 given by @xmath168 secondly , one can compare the gfa technique with the signal - to - noise analysis for the three - state ising network @xcite .
this comparison is formally completely analogous to the one for the hopfield model discussed in detail in @xcite .
the only point at which one has to be careful is in deriving the recursion relations for the coloured noise @xmath169 .
the diagonal of @xmath170 , namely , is no longer equal to 1 but depends on time .
taking this into account one can take the results for the hopfield model and extend it to @xmath171-ising models .
the outcome is that , even for general @xmath0 , the signal - to - noise analysis is a short memory approximation to the real effective dynamics giving results correct up to the third time step . like for the other models ,
this approximation is extremely good in the retrieval region but fails in the spin glass region .
it is then a rather straightforward exercise to extend the revisited signal - to - noise analysis , proposed in @xcite to the @xmath0-ising case . since the final results are completely equivalent to those of the gfa eqs .
( [ eq : h])-([selfmatrix ] ) , we refrain from repeating further explicit details and refer to the work mentioned above ( @xcite ) .
we have studied the statics and dynamics of the three - state ising neural network model with synchronous updating of the neurons and variable dilution .
we have followed as closely as possible the discussion for the hopfield model adapting the methods to the multi - state nature of the neurons .
although the equations that describe both statics and dynamics are formally rather similar to those of the hopfield model , we have seen that the physics behind it is quite different .
we have examined the thermodynamic and retrieval properties for this model using replica symmetric mean - field theory and have made a detailed comparison of the results with those for sequential updating .
capacity - temperature phase diagrams are derived for several values of the pattern activity and different gradations of dilution .
apart from the appearance of cycles the asymptotic behaviour is almost identical to the one for sequential updating .
the spin - glass region is visibly enhanced , while the retrieval region , however , is only marginally enhanced .
only the addition of self - couplings can enlarge the retrieval region substantially , especially in the case of strong dilution .
a calculation of the information content shows that both for synchronous and sequential updating the three - state networks are robust against the interference of static noise coming from random dilution .
concerning the dynamics , we have extended the generating functional analysis to the study of @xmath0-state spins . as an illustration
some typical flow diagrams for the overlap order parameter are presented in the case @xmath1 .
it is possible to extract the result for sequential updating from the one for synchronous updating .
a comparison with the signal - to - noise approach is made .
as for the hopfield model one can argue that the signal - to - noise analysis used before in the literature is a short memory approximation correct up to the third time step .
it can also be shown that this signal - to - noise analysis can be made exact .
the authors would like to thank jordi busquets blanco , gyoung moo shim and walter k. theumann for useful discussions .
r. e. thanks the kind hospitality and the support of the instituut voor theoretische fysica , kuleuven .
this work has been supported in part by the fund of scientific research , flanders - belgium .
we write down explicitly the saddle - point equations discussed in section 3 .
therefore we need the averages @xmath172 , @xmath173 and @xmath174 with respect to the effective hamiltonian ( [ eq : qising : ham - par ] ) @xmath175 } + \sinh(\beta m)\,{\rm e}^{\beta\left[-b+\frac{\alpha}{2}\hat{\chi}\right ] } \right\}\ , , \label{eq19}\ ] ] @xmath176 } - { \rm e}^{\beta\left[2\left(-b+\frac{\alpha}{2}\hat{\chi}\right ) -\alpha\hat{\chi}_r\right ] } \right\}\ , , \label{eq20}\ ] ] @xmath177 } \right .
\nonumber \\ & + & \left . \cosh(\beta
m)\,{\rm e}^{\beta\left[-b+\frac{\alpha}{2}\hat{\chi}\right ] } + { \rm e}^{\beta\left[2\left(-b+\frac{\alpha}{2}\hat{\chi}\right ) -\alpha\hat{\chi}_r\right ] } \right\}\ , , \label{eq21}\end{aligned}\ ] ] with @xmath178 using the symmetry properties of these functions , we average over @xmath179 to obtain the saddle - point equations for the retrieval state of one pattern at finite temperature .
we get @xmath180 @xmath181 @xmath182 @xmath183 ^ 2 ( m+\sqrt{\alpha\hat{q}_1}z ) + ( 1-a)\int\mathcal{d}z\left[\left\langle\sigma\right\rangle_z\right]^2 ( \sqrt{\alpha\hat{q}_1}z)\ , , \label{eq31}\ ] ] that need to be solved together with the algebraic equations ( [ saddlecon0])-([saddlecon ] ) .
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* 68 * ( 1992 ) 2094 . | the three - state ising neural network with synchronous updating and variable dilution is discussed starting from the appropriate hamiltonians .
the thermodynamic and retrieval properties are examined using replica mean - field theory .
capacity - temperature phase diagrams are derived for several values of the pattern activity and different gradations of dilution , and the information content is calculated .
the results are compared with those for sequential updating .
the effect of self - coupling is established .
also the dynamics is studied using the generating function technique for both synchronous and sequential updating .
typical flow diagrams for the overlap order parameter are presented .
the differences with the signal - to - noise approach are outlined . _ pacs _ : 05.20-y , 64.60.cn , 75.10.hk , 87.10+e + _ key words : _ multistate diluted networks ; synchronous updating ; sequential updating ; statics ; dynamics ; phase diagrams . , and , | <s>[INST]the dynamics and the storage and retrieval properties of multi - state attractor neural networks have been studied over some time now and numerous results are available ( see , e.g. , @xcite and references therein ) . the majority of the results obtained on the storage and retrieval properties concern sequential updating of the neurons .
recently , it has been realized that synchronous updating of the spins in disordered systems can lead to different physics @xcite-@xcite .
for example , for binary spins , it is known that the phase diagram of the sequential and synchronous little - hopfield neural network @xcite in the replica - symmetric approximation are different @xcite , whereas the phase diagrams of the sherrington - kirkpatrick model @xcite are the same @xcite .
for the three - state ising ferromagnet the same stationary solutions appear except for negative couplings , while for the blume - emery - griffiths ferromagnet the phase diagram for synchronous updating is much richer @xcite .
for the three - state ising neural network the possible different physics between sequential and synchronous updating has not yet been studied .
looking at the literature we see that using sequential updating the equilibrium properties of the @xmath0-ising model for the fully connected architecture have been studied in @xcite and @xcite making a replica symmetric ansatz .
the results for the extremely diluted architecture appeared in @xcite and have been extended later to the whole dilution range in @xcite .
the layered architecture with variable dilution has been examined recently @xcite .
nothing has been reported on the equilibrium properties for the recurrent architectures , however , when synchronous updating is used . on the other hand , concerning dynamics no calculations were done for the @xmath0-ising model with sequential updating . for synchronous updating the work of @xcite on the exactly solvable extremely diluted asymmetric little - hopfield model has been extended to the @xmath0-ising model in @xcite .
later on , the dynamics for the fully connected and the extremely diluted symmetric @xmath0-ising architecture have been solved in @xcite and , respectively , @xcite .
the latter studies make use of the so - called signal - to - noise analysis ( see , e.g. , @xcite for references on this method ) .
an extension to the whole dilution range , in analogy with @xcite has not yet been given .
the aim of this work is precisely to fill the gaps mentioned above with a report on the study of the @xmath1-ising network with synchronous updating and variable dilution and a detailed comparison of the results obtained with the ones for sequential updating .
first , the thermodynamic and retrieval properties are examined using replica symmetric mean - field theory .
capacity - temperature phase diagrams are derived for several values of the pattern activity and different gradations of dilution . apart from the appearance of cycles
the asymptotic behaviour is almost identical to the one for sequential updating .
the spin - glass region is visibly enhanced , while the retrieval region , however , is only marginally enhanced .
only the addition of self - couplings can enlarge the retrieval region substantially , especially in the case of strong dilution .
a calculaton of the information content shows that both for synchronous and sequential updating the three - state networks are robust against the interference of static noise coming from random dilution .
next , the dynamics of the model is studied using the generating function technique @xcite . as an illustration
some typical flow diagrams for the overlap order parameter are presented .
it is possible to extract the result for sequential updating from the one for synchronous updating . as in the hopfield model
@xcite one can argue that the signal - to - noise analysis used before in the literature is a short memory approximation correct up to the third time step . and
it can also be shown that the signal - to - noise analysis can be made exact .
the rest of the paper is organized as follows . in section 2
the three - state ising neural network with synchronous updating and variable dilution is introduced . section 3 reports on the replica symmetric mean field theory calculation of the free energy and the fixed - point equations for the relevant order parameters . in section 4
the phase diagrams and retrieval properties are discussed for arbitrary temperatures as a function of the gain parameter , the amount of dilution and the strength of the self - coupling .
section 5 discusses the dynamics for the model using the generating functional analysis and comments on the relation with the signal - to - noise analysis . in section 6
some concluding remarks are given .
finally , the appendix presents the explicit saddle - point equations .
consider a network of n neurons , @xmath2 , which can take values from the set @xmath3 . in this network
we want to store @xmath4 patterns , @xmath5 , @xmath6 and @xmath7 .
they are supposed to be independent identically distributed random variables ( i.i.d.r.v . ) with respect to @xmath8 and @xmath9 , drawn from a probability distribution given by @xmath10 with @xmath11 the pattern activity defined by the expectation value @xmath12 the neurons are updated synchronously according to the transition probability @xmath13= \prod_{i=1}^n\mbox{pr}\left(\sigma_i(t+1)=s\in \mathcal{s}|{\mbox{\boldmath $ \sigma'$}}(t ) \right ) \\
\label{three } & & \mbox{pr}\left(\sigma_i(t+1)=s\in\mathcal{s}|{\mbox{\boldmath $ \sigma'$}}(t ) \right)= \frac{\exp[-\beta \epsilon_i(s|{\mbox{\boldmath $ \sigma'$}}(t ) ) ] } { \displaystyle{\sum_{s \in\mathcal{s } } \exp[-\beta \epsilon_i(s|{\mbox{\boldmath $ \sigma'$}}(t ) ) ] } } \end{aligned}\ ] ] with @xmath14 the inverse temperature and @xmath15 an effective single site energy function given by @xcite @xmath16 \ , , \label{eq : energy}\ ] ] where @xmath17 is the gain parameter of the system suppressing or enhancing the zero state of the neurons .
the random local fields are defined by @xmath18 the couplings @xmath19 are taken to be of the form @xmath20 where the probability distribution of the @xmath21 is given by @xmath22 hence , they allow for a diluted architecture .
the @xmath23 are determined via the hebb rule @xmath24 in order for the model to satisfy detailed balance ( see , e.g . , @xcite )
, the dilution has to be symmetric ( @xmath25 ) . in the case of extreme dilution ,
when @xmath26 , the average number of connections per neuron , @xmath27 , is still infinite @xmath28 finally , we recall that the detailed balance property for synchronous updating is not destroyed by the presence of self - couplings , i.e. , couplings of the form @xmath29 . hence , we do allow for this type of couplings and redefine @xmath30 , with @xmath31 a parameter and @xmath32 the capacity .
the long - time behaviour is governed by the hamiltonian @xcite @xmath33)}\right ] } + b\sum_{i=1}^n\sigma_i^2 \ , .
\label{parqham}\ ] ] in addition , when evaluating traces over spins in the calculation of , e.g. , the partition function , one realizes that the system is equivalent to one with a hamiltonian involving a set of duplicate ising spins ( see , e.g. , @xcite ) , which can be written as @xmath34\ ] ] such that @xmath35= \underset{{\mbox{\boldmath $ \sigma$}}}{{\mbox{tr}}}\underset{{\mbox{\boldmath $ \tau$}}}{{\mbox{tr}}}\exp [ -\beta h({\mbox{\boldmath $ \sigma$ } } , { \mbox{\boldmath $ \tau$ } } ) ] $ ] .
it is well - known that the equilibrium behaviour can be fixed - points and/or cycles of period 2 , i.e. , @xmath36 . in the next section we study the thermodynamic and retrieval properties of this model starting from the free energy .
in order to calculate the free energy we use the replica method as applied to dilute systems @xcite,@xcite,@xcite-@xcite .
since this method is really standard by now , at least for sequential updating , we refrain from giving any detailed calculations but concentrate on the main results and the differences between sequential and synchronous updating . indeed , some complications arise due to the symmetry between the two types of spins in the hamiltonian . starting from the replicated partition function , performing the dilution average and the average over the condensed ( @xmath37 ) and non - condensed ( @xmath38 ) patterns we obtain for the replicated free energy density @xmath39 with @xmath40 the symbol
@xmath41 denotes the unit matrix in replica space and @xmath42 hereby the usual order parameters are introduced as replica matrices ( @xmath43 is the replica index ) with elements @xmath44 their conjugate variables are denoted with a hat .
the free energy should be interpreted as being extremised with respect to @xmath45 , @xmath46 , @xmath47 , @xmath48 and @xmath49 .
we remark that the corresponding result for sequential dynamics ( see , e.g. , @xcite ) is recovered by assuming @xmath50 and rescaling the temperature with a factor 2 .
furthermore , we notice that compared with sequential updating , the replicated free energy ( [ eq : qisingp : fe_n ] ) is more involved .
it is clear that a priori the matrices appearing in this expression are not necessarily symmetric .
as mentioned in the introduction it is known that synchronous updating can lead to two - cycles as stationary solutions .
results for the hopfield model @xcite and the blume - emery - griffiths model @xcite show that such cycles do not appear in the retrieval region of the corresponding phase diagrams .
therefore , cycles have been neglected in the replica calculation of the retrieval properties of these models . in analogy , for the three - state ising model discussed here we make a similar ansatz .
we neglect cycles in the sequel of the replica calculation and we assume that the two sets of spins behave in a completely symmetric way . consequently , @xmath51 , @xmath52 , and similarly for the conjugate variables .
the same symmetry applies to @xmath45 and @xmath53 .
the free energy then becomes @xmath54 with @xmath55 next , we take the replica symmetry ( rs ) ansatz @xmath56 and similarly for the conjugated variables . due to the non - cycle ansatz , we have in addition @xmath57 such that the rs free energy reads @xmath58 - \alpha c \frac{q}{1-\chi_r - \chi } \nonumber \\ & & \hspace{1 cm } - ( 1-c)\frac{\alpha \beta } { 2 } { \ensuremath{\left ( q_0 ^ 2 - 2 q^2 + r^2 \right ) } } + { \alpha \beta } { \ensuremath{\left ( \hat q_0 q_0 - 2 \hat{q_1 } q_1 + \hat{r } r \right ) } } \nonumber \\ & & \hspace{1 cm } + \alpha ( c - j_0 ) r - \frac{1}{\beta } { \ensuremath{\left\langle \int { { \mathcal d } z } \log \underset{{\sigma \tau}}{\mbox{tr}}\exp{\ensuremath{\left ( -\beta \tilde h(\sigma,\tau|z ) \right ) } } \right\rangle}}_\xi \ , \label{eq : qising : fe - par}\end{aligned}\ ] ] with the effective hamiltonian @xmath59 and @xmath60 the gaussian measure @xmath61 .
we have also defined the susceptibilities @xmath62 and their conjugate expressions @xmath63 the phase structure of the network is then determined by the solution of the following set of saddle - point equations @xmath64 where the average @xmath65 is defined with respect to the effective hamiltonian ( [ eq : qising : ham - par ] ) and @xmath66 \ , \label{saddlecon0 } \\ & & \hat \chi = ( 1-c ) \chi + c \frac{\chi}{(1-\chi_r)^2 - \chi^2 } \ , \label{saddlecon1 } \\ & & \hat \chi_r = ( 1-c ) \chi_r + c
\frac{1-\chi_r}{(1-\chi_r)^2 - \chi^2 } + ( j - c ) \ . \label{saddlecon}\end{aligned}\ ] ] compared with sequential updating @xcite we notice the extra equations for @xmath67 and @xmath68 expressing that @xmath69 and @xmath70 can be affected differently by thermal fluctuations and the fact that the equations for the conjugate parameters are different . in the appendix we present the explicit forms for ( [ eq : pising : sp : rs : mr])-([eq : pising : sp : rs : q01 ] ) .
first , we look at the special case of low loading ( @xmath71 ) . in that case
the effective hamiltonian ( [ eq : qising : ham - par ] ) simplifies to @xmath72 which practically means that the two spin variables occurring in the expression for the free energy ( [ eq : qising : fe - par ] ) become independent yielding @xmath73 as found before for other models @xcite .
consequently , the saddle point equations are the same for synchronous and sequential updating and both yield the same stationary states .
an explicit calculation shows that the low loading results correspond to those of the @xmath74-ising ferromagnet . for the relevant phase diagram
we refer to @xcite ( fig . 2 for @xmath75 ) .
next , we turn to finite loading and solve the saddle point equations ( [ eq : pising : sp : rs : mr])-([saddlecon ] ) numerically for arbitrary temperature @xmath76 .
we present the phase diagrams for some representative values of the parameters @xmath77 , @xmath17 and @xmath78 .
we focuss on uniformly distributed patterns ( @xmath79 ) .
results for sequential updating of the network are included for comparison .
phase diagram for the 3-ising network with @xmath80 , @xmath79 , @xmath81 ( a ) and @xmath82 ( b ) .
solid ( dotted ) lines present synchronous updating for @xmath83 ( @xmath84 ) .
dashed lines are for sequential updating .
the retrieval state is stable below the thick lines .
the spin glass state is stable at the left of the thin lines.,title="fig:",width=245,height=170 ] phase diagram for the 3-ising network with @xmath80 , @xmath79 , @xmath81 ( a ) and @xmath82 ( b ) .
solid ( dotted ) lines present synchronous updating for @xmath83 ( @xmath84 ) .
dashed lines are for sequential updating .
the retrieval state is stable below the thick lines .
the spin glass state is stable at the left of the thin lines.,title="fig:",width=245,height=170 ] in figure 1 we present the rs @xmath85 phase diagrams with ( @xmath86 ) and without ( @xmath83 ) self - coupling for the fully connectivity architecture ( @xmath80 ) and gain parameter @xmath81 and @xmath82 .
the retrieval transition is discontinuous in all cases . for a fixed @xmath76 ,
the retrieval capacity of the synchronously updated network with self - coupling is slightly larger than the one for the network without self - coupling , and both are slightly larger than the one for the sequentially updated network .
however , the enhancement stays marginal , also for growing self - coupling .
the spin glass transition is always continuous . for @xmath82 ,
contrary to @xmath81 , the spin glass phase is not stable at small @xmath87 . but the retrieval phase is stable .
this means that for @xmath82 , small @xmath87 and low @xmath76 the retrieval phase co - exists only with the paramagnetic phase , and not with the spin glass phase .
.,title="fig:",width=245,height=170 ] .,title="fig:",width=245,height=170 ] in figure 2 we show the rs phase diagrams for the symmetrically diluted networks with @xmath88 .
the other network parameters are kept identical to those in figure 1 .
the retrieval ( spin - glass ) transitions remain discontinuous ( continuous ) .
the enhancement of the retrieval capacity is again marginal for the network with synchronous updating and without self - coupling , compared to the one for sequential updating .
however , increasing the self - coupling shows a substantial improvement , except for @xmath71 . also the spin - glass region is visibly enlarged in that case .
the remark concerning the stability of the spin - glass phase for @xmath82 and low @xmath76 also applies to the diluted network , but with a small change : one remarks ( see the bottom left corner of figure 2 ( b ) ) that the spin - glass phase becomes stable at small @xmath87 and low @xmath76 , although there remains a region where only the retrieval and paramagnetic phases are stable .
finally , we notice a strong re - entrant behaviour in the retrieval region .
this is related to the replica - symmetric approximation and is also seen in the hopfield model @xcite .
consequently , we conjecture that the fact that for @xmath82 , e.g. , the maximal critical capacity for the network with self - coupling is larger compared to the one for the network without self - coupling , is an effect of this approximation . . the curves for the sequentially and synchronously updated network without self coupling coincide.,title="fig:",width=245,height=170 ] .
the curves for the sequentially and synchronously updated network without self coupling coincide.,title="fig:",width=245,height=170 ] the rs phase diagrams for the extremely diluted symmetric ( @xmath26 ) network are shown in figure 3 .
the other parameters are kept identical to those in figures 1 and 2 .
the results for sequential and synchronous updating without self - coupling coincide .
all transitions are continuous .
again , we notice a strong re - entrance behaviour in the retrieval region , in agreement with earlier results for this extremely diluted limit @xcite . increasing the self - coupling
makes the synchronously updated network more robust against temperature , although , as expected , it has no effect on the critical temperature at zero @xmath87 .
the re - entrance point is reached for the same value of @xmath87 . as a function of the loading capacity @xmath87 for the @xmath74-ising model with synchronous updating at @xmath89 with uniform patterns ( @xmath79 ) , two values of @xmath17 , with and without self - coupling and @xmath90 ( a ) and @xmath91 ( b).,title="fig:",width=226,height=170 ] as a function of the loading capacity @xmath87 for the @xmath74-ising model with synchronous updating at @xmath89 with uniform patterns ( @xmath79 ) , two values of @xmath17 , with and without self - coupling and @xmath90 ( a ) and @xmath91 ( b).,title="fig:",width=226,height=170 ] as a function of the loading capacity @xmath87 for the @xmath74-ising model with sequential updating , uniform patterns , @xmath82 , @xmath89 , and @xmath88 , @xmath92 and @xmath93 . ] finally
, we briefly study the robustness of these three - state networks against the interference of static noise coming from random dilution . in fig .
4 we show the information content of the model , being the product of the loading capacity and the mutual information @xcite , for synchronous updating and several amounts of dilution @xmath77 with and without self - coupling .
we see that for the fully connected network ( @xmath90 , left figure ) , the results for @xmath83 and @xmath86 do practically coincide , in agreement with fig . 1
. we remark that for b=0.2 , two solutions co - exist at small @xmath87 ( @xmath94 ) .
one of them corresponds to perfect retrieval , with @xmath95 , @xmath96 .
the corresponding information content is very close to that for @xmath82 . for the diluted network ( @xmath88 , right figure ) , in agreement with fig . 2
, self - coupling mostly leads to a higher information content for the optimal gain parameter @xmath82 .
( again , for @xmath81 there exist two solutions for small @xmath87 but the difference is very small and can hardly be seen on the scale of the figure . ) next , by comparing with fig . 5 for sequential updating ,
one notices that the results for sequential and synchronous updating ( without self - coupling ) are almost coincident . in all cases ,
we find that the quality of the retrieval properties is affected very little , unless the amount of dilution is high .
as mentioned in the introduction most studies in the literature on the dynamics of the @xmath0-ising model are based upon the signal - to - noise analysis . except for the extremely diluted asymmetric and layered architectures , which can be solved
exactly in closed form , the dynamics for the other architectures , only examined for synchronous updating , is obtained in the form of a recursive scheme .
recently , by a comparison with the generating functional analysis ( gfa ) , it has been found @xcite for the hopfield model that the application of this method in the study of the dynamics involves a short - memory approximation implying that the results are only exact up to the third time step , although they stay very accurate in the retrieval region for further time steps , but not so in the spin - glass region .
it has also been shown that the signal - to - noise analysis can be made exact , leading to the same results as the generating functional analysis . therefore , it is interesting to reconsider the dynamics for the @xmath1-state ising model using this generating functional technique , which was introduced in @xcite to the field of statistical mechanics and , by now , is part of many textbooks .
we closely follow the derivation in @xcite , extend it to variable dilution and indicate the differences for the model at hand . both sequential and synchronous updating
are discussed .
in fact , the discussion is made for general @xmath0 . since the method
itself has become rather standard , we restrict ourselves to a presentation of the main arguments .
the idea of the gfa approach to study dynamics @xcite is to look at the probability to find a certain microscopic path in time .
the basic tool to study the statistics of these paths is the generating functional @xmath97 = \sum_{{\mbox{\boldmath $ \sigma$}}(0 ) , \dots , { { \mbox{\boldmath $ \sigma$}}}(t ) } p[{{\mbox{\boldmath $ \sigma$}}}(0 ) , \dots , { { \mbox{\boldmath $ \sigma$}}}(t ) ] \ , \prod_{i=1}^n \prod_{t'=0}^t e^{-i \ , \psi_i(t ' ) \ , \sigma_i(t ' ) } \label{functional}\ ] ] with @xmath98 $ ] the probability to have a certain path in phase space @xmath99 = p[{{\mbox{\boldmath $ \sigma$}}(0 ) } ] \prod_{t'=0}^{t-1 } w[{{\mbox{\boldmath $ \sigma$}}}(t'+1)|{{\mbox{\boldmath $ \sigma$}}}(t')]\ ] ] and @xmath100 $ ] the transition probabilities from @xmath101 to @xmath102 .
synchronous updating is expressed by ( recall eq .
( [ three ] ) ) . @xmath103=
\prod_{i=1}^n\frac{\exp{\left(\beta\sigma_i(t'+1 ) \epsilon_i(\sigma_i(t'+1)|{\mbox{\boldmath $ \sigma$}}(t'))\right ) } } { \underset{\sigma}{\textrm{tr } } \exp{\left(\beta\sigma \epsilon_i(\sigma|{\mbox{\boldmath $ \sigma$}}(t ' ) ) \right)}}\ ] ] where @xmath104 now includes a time - dependent external field @xmath105 in order to define a response function @xmath106 + \theta_i(t')\,.\ ] ] one can find all the relevant order parameters , i.e. , the overlap @xmath107 , the correlation function @xmath108 and the response function @xmath109 , by calculating appropriate derivatives of the above functional ( [ functional ] ) and letting @xmath110 tend to zero afterwards @xmath111}{\delta\psi_i(t ) } \ , , \label{factora } \\
g(t , t ' ) & = & i \lim_{{\mbox{\boldmath $ { \psi}$}}\to0 } \frac{1}{n } \sum_{i } \frac{\delta^2 z[{\mbox{\boldmath $ { \psi}$}}]}{\delta\psi_i(t ) \delta\theta_i(t ' ) } \ , , \\ c(t , t ' ) & = & - \lim_{{\mbox{\boldmath $ { \psi}$}}\to0 } \frac{1}{n } \sum_{i } \frac{\delta^2 z[{\mbox{\boldmath $ { \psi}$}}]}{\delta\psi_i(t ) \delta\psi_i(t')}\,.\end{aligned}\ ] ] a difference with the little - hopfield model @xcite is the presence of the factor @xmath112 in ( [ factora ] ) .
first , due to the proper scaling of the couplings with this factor ( recall eq .
( [ couphebb ] ) ) the average over the non - condensed patterns does not introduce an extra factor .
secondly , in the saddle point , terms containing this extra factor vanish . as a consequence
, the factor @xmath112 does not appear explicitly in the expressions at all .
the only point to keep in mind is the occurrence of the term proportional to the factor @xmath17 in the dynamics ( recall eq .
( [ eq : energy ] ) ) .
another difference with respect to the treatment in @xcite is that one needs to average over the dilution .
this is done before averaging over the non - condensed patterns by using the fact that the diluted couplings @xmath113 are of order @xmath114 and that the @xmath115 .
noting that the distribution for the dilution eq .
( [ propdil ] ) is i.i.d.r.v . for @xmath116 and expanding the exponential containing the @xmath113 up to order @xmath117 makes this average then straightforward
. in the thermodynamic limit one expects the physics of the problem to be independent of the quenched disorder and , therefore , one is interested in derivatives of @xmath118}$ ] , whereby the overline denotes the average over this disorder , i.e. , over all pattern realizations .
this results in an effective single spin local field given by @xmath119 with @xmath120 temporally correlated noise with zero mean and correlation matrix @xmath121 and the retarded self - interactions @xmath122 the order parameters defined above can be written as @xmath123 the average over the effective path measure @xmath124 is given by @xmath125 where @xmath126 and with @xmath127 where @xmath128 . the average denoted by the double brackets in ( [ eq : ordergfa ] ) is over the condensed pattern and initial conditions .
the set of eqs .
( [ eq : h])-([selfmatrix ] ) and ( [ eq : noise : dist])-([eq : eta ] ) represent an exact dynamical scheme for the evolution of the network from which all relevant order parameters can be obtained at all time steps .
the order parameters are given by ( [ orderm])-([eq : ordergfa ] ) .
to acquire a more intuitive expression for the response function we note that also @xmath129 we remark that @xmath130 for @xmath131 and @xmath132 and that for all @xmath133 @xmath134 \right\rangle}}_\star \right\rangle\!\right\rangle\ ] ] where @xmath135 appearing in @xmath136 is given by ( [ eq : h ] ) . for sequential updating
we have to start from the stochastic process @xmath137\,p_s({\mbox{\boldmath $ \sigma$}}')\ ] ] with @xmath138 the probability to be in a state @xmath102 at time @xmath139 and @xmath140 $ ] given by @xmath141= \frac{1}{n}\sum_i\left\ { w_i({\mbox{\boldmath $ \sigma$}})\delta_{{\mbox{\boldmath $ \sigma$}},{\mbox{\boldmath $ \sigma$ } } ' } + w_i(f_i{\mbox{\boldmath $ \sigma$}})\delta_{{\mbox{\boldmath $ \sigma$}},g_i{\mbox{\boldmath $ \sigma$}}'}+ w_i(g_i{\mbox{\boldmath $ \sigma$}})\delta_{{\mbox{\boldmath $ \sigma$}},f_i{\mbox{\boldmath $ \sigma$}}'}\right\ } \,,\ ] ] with the shorthand @xmath142 and where @xmath143 and @xmath144 are cyclic spin - flip operators between the spin states .
each time step a randomly chosen spin is updated . in the thermodynamic limit the dynamics becomes continuous because the characteristic time scale is @xmath145 .
the standard procedure is then to update a random spin according to ( [ three ] ) and ( [ eq : energy ] ) with time intervals @xmath146 that are poisson distributed with mean @xmath145
. we can then write a continuous master equation in the thermodynamic limit @xmath147 in that case the effective path average reads @xmath148 _ { { \mbox{\boldmath $ \eta$}}}\ , \ ] ] where @xmath149 _ { { \mbox{\boldmath $ \eta$}}}$ ] is an average over the ( effective ) stochastic process conditioned to the noise @xmath150 generated by the dynamics ( [ conp ] ) and the distribution @xmath151 is gaussian with correlation matrix @xmath152 @xmath153 this result is very similar to the one for synchronous dynamics ( recall eq .
[ eq : eta ] ) .
the main reason is that one does not need the explicit form of the transition rates of the markovian process in order to derive the effective path average .
if only the initial conditions factorize over the site index @xmath8 then all sites become independent in the thermodynamic limit . in general , this is a characteristic feature of mean - field systems . specialising this discussion to three ising states
@xmath154 we have that for synchronous updating the trace in eq .
( [ eq : s|eta ] ) is given by @xmath155 for sequential updating the spin - flip operators in eq .
( [ put2 ] ) are defined by @xmath156 we have solved the dynamics numerically using the eissfeller - opper method @xcite .
the idea thereby is to replicate the system into @xmath157 copies of the effective spin and let each of them evolve independently in time according to their own stochastic path with its own noise variable .
averages over the effective path measure ( recall eqs .
( [ eq : noise : dist ] ) and ( [ eq : noise : distseq ] ) ) are replaced by averages over the ensemble of copies for large @xmath157 .
we have taken @xmath158 .
as a function of time using the eissfeller - opper algorithm with @xmath159 samples for the fully connected ( @xmath80 , top ) and diluted ( @xmath88 , bottom ) @xmath74-ising model with synchronous updating and uniform patterns ( @xmath79 ) for @xmath160 and @xmath83 .
the other model parameters are @xmath161 ( top left ) , @xmath162 ( top right ) , @xmath163 ( bottom left ) and @xmath164 ( bottom right ) . ,
title="fig:",width=226,height=170 ] as a function of time using the eissfeller - opper algorithm with @xmath159 samples for the fully connected ( @xmath80 , top ) and diluted ( @xmath88 , bottom ) @xmath74-ising model with synchronous updating and uniform patterns ( @xmath79 ) for @xmath160 and @xmath83 .
the other model parameters are @xmath161 ( top left ) , @xmath162 ( top right ) , @xmath163 ( bottom left ) and @xmath164 ( bottom right ) . , title="fig:",width=226,height=170 ]
+ as a function of time using the eissfeller - opper algorithm with @xmath159 samples for the fully connected ( @xmath80 , top ) and diluted ( @xmath88 , bottom ) @xmath74-ising model with synchronous updating and uniform patterns ( @xmath79 ) for @xmath160 and @xmath83 .
the other model parameters are @xmath161 ( top left ) , @xmath162 ( top right ) , @xmath163 ( bottom left ) and @xmath164 ( bottom right ) . ,
title="fig:",width=226,height=170 ] as a function of time using the eissfeller - opper algorithm with @xmath159 samples for the fully connected ( @xmath80 , top ) and diluted ( @xmath88 , bottom ) @xmath74-ising model with synchronous updating and uniform patterns ( @xmath79 ) for @xmath160 and @xmath83 .
the other model parameters are @xmath161 ( top left ) , @xmath162 ( top right ) , @xmath163 ( bottom left ) and @xmath164 ( bottom right ) .
, title="fig:",width=226,height=170 ] as an illustration we show some typical flow diagrams for the overlap order parameter in figure 6 for some fully connected ( @xmath80 , top figures ) and diluted ( @xmath88 , bottom figures ) models .
the model parameters are @xmath160 and @xmath161 ( top left ) , @xmath162 ( top right ) , @xmath163 ( bottom left ) and @xmath164 ( bottom right ) .
self - couplings are set to zero .
several remarks are in order .
all situations shown are in the retrieval phase of the corresponding phase diagrams figures 1 and 2 .
they all converge to the corresponding rs equilibrium results provided the initial overlap order parameter is large enough .
this gives us also an idea of the basins of attraction .
these basins are bigger for @xmath81 since the relevant model parameters are chosen deeper in the retrieval region , i.e. , closer to the line of thermodynamic stability .
for completeness we end this section on the discussion of the dynamics employing the gfa approach with a couple of remarks . first , this technique can also be applied to asymmetric dilution ( @xmath165 ) and we then get for the correlation matrix and retarded self - interactions @xmath166 with the asymmetry factor @xmath167 given by @xmath168 secondly , one can compare the gfa technique with the signal - to - noise analysis for the three - state ising network @xcite .
this comparison is formally completely analogous to the one for the hopfield model discussed in detail in @xcite .
the only point at which one has to be careful is in deriving the recursion relations for the coloured noise @xmath169 .
the diagonal of @xmath170 , namely , is no longer equal to 1 but depends on time .
taking this into account one can take the results for the hopfield model and extend it to @xmath171-ising models .
the outcome is that , even for general @xmath0 , the signal - to - noise analysis is a short memory approximation to the real effective dynamics giving results correct up to the third time step . like for the other models ,
this approximation is extremely good in the retrieval region but fails in the spin glass region .
it is then a rather straightforward exercise to extend the revisited signal - to - noise analysis , proposed in @xcite to the @xmath0-ising case . since the final results are completely equivalent to those of the gfa eqs .
( [ eq : h])-([selfmatrix ] ) , we refrain from repeating further explicit details and refer to the work mentioned above ( @xcite ) .
we have studied the statics and dynamics of the three - state ising neural network model with synchronous updating of the neurons and variable dilution .
we have followed as closely as possible the discussion for the hopfield model adapting the methods to the multi - state nature of the neurons .
although the equations that describe both statics and dynamics are formally rather similar to those of the hopfield model , we have seen that the physics behind it is quite different .
we have examined the thermodynamic and retrieval properties for this model using replica symmetric mean - field theory and have made a detailed comparison of the results with those for sequential updating .
capacity - temperature phase diagrams are derived for several values of the pattern activity and different gradations of dilution .
apart from the appearance of cycles the asymptotic behaviour is almost identical to the one for sequential updating .
the spin - glass region is visibly enhanced , while the retrieval region , however , is only marginally enhanced .
only the addition of self - couplings can enlarge the retrieval region substantially , especially in the case of strong dilution .
a calculation of the information content shows that both for synchronous and sequential updating the three - state networks are robust against the interference of static noise coming from random dilution .
concerning the dynamics , we have extended the generating functional analysis to the study of @xmath0-state spins . as an illustration
some typical flow diagrams for the overlap order parameter are presented in the case @xmath1 .
it is possible to extract the result for sequential updating from the one for synchronous updating .
a comparison with the signal - to - noise approach is made .
as for the hopfield model one can argue that the signal - to - noise analysis used before in the literature is a short memory approximation correct up to the third time step .
it can also be shown that this signal - to - noise analysis can be made exact .
the authors would like to thank jordi busquets blanco , gyoung moo shim and walter k. theumann for useful discussions .
r. e. thanks the kind hospitality and the support of the instituut voor theoretische fysica , kuleuven .
this work has been supported in part by the fund of scientific research , flanders - belgium .
we write down explicitly the saddle - point equations discussed in section 3 .
therefore we need the averages @xmath172 , @xmath173 and @xmath174 with respect to the effective hamiltonian ( [ eq : qising : ham - par ] ) @xmath175 } + \sinh(\beta m)\,{\rm e}^{\beta\left[-b+\frac{\alpha}{2}\hat{\chi}\right ] } \right\}\ , , \label{eq19}\ ] ] @xmath176 } - { \rm e}^{\beta\left[2\left(-b+\frac{\alpha}{2}\hat{\chi}\right ) -\alpha\hat{\chi}_r\right ] } \right\}\ , , \label{eq20}\ ] ] @xmath177 } \right .
\nonumber \\ & + & \left . \cosh(\beta
m)\,{\rm e}^{\beta\left[-b+\frac{\alpha}{2}\hat{\chi}\right ] } + { \rm e}^{\beta\left[2\left(-b+\frac{\alpha}{2}\hat{\chi}\right ) -\alpha\hat{\chi}_r\right ] } \right\}\ , , \label{eq21}\end{aligned}\ ] ] with @xmath178 using the symmetry properties of these functions , we average over @xmath179 to obtain the saddle - point equations for the retrieval state of one pattern at finite temperature .
we get @xmath180 @xmath181 @xmath182 @xmath183 ^ 2 ( m+\sqrt{\alpha\hat{q}_1}z ) + ( 1-a)\int\mathcal{d}z\left[\left\langle\sigma\right\rangle_z\right]^2 ( \sqrt{\alpha\hat{q}_1}z)\ , , \label{eq31}\ ] ] that need to be solved together with the algebraic equations ( [ saddlecon0])-([saddlecon ] ) .
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* 68 * ( 1992 ) 2094 .[/INST] the three - state ising neural network with synchronous updating and variable dilution is discussed starting from the appropriate hamiltonians .
the thermodynamic and retrieval properties are examined using replica mean - field theory .
capacity - temperature phase diagrams are derived for several values of the pattern activity and different gradations of dilution , and the information content is calculated .
the results are compared with those for sequential updating .
the effect of self - coupling is established .
also the dynamics is studied using the generating function technique for both synchronous and sequential updating .
typical flow diagrams for the overlap order parameter are presented .
the differences with the signal - to - noise approach are outlined . _ pacs _ : 05.20-y , 64.60.cn , 75.10.hk , 87.10+e + _ key words : _ multistate diluted networks ; synchronous updating ; sequential updating ; statics ; dynamics ; phase diagrams . , and , </s> |
dentine sensitivity is defined as short , sharp pain from exposed dentine in response to thermal , tactile , osmotic , or chemical stimuli that can not be ascribed to any other dental defect or disease .
clinically the presence of dentine sensitivity creates challenges for both patients and dental practitioners ; in addition to causing patient discomfort , dentine sensitivity can complicate the provision of restorative treatment and the treatment of periodontal tissues [ 3 , 4 ] .
dentine sensitivity is related to the exposure of dentine tubules resulting from either loss of tooth enamel or loss of periodontal tissue ( gingival recession ) [ 5 , 6 ] . for dentine sensitivity to be incited , dentine tubules must be open at the dentine surface as well as remaining patent to the dental pulp [ 6 , 7 ] . at the microscopic level dentine sensitivity
is currently still described by the hydrodynamic theory proposed by brannstrom [ 8 , 9 ] , which states that following dentine exposure to stimuli such as physical touch , temperature alteration , sweet liquid , and acidic liquid , changes in intratubular fluid movement and intratubular pressure occur .
these changes can cause activation of intratubular nerve fibres of pulpal origin ; this nerve excitation causes pain to be experienced [ 8 , 10 ] . to manage dentine sensitivity products
have been developed for at home use functioning primarily through two modalities : suppressing the excitability of intratubular nerve fibres or reducing the patency of exposed dentine tubules [ 2 , 11 , 12 ] .
when acting to suppress the excitability of nerve fibres within dentine tubules , the most common approach is to elevate the extracellular potassium concentration within the dental pulp .
this can be achieved through a patient applying a dentifrice containing potassium ions in a relatively soluble form to exposed dentine .
movement of potassium ions through patent dentinal tubules will act to raise the response threshold of pulpal nociceptors and reduce their ability to fire when provoked [ 13 , 14 ] .
when considering the effectiveness of agents that reduce dentine sensitivity through reduction in the patency of exposed dentine tubules , the most successful outcomes have been achieved through application of fluoride based gels to dentine [ 2 , 11 , 12 ] .
it is well documented that application of dentifrices containing stannous fluoride [ 1517 ] and sodium fluoride [ 1821 ] can promote the deposition of mineral precipitates within open dentinal tubules , thereby reducing fluid flow in dentine tubules following exposure to stimuli .
a dentifrice containing functionalised tricalcium phosphate and 950 ppm sodium fluoride has been shown to enable dentine tubule occlusion in vitro ; application of this dentifrice to extracted bovine teeth following ph cycling was observed to reduce both dentine tubule opening and tubule diameter in comparison to pretreatment levels .
this finding is notable , as not only there is limited data demonstrating that 1000 ppmf dentifrices can effectively reduce dentine sensitivity , but the availability of such a dentifrice could lower the cost and complexity of at home treatment undertaken by a patient suffering from dentine sensitivity , a dentifrice containing 1000 ppmf being appropriate for the control of dental caries in low caries risk patients [ 23 , 24 ] .
importantly , while assessment of the anticaries benefits of this dentifrice has been reported , no assessment of the efficacy of this dentifrice to reduce dentine sensitivity in vivo has taken place .
the aim of the present study was therefore to assess the effectiveness of a dentifrice containing 950 ppm fluoride and functionalised tricalcium phosphate ( ftcp ) in the reduction of dentine sensitivity in vivo .
the null hypothesis was that the effectiveness of the dentifrice containing ftcp and 950 ppm fluoride would not be different to the effectiveness of a dentifrice containing 1000 ppm fluoride in reducing dentine sensitivity .
the present study was a single centre , parallel group , blinded ( subjects and examiners ) randomised controlled clinical trial conducted at the westmead centre for oral health , westmead hospital , sydney , australia .
ethical approval from the western sydney local health network human research ethics committee was obtained prior to commencement of the study ( sac2010/11/4.6 ( 3223 ) hrec/10/wmead/202 ) and the trial was registered with the australia new zealand clinical trials register .
subjects included within the study were from the pool of patients eligible to receive treatment at the westmead centre for oral health . from this patient pool , during an initial off waiting list examination ,
eight hundred and fifty individuals indicated they suffered from dentine hypersensitivity and were willing to participate in the study .
of these 850 individuals a total of 71 subjects were recruited for the study having met the strict inclusion criteria . all subjects which participated in the study consented to participation prior to the inclusion . as part of the consent process
, patients were made aware of adverse effects of dentifrices , namely , abrasion and staining of hard and soft tissues and the detrimental sequelae of excessive fluoride ingestion . to be considered for this study ,
subjects were required to meet all of the following inclusion criteria : being aged between 18 and 70 years;demonstrating good general health with no history of chronic illness;possession of at least 2 teeth with an exposed root surface which are responsive on probing ( 50 g force ) or a 1 s duration cold air blast ( 70 psi ) ; these teeth were not to exhibit diagnosed caries , defective restorations , or signs of fracture on initial assessment ; these teeth were not to have had dental restorations , periodontal surgery , or orthodontics that has resulted in postoperative pain in the immediate past 3 months;a willingness to read , understand , and sign the consent form;a capability and willingness to brush teeth at least 2 times a day for 2 minutes on each occasion .
being aged between 18 and 70 years ; demonstrating good general health with no history of chronic illness ; possession of at least 2 teeth with an exposed root surface which are responsive on probing ( 50 g force ) or a 1 s duration cold air blast ( 70 psi ) ; these teeth were not to exhibit diagnosed caries , defective restorations , or signs of fracture on initial assessment ; these teeth were not to have had dental restorations , periodontal surgery , or orthodontics that has resulted in postoperative pain in the immediate past 3 months ; a willingness to read , understand , and sign the consent form ; a capability and willingness to brush teeth at least 2 times a day for 2 minutes on each occasion .
a subject was excluded from participation in the study if any of the following conditions applied : use of a desensitising agent in the 3 months prior to the study;undertaking regular medical treatment involving anti - inflammatory or analgesic use;being pregnant or nursing;exhibiting a known allergy to any ingredients in the examined dentifrices;suffering from conditions which could increase the level of acid within the oral cavity : bulimia , gastric reflux disease;excessive dietary exposure to acids ; lemons 2 times per day , raw tomatoes 2 times per day , acidic drinks 1 litre per day ( sports drinks , energy drinks , or fruit juice ) , wine 3 standard glasses per day;an inability to read the oral hygiene instructions provided to each participant . use of a desensitising agent in the 3 months prior to the study ; undertaking regular medical treatment involving anti - inflammatory or analgesic use ; being pregnant or nursing ; exhibiting a known allergy to any ingredients in the examined dentifrices ; suffering from conditions which could increase the level of acid within the oral cavity : bulimia , gastric reflux disease ; excessive dietary exposure to acids ; lemons 2 times per day , raw tomatoes 2 times per day , acidic drinks 1 litre per day ( sports drinks , energy drinks , or fruit juice ) , wine 3 standard glasses per day ; an inability to read the oral hygiene instructions provided to each participant . allocation of subjects to four study groups was randomised through use of a computer algorithm to limit the impact of age , gender , diet , and current level of oral hygiene on the study results .
group a. this group brushed teeth twice daily with a dentifrice containing 1000 ppm fluoride ions ( mfp ) : colgate cavity protection ( colgate - palmolive , new york , ny , usa , ) .
group b. this group brushed teeth twice daily with a dentifrice containing 1000 ppm fluoride ions ( naf ) + 19300 ppm potassium ions ( kno3 ) : sensodyne total care ( glaxosmithkline , sydney , nsw , australia ) .
group c. this group brushed teeth twice daily with a dentifrice containing ftcp and 950 ppm fluoride ions ( naf ) : clinpro tooth crme ( 3 m espe , st .
group d. this group brushed teeth twice daily with a dentifrice containing ftcp and 950 ppm fluoride ions ( naf ) : clinpro tooth crme ( 3 m espe , st .
paul , mn , usa ) and a directed pea sized topical application of clinpro tooth crme onto sensitive teeth before sleeping without rinsing . at no time during the trial were subjects made aware of what test group they belonged to or which product they were using ; all packaging was discarded prior to distribution and toothpaste tubes were wrapped in generic sticky white labelling . at the study commencement ,
all subjects were provided with a new toothbrush and dental floss and were given the same oral hygiene instructions verbally and as a take home pamphlet .
subjects were also provided with a two - minute timer in a bid to maintain strict and consistent adherence to the prescribed two - minute brushing time twice daily .
patients were assessed at three time points during the study : baseline , 6 weeks , and 10 weeks .
the clinical assessment was completed by three senior dental officers at westmead centre for oral health to limit the effect of clinician variation on study results .
standardisation was also maintained through each clinician recalibrating the process of stimulus provision to sensitive surfaces at the commencement of each assessment day .
examiners remained blinded to test groups to which participants belonged at all examination points throughout the study .
at each assessment , each sensitive tooth surface was exposed to three different stimuli that were applied directly onto the identified sensitive tooth .
the three stimuli included an air blast , tactile stimulation , and application of a hypertonic solution .
the identified tooth surface was exposed to air delivered from a standard dental unit triplex syringe from an operating distance of approximately 1 cm for a period of 1 s at an operating temperature of 21c ( 5c ) .
a pressure gauge was mounted to the dental unit and calibrated prior to each assessment day to ensure air was delivered at a standard pressure of 70 psi .
the identified tooth surface was stroked for 3 s using a standard dental explorer probe that was held perpendicular to the surface using a force of 50 g.
hypertonic solution .
a 70% hypertonic sucrose solution was applied to the identified tooth surface for 3 s. the solution was at room temperature at the time of application . following application of each stimulus patients
rated the pain / sensitivity experienced using an 11-point numbered pain rating scale ( nrs-11 ; figure 1 ) .
these scores were recorded on clinical test forms . following the 6-week examination patients returned the study dentifrice
wash - out period to elapse before reexamination at 10 weeks to quantify any prolonged actions of each test dentifrice ; 6-week usage of a dentifrice has been shown to provide sufficient time to allow maximum benefit of a desensitising product .
patient compliance in the use of the study dentifrice was established at the 6-week examination .
patients were asked to return products which were issued and each tube was weighed to calculate the total amount of toothpaste used over the 6-week period . for each test group
the mean pain score for each stimulus modality ( air blast , tactile , and hypertonic solution ) was calculated by patient and by tooth at each assessment point ( baseline , 6 weeks , and 10 weeks ) . additionally , the mean pain scores for each test group for each stimulus were combined and divided by 3 to give a total combined modalities sensitivity ( cms ) score at each assessment point .
the percentage change relative to baseline in mean pain score for each stimulus and the percentage change in cms relative to baseline were calculated for each test group .
ancova ( with baseline as the covariate ) with a tukey hsd post hoc test was used for between group comparisons .
of the 850 individuals from the westmead centre for oral health patient pool who indicated suffering from dentine sensitivity , 80 individuals satisfied the inclusion criteria .
these 80 individuals were randomly allocated to the four study groups ( a d ) .
the study population exhibited a mean age of 40.9 and a range of 1767 years of age .
seventy - one of the 80 subjects completed the 10-week clinical study and complied with the protocol given .
of the participants who completed the study , there were 54 females and 17 males .
no adverse soft tissue or hard tissue effects were observed by the assessing clinicians during the study ; however one participant withdrew from the study reporting an allergic reaction to colgate cavity protection .
the 9 patients that did not complete the study did so as they no longer wanted to attend the recall appointments on the basis of convenience .
at 6 weeks ( end of the treatment phase ) all groups showed a reduction in evaporative sensitivity score from baseline , with colgate cavity protection showing a 12% reduction , sensodyne total care a 19% reduction , clinpro tooth crme ( brushing only ) a 45% reduction , and clinpro tooth crme ( brushing + topical application ) showing a 43% reduction .
the reduction in evaporative sensitivity scores from base line of both clinpro tooth crme groups at 6 weeks was significantly greater ( p 0.05 , 95% ci ) than the reduction in evaporative sensitivity scores of both the positive control group ( sensodyne total care ) and the negative control group ( colgate cavity protection ) .
there was no significant difference ( p 0.05 , 95% ci ) in the reduction of evaporative sensitivity scores from baseline when comparing the sensodyne total care and colgate cavity protection groups at the end of the 6-week treatment phase ( tables 1 and 2 and figure 2 ) . at 10 weeks ( four weeks after cessation of treatment )
, all four groups demonstrated a reduction in evaporative sensitivity score from baseline , with colgate cavity protection showing a 18% reduction , sensodyne total care a 40% reduction , clinpro tooth crme ( brushing only ) a 24% reduction , and clinpro tooth crme ( brushing + topical application ) showing a 54% reduction .
the reduction in evaporative sensitivity scores at 10 weeks for clinpro tooth crme ( brushing + topical application ) and sensodyne total care was significantly greater ( p 0.05 , 95% ci ) than the reduction in evaporative sensitivity demonstrated by the negative control colgate cavity protection .
there was no significant difference ( p 0.05 , 95% ci ) in the reduction in evaporative sensitivity scores at 10 weeks from baseline when comparing groups using sensodyne total care , clinpro tooth crme ( brushing only ) , and clinpro tooth crme ( brushing + topical application ) . at 6 weeks ( end of the treatment phase )
all groups showed a reduction in tactile sensitivity from baseline , with colgate cavity protection showing a 20% reduction , sensodyne total care a 39% reduction , clinpro tooth crme ( brushing only ) a 44% reduction , and clinpro tooth crme ( brushing + topical application ) a 62% reduction . at 6 weeks the only group to show a significant reduction ( p 0.05 , 95% ci ) in tactile sensitivity scores in comparison to the negative control group ( colgate total protection ) was clinpro tooth crme ( brushing + topical application ) .
there were no other comparisons that displayed significantly different sensitivity scores ; both clinpro tooth crme groups were not significantly different ( p 0.05 , 95% ci ) from the positive control group , sensodyne total care ( tables 1 and 2 and figure 3 ) . at 10 weeks ( four weeks after cessation of treatment ) , not all groups showed a reduction in tactile sensitivity from baseline , with colgate cavity protection showing a 6% increase in sensitivity .
however , sensodyne total care showed a 37% reduction in tactile sensitivity , clinpro tooth crme ( brushing only ) a 14% reduction , and clinpro tooth crme ( brushing + topical application ) a 64% reduction from baseline . a significant reduction ( p 0.05 , 95% ci ) in tactile sensitivity at 10 weeks from baseline for clinpro tooth crme ( brushing + topical application ) and sensodyne total care in comparison to colgate cavity protection was observed .
no significant difference ( p 0.05 , 95% ci ) in the reduction in tactile sensitivity scores from baseline to 10 weeks was observed between clinpro tooth crme ( brushing only ) and sensodyne total care .
additionally , no significant difference ( p 0.05 , 95% ci ) in tactile sensitivity score reduction at 10 weeks was observed between clinpro tooth crme ( brushing only ) and colgate cavity protection ( tables 1 and 2 and figure 3 ) . at 6 weeks
all groups exhibited a reduction in hypertonic sensitivity from baseline , with colgate cavity protection showing a 32% reduction , sensodyne total care a 41% reduction , clinpro tooth crme ( brushing only ) a 40% reduction , and clinpro tooth crme ( brushing + topical application ) showing a 61% reduction . at 6 weeks the difference in % reduction from baseline was not significant ( p 0.05 , 95% ci ) for any of the four groups ( tables 1 and 2 and figure 4 ) . at 10 weeks
, all groups exhibited a reduction in hypertonic sensitivity from baseline , with colgate cavity protection showing a 42% reduction , sensodyne total care a 56% reduction , clinpro tooth crme ( brushing only ) a 22% reduction , and clinpro tooth crme ( brushing + topical application ) showing a 66% reduction .
the only groups to exhibit a significant difference ( p 0.05 , 95% ci ) in hypertonic sensitivity reduction at 10 weeks compared to baseline were sensodyne total care and clinpro tooth crme ( brushing + topical application ) .
there was no significant difference ( p 0.05 , 95% ci ) in hypertonic sensitivity reduction at 10 weeks between the groups using colgate cavity protection , sensodyne total care , and clinpro tooth crme ( brushing + topical application ) ( tables 1 and 2 and figure 4 ) . at 6 weeks ( end of the treatment phase )
all groups exhibited a reduction in the combined sensitivity score ( cms ) from baseline , with colgate cavity protection showing a 20% reduction , sensodyne total care a 30% reduction , clinpro tooth crme ( brushing only ) a 42% , and clinpro tooth crme ( brushing + topical application ) showing a 52% reduction . at the end of the 6-week treatment phase , both clinpro tooth crme study groups showed a significant reduction ( p 0.05 , 95% ci ) in cms when compared to the negative control group using colgate cavity protection .
clinpro tooth crme when used with an additional topical application also demonstrated a significant reduction ( p 0.05 , 95% ci ) in dentine sensitivity compared to the positive control , sensodyne total care , after 6 weeks ( tables 1 and 2 and figure 5 ) . at 10 weeks ( 4 weeks after cessation of treatment ) , all groups showed a reduction in combined sensitivity score ( cms ) from baseline , with colgate cavity protection showing an 18% reduction , sensodyne total care a 40% reduction , clinpro tooth crme ( brushing only ) a 24% reduction , and clinpro tooth crme ( brushing + topical application ) a 54% reduction .
the reduction in cms for clinpro tooth crme ( brushing + topical application ) and sensodyne total care was significantly greater ( p 0.05 , 95% ci ) than the reduction in cms from baseline of the negative control colgate cavity protection at four weeks after cessation of treatment .
there was no significant difference ( p 0.05 , 95% ci ) in cms reduction from baseline to 10 weeks between groups using sensodyne total care , clinpro tooth crme ( brushing only ) , and clinpro tooth crme ( brushing + topical application ) ( tables 1 and 2 and figure 5 ) .
the ability for fluoride ions sourced from a dentifrice to form fluoride - calcium precipitates that occlude dentine tubules with the consequence of reducing dentine sensitivity is well documented [ 1821 , 27 , 28 ] .
this ability occurs due to the negative electric charge of fluoride ions , which results in their binding with calcium cations .
once bound to calcium cations present within a dentifrice the fluoride ions are rendered incapable of combining with cations present at the tooth surface . to overcome the effect of reduced fluoride ion availability at the tooth surface caused by intradentifrice fluoride - calcium bonding
, dentifrice manufacturers have traditionally acted to increase the concentration of fluoride ions within a dentifrice . in recent times , however , altering the chemical structure of calcium complexes within a dentifrice to reduce the bonding affinity between calcium cations and fluoride anions has been undertaken as an alternative solution to simple fluoride ion concentration increase .
one such example of this has been the development and incorporation of altered calcium phosphate complexes , such as functionalised tricalcium phosphate , which is currently incorporated within clinpro tooth crme . functionalised tricalcium phosphate ( ftcp ) is produced through beta tricalcium phosphate ( tcp ) complexes being milled with sodium lauryl sulfate ( sls ) .
the tcp crystal structure exhibits several reactive sites including calcium - oxygen clusters ( cao3 , cao7 , and cao8 ) and lattice defects .
these reactive sites are available to undergo chemical interaction with anions such as fluoride ions . to reduce the reactivity of these sites within b - tcp complexes
the incorporation of sls within the tcp structure therefore impedes fluoride ions from combining with calcium ions in the dentifrice , so in turn potentially increasing the concentration of both calcium and fluoride to tooth surfaces .
[ 25 , 3234 ] have reported a synergistic relationship between ftcp and fluoride with regard to enamel remineralisation ; enamel that is remineralised through a fluoride / ftcp combination demonstrates significantly greater surface and subsurface rehardening following ph cycling compared to that achieved by fluoride application alone .
notably , the results of the present study suggest that this remineralisation synergy between fluoride and ftcp may also produce a benefit in terms of enhancing dentine tubule occlusion ; the two test groups that utilised clinpro tooth crme ( 950 ppm f ) demonstrated a greater level of sensitivity relief for all stimuli except the hypertonic test at 10 weeks ( group c ) in comparison to the group using colgate total , despite the fact that colgate total contains a greater concentration of fluoride ions ( 1000 ppm f ) .
previous microscopic analysis showing the ability of clinpro tooth crme to reduce the diameter of tubule openings following ph cycling to a greater degree than sensodyne nupro 5000 and topex renew supports this possibility . within the present study a greater reduction in dentine sensitivity
was observed when an additional topical application of clinpro tooth crme was placed to supplement application provided through brushing alone .
this finding is in contrast to reports in the literature stating that there is no evidence to suggest that additional topical application increases the effectiveness of a desensitizing dentifrice .
first an intentional topical application of a dentifrice potentially allows a greater concentration of fluoride ions to be applied to a tooth surface in comparison to that applied through unintentional brushing alone .
secondly , through an additional topical application , fluoride ions can remain at a sensitive surface for a longer duration than following brushing and rinsing and thirdly through increasing the duration of fluoride ion presence upon a sensitive surface , the propensity for fluoride migration and tubule occlusion is raised .
the greater success of clinpro tooth crme when applied as an additional topical application rather than brushing alone may also be a result of greater salivary fluoride concentration as a by - product of topical application and no rinsing following application .
this possibility is consistent with studies that have examined the effect of patient activity following dentifrice application on the level of salivary fluoride .
nordstrm and birkhed determined that a topical application of dentifrice to a tooth surface combined with regular brushing resulted in a greater concentration of salivary fluoride than when compared to brushing alone .
sjgren and melin identified that a single post - brushing rinse with fluoridated water decreased fluoride concentration by a factor of two when compared to no rinsing , while rinsing with fluoridated water two times following brushing decreased salivary concentration by a factor of 5 when compared to no rinsing .
the reduction in cms of the negative control group over the study duration can be in part attributed to the placebo effect which is well documented in dentine sensitivity studies [ 7 , 38 , 39 ] .
additionally the hawthorne effect , which describes a positive response to noninterventional treatment , should also be assumed to have had some impact on the study results . improved oral hygiene in patients enrolled in the study
could have also reduced perceived dentine sensitivity across all groups as a reduction in tooth surface plaque facilitated increased dentifrice access to dentine tubules .
these reasons may also account for the antihypersensitivity effects continuing for the month following the cessation of the use of the treatment dentifrices .
an identified limitation of the study was the numbers of patients enrolled in each study group . due to the breadth of the potential patient pool , patients eligible for treatment at westmead centre for oral health ,
it was anticipated that including 40 subjects per group would be an achievable goal over a 3-year study period . as a result of the very strict exclusion criteria , especially the requirement that the use of a desensitising agent in the 3 months prior to the study excluded an individual from being a subject , patient recruitment was extremely difficult .
however despite the smaller numbers than originally forecast per group , the results of the present study provide useful information . not only are the numbers sufficient to demonstrate statistical significance , but when tooth number rather than patient number is used for analysis the subject number exceeds 50 for each group and the statistical outcomes remain the same .
the addition of ftcp to a dentifrice suitable for daily oral hygiene can enhance the ability of dentifrice fluoride to reduce dentine sensitivity . in the present study
twice daily brushing with clinpro tooth crme resulted in a similar reduction in dentine sensitivity to that achieved through brushing with a dentifrice containing kno3 + f ( sensodyne total care ) .
if clinpro tooth crme is used twice daily for brushing in combination with a nightly topical application , it can be more effective in reducing dentine sensitivity than twice daily brushing with sensodyne total care . | background . to assess the clinical efficacy of a dentifrice containing fluoride and functionalised tricalcium phosphate ( ftcp ) in reducing dentine sensitivity . methods . a 10-week parallel blind randomised control trial was conducted .
subjects were assigned to one of four groups and instructed to brush twice daily : a : colgate cavity protection ( 1000 ppmf - mfp ) ; b : sensodyne total care ( 1000 ppmf - naf + 19300 ppmk+-kno3 ) ; c : clinpro tooth crme ( 950 ppmf - naf + ftcp ) ; and d : clinpro tooth crme ( brushing + additional topical application ) .
seventy - one patients were assessed at baseline , 6 weeks , and 10 weeks for cold , tactile , and hypertonic sensitivity using the nrs-11 pain rating scale . a combined modalities sensitivity score ( cms ) was calculated . results . at 6 weeks , patients reported the following reduction in cms : a ( 20% ) ; b ( 30% ) ; c ( 42% ) ; d ( 52% ) . at 10 weeks , patients reported the following reduction in cms : a ( 18% ) , b ( 40% ) , c ( 24% ) , and d ( 54% ) .
the only cms comparisons to show a significant difference ( p < 0.05 ) were between groups a and d ( 6 and 10 weeks ) .
conclusions .
addition of ftcp to a dentifrice enhances the ability of dentifrice fluoride in reducing dentine sensitivity .
using clinpro tooth crme twice daily for brushing can be as effective to reduce dentine sensitivity as twice daily brushing using sensodyne total care
. however , additional nightly topical application of ftcp , in addition to twice daily brushing , showed an enhanced reduction in dentine sensitivity . | <s>[INST]dentine sensitivity is defined as short , sharp pain from exposed dentine in response to thermal , tactile , osmotic , or chemical stimuli that can not be ascribed to any other dental defect or disease .
clinically the presence of dentine sensitivity creates challenges for both patients and dental practitioners ; in addition to causing patient discomfort , dentine sensitivity can complicate the provision of restorative treatment and the treatment of periodontal tissues [ 3 , 4 ] .
dentine sensitivity is related to the exposure of dentine tubules resulting from either loss of tooth enamel or loss of periodontal tissue ( gingival recession ) [ 5 , 6 ] . for dentine sensitivity to be incited , dentine tubules must be open at the dentine surface as well as remaining patent to the dental pulp [ 6 , 7 ] . at the microscopic level dentine sensitivity
is currently still described by the hydrodynamic theory proposed by brannstrom [ 8 , 9 ] , which states that following dentine exposure to stimuli such as physical touch , temperature alteration , sweet liquid , and acidic liquid , changes in intratubular fluid movement and intratubular pressure occur .
these changes can cause activation of intratubular nerve fibres of pulpal origin ; this nerve excitation causes pain to be experienced [ 8 , 10 ] . to manage dentine sensitivity products
have been developed for at home use functioning primarily through two modalities : suppressing the excitability of intratubular nerve fibres or reducing the patency of exposed dentine tubules [ 2 , 11 , 12 ] .
when acting to suppress the excitability of nerve fibres within dentine tubules , the most common approach is to elevate the extracellular potassium concentration within the dental pulp .
this can be achieved through a patient applying a dentifrice containing potassium ions in a relatively soluble form to exposed dentine .
movement of potassium ions through patent dentinal tubules will act to raise the response threshold of pulpal nociceptors and reduce their ability to fire when provoked [ 13 , 14 ] .
when considering the effectiveness of agents that reduce dentine sensitivity through reduction in the patency of exposed dentine tubules , the most successful outcomes have been achieved through application of fluoride based gels to dentine [ 2 , 11 , 12 ] .
it is well documented that application of dentifrices containing stannous fluoride [ 1517 ] and sodium fluoride [ 1821 ] can promote the deposition of mineral precipitates within open dentinal tubules , thereby reducing fluid flow in dentine tubules following exposure to stimuli .
a dentifrice containing functionalised tricalcium phosphate and 950 ppm sodium fluoride has been shown to enable dentine tubule occlusion in vitro ; application of this dentifrice to extracted bovine teeth following ph cycling was observed to reduce both dentine tubule opening and tubule diameter in comparison to pretreatment levels .
this finding is notable , as not only there is limited data demonstrating that 1000 ppmf dentifrices can effectively reduce dentine sensitivity , but the availability of such a dentifrice could lower the cost and complexity of at home treatment undertaken by a patient suffering from dentine sensitivity , a dentifrice containing 1000 ppmf being appropriate for the control of dental caries in low caries risk patients [ 23 , 24 ] .
importantly , while assessment of the anticaries benefits of this dentifrice has been reported , no assessment of the efficacy of this dentifrice to reduce dentine sensitivity in vivo has taken place .
the aim of the present study was therefore to assess the effectiveness of a dentifrice containing 950 ppm fluoride and functionalised tricalcium phosphate ( ftcp ) in the reduction of dentine sensitivity in vivo .
the null hypothesis was that the effectiveness of the dentifrice containing ftcp and 950 ppm fluoride would not be different to the effectiveness of a dentifrice containing 1000 ppm fluoride in reducing dentine sensitivity .
the present study was a single centre , parallel group , blinded ( subjects and examiners ) randomised controlled clinical trial conducted at the westmead centre for oral health , westmead hospital , sydney , australia .
ethical approval from the western sydney local health network human research ethics committee was obtained prior to commencement of the study ( sac2010/11/4.6 ( 3223 ) hrec/10/wmead/202 ) and the trial was registered with the australia new zealand clinical trials register .
subjects included within the study were from the pool of patients eligible to receive treatment at the westmead centre for oral health . from this patient pool , during an initial off waiting list examination ,
eight hundred and fifty individuals indicated they suffered from dentine hypersensitivity and were willing to participate in the study .
of these 850 individuals a total of 71 subjects were recruited for the study having met the strict inclusion criteria . all subjects which participated in the study consented to participation prior to the inclusion . as part of the consent process
, patients were made aware of adverse effects of dentifrices , namely , abrasion and staining of hard and soft tissues and the detrimental sequelae of excessive fluoride ingestion . to be considered for this study ,
subjects were required to meet all of the following inclusion criteria : being aged between 18 and 70 years;demonstrating good general health with no history of chronic illness;possession of at least 2 teeth with an exposed root surface which are responsive on probing ( 50 g force ) or a 1 s duration cold air blast ( 70 psi ) ; these teeth were not to exhibit diagnosed caries , defective restorations , or signs of fracture on initial assessment ; these teeth were not to have had dental restorations , periodontal surgery , or orthodontics that has resulted in postoperative pain in the immediate past 3 months;a willingness to read , understand , and sign the consent form;a capability and willingness to brush teeth at least 2 times a day for 2 minutes on each occasion .
being aged between 18 and 70 years ; demonstrating good general health with no history of chronic illness ; possession of at least 2 teeth with an exposed root surface which are responsive on probing ( 50 g force ) or a 1 s duration cold air blast ( 70 psi ) ; these teeth were not to exhibit diagnosed caries , defective restorations , or signs of fracture on initial assessment ; these teeth were not to have had dental restorations , periodontal surgery , or orthodontics that has resulted in postoperative pain in the immediate past 3 months ; a willingness to read , understand , and sign the consent form ; a capability and willingness to brush teeth at least 2 times a day for 2 minutes on each occasion .
a subject was excluded from participation in the study if any of the following conditions applied : use of a desensitising agent in the 3 months prior to the study;undertaking regular medical treatment involving anti - inflammatory or analgesic use;being pregnant or nursing;exhibiting a known allergy to any ingredients in the examined dentifrices;suffering from conditions which could increase the level of acid within the oral cavity : bulimia , gastric reflux disease;excessive dietary exposure to acids ; lemons 2 times per day , raw tomatoes 2 times per day , acidic drinks 1 litre per day ( sports drinks , energy drinks , or fruit juice ) , wine 3 standard glasses per day;an inability to read the oral hygiene instructions provided to each participant . use of a desensitising agent in the 3 months prior to the study ; undertaking regular medical treatment involving anti - inflammatory or analgesic use ; being pregnant or nursing ; exhibiting a known allergy to any ingredients in the examined dentifrices ; suffering from conditions which could increase the level of acid within the oral cavity : bulimia , gastric reflux disease ; excessive dietary exposure to acids ; lemons 2 times per day , raw tomatoes 2 times per day , acidic drinks 1 litre per day ( sports drinks , energy drinks , or fruit juice ) , wine 3 standard glasses per day ; an inability to read the oral hygiene instructions provided to each participant . allocation of subjects to four study groups was randomised through use of a computer algorithm to limit the impact of age , gender , diet , and current level of oral hygiene on the study results .
group a. this group brushed teeth twice daily with a dentifrice containing 1000 ppm fluoride ions ( mfp ) : colgate cavity protection ( colgate - palmolive , new york , ny , usa , ) .
group b. this group brushed teeth twice daily with a dentifrice containing 1000 ppm fluoride ions ( naf ) + 19300 ppm potassium ions ( kno3 ) : sensodyne total care ( glaxosmithkline , sydney , nsw , australia ) .
group c. this group brushed teeth twice daily with a dentifrice containing ftcp and 950 ppm fluoride ions ( naf ) : clinpro tooth crme ( 3 m espe , st .
group d. this group brushed teeth twice daily with a dentifrice containing ftcp and 950 ppm fluoride ions ( naf ) : clinpro tooth crme ( 3 m espe , st .
paul , mn , usa ) and a directed pea sized topical application of clinpro tooth crme onto sensitive teeth before sleeping without rinsing . at no time during the trial were subjects made aware of what test group they belonged to or which product they were using ; all packaging was discarded prior to distribution and toothpaste tubes were wrapped in generic sticky white labelling . at the study commencement ,
all subjects were provided with a new toothbrush and dental floss and were given the same oral hygiene instructions verbally and as a take home pamphlet .
subjects were also provided with a two - minute timer in a bid to maintain strict and consistent adherence to the prescribed two - minute brushing time twice daily .
patients were assessed at three time points during the study : baseline , 6 weeks , and 10 weeks .
the clinical assessment was completed by three senior dental officers at westmead centre for oral health to limit the effect of clinician variation on study results .
standardisation was also maintained through each clinician recalibrating the process of stimulus provision to sensitive surfaces at the commencement of each assessment day .
examiners remained blinded to test groups to which participants belonged at all examination points throughout the study .
at each assessment , each sensitive tooth surface was exposed to three different stimuli that were applied directly onto the identified sensitive tooth .
the three stimuli included an air blast , tactile stimulation , and application of a hypertonic solution .
the identified tooth surface was exposed to air delivered from a standard dental unit triplex syringe from an operating distance of approximately 1 cm for a period of 1 s at an operating temperature of 21c ( 5c ) .
a pressure gauge was mounted to the dental unit and calibrated prior to each assessment day to ensure air was delivered at a standard pressure of 70 psi .
the identified tooth surface was stroked for 3 s using a standard dental explorer probe that was held perpendicular to the surface using a force of 50 g.
hypertonic solution .
a 70% hypertonic sucrose solution was applied to the identified tooth surface for 3 s. the solution was at room temperature at the time of application . following application of each stimulus patients
rated the pain / sensitivity experienced using an 11-point numbered pain rating scale ( nrs-11 ; figure 1 ) .
these scores were recorded on clinical test forms . following the 6-week examination patients returned the study dentifrice
wash - out period to elapse before reexamination at 10 weeks to quantify any prolonged actions of each test dentifrice ; 6-week usage of a dentifrice has been shown to provide sufficient time to allow maximum benefit of a desensitising product .
patient compliance in the use of the study dentifrice was established at the 6-week examination .
patients were asked to return products which were issued and each tube was weighed to calculate the total amount of toothpaste used over the 6-week period . for each test group
the mean pain score for each stimulus modality ( air blast , tactile , and hypertonic solution ) was calculated by patient and by tooth at each assessment point ( baseline , 6 weeks , and 10 weeks ) . additionally , the mean pain scores for each test group for each stimulus were combined and divided by 3 to give a total combined modalities sensitivity ( cms ) score at each assessment point .
the percentage change relative to baseline in mean pain score for each stimulus and the percentage change in cms relative to baseline were calculated for each test group .
ancova ( with baseline as the covariate ) with a tukey hsd post hoc test was used for between group comparisons .
of the 850 individuals from the westmead centre for oral health patient pool who indicated suffering from dentine sensitivity , 80 individuals satisfied the inclusion criteria .
these 80 individuals were randomly allocated to the four study groups ( a d ) .
the study population exhibited a mean age of 40.9 and a range of 1767 years of age .
seventy - one of the 80 subjects completed the 10-week clinical study and complied with the protocol given .
of the participants who completed the study , there were 54 females and 17 males .
no adverse soft tissue or hard tissue effects were observed by the assessing clinicians during the study ; however one participant withdrew from the study reporting an allergic reaction to colgate cavity protection .
the 9 patients that did not complete the study did so as they no longer wanted to attend the recall appointments on the basis of convenience .
at 6 weeks ( end of the treatment phase ) all groups showed a reduction in evaporative sensitivity score from baseline , with colgate cavity protection showing a 12% reduction , sensodyne total care a 19% reduction , clinpro tooth crme ( brushing only ) a 45% reduction , and clinpro tooth crme ( brushing + topical application ) showing a 43% reduction .
the reduction in evaporative sensitivity scores from base line of both clinpro tooth crme groups at 6 weeks was significantly greater ( p 0.05 , 95% ci ) than the reduction in evaporative sensitivity scores of both the positive control group ( sensodyne total care ) and the negative control group ( colgate cavity protection ) .
there was no significant difference ( p 0.05 , 95% ci ) in the reduction of evaporative sensitivity scores from baseline when comparing the sensodyne total care and colgate cavity protection groups at the end of the 6-week treatment phase ( tables 1 and 2 and figure 2 ) . at 10 weeks ( four weeks after cessation of treatment )
, all four groups demonstrated a reduction in evaporative sensitivity score from baseline , with colgate cavity protection showing a 18% reduction , sensodyne total care a 40% reduction , clinpro tooth crme ( brushing only ) a 24% reduction , and clinpro tooth crme ( brushing + topical application ) showing a 54% reduction .
the reduction in evaporative sensitivity scores at 10 weeks for clinpro tooth crme ( brushing + topical application ) and sensodyne total care was significantly greater ( p 0.05 , 95% ci ) than the reduction in evaporative sensitivity demonstrated by the negative control colgate cavity protection .
there was no significant difference ( p 0.05 , 95% ci ) in the reduction in evaporative sensitivity scores at 10 weeks from baseline when comparing groups using sensodyne total care , clinpro tooth crme ( brushing only ) , and clinpro tooth crme ( brushing + topical application ) . at 6 weeks ( end of the treatment phase )
all groups showed a reduction in tactile sensitivity from baseline , with colgate cavity protection showing a 20% reduction , sensodyne total care a 39% reduction , clinpro tooth crme ( brushing only ) a 44% reduction , and clinpro tooth crme ( brushing + topical application ) a 62% reduction . at 6 weeks the only group to show a significant reduction ( p 0.05 , 95% ci ) in tactile sensitivity scores in comparison to the negative control group ( colgate total protection ) was clinpro tooth crme ( brushing + topical application ) .
there were no other comparisons that displayed significantly different sensitivity scores ; both clinpro tooth crme groups were not significantly different ( p 0.05 , 95% ci ) from the positive control group , sensodyne total care ( tables 1 and 2 and figure 3 ) . at 10 weeks ( four weeks after cessation of treatment ) , not all groups showed a reduction in tactile sensitivity from baseline , with colgate cavity protection showing a 6% increase in sensitivity .
however , sensodyne total care showed a 37% reduction in tactile sensitivity , clinpro tooth crme ( brushing only ) a 14% reduction , and clinpro tooth crme ( brushing + topical application ) a 64% reduction from baseline . a significant reduction ( p 0.05 , 95% ci ) in tactile sensitivity at 10 weeks from baseline for clinpro tooth crme ( brushing + topical application ) and sensodyne total care in comparison to colgate cavity protection was observed .
no significant difference ( p 0.05 , 95% ci ) in the reduction in tactile sensitivity scores from baseline to 10 weeks was observed between clinpro tooth crme ( brushing only ) and sensodyne total care .
additionally , no significant difference ( p 0.05 , 95% ci ) in tactile sensitivity score reduction at 10 weeks was observed between clinpro tooth crme ( brushing only ) and colgate cavity protection ( tables 1 and 2 and figure 3 ) . at 6 weeks
all groups exhibited a reduction in hypertonic sensitivity from baseline , with colgate cavity protection showing a 32% reduction , sensodyne total care a 41% reduction , clinpro tooth crme ( brushing only ) a 40% reduction , and clinpro tooth crme ( brushing + topical application ) showing a 61% reduction . at 6 weeks the difference in % reduction from baseline was not significant ( p 0.05 , 95% ci ) for any of the four groups ( tables 1 and 2 and figure 4 ) . at 10 weeks
, all groups exhibited a reduction in hypertonic sensitivity from baseline , with colgate cavity protection showing a 42% reduction , sensodyne total care a 56% reduction , clinpro tooth crme ( brushing only ) a 22% reduction , and clinpro tooth crme ( brushing + topical application ) showing a 66% reduction .
the only groups to exhibit a significant difference ( p 0.05 , 95% ci ) in hypertonic sensitivity reduction at 10 weeks compared to baseline were sensodyne total care and clinpro tooth crme ( brushing + topical application ) .
there was no significant difference ( p 0.05 , 95% ci ) in hypertonic sensitivity reduction at 10 weeks between the groups using colgate cavity protection , sensodyne total care , and clinpro tooth crme ( brushing + topical application ) ( tables 1 and 2 and figure 4 ) . at 6 weeks ( end of the treatment phase )
all groups exhibited a reduction in the combined sensitivity score ( cms ) from baseline , with colgate cavity protection showing a 20% reduction , sensodyne total care a 30% reduction , clinpro tooth crme ( brushing only ) a 42% , and clinpro tooth crme ( brushing + topical application ) showing a 52% reduction . at the end of the 6-week treatment phase , both clinpro tooth crme study groups showed a significant reduction ( p 0.05 , 95% ci ) in cms when compared to the negative control group using colgate cavity protection .
clinpro tooth crme when used with an additional topical application also demonstrated a significant reduction ( p 0.05 , 95% ci ) in dentine sensitivity compared to the positive control , sensodyne total care , after 6 weeks ( tables 1 and 2 and figure 5 ) . at 10 weeks ( 4 weeks after cessation of treatment ) , all groups showed a reduction in combined sensitivity score ( cms ) from baseline , with colgate cavity protection showing an 18% reduction , sensodyne total care a 40% reduction , clinpro tooth crme ( brushing only ) a 24% reduction , and clinpro tooth crme ( brushing + topical application ) a 54% reduction .
the reduction in cms for clinpro tooth crme ( brushing + topical application ) and sensodyne total care was significantly greater ( p 0.05 , 95% ci ) than the reduction in cms from baseline of the negative control colgate cavity protection at four weeks after cessation of treatment .
there was no significant difference ( p 0.05 , 95% ci ) in cms reduction from baseline to 10 weeks between groups using sensodyne total care , clinpro tooth crme ( brushing only ) , and clinpro tooth crme ( brushing + topical application ) ( tables 1 and 2 and figure 5 ) .
the ability for fluoride ions sourced from a dentifrice to form fluoride - calcium precipitates that occlude dentine tubules with the consequence of reducing dentine sensitivity is well documented [ 1821 , 27 , 28 ] .
this ability occurs due to the negative electric charge of fluoride ions , which results in their binding with calcium cations .
once bound to calcium cations present within a dentifrice the fluoride ions are rendered incapable of combining with cations present at the tooth surface . to overcome the effect of reduced fluoride ion availability at the tooth surface caused by intradentifrice fluoride - calcium bonding
, dentifrice manufacturers have traditionally acted to increase the concentration of fluoride ions within a dentifrice . in recent times , however , altering the chemical structure of calcium complexes within a dentifrice to reduce the bonding affinity between calcium cations and fluoride anions has been undertaken as an alternative solution to simple fluoride ion concentration increase .
one such example of this has been the development and incorporation of altered calcium phosphate complexes , such as functionalised tricalcium phosphate , which is currently incorporated within clinpro tooth crme . functionalised tricalcium phosphate ( ftcp ) is produced through beta tricalcium phosphate ( tcp ) complexes being milled with sodium lauryl sulfate ( sls ) .
the tcp crystal structure exhibits several reactive sites including calcium - oxygen clusters ( cao3 , cao7 , and cao8 ) and lattice defects .
these reactive sites are available to undergo chemical interaction with anions such as fluoride ions . to reduce the reactivity of these sites within b - tcp complexes
the incorporation of sls within the tcp structure therefore impedes fluoride ions from combining with calcium ions in the dentifrice , so in turn potentially increasing the concentration of both calcium and fluoride to tooth surfaces .
[ 25 , 3234 ] have reported a synergistic relationship between ftcp and fluoride with regard to enamel remineralisation ; enamel that is remineralised through a fluoride / ftcp combination demonstrates significantly greater surface and subsurface rehardening following ph cycling compared to that achieved by fluoride application alone .
notably , the results of the present study suggest that this remineralisation synergy between fluoride and ftcp may also produce a benefit in terms of enhancing dentine tubule occlusion ; the two test groups that utilised clinpro tooth crme ( 950 ppm f ) demonstrated a greater level of sensitivity relief for all stimuli except the hypertonic test at 10 weeks ( group c ) in comparison to the group using colgate total , despite the fact that colgate total contains a greater concentration of fluoride ions ( 1000 ppm f ) .
previous microscopic analysis showing the ability of clinpro tooth crme to reduce the diameter of tubule openings following ph cycling to a greater degree than sensodyne nupro 5000 and topex renew supports this possibility . within the present study a greater reduction in dentine sensitivity
was observed when an additional topical application of clinpro tooth crme was placed to supplement application provided through brushing alone .
this finding is in contrast to reports in the literature stating that there is no evidence to suggest that additional topical application increases the effectiveness of a desensitizing dentifrice .
first an intentional topical application of a dentifrice potentially allows a greater concentration of fluoride ions to be applied to a tooth surface in comparison to that applied through unintentional brushing alone .
secondly , through an additional topical application , fluoride ions can remain at a sensitive surface for a longer duration than following brushing and rinsing and thirdly through increasing the duration of fluoride ion presence upon a sensitive surface , the propensity for fluoride migration and tubule occlusion is raised .
the greater success of clinpro tooth crme when applied as an additional topical application rather than brushing alone may also be a result of greater salivary fluoride concentration as a by - product of topical application and no rinsing following application .
this possibility is consistent with studies that have examined the effect of patient activity following dentifrice application on the level of salivary fluoride .
nordstrm and birkhed determined that a topical application of dentifrice to a tooth surface combined with regular brushing resulted in a greater concentration of salivary fluoride than when compared to brushing alone .
sjgren and melin identified that a single post - brushing rinse with fluoridated water decreased fluoride concentration by a factor of two when compared to no rinsing , while rinsing with fluoridated water two times following brushing decreased salivary concentration by a factor of 5 when compared to no rinsing .
the reduction in cms of the negative control group over the study duration can be in part attributed to the placebo effect which is well documented in dentine sensitivity studies [ 7 , 38 , 39 ] .
additionally the hawthorne effect , which describes a positive response to noninterventional treatment , should also be assumed to have had some impact on the study results . improved oral hygiene in patients enrolled in the study
could have also reduced perceived dentine sensitivity across all groups as a reduction in tooth surface plaque facilitated increased dentifrice access to dentine tubules .
these reasons may also account for the antihypersensitivity effects continuing for the month following the cessation of the use of the treatment dentifrices .
an identified limitation of the study was the numbers of patients enrolled in each study group . due to the breadth of the potential patient pool , patients eligible for treatment at westmead centre for oral health ,
it was anticipated that including 40 subjects per group would be an achievable goal over a 3-year study period . as a result of the very strict exclusion criteria , especially the requirement that the use of a desensitising agent in the 3 months prior to the study excluded an individual from being a subject , patient recruitment was extremely difficult .
however despite the smaller numbers than originally forecast per group , the results of the present study provide useful information . not only are the numbers sufficient to demonstrate statistical significance , but when tooth number rather than patient number is used for analysis the subject number exceeds 50 for each group and the statistical outcomes remain the same .
the addition of ftcp to a dentifrice suitable for daily oral hygiene can enhance the ability of dentifrice fluoride to reduce dentine sensitivity . in the present study
twice daily brushing with clinpro tooth crme resulted in a similar reduction in dentine sensitivity to that achieved through brushing with a dentifrice containing kno3 + f ( sensodyne total care ) .
if clinpro tooth crme is used twice daily for brushing in combination with a nightly topical application , it can be more effective in reducing dentine sensitivity than twice daily brushing with sensodyne total care .[/INST]background . to assess the clinical efficacy of a dentifrice containing fluoride and functionalised tricalcium phosphate ( ftcp ) in reducing dentine sensitivity . methods . a 10-week parallel blind randomised control trial was conducted .
subjects were assigned to one of four groups and instructed to brush twice daily : a : colgate cavity protection ( 1000 ppmf - mfp ) ; b : sensodyne total care ( 1000 ppmf - naf + 19300 ppmk+-kno3 ) ; c : clinpro tooth crme ( 950 ppmf - naf + ftcp ) ; and d : clinpro tooth crme ( brushing + additional topical application ) .
seventy - one patients were assessed at baseline , 6 weeks , and 10 weeks for cold , tactile , and hypertonic sensitivity using the nrs-11 pain rating scale . a combined modalities sensitivity score ( cms ) was calculated . results . at 6 weeks , patients reported the following reduction in cms : a ( 20% ) ; b ( 30% ) ; c ( 42% ) ; d ( 52% ) . at 10 weeks , patients reported the following reduction in cms : a ( 18% ) , b ( 40% ) , c ( 24% ) , and d ( 54% ) .
the only cms comparisons to show a significant difference ( p < 0.05 ) were between groups a and d ( 6 and 10 weeks ) .
conclusions .
addition of ftcp to a dentifrice enhances the ability of dentifrice fluoride in reducing dentine sensitivity .
using clinpro tooth crme twice daily for brushing can be as effective to reduce dentine sensitivity as twice daily brushing using sensodyne total care
. however , additional nightly topical application of ftcp , in addition to twice daily brushing , showed an enhanced reduction in dentine sensitivity .</s> |
high-@xmath1 jet production and other hard processes are considered as a one of the most promising tools for studying properties of super - dense and hot matter created in nucleus - nucleus collisions at rhic and lhc .
the challenging problem here is the behaviour of colour charge in quark - gluon matter associated with the coherence pattern of the medium - induced radiation , resulting in a number of interesting non - linear phenomena , in particular , the dependence of radiative energy loss per unit distance @xmath2 along the total distance traversed ( see review @xcite and references therein ) . in our previous work @xcite we predicted that medium - induced parton rescattering and energy loss should result in a dramatic change in the distribution of jets over impact parameter as compared to what is expected from independent nucleon - nucleon interactions pattern . in this paper we concentrate on the phenomena related to the azimuthal dependence of jet energy loss and corresponding jet spectra in semi - central heavy ion collisions at lhc energies , when the cross section for hard jet production at @xmath3 gev scale is large enough to study the impact parameter dependence of such processes .
we consider the experimental conditions of cms experiment at lhc @xcite , which can provide jet reconstruction and adequate measurement of impact parameter of nuclear collision using calorimetric information @xcite .
note that the possible azimuthal anisotropy of high-@xmath1 hadron spectra at rhic was discussed in a number of papers @xcite .
the details of geometrical model of jet production and jet passing through a dense matter in high energy symmetric nucleus - nucleus collision can be found in @xcite .
the figure 1 shows the essence of the problem in the plane of impact parameter * b * of two colliding nuclei @xmath4-@xmath4 .
the initial distribution over jet production vertex @xmath5 in nuclear overlap zone at given impact parameter @xmath6 is written as @xmath7 where @xmath8 is the vector from beam axis @xmath9 to vertex @xmath10 ; @xmath11 is the distance between nucleus centers ( @xmath12 ) and vertex @xmath10 ; @xmath13 and @xmath14 are the standard nuclear overlap and nuclear thickness functions respectively .
the basic kinetic integral equation for the energy loss @xmath15 as a function of initial energy @xmath16 and path length @xmath17 has the form @xmath18 where @xmath19 is the current transverse coordinate of a parton , @xmath20 is the scattering probability density , @xmath2 is the energy loss per unit length , @xmath21 is in - medium mean free path , @xmath22 is medium density at temperature @xmath23 , @xmath24 is the integral cross section of parton interaction in the medium .
it is straightforward to evaluate the time @xmath25 it takes for jet to traverse the dense zone : @xmath26 where @xmath27 is the isotropically distributed angle which determines the direction of a jet relatively to vector @xmath28 , @xmath29 is the azimuthal angle between the direction of a jet motion and vector @xmath30 , @xmath31 is angle between vectors @xmath28 and @xmath32 .
one can see from eq.([taul ] ) that for non - central collisions , @xmath33 , value @xmath34 depends on @xmath29 : it is maximum at @xmath35 and minimum at @xmath36 ( see fig.2 for pb@xmath0pb collisions and impact parameters values @xmath37 , @xmath38 and @xmath39 fm ) .
since energy loss is increasing function of jet in - medium path - length , it will then depends on @xmath29 also . in order to illustrate the azimuthal anisotropy of parton energy loss
, we treat the medium as a boost - invariant longitudinally expanding quark - gluon fluid , and partons as being produced on a hyper - surface of equal proper times @xmath40 @xcite . for certainty
we used the initial conditions for the gluon - dominated plasma formation expected for central @xmath41 collisions at lhc @xcite : @xmath42
fm / c , @xmath43 gev , @xmath44 , @xmath45 . for non - central collisions
we suggest the proportionality of the initial energy density @xmath46 to the ratio of nuclear overlap function @xmath13 and effective transverse area @xmath47 of nuclear overlapping , @xmath48 @xcite .
our approach relies on an accumulative energy losses , when gluon radiation is associated with each scattering in expanding medium together including the interference effect by the modified radiation spectrum as a function of decreasing temperature @xmath49 . for our calculations we have used collisional
part of loss and differential scattering cross section from our work @xcite ; the energy spectrum of coherent medium - induced gluon radiation was estimated using bdms formalism @xcite .
it is important to notice that the coherent lpm radiation induces a strong dependence of the jet energy on the jet cone size @xcite , while the collisional energy loss turns out to be practically independent on cone size , because the bulk of `` thermal '' particles knocked out of the dense matter by elastic scatterings fly away in almost transverse direction relative to the jet axis @xcite .
figure 3 shows the average value of medium - induced radiative ( a ) and collisional ( b ) energy loss of quark with initial transverse energy @xmath50 gev as a function of @xmath29 .
as it might be expected , azimuthal anisotropy of energy loss goes up with increasing @xmath6 , because azimuthal asymmetry of the volume gets stronger in this case . on the other hand ,
the absolute value of energy loss , of course , goes down with increasing @xmath6 due to reducing absolute value of mean distance traversed ( and also due to decreasing initial energy density of the medium at @xmath51 ) .
then the non - uniform dependence of energy loss on azimuthal angle results in azimuthal anisotropy of jet spectra in semi - central collisions .
figure 4 shows the distribution of jets over azimuthal angle @xmath52 for the cases with collisional and radiative loss ( a ) and collisional loss only ( b ) for @xmath37 , @xmath38 and @xmath39 fm ( the initial jet distributions have been generated using pytha@xmath53 model @xcite ) .
the cms kinematical acceptance for jets was taken into account : @xmath54 gev , @xmath55 .
the distributions are normalized on the initial distributions of jets over @xmath29 in pb@xmath0pb collisions ( without any energy loss ) .
we can see that the azimuthal anisotropy gets stronger as going from central to semi - central collisions , but the absolute suppression factor reduces with increasing @xmath6 . for jets with finite cone size one can expect the intermediate result between cases ( a ) and ( b ) , because , as we have mentioned before , radiative loss dominates at relatively small angular sizes of jet cone @xmath56 , while the relative contribution of collisional loss grows with increasing @xmath57 . in non - central collisions the jet distribution over @xmath29
is approximated well by the following form , @xmath58 , where @xmath59 and @xmath60 .
the average cosines of @xmath61 for particle flow is called as coefficient of azimuthal anisotropy @xmath62 @xcite . in our model
the coefficient of jet azimuthal anisotropy increases almost linearly with growth of @xmath6 and becomes maximum at @xmath63 , after that it reduces rapidly with increasing @xmath6 ( the domain of impact parameter values , where the effect of decreasing energy loss due to reducing effective transverse size of dense zone and initial energy density of the medium is crucial and not compensated anymore by stronger non - symmetry of the volume ) .
other important feature is the jet azimuthal anisotropy decreases with increasing jet energy , because the energy dependence of medium - induced loss is rather weak @xcite . in conclusion of this section
we remark , that the methodical advantage of azimuthal jet observables is obvious : one needs to reconstruct only azimuthal position of jet , but not the total jet energy .
it can be done more easily and with high accuracy , while the reconstruction of the jet energy is more ambiguous task @xcite . on the other hand , the performance of inclusive analysis of jet production as a function of azimuthal angle requires event - by - event determination of the reaction plane angle . summarized in papers
@xcite present methods of determination of the reaction plane angle are applied to study elliptic flow of soft particles in current heavy ion dedicated experiments at sps and rhic .
the capability of cms tracker to reconstruct momenta of all semi - hard ( @xmath64gev@xmath65 ) , and especially soft ( @xmath66gev@xmath65 ) charged particles is not clear at the moment .
however the transverse energy flow in central cms calorimeters should reflect the pattern of semi - hard particles flow , in particular , including any azimuthal anisotropy manifestation .
thus the determination of nuclear reaction plane angle using semi - hard particles flow ( not incorporated in high-@xmath1 jet pair ) could be , in principle , possible due to two factors : ( _ 1 _ ) sensitivity of semi - hard particles to the azimuthal asymmetry of reaction volume under condition that the most part of them being the products of in - medium radiated gluons @xcite ; ( _ 2 _ ) predicted high enough multiplicity of such particles at lhc energies ( which is comparable , for example , with the total multiplicity at sps ) .
the interesting phenomenon is predicted to be observed in semi - central heavy ion collisions at lhc : the appearance of azimuthal anisotropy of jet spectra due to energy loss of jet partons in azimuthally non - symmetric volume of dense quark - gluon matter , created initially in nuclear overlap zone .
we have found that the coefficient of jet azimuthal anisotropy increases almost linearly with growth of @xmath6 up to @xmath63 fm .
the effect of jet azimuthal anisotropy decreases slightly with jet energy .
the methodical advantage of azimuthal jet observables is that one needs to reconstruct only azimuthal position of jet , but not the total jet energy . on the other hand , the performance of inclusive analysis of jet production as a function of azimuthal angle requires event - by - event determination of the reaction plane angle .
we suggest that under lhc conditions the existing methods of determination of nuclear reaction plane angle might be applied with measuring the azimuthal anisotropy of global transverse energy flow originated from mini - jet production in non - symmetric volume of dense qcd - medium .
_ acknowledgements _ discussions with m. bedjidian , d. denegri , p. filip , v. uzhinskii and u. wiedemann are gratefully acknowledged .
i. lokhtin thanks the organizers of fourth international conference `` physics and astrophysics of quark - gluon plasma '' for the warm welcome and stimulating atmosphere .
99 r. baier , d. schiff and b.g .
zakharov , annual rev .
nucl . part .
50 , 37 ( 2000 ) i.p .
lokhtin and a.m. snigirev , eur .
j. c16 , 527 ( 2000 ) cms collaboration , technical proposal , cern / lhcc 94 - 38 m. bedjidian et al . , heavy ion physics programme in cms " , cern cms note 2000/060 , eur . phys .
j. c , in press a.s . galoyan and v.v .
uzhinskii , e - print hep - ph/0007122 x .- n .
wang , phys .
c 63 , 054902 ( 2001 ) m. gyulassy , i. vitev and x .-
wang , phys .
86 , 2537 ( 2001 ) j.d .
bjorken , phys .
d27 , 140 ( 1983 ) k.j .
eskola , k. kajantie and p.v .
ruuskanen , phys .
b332 , 191 ( 1994 ) ; k.j.eskola , prog .
129 , 1 ( 1997 ) ; comments nucl .
22 , 185 ( 1998 ) r. baier , yu . l. dokshitzer , a.h .
mueller and d. schiff , nucl .
b531 , 403 ( 1998 ) ; phys .
c58 , 1706 ( 1998 ) i.p . lokhtin and a.m. snigirev ,
b440 , 163 ( 1998 ) u. wiedemann , nucl .
b 588 , 303 ( 2000 ) ; nucl .
a 690 , 731 ( 2001 ) m. gyulassy , p. levai and i. vitev , nucl .
b 571 , 197 ( 2000 ) ; phys
85 , 5535 ( 2000 ) ; nucl .
b 594 , 371 ( 2001 ) t. sjostrand , comp . phys . com .
82 , 74 ( 1994 ) s. voloshin and y. zhang , z. phys .
c 70 , 665 ( 1996 ) ; a.m. poskanzer and s.a .
voloshin , phys .
c 58 , 1671 ( 1998 ) | we analyze the azimuthal anisotropy of jet spectra due to energy loss of hard partons in quark - gluon plasma , created initially in nuclear overlap zone in collisions with non - zero impact parameter .
the calculations are performed for semi - central pb@xmath0pb collisions at lhc energy .
-2.0 cm -2.0 cm # 1#23.6pt * azimuthal anisotropy of jet quenching at lhc * + , s.v .
petrushanko , l.i .
sarycheva and a.m. snigirev + m.v.lomonosov moscow state university , d.v.skobeltsyn institute of nuclear physics + 119899 , vorobievy gory , moscow , russia + | <s>[INST]high-@xmath1 jet production and other hard processes are considered as a one of the most promising tools for studying properties of super - dense and hot matter created in nucleus - nucleus collisions at rhic and lhc .
the challenging problem here is the behaviour of colour charge in quark - gluon matter associated with the coherence pattern of the medium - induced radiation , resulting in a number of interesting non - linear phenomena , in particular , the dependence of radiative energy loss per unit distance @xmath2 along the total distance traversed ( see review @xcite and references therein ) . in our previous work @xcite we predicted that medium - induced parton rescattering and energy loss should result in a dramatic change in the distribution of jets over impact parameter as compared to what is expected from independent nucleon - nucleon interactions pattern . in this paper we concentrate on the phenomena related to the azimuthal dependence of jet energy loss and corresponding jet spectra in semi - central heavy ion collisions at lhc energies , when the cross section for hard jet production at @xmath3 gev scale is large enough to study the impact parameter dependence of such processes .
we consider the experimental conditions of cms experiment at lhc @xcite , which can provide jet reconstruction and adequate measurement of impact parameter of nuclear collision using calorimetric information @xcite .
note that the possible azimuthal anisotropy of high-@xmath1 hadron spectra at rhic was discussed in a number of papers @xcite .
the details of geometrical model of jet production and jet passing through a dense matter in high energy symmetric nucleus - nucleus collision can be found in @xcite .
the figure 1 shows the essence of the problem in the plane of impact parameter * b * of two colliding nuclei @xmath4-@xmath4 .
the initial distribution over jet production vertex @xmath5 in nuclear overlap zone at given impact parameter @xmath6 is written as @xmath7 where @xmath8 is the vector from beam axis @xmath9 to vertex @xmath10 ; @xmath11 is the distance between nucleus centers ( @xmath12 ) and vertex @xmath10 ; @xmath13 and @xmath14 are the standard nuclear overlap and nuclear thickness functions respectively .
the basic kinetic integral equation for the energy loss @xmath15 as a function of initial energy @xmath16 and path length @xmath17 has the form @xmath18 where @xmath19 is the current transverse coordinate of a parton , @xmath20 is the scattering probability density , @xmath2 is the energy loss per unit length , @xmath21 is in - medium mean free path , @xmath22 is medium density at temperature @xmath23 , @xmath24 is the integral cross section of parton interaction in the medium .
it is straightforward to evaluate the time @xmath25 it takes for jet to traverse the dense zone : @xmath26 where @xmath27 is the isotropically distributed angle which determines the direction of a jet relatively to vector @xmath28 , @xmath29 is the azimuthal angle between the direction of a jet motion and vector @xmath30 , @xmath31 is angle between vectors @xmath28 and @xmath32 .
one can see from eq.([taul ] ) that for non - central collisions , @xmath33 , value @xmath34 depends on @xmath29 : it is maximum at @xmath35 and minimum at @xmath36 ( see fig.2 for pb@xmath0pb collisions and impact parameters values @xmath37 , @xmath38 and @xmath39 fm ) .
since energy loss is increasing function of jet in - medium path - length , it will then depends on @xmath29 also . in order to illustrate the azimuthal anisotropy of parton energy loss
, we treat the medium as a boost - invariant longitudinally expanding quark - gluon fluid , and partons as being produced on a hyper - surface of equal proper times @xmath40 @xcite . for certainty
we used the initial conditions for the gluon - dominated plasma formation expected for central @xmath41 collisions at lhc @xcite : @xmath42
fm / c , @xmath43 gev , @xmath44 , @xmath45 . for non - central collisions
we suggest the proportionality of the initial energy density @xmath46 to the ratio of nuclear overlap function @xmath13 and effective transverse area @xmath47 of nuclear overlapping , @xmath48 @xcite .
our approach relies on an accumulative energy losses , when gluon radiation is associated with each scattering in expanding medium together including the interference effect by the modified radiation spectrum as a function of decreasing temperature @xmath49 . for our calculations we have used collisional
part of loss and differential scattering cross section from our work @xcite ; the energy spectrum of coherent medium - induced gluon radiation was estimated using bdms formalism @xcite .
it is important to notice that the coherent lpm radiation induces a strong dependence of the jet energy on the jet cone size @xcite , while the collisional energy loss turns out to be practically independent on cone size , because the bulk of `` thermal '' particles knocked out of the dense matter by elastic scatterings fly away in almost transverse direction relative to the jet axis @xcite .
figure 3 shows the average value of medium - induced radiative ( a ) and collisional ( b ) energy loss of quark with initial transverse energy @xmath50 gev as a function of @xmath29 .
as it might be expected , azimuthal anisotropy of energy loss goes up with increasing @xmath6 , because azimuthal asymmetry of the volume gets stronger in this case . on the other hand ,
the absolute value of energy loss , of course , goes down with increasing @xmath6 due to reducing absolute value of mean distance traversed ( and also due to decreasing initial energy density of the medium at @xmath51 ) .
then the non - uniform dependence of energy loss on azimuthal angle results in azimuthal anisotropy of jet spectra in semi - central collisions .
figure 4 shows the distribution of jets over azimuthal angle @xmath52 for the cases with collisional and radiative loss ( a ) and collisional loss only ( b ) for @xmath37 , @xmath38 and @xmath39 fm ( the initial jet distributions have been generated using pytha@xmath53 model @xcite ) .
the cms kinematical acceptance for jets was taken into account : @xmath54 gev , @xmath55 .
the distributions are normalized on the initial distributions of jets over @xmath29 in pb@xmath0pb collisions ( without any energy loss ) .
we can see that the azimuthal anisotropy gets stronger as going from central to semi - central collisions , but the absolute suppression factor reduces with increasing @xmath6 . for jets with finite cone size one can expect the intermediate result between cases ( a ) and ( b ) , because , as we have mentioned before , radiative loss dominates at relatively small angular sizes of jet cone @xmath56 , while the relative contribution of collisional loss grows with increasing @xmath57 . in non - central collisions the jet distribution over @xmath29
is approximated well by the following form , @xmath58 , where @xmath59 and @xmath60 .
the average cosines of @xmath61 for particle flow is called as coefficient of azimuthal anisotropy @xmath62 @xcite . in our model
the coefficient of jet azimuthal anisotropy increases almost linearly with growth of @xmath6 and becomes maximum at @xmath63 , after that it reduces rapidly with increasing @xmath6 ( the domain of impact parameter values , where the effect of decreasing energy loss due to reducing effective transverse size of dense zone and initial energy density of the medium is crucial and not compensated anymore by stronger non - symmetry of the volume ) .
other important feature is the jet azimuthal anisotropy decreases with increasing jet energy , because the energy dependence of medium - induced loss is rather weak @xcite . in conclusion of this section
we remark , that the methodical advantage of azimuthal jet observables is obvious : one needs to reconstruct only azimuthal position of jet , but not the total jet energy .
it can be done more easily and with high accuracy , while the reconstruction of the jet energy is more ambiguous task @xcite . on the other hand , the performance of inclusive analysis of jet production as a function of azimuthal angle requires event - by - event determination of the reaction plane angle . summarized in papers
@xcite present methods of determination of the reaction plane angle are applied to study elliptic flow of soft particles in current heavy ion dedicated experiments at sps and rhic .
the capability of cms tracker to reconstruct momenta of all semi - hard ( @xmath64gev@xmath65 ) , and especially soft ( @xmath66gev@xmath65 ) charged particles is not clear at the moment .
however the transverse energy flow in central cms calorimeters should reflect the pattern of semi - hard particles flow , in particular , including any azimuthal anisotropy manifestation .
thus the determination of nuclear reaction plane angle using semi - hard particles flow ( not incorporated in high-@xmath1 jet pair ) could be , in principle , possible due to two factors : ( _ 1 _ ) sensitivity of semi - hard particles to the azimuthal asymmetry of reaction volume under condition that the most part of them being the products of in - medium radiated gluons @xcite ; ( _ 2 _ ) predicted high enough multiplicity of such particles at lhc energies ( which is comparable , for example , with the total multiplicity at sps ) .
the interesting phenomenon is predicted to be observed in semi - central heavy ion collisions at lhc : the appearance of azimuthal anisotropy of jet spectra due to energy loss of jet partons in azimuthally non - symmetric volume of dense quark - gluon matter , created initially in nuclear overlap zone .
we have found that the coefficient of jet azimuthal anisotropy increases almost linearly with growth of @xmath6 up to @xmath63 fm .
the effect of jet azimuthal anisotropy decreases slightly with jet energy .
the methodical advantage of azimuthal jet observables is that one needs to reconstruct only azimuthal position of jet , but not the total jet energy . on the other hand , the performance of inclusive analysis of jet production as a function of azimuthal angle requires event - by - event determination of the reaction plane angle .
we suggest that under lhc conditions the existing methods of determination of nuclear reaction plane angle might be applied with measuring the azimuthal anisotropy of global transverse energy flow originated from mini - jet production in non - symmetric volume of dense qcd - medium .
_ acknowledgements _ discussions with m. bedjidian , d. denegri , p. filip , v. uzhinskii and u. wiedemann are gratefully acknowledged .
i. lokhtin thanks the organizers of fourth international conference `` physics and astrophysics of quark - gluon plasma '' for the warm welcome and stimulating atmosphere .
99 r. baier , d. schiff and b.g .
zakharov , annual rev .
nucl . part .
50 , 37 ( 2000 ) i.p .
lokhtin and a.m. snigirev , eur .
j. c16 , 527 ( 2000 ) cms collaboration , technical proposal , cern / lhcc 94 - 38 m. bedjidian et al . , heavy ion physics programme in cms " , cern cms note 2000/060 , eur . phys .
j. c , in press a.s . galoyan and v.v .
uzhinskii , e - print hep - ph/0007122 x .- n .
wang , phys .
c 63 , 054902 ( 2001 ) m. gyulassy , i. vitev and x .-
wang , phys .
86 , 2537 ( 2001 ) j.d .
bjorken , phys .
d27 , 140 ( 1983 ) k.j .
eskola , k. kajantie and p.v .
ruuskanen , phys .
b332 , 191 ( 1994 ) ; k.j.eskola , prog .
129 , 1 ( 1997 ) ; comments nucl .
22 , 185 ( 1998 ) r. baier , yu . l. dokshitzer , a.h .
mueller and d. schiff , nucl .
b531 , 403 ( 1998 ) ; phys .
c58 , 1706 ( 1998 ) i.p . lokhtin and a.m. snigirev ,
b440 , 163 ( 1998 ) u. wiedemann , nucl .
b 588 , 303 ( 2000 ) ; nucl .
a 690 , 731 ( 2001 ) m. gyulassy , p. levai and i. vitev , nucl .
b 571 , 197 ( 2000 ) ; phys
85 , 5535 ( 2000 ) ; nucl .
b 594 , 371 ( 2001 ) t. sjostrand , comp . phys . com .
82 , 74 ( 1994 ) s. voloshin and y. zhang , z. phys .
c 70 , 665 ( 1996 ) ; a.m. poskanzer and s.a .
voloshin , phys .
c 58 , 1671 ( 1998 )[/INST] we analyze the azimuthal anisotropy of jet spectra due to energy loss of hard partons in quark - gluon plasma , created initially in nuclear overlap zone in collisions with non - zero impact parameter .
the calculations are performed for semi - central pb@xmath0pb collisions at lhc energy .
-2.0 cm -2.0 cm # 1#23.6pt * azimuthal anisotropy of jet quenching at lhc * + , s.v .
petrushanko , l.i .
sarycheva and a.m. snigirev + m.v.lomonosov moscow state university , d.v.skobeltsyn institute of nuclear physics + 119899 , vorobievy gory , moscow , russia + </s> |
the quest for the realization of different topological states of matter marks one of the major challenges in quantum many - body physics . a well established concept for the generation of two - dimensional topologically ordered
states exhibiting anyonic excitations are flat bands characterized by a topological invariant in combination with strong interactions @xcite .
the prime example is the fractional quantum hall effect , where strong magnetic fields generate landau levels @xcite .
furthermore , lattice models without landau levels have been proposed for the realization of topological bands @xcite .
notably , spin - orbit coupling has emerged as an experimentally promising tool for band structures with topological invariants @xcite . in this letter , we show that dipolar interactions , exhibiting intrinsic spin - orbit coupling , can be exploited for the realization of topological bands with cold polar molecules . in cold gases experiments , the phenomenon that dipolar interactions exhibit
spin - orbit coupling is at the heart of demagnetization cooling @xcite , and has been identified as the driving mechanism for the einstein - de haas effect in bose - einstein condensates @xcite and the pattern formation in spinor condensates @xcite .
dipolar relaxation was proposed as a mechanism to reach the quantum hall regime by the controlled insertion of orbital angular momentum @xcite .
recently , it has been pointed out that dipolar spin - orbit coupling can be observed in band structures realized with polar molecules @xcite .
these ideas are motivated by the experimental success in cooling and trapping polar molecules in optical lattices @xcite .
( a ) setup : each lattice site of a two - dimensional optical lattice is occupied by a single polar molecule .
the molecules can be excited into two different rotational states .
dipole - dipole interactions induce long - range tunneling links for the excitations .
( b ) rotational level structure of each molecule with applied electric field and additional microwave field with rabi frequency @xmath1 and detuning @xmath2 . ] here we show that a system of polar molecules gives rise to topological band structures , exploiting the spin - orbit coupling of dipolar interactions in combination with a term that breaks time - reversal symmetry .
the main idea is based on polar molecules trapped in a two - dimensional deep optical lattice with quenched tunneling between the sites .
the relevant degree of freedom of the polar molecules is given by two different rotational excitations which can be transferred between different lattice sites due to the dipolar exchange interaction .
we demonstrate that the band structure for such an excitation is characterized by a chern number which depends on the underlying lattice structure .
in particular , we find that the system on a square lattice gives rise to chern number @xmath0 , while a rich phase diagram appears on the honeycomb lattice . ideally , the setup is initialized with one polar molecule per lattice site , but we demonstrate that the topological properties are robust , even if nearly half of the molecules are randomly removed .
in contrast to non - interacting fermions , free bosons can not form a topological insulator .
however , the bosonic excitations in our system are subject to a hard - core constraint . such a setup in combination with flat bands
is then expected to give rise to a fractional chern insulator at @xmath3 filling in @xmath0 topological bands @xcite .
the main advantages of our realization , using the spin - orbit coupling present in dipolar interactions , are its robustness and the low experimental requirements , while many alternative theoretical proposals with cold gases require strong spatially inhomogeneous laser fields with variations on the scale of one lattice constant @xcite ; by using such ideas in combination with dipolar exchange interactions , it is also possible to engineer flat @xmath0 bands @xcite .
we point out that our proposal can also be applied to rydberg atoms in similar setups @xcite .
we consider a two - dimensional system of ultracold polar molecules in a deep optical lattice with one molecule pinned at each lattice site , as shown in fig .
[ fig : fig1]a . the remaining degree of freedom is given by the internal rotational excitations of the molecules with the hamiltonian @xmath4 here , @xmath5 is the rotational splitting , @xmath6 is the angular momentum of the @xmath7th molecule and @xmath8 is its dipole moment which is coupled to the applied static and microwave electric fields @xmath9 . in the absence of external fields ,
the eigenstates @xmath10 of @xmath11 are conveniently labeled by the total angular momentum @xmath12 and its projection @xmath13 . applying a static electric field
mixes states with different @xmath12 .
the projection @xmath13 , however , can still be used to characterize the states . in the following ,
we focus on the lowest state @xmath14 with @xmath15 and the two degenerate excited states @xmath16 with @xmath17 , see fig . [
fig : fig1]b .
the first excited @xmath15 state , called @xmath18 , will be used later .
the full system , including pairwise dipole - dipole interactions between the polar molecules , is described by @xmath19 . in the two - dimensional setup with the electric field perpendicular to the lattice
, the interaction can be expressed as @xmath20 \label{eq : ddint}\end{aligned}\ ] ] with @xmath21 . here
, @xmath22 denotes the in - plane polar angle of the vector @xmath23 which connects the two molecules at lattice sites @xmath7 and @xmath24 , and the operators @xmath25 and @xmath26 are the spherical components of the dipole operator .
the intrinsic spin - orbit coupling is visible in the second line in eq . , where a change in internal angular momentum by @xmath27 is associated with a change in orbital angular momentum encoded in the phase factor @xmath28 . for molecules with a permanent dipole moment @xmath29 in an optical lattice with spacing @xmath30 ,
the characteristic interaction energy @xmath31 is much weaker than the rotational splitting @xmath5 . for strong electric fields ,
the energy separation between the states @xmath32 and @xmath33 is also much larger than the interaction energy . then the number of @xmath16 excitations is conserved .
this allows us to map the hamiltonian to a bosonic model : the lowest energy state with all molecules in the @xmath14 state is the vacuum state , while excitations of a polar molecule into the state @xmath34 are described by hard - core boson operators @xmath35 .
note that these effective bosonic particles have a spin angular momentum of @xmath36 .
a crucial aspect for the generation of topological bands with a nonzero chern number is the breaking of time - reversal symmetry . in our setup
, this is achieved by coupling the state @xmath37 to the rotational state @xmath38 with an off - resonant microwave field , state to the third @xmath15 state can be neglected due to a large detuning from the difference in stark shifts between @xmath15 and @xmath39 see fig .
[ fig : fig1]b .
this coupling lifts the degeneracy between the two excitations @xmath40 and provides an energy splitting denoted by @xmath41 .
the dipole - dipole interaction gives rise to an effective hopping hamiltonian for the bosonic particles due to the dipolar exchange terms : @xmath42 , for example , leads to a ( long - range ) tunneling @xmath43 for the @xmath44-bosons while the term @xmath45 generates spin - flip tunneling processes @xmath46 with a phase that depends on the direction of tunneling . for the study of the single particle band structure we can drop the term proportional to @xmath47 which describes a static dipolar interaction between the bosons .
the interaction hamiltonian reduces to @xmath48 where we use the spinor notation @xmath49 .
the energy scale of the hopping rates @xmath50 , @xmath51 , and @xmath52 is given by @xmath53 .
the precise form depends on the microscopic parameters and is detailed in the appendix .
note that @xmath54 without the applied microwave . in momentum space with @xmath55 , including the internal energy @xmath56 of the excitations @xmath40 , the hamiltonian can be rewritten as @xmath57 where it is useful to express the traceless part of the hamiltonian as the product of a three dimensional real vector @xmath58 and the vector of pauli matrices @xmath59 @xcite .
the real vector characterizes the spin - orbit coupling terms and takes the form @xmath60 with @xmath61 .
the spin - independent hopping is determined by @xmath62 with @xmath63 .
we have introduced the dipolar dispersion relation @xcite @xmath64 the precise determination of this function can be achieved by an ewald summation technique providing a non - analytic low momentum behavior @xmath65 and @xmath66 . here , @xmath67 and @xmath68 is defined by @xmath69 .
( a ) dispersion relation for the @xmath70 and @xmath71 states on the square lattice .
the dashed line shows the time - reversal invariant point @xmath72 with band touching at the @xmath73 and @xmath74 point .
the solid line shows the gapped topological bands in the time - reversal - broken system for @xmath75 and @xmath76 .
( b ) dispersion relation for the @xmath70 and @xmath18 states for electric field angles @xmath77 ( dashed ) and @xmath78 ( solid ) , respectively .
the latter has a lower band with flatness @xmath79 .
, title="fig : " ] ( a ) dispersion relation for the @xmath70 and @xmath71 states on the square lattice .
the dashed line shows the time - reversal invariant point @xmath72 with band touching at the @xmath73 and @xmath74 point .
the solid line shows the gapped topological bands in the time - reversal - broken system for @xmath75 and @xmath76 .
( b ) dispersion relation for the @xmath70 and @xmath18 states for electric field angles @xmath77 ( dashed ) and @xmath78 ( solid ) , respectively .
the latter has a lower band with flatness @xmath79 .
, title="fig : " ] in the presence of time - reversal symmetry , represented by @xmath80 with @xmath81 being complex conjugation , the system reduces to the one discussed in ref . @xcite . at the @xmath82-invariant point ,
i.e. @xmath72 , the two energy bands of the system exhibit a band touching at the high - symmetry points @xmath83 and @xmath84 where @xmath85 vanishes , see fig .
[ fig : fig2]a .
the touching at the @xmath73 point is linear due to the low - momentum behavior of @xmath86 .
note that each of the touching points splits into two dirac points if the square lattice is stretched into a rectangular lattice .
breaking of time - reversal symmetry by the microwave field leads to an opening of a gap between the two bands .
the dispersion relation is given by @xmath87 and shown in fig .
[ fig : fig2]a .
it is gapped whenever the vector @xmath88 .
the first two components can only vanish at the @xmath73 or @xmath74 point .
consequently , the gap closes iff the third component is zero at one of these two points , that is for @xmath89 in the gapped system , the chern number @xcite can be calculated as the winding number of the normalized vector @xmath90 via to perform the calculation of the chern number .
we can check , however , that the remaining terms are not strong enough to close a gap .
conversely , note that the cutoff radius has to be larger than @xmath91 , as the next - to - nearest neighbor terms are crucial for the @xmath0 phase and may not be neglected . ]
@xmath92 we find that the chern number of the lower band is @xmath0 for @xmath93 , and zero outside this range .
note that the non - trivial topology solely results from dipolar spin - orbit coupling and time - reversal symmetry breaking .
( a ) sample - averaged chern number @xmath94 in the disordered system for increasing density @xmath95 of defects . a single realization either yields @xmath0 or @xmath96 .
bars indicate two standard errors .
the results are shown for square lattices of size @xmath97 with @xmath98 .
the long - range tunneling stabilizes the topological phase for defect densities @xmath99 .
( b ) two - dimensional projection of the dispersion relation in the honeycomb lattice for @xmath100 and @xmath101 .
the lowest band has a flatness ratio of @xmath102 and a chern number of @xmath103 .
( c ) topological phase diagram in the honeycomb lattice for @xmath104 .
the labels give the chern numbers of the four bands ( bar indicates negative number ) from bottom to top while the solid lines correspond to touching points between two bands .
the color indicates the flatness @xmath105 of the lowest band .
the arrow shows the parameters of the flat - band model in ( b ) . ,
title="fig : " ] ( a ) sample - averaged chern number @xmath94 in the disordered system for increasing density @xmath95 of defects .
a single realization either yields @xmath0 or @xmath96 .
bars indicate two standard errors .
the results are shown for square lattices of size @xmath97 with @xmath98 .
the long - range tunneling stabilizes the topological phase for defect densities @xmath99 .
( b ) two - dimensional projection of the dispersion relation in the honeycomb lattice for @xmath100 and @xmath101 .
the lowest band has a flatness ratio of @xmath102 and a chern number of @xmath103 .
( c ) topological phase diagram in the honeycomb lattice for @xmath104 .
the labels give the chern numbers of the four bands ( bar indicates negative number ) from bottom to top while the solid lines correspond to touching points between two bands .
the color indicates the flatness @xmath105 of the lowest band . the arrow shows the parameters of the flat - band model in ( b ) .
, title="fig : " ] ( a ) sample - averaged chern number @xmath94 in the disordered system for increasing density @xmath95 of defects .
a single realization either yields @xmath0 or @xmath96 .
bars indicate two standard errors .
the results are shown for square lattices of size @xmath97 with @xmath98 .
the long - range tunneling stabilizes the topological phase for defect densities @xmath99 .
( b ) two - dimensional projection of the dispersion relation in the honeycomb lattice for @xmath100 and @xmath101 .
the lowest band has a flatness ratio of @xmath102 and a chern number of @xmath103 .
( c ) topological phase diagram in the honeycomb lattice for @xmath104 .
the labels give the chern numbers of the four bands ( bar indicates negative number ) from bottom to top while the solid lines correspond to touching points between two bands .
the color indicates the flatness @xmath105 of the lowest band .
the arrow shows the parameters of the flat - band model in ( b ) .
, title="fig : " ] the challenge is to find a specific setup that optimizes the flatness of the topological bands .
this can be achieved either by focusing on different lattice structures ( see honeycomb lattice below and fig .
[ fig : fig3]b ) or by an alternative choice for the two excitations .
the latter is less intuitive when trying to understand the spin - orbit coupling , but gives rise to significantly flatter bands : instead of considering @xmath70 and @xmath71 , we choose a model including the @xmath70 and @xmath18 states .
this is possible for weak electric fields , if the @xmath71 state is shifted by a microwave field , or by exploiting the coupling between the nuclear spins of the polar molecules and the rotational degree of freedom @xcite .
this model intrinsically breaks time - reversal symmetry and has the advantage that the @xmath70 and @xmath18 states have different signs for the tunneling strength , making the @xmath82-breaking parameter @xmath106 large compared to @xmath107 . for an electric field direction perpendicular to the lattice , this system is gapless .
opening the gap is achieved by rotating the electric field away from the @xmath108-axis by an angle @xmath109 .
the dispersion relation for @xmath110 and @xmath111 is shown in fig .
[ fig : fig2]b .
the lower band has a flatness ratio of @xmath112 .
topological band structures are classified by considering equivalence classes of models that can be continuously deformed into each other without closing the energy gap @xcite .
using this idea , we can demonstrate that our model with @xmath0 is adiabatically equivalent to a system of two uncoupled copies of a @xmath113 layer ( see appendix for details ) .
the resulting single layer model can be described by a staggered flux pattern and is reminiscent of the famous haldane model @xcite , adapted to the square lattice @xcite .
it is rather remarkable that uniform dipole - dipole interactions give rise to a model usually requiring strong modulations on the order of the lattice spacing .
an experimental initialization with a perfectly uniform filling of one molecule per site is challenging .
consequently , we analyze the stability of the topological band structure for random samples with a nonzero probability @xmath95 for an empty lattice site .
the determination of the chern number for the disordered system follows ideas from refs .
we start with a finite geometry of @xmath97 lattice sites and twisted boundary conditions @xmath114 and @xmath115 for the single particle wave function .
next , we randomly remove @xmath116 lattice sites ( dipoles ) .
we are interested in the chern number of the lower ` band ' , composed of the lowest @xmath117 states ( there are @xmath118 states in total ) . to this end
, we pretend to have a free fermionic system at half filling whose many - body ground state @xmath119 is given by the slater determinant of the lowest @xmath120 states .
then , the chern number can be calculated as @xmath121 where @xmath122 is the many - body berry curvature depending on the boundary condition twists .
note that eq .
reduces to eq . in the translationally invariant case . for the numerical computations , we use a discretized version @xcite .
the results for the disordered system are summarized in fig .
[ fig : fig3]a .
we find that the long - range tunneling stabilizes the topological phase for defect densities @xmath123 .
returning to the simple setup in fig . [
fig : fig1]b , the influence of the lattice geometry can be exemplified by going to the honeycomb lattice . due to the two distinct sublattices , we generally obtain four bands in the presence of broken time - reversal symmetry .
depending on the microscopic parameters , the bands exhibit a rich topological structure , characterized by their chern numbers .
note that the chern numbers are calculated with a numerical method similar to the one for the disordered system . in fig .
[ fig : fig3]c , we show a two - dimensional cut through the topological phase diagram , spanned by the parameters @xmath124 and @xmath125 .
we find a multitude of different topological phases with large areas of flatness @xmath126 for the lowest band .
a flatness @xmath127 indicates that the maximum of the lowest band is higher than the minimum of the second band .
in contrast to the square lattice , an energy splitting @xmath128 is sufficient for a nonzero chern number ; @xmath129 is not necessarily needed .
[ fig : fig3]b shows the dispersion relation with a lowest band of flatness @xmath102 and a chern number @xmath103 .
( a ) dispersion relation for the @xmath70 and @xmath18 states on a cylindrical square lattice geometry with infinite extent in @xmath130 direction and @xmath131 sites in @xmath132 direction . four
edge states cross the bandgap in the @xmath0 phase ( two for each edge ) .
( b ) exponentially decaying amplitude of the two edge states in logarithmic scale , corresponding to the points shown in the spectrum .
( c ) edge state amplitude @xmath133 on a finite @xmath134 square lattice with a filling fraction of @xmath135 ( missing sites are indicated by crosses ) . ] ( a ) dispersion relation for the @xmath70 and @xmath18 states on a cylindrical square lattice geometry with infinite extent in @xmath130 direction and @xmath131 sites in @xmath132 direction .
four edge states cross the bandgap in the @xmath0 phase ( two for each edge ) .
( b ) exponentially decaying amplitude of the two edge states in logarithmic scale , corresponding to the points shown in the spectrum .
( c ) edge state amplitude @xmath133 on a finite @xmath134 square lattice with a filling fraction of @xmath135 ( missing sites are indicated by crosses ) .
, title="fig : " ] + ( a ) dispersion relation for the @xmath70 and @xmath18 states on a cylindrical square lattice geometry with infinite extent in @xmath130 direction and @xmath131 sites in @xmath132 direction .
four edge states cross the bandgap in the @xmath0 phase ( two for each edge ) .
( b ) exponentially decaying amplitude of the two edge states in logarithmic scale , corresponding to the points shown in the spectrum .
( c ) edge state amplitude @xmath133 on a finite @xmath134 square lattice with a filling fraction of @xmath135 ( missing sites are indicated by crosses ) .
, title="fig : " ]
one way to detect the topological band structure experimentally is to create a local excitation close to the edge of the system . in fig .
[ fig : fig4 ] we show the edge states in the @xmath0 phase on the square lattice .
the states are exponentially localized on the boundary of the system and the propagation of a single excitation along the edge can be used as an indication of the topological nature of the bands @xcite . in fig .
[ fig : fig4]c , we show the robustness of the edge states against missing molecules .
the edge state is also visible in a spectroscopic analysis , as a single mode between the broad continuum of the two bands ( see fig . [
fig : fig4]a ) .
finally , the most spectacular evidence of the topological nature would be the appearance of fractional chern insulators in the interacting many - body system at a fixed density of excitations . in our system
, the hard - core constraint naturally provides a strong on - site interaction for the bosons .
in addition , the remaining static dipolar interactions are a tunable knob to control the interaction strength .
the most promising candidate for a hard - core bosonic fractional chern insulator in a band with @xmath0 appears for a filling of @xmath136 , as suggested by numerical calculations @xcite , in agreement with the general classification scheme for interacting bosonic topological phases @xcite .
we acknowledge the support of the center for integrated quantum science and technology ( iqst ) , the deutsche forschungsgemeinschaft ( dfg ) within the sfb / trr 21 and the swiss national science foundation .
as described in the main text , in the presence of the static electric field , we denote the lowest rotational states having @xmath137 by @xmath14 and @xmath16 , respectively .
in addition , let @xmath138 be the lowest @xmath139 state .
a microwave with rabi frequency @xmath140 and detuning @xmath2 couples the states @xmath70 and @xmath138 . for a large detuning @xmath141 , the number of @xmath70 ( and @xmath71 )
excitations is conserved . in the rotating frame , within rotating wave approximation , the ac - dressed @xmath70 state is given by @xmath142 up to second order in @xmath143 .
for sufficiently strong electric fields , the states @xmath14 and @xmath71 are essentially unaffected by the microwave .
to derive the parameters of the hopping hamiltonian ( 3 ) in the main text , we introduce the vacuum state @xmath144 and the single particle states @xmath145 .
then , the hopping amplitudes are given by @xmath146 we set the spin - conserving term @xmath147 and the spin - flip tunneling @xmath148 to get the final expressions for the nearest - neighbor tunneling rates @xmath149 with the transition dipole element @xmath150 .
the evaluation of the dipole matrix elements for finite electric fields is straightforward and has been described in detail @xcite . in the absence of other techniques to shift the energy , the expression for the offset between the @xmath70 and @xmath71 state is given by the ac stark shift @xmath151 .
_ model with @xmath70 and @xmath18 state : _ using the @xmath70 and the @xmath18 state ( first excited @xmath15 state ) , the microwave field is no longer necessary , as the model intrinsically breaks time - reversal symmetry .
however , the electric field has to be rotated away from the @xmath108 axis to open a gap in the spectrum .
let @xmath152 denote the angles of the electric field axis in a spherical coordinate system with the lattice in the equatorial plane .
then , the dipole - dipole interaction can be expressed as @xmath153\end{aligned}\ ] ] where @xmath154 for @xmath110 , the interaction reduces to expression ( 2 ) given in the main text .
for the tunneling rates we find @xmath155 where @xmath156 . note that @xmath157 for @xmath110 , leading to the gapless spectrum for an electric field perpendicular to the lattice .
hopping strengths and flux pattern of a single layer in different lattices .
tunneling elements without arrow are real numbers .
complex hoppings have the indicated strength along the arrow and the complex conjugate in the opposite direction . ( a ) square lattice : a single layer can be constructed by stripes of one component along one of the primitive vectors , effectively doubling the unit cell . the second layer is given by a translation along the second primitive vector .
( b ) honeycomb lattice : by distributing the @xmath158 orbitals to the two distinct sublattices it is possible to retain the symmetry of the lattice .
the second layer is given by a @xmath159 rotation . ]
topological band structures can be classified by considering equivalence classes of models that can be continuously deformed into each other without closing the energy gap @xcite .
in particular , the chern number of a single band can only change if it touches another band .
using this idea , we show that the model introduced in the main text in its @xmath0 phase is adiabatically equivalent to a system of two uncoupled copies of a @xmath113 layer . to see this , imagine separating the two orbitals @xmath70 and @xmath71 per site spatially along the @xmath108-direction ( without changing any tunneling rates ) such that we obtain two separate square lattice layers , called a and b. sorting all terms in the hamiltonian into intra- and inter - layer processes , we can write @xmath160 where @xmath161 . the choice
which orbital resides in layer a ( and b ) can be made individually for each lattice site . in any case , the resulting two layers will be interconnected by an infinite number of tunneling links @xmath162 .
the idea is to find a specific arrangement of the orbitals such that we can continuously let @xmath163 _ without _ closing a gap in the excitation spectrum , preserving the topological phase while disentangling the layers .
focusing on layer a ( layer b being simply the complement ) , one possible arrangement is shown in fig .
[ fig : fig5](a ) .
the @xmath44 ( @xmath164 ) orbitals are assigned to odd ( even ) columns along the @xmath132-direction .
for the chern number of such a single layer we find @xmath113 , using methods analogous to the ones described in the main text .
the full system can be understood as two such layers , shifted by one lattice site in @xmath130-direction . with a unit cell twice the size of the original model
, each layer contributes to one half of the full brillouin zone , effectively doubling the chern number to @xmath0 .
the single layer system has some interesting properties . in fig .
[ fig : fig5](a ) we show that it is possible to find a staggered magnetic flux pattern which creates the same tunneling phases as the dipole - dipole interaction , including tunneling up to the next - to - nearest neighbor level .
using a site - dependent microwave dressing , it has been shown that a model similar to our single - layer system can be realized , giving rise to a @xmath165 fractional chern insulating phase @xcite . on the honeycomb lattice
, a single layer can be constructed which retains the original symmetry of the lattice , see fig .
[ fig : fig5](b ) . here
, the two bands of the single layer also have @xmath166 but occupy the same brillouin zone as the double layer system .
consequently , the four bands of the full system are constructed from the combination of two @xmath113 and two @xmath103 bands , giving rise to a multitude of different topological phases . | we demonstrate the realization of topological band structures by exploiting the intrinsic spin - orbit coupling of dipolar interactions in combination with broken time - reversal symmetry .
the system is based on polar molecules trapped in a deep optical lattice , where the dynamics of rotational excitations follows a hopping hamiltonian which is determined by the dipolar exchange interactions .
we find topological bands with chern number @xmath0 on the square lattice , while a very rich structure of different topological bands appears on the honeycomb lattice .
we show that the system is robust against missing molecules . for certain parameters we obtain flat bands , providing a promising candidate for the realization of hard - core bosonic fractional chern insulators . | <s>[INST]the quest for the realization of different topological states of matter marks one of the major challenges in quantum many - body physics . a well established concept for the generation of two - dimensional topologically ordered
states exhibiting anyonic excitations are flat bands characterized by a topological invariant in combination with strong interactions @xcite .
the prime example is the fractional quantum hall effect , where strong magnetic fields generate landau levels @xcite .
furthermore , lattice models without landau levels have been proposed for the realization of topological bands @xcite .
notably , spin - orbit coupling has emerged as an experimentally promising tool for band structures with topological invariants @xcite . in this letter , we show that dipolar interactions , exhibiting intrinsic spin - orbit coupling , can be exploited for the realization of topological bands with cold polar molecules . in cold gases experiments , the phenomenon that dipolar interactions exhibit
spin - orbit coupling is at the heart of demagnetization cooling @xcite , and has been identified as the driving mechanism for the einstein - de haas effect in bose - einstein condensates @xcite and the pattern formation in spinor condensates @xcite .
dipolar relaxation was proposed as a mechanism to reach the quantum hall regime by the controlled insertion of orbital angular momentum @xcite .
recently , it has been pointed out that dipolar spin - orbit coupling can be observed in band structures realized with polar molecules @xcite .
these ideas are motivated by the experimental success in cooling and trapping polar molecules in optical lattices @xcite .
( a ) setup : each lattice site of a two - dimensional optical lattice is occupied by a single polar molecule .
the molecules can be excited into two different rotational states .
dipole - dipole interactions induce long - range tunneling links for the excitations .
( b ) rotational level structure of each molecule with applied electric field and additional microwave field with rabi frequency @xmath1 and detuning @xmath2 . ] here we show that a system of polar molecules gives rise to topological band structures , exploiting the spin - orbit coupling of dipolar interactions in combination with a term that breaks time - reversal symmetry .
the main idea is based on polar molecules trapped in a two - dimensional deep optical lattice with quenched tunneling between the sites .
the relevant degree of freedom of the polar molecules is given by two different rotational excitations which can be transferred between different lattice sites due to the dipolar exchange interaction .
we demonstrate that the band structure for such an excitation is characterized by a chern number which depends on the underlying lattice structure .
in particular , we find that the system on a square lattice gives rise to chern number @xmath0 , while a rich phase diagram appears on the honeycomb lattice . ideally , the setup is initialized with one polar molecule per lattice site , but we demonstrate that the topological properties are robust , even if nearly half of the molecules are randomly removed .
in contrast to non - interacting fermions , free bosons can not form a topological insulator .
however , the bosonic excitations in our system are subject to a hard - core constraint . such a setup in combination with flat bands
is then expected to give rise to a fractional chern insulator at @xmath3 filling in @xmath0 topological bands @xcite .
the main advantages of our realization , using the spin - orbit coupling present in dipolar interactions , are its robustness and the low experimental requirements , while many alternative theoretical proposals with cold gases require strong spatially inhomogeneous laser fields with variations on the scale of one lattice constant @xcite ; by using such ideas in combination with dipolar exchange interactions , it is also possible to engineer flat @xmath0 bands @xcite .
we point out that our proposal can also be applied to rydberg atoms in similar setups @xcite .
we consider a two - dimensional system of ultracold polar molecules in a deep optical lattice with one molecule pinned at each lattice site , as shown in fig .
[ fig : fig1]a . the remaining degree of freedom is given by the internal rotational excitations of the molecules with the hamiltonian @xmath4 here , @xmath5 is the rotational splitting , @xmath6 is the angular momentum of the @xmath7th molecule and @xmath8 is its dipole moment which is coupled to the applied static and microwave electric fields @xmath9 . in the absence of external fields ,
the eigenstates @xmath10 of @xmath11 are conveniently labeled by the total angular momentum @xmath12 and its projection @xmath13 . applying a static electric field
mixes states with different @xmath12 .
the projection @xmath13 , however , can still be used to characterize the states . in the following ,
we focus on the lowest state @xmath14 with @xmath15 and the two degenerate excited states @xmath16 with @xmath17 , see fig . [
fig : fig1]b .
the first excited @xmath15 state , called @xmath18 , will be used later .
the full system , including pairwise dipole - dipole interactions between the polar molecules , is described by @xmath19 . in the two - dimensional setup with the electric field perpendicular to the lattice
, the interaction can be expressed as @xmath20 \label{eq : ddint}\end{aligned}\ ] ] with @xmath21 . here
, @xmath22 denotes the in - plane polar angle of the vector @xmath23 which connects the two molecules at lattice sites @xmath7 and @xmath24 , and the operators @xmath25 and @xmath26 are the spherical components of the dipole operator .
the intrinsic spin - orbit coupling is visible in the second line in eq . , where a change in internal angular momentum by @xmath27 is associated with a change in orbital angular momentum encoded in the phase factor @xmath28 . for molecules with a permanent dipole moment @xmath29 in an optical lattice with spacing @xmath30 ,
the characteristic interaction energy @xmath31 is much weaker than the rotational splitting @xmath5 . for strong electric fields ,
the energy separation between the states @xmath32 and @xmath33 is also much larger than the interaction energy . then the number of @xmath16 excitations is conserved .
this allows us to map the hamiltonian to a bosonic model : the lowest energy state with all molecules in the @xmath14 state is the vacuum state , while excitations of a polar molecule into the state @xmath34 are described by hard - core boson operators @xmath35 .
note that these effective bosonic particles have a spin angular momentum of @xmath36 .
a crucial aspect for the generation of topological bands with a nonzero chern number is the breaking of time - reversal symmetry . in our setup
, this is achieved by coupling the state @xmath37 to the rotational state @xmath38 with an off - resonant microwave field , state to the third @xmath15 state can be neglected due to a large detuning from the difference in stark shifts between @xmath15 and @xmath39 see fig .
[ fig : fig1]b .
this coupling lifts the degeneracy between the two excitations @xmath40 and provides an energy splitting denoted by @xmath41 .
the dipole - dipole interaction gives rise to an effective hopping hamiltonian for the bosonic particles due to the dipolar exchange terms : @xmath42 , for example , leads to a ( long - range ) tunneling @xmath43 for the @xmath44-bosons while the term @xmath45 generates spin - flip tunneling processes @xmath46 with a phase that depends on the direction of tunneling . for the study of the single particle band structure we can drop the term proportional to @xmath47 which describes a static dipolar interaction between the bosons .
the interaction hamiltonian reduces to @xmath48 where we use the spinor notation @xmath49 .
the energy scale of the hopping rates @xmath50 , @xmath51 , and @xmath52 is given by @xmath53 .
the precise form depends on the microscopic parameters and is detailed in the appendix .
note that @xmath54 without the applied microwave . in momentum space with @xmath55 , including the internal energy @xmath56 of the excitations @xmath40 , the hamiltonian can be rewritten as @xmath57 where it is useful to express the traceless part of the hamiltonian as the product of a three dimensional real vector @xmath58 and the vector of pauli matrices @xmath59 @xcite .
the real vector characterizes the spin - orbit coupling terms and takes the form @xmath60 with @xmath61 .
the spin - independent hopping is determined by @xmath62 with @xmath63 .
we have introduced the dipolar dispersion relation @xcite @xmath64 the precise determination of this function can be achieved by an ewald summation technique providing a non - analytic low momentum behavior @xmath65 and @xmath66 . here , @xmath67 and @xmath68 is defined by @xmath69 .
( a ) dispersion relation for the @xmath70 and @xmath71 states on the square lattice .
the dashed line shows the time - reversal invariant point @xmath72 with band touching at the @xmath73 and @xmath74 point .
the solid line shows the gapped topological bands in the time - reversal - broken system for @xmath75 and @xmath76 .
( b ) dispersion relation for the @xmath70 and @xmath18 states for electric field angles @xmath77 ( dashed ) and @xmath78 ( solid ) , respectively .
the latter has a lower band with flatness @xmath79 .
, title="fig : " ] ( a ) dispersion relation for the @xmath70 and @xmath71 states on the square lattice .
the dashed line shows the time - reversal invariant point @xmath72 with band touching at the @xmath73 and @xmath74 point .
the solid line shows the gapped topological bands in the time - reversal - broken system for @xmath75 and @xmath76 .
( b ) dispersion relation for the @xmath70 and @xmath18 states for electric field angles @xmath77 ( dashed ) and @xmath78 ( solid ) , respectively .
the latter has a lower band with flatness @xmath79 .
, title="fig : " ] in the presence of time - reversal symmetry , represented by @xmath80 with @xmath81 being complex conjugation , the system reduces to the one discussed in ref . @xcite . at the @xmath82-invariant point ,
i.e. @xmath72 , the two energy bands of the system exhibit a band touching at the high - symmetry points @xmath83 and @xmath84 where @xmath85 vanishes , see fig .
[ fig : fig2]a .
the touching at the @xmath73 point is linear due to the low - momentum behavior of @xmath86 .
note that each of the touching points splits into two dirac points if the square lattice is stretched into a rectangular lattice .
breaking of time - reversal symmetry by the microwave field leads to an opening of a gap between the two bands .
the dispersion relation is given by @xmath87 and shown in fig .
[ fig : fig2]a .
it is gapped whenever the vector @xmath88 .
the first two components can only vanish at the @xmath73 or @xmath74 point .
consequently , the gap closes iff the third component is zero at one of these two points , that is for @xmath89 in the gapped system , the chern number @xcite can be calculated as the winding number of the normalized vector @xmath90 via to perform the calculation of the chern number .
we can check , however , that the remaining terms are not strong enough to close a gap .
conversely , note that the cutoff radius has to be larger than @xmath91 , as the next - to - nearest neighbor terms are crucial for the @xmath0 phase and may not be neglected . ]
@xmath92 we find that the chern number of the lower band is @xmath0 for @xmath93 , and zero outside this range .
note that the non - trivial topology solely results from dipolar spin - orbit coupling and time - reversal symmetry breaking .
( a ) sample - averaged chern number @xmath94 in the disordered system for increasing density @xmath95 of defects . a single realization either yields @xmath0 or @xmath96 .
bars indicate two standard errors .
the results are shown for square lattices of size @xmath97 with @xmath98 .
the long - range tunneling stabilizes the topological phase for defect densities @xmath99 .
( b ) two - dimensional projection of the dispersion relation in the honeycomb lattice for @xmath100 and @xmath101 .
the lowest band has a flatness ratio of @xmath102 and a chern number of @xmath103 .
( c ) topological phase diagram in the honeycomb lattice for @xmath104 .
the labels give the chern numbers of the four bands ( bar indicates negative number ) from bottom to top while the solid lines correspond to touching points between two bands .
the color indicates the flatness @xmath105 of the lowest band .
the arrow shows the parameters of the flat - band model in ( b ) . ,
title="fig : " ] ( a ) sample - averaged chern number @xmath94 in the disordered system for increasing density @xmath95 of defects .
a single realization either yields @xmath0 or @xmath96 .
bars indicate two standard errors .
the results are shown for square lattices of size @xmath97 with @xmath98 .
the long - range tunneling stabilizes the topological phase for defect densities @xmath99 .
( b ) two - dimensional projection of the dispersion relation in the honeycomb lattice for @xmath100 and @xmath101 .
the lowest band has a flatness ratio of @xmath102 and a chern number of @xmath103 .
( c ) topological phase diagram in the honeycomb lattice for @xmath104 .
the labels give the chern numbers of the four bands ( bar indicates negative number ) from bottom to top while the solid lines correspond to touching points between two bands .
the color indicates the flatness @xmath105 of the lowest band . the arrow shows the parameters of the flat - band model in ( b ) .
, title="fig : " ] ( a ) sample - averaged chern number @xmath94 in the disordered system for increasing density @xmath95 of defects .
a single realization either yields @xmath0 or @xmath96 .
bars indicate two standard errors .
the results are shown for square lattices of size @xmath97 with @xmath98 .
the long - range tunneling stabilizes the topological phase for defect densities @xmath99 .
( b ) two - dimensional projection of the dispersion relation in the honeycomb lattice for @xmath100 and @xmath101 .
the lowest band has a flatness ratio of @xmath102 and a chern number of @xmath103 .
( c ) topological phase diagram in the honeycomb lattice for @xmath104 .
the labels give the chern numbers of the four bands ( bar indicates negative number ) from bottom to top while the solid lines correspond to touching points between two bands .
the color indicates the flatness @xmath105 of the lowest band .
the arrow shows the parameters of the flat - band model in ( b ) .
, title="fig : " ] the challenge is to find a specific setup that optimizes the flatness of the topological bands .
this can be achieved either by focusing on different lattice structures ( see honeycomb lattice below and fig .
[ fig : fig3]b ) or by an alternative choice for the two excitations .
the latter is less intuitive when trying to understand the spin - orbit coupling , but gives rise to significantly flatter bands : instead of considering @xmath70 and @xmath71 , we choose a model including the @xmath70 and @xmath18 states .
this is possible for weak electric fields , if the @xmath71 state is shifted by a microwave field , or by exploiting the coupling between the nuclear spins of the polar molecules and the rotational degree of freedom @xcite .
this model intrinsically breaks time - reversal symmetry and has the advantage that the @xmath70 and @xmath18 states have different signs for the tunneling strength , making the @xmath82-breaking parameter @xmath106 large compared to @xmath107 . for an electric field direction perpendicular to the lattice , this system is gapless .
opening the gap is achieved by rotating the electric field away from the @xmath108-axis by an angle @xmath109 .
the dispersion relation for @xmath110 and @xmath111 is shown in fig .
[ fig : fig2]b .
the lower band has a flatness ratio of @xmath112 .
topological band structures are classified by considering equivalence classes of models that can be continuously deformed into each other without closing the energy gap @xcite .
using this idea , we can demonstrate that our model with @xmath0 is adiabatically equivalent to a system of two uncoupled copies of a @xmath113 layer ( see appendix for details ) .
the resulting single layer model can be described by a staggered flux pattern and is reminiscent of the famous haldane model @xcite , adapted to the square lattice @xcite .
it is rather remarkable that uniform dipole - dipole interactions give rise to a model usually requiring strong modulations on the order of the lattice spacing .
an experimental initialization with a perfectly uniform filling of one molecule per site is challenging .
consequently , we analyze the stability of the topological band structure for random samples with a nonzero probability @xmath95 for an empty lattice site .
the determination of the chern number for the disordered system follows ideas from refs .
we start with a finite geometry of @xmath97 lattice sites and twisted boundary conditions @xmath114 and @xmath115 for the single particle wave function .
next , we randomly remove @xmath116 lattice sites ( dipoles ) .
we are interested in the chern number of the lower ` band ' , composed of the lowest @xmath117 states ( there are @xmath118 states in total ) . to this end
, we pretend to have a free fermionic system at half filling whose many - body ground state @xmath119 is given by the slater determinant of the lowest @xmath120 states .
then , the chern number can be calculated as @xmath121 where @xmath122 is the many - body berry curvature depending on the boundary condition twists .
note that eq .
reduces to eq . in the translationally invariant case . for the numerical computations , we use a discretized version @xcite .
the results for the disordered system are summarized in fig .
[ fig : fig3]a .
we find that the long - range tunneling stabilizes the topological phase for defect densities @xmath123 .
returning to the simple setup in fig . [
fig : fig1]b , the influence of the lattice geometry can be exemplified by going to the honeycomb lattice . due to the two distinct sublattices , we generally obtain four bands in the presence of broken time - reversal symmetry .
depending on the microscopic parameters , the bands exhibit a rich topological structure , characterized by their chern numbers .
note that the chern numbers are calculated with a numerical method similar to the one for the disordered system . in fig .
[ fig : fig3]c , we show a two - dimensional cut through the topological phase diagram , spanned by the parameters @xmath124 and @xmath125 .
we find a multitude of different topological phases with large areas of flatness @xmath126 for the lowest band .
a flatness @xmath127 indicates that the maximum of the lowest band is higher than the minimum of the second band .
in contrast to the square lattice , an energy splitting @xmath128 is sufficient for a nonzero chern number ; @xmath129 is not necessarily needed .
[ fig : fig3]b shows the dispersion relation with a lowest band of flatness @xmath102 and a chern number @xmath103 .
( a ) dispersion relation for the @xmath70 and @xmath18 states on a cylindrical square lattice geometry with infinite extent in @xmath130 direction and @xmath131 sites in @xmath132 direction . four
edge states cross the bandgap in the @xmath0 phase ( two for each edge ) .
( b ) exponentially decaying amplitude of the two edge states in logarithmic scale , corresponding to the points shown in the spectrum .
( c ) edge state amplitude @xmath133 on a finite @xmath134 square lattice with a filling fraction of @xmath135 ( missing sites are indicated by crosses ) . ] ( a ) dispersion relation for the @xmath70 and @xmath18 states on a cylindrical square lattice geometry with infinite extent in @xmath130 direction and @xmath131 sites in @xmath132 direction .
four edge states cross the bandgap in the @xmath0 phase ( two for each edge ) .
( b ) exponentially decaying amplitude of the two edge states in logarithmic scale , corresponding to the points shown in the spectrum .
( c ) edge state amplitude @xmath133 on a finite @xmath134 square lattice with a filling fraction of @xmath135 ( missing sites are indicated by crosses ) .
, title="fig : " ] + ( a ) dispersion relation for the @xmath70 and @xmath18 states on a cylindrical square lattice geometry with infinite extent in @xmath130 direction and @xmath131 sites in @xmath132 direction .
four edge states cross the bandgap in the @xmath0 phase ( two for each edge ) .
( b ) exponentially decaying amplitude of the two edge states in logarithmic scale , corresponding to the points shown in the spectrum .
( c ) edge state amplitude @xmath133 on a finite @xmath134 square lattice with a filling fraction of @xmath135 ( missing sites are indicated by crosses ) .
, title="fig : " ]
one way to detect the topological band structure experimentally is to create a local excitation close to the edge of the system . in fig .
[ fig : fig4 ] we show the edge states in the @xmath0 phase on the square lattice .
the states are exponentially localized on the boundary of the system and the propagation of a single excitation along the edge can be used as an indication of the topological nature of the bands @xcite . in fig .
[ fig : fig4]c , we show the robustness of the edge states against missing molecules .
the edge state is also visible in a spectroscopic analysis , as a single mode between the broad continuum of the two bands ( see fig . [
fig : fig4]a ) .
finally , the most spectacular evidence of the topological nature would be the appearance of fractional chern insulators in the interacting many - body system at a fixed density of excitations . in our system
, the hard - core constraint naturally provides a strong on - site interaction for the bosons .
in addition , the remaining static dipolar interactions are a tunable knob to control the interaction strength .
the most promising candidate for a hard - core bosonic fractional chern insulator in a band with @xmath0 appears for a filling of @xmath136 , as suggested by numerical calculations @xcite , in agreement with the general classification scheme for interacting bosonic topological phases @xcite .
we acknowledge the support of the center for integrated quantum science and technology ( iqst ) , the deutsche forschungsgemeinschaft ( dfg ) within the sfb / trr 21 and the swiss national science foundation .
as described in the main text , in the presence of the static electric field , we denote the lowest rotational states having @xmath137 by @xmath14 and @xmath16 , respectively .
in addition , let @xmath138 be the lowest @xmath139 state .
a microwave with rabi frequency @xmath140 and detuning @xmath2 couples the states @xmath70 and @xmath138 . for a large detuning @xmath141 , the number of @xmath70 ( and @xmath71 )
excitations is conserved . in the rotating frame , within rotating wave approximation , the ac - dressed @xmath70 state is given by @xmath142 up to second order in @xmath143 .
for sufficiently strong electric fields , the states @xmath14 and @xmath71 are essentially unaffected by the microwave .
to derive the parameters of the hopping hamiltonian ( 3 ) in the main text , we introduce the vacuum state @xmath144 and the single particle states @xmath145 .
then , the hopping amplitudes are given by @xmath146 we set the spin - conserving term @xmath147 and the spin - flip tunneling @xmath148 to get the final expressions for the nearest - neighbor tunneling rates @xmath149 with the transition dipole element @xmath150 .
the evaluation of the dipole matrix elements for finite electric fields is straightforward and has been described in detail @xcite . in the absence of other techniques to shift the energy , the expression for the offset between the @xmath70 and @xmath71 state is given by the ac stark shift @xmath151 .
_ model with @xmath70 and @xmath18 state : _ using the @xmath70 and the @xmath18 state ( first excited @xmath15 state ) , the microwave field is no longer necessary , as the model intrinsically breaks time - reversal symmetry .
however , the electric field has to be rotated away from the @xmath108 axis to open a gap in the spectrum .
let @xmath152 denote the angles of the electric field axis in a spherical coordinate system with the lattice in the equatorial plane .
then , the dipole - dipole interaction can be expressed as @xmath153\end{aligned}\ ] ] where @xmath154 for @xmath110 , the interaction reduces to expression ( 2 ) given in the main text .
for the tunneling rates we find @xmath155 where @xmath156 . note that @xmath157 for @xmath110 , leading to the gapless spectrum for an electric field perpendicular to the lattice .
hopping strengths and flux pattern of a single layer in different lattices .
tunneling elements without arrow are real numbers .
complex hoppings have the indicated strength along the arrow and the complex conjugate in the opposite direction . ( a ) square lattice : a single layer can be constructed by stripes of one component along one of the primitive vectors , effectively doubling the unit cell . the second layer is given by a translation along the second primitive vector .
( b ) honeycomb lattice : by distributing the @xmath158 orbitals to the two distinct sublattices it is possible to retain the symmetry of the lattice .
the second layer is given by a @xmath159 rotation . ]
topological band structures can be classified by considering equivalence classes of models that can be continuously deformed into each other without closing the energy gap @xcite .
in particular , the chern number of a single band can only change if it touches another band .
using this idea , we show that the model introduced in the main text in its @xmath0 phase is adiabatically equivalent to a system of two uncoupled copies of a @xmath113 layer . to see this , imagine separating the two orbitals @xmath70 and @xmath71 per site spatially along the @xmath108-direction ( without changing any tunneling rates ) such that we obtain two separate square lattice layers , called a and b. sorting all terms in the hamiltonian into intra- and inter - layer processes , we can write @xmath160 where @xmath161 . the choice
which orbital resides in layer a ( and b ) can be made individually for each lattice site . in any case , the resulting two layers will be interconnected by an infinite number of tunneling links @xmath162 .
the idea is to find a specific arrangement of the orbitals such that we can continuously let @xmath163 _ without _ closing a gap in the excitation spectrum , preserving the topological phase while disentangling the layers .
focusing on layer a ( layer b being simply the complement ) , one possible arrangement is shown in fig .
[ fig : fig5](a ) .
the @xmath44 ( @xmath164 ) orbitals are assigned to odd ( even ) columns along the @xmath132-direction .
for the chern number of such a single layer we find @xmath113 , using methods analogous to the ones described in the main text .
the full system can be understood as two such layers , shifted by one lattice site in @xmath130-direction . with a unit cell twice the size of the original model
, each layer contributes to one half of the full brillouin zone , effectively doubling the chern number to @xmath0 .
the single layer system has some interesting properties . in fig .
[ fig : fig5](a ) we show that it is possible to find a staggered magnetic flux pattern which creates the same tunneling phases as the dipole - dipole interaction , including tunneling up to the next - to - nearest neighbor level .
using a site - dependent microwave dressing , it has been shown that a model similar to our single - layer system can be realized , giving rise to a @xmath165 fractional chern insulating phase @xcite . on the honeycomb lattice
, a single layer can be constructed which retains the original symmetry of the lattice , see fig .
[ fig : fig5](b ) . here
, the two bands of the single layer also have @xmath166 but occupy the same brillouin zone as the double layer system .
consequently , the four bands of the full system are constructed from the combination of two @xmath113 and two @xmath103 bands , giving rise to a multitude of different topological phases .[/INST] we demonstrate the realization of topological band structures by exploiting the intrinsic spin - orbit coupling of dipolar interactions in combination with broken time - reversal symmetry .
the system is based on polar molecules trapped in a deep optical lattice , where the dynamics of rotational excitations follows a hopping hamiltonian which is determined by the dipolar exchange interactions .
we find topological bands with chern number @xmath0 on the square lattice , while a very rich structure of different topological bands appears on the honeycomb lattice .
we show that the system is robust against missing molecules . for certain parameters we obtain flat bands , providing a promising candidate for the realization of hard - core bosonic fractional chern insulators . </s> |
it is known that the deficit of the solar and atmospheric neutrinos are due to neutrino oscillations among three flavors of neutrinos , and these observations offer evidence of neutrino masses and mixings.@xcite the standard three flavor framework of neutrino oscillations are described by six oscillation parameters : three mixing angles @xmath4 , @xmath5 , @xmath6 , the two independent mass squared differences @xmath7 , @xmath8 , and one cp violating phase @xmath9 , where @xmath10 and @xmath11 stands for the mass of the neutrino mass eigenstate . from the solar neutrino data , we have @xmath12 , and from the atmospheric neutrino data we have @xmath13 . on the other hand , only the upper bound on @xmath5 is known ( @xmath14 ) , is found .
this result , however , is compatible with @xmath15 at less than @xmath16 , and it is not yet statistically significant enough to be taken seriously . ] and no information on @xmath9 is known at present . to determine @xmath5 and @xmath9 , various neutrino long baseline experiments have been proposed@xcite , and the ongoing and proposed future neutrino long baseline experiments with an intense beam include conventional super ( neutrino ) beam experiments such as t2k,@xcite no@xmath17a,@xcite lbne,@xcite t2kk,@xcite the @xmath18 beam proposal,@xcite which uses a @xmath19 ( @xmath20 ) beam from @xmath18-decays of radioactive isotopes , and the neutrino factory proposal,@xcite in which @xmath20 and @xmath21 ( @xmath19 and @xmath22 ) are produced from decays of @xmath23 ( @xmath24 ) .
as in the case of the b factories@xcite , precise measurements in these experiments allow us not only to determine the oscillation parameters precisely but also to probe new physics by looking for deviation from the standard three flavor scheme .
in particular , test of unitarity is one of the important subjects in neutrino oscillations , and tau detection is crucial for that purpose . among the proposals for future long baseline experiments , the neutrino factory facility produces a neutrino beam of the highest neutrino energy , and it is advantageous to detect @xmath25 , because of the large cross section at high energy .
new physics which has been discussed in the context of neutrino oscillation includes sterile neutrinos,@xcite the non - standard interactions during neutrino propagation@xcite , the non - standard interactions at production and detection@xcite , violation of unitarity due to heavy particles@xcite , etc .
these scenarios , except the non - standard interactions during neutrino propagation , offer interesting possibilities for violation of three flavor unitarity . among these possibilities ,
phenomenological bound of unitarity violation is typically of @xmath26(1% ) in the case of non - standard interactions at production and detection , and it is of @xmath26(0.1% ) in the case of unitarity violation due to heavy particles.@xcite on the other hand , the bound in the case of sterile neutrinos is of @xmath26(10% ) which comes mainly from the constraints of the atmospheric neutrino data,@xcite so scenarios with sterile neutrinos seem to be phenomenologically more promising to look for than other possibilities of unitarity violation .
in this talk i will discuss phenomenology of schemes with sterile neutrinos at a neutrino factory .
schemes with sterile neutrinos have attracted a lot of attention since the lsnd group announced the anomaly which suggest neutrino oscillations with mass squared difference of @xmath26(1ev@xmath27).@xcite .
the reason that we need one extra neutrino to account for lsnd is because the standard three flavor scheme has only two independent mass squared differences , i.e. , @xmath28ev@xmath27 for the solar neutrino oscillation , and @xmath29ev@xmath27 for the atmospheric neutrino oscillation , and it does not have room for the mass squared difference of @xmath26(1ev@xmath27 ) . and
the reason that the extra state has to be sterile neutrino , which is singlet with respect to the gauge group of the standard model , is because the number of weakly interacting light neutrinos has to be three from the lep data.@xcite the lsnd anomaly has been tested by the miniboone experiment , and it gave a negative result for neutrino oscillations with mass squared difference of @xmath26(1ev@xmath27).@xcite while the miniboone data disfavor the region suggested by lsnd , ref . gave the allowed region from the combined analysis of the lsnd and miniboone data , and it is not so clear whether the miniboone data alone are significant enough to exclude the lsnd region . on the other hand , even if the miniboone data are taken as negative evidence against the lsnd region , there still remains a possibility for sterile neutrino scenarios whose mixing angles are small enough to satisfy the constraints of miniboone and the other negative results .
the effect of these scenarios could reveal as violation of three flavor unitarity in the future neutrino experiments .
so in this talk i will discuss sterile neutrino schemes as one of phenomenologically viable possibilities for unitarity violation , regardless of whether the lsnd anomaly is excluded by the miniboone data or not . it has been known that sterile neutrino schemes may have cosmological problems ( see , e.g. , ref . )
. however , these cosmological discussions depend on models and assumptions , and i will not discuss cosmological constraints in this talk . also it has been pointed out that some sterile neutrino models@xcite have absorption effects even for neutrino energy below 1tev , but i will not take such effects into consideration for simplicity .
for simplicity i will discuss schemes with four neutrinos , although phenomenology of the schemes with two@xcite or three@xcite sterile neutrinos have also been discussed . denoting sterile neutrinos as @xmath30 , we have the following mixing between the flavor eigen states @xmath31 and the mass eigenstates @xmath32 : @xmath33 there are two kind of schemes with four neutrinos , depending on how the mass eigenstates are separated by the largest mass squared difference .
one is the ( 2 + 2)-scheme in which two mass eigenstates are separated by other two , and the other one is the ( 3 + 1)-scheme in which one mass eigenstate is separated by other three ( cf .
fig.[aba : fig1 ] ) . -0.7 cm
-0.5 cm in this scheme the fraction of sterile neutrino contributions to solar and atmospheric oscillations is given by @xmath34 and @xmath35 , respectively , where the mass squared differences @xmath7 and @xmath36 are assumed to be those of the solar and atmospheric oscillations .
the experimental results show that mixing among active neutrinos give dominant contributions to both the solar and atmospheric oscillations ( see , e.g. , ref . ) . in particular , in fig .
19 of ref .
we can see that at the 99% level @xmath37 and @xmath38 , from the solar and atmospheric oscillations , respectively , and this contradicts the unitarity condition @xmath39 .
in fact the ( 2 + 2)-schemes are excluded at 5.1@xmath40 cl @xcite .
this conclusion is independent of whether we take the lsnd data into consideration or not and i will not consider ( 2 + 2)-schemes in this talk .
phenomenology of the ( 3 + 1)-scheme is almost the same as that of the standard three flavor scenario , as far as the solar and atmospheric oscillations are concerned . on the other hand
, this scheme has tension between the lsnd data and other negative results of the short baseline experiments . among others ,
the cdhsw@xcite and bugey@xcite experiments give the bound on @xmath41 and @xmath42 , respectively , and in order for the lsnd data to be affirmative , the following relation has to be satisfied@xcite : @xmath43 where @xmath44 , @xmath45 , @xmath46 are the value of the effective two - flavor mixing angle as a function of the mass squared difference @xmath47 in the allowed region for lsnd ( @xmath48 ) , the cdhsw experiment ( @xmath49 ) , and the bugey experiment ( @xmath50 ) , respectively .
the ( 3 + 1)-scheme to account for lsnd in terms of neutrino oscillations is disfavored because eq .
( [ relation31 ] ) is not satisfied for any value of @xmath47 .
this argument has been shown quantitatively by ref . including the atmospheric neutrino data and other negative results . in fig.[aba : fig2 ] the right hand side of the lines denoted as `` null sbl 90% ( 99% ) '' is the excluded region at 90% ( 99% ) cl by the atmospheric neutrino data and all the negative results of short baseline experiments , whereas the allowed region by the combined analysis of the lsnd and miniboone data at 90% ( 99% ) cl is also shown . in the following discussions i will assume the mass pattern depicted in fig.[aba : fig1](b ) because the inverted ( 3 + 1)-scheme is disfavored by cosmology , and
i will also assume for simplicity that the largest mass squared difference @xmath51 is larger than @xmath52(0.1ev@xmath27 ) , so that i can average over rapid oscillations due to @xmath51 in the long baseline experiments as well as in the atmospheric neutrino observations .
-1.0 cm -0.3 cm
unlike conventional long baseline neutrino experiments , neutrino factories use muon decays @xmath53 and @xmath54 to produce neutrinos . in the setup suggested in the physics report@xcite of _ international scoping study for a future neutrino factory and super - beam facility _ , muons of both polarities are accelerated up to @xmath55 gev and injected into one storage ring with a geometry that allows to aim at two far detectors , the first located at 4000 km and the second at 7500 km from the source .
the reason to put far detectors at two locations is to resolve so - called parameter degeneracy.@xcite the useful channels at neutrino factories are the following : @xmath56 @xmath0 and @xmath57 : the golden channel @xmath56 @xmath1 and @xmath58 : the disappearance channel @xmath56 @xmath2 and @xmath59 : the silver channel @xmath56 @xmath3 and @xmath60 : the discovery channel at neutrino factories , electrons and positrons produced out of @xmath19 and @xmath61 create electromagnetic showers , which make it difficult to identify their charges . on the other hand ,
charge identification is much easier for @xmath62 detection , so the golden channel @xmath0 is used unlike the conventional long baseline neutrino experiments which use @xmath63 .
the golden channel turns out to be powerful because of very low backgrounds .
the disappearance channel is also useful because of a lot of statistics .
the golden and disappearance channels are observed by looking for muons with magnetized iron calorimeters.@xcite on the other hand , the silver and discovery channels are observed by looking for @xmath64 s with emulsion cloud chambers ( nonmagnetized@xcite or magnetized@xcite ) , and the statistics of the silver channel is limited .
the silver channel is useful to resolve parameter degeneracy .
combination of the golden , disappearance and discovery channels is expected to enable us to check unitarity .
studied sensitivity of a neutrino factory with far detectors to sterile neutrino mixings .
the setup is the following:=3000 km and @xmath65=7500 km , and it was shown that sensitivity with @xmath64 detectors increases for 50gev because of higher statistics . in this talk , however , i will only mention the results for the neutrino factory with muon energy 20gev for simplicity . ]
the muon energy is 20gev , the number of useful muons is @xmath66 @xmath23 s _ and _
@xmath24 s per year , the measurements are supposed to continue for 4 years , the baseline lengths are @xmath65=4000 km and @xmath65=7500 km , the volume of each magnetized iron calorimeter at the two distances is 50kton , that of each magnetized emulsion cloud chamber at the two distances is 4kton , and the statistical as well as systematic errors and the backgrounds are taken into account . at long baseline lengths such as @xmath65=7500 km , matter effects become important .
the oscillation probability in constant - density matter can be obtained by the formalism of kimura , takamura and yokomakura@xcite .
the oscillation probability in matter can be written as @xmath67 -2 mm where @xmath68 , @xmath69 , @xmath70 and @xmath71 are the energy eigenvalue and the neutrino mixing matrix element in matter defined by @xmath72 ( @xmath73 ) .
the matter potentials @xmath74 , @xmath75 are given by @xmath76 , @xmath77 , where @xmath78 and @xmath79 are the density of electrons and neutrinos , respectively .
the neutrino energy @xmath80 and the baseline length @xmath65 which are typical at a neutrino factory satisfy @xmath81 , @xmath82 and @xmath83 , and the energy eigenvalues in this case to the lowest order in the small mixing angles and to first order in @xmath84 are @xmath85 , @xmath86 , @xmath87 , @xmath88 .
it can be shown that the 4-th component @xmath89 in matter is the same as that in vacuum : @xmath90 , where the notation @xmath91 has been also introduced for the quantity in vacuum .
on the other hand , other three components are given by @xmath92 where @xmath93 in eq .
( [ x ] ) @xmath94 is the matrix element of the matter potential , and no sum is understood over the indices @xmath95 .
if the sterile neutrino mixings @xmath96 are small , then @xmath97 reproduce those for the standard three flavor case
. these sterile neutrino mixings @xmath98 appear in the coefficients @xmath97 in front of the sine factors @xmath99 , so we can get information on the sterile neutrino mixings from precise measurements of the coefficients of the oscillation mode @xmath100 , which are the dominant contribution to the probability .
we have evaluated sensitivity numerically by taking matter effects into account , and the results are given in figs.[aba : fig2]-[aba : fig5 ] . since we have assumed @xmath101ev@xmath27 ) , the results for @xmath102 ev@xmath27 are not given in the figures .
the advantage of measurements with the far detectors is that sensitivity is independent of @xmath103 and it is good even for lower values of @xmath103 in most cases . in particular , in the case of the golden channel @xmath104 , the far detectors improve the present bound on @xmath105 by two orders of magnitude for all the values of @xmath101ev@xmath27 ) .
the neutrino factory with far detectors , therefore , can provide a very powerful test of the lsnd anomaly .
their disadvantage of measurements with the far detectors is that sensitivity is not as good as that of the near detectors , which will be described in the next subsection , at the peak .
-0.3 cm -3 mm -3 mm in my talk i skipped the discussions on sensitivity of a neutrino factory with near detectors , but because of recent interest on the near detector issues,@xcite i will describe sensitivity of measurements with near detectors for the sake of completeness . in ref .
sensitivity of a neutrino factory with near detectors to sterile neutrino mixings was studied .
the setup used in this analysis is the following : the muon energy is 20gev , the number of useful muons is @xmath106 @xmath23 s per year , the measurements are supposed to continue for 5 years , the volume of a magnetized iron calorimeter at the distance @xmath65=40 km is 40kton , that of an emulsion cloud chamber at @xmath65=1 km is 1kton , and the statistical errors and the backgrounds are taken into account . at such short baselines , latexmath:[$|\delta m^2_{41}l/2e|\sim{\cal o}(1)\gg only relevant mass squared difference is @xmath51 .
so we have the following oscillation probabilities : @xmath108 thus we can determine @xmath109 or @xmath110 from the coefficient of the dominant oscillation mode @xmath111 .
the results are shown in figs.[aba : fig2]-[aba : fig5 ] .
the mass squared difference for which this neutrino factory setup has the best performance depends on the baseline length @xmath65 , and in the present case it is approximately 10ev@xmath27 .
the advantage of measurements with the near detectors is that sensitivity to the sterile neutrino mixings is very good at the peak while their disadvantage is that sensitivity becomes poorer for lower values of @xmath51 . from these results ,
we conclude that the near and far detectors are complementary in their performance .
the results in the previous section suggest that the discovery channel @xmath3 may not be so powerful in giving the upper bound on the mixing angles . to see the role of the discovery channel ,
let us now consider the effects of the cp phases in neutrino oscillations
. in matter t violation @xmath112 is more useful than cp violation @xmath113 , so i will discuss t violation in four neutrino schemes . , and the second term is proportional to @xmath114 in the standard three flavor framework@xcite in constant - density matter , as in the case in vacuum .
so t violation is phenomenologically suitable to examine @xmath9 . in the case of cp violation , on the other hand
, cp is violated in matter even if the cp phase vanishes . in practice
, people perform a numerical analysis by fitting the hypothetical oscillation probability to the full data including neutrinos and anti - neutrinos , instead of measuring @xmath113 or @xmath115 .
so discussions on cp violation or t violation should be regarded as tools to help us understand the results intuitively . ] in the three flavor scheme it is known that t violation is given by @xmath116 the jarlskog factor im@xmath117 can be written as@xcite @xmath118 if @xmath119 , then the differences of the eigenvalues in this case are all of @xmath120 in the zeroth order in @xmath121 . in that case the product of the sine factors @xmath122 is of @xmath123(1 ) , but in eq.([j3 ] ) we have a suppression factor @xmath124 ) is replaced by @xmath125 in the case of neutrino energy with @xmath119 , the dominant contribution in eq.([cp4 ] ) to the leading order in the small mixing angles is given by @xmath126 where we have averaged over rapid oscillations due to @xmath51 , i.e. , @xmath127 = @xmath128 . to compare t violation in the different schemes or in different channels
, we have only to compare the jarlskog factors im(@xmath129 ) in eqs.([j4 ] ) and ( [ j3 ] ) , since the sine factors @xmath122 in eq.([cp3 ] ) and @xmath130 in eq.([j4 ] ) are both of @xmath131 .
if the sterile neutrino mixing angles are roughly as large as @xmath5 , then it turns out the dominant contribution to the jarlskog factor comes from im@xmath132 , which appears in im@xmath133 with coefficients of @xmath131 if we plug eq.([x3 ] ) in eq.([j4 ] ) .
furthermore , let us introduce a parametrization for the @xmath134 mixing matrix with three cp phases @xmath135 : -5 mm @xmath136 where @xmath137 are the @xmath134 complex rotation matrices defined by @xmath138_{pq } = \left\ { \begin{array}{ll } \cos \theta_{ij } & p = q = i , j \\ 1 & p = q \not= i , j \\
\sin \theta_{ij } \ e^{-i\delta_{l } } & p = i;q = j \\ -\sin \theta_{ij } \
e^{i\delta_{l } } & p = j;q = i \\ 0 & \mbox{\rm otherwise.}\end{array } \right\}. \nonumber\end{aligned}\ ] ] @xmath139 stands for the mixing angle in short baseline reactor neutrino oscillations , and @xmath140 ( @xmath141 ) represents the ratio of the oscillation modes due to @xmath8 and @xmath51 ( the ratio of the active and sterile neutrino oscillations ) in the atmospheric neutrinos , respectively . in the limit when these extra mixing angles @xmath142 become zero , @xmath143 becomes the standard cp phase in the three flavor scheme .
the explicit forms of the mixing matrix elements @xmath144 can be found in the appendix a in ref . .
from the constraints of the short baseline reactor experiments and the atmospheric neutrino data , these angles are constrained as@xcite @xmath145 , @xmath146 , @xmath147 .
if we assume the upper bounds for @xmath142 and @xmath5 , for which we have @xmath148 , then together with the best fit values for the solar and atmospheric oscillation angles @xmath149 , @xmath150 , we obtain the following jarlskog factor : @xmath151 for the ( 3 + 1)-scheme , where @xmath152 and @xmath153 .
these results should be compared with the standard jarlskog factor : @xmath154 notice that the jarlskog factor is independent of the flavor @xmath155 in the three flavor case .
assuming that all the cp phases are maximal , i.e. , @xmath156 note that the term which would reduce to the three flavor t violation in the limit @xmath157 is contained in eq.([j4 ] ) as a subdominant contribution which is suppressed by @xmath158 . from this
we see that dominant contribution to t violation in the ( 3 + 1)-scheme could be potentially much larger when measured with the discovery channel than that in the ( 3 + 1)-scheme with the golden channel or than that in the standard three flavor scheme .
in fact it was shown in ref . by a detailed analysis that the cp phase may be measured using the discovery and disappearance channels . in generic
see - saw models the kinetic term gets modified after integrating out the right handed neutrino and unitarity is expected to be violated.@xcite in the case of the so - called minimal unitarity violation , in which only three light neutrinos are involved and sources of unitarity violation are assumed to appear only in the neutrino sector , deviation from unitarity is strongly constrained from the rare decays of charged leptons . expressing the nonunitary mixing matrix @xmath159 as @xmath160 , where @xmath161 is a unitary matrix while @xmath162 is a hermitian matrix which stands for deviation from unitarity , the bounds are typically @xmath163(0.1% ) @xcite .
the cp asymmetry in this scenario in the two flavor framework can be expressed as@xcite @xmath164 the constraint on @xmath165 is weaker that than on @xmath166 , and it was shown@xcite that the cp violating phase arg@xmath167 may be measured at a neutrino factory with the discovery channel .
in this talk i described sensitivity of a neutrino factory to the sterile neutrino mixings .
the golden channel @xmath0 improves the present upper bound on @xmath105 by two orders of magnitude , and provides a powerful test for the lsnd anomaly .
it is emphasized that @xmath64 detection at a neutrino factory is important to check unitarity , and the discovery channel @xmath3 is one of the promising channels to look for physics beyond the standard three flavor scenario .
we may be able measure the new cp violating phase using this channel in the sterile neutrino schemes and in the scenario with unitarity violation due to heavy particles .
i would like to thank h.v .
klapdor - kleingrothaus , r.d .
viollier and other organizers for invitation and hospitality during the conference .
i would also like to thank a. donini , k. fuki , j. lopez - pavon and d. meloni for collaboration on ref . .
this research was supported in part by a grant - in - aid for scientific research of the ministry of education , science and culture , # 21540274 . c. amsler _ et al . _
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d * 80 * , 033002 ( 2009 ) [ arxiv:0903.3986 [ hep - ph ] ] . | sensitivity of a neutrino factory to various mixing angles in a scheme with one sterile neutrino is studied using @xmath0 , @xmath1 , @xmath2 and @xmath3 .
while the `` discovery - channel '' @xmath3 is neither useful in the standard three flavor scheme nor very powerful in the sensitivity study of sterile neutrino mixings , this channel is important to check unitarity and to probe the new cp phase in the scheme beyond the standard neutrino mixing framework . | <s>[INST]it is known that the deficit of the solar and atmospheric neutrinos are due to neutrino oscillations among three flavors of neutrinos , and these observations offer evidence of neutrino masses and mixings.@xcite the standard three flavor framework of neutrino oscillations are described by six oscillation parameters : three mixing angles @xmath4 , @xmath5 , @xmath6 , the two independent mass squared differences @xmath7 , @xmath8 , and one cp violating phase @xmath9 , where @xmath10 and @xmath11 stands for the mass of the neutrino mass eigenstate . from the solar neutrino data , we have @xmath12 , and from the atmospheric neutrino data we have @xmath13 . on the other hand , only the upper bound on @xmath5 is known ( @xmath14 ) , is found .
this result , however , is compatible with @xmath15 at less than @xmath16 , and it is not yet statistically significant enough to be taken seriously . ] and no information on @xmath9 is known at present . to determine @xmath5 and @xmath9 , various neutrino long baseline experiments have been proposed@xcite , and the ongoing and proposed future neutrino long baseline experiments with an intense beam include conventional super ( neutrino ) beam experiments such as t2k,@xcite no@xmath17a,@xcite lbne,@xcite t2kk,@xcite the @xmath18 beam proposal,@xcite which uses a @xmath19 ( @xmath20 ) beam from @xmath18-decays of radioactive isotopes , and the neutrino factory proposal,@xcite in which @xmath20 and @xmath21 ( @xmath19 and @xmath22 ) are produced from decays of @xmath23 ( @xmath24 ) .
as in the case of the b factories@xcite , precise measurements in these experiments allow us not only to determine the oscillation parameters precisely but also to probe new physics by looking for deviation from the standard three flavor scheme .
in particular , test of unitarity is one of the important subjects in neutrino oscillations , and tau detection is crucial for that purpose . among the proposals for future long baseline experiments , the neutrino factory facility produces a neutrino beam of the highest neutrino energy , and it is advantageous to detect @xmath25 , because of the large cross section at high energy .
new physics which has been discussed in the context of neutrino oscillation includes sterile neutrinos,@xcite the non - standard interactions during neutrino propagation@xcite , the non - standard interactions at production and detection@xcite , violation of unitarity due to heavy particles@xcite , etc .
these scenarios , except the non - standard interactions during neutrino propagation , offer interesting possibilities for violation of three flavor unitarity . among these possibilities ,
phenomenological bound of unitarity violation is typically of @xmath26(1% ) in the case of non - standard interactions at production and detection , and it is of @xmath26(0.1% ) in the case of unitarity violation due to heavy particles.@xcite on the other hand , the bound in the case of sterile neutrinos is of @xmath26(10% ) which comes mainly from the constraints of the atmospheric neutrino data,@xcite so scenarios with sterile neutrinos seem to be phenomenologically more promising to look for than other possibilities of unitarity violation .
in this talk i will discuss phenomenology of schemes with sterile neutrinos at a neutrino factory .
schemes with sterile neutrinos have attracted a lot of attention since the lsnd group announced the anomaly which suggest neutrino oscillations with mass squared difference of @xmath26(1ev@xmath27).@xcite .
the reason that we need one extra neutrino to account for lsnd is because the standard three flavor scheme has only two independent mass squared differences , i.e. , @xmath28ev@xmath27 for the solar neutrino oscillation , and @xmath29ev@xmath27 for the atmospheric neutrino oscillation , and it does not have room for the mass squared difference of @xmath26(1ev@xmath27 ) . and
the reason that the extra state has to be sterile neutrino , which is singlet with respect to the gauge group of the standard model , is because the number of weakly interacting light neutrinos has to be three from the lep data.@xcite the lsnd anomaly has been tested by the miniboone experiment , and it gave a negative result for neutrino oscillations with mass squared difference of @xmath26(1ev@xmath27).@xcite while the miniboone data disfavor the region suggested by lsnd , ref . gave the allowed region from the combined analysis of the lsnd and miniboone data , and it is not so clear whether the miniboone data alone are significant enough to exclude the lsnd region . on the other hand , even if the miniboone data are taken as negative evidence against the lsnd region , there still remains a possibility for sterile neutrino scenarios whose mixing angles are small enough to satisfy the constraints of miniboone and the other negative results .
the effect of these scenarios could reveal as violation of three flavor unitarity in the future neutrino experiments .
so in this talk i will discuss sterile neutrino schemes as one of phenomenologically viable possibilities for unitarity violation , regardless of whether the lsnd anomaly is excluded by the miniboone data or not . it has been known that sterile neutrino schemes may have cosmological problems ( see , e.g. , ref . )
. however , these cosmological discussions depend on models and assumptions , and i will not discuss cosmological constraints in this talk . also it has been pointed out that some sterile neutrino models@xcite have absorption effects even for neutrino energy below 1tev , but i will not take such effects into consideration for simplicity .
for simplicity i will discuss schemes with four neutrinos , although phenomenology of the schemes with two@xcite or three@xcite sterile neutrinos have also been discussed . denoting sterile neutrinos as @xmath30 , we have the following mixing between the flavor eigen states @xmath31 and the mass eigenstates @xmath32 : @xmath33 there are two kind of schemes with four neutrinos , depending on how the mass eigenstates are separated by the largest mass squared difference .
one is the ( 2 + 2)-scheme in which two mass eigenstates are separated by other two , and the other one is the ( 3 + 1)-scheme in which one mass eigenstate is separated by other three ( cf .
fig.[aba : fig1 ] ) . -0.7 cm
-0.5 cm in this scheme the fraction of sterile neutrino contributions to solar and atmospheric oscillations is given by @xmath34 and @xmath35 , respectively , where the mass squared differences @xmath7 and @xmath36 are assumed to be those of the solar and atmospheric oscillations .
the experimental results show that mixing among active neutrinos give dominant contributions to both the solar and atmospheric oscillations ( see , e.g. , ref . ) . in particular , in fig .
19 of ref .
we can see that at the 99% level @xmath37 and @xmath38 , from the solar and atmospheric oscillations , respectively , and this contradicts the unitarity condition @xmath39 .
in fact the ( 2 + 2)-schemes are excluded at 5.1@xmath40 cl @xcite .
this conclusion is independent of whether we take the lsnd data into consideration or not and i will not consider ( 2 + 2)-schemes in this talk .
phenomenology of the ( 3 + 1)-scheme is almost the same as that of the standard three flavor scenario , as far as the solar and atmospheric oscillations are concerned . on the other hand
, this scheme has tension between the lsnd data and other negative results of the short baseline experiments . among others ,
the cdhsw@xcite and bugey@xcite experiments give the bound on @xmath41 and @xmath42 , respectively , and in order for the lsnd data to be affirmative , the following relation has to be satisfied@xcite : @xmath43 where @xmath44 , @xmath45 , @xmath46 are the value of the effective two - flavor mixing angle as a function of the mass squared difference @xmath47 in the allowed region for lsnd ( @xmath48 ) , the cdhsw experiment ( @xmath49 ) , and the bugey experiment ( @xmath50 ) , respectively .
the ( 3 + 1)-scheme to account for lsnd in terms of neutrino oscillations is disfavored because eq .
( [ relation31 ] ) is not satisfied for any value of @xmath47 .
this argument has been shown quantitatively by ref . including the atmospheric neutrino data and other negative results . in fig.[aba : fig2 ] the right hand side of the lines denoted as `` null sbl 90% ( 99% ) '' is the excluded region at 90% ( 99% ) cl by the atmospheric neutrino data and all the negative results of short baseline experiments , whereas the allowed region by the combined analysis of the lsnd and miniboone data at 90% ( 99% ) cl is also shown . in the following discussions i will assume the mass pattern depicted in fig.[aba : fig1](b ) because the inverted ( 3 + 1)-scheme is disfavored by cosmology , and
i will also assume for simplicity that the largest mass squared difference @xmath51 is larger than @xmath52(0.1ev@xmath27 ) , so that i can average over rapid oscillations due to @xmath51 in the long baseline experiments as well as in the atmospheric neutrino observations .
-1.0 cm -0.3 cm
unlike conventional long baseline neutrino experiments , neutrino factories use muon decays @xmath53 and @xmath54 to produce neutrinos . in the setup suggested in the physics report@xcite of _ international scoping study for a future neutrino factory and super - beam facility _ , muons of both polarities are accelerated up to @xmath55 gev and injected into one storage ring with a geometry that allows to aim at two far detectors , the first located at 4000 km and the second at 7500 km from the source .
the reason to put far detectors at two locations is to resolve so - called parameter degeneracy.@xcite the useful channels at neutrino factories are the following : @xmath56 @xmath0 and @xmath57 : the golden channel @xmath56 @xmath1 and @xmath58 : the disappearance channel @xmath56 @xmath2 and @xmath59 : the silver channel @xmath56 @xmath3 and @xmath60 : the discovery channel at neutrino factories , electrons and positrons produced out of @xmath19 and @xmath61 create electromagnetic showers , which make it difficult to identify their charges . on the other hand ,
charge identification is much easier for @xmath62 detection , so the golden channel @xmath0 is used unlike the conventional long baseline neutrino experiments which use @xmath63 .
the golden channel turns out to be powerful because of very low backgrounds .
the disappearance channel is also useful because of a lot of statistics .
the golden and disappearance channels are observed by looking for muons with magnetized iron calorimeters.@xcite on the other hand , the silver and discovery channels are observed by looking for @xmath64 s with emulsion cloud chambers ( nonmagnetized@xcite or magnetized@xcite ) , and the statistics of the silver channel is limited .
the silver channel is useful to resolve parameter degeneracy .
combination of the golden , disappearance and discovery channels is expected to enable us to check unitarity .
studied sensitivity of a neutrino factory with far detectors to sterile neutrino mixings .
the setup is the following:=3000 km and @xmath65=7500 km , and it was shown that sensitivity with @xmath64 detectors increases for 50gev because of higher statistics . in this talk , however , i will only mention the results for the neutrino factory with muon energy 20gev for simplicity . ]
the muon energy is 20gev , the number of useful muons is @xmath66 @xmath23 s _ and _
@xmath24 s per year , the measurements are supposed to continue for 4 years , the baseline lengths are @xmath65=4000 km and @xmath65=7500 km , the volume of each magnetized iron calorimeter at the two distances is 50kton , that of each magnetized emulsion cloud chamber at the two distances is 4kton , and the statistical as well as systematic errors and the backgrounds are taken into account . at long baseline lengths such as @xmath65=7500 km , matter effects become important .
the oscillation probability in constant - density matter can be obtained by the formalism of kimura , takamura and yokomakura@xcite .
the oscillation probability in matter can be written as @xmath67 -2 mm where @xmath68 , @xmath69 , @xmath70 and @xmath71 are the energy eigenvalue and the neutrino mixing matrix element in matter defined by @xmath72 ( @xmath73 ) .
the matter potentials @xmath74 , @xmath75 are given by @xmath76 , @xmath77 , where @xmath78 and @xmath79 are the density of electrons and neutrinos , respectively .
the neutrino energy @xmath80 and the baseline length @xmath65 which are typical at a neutrino factory satisfy @xmath81 , @xmath82 and @xmath83 , and the energy eigenvalues in this case to the lowest order in the small mixing angles and to first order in @xmath84 are @xmath85 , @xmath86 , @xmath87 , @xmath88 .
it can be shown that the 4-th component @xmath89 in matter is the same as that in vacuum : @xmath90 , where the notation @xmath91 has been also introduced for the quantity in vacuum .
on the other hand , other three components are given by @xmath92 where @xmath93 in eq .
( [ x ] ) @xmath94 is the matrix element of the matter potential , and no sum is understood over the indices @xmath95 .
if the sterile neutrino mixings @xmath96 are small , then @xmath97 reproduce those for the standard three flavor case
. these sterile neutrino mixings @xmath98 appear in the coefficients @xmath97 in front of the sine factors @xmath99 , so we can get information on the sterile neutrino mixings from precise measurements of the coefficients of the oscillation mode @xmath100 , which are the dominant contribution to the probability .
we have evaluated sensitivity numerically by taking matter effects into account , and the results are given in figs.[aba : fig2]-[aba : fig5 ] . since we have assumed @xmath101ev@xmath27 ) , the results for @xmath102 ev@xmath27 are not given in the figures .
the advantage of measurements with the far detectors is that sensitivity is independent of @xmath103 and it is good even for lower values of @xmath103 in most cases . in particular , in the case of the golden channel @xmath104 , the far detectors improve the present bound on @xmath105 by two orders of magnitude for all the values of @xmath101ev@xmath27 ) .
the neutrino factory with far detectors , therefore , can provide a very powerful test of the lsnd anomaly .
their disadvantage of measurements with the far detectors is that sensitivity is not as good as that of the near detectors , which will be described in the next subsection , at the peak .
-0.3 cm -3 mm -3 mm in my talk i skipped the discussions on sensitivity of a neutrino factory with near detectors , but because of recent interest on the near detector issues,@xcite i will describe sensitivity of measurements with near detectors for the sake of completeness . in ref .
sensitivity of a neutrino factory with near detectors to sterile neutrino mixings was studied .
the setup used in this analysis is the following : the muon energy is 20gev , the number of useful muons is @xmath106 @xmath23 s per year , the measurements are supposed to continue for 5 years , the volume of a magnetized iron calorimeter at the distance @xmath65=40 km is 40kton , that of an emulsion cloud chamber at @xmath65=1 km is 1kton , and the statistical errors and the backgrounds are taken into account . at such short baselines , latexmath:[$|\delta m^2_{41}l/2e|\sim{\cal o}(1)\gg only relevant mass squared difference is @xmath51 .
so we have the following oscillation probabilities : @xmath108 thus we can determine @xmath109 or @xmath110 from the coefficient of the dominant oscillation mode @xmath111 .
the results are shown in figs.[aba : fig2]-[aba : fig5 ] .
the mass squared difference for which this neutrino factory setup has the best performance depends on the baseline length @xmath65 , and in the present case it is approximately 10ev@xmath27 .
the advantage of measurements with the near detectors is that sensitivity to the sterile neutrino mixings is very good at the peak while their disadvantage is that sensitivity becomes poorer for lower values of @xmath51 . from these results ,
we conclude that the near and far detectors are complementary in their performance .
the results in the previous section suggest that the discovery channel @xmath3 may not be so powerful in giving the upper bound on the mixing angles . to see the role of the discovery channel ,
let us now consider the effects of the cp phases in neutrino oscillations
. in matter t violation @xmath112 is more useful than cp violation @xmath113 , so i will discuss t violation in four neutrino schemes . , and the second term is proportional to @xmath114 in the standard three flavor framework@xcite in constant - density matter , as in the case in vacuum .
so t violation is phenomenologically suitable to examine @xmath9 . in the case of cp violation , on the other hand
, cp is violated in matter even if the cp phase vanishes . in practice
, people perform a numerical analysis by fitting the hypothetical oscillation probability to the full data including neutrinos and anti - neutrinos , instead of measuring @xmath113 or @xmath115 .
so discussions on cp violation or t violation should be regarded as tools to help us understand the results intuitively . ] in the three flavor scheme it is known that t violation is given by @xmath116 the jarlskog factor im@xmath117 can be written as@xcite @xmath118 if @xmath119 , then the differences of the eigenvalues in this case are all of @xmath120 in the zeroth order in @xmath121 . in that case the product of the sine factors @xmath122 is of @xmath123(1 ) , but in eq.([j3 ] ) we have a suppression factor @xmath124 ) is replaced by @xmath125 in the case of neutrino energy with @xmath119 , the dominant contribution in eq.([cp4 ] ) to the leading order in the small mixing angles is given by @xmath126 where we have averaged over rapid oscillations due to @xmath51 , i.e. , @xmath127 = @xmath128 . to compare t violation in the different schemes or in different channels
, we have only to compare the jarlskog factors im(@xmath129 ) in eqs.([j4 ] ) and ( [ j3 ] ) , since the sine factors @xmath122 in eq.([cp3 ] ) and @xmath130 in eq.([j4 ] ) are both of @xmath131 .
if the sterile neutrino mixing angles are roughly as large as @xmath5 , then it turns out the dominant contribution to the jarlskog factor comes from im@xmath132 , which appears in im@xmath133 with coefficients of @xmath131 if we plug eq.([x3 ] ) in eq.([j4 ] ) .
furthermore , let us introduce a parametrization for the @xmath134 mixing matrix with three cp phases @xmath135 : -5 mm @xmath136 where @xmath137 are the @xmath134 complex rotation matrices defined by @xmath138_{pq } = \left\ { \begin{array}{ll } \cos \theta_{ij } & p = q = i , j \\ 1 & p = q \not= i , j \\
\sin \theta_{ij } \ e^{-i\delta_{l } } & p = i;q = j \\ -\sin \theta_{ij } \
e^{i\delta_{l } } & p = j;q = i \\ 0 & \mbox{\rm otherwise.}\end{array } \right\}. \nonumber\end{aligned}\ ] ] @xmath139 stands for the mixing angle in short baseline reactor neutrino oscillations , and @xmath140 ( @xmath141 ) represents the ratio of the oscillation modes due to @xmath8 and @xmath51 ( the ratio of the active and sterile neutrino oscillations ) in the atmospheric neutrinos , respectively . in the limit when these extra mixing angles @xmath142 become zero , @xmath143 becomes the standard cp phase in the three flavor scheme .
the explicit forms of the mixing matrix elements @xmath144 can be found in the appendix a in ref . .
from the constraints of the short baseline reactor experiments and the atmospheric neutrino data , these angles are constrained as@xcite @xmath145 , @xmath146 , @xmath147 .
if we assume the upper bounds for @xmath142 and @xmath5 , for which we have @xmath148 , then together with the best fit values for the solar and atmospheric oscillation angles @xmath149 , @xmath150 , we obtain the following jarlskog factor : @xmath151 for the ( 3 + 1)-scheme , where @xmath152 and @xmath153 .
these results should be compared with the standard jarlskog factor : @xmath154 notice that the jarlskog factor is independent of the flavor @xmath155 in the three flavor case .
assuming that all the cp phases are maximal , i.e. , @xmath156 note that the term which would reduce to the three flavor t violation in the limit @xmath157 is contained in eq.([j4 ] ) as a subdominant contribution which is suppressed by @xmath158 . from this
we see that dominant contribution to t violation in the ( 3 + 1)-scheme could be potentially much larger when measured with the discovery channel than that in the ( 3 + 1)-scheme with the golden channel or than that in the standard three flavor scheme .
in fact it was shown in ref . by a detailed analysis that the cp phase may be measured using the discovery and disappearance channels . in generic
see - saw models the kinetic term gets modified after integrating out the right handed neutrino and unitarity is expected to be violated.@xcite in the case of the so - called minimal unitarity violation , in which only three light neutrinos are involved and sources of unitarity violation are assumed to appear only in the neutrino sector , deviation from unitarity is strongly constrained from the rare decays of charged leptons . expressing the nonunitary mixing matrix @xmath159 as @xmath160 , where @xmath161 is a unitary matrix while @xmath162 is a hermitian matrix which stands for deviation from unitarity , the bounds are typically @xmath163(0.1% ) @xcite .
the cp asymmetry in this scenario in the two flavor framework can be expressed as@xcite @xmath164 the constraint on @xmath165 is weaker that than on @xmath166 , and it was shown@xcite that the cp violating phase arg@xmath167 may be measured at a neutrino factory with the discovery channel .
in this talk i described sensitivity of a neutrino factory to the sterile neutrino mixings .
the golden channel @xmath0 improves the present upper bound on @xmath105 by two orders of magnitude , and provides a powerful test for the lsnd anomaly .
it is emphasized that @xmath64 detection at a neutrino factory is important to check unitarity , and the discovery channel @xmath3 is one of the promising channels to look for physics beyond the standard three flavor scenario .
we may be able measure the new cp violating phase using this channel in the sterile neutrino schemes and in the scenario with unitarity violation due to heavy particles .
i would like to thank h.v .
klapdor - kleingrothaus , r.d .
viollier and other organizers for invitation and hospitality during the conference .
i would also like to thank a. donini , k. fuki , j. lopez - pavon and d. meloni for collaboration on ref . .
this research was supported in part by a grant - in - aid for scientific research of the ministry of education , science and culture , # 21540274 . c. amsler _ et al . _
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while the `` discovery - channel '' @xmath3 is neither useful in the standard three flavor scheme nor very powerful in the sensitivity study of sterile neutrino mixings , this channel is important to check unitarity and to probe the new cp phase in the scheme beyond the standard neutrino mixing framework . </s> |
the second law of thermodynamics gives a fundamental limit to thermodynamic operations on systems in equilibrium states .
one of its formulations provides the lower bound for the work performed on a system during a thermodynamics operation that induces a transition between equilibrium states ; the lower bound is given by the change in the free energy and is achieved for quasistatic operations .
to establish analogous thermodynamic theory for nonequilibrium steady state ( ness ) is one of the challenging problems in physics . in recent attempts
@xcite , particularly investigated are relations to be satisfied by the work and entropy production ( or heat ) for transitions between nesss .
one of the candidates for nonequilibrium thermodynamics is the steady state thermodynamics ( sst ) proposed in @xcite . a central idea of the sst is to use excess work ( and excess heat ) , which is defined as follows . in nonequilibrium states ,
work is continuously supplied to the system , so that the total work @xmath0 during the transition between nesss diverges . therefore , for the construction of a meaningful thermodynamic theory for the transition , it is necessary to take a finite part out of @xmath0 . to this end , the excess work @xmath1 is defined by subtracting from @xmath0 the integral of the steady work flow in the instantaneous ness at each point of the operation @xcite .
studies along this idea have been developed in refs .
we here concentrate our attention on quasistatic transitions . in the regime near to equilibrium , the work version of the results in refs .
@xcite states that the excess work @xmath1 for quasistatic transitions is given by the change in a certain scalar potential . in the regime far from equilibrium , by contrast , the work version of refs .
@xcite states that in general it is not equal to the change in any scalar function but equal to a geometrical quantity ; i.e. , it is given by a line integral of a vector potential @xmath2 in the operation parameter space .
this suggests that @xmath2 plays an important role in sst .
since these studies are based on the microscopic dynamics , the relationship with the microscopic state has been developed .
in contrast , the relationship with macroscopic quantities has been less clear although there exist some studies on this issue @xcite .
particularly important is to clarify how the transport coefficients and response functions are treated in the framework of sst , because the transport coefficients are main quantities to characterize ness and are accessible in experiments . in this paper , as a first step toward this issue , we derive an expression of @xmath1 for quasistatic transitions in terms of the linear response function of ness .
we show that @xmath1 is equal to the line integral of a vector potential @xmath2 and clarify the relation between @xmath2 and the response function .
since the derivation relies only on the macroscopic phenomenological equation ( linear response relation ) , the result is universally valid ( independent of microscopic detail ) .
we also show that in the regime near to equilibrium @xmath1 is given by the change of a scalar potential thanks to the reciprocal relation .
furthermore , we connect the macroscopic theory for @xmath2 to microscopic physics by using a microscopic expression of the response function , which is called response - correlation relation ( rcr ) @xcite . we obtain a microscopic expression of @xmath2 that is consistent with the work version of the results in refs . @xcite .
we consider a system s that is in contact with multiple ( say @xmath3 ) reservoirs . a schematic diagram of the setup is shown in fig .
[ fig : schematic ] .
the @xmath4th reservoir is in the equilibrium state characterized by the chemical potential @xmath5 .
we denote the set of the chemical potentials by @xmath6 , i.e. , @xmath7 .
the temperatures of all the reservoirs are set to the same value .
we denote the particle current between s and the @xmath4th reservoir by @xmath8 , where we take the sign of @xmath8 positive when it flows from the reservoir to s. more precisely , @xmath8 at time @xmath9 is defined as @xmath10 , where @xmath11 is the particle number in the @xmath4th reservoir .
we assume that the reservoirs are sufficiently large so that they are not affected by the change in @xmath11 and remain in the equilibrium states on the time scale of interest .
we also assume that for a fixed @xmath6 a stable ness is realized in s uniquely and independently of initial states after a relaxation time .
we note that in the ness @xmath12 holds due to the particle number conservation in the total system ( s plus reservoirs ) , where @xmath13 is the expectation value of the current @xmath8 in the ness characterized by @xmath6 . reservoirs .
the @xmath4th reservoir is characterized by the chemical potential @xmath5 .
the particle current @xmath8 flows from the @xmath4th reservoir into the system .
, title="fig : " ] [ fig : illustration1 ] examples of such a setup are seen in field - effect semiconductor devices . a typical
one is the modulation - doped field - effect transistor ( modfet ) @xcite . in this example
, the system s is realized as the two - dimensional electron system , and the reservoirs are the electrodes ( source , drain , and gate ) .
suppose that at the initial time @xmath14 the system s is in a ness characterized by @xmath6 .
the difference @xmath15 may be so large that the initial ness is far from equilibrium . at @xmath16 , we change the chemical potentials from @xmath6 to @xmath17 with small constants @xmath18 .
then the state of the system s varies in time for @xmath19 , and after a sufficiently long time it settles to a new ness characterized by @xmath20 .
in this paper we investigate the work @xmath21 done on s during the transition between the nesss . for this purpose , we here consider the expectation value of the current @xmath8 from the macroscopic viewpoint of the linear response relation . to the linear order in @xmath22
, we can express the expectation value @xmath23 at @xmath19 as @xmath24 where @xmath25 , and @xmath26 is the linear response function of the ness @xcite , which satisfies the causality relation @xmath27 .
we note that the linear response relation ( [ linearresponse ] ) is a relation around a ness ( not equilibrium state ) and is valid for a ness even far from equilibrium if the ness is stable to perturbations .
also we can express the expectation value of the current @xmath8 in the final ness ( characterized by @xmath20 ) by the long - time limit of eq .
( [ linearresponse ] ) : @xmath28 where @xmath29 is the transport coefficient ( differential conductivity ) of the initial ness ( characterized by @xmath6 ) .
we again note that the limit exists if the ness is stable .
in nonequilibrium states , work @xmath21 is continuously supplied to the system s from the reservoirs , accompanied by the particle current to s. we can use the equilibrium thermodynamics to estimate the work done by the reservoirs since they are in the equilibrium states ; when the particle number in the @xmath4th reservoir increases by @xmath30 , the work done by the @xmath4th reservoir is given by @xmath31 therefore , the unit - time work by the @xmath4th reservoir is @xmath32 . from eq .
( [ linearresponse ] ) , we obtain the average work flow @xmath33 at time @xmath19 as @xmath34 where we neglected the @xmath35 terms in the second line .
the total work @xmath0 during the transition between the nesss is given by the time - integral of eq .
( [ workflow_t ] ) .
however , @xmath0 is a diverging quantity because the system s remains to be supplied with the work from the reservoirs after it reaches the final ness . to extract a finite quantity intrinsic to the transition
, we employ the idea of the sst @xcite ; we subtract from @xmath0 the contribution of the steady work flow @xmath36 in the final ness : @xmath37 we refer to this quantity as the excess work .
we note that @xmath1 is related to the excess heat @xmath38 as @xmath39 , where @xmath40 is the change in the energy of s between the nesss , due to the energy conservation in the transition between the nesss and the energy balance in the steady states .
our definition ( [ excesswork ] ) of @xmath1 is consistent with the definition of @xmath38 in refs .
we also note that the steady flow @xmath36 is equal to the long - time limit of eq .
( [ workflow_t ] ) : @xmath41 by substituting eqs .
( [ workflow_t ] ) and ( [ workflow_ss ] ) into eq .
( [ excesswork ] ) , we obtain @xmath42 where the @xmath43th component @xmath44 of the vector potential @xmath2 is given by @xmath45 .
\label{vectorpotentialresponse}\end{aligned}\ ] ] equation ( [ geometricalexcesswork ] ) indicates that the excess work during quasistatic transitions between nesss is not given by the difference of some scalar function @xmath46 but given by the geometrical quantity unless @xmath44 is equal to the @xmath47-derivative of @xmath46 for all @xmath43 .
this is consistent with the results in @xcite .
equation ( [ vectorpotentialresponse ] ) relates the nonequilibrium linear response function @xmath48 with the vector potential @xmath2 in the expression ( [ geometricalexcesswork ] ) .
therefore @xmath2 can be experimentally determined in principle , because @xmath48 is measurable .
the sufficient condition for @xmath49 for all @xmath43 is that @xmath50 holds for all @xmath51 , where @xmath52 is the abbreviation of @xmath53 . in the regime near to equilibrium ( linear response regime ) , we can use the response function @xmath54 of the equilibrium state in eq .
( [ vectorpotentialresponse ] ) .
then eq .
( [ maxwellrelation ] ) is valid because @xmath54 is independent of @xmath5 and the reciprocal relation @xmath55 holds .
therefore the extension of the clausius equality is possible in this regime , which is consistent with the results in refs
. @xcite .
up to here our formulation is closed on the macroscopic level .
now we connect it to microscopic physics . in this paper
we assume that the microscopic dynamics of the system s is governed by the quantum master equation ( qme ) @xcite : @xmath56 here , @xmath57 is the density matrix of s , and the generator @xmath58 is written as @xmath59/i\hbar + \sum_j \mathcal{l}_j$ ] , where @xmath60 is the hamiltonian of s and @xmath61 is the dissipator induced by the interaction with the @xmath43th reservoir . as in the previous sections , we assume that there exists a unique steady state in the qme .
the steady state density matrix @xmath62 satisfies @xmath63 .
first , we consider the connection to microscopic physics through the response function @xmath48 of ness .
for this purpose we employ the response - correlation relation ( rcr ) @xcite , which is a microscopic expression of @xmath48 . in the framework of the qme and for the response of the current @xmath8 from the @xmath4th reservoir into s , the rcr reads @xmath64 \delta(\tau ) + { \rm tr } \bigl [ \hat{i}_i e^{\mathcal{k}\tau } ( \partial_j \mathcal{k } ) \hat{\rho}_{\rm ss } \bigr ] , \label{rcr}\end{aligned}\ ] ] where @xmath65 is the trace over s and @xmath66 with @xmath67 being the particle number operator in s. see [ appendix : rcr ] for the derivation of eq .
( [ rcr ] ) .
note that @xmath68 can be regarded as the particle current operator from the @xmath4th reservoir into s because it satisfies the continuity equation : @xmath69 = \sum_i { \rm tr } [ \hat{i}_i \hat{\rho}(t)]$ ] . substituting eq .
( [ rcr ] ) into eq .
( [ vectorpotentialresponse ] ) , we obtain @xmath70 + { \rm tr } \bigl [ \hat{i}_i \mathcal{r } ( \partial_j \mathcal{k } ) \hat{\rho}_{\rm ss } \bigr ] \biggr\}. \label{vectorpotentialrcr}\end{aligned}\ ] ] note that the contribution from the first term in eq .
( [ rcr ] ) vanishes .
here we defined @xmath71 and @xmath72 , where the projection superoperator @xmath73 is defined such that @xmath74 holds for any linear operator @xmath75 .
see [ appendix : inverse ] for the fact that @xmath76 is a well - defined superopertor . to rewrite eq .
( [ vectorpotentialrcr ] ) further , we note the following relation : @xmath77 & = -{\rm tr}\bigl [ \hat{i}_i e^{\mathcal{k}(t - t ' ) } \mathcal{k } \mathcal{r } ( \partial_j \mathcal{k } ) \hat{\rho}_{\rm ss } \bigr ] \nonumber\\ & = -{\rm tr}\bigl [ \hat{i}_i e^{\mathcal{k}(t - t ' ) } \mathcal{q}_0 ( \partial_j \mathcal{k } ) \hat{\rho}_{\rm ss } \bigr ] \nonumber\\ & = -{\rm tr}\bigl [ \hat{i}_i e^{\mathcal{k}(t - t ' ) } ( \partial_j \mathcal{k } ) \hat{\rho}_{\rm ss } \bigr ] + { \rm tr}\bigl [ \hat{i}_i \hat{\rho}_{\rm ss } \bigr ] { \rm tr}\bigl[(\partial_j \mathcal{k } ) \hat{\rho}_{\rm ss } \bigr ] \nonumber\\ & = -{\rm tr}\bigl [ \hat{i}_i e^{\mathcal{k}(t - t ' ) } ( \partial_j \mathcal{k } ) \hat{\rho}_{\rm ss } \bigr ] . \label{integrand_vec}\end{aligned}\ ] ] in the third line we used @xmath78 see [ appendix : inverse ] for the derivation of eq .
( [ rk ] ) . in the last line of eq .
( [ integrand_vec ] ) we used @xmath79 = \partial_j { \rm tr}\bigl[\mathcal{k } \hat{\rho}_{\rm ss } \bigr ] - { \rm tr}\bigl[\mathcal{k } \partial_j \hat{\rho}_{\rm ss } \bigr ] = 0 $ ] .
this follows from @xmath80 and @xmath81=0 $ ] for any @xmath75 ( trace - preserving property of the qme ) . integrating eq .
( [ integrand_vec ] ) , we can rewrite the first term on the right hand side of eq .
( [ vectorpotentialrcr ] ) as @xmath82 = { \rm tr } \bigl
[ \hat{i}_i e^{\mathcal{k}(t - t_0 ) } \mathcal{r } ( \partial_j \mathcal{k } ) \hat{\rho}_{\rm ss } \bigr ] -{\rm tr } \bigl [ \hat{i}_i \mathcal{r } ( \partial_j \mathcal{k } ) \hat{\rho}_{\rm ss } \bigr ] .
\nonumber\end{aligned}\ ] ] the second term on the right hand side of this equation cancels out the second term on the right hand side of eq .
( [ vectorpotentialrcr ] ) .
we thus rewrite eq .
( [ vectorpotentialrcr ] ) as @xmath83 , \label{vectorpotentialrr}\end{aligned}\ ] ] where we used @xmath84 .
this is a microscopic expression of the vector potential @xmath2 .
next , we investigate the consistency of eq .
( [ vectorpotentialrr ] ) with the results in refs .
@xcite . in a manner almost the same as those in refs .
@xcite , we can derive another microscopic expression of @xmath2 without relying on eq .
( [ vectorpotentialresponse ] ) : @xmath85 where @xmath86 . here
, @xmath87 is the counting field in the full counting statistics ( fcs ) of the work @xmath21 from the reservoirs , and @xmath88 is the left eigenvector of @xmath89 corresponding to the eigenvalue @xmath90 that has the maximum real part .
@xmath91/i\hbar + \sum_j \mathcal{l}_j^\chi$ ] is the @xmath87-modified generator , which is introduced for the fcs in the framework of the qme @xcite .
see [ appendix : vectorpotentialqme ] for the details and derivation .
we note that @xmath92 ( identity operator ) , @xmath93 , and @xmath94 . in the following
we rewrite eq .
( [ vectorpotentialqme ] ) to show its equivalence to eq .
( [ vectorpotentialrr ] ) .
we first rewrite @xmath95 in eq .
( [ vectorpotentialqme ] ) . by differentiating the left eigenvalue equation @xmath96 with respect to @xmath97 and setting @xmath98
, we obtain @xmath99 here @xmath100 and the adjoint @xmath101 of a superoperator @xmath102 is defined by @xmath103 = { \rm tr } [ \hat{x}_1^\dag \mathcal{o } \hat{x}_2]$ ] for any pair @xmath104 of linear operators . by operating on the both sides of eq .
( [ kdag_ellprime ] ) with @xmath105 , we obtain @xmath106 where @xmath107 $ ] and we used eq .
( [ rk ] ) . substituting eq .
( [ ellprime ] ) into eq .
( [ vectorpotentialqme ] ) and using @xmath108 = \partial_j { \rm tr } [ \hat{\rho}_{\rm ss } ] = 0 $ ] , we have @xmath109 $ ]
. furthermore we can show @xmath110 .
with this equation we have @xmath111 .
\label{vectorpotentialqme_middle}\end{aligned}\ ] ] we next rewrite @xmath112 . by differentiating the steady - state equation @xmath113 with respect to @xmath47 and operating on it with @xmath76 , we have @xmath114 . substituting this equation into eq .
( [ vectorpotentialqme_middle ] ) we obtain @xmath83 .
\nonumber\end{aligned}\ ] ] this is the same as eq .
( [ vectorpotentialrr ] ) .
we thus show that eq .
( [ vectorpotentialrr ] ) [ and therefore eq .
( [ vectorpotentialresponse ] ) ] is consistent with the results in refs .
we have derived an expression of the excess work for quasistatic transitions between nesss in particle transport systems on the basis of the linear response relation .
we have related the vector potential @xmath2 in the expression with the response function .
we note that it is possible to extend our formulation to situations where other control parameters for transition between ness are varied .
in particular , we can obtain a similar result in heat conducting systems , where the temperatures of heat reservoirs are changed .
we finally make remarks .
first , the relationship between the excess work and the response function suggests that the response functions can be calculated in the framework of the sst .
we expect that this expression becomes a first step for understanding of how transport phenomena are treated in the sst .
second , as is mentioned below eq .
( [ excesswork ] ) , our definition of the excess work is consistent with the definition of the excess heat in refs .
. however the definition of the excess work and heat is not unique ; e.g. , there are hatano - sasa type @xcite and maes - neton type @xcite approaches .
recently , ref .
@xcite gave evidence that the hatano - sasa approach is appropriate for the definition .
since the hatano - sasa approach relies on microscopic information ( e.g. , steady - state distribution and transition rate ) , the connection to macroscopic quantities is not clear .
it is therefore important to investigate the definition from the viewpoint of response function as a future work .
third , in recent years the nonequilibrium response function is a hot topic in the statistical physics @xcite .
one of the points in recent works is decomposition of the response function @xcite .
we expect that the application of these results to the expression of the excess work would lead to a further decomposition of the work that is appropriate for the construction of the sst .
the author thanks k. akiba and m. yamaguchi for helpful discussions .
this work was supported by a jsps research fellowship for young scientists ( no .
24 - 1112 ) , kakenhi ( no .
26287087 ) , and impact program of council for science , technology and innovation ( cabinet office , government of japan ) .
here we derive eq .
( [ rcr ] ) , the rcr in qme .
we consider the qme ( [ qme ] ) that depends on multiple parameters @xmath115 like chemical potentials ; i.e. , we assume that the generator of the qme depends on these parameters : @xmath116 .
suppose that at time @xmath117 the system s is in the ness with @xmath118 ; i.e. , @xmath119 for @xmath117 , where @xmath120 satisfies @xmath121 with @xmath122 .
for @xmath19 , we weakly modulate the parameters in time : @xmath123 ( @xmath124 ) , where @xmath125 is much smaller than a typical value of @xmath126
. then we can expand the generator @xmath58 around @xmath127 in terms of @xmath128 : @xmath129 where @xmath130 . to solve the qme ( [ qme ] ) with the weakly time - dependent @xmath131 and the initial condition @xmath132
, we transform the qme into an `` interaction picture '' .
that is , we introduce @xmath133 .
then , from the qme ( [ qme ] ) , we have the equation of motion for @xmath134 as @xmath135 where we used eq .
( [ expandk ] ) . by integrating this equation form @xmath14
to @xmath9 with @xmath136 , we obtain @xmath137 in going from the first line to the second , we approximately replaced @xmath138 in the integral with @xmath120 .
this approximation corresponds to the first - order time - dependent perturbation theory in quantum mechanics .
going back to the schrdinger picture , we have @xmath139 we thus obtain the time dependence of the expectation value of a quantity @xmath75 that is independent of @xmath131 : @xmath140 \nonumber\\ & = \langle x \rangle^{\rm ss}_{\bm{\alpha}_0 } + \sum_l \int_{t_0}^t dt ' { \rm tr } \big [ \hat{x } e^{\mathcal{k}^0(t - t ' ) } ( \partial_l \mathcal{k}^0 ) \hat{\rho}_{\rm ss}^0 \bigr ] f_l(t ' ) \label{linearresponseqme1 } \\ & = \langle x \rangle^{\rm ss}_{\bm{\alpha}_0 } + \sum_l \int_{t_0}^t dt ' { \rm tr } \big [ \bigl\ { ( \partial_l \mathcal{k}^0)^\dag e^{\mathcal{k}^{0\dag}(t - t ' ) } \hat{x } \bigr\ } \hat{\rho}_{\rm ss}^0 \bigr ] f_l(t ' ) . \label{linearresponseqme2}\end{aligned}\ ] ] equations ( [ linearresponseqme1 ] ) and ( [ linearresponseqme2 ] ) give the rcr in the qme .
we note that eq .
( [ linearresponseqme2 ] ) reduces to the kubo formula if @xmath120 is an equilibrium state ( i.e. , when we consider the response of an equilibrium state ) @xcite .
now we consider the current @xmath141 from the @xmath4th reservoir into the system s. we note that @xmath68 is dependent on @xmath131 because so is @xmath142 .
therefore we have the average current at time @xmath9 as @xmath143 - { \rm tr } \big [ \hat{i}_i\bigl(\bm{\alpha}_0\bigr ) \hat{\rho}^0_{\rm ss } \bigr ] \nonumber\\ & = \sum_l { \rm tr } \big [ ( \partial_l \hat{i}_i^0 ) \hat{\rho}^0_{\rm ss } \bigr ] f_l(t ) + { \rm tr } \big [ \hat{i}_i^0 \hat{\rho}(t ) \bigr ] - { \rm tr } \big [ \hat{i}_i^0 \hat{\rho}^0_{\rm ss } \bigr ] \nonumber\\ & = \sum_l { \rm tr } \big [ ( \partial_l \hat{i}_i^0 ) \hat{\rho}^0_{\rm ss } \bigr ] f_l(t ) + \sum_l \int_{t_0}^t dt ' { \rm tr } \big [ \hat{i}_i^0 e^{\mathcal{k}^0(t - t ' ) } ( \partial_l \mathcal{k}^0 ) \hat{\rho}_{\rm ss}^0 \bigr ] f_l(t ' ) , \end{aligned}\ ] ] where @xmath144 and @xmath145 .
we used eq .
( [ linearresponseqme1 ] ) in the third line . finally , by performing the functional differentiation with respect to @xmath146
, we obtain @xmath147 \delta(t - t ' ) + { \rm tr } \bigl [ \hat{i}_i^0 e^{\mathcal{k}(t - t ' ) } ( \partial_j \mathcal{k } ) \hat{\rho}_{\rm ss}^0 \bigr ] .
\nonumber\end{aligned}\ ] ] this is equivalent to eq .
( [ rcr ] ) .
first we show that @xmath76 in eq . ( [ r ] )
is well defined . to this end
, we denote the eigenvalue and corresponding left and right eigenvectors of @xmath58 as @xmath148 , @xmath149 , and @xmath150 .
we assign the steady state of @xmath58 to the index @xmath151 ; i.e. , @xmath152 , @xmath153 , and @xmath154 . by the assumption of the unique existence of the stable steady state , @xmath155 for @xmath156 .
then , for any linear operator @xmath75 , we obtain the following equation : @xmath157 \hat{r}_m \nonumber\\ & = - \int_0^\infty dt \sum_{m\neq 0 } e^{\lambda_m t } { \rm tr}[\hat{\ell}_m^\dag \hat{x } ] \hat{r}_m \nonumber\\ & = \sum_{m\neq 0 } \frac{{\rm tr}[\hat{\ell}_m^\dag \hat{x}]}{\lambda_m } \hat{r}_m.\end{aligned}\ ] ] since this is not diverging , @xmath76 is well defined .
we here show that eq .
( [ rk ] ) holds for the generator @xmath58 of the qme .
we first note that @xmath158 follows from @xmath159 , which we can derive from the fact that @xmath160 = 0 , \label{pkx } \\
\mathcal{k } \mathcal{p}_0 \hat{x } & = \mathcal{k } \hat{\rho}_{\rm ss } { \rm tr } \hat{x } = 0 , \label{kpx}\end{aligned}\ ] ] hold for any linear operator @xmath75 .
equation ( [ pkx ] ) follows from @xmath161 = 0 $ ] ( trace - preserving property of qme ) , and eq .
( [ kpx ] ) from @xmath80 ( steady - state equation )
. then we can show eq .
( [ rk ] ) as follows : @xmath162 here the third line follows from the convergence theorem of the markov process , which we can derive from the fact that for any linear operator @xmath75 the following equation holds : @xmath163 \hat{r}_m \nonumber\\ & = \sum_m { \rm tr}[\hat{\ell}_m^\dag \hat{x } ] \hat{r}_m \lim_{t\to\infty } e^{\lambda_m(t - t_0 ) } \nonumber\\ & = \hat{\rho}_{\rm ss } { \rm tr}\hat{x}. \end{aligned}\ ] ] this gives the third line in eq .
( [ rk_a ] ) .
we note that eq .
( [ rk_a ] ) leads to @xmath164 .
this implies that @xmath76 satisfies one of the conditions for the moore - penrose pseudoinverse of @xmath58 .
for completeness we here derive eq .
( [ vectorpotentialqme ] ) , the work version of the results in refs . @xcite .
first we note that we can measure the work @xmath21 during varying the chemical potentials @xmath165 with a time interval @xmath166 as follows . at the initial time @xmath167
, we perform a projection measurement of reservoir particle numbers @xmath168 to obtain measurement outcomes @xmath169 . for @xmath19 , we vary @xmath6 , where the system evolves with interacting with the reservoirs . at @xmath170 , we again perform a measurement of @xmath171 to obtain outcomes @xmath172 .
the difference of the outcomes gives the work @xmath173 $ ] .
repeating the measurements , we obtain a probability distribution @xmath174 .
the average work is given by @xmath175 , and the average work flow in a ness is given by @xmath176 with @xmath6 being fixed . in the following ,
we calculate the average work by @xmath177 , where @xmath178 is the cumulant generating function and @xmath87 is the counting field . by using the full counting statistics
@xcite , we can calculate @xmath179 by @xmath180 here @xmath181 is the solution of the generalized quantum master equation ( gqme ) : @xmath182 where the generalized generator is given by @xmath183 /i\hbar
+ \sum_j \mathcal{l}_j^\chi$ ] , with the generalized dissipator @xmath184_\chi \bigr]_\chi$ ] .
@xmath185 is the trace over the @xmath43th reservoir , @xmath186 is the interaction hamiltonian between the system and the @xmath43th reservoir , @xmath187 is its interaction picture , @xmath188 is the thermal equilibrium state of the @xmath43th reservoir with the chemical potential @xmath47 , @xmath189_\chi \equiv \hat{o}_1^\chi \hat{o}_2 - \hat{o}_2 \hat{o}_1^{-\chi}$ ] , and @xmath190 .
note that , if we set @xmath98 , the gqme ( [ gqme ] ) reduces to the original qme ( [ qme ] ) , and @xmath89 , @xmath88 , and @xmath191 also reduce to @xmath58 , @xmath192 , and @xmath62 , respectively . for fixed @xmath6
, we can define the left and right eigenvectors of @xmath193 corresponding to the eigenvalue @xmath194 , which are respectively denoted by @xmath195 and @xmath196 .
they are normalized as @xmath197 .
we assign the label for the eigenvalue with the maximum real part to @xmath151 .
it is known that @xmath198 holds @xcite .
therefore , the average work flow @xmath199 in the ness can be calculated by @xmath200 we now derive eq .
( [ vectorpotentialqme ] ) .
we first note that the excess work can be written as @xmath201 , where @xmath202 and @xmath203 .
this is because @xmath177 and eq .
( [ workflux ] ) . to calculate @xmath204 , we solve the gqme ( [ gqme ] ) . for this purpose
we expand @xmath205 as @xmath206 substituting this expansion into eq .
( [ gqme ] ) and taking the hilbert - schmidt inner product with @xmath207 , we obtain @xmath208 .
\nonumber\end{aligned}\ ] ] if the time scale of varying @xmath6 is sufficiently slower than the relaxation time of the system , we can approximate the sum on the rhs by the contribution only from the term with @xmath151 ( adiabatic approximation ) . by solving the approximate equation
we obtain @xmath209 \right\ } , \label{c_0}\end{aligned}\ ] ] where @xmath210 is a path connecting @xmath211 and @xmath212 in the parameter space and @xmath213 . if @xmath214 , then @xmath215 $ ] . at long time ,
only the @xmath151 term remains in eq .
( [ expansion_rho ] ) since @xmath216 has the maximum real part
. therefore we obtain @xmath217 substituting eq .
( [ c_0 ] ) into this equation we obtain an expression for @xmath218 as @xmath219 + \ln { \rm tr}_{\rm s } \bigl [ \hat{\ell}_0^{\chi\dag } \bigl(\mu(t_0)\bigr ) \hat{\rho}_{\rm ss } \bigl(\mu(t_0)\bigr ) \bigr ] \nonumber\\ & + \ln { \rm tr}_{\rm s } \hat{r}_0^{\chi } \bigl(\mu(t_0+\tau)\bigr ) .
\label{cgf_ex}\end{aligned}\ ] ] finally , by differentiating eq .
( [ cgf_ex ] ) with respect to @xmath97 and setting @xmath98 , we obtain an expression for the excess work : @xmath220 . \label{excess_derived}\end{aligned}\ ] ] we thus obtain eq .
( [ vectorpotentialqme ] ) . | excess work is a non - diverging part of the work during transition between nonequilibrium steady states ( nesss ) .
it is a central quantity in the steady state thermodynamics ( sst ) , which is a candidate for nonequilibrium thermodynamics theory .
we derive an expression of excess work during quasistatic transitions between nesss by using the macroscopic linear response relation of ness .
this expression is a line integral of a vector potential in the space of control parameters .
we show a relationship between the vector potential and the response function of ness , and thus obtain a relationship between the sst and a macroscopic quantity .
we also connect the macroscopic formulation to microscopic physics through a microscopic expression of the nonequilibrium response function , which gives a result consistent with the previous studies . | <s>[INST]the second law of thermodynamics gives a fundamental limit to thermodynamic operations on systems in equilibrium states .
one of its formulations provides the lower bound for the work performed on a system during a thermodynamics operation that induces a transition between equilibrium states ; the lower bound is given by the change in the free energy and is achieved for quasistatic operations .
to establish analogous thermodynamic theory for nonequilibrium steady state ( ness ) is one of the challenging problems in physics . in recent attempts
@xcite , particularly investigated are relations to be satisfied by the work and entropy production ( or heat ) for transitions between nesss .
one of the candidates for nonequilibrium thermodynamics is the steady state thermodynamics ( sst ) proposed in @xcite . a central idea of the sst is to use excess work ( and excess heat ) , which is defined as follows . in nonequilibrium states ,
work is continuously supplied to the system , so that the total work @xmath0 during the transition between nesss diverges . therefore , for the construction of a meaningful thermodynamic theory for the transition , it is necessary to take a finite part out of @xmath0 . to this end , the excess work @xmath1 is defined by subtracting from @xmath0 the integral of the steady work flow in the instantaneous ness at each point of the operation @xcite .
studies along this idea have been developed in refs .
we here concentrate our attention on quasistatic transitions . in the regime near to equilibrium , the work version of the results in refs .
@xcite states that the excess work @xmath1 for quasistatic transitions is given by the change in a certain scalar potential . in the regime far from equilibrium , by contrast , the work version of refs .
@xcite states that in general it is not equal to the change in any scalar function but equal to a geometrical quantity ; i.e. , it is given by a line integral of a vector potential @xmath2 in the operation parameter space .
this suggests that @xmath2 plays an important role in sst .
since these studies are based on the microscopic dynamics , the relationship with the microscopic state has been developed .
in contrast , the relationship with macroscopic quantities has been less clear although there exist some studies on this issue @xcite .
particularly important is to clarify how the transport coefficients and response functions are treated in the framework of sst , because the transport coefficients are main quantities to characterize ness and are accessible in experiments . in this paper , as a first step toward this issue , we derive an expression of @xmath1 for quasistatic transitions in terms of the linear response function of ness .
we show that @xmath1 is equal to the line integral of a vector potential @xmath2 and clarify the relation between @xmath2 and the response function .
since the derivation relies only on the macroscopic phenomenological equation ( linear response relation ) , the result is universally valid ( independent of microscopic detail ) .
we also show that in the regime near to equilibrium @xmath1 is given by the change of a scalar potential thanks to the reciprocal relation .
furthermore , we connect the macroscopic theory for @xmath2 to microscopic physics by using a microscopic expression of the response function , which is called response - correlation relation ( rcr ) @xcite . we obtain a microscopic expression of @xmath2 that is consistent with the work version of the results in refs . @xcite .
we consider a system s that is in contact with multiple ( say @xmath3 ) reservoirs . a schematic diagram of the setup is shown in fig .
[ fig : schematic ] .
the @xmath4th reservoir is in the equilibrium state characterized by the chemical potential @xmath5 .
we denote the set of the chemical potentials by @xmath6 , i.e. , @xmath7 .
the temperatures of all the reservoirs are set to the same value .
we denote the particle current between s and the @xmath4th reservoir by @xmath8 , where we take the sign of @xmath8 positive when it flows from the reservoir to s. more precisely , @xmath8 at time @xmath9 is defined as @xmath10 , where @xmath11 is the particle number in the @xmath4th reservoir .
we assume that the reservoirs are sufficiently large so that they are not affected by the change in @xmath11 and remain in the equilibrium states on the time scale of interest .
we also assume that for a fixed @xmath6 a stable ness is realized in s uniquely and independently of initial states after a relaxation time .
we note that in the ness @xmath12 holds due to the particle number conservation in the total system ( s plus reservoirs ) , where @xmath13 is the expectation value of the current @xmath8 in the ness characterized by @xmath6 . reservoirs .
the @xmath4th reservoir is characterized by the chemical potential @xmath5 .
the particle current @xmath8 flows from the @xmath4th reservoir into the system .
, title="fig : " ] [ fig : illustration1 ] examples of such a setup are seen in field - effect semiconductor devices . a typical
one is the modulation - doped field - effect transistor ( modfet ) @xcite . in this example
, the system s is realized as the two - dimensional electron system , and the reservoirs are the electrodes ( source , drain , and gate ) .
suppose that at the initial time @xmath14 the system s is in a ness characterized by @xmath6 .
the difference @xmath15 may be so large that the initial ness is far from equilibrium . at @xmath16 , we change the chemical potentials from @xmath6 to @xmath17 with small constants @xmath18 .
then the state of the system s varies in time for @xmath19 , and after a sufficiently long time it settles to a new ness characterized by @xmath20 .
in this paper we investigate the work @xmath21 done on s during the transition between the nesss . for this purpose , we here consider the expectation value of the current @xmath8 from the macroscopic viewpoint of the linear response relation . to the linear order in @xmath22
, we can express the expectation value @xmath23 at @xmath19 as @xmath24 where @xmath25 , and @xmath26 is the linear response function of the ness @xcite , which satisfies the causality relation @xmath27 .
we note that the linear response relation ( [ linearresponse ] ) is a relation around a ness ( not equilibrium state ) and is valid for a ness even far from equilibrium if the ness is stable to perturbations .
also we can express the expectation value of the current @xmath8 in the final ness ( characterized by @xmath20 ) by the long - time limit of eq .
( [ linearresponse ] ) : @xmath28 where @xmath29 is the transport coefficient ( differential conductivity ) of the initial ness ( characterized by @xmath6 ) .
we again note that the limit exists if the ness is stable .
in nonequilibrium states , work @xmath21 is continuously supplied to the system s from the reservoirs , accompanied by the particle current to s. we can use the equilibrium thermodynamics to estimate the work done by the reservoirs since they are in the equilibrium states ; when the particle number in the @xmath4th reservoir increases by @xmath30 , the work done by the @xmath4th reservoir is given by @xmath31 therefore , the unit - time work by the @xmath4th reservoir is @xmath32 . from eq .
( [ linearresponse ] ) , we obtain the average work flow @xmath33 at time @xmath19 as @xmath34 where we neglected the @xmath35 terms in the second line .
the total work @xmath0 during the transition between the nesss is given by the time - integral of eq .
( [ workflow_t ] ) .
however , @xmath0 is a diverging quantity because the system s remains to be supplied with the work from the reservoirs after it reaches the final ness . to extract a finite quantity intrinsic to the transition
, we employ the idea of the sst @xcite ; we subtract from @xmath0 the contribution of the steady work flow @xmath36 in the final ness : @xmath37 we refer to this quantity as the excess work .
we note that @xmath1 is related to the excess heat @xmath38 as @xmath39 , where @xmath40 is the change in the energy of s between the nesss , due to the energy conservation in the transition between the nesss and the energy balance in the steady states .
our definition ( [ excesswork ] ) of @xmath1 is consistent with the definition of @xmath38 in refs .
we also note that the steady flow @xmath36 is equal to the long - time limit of eq .
( [ workflow_t ] ) : @xmath41 by substituting eqs .
( [ workflow_t ] ) and ( [ workflow_ss ] ) into eq .
( [ excesswork ] ) , we obtain @xmath42 where the @xmath43th component @xmath44 of the vector potential @xmath2 is given by @xmath45 .
\label{vectorpotentialresponse}\end{aligned}\ ] ] equation ( [ geometricalexcesswork ] ) indicates that the excess work during quasistatic transitions between nesss is not given by the difference of some scalar function @xmath46 but given by the geometrical quantity unless @xmath44 is equal to the @xmath47-derivative of @xmath46 for all @xmath43 .
this is consistent with the results in @xcite .
equation ( [ vectorpotentialresponse ] ) relates the nonequilibrium linear response function @xmath48 with the vector potential @xmath2 in the expression ( [ geometricalexcesswork ] ) .
therefore @xmath2 can be experimentally determined in principle , because @xmath48 is measurable .
the sufficient condition for @xmath49 for all @xmath43 is that @xmath50 holds for all @xmath51 , where @xmath52 is the abbreviation of @xmath53 . in the regime near to equilibrium ( linear response regime ) , we can use the response function @xmath54 of the equilibrium state in eq .
( [ vectorpotentialresponse ] ) .
then eq .
( [ maxwellrelation ] ) is valid because @xmath54 is independent of @xmath5 and the reciprocal relation @xmath55 holds .
therefore the extension of the clausius equality is possible in this regime , which is consistent with the results in refs
. @xcite .
up to here our formulation is closed on the macroscopic level .
now we connect it to microscopic physics . in this paper
we assume that the microscopic dynamics of the system s is governed by the quantum master equation ( qme ) @xcite : @xmath56 here , @xmath57 is the density matrix of s , and the generator @xmath58 is written as @xmath59/i\hbar + \sum_j \mathcal{l}_j$ ] , where @xmath60 is the hamiltonian of s and @xmath61 is the dissipator induced by the interaction with the @xmath43th reservoir . as in the previous sections , we assume that there exists a unique steady state in the qme .
the steady state density matrix @xmath62 satisfies @xmath63 .
first , we consider the connection to microscopic physics through the response function @xmath48 of ness .
for this purpose we employ the response - correlation relation ( rcr ) @xcite , which is a microscopic expression of @xmath48 . in the framework of the qme and for the response of the current @xmath8 from the @xmath4th reservoir into s , the rcr reads @xmath64 \delta(\tau ) + { \rm tr } \bigl [ \hat{i}_i e^{\mathcal{k}\tau } ( \partial_j \mathcal{k } ) \hat{\rho}_{\rm ss } \bigr ] , \label{rcr}\end{aligned}\ ] ] where @xmath65 is the trace over s and @xmath66 with @xmath67 being the particle number operator in s. see [ appendix : rcr ] for the derivation of eq .
( [ rcr ] ) .
note that @xmath68 can be regarded as the particle current operator from the @xmath4th reservoir into s because it satisfies the continuity equation : @xmath69 = \sum_i { \rm tr } [ \hat{i}_i \hat{\rho}(t)]$ ] . substituting eq .
( [ rcr ] ) into eq .
( [ vectorpotentialresponse ] ) , we obtain @xmath70 + { \rm tr } \bigl [ \hat{i}_i \mathcal{r } ( \partial_j \mathcal{k } ) \hat{\rho}_{\rm ss } \bigr ] \biggr\}. \label{vectorpotentialrcr}\end{aligned}\ ] ] note that the contribution from the first term in eq .
( [ rcr ] ) vanishes .
here we defined @xmath71 and @xmath72 , where the projection superoperator @xmath73 is defined such that @xmath74 holds for any linear operator @xmath75 .
see [ appendix : inverse ] for the fact that @xmath76 is a well - defined superopertor . to rewrite eq .
( [ vectorpotentialrcr ] ) further , we note the following relation : @xmath77 & = -{\rm tr}\bigl [ \hat{i}_i e^{\mathcal{k}(t - t ' ) } \mathcal{k } \mathcal{r } ( \partial_j \mathcal{k } ) \hat{\rho}_{\rm ss } \bigr ] \nonumber\\ & = -{\rm tr}\bigl [ \hat{i}_i e^{\mathcal{k}(t - t ' ) } \mathcal{q}_0 ( \partial_j \mathcal{k } ) \hat{\rho}_{\rm ss } \bigr ] \nonumber\\ & = -{\rm tr}\bigl [ \hat{i}_i e^{\mathcal{k}(t - t ' ) } ( \partial_j \mathcal{k } ) \hat{\rho}_{\rm ss } \bigr ] + { \rm tr}\bigl [ \hat{i}_i \hat{\rho}_{\rm ss } \bigr ] { \rm tr}\bigl[(\partial_j \mathcal{k } ) \hat{\rho}_{\rm ss } \bigr ] \nonumber\\ & = -{\rm tr}\bigl [ \hat{i}_i e^{\mathcal{k}(t - t ' ) } ( \partial_j \mathcal{k } ) \hat{\rho}_{\rm ss } \bigr ] . \label{integrand_vec}\end{aligned}\ ] ] in the third line we used @xmath78 see [ appendix : inverse ] for the derivation of eq .
( [ rk ] ) . in the last line of eq .
( [ integrand_vec ] ) we used @xmath79 = \partial_j { \rm tr}\bigl[\mathcal{k } \hat{\rho}_{\rm ss } \bigr ] - { \rm tr}\bigl[\mathcal{k } \partial_j \hat{\rho}_{\rm ss } \bigr ] = 0 $ ] .
this follows from @xmath80 and @xmath81=0 $ ] for any @xmath75 ( trace - preserving property of the qme ) . integrating eq .
( [ integrand_vec ] ) , we can rewrite the first term on the right hand side of eq .
( [ vectorpotentialrcr ] ) as @xmath82 = { \rm tr } \bigl
[ \hat{i}_i e^{\mathcal{k}(t - t_0 ) } \mathcal{r } ( \partial_j \mathcal{k } ) \hat{\rho}_{\rm ss } \bigr ] -{\rm tr } \bigl [ \hat{i}_i \mathcal{r } ( \partial_j \mathcal{k } ) \hat{\rho}_{\rm ss } \bigr ] .
\nonumber\end{aligned}\ ] ] the second term on the right hand side of this equation cancels out the second term on the right hand side of eq .
( [ vectorpotentialrcr ] ) .
we thus rewrite eq .
( [ vectorpotentialrcr ] ) as @xmath83 , \label{vectorpotentialrr}\end{aligned}\ ] ] where we used @xmath84 .
this is a microscopic expression of the vector potential @xmath2 .
next , we investigate the consistency of eq .
( [ vectorpotentialrr ] ) with the results in refs .
@xcite . in a manner almost the same as those in refs .
@xcite , we can derive another microscopic expression of @xmath2 without relying on eq .
( [ vectorpotentialresponse ] ) : @xmath85 where @xmath86 . here
, @xmath87 is the counting field in the full counting statistics ( fcs ) of the work @xmath21 from the reservoirs , and @xmath88 is the left eigenvector of @xmath89 corresponding to the eigenvalue @xmath90 that has the maximum real part .
@xmath91/i\hbar + \sum_j \mathcal{l}_j^\chi$ ] is the @xmath87-modified generator , which is introduced for the fcs in the framework of the qme @xcite .
see [ appendix : vectorpotentialqme ] for the details and derivation .
we note that @xmath92 ( identity operator ) , @xmath93 , and @xmath94 . in the following
we rewrite eq .
( [ vectorpotentialqme ] ) to show its equivalence to eq .
( [ vectorpotentialrr ] ) .
we first rewrite @xmath95 in eq .
( [ vectorpotentialqme ] ) . by differentiating the left eigenvalue equation @xmath96 with respect to @xmath97 and setting @xmath98
, we obtain @xmath99 here @xmath100 and the adjoint @xmath101 of a superoperator @xmath102 is defined by @xmath103 = { \rm tr } [ \hat{x}_1^\dag \mathcal{o } \hat{x}_2]$ ] for any pair @xmath104 of linear operators . by operating on the both sides of eq .
( [ kdag_ellprime ] ) with @xmath105 , we obtain @xmath106 where @xmath107 $ ] and we used eq .
( [ rk ] ) . substituting eq .
( [ ellprime ] ) into eq .
( [ vectorpotentialqme ] ) and using @xmath108 = \partial_j { \rm tr } [ \hat{\rho}_{\rm ss } ] = 0 $ ] , we have @xmath109 $ ]
. furthermore we can show @xmath110 .
with this equation we have @xmath111 .
\label{vectorpotentialqme_middle}\end{aligned}\ ] ] we next rewrite @xmath112 . by differentiating the steady - state equation @xmath113 with respect to @xmath47 and operating on it with @xmath76 , we have @xmath114 . substituting this equation into eq .
( [ vectorpotentialqme_middle ] ) we obtain @xmath83 .
\nonumber\end{aligned}\ ] ] this is the same as eq .
( [ vectorpotentialrr ] ) .
we thus show that eq .
( [ vectorpotentialrr ] ) [ and therefore eq .
( [ vectorpotentialresponse ] ) ] is consistent with the results in refs .
we have derived an expression of the excess work for quasistatic transitions between nesss in particle transport systems on the basis of the linear response relation .
we have related the vector potential @xmath2 in the expression with the response function .
we note that it is possible to extend our formulation to situations where other control parameters for transition between ness are varied .
in particular , we can obtain a similar result in heat conducting systems , where the temperatures of heat reservoirs are changed .
we finally make remarks .
first , the relationship between the excess work and the response function suggests that the response functions can be calculated in the framework of the sst .
we expect that this expression becomes a first step for understanding of how transport phenomena are treated in the sst .
second , as is mentioned below eq .
( [ excesswork ] ) , our definition of the excess work is consistent with the definition of the excess heat in refs .
. however the definition of the excess work and heat is not unique ; e.g. , there are hatano - sasa type @xcite and maes - neton type @xcite approaches .
recently , ref .
@xcite gave evidence that the hatano - sasa approach is appropriate for the definition .
since the hatano - sasa approach relies on microscopic information ( e.g. , steady - state distribution and transition rate ) , the connection to macroscopic quantities is not clear .
it is therefore important to investigate the definition from the viewpoint of response function as a future work .
third , in recent years the nonequilibrium response function is a hot topic in the statistical physics @xcite .
one of the points in recent works is decomposition of the response function @xcite .
we expect that the application of these results to the expression of the excess work would lead to a further decomposition of the work that is appropriate for the construction of the sst .
the author thanks k. akiba and m. yamaguchi for helpful discussions .
this work was supported by a jsps research fellowship for young scientists ( no .
24 - 1112 ) , kakenhi ( no .
26287087 ) , and impact program of council for science , technology and innovation ( cabinet office , government of japan ) .
here we derive eq .
( [ rcr ] ) , the rcr in qme .
we consider the qme ( [ qme ] ) that depends on multiple parameters @xmath115 like chemical potentials ; i.e. , we assume that the generator of the qme depends on these parameters : @xmath116 .
suppose that at time @xmath117 the system s is in the ness with @xmath118 ; i.e. , @xmath119 for @xmath117 , where @xmath120 satisfies @xmath121 with @xmath122 .
for @xmath19 , we weakly modulate the parameters in time : @xmath123 ( @xmath124 ) , where @xmath125 is much smaller than a typical value of @xmath126
. then we can expand the generator @xmath58 around @xmath127 in terms of @xmath128 : @xmath129 where @xmath130 . to solve the qme ( [ qme ] ) with the weakly time - dependent @xmath131 and the initial condition @xmath132
, we transform the qme into an `` interaction picture '' .
that is , we introduce @xmath133 .
then , from the qme ( [ qme ] ) , we have the equation of motion for @xmath134 as @xmath135 where we used eq .
( [ expandk ] ) . by integrating this equation form @xmath14
to @xmath9 with @xmath136 , we obtain @xmath137 in going from the first line to the second , we approximately replaced @xmath138 in the integral with @xmath120 .
this approximation corresponds to the first - order time - dependent perturbation theory in quantum mechanics .
going back to the schrdinger picture , we have @xmath139 we thus obtain the time dependence of the expectation value of a quantity @xmath75 that is independent of @xmath131 : @xmath140 \nonumber\\ & = \langle x \rangle^{\rm ss}_{\bm{\alpha}_0 } + \sum_l \int_{t_0}^t dt ' { \rm tr } \big [ \hat{x } e^{\mathcal{k}^0(t - t ' ) } ( \partial_l \mathcal{k}^0 ) \hat{\rho}_{\rm ss}^0 \bigr ] f_l(t ' ) \label{linearresponseqme1 } \\ & = \langle x \rangle^{\rm ss}_{\bm{\alpha}_0 } + \sum_l \int_{t_0}^t dt ' { \rm tr } \big [ \bigl\ { ( \partial_l \mathcal{k}^0)^\dag e^{\mathcal{k}^{0\dag}(t - t ' ) } \hat{x } \bigr\ } \hat{\rho}_{\rm ss}^0 \bigr ] f_l(t ' ) . \label{linearresponseqme2}\end{aligned}\ ] ] equations ( [ linearresponseqme1 ] ) and ( [ linearresponseqme2 ] ) give the rcr in the qme .
we note that eq .
( [ linearresponseqme2 ] ) reduces to the kubo formula if @xmath120 is an equilibrium state ( i.e. , when we consider the response of an equilibrium state ) @xcite .
now we consider the current @xmath141 from the @xmath4th reservoir into the system s. we note that @xmath68 is dependent on @xmath131 because so is @xmath142 .
therefore we have the average current at time @xmath9 as @xmath143 - { \rm tr } \big [ \hat{i}_i\bigl(\bm{\alpha}_0\bigr ) \hat{\rho}^0_{\rm ss } \bigr ] \nonumber\\ & = \sum_l { \rm tr } \big [ ( \partial_l \hat{i}_i^0 ) \hat{\rho}^0_{\rm ss } \bigr ] f_l(t ) + { \rm tr } \big [ \hat{i}_i^0 \hat{\rho}(t ) \bigr ] - { \rm tr } \big [ \hat{i}_i^0 \hat{\rho}^0_{\rm ss } \bigr ] \nonumber\\ & = \sum_l { \rm tr } \big [ ( \partial_l \hat{i}_i^0 ) \hat{\rho}^0_{\rm ss } \bigr ] f_l(t ) + \sum_l \int_{t_0}^t dt ' { \rm tr } \big [ \hat{i}_i^0 e^{\mathcal{k}^0(t - t ' ) } ( \partial_l \mathcal{k}^0 ) \hat{\rho}_{\rm ss}^0 \bigr ] f_l(t ' ) , \end{aligned}\ ] ] where @xmath144 and @xmath145 .
we used eq .
( [ linearresponseqme1 ] ) in the third line . finally , by performing the functional differentiation with respect to @xmath146
, we obtain @xmath147 \delta(t - t ' ) + { \rm tr } \bigl [ \hat{i}_i^0 e^{\mathcal{k}(t - t ' ) } ( \partial_j \mathcal{k } ) \hat{\rho}_{\rm ss}^0 \bigr ] .
\nonumber\end{aligned}\ ] ] this is equivalent to eq .
( [ rcr ] ) .
first we show that @xmath76 in eq . ( [ r ] )
is well defined . to this end
, we denote the eigenvalue and corresponding left and right eigenvectors of @xmath58 as @xmath148 , @xmath149 , and @xmath150 .
we assign the steady state of @xmath58 to the index @xmath151 ; i.e. , @xmath152 , @xmath153 , and @xmath154 . by the assumption of the unique existence of the stable steady state , @xmath155 for @xmath156 .
then , for any linear operator @xmath75 , we obtain the following equation : @xmath157 \hat{r}_m \nonumber\\ & = - \int_0^\infty dt \sum_{m\neq 0 } e^{\lambda_m t } { \rm tr}[\hat{\ell}_m^\dag \hat{x } ] \hat{r}_m \nonumber\\ & = \sum_{m\neq 0 } \frac{{\rm tr}[\hat{\ell}_m^\dag \hat{x}]}{\lambda_m } \hat{r}_m.\end{aligned}\ ] ] since this is not diverging , @xmath76 is well defined .
we here show that eq .
( [ rk ] ) holds for the generator @xmath58 of the qme .
we first note that @xmath158 follows from @xmath159 , which we can derive from the fact that @xmath160 = 0 , \label{pkx } \\
\mathcal{k } \mathcal{p}_0 \hat{x } & = \mathcal{k } \hat{\rho}_{\rm ss } { \rm tr } \hat{x } = 0 , \label{kpx}\end{aligned}\ ] ] hold for any linear operator @xmath75 .
equation ( [ pkx ] ) follows from @xmath161 = 0 $ ] ( trace - preserving property of qme ) , and eq .
( [ kpx ] ) from @xmath80 ( steady - state equation )
. then we can show eq .
( [ rk ] ) as follows : @xmath162 here the third line follows from the convergence theorem of the markov process , which we can derive from the fact that for any linear operator @xmath75 the following equation holds : @xmath163 \hat{r}_m \nonumber\\ & = \sum_m { \rm tr}[\hat{\ell}_m^\dag \hat{x } ] \hat{r}_m \lim_{t\to\infty } e^{\lambda_m(t - t_0 ) } \nonumber\\ & = \hat{\rho}_{\rm ss } { \rm tr}\hat{x}. \end{aligned}\ ] ] this gives the third line in eq .
( [ rk_a ] ) .
we note that eq .
( [ rk_a ] ) leads to @xmath164 .
this implies that @xmath76 satisfies one of the conditions for the moore - penrose pseudoinverse of @xmath58 .
for completeness we here derive eq .
( [ vectorpotentialqme ] ) , the work version of the results in refs . @xcite .
first we note that we can measure the work @xmath21 during varying the chemical potentials @xmath165 with a time interval @xmath166 as follows . at the initial time @xmath167
, we perform a projection measurement of reservoir particle numbers @xmath168 to obtain measurement outcomes @xmath169 . for @xmath19 , we vary @xmath6 , where the system evolves with interacting with the reservoirs . at @xmath170 , we again perform a measurement of @xmath171 to obtain outcomes @xmath172 .
the difference of the outcomes gives the work @xmath173 $ ] .
repeating the measurements , we obtain a probability distribution @xmath174 .
the average work is given by @xmath175 , and the average work flow in a ness is given by @xmath176 with @xmath6 being fixed . in the following ,
we calculate the average work by @xmath177 , where @xmath178 is the cumulant generating function and @xmath87 is the counting field . by using the full counting statistics
@xcite , we can calculate @xmath179 by @xmath180 here @xmath181 is the solution of the generalized quantum master equation ( gqme ) : @xmath182 where the generalized generator is given by @xmath183 /i\hbar
+ \sum_j \mathcal{l}_j^\chi$ ] , with the generalized dissipator @xmath184_\chi \bigr]_\chi$ ] .
@xmath185 is the trace over the @xmath43th reservoir , @xmath186 is the interaction hamiltonian between the system and the @xmath43th reservoir , @xmath187 is its interaction picture , @xmath188 is the thermal equilibrium state of the @xmath43th reservoir with the chemical potential @xmath47 , @xmath189_\chi \equiv \hat{o}_1^\chi \hat{o}_2 - \hat{o}_2 \hat{o}_1^{-\chi}$ ] , and @xmath190 .
note that , if we set @xmath98 , the gqme ( [ gqme ] ) reduces to the original qme ( [ qme ] ) , and @xmath89 , @xmath88 , and @xmath191 also reduce to @xmath58 , @xmath192 , and @xmath62 , respectively . for fixed @xmath6
, we can define the left and right eigenvectors of @xmath193 corresponding to the eigenvalue @xmath194 , which are respectively denoted by @xmath195 and @xmath196 .
they are normalized as @xmath197 .
we assign the label for the eigenvalue with the maximum real part to @xmath151 .
it is known that @xmath198 holds @xcite .
therefore , the average work flow @xmath199 in the ness can be calculated by @xmath200 we now derive eq .
( [ vectorpotentialqme ] ) .
we first note that the excess work can be written as @xmath201 , where @xmath202 and @xmath203 .
this is because @xmath177 and eq .
( [ workflux ] ) . to calculate @xmath204 , we solve the gqme ( [ gqme ] ) . for this purpose
we expand @xmath205 as @xmath206 substituting this expansion into eq .
( [ gqme ] ) and taking the hilbert - schmidt inner product with @xmath207 , we obtain @xmath208 .
\nonumber\end{aligned}\ ] ] if the time scale of varying @xmath6 is sufficiently slower than the relaxation time of the system , we can approximate the sum on the rhs by the contribution only from the term with @xmath151 ( adiabatic approximation ) . by solving the approximate equation
we obtain @xmath209 \right\ } , \label{c_0}\end{aligned}\ ] ] where @xmath210 is a path connecting @xmath211 and @xmath212 in the parameter space and @xmath213 . if @xmath214 , then @xmath215 $ ] . at long time ,
only the @xmath151 term remains in eq .
( [ expansion_rho ] ) since @xmath216 has the maximum real part
. therefore we obtain @xmath217 substituting eq .
( [ c_0 ] ) into this equation we obtain an expression for @xmath218 as @xmath219 + \ln { \rm tr}_{\rm s } \bigl [ \hat{\ell}_0^{\chi\dag } \bigl(\mu(t_0)\bigr ) \hat{\rho}_{\rm ss } \bigl(\mu(t_0)\bigr ) \bigr ] \nonumber\\ & + \ln { \rm tr}_{\rm s } \hat{r}_0^{\chi } \bigl(\mu(t_0+\tau)\bigr ) .
\label{cgf_ex}\end{aligned}\ ] ] finally , by differentiating eq .
( [ cgf_ex ] ) with respect to @xmath97 and setting @xmath98 , we obtain an expression for the excess work : @xmath220 . \label{excess_derived}\end{aligned}\ ] ] we thus obtain eq .
( [ vectorpotentialqme ] ) .[/INST] excess work is a non - diverging part of the work during transition between nonequilibrium steady states ( nesss ) .
it is a central quantity in the steady state thermodynamics ( sst ) , which is a candidate for nonequilibrium thermodynamics theory .
we derive an expression of excess work during quasistatic transitions between nesss by using the macroscopic linear response relation of ness .
this expression is a line integral of a vector potential in the space of control parameters .
we show a relationship between the vector potential and the response function of ness , and thus obtain a relationship between the sst and a macroscopic quantity .
we also connect the macroscopic formulation to microscopic physics through a microscopic expression of the nonequilibrium response function , which gives a result consistent with the previous studies . </s> |