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1101.4026

i

we have identified a population of objects which require powerful jets to be present but have no x - ray detectable nucleus . we have also identified a range of possible explanations , each of which carries significant implication for the origin and operation of jets . the black holes may be ultramassive ( @xmath18 ) , or have very high spin , or be highly obscured . they may also be mostly off , yet unobservable when they are switched on , or have highly radiatively inefficient jets . ( letters ) , 363 , l91 2010 , accepted to _ _ , arxiv : 1007.1974 1997 , _ _ , 489 , 579 2009 , _ _ , 698 , 594 2007 , _ _ , 381 , 589 1993 , _ legacy _ , 3 , 21 2008 , _ new astron . revs _ , 51 , 733 2008 , _ _ , 681 , 1035

we present a study of strong cool core , highly - luminous ( most with @xmath0 ) , clusters of galaxies in which the mean central agn jet power must be very high yet no central point x - ray source is detected . using the unique spatial resolution of @xmath1 , a sample of 13 clusters is analysed , including a1835 , a2204 , and one of the most massive cool core clusters , rxcj1504.1 - 0248 . we investigate how these clusters can have such strong x - ray luminosities , short radiative cooling - times of the inner intracluster gas requiring strong energy feedback to counterbalance that cooling , and yet have such radiatively - inefficient cores with , on average , @xmath2/@xmath3 exceeding 200 . explanations of this puzzle carry significant implications for the origin and operation of jets , as well as on establishing the importance of kinetic feedback for the evolution of galaxies and their surrounding medium .

cool core clusters of galaxies require strong feedback from their central agn to offset cooling . we present a study of strong cool core , highly - luminous ( most with @xmath0 ) , clusters of galaxies in which the mean central agn jet power must be very high yet no central point x - ray source is detected . using the unique spatial resolution of @xmath1 , a sample of 13 clusters is analysed , including a1835 , a2204 , and one of the most massive cool core clusters , rxcj1504.1 - 0248 . all of the central galaxies host a radio source , indicating an active nucleus , and no obvious x - ray point source . for all clusters in the sample , the nucleus has an x - ray bolometric luminosity below 2 per cent of that of the entire cluster . we investigate how these clusters can have such strong x - ray luminosities , short radiative cooling - times of the inner intracluster gas requiring strong energy feedback to counterbalance that cooling , and yet have such radiatively - inefficient cores with , on average , @xmath2/@xmath3 exceeding 200 . explanations of this puzzle carry significant implications for the origin and operation of jets , as well as on establishing the importance of kinetic feedback for the evolution of galaxies and their surrounding medium . ps . -.4 in

1512.03453

i

the observations of significant amounts of dust in high redshift quasars ( bertoldi et al . 2003 ; priddey et al . 2003 ; robson et al . 2004 ; beelen et al . 2006 ; wang et al . 2008 ) have highlighted the requirement for an alternative to asymptotic giant branch ( agb ) stars as the dominant dust factories in the early universe ( e.g. , maiolino et al . 2004 , valiante et al . 2009 , 2011 ) . an ideal alternative are core - collapse supernovae ( ccsne ) , since the short main sequence time of their progenitor stars allows them to enrich the interstellar medium with the first solids with no noticeable delay on cosmological timescales . theoretical calculations of the dust yields of ccsne , however , have produced controversial results . calculations based on the classical nucleation theory ( e.g. , feder et al . 1966 ) typically predict the prompt formation of fairly large amounts of dust , of the order of one solar mass or more , within one year from the explosion ( kozasa et al.1989 , 1991 ; clayton et al . 2001 ; todini & ferrara 2001 ; nozawa et al . 2003 , 2010 ) . the result is robust to the unknown parameters of the theory , such as the shape and sticking coefficients of the grains , at least to first order ( fallest et al . on the other hand , calculations that model the formation of solid grains with a chemical network with well - defined reaction rates resulted in the prediction of only modest amount of dust , its condensation starting only years after the supernova explosion ( cherchneff & dwek 2009 , 2010 ; sarangi & cherchneff 2013 ; biscaro & cherchneff 2014 ) . such calculations , however , can not follow the grain formation up to large molecular clusters and/or micron - sized crystals . most current results only predict the formation of molecular precursors , such as c@xmath0 . a recent paper ( sarangi et al . 2015 ) follows carbon cluster formation up to c@xmath1 , assuming that coalescence is responsible for the growth of astrophysical grains from the clusters . the discrepancy between the two theoretical predictions seems to be brought about by the approximations and intrinsic limitations of the two theories . calculations based on the nucleation theory assume that the grain formation happens in virtual isolation , ignoring the fact that the growing proto - grains are exposed to the rich field of damaging radiation of a young supernova remnant ( snr ) . they also assume that even the smallest molecular clusters are continuum entities , ignoring their atomic structure and quantum behaviour . on the other hand , chemical network calculations provide a deterministic growth of grains and therefore ignore the fact that , as grains grow beyond the molecular cluster phase , self shielding allow the few grains that grew by statistical fluctuations to become more and more resilient and grow even further . chemical calculations , as such , ignore the fact that grain growth becomes a runaway process , the few grains able to make it beyond a few hundred monomers allowed to grow and become stable . not surprisingly , observations of nearby core - collapse supernovae ( sn1987a and , only recently , sn2010jl ) are in disagreement with both results . they show dust formation beginning as early as half a year after the explosion ( gall et al . 2014 ; earlier dust formation being possible but hidden under the more abundant curcumstellar dust component ) , in disagreement with chemical network results . the early dust formation , however , is modest , at most a fraction of a per cent of a solar mass being condensed ( in disagreement with the classical nucleation results ) . to add confusion to the picture , recent herschel ( matsuura et al . 2013 ) and alma ( indebetouw et al . 2014 ) observations of sn1987a show the presence of large amounts of dust in emission in the center of the remnant . taken at face value , the collective data from all nearby core - collapse supernovae suggests a scenario in which dust formation is a slow and continuous process that starts at most a few months after core collapse and continues for at least several years , eventually yielding amounts of solid particles totalling approximately one solar mass . not all core - collapse supernovae may be dust producers , however . in a recent study , szalai & vink ( 2013 ) find that only two out of twelve type ii - p sne show signs of newly sinthsized dust in emission . connecting the chemistry of the molecular precursor with a formalism for dust growth is necessary to properly describe the formation and growth of grains into stable microscopic solids ( sarangi & cherchneff 2015 ) . in this paper we present a new framework for the calculation of dust formation in supernova explosions based on the kinetic nucleation theory ( e.g. , kashchiev 2000 ) . whereas the kinetic nucleation theory is equivalent to the standard thermodynamic theory for homologous nucleation in isolation , it allows to introduce deviations from the capillary approximation for very small clusters and chemical weathering of the forming grains in the harsh supernova environment . the theory is presented , and applied as a proof of concept , to the formation of carbonaceous grains , but can be readily extended to the formation of any grain species , provided that its susceptibility to weathering in the remnant environment is known . this paper is organized as follows : in section 2 we present the chemical network and the nucleation theory that we adopt . in section 3 we describe the stellar explosions model adopted and in section 4 we present out results . a summary and discussion are in section 5 .

core - collapse supernovae are considered to be important contributors to the primitive dust enrichment of the interstellar medium in the high - redshift universe . we present a new methodology for the calculation of carbonaceous dust formation in young supernova remnants . our new technique uses both the nucleation theory and a chemical reaction network to allow us to compute the dust growth beyond the molecular level as well as to consider chemical erosion of the forming grains .

core - collapse supernovae are considered to be important contributors to the primitive dust enrichment of the interstellar medium in the high - redshift universe . theoretical models of dust formation in stellar explosions have so far provided controversial results and a generally poor fit to the observations of dust formation in local supernovae . we present a new methodology for the calculation of carbonaceous dust formation in young supernova remnants . our new technique uses both the nucleation theory and a chemical reaction network to allow us to compute the dust growth beyond the molecular level as well as to consider chemical erosion of the forming grains . we find that carbonaceous dust forms efficiently in the core of the ejecta , but takes several years to condensate , longer than previously estimated . it forms unevenly and remains concentrated in the inner part of the remnant . these results support the role of core - collapse supernovae as dust factories and provide new insight on the observations of sn 1987a , in which large amounts of dust have been detected to form on a timescale of years after core collapse .

1512.03453

i

we have presented a calculation of carbonaceous dust formation in a @xmath59 progenitor star exploding as a core - collapse supernova . our study is based on a novel nucleation code that was developed to address the particular conditions of the exploding supernova . this is a rapidly evolving environment with plenty of ionizing radiation and reactive agents that can harm the forming grains . our code uses the kinetic theory of nucleation in order to be suitable for possible non - steady state conditions in the fast evolving remnant . in addition , the flexibility of the kinetic theory allows us to relax the capillary approximation for the dimer ( @xmath60 ) formation and to include the effect of oxidation and ion - molecule reactions in the calculation . an alternative framework for joining the chemical and nucleation approaches has been recently presented by sarangi & cherchneff ( 2015 ) . their approach differs fundamentally from what presented in this paper in that the chemical phase is joined to a coalescence phase , rather than to a growth phase . this means that in their scheme carbon clusters form up to a maximum size of ten atoms until all the carbon gas has been used and subsequently grow by coagulation with other clusters rather than grow by adsorption of gas monomers ( or molecules ) . we find that , at least for carbon , the chance of collisions of molecular clusters with monomers is far larger than with other clusters . in our calculations monomers are more abundant than clusters and , being lighter , have a larger thermal velocity that makes collisions more frequent . as a subsequent step in understanding nucleation , however , the coagulation and growth should be integrated and taken into account simultaneously . with respect to classical calculations ( kozasa et al . 1989 , 1991 ; todini & ferrara 2001 ; nozawa et al . 2003 ; fallest et al . 2011 ) and to the results of sarangi & cherchneff ( 2015 ) , we find that our new code predicts a much more gradual carbon dust formation , beginning just a few months after the core collapse and continuing for a few years . despite the more gradual formation , however , we are not able to fully reproduce the observational results that require an even more gradual and continuous dust formation in the ejecta , with dust appearing as early as two months after core collapse and gradually increasing for a few years to a decade ( gall et al . 2014 ) eventually leading to a highly efficient condensation of a sizable fraction of a solar mass ( indebetouw et al . addition of non - carbonaceous dust chemistry ( e.g. , sarangi & cherchneff 2015 ) and/or a fully three - dimensional calculation ( lazzati & fallest , in preparation ) can ameliorate the discrepancy . it must be also noted that the explosion model plays a role in the grain formation . a less energetic explosion than the one we used ( or one with more massive ejecta ) would result in higher densities and temperatures at long timescales , allowing for a longer period of growth and , potentially , more dust condensation . on the other hand , a more energetic explosion or one with lighter ejecta would result in colder and less dense gas , likely going earlier into freeze - out . the role of explosion diversity is certainly as important as the proper dimensionality of the simulation , since a 3d model is likely going to contain both faster and slower ejecta than the 1d spherically simmetric model presented here and elswhere in the literature . even though we consider this work a step forward towards a complete understanding of dust formation in stellar explosions ( and in general ) , it is still plagued by some serious limitations . the most obvious is the fact that we consider only carbonaceous dust , while more species are known to condensate in supernova explosions . condensation of silicates and other dust species can begin earlier and explain the early dust formation observed in some sne ( wooden et al.1993 ; gall et al . 2014 ; sarangi & cherchneff 2015 ) . on a more fundamental level , our code still assumes a constant sticking coefficient @xmath61 , a spherical shape for the forming grains , down to the smallest sizes , and the capillary approximation of a size - independent surface energy for any cluster with @xmath62 . all these are important limitations that need to be corrected ( see , e.g. , mauney & lazzati 2015 ) before a serious comparison with data can be performed . as any nucleation based work , we also assume that grain formation and growth takes place by addition of single carbon atoms , and that grain erosion as well takes place by removing one atom at a time from a cluster . reactions that cause the splitting of a cluster in two fragments are not considered , even though they might be important , especially at low temperature ( see , e.g. , wakelam et al.2009 ) . another important issue is whether the chemical and nucleation approaches are fully consistent with each other . as we show in fig . [ fig : rates ] , that might not be the case , creating a serious issue when they are joined . more theoretical and experimental work needs to be devoted to understanding the formation rates of carbon clusters with a few up to a few tens of atoms , and the relative importance of radiative and non - radiative association processes need to be pinned down from first principles . the reaction network is also incomplete , lacking the consideration of the effect of other potentially harmful cations , such as ar@xmath6 and ne@xmath6 . the role of these cations in silicate nucleation and growth was included in the work of sarangi & cherchneff ( 2013 , 2015 ) , but ion - molecule reaction rates for such cations with carbon clusters are not available in the literature and are therefore omitted in this work . we are very grateful to the anonymous referee for her / his useful and constructive comments . this work was supported in part by nsf grants ast-1150365 and ast-1461362 ( dl ) , and by an arc future fellowship ft120100363 ( ah ) .

theoretical models of dust formation in stellar explosions have so far provided controversial results and a generally poor fit to the observations of dust formation in local supernovae . we find that carbonaceous dust forms efficiently in the core of the ejecta , but takes several years to condensate , longer than previously estimated . these results support the role of core - collapse supernovae as dust factories and provide new insight on the observations of sn 1987a , in which large amounts of dust have been detected to form on a timescale of years after core collapse .

core - collapse supernovae are considered to be important contributors to the primitive dust enrichment of the interstellar medium in the high - redshift universe . theoretical models of dust formation in stellar explosions have so far provided controversial results and a generally poor fit to the observations of dust formation in local supernovae . we present a new methodology for the calculation of carbonaceous dust formation in young supernova remnants . our new technique uses both the nucleation theory and a chemical reaction network to allow us to compute the dust growth beyond the molecular level as well as to consider chemical erosion of the forming grains . we find that carbonaceous dust forms efficiently in the core of the ejecta , but takes several years to condensate , longer than previously estimated . it forms unevenly and remains concentrated in the inner part of the remnant . these results support the role of core - collapse supernovae as dust factories and provide new insight on the observations of sn 1987a , in which large amounts of dust have been detected to form on a timescale of years after core collapse .

astro-ph9706278

r

with the formalism presented in the previous section we have calculated the correlations @xmath17 , @xmath14 and @xmath16 . we assume a cdm model with a primordial harrison - zeldovich spectrum , a hubble parameter h@xmath109 ( h@xmath110h km s@xmath111 mpc@xmath111 ) and flat as well as open universe models . for the power spectrum we have used the fit given by equation ( g3 ) of bardeen et al . ( 1986 ) which is normalized to the cluster abundance : @xmath112 , following viana and liddle ( 1996 ) ( see also white , efstathiou and frenk 1993 ; eke , cole and frenk 1996 ; see kaiser 1997 for a discussion on alternative normalizations ) . for the nonlinear evolution of the power spectrum we use the recently improved fitting formula given by peacock and dodds ( 1996 ) . that formula is based on the hamilton et al . ( 1991 ) scaling procedure to describe the transition between linear and nonlinear regimes . it accounts for the correction introduced by jain , mo and white ( 1995 ) for spectra with @xmath113 and applies to flat as well as open universes . for the redshift distributions of the background and foreground sources we consider a dirac delta distribution peaked at @xmath114 and @xmath115 respectively , @xmath116 and @xmath117 . these simple distributions are very useful since they reduce the calculations and the results differ only slightly when compared to other more realistic distributions ( see below ) . @xmath17 and @xmath14 are computed using equations ( 14,15,19 ) . @xmath118 is obtained from equation ( 25 ) where the function @xmath82 is given by equation ( 18 ) . the crosscorrelation @xmath119 for a population of background sources peaked at @xmath120 and another of foreground lenses at @xmath121 is given in figure ( 1 ) . the effect is maximum at zero lag and rapidly decreases for scales above a few arcmin . the amplitude is always above a few percent for scales @xmath122 and at these scales the linear contribution is negligible compared to the nonlinear one for all the @xmath0 values . notice that @xmath17 increases when @xmath0 decreases whereas considering only the linear contribution the situation is reversed . from the observational point of view it is useful to calculate the average crosscorrelation ( or equivalently the mean relative excess of background sources around foreground lenses ) within a given radius @xmath123 , @xmath124 . the variation of @xmath125 with @xmath126 for different values of @xmath79 and a @xmath127 radius is shown in figures ( 2a , b , c ) . a maximum amplitude of a few percent is obtained at a @xmath126 in the range @xmath128 for all background populations and all cosmological models . ( at this point it is important to recall that to compare with observations of background - foreground object correlations @xmath129 , the bias factor @xmath13 of the foreground population and the slope @xmath9 of the background population enter in the calculation following equation 16 ) . it is interesting to notice that there are already available large galaxy samples , like the apm or cosmos catalogues , which peak at a redshift within that range ( for the apm catalogue @xmath130 for a magnitude limit @xmath131 , see efstathiou 1995 ) . moreover , the use of realistic redshift distributions to represent the foreground and background populations ( with a bell - like shape similar to that of the apm one ) , changes the results in only @xmath132 for the relevant angular scales compared to the dirac delta distribution used here . those catalogues , which except for a bias factor are assumed to follow the large scale matter distribution , are therefore very suitable to crosscorrelate with a background source population . this has already been done by bentez and martnez - gonzlez ( 1995 , 1997 ) for the 1 jansky and parkes samples of radio loud qsos as background populations , finding clear evidences of positive crosscorrelations . in figure 3 , we show @xmath119 for @xmath133 and for @xmath134 and @xmath120 , mean redshift values appropriate for the galaxy and radio qso samples considered above . the dependence of @xmath17 with @xmath0 is more relevant at small angular scales . in figure 4 , we also represent the average crosscorrelation @xmath125 as a function of @xmath0 . a rough comparison between its expected amplitude and the measured value for the cosmos - parkes samples , as given in figure 4 of bentez and martnez - gonzlez 1997 , shows agreement for realistic values of @xmath0 and the bias parameter . a detailed comparison of the theoretical calculations with the observational results will be given elsewhere . dolag and bartelmann ( 1997 ) have recently presented calculations of the qso - galaxy correlation function for such qso and galaxy populations produced by gravitational lensing due to the large scale structure , following a similar theoretical scheme . the crosscorrelation between the polarization of a background source population peaked at @xmath79 and the matter density fluctuations peaked at @xmath126 , @xmath135 , is given in figure ( 5 ) for @xmath120 and @xmath136 . the maximum value is in the angular range @xmath137 and this scale is smaller for low @xmath0 models . as in the case of @xmath17 , the linear contribution is negligible ; however , it peaks at a much larger angle of @xmath138 as a consequence of the much larger scales which contribute to the linear level . including the nonlinear evolution , a correlation of @xmath139 can be expected at angular scales @xmath122 for realistic models of structure formation . the use of realistic redshift distributions to represent the foreground and background populations ( with a bell - like shape typical of magnitude limited samples ) changes the results in only @xmath132 for the relevant angular scales compared to the dirac delta distribution used here . in analogy to the previous subsection , it is useful to calculate the average crosscorrelation within a given radius @xmath123 , @xmath140 . the variation of @xmath141 with @xmath126 for several values of @xmath79 and @xmath0 is shown in figures ( 6a , b , c ) . maximum amplitudes of the order of @xmath142 are found for @xmath126 within a relatively wide range @xmath143 . the amplitude grows appreciably with @xmath79 being a factor of @xmath144 difference between @xmath145 and @xmath146 . considering the behavior of @xmath140 from these figures , suitable populations to detect the crosscorrelation would be a foreground sample with @xmath147 and a background one peaked at @xmath148 . in this subsection we concentrate on a single population of background sources peaked at a given @xmath79 and calculate @xmath149 . this is done in figure ( 7 ) for @xmath120 . the maximum effect is at zero lag and its amplitude is relatively small @xmath150 . the nonlinear contribution clearly dominates over the linear one but now the amplitude grows with @xmath0 , contrary to the crosscorrelations @xmath119 and @xmath135 . our results are in agreement with jain & seljak ( 1996 ) , and with kaiser ( 1997 ) for one degree scales ( see also those papers for a more detailed analysis of @xmath16 ) , where the dominant contribution is the linear one . considering also the slope of the population of sources following equation ( 26 ) , @xmath16 could be estimated from the observed autocorrelation of faint galaxies . nevertheless , measuring @xmath91 should be more feasible from the practical point of view , as we do not have to disentangle the contribution caused by lensing from the intrinsic correlations ; it is usually assumed ( and strongly hoped ) that the intrinsic ellipticities of background galaxies are not correlated .

the contribution of the linear evolution is negligible at scales below several arcminutes . detailed results on the dependence of the correlations on the redshift of the foreground and background populations for different cosmological models are presented . cosmology : theory - gravitational lensing - large - scale structure

correlations between the magnification or polarization of background sources , induced by gravitational lensing due to the large - scale structure , and the positions of foreground galaxies are investigated . we found that their amplitude is enhanced with respect to correlations for a single population . we analize the dependence of the correlations with the density parameter @xmath0 considering a nonlinear evolution of the matter power spectrum . the contribution of the linear evolution is negligible at scales below several arcminutes . detailed results on the dependence of the correlations on the redshift of the foreground and background populations for different cosmological models are presented . the effect reaches its maximum amplitude for foreground populations with relatively small redshifts due to the fast increase of the nonlinear matter power spectrum at recent times . cosmology : theory - gravitational lensing - large - scale structure

astro-ph9706278

c

we have obtained the expressions for the correlations between the magnification or polarization of background sources and the foreground matter distribution as function of the nonlinear evolution of the power spectrum . these formuli are valid for flat and open universes . for the crosscorrelation of the background magnification and foreground matter distribution , @xmath119 , the maximum is at zero lag and the amplitude remains above a few percent for scales @xmath122 . @xmath119 increases significantly when @xmath0 decreases . the linear contribution is negligible compared to the nonlinear one for the relevant scales below a few arcmin . varying the redshift of the foreground population , @xmath126 , a maximum amplitude of a few percent for the integrated correlation @xmath125 is obtained at @xmath151 for all background populations and all cosmological models . the crosscorrelation of the background polarization and foreground matter distribution , @xmath135 , presents a maximum of the order of @xmath142 at a non - null angle , typically in the range @xmath152 . fixing the redshifts @xmath126 and @xmath79 of the two populations , the angular scale of the maximum decreases with @xmath0 . @xmath135 increases significantly when @xmath0 decreases . the linear contribution is negligible compared to the nonlinear one for the relevant scales below a few arcmin . varying the redshift of the foreground population , @xmath126 , a maximum amplitude of @xmath153 for the integrated correlation @xmath141 is obtained within a relatively wide range @xmath154 . this amplitude grows appreciably with @xmath79 being a factor of @xmath144 difference between @xmath145 and @xmath146 . finally , the correlation of the magnifications for a single population , @xmath149 , has a relatively small maximum amplitude @xmath155 in all cases . the amplitude grows with @xmath0 , contrary to the crosscorrelations @xmath119 , @xmath135 .

correlations between the magnification or polarization of background sources , induced by gravitational lensing due to the large - scale structure , and the positions of foreground galaxies are investigated . we found that their amplitude is enhanced with respect to correlations for a single population . we analize the dependence of the correlations with the density parameter @xmath0 considering a nonlinear evolution of the matter power spectrum .

correlations between the magnification or polarization of background sources , induced by gravitational lensing due to the large - scale structure , and the positions of foreground galaxies are investigated . we found that their amplitude is enhanced with respect to correlations for a single population . we analize the dependence of the correlations with the density parameter @xmath0 considering a nonlinear evolution of the matter power spectrum . the contribution of the linear evolution is negligible at scales below several arcminutes . detailed results on the dependence of the correlations on the redshift of the foreground and background populations for different cosmological models are presented . the effect reaches its maximum amplitude for foreground populations with relatively small redshifts due to the fast increase of the nonlinear matter power spectrum at recent times . cosmology : theory - gravitational lensing - large - scale structure

q-bio0605042

c

motivated by recent _ in vitro _ and _ in vivo _ experiments aimed at identifying mechanisms responsible for biodiversity in populations of _ escherichia coli _ @xcite , we have considered the stochastic version of the ` rock - paper - scissors ' , or three - species cyclic lotka - volterra , system within an urn model formulation . this approach allowed us to quantitatively study the effect of finite - size fluctuations in a system with a large , yet _ finite _ , number @xmath3 of agents . while the classical rate equations of the cyclic lotka - volterra model predict the existence of one ( neutrally stable ) center fixed point , associated with the _ coexistence _ of all the species , this picture is _ dramatically _ invalidated by the fluctuations which unavoidably appear in a finite system . the latter were taken into account by a fokker - planck equation derived from the underlying master equation through a van kampen expansion . within this scheme , we were able to show that the variances of the densities of individuals grow in time ( first linearly ) until extinction of two of the species occurs . in this context , we have investigated the probability for such extinction to occur at a given time @xmath15 . as a main result of this work , we have shown that this extinction probability is a function of the scaling variable @xmath183 . exploiting polar symmetries displayed by the deterministic trajectories in the phase portrait and using a mapping onto a classical first - passage problem , we were able to provide analytic estimates ( upper and lower bounds ) of the extinction probability , which have been successfully compared to numerical computation . from our results , it turns out that the classical rate equation predictions apply to the urn model with a finite number of agents only for short enough time , i.e. in the regime @xmath190 . as time increases , the probability of extinction grows , asymptotically reaching @xmath191 for @xmath192 , so that , for finite @xmath3 , fluctuations are _ always _ responsible for extinction and thus dramatically jeopardize the possibility of coexistence and biodiversity . interestingly , these findings are in qualitative agreement with those ( both experimental and numerical ) reported in ref . @xcite , where it was found that in a well mixed environment ( as in the urn model considered here ) two species get extinct . while this work has specifically focused on the stochastic cyclic lotka - volterra model , the addressed issues are generic . indeed , we think that our results and technical approach , here illustrated by considering the case of a paradigmatic model , might actually shed further light on the role of fluctuations and the validity of the rate equations in a whole class of stochastic systems . in fact , while one might believe that fluctuations in an urn model should always vanish in the thermodynamic limit , we have shown that this issue should be dealt with due care : this is true for systems where the rate equations predict the existence of an asymptotically stable fixed point , which is always reached by the stochastic dynamics @xcite . in contrast , in systems where the deterministic ( rate equation ) description predicts the existence of ( neutrally stable ) center fixed points , such as the cyclic lotka - volterra model , fluctuations have dramatic consequences and hinder biodiversity by being responsible ( at long , yet finite , time ) for extinction of species @xcite . in this case , instead of a deterministic oscillatory behavior around the linearly ( neutrally ) stable fixed point , the stochastic dynamics always drives the system toward one of its absorbing states . thus , the absorbing fixed points , predicted to be linearly unstable within the rate equation theory , actually turn out to be the _ only stable fixed points _ available at long time .

, we address this issue by studying the properties of a paradigmatic non - spatial three - species stochastic system , namely the ` rock - paper - scissors ' or cyclic lotka - volterra model . while the deterministic approach ( rate equations ) predicts the coexistence of the species resulting in regular ( yet neutrally stable ) oscillations of the population densities , we demonstrate that fluctuations arising in the system with a _ finite number of agents _ drastically alter this picture and are responsible for extinction : after long enough time , two of the three species die out . as main findings we provide analytic estimates and numerical computation of the extinction probability at a given time . we also discuss the implications of our results for a broad class of competing population systems .

cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity , see e.g. b. kerr , m. a. riley , m. w. feldman and b. j. m. bohannan [ nature * 418 * , 171 ( 2002 ) ] and b. kirkup and m. a. riley [ nature * 428 * , 412 ( 2004 ) ] . through analytical methods supported by numerical simulations , we address this issue by studying the properties of a paradigmatic non - spatial three - species stochastic system , namely the ` rock - paper - scissors ' or cyclic lotka - volterra model . while the deterministic approach ( rate equations ) predicts the coexistence of the species resulting in regular ( yet neutrally stable ) oscillations of the population densities , we demonstrate that fluctuations arising in the system with a _ finite number of agents _ drastically alter this picture and are responsible for extinction : after long enough time , two of the three species die out . as main findings we provide analytic estimates and numerical computation of the extinction probability at a given time . we also discuss the implications of our results for a broad class of competing population systems .

0912.4546

i

is limited by noise in channels , but error correction methods can efficiently offset this restriction in both classical @xcite and quantum @xcite cases . at a simple level , multiple copies of the information can be transmitted , and a majority rule can be applied to discern the correct code , but such coding is neither practical nor efficient . sparse graph coding , such as gallager s low - density parity - check ( ldpc ) codes , offers an efficient alternative that approaches the shannon information limit @xcite . fortunately quantum coding and decoding strategies can be constructed from their classical counterparts , but unfortunately this mapping from classical to quantum coding can be problematic due to the requirement that quantum codes satisfy the duality - containing condition @xcite . moreover , due to increased challenges posed by these quantum codes , performance improvement requires further progress in the proposed decoding algorithm @xcite . the entanglement - assisted ( ea ) stabilizer formalism adds error - free entangled bits as a consumable resource for performing quantum error correction . this ea approach overcomes the duality - containing requirement and thus offers a rich lode of quantum error correction protocols inspired by classical protocols @xcite . using the ea approach , modern codes for classical channels , such as sparse codes , can easily be imported as quantum error - correcting codes @xcite . our aim is to improve belief propagation ( bp ) decoding methods so that quantum coding is dramatically improved over existing techniques . specifically our numerical results presented here show that an improved bp method whose heuristical feedback strategies based on exploiting all accessible information from stabilizer measurements , yield a dramatically improved block error rate ( ber ) for any depolarizing channel . our methods should work for any pauli noise channel . for @xmath0 qubits , a pauli channel is defined by the mapping @xmath1 with @xmath2 the @xmath0-fold tensor product of single - qubit pauli operators @xmath3 . our interest is focused on memory - less channels wherein the error on each qubit is independent of the error on any other qubit . in particular we consider the depolarizing channel , which is the most - studied case @xcite : for fixed channel error probability @xmath4 , the error on qubit @xmath5 is given by @xmath6 with @xmath7 denoting the probability of no error occurring . in quantum settings , due to the inability to measure each and every qubit , syndrome - based decoding is typically chosen . consequently , decoders using pauli channels are generally considered to be hard - decision decoders . in other words , in quantum decoding , the conventional soft - decision techniques are not applicable when the channel is in the pauli channel model . generally , sparse quantum codes are decoded by using syndrome - based bp decoding algorithms which automatically imply hard - decision decoding . though there is an equivalence between syndrome - based decoding and a posteriori probability decoding ( signal - based decoding ) under this setting , the syndrome - based decoding results in a serious drawback to bp decoder : the symmetric degeneracy error @xcite . fortunately , poulin and chung ( pc08 ) @xcite propose a solution to the symmetric degeneracy error by using the random perturbation method . motivated by the soft - decision techniques used in classical settings , which provide extra reliable information on the message nodes thereby yielding a better error correcting capacity @xcite , we develop a new heuristical feedback adjustment strategy for the standard bp decoder . when used in decoding sparse quantum codes , our method can on one hand solve the symmetric degeneracy error problem , and on the other hand can provide more useful information to the message nodes . the difference between pc08 and our approach is that , in pc08 , they feed back only the syndrome of the decoder output to adjust prior error probability distributions for received qubits . these adjusted distributions are then fed back into the decoder . we significantly improve this protocol by feeding back not just the syndrome but also the values of the frustrated checks on individual qubits of the code and the channel model ; accordingly we introduce a new adjustment strategy . specifically , our approach , which is based not only on syndromes but also on frustrated checks obtained from full stabilizer measurements and the channel model , yields a better ber for the case of depolarizing quantum channels . we provide a detailed description of our basic bp decoder for decoding sparse quantum codes . the basic bp decoder introduced here is inspired by the strategy used for decoding sparse classical quaternary codes under the bp algorithm . using this strategy , we can decode sparse quantum codes directly regardless of whether they arise from classical binary codes or not and regardless of whether they are calderbank - shor - steane ( css ) construction @xcite codes or not .

decoding sparse quantum codes can be accomplished by syndrome - based decoding using a belief propagation ( bp ) algorithm . we significantly improve this decoding scheme by developing a new feedback adjustment strategy for the standard bp algorithm . in our feedback procedure , we exploit much of the information from stabilizers , not just the syndrome but also the values of the frustrated checks on individual qubits of the code and the channel model .

decoding sparse quantum codes can be accomplished by syndrome - based decoding using a belief propagation ( bp ) algorithm . we significantly improve this decoding scheme by developing a new feedback adjustment strategy for the standard bp algorithm . in our feedback procedure , we exploit much of the information from stabilizers , not just the syndrome but also the values of the frustrated checks on individual qubits of the code and the channel model . furthermore we show that our decoding algorithm is superior to belief propagation algorithms using only the syndrome in the feedback procedure for all cases of the depolarizing channel . our algorithm does not increase the measurement overhead compared to the previous method , as the extra information comes for free from the requisite stabilizer measurements . shell : bare demo of ieeetran.cls for journals sparse quantum codes , quantum error correction , quantum channels , belief propagation , stabilizers .

astro-ph0001398

i

long before the supernovae were used to explore the distant universe , faint galaxy counts were known to be very sensitive to the cosmological parameters and to the redshift of formation . robust conclusions were derived on the inconsistency with the data of a deceleration parameter @xmath10 and a null cosmological constant ( yoshii and peterson , 1991 ; koo , 1990 ; guiderdoni and rocca - volmerange , 1990 ) . a flat universe @xmath11 could be saved only by either invoking a non - zero cosmological constant @xmath12 ( fukugita et al . , 1990 ) or by number evolution ( rocca - volmerange and guiderdoni , 1990 ) . no plausible change in star formation parameters might alter these conclusions . so that we adopt hereafter the best values of the cosmological parameters for our analysis of the cosmic star formation rate ( sfr ) in the universe , leaving to further studies , the sensitivity of results to this choice . a large variety of redshift and photometric surveys have been used to trace the sfh . between @xmath13 , a ten - fold increase of the sfr ( madau et al . , 1996 ) has been derived from the canada - france redshift survey ( cfrs , lilly et al . , 1996 ) from rest - frame 2800 computed by interpolation or , at low-@xmath9 , extrapolation of observed optical and near - infrared data . similar results were claimed using the h@xmath1 surveys ( gallego et al . , 1995 , tresse et al . , 1998 ) and the iso / cfrs data ( flores et al . , 1998 ) . on the other hand , the complete redshift and photometric ( from u to k bands ) surveys of galaxies observed by cowie et al . , 1996 , 1999 conclude to a milder evolution @xmath14 on the same range of redshift and to a higher local sfr , in agreement with the results of the foca2000 @xmath9-survey ( treyer et al . 1998 ; sullivan et al . 1999 ) . multiwavelength galaxy counts might help to solve this controversy . interpretations of faint galaxy counts were recently proposed by pozzetti et al . , ( 1998 ) and , using the spectral evolution model pgase , by fioc & rocca - volmerange ( 1999a ) . the latter notably identified a significant population of bursting dwarf galaxies in the foca 2000 photometric survey ( armand & milliard , 1994 ) , whose contribution in the optical and near - infrared is however much smaller than that due to the bulk of normal galaxies . in the optical - nir domain , galaxy counts are attributed to various populations of the hubble sequence , distributed according to the observed local luminosity functions by spectral types ( marzke et al , 1994 , heyl et al , 1997 ) . each evolution scenario , mainly constrained by local and low @xmath9 observations , corresponds to a star formation law . the 9 types computed are hereafter gathered in three groups : ellipticals - s0 , spirals sa - sbc , sc - irr - dwarfs . in the following we shortly recall the evolutionary modeling of galaxy counts with pgase . then we present the global sfh with a flat increase for 0@xmath151 , lightly shallower that cowie s et al . , 1999 . at higher redshifts , the evolution of elliptical and spiral sfhs is followed on the large 1@xmath154 domain , with different tendencies for the two groups .

deep galaxy counts are among the best constraints on the cosmic star formation history ( sfh ) of galaxies . using various tracers , the evolution of the star formation activity may now be followed on a wide range of redshifts ( @xmath0 ) covering most of the history of the universe . two incompatible interpretations of the observations are currently competing . after applying star formation rate ( sfr ) conversion factors to the cfrs , h@xmath1 or iso samples , many authors conclude to a strong increase ( @xmath2 a factor 10 ) of the sfr from @xmath3 to @xmath4 . , 1996 , 1999 ) . in this paper , we tackle this problem from the point of view of the modelist of the spectral evolution of galaxies . to understand the reason for these discrepant interpretations , we consider three classes of galaxies : e / s0 ( `` early - type '' ) ; sa sbc ( `` intermediate - type '' ) ; sc sd , irregulars and bursting dwarfs ( `` late - type '' ) . iii ) the contribution of early - type galaxies increases rapidly from @xmath4 to their redshift of formation ( @xmath8 - 3 for cosmological reasons ) .

deep galaxy counts are among the best constraints on the cosmic star formation history ( sfh ) of galaxies . using various tracers , the evolution of the star formation activity may now be followed on a wide range of redshifts ( @xmath0 ) covering most of the history of the universe . two incompatible interpretations of the observations are currently competing . after applying star formation rate ( sfr ) conversion factors to the cfrs , h@xmath1 or iso samples , many authors conclude to a strong increase ( @xmath2 a factor 10 ) of the sfr from @xmath3 to @xmath4 . they also find some evidence for a peak at @xmath5 and for a rapid decrease at higher redshifts . on the other side , the hawaii deep surveys favor only a mild increase between @xmath3 and @xmath6 ( cowie et al . , 1996 , 1999 ) . in this paper , we tackle this problem from the point of view of the modelist of the spectral evolution of galaxies . to understand the reason for these discrepant interpretations , we consider three classes of galaxies : e / s0 ( `` early - type '' ) ; sa sbc ( `` intermediate - type '' ) ; sc sd , irregulars and bursting dwarfs ( `` late - type '' ) . we use the new version of our evolutionary synthesis code , pgase ( fioc and rocca - volmerange , 2000 , in preparation ) , which takes into account metallicity and dust effects . the main results are : i ) late - type galaxies contribute significantly to the local sfr , especially bursting dwarfs ( fioc and rocca - volmerange , 1999 ) . because of that , the _ cosmic _ sfr can not decrease by a factor @xmath7 from @xmath3 to @xmath6 . this is in agreement with cowie et al . , 1999 s result . ii ) the sfr of intermediate - type galaxies has strongly decreased since @xmath4 . though the decrease is less than what find lilly et al . , 1996 , this suggests that the cfrs and h@xmath1 surveys are dominated by such bright early spirals . the limits in surface brightness and magnitudes of the observed samples may be the main reason for this selection . iii ) the contribution of early - type galaxies increases rapidly from @xmath4 to their redshift of formation ( @xmath8 - 3 for cosmological reasons ) . their intense star formation rates at high-@xmath9 give strong constraints on early ionization phases , primeval populations or metal enrichments .

1401.8204

i

lab on a chip technologies offer a range of unique opportunities for preparation and manipulation of molecular species . in particular , the compartmentalisation of biomolecules into monodisperse , micrometer - sized droplets allows for quantitative , high - throughput biochemical studies such as directed evolution,@xcite screening for reagents , reaction conditions or cells,@xcite as well as for the fabrication of designer emulsions and microgels.@xcite microdroplets can also allow the study of rare events , such as nucleation , and have thus enabled studies of the nucleation step of a@xmath0 aggregation@xcite as well as insulin amyloid growth.@xcite with the rapid development of microfluidic technologies , the need of ultra - sensitive detection methods becomes ever more pressing . a large fraction of present - day experiments rely on optical detection,@xcite with alternative strategies including , for instance , electrochemistry,@xcite mass spectrometry@xcite or raman spectroscopy.@xcite also , infrared ( ir ) spectroscopy techniques have been utilised to monitor the contents of microfluidic flows.@xcite here , we demonstrate an approach for performing off - line ir spectroscopy on the contents of single microdroplets with sub - micrometer spatial resolution . fourier transform infrared spectroscopy ( ftir ) is a key method for studying conformational properties of proteins and in particular for inferring their secondary structure.@xcite exposed to ir radiation , chemical bonds undergo vibrations such as stretching , bending and rotating . in the case of proteins , this leads to a spectrum characterised by a set of absorption features in the amide bands.@xcite thereby , the modes most commonly used to study the structural properties of polypeptides are the amide i , amide ii and amide iii bands . amide i arises mainly from stretching vibrations and is generally localised within 1690 - 1600 @xmath1 ; the exact band position is determined by the backbone conformation - in other words by the secondary structure of the protein . in contrast , amide ii originates from a combination of bending and stretching and is localised around 1580 - 1510 @xmath1 . it is still possible to associate the position of the band to the protein s secondary structure , but the fact that this band stems from a combination of two different modes makes this analysis less straightforward . finally , the amide iii band is a combination of many modes such as stretching , in - plane bending , stretching as well as bending and occurs in the range of 1300 - 1200 @xmath1 . in practice , @xmath2-helical structures have this band centred around 1654 @xmath1 , random coil proteins show a maximum around 1640 @xmath1 , and @xmath0-sheet - rich amyloidic aggregates exhibit an amide i maximum within 1610 - 1630 @xmath1.@xcite to achieve sub - micron spatial resolution for protein ir spectroscopy experiments , we utilised an thermomechanical detection technique based on atomic force microscopy ( afm ) : if an ir pulse at a given wavelength is absorbed by a sample , the local temperature rise leads to local thermal expansion.@xcite this deformation excites a mechanical resonance in the afm cantilever which is in contact with the analyte . afm detection of this temporary expansion of the scanned region therefore allows nanoscale resolution ir imaging and acquisition of local chemical spectra . simultaneously with the ir - absorption image , the system is able to scan topography ( with conventional contact mode ) and sample stiffness ( related to the frequency of the cantilever oscillations ) . in order to be able to reliably locate and distinguish the protein contents of individual microdroplets for performing nanoscale ir spectroscopy as well as to provide for an enormous amount of statistics , the droplets are aligned on a znse prism using a pre - patterned polymer stamp and dried overnight , as shown schematically in fig . [ fig : scheme](a)-(c ) . thereafter , spectra of single dried microdroplets containing monomeric and aggregated protein are acquired , and the ability to easily differentiate between the two demonstrates the efficacy of the presented approach . the capability of studying the contents of single microdroplets individually with a high - precision method paves the way for a wide range of experiments harnessing the advantages of microfluidics . for instance , combination with on - chip selection techniques@xcite that pre - screen for a predefined species within droplets could allow for specific in - depth investigation of analytes in the context of protein aggregation as well as directed evolution . in addition , it should be emphasised that the technique of aligning individual microfluidic droplets off - chip offers further possibilities for systematic ex - situ assays beyond ir spectroscopy or afm .

droplet microfluidics has emerged as a powerful platform allowing a large number of individual reactions to be carried out in spatially distinct microcompartments . due to their small size , however , the spectroscopic characterisation of species encapsulated in such systems remains challenging . in this paper

droplet microfluidics has emerged as a powerful platform allowing a large number of individual reactions to be carried out in spatially distinct microcompartments . due to their small size , however , the spectroscopic characterisation of species encapsulated in such systems remains challenging . in this paper , we demonstrate the acquisition of infrared spectra from single microdroplets containing aggregation - prone proteins . to this effect , droplets are generated in a microfluidic flow - focussing device and subsequently deposited in a square array onto a znse prism using a micro stamp . after drying , the solutes present in the droplets are illuminated locally by an infrared laser through the prism , and their thermal expansion upon absorption of infrared radiation is measured with an atomic force microscopy tip , granting nanoscale resolution . using this approach , we resolve structural differences in the amide bands of the spectra of monomeric and aggregated lysozyme from single microdroplets with picolitre volume .

1401.8204

r

our results demonstrate that using the approach presented here , it is feasible to align tens to hundreds - if desired even thousands - of microdroplets , as shown in fig . [ fig : pics](b ) . such a regular deposition allows for reliable , systematic off - line assays including ultra - high precision analytical tools as , for instance , the nanoscale ir spectroscopy utilised in this work . figures [ fig : meas](a)-(d ) show how the aggregated lysozyme from an individual microdroplet can be analysed accurately . presented is the spatially resolved absorption of infrared radiation , determined via thermal expansion as measured by an afm tip . the wavenumbers are fixed at 1640 @xmath1 ( a ) , 1620 @xmath1 ( b ) , 1530 @xmath1 ( c ) , 1250 @xmath1 ( d ) , corresponding to two instances from the amide i band , one from the amide ii band , and one from the amide iii band , respectively . while all the four plots share their topographical features , it is readily apparent that absorption is higher in the amide i band than the amide ii and iii bands . moreover , the absorption in the amide iii band exhibits a stronger spatial dependence . this could be linked to the fact that this band is sensitive to different vibrational modes and therefore is influenced by local conformational changes accompanying the transition of protein from its monomeric form into aggregates.@xcite thus , it is possible to investigate the ir absorption behaviour of the contents of individual droplets locally . furthermore , the correlation with the height measurement from the afm scan in fig . [ fig : pics](c ) emphasises that the recorded absorption originates from the contents of a single microdroplet . the complete spectrum of the lysozyme aggregates in this droplet - averaged over 12 spectra recorded at different locations and smoothed by a savitzky - golay filter - is given by the dashed blue line in fig . [ fig : meas](e ) . as expected from the spatially resolved data , the nearly constant absorption observed in the amide i band - lightly peaked at approximately 1640 @xmath1 - is higher than in the amide ii and iii bands . remarkably , when comparing with a spectrum taken from a droplet containing only monomeric protein ( the solid red line is the smoothed average over 15 individual spectra ) , striking differences are apparent . first and foremost , the monomeric protein exhibits a sharp peak at around 1655 @xmath1 , due to the high @xmath2-helical content of lysozyme , and a shoulder at 1640 @xmath1 originating from random coils and @xmath0-sheets - all in good agreement with the structure of lysozyme@xcite and providing evidence that the secondary structural elements are largely unaffected by the gentle drying procedure . secondly , the amide ii band seems slightly shifted towards higher energies for the monomer , and thirdly , absorption in the amide iii band is significantly higher in monomeric than in aggregated protein . the shift of the amide i peak as well as the dramatic increase of absorption at 1620 @xmath1 are the typical signatures of the formation of amyloid - like cross-@xmath0 structure@xcite and have been studied extensively for the case of lysozyme.@xcite notably , our spectra from dried lysozyme correspond very well to measurements obtained in bulk solution.@xcite in fact , even if monomers already contain @xmath0-sheet domains their spectra differ from the amyloidic @xmath0-sheets and can be distinguished by the change in the location of the amide i peak.@xcite similarly , the position of the amide ii band is expected to shift towards lower wavenumbers if the secondary structure changes from predominantly @xmath2 helical to @xmath0-sheet.@xcite as the amide iii band has a significantly more complex origin , the differences in the monomeric and aggregated spectra are less directly explainable , but strong deviations are reasonable bearing in mind the extensive structural modification proteins undergo during aggregation . finally , comparison to a spectrum from a droplet containing initially monomeric protein that was dried at @xmath3c and ambient pressure for 15 h - such that aggregation can occur within the droplet - reveals that the monomeric features of the amide i and iii bands are lost upon fibrillation ( dash - dotted green line ; average over 21 spectra ) . note that due to the normalisation of the spectra to 1 the amide ii band seems more pronounced . nevertheless , the relative amplitudes of the amide ii and iii bands correspond very well to the spectra from the aggregates . for a znse prism that was covered with sio@xmath15 and heated with droplets containing monomeric lysozyme , we observed a similar increase of absorption in the amide i band but the peak in the amide iii band did not vanish , which may be an indication of partial aggregation ( see sec . [ sec : si ] ) .

, we demonstrate the acquisition of infrared spectra from single microdroplets containing aggregation - prone proteins . to this effect after drying , the solutes present in the droplets are illuminated locally by an infrared laser through the prism , and their thermal expansion upon absorption of infrared radiation is measured with an atomic force microscopy tip , granting nanoscale resolution . using this approach , we resolve structural differences in the amide bands of the spectra of monomeric and aggregated lysozyme from single microdroplets with picolitre volume .

droplet microfluidics has emerged as a powerful platform allowing a large number of individual reactions to be carried out in spatially distinct microcompartments . due to their small size , however , the spectroscopic characterisation of species encapsulated in such systems remains challenging . in this paper , we demonstrate the acquisition of infrared spectra from single microdroplets containing aggregation - prone proteins . to this effect , droplets are generated in a microfluidic flow - focussing device and subsequently deposited in a square array onto a znse prism using a micro stamp . after drying , the solutes present in the droplets are illuminated locally by an infrared laser through the prism , and their thermal expansion upon absorption of infrared radiation is measured with an atomic force microscopy tip , granting nanoscale resolution . using this approach , we resolve structural differences in the amide bands of the spectra of monomeric and aggregated lysozyme from single microdroplets with picolitre volume .

physics0006018

r

to understand the influence of the external magnetic field on the electronic structure of the hydrogen molecule we first have to remind ourselves of the properties in the absence of the field . accurate data for hydrogen are of great importance both in astrophysics as well as laboratory physics . it is a paradigm for many molecular phenomena like charge transfer , excitation , ionization or scattering processes . indeed our ci calculations on the basis of an anisotropic gaussian basis set provided also significant progress with respect to the knowledge of the field - free excitations of the molecule : several highly excited states have been calculated for the first time and some of the pecs for the lower lying states have been improved . the corresponding results have been presented to some detail in ref.@xcite and contain elaborate information on the first eight excited singlet and triplet states for both gerade and ungerade parity . in the following we will first summarize the main properties of the excited singlet states in the absence of the field and then investigate the electronic structure in the presence of the magnetic field with increasing field strength . we hereby first deal with the gerade and subsequently with the ungerade states . the investigation of the electronic states and pecs has been done for all internuclear distances considered ( @xmath70 ) with the same atomic orbital basis set . the latter has been optimized to yield precise energies ( accuracy @xmath71 ) of the hydrogen atom for the six lowest states for both parities for vanishing atomic magnetic quantum number . additionally , in order to describe correlation effects , we have included basis functions with atomic magnetic quantum numbers @xmath72 . the approximate number of two - particle configurations resulting from the above basis set is @xmath73 . the accuracy of the electronic energies for the higher excited states @xmath74 ( @xmath75 indicates the degree of excitation ) is , due to the above choice of the optimized basis set , lower than that for less excited states . figure 1 shows the pecs for the states @xmath76 where the dotted lines represent the curves for the higher excited states @xmath77 . there is a large energetical gap ( @xmath78 ) between the ground and the excited states of @xmath79 symmetry . the first five excited states are well - known from the literature @xcite . our calculations @xcite show in most cases an agreement within @xmath80 compared to the literature and in several cases also a variationally lower energy . as already mentioned the results on the higher excited states ( @xmath77 ) have for the first time been reported very recently in ref.@xcite . as can be seen from figure 1 all the pecs of the states @xmath76 possess a deep potential well around a minimum located approximately at @xmath81 . a particular feature occuring for most of the considered @xmath82 states is the existence of a second outer minimum and therefore the corresponding pecs exhibit a double well . vibrational states in these outer wells @xcite attracted recently significant experimental interest @xcite since they allow the experimental observation of long - lived and highly excited valence states of the hydrogen molecule . the two minima of the @xmath83 state arise due to the fact that two different configurations of the same symmetry , namely the @xmath84 and the @xmath85 configurations , are energetically minimized at two significantly different internuclear distances . the deep outer wells of the @xmath86 states arise due to a series of avoided crossings between the heitler - london configurations @xmath87 and the ionic configurations @xmath88 . particularly the @xmath89 state possesses a very broad and deep ( @xmath90 ! ) outer potential well which is separated by a broad barrier from the inner well located at @xmath91 . the outer minimum is located at @xmath92 . a series of avoided crossings at very large internuclear distances @xmath93 leads to the energetically equal dissociation limits @xmath94 of the @xmath95 states . the dissociation channel of the @xmath96 state is the ionic configuration @xmath97 . tables 1 to 3 contain ( among the data in the presence of a magnetic field ) the total and dissociation energies at the equilibrium internuclear distances , the equilibrium internuclear distances and the total energies in the dissociation limit for the first to third excited @xmath98 states in the absence of the magnetic field . the subspace of @xmath7 symmetry contains the electronic ground state of the hydrogen molecule in field - free space and in the presence of a magnetic field in the regime @xmath99 for a detailed discussion of the appearance of this state and the global ground state with increasing field strength in general we refer the reader to refs.@xcite ( see also introduction of the present work ) . in the following we investigate the evolution of the excited @xmath100 states with increasing magnetic field strength for the regime @xmath101 . we will first study the changes of the pecs of individual states with increasing field strength and thereafter we present a global view of the evolution of the spectrum . in order to compare the pecs for the same state for different field strengths we subtract from the total energies the corresponding energies in the dissociation limit ( which is different for different field strengths ) , i.e. we show the quantity @xmath102 . in general the dissociation limit of a certain state of @xmath1 symmetry changes with increasing field strength which is due to the reordering of the energy levels of the atoms ( hydrogen , hydrogen negative ion ) in the external field . for the atomic states we will use in the following the notation @xmath103 where @xmath75 specifies the degree of excitation and @xmath104 the atomic magnetic quantum number and z - parity , respectively . let us begin our investigation of the evolution of individual states with increasing field strength with the @xmath105 state whose pecs are shown in figure 2a . the positions of the two minima and the corresponding maximum decrease with increasing field strength . the depth of the inner potential well decreases for @xmath106 and increases rapidly for @xmath107 . the depth of the outer well is monotonically increasing for the complete regime @xmath101 . for @xmath108 and @xmath109 the inner well is therefore deeper than the outer well and vice versa for @xmath110 ( see figure 2a ) . the dissociative behaviour of the pecs changes significantly with increasing field strength . the origin of these changes is the fact that for @xmath111 the dissociation channel is @xmath112 whereas for @xmath113 we have the asymptotic behaviour @xmath114 ( the index @xmath115 stands for spin singlet ) . the appearance of the ionic configuration as the dissociation channel for the low - lying electronic @xmath105 state can be explained as follows . it is well - known that the hydrogen negative ion possesses infinitely many bound states in the presence of a magnetic field of arbitrary strength assuming an infinite nuclear mass @xcite . certain of these bound states show a monotonically increasing binding energy with increasing field strength . the latter surpass then more and more of the energy levels belonging to two hydrogen atoms one being in the global ground state and the other one in the corresponding excited state . for a sufficiently strong magnetic field we therefore expect the configuration @xmath116 to become the dissociation channel particularly for the first excited state of @xmath7 symmetry . due to the long range forces the onset of the asymptotic ( @xmath117 ) behaviour of the corresponding pecs with the ionic channel ( @xmath118 ) is qualitatively different from the pecs with a neutral dissociation limit ( @xmath119 ) . this explains the different asymptotic behaviour of the pecs shown in figure 2a with increasing field strength . finalizing the discussion of the @xmath105 state we remark that its pecs possesses a second maximum for @xmath120 which however occurs at large internuclear distances ( @xmath121 ) and is only of the order of @xmath122 above the dissociation limit . table 1 contains relevant data of the pecs of the @xmath105 state with increasing field strength . next we turn to the second excited i.e. the @xmath123 state whose pecs are shown in figure 2b . the positions of the two minima and the corresponding maximum already present in field - free space decrease monotonically with increasing field strength . starting from @xmath124 the depth of the inner well decreases with increasing field strength whereas it increases for @xmath125 . besides a very small interval of field strengths the depth of the outer well increases with increasing field strength . for @xmath126 the outer well is deeper than the inner one whereas for @xmath127 the deep inner well dominates the shape of the pec . we remark that the curvature at the ( first ) maximum and the outer minimum increases significantly with increasing field strength . the evolution of these increasingly sharper turns can only be fully understood if one looks at the complete spectrum ( see figure 3 and in particular 3(e ) ) with increasing field strength : they develop due to a number of narrow avoided crossing of the first to third excited states in strong fields . an interesting property of the pec of the @xmath123 state is the existence of an additional outer ( third ) minimum for the interval @xmath128 which is shown in figure 2c . this minimum arises due to the interaction with the ionic configuration @xmath118 . in field - free space the lowest and only bound ionic channel @xmath116 is the dissociation channel of the @xmath129 state . with increasing field strength the hydrogen negative ion becomes increasingly stronger bound ( see discussion above ) and therefore it occurs as the dissociation channel for the sequence of excited states @xmath130 finally becoming the dissocation channel of the @xmath105 state for @xmath113 . the existence of the additional outer minimum becomes now understandable : due to the energetical lowering of the ionic dissociation channel with increasing field strength the higher excited states of @xmath7 symmetry evolve outer minima and corresponding wells for certain regimes of the field strength . for the @xmath123 state this outer well is extremely shallow for @xmath131 and therefore almost invisible in figure 2c . for @xmath132 it becomes however well - pronounced . between @xmath133 and @xmath134 there occurs a change with respect to the dissociation channel of the @xmath123 . for @xmath135 the dissociation channel is @xmath136 and for @xmath137 it is @xmath138 . the similar asymptotic behaviour of the pecs belonging to different field strengths ( see figure 2c for @xmath139 and @xmath140 ) arises due to the fact that they possess all the ionic dissociation channel . in the latter regime the position of the ( third ) outer minimum increases with increasing field strength ( for @xmath141 the outer minimum is located at @xmath142 ) . finally there is a second change of the dissociation channel of the @xmath123 state to @xmath143 and therefore the outer minimum disappears for @xmath113 . table 2 contains the total and dissociation energies at the equilibrium internuclear distances , the equilibrium internuclear distances and the total energies in the dissociation limit for the second excited @xmath144 state in the regime @xmath101 next we focus on the third excited @xmath145 whose pecs with increasing field strength are shown in figure 2d . in field - free space it possesses two minima and associated potential wells located at @xmath146 and @xmath147 , respectively . the position of the inner minimum increases with increasing field strength whereas the corresponding dissociation energy decreases . finally for @xmath148 the associated well disappears but reappears for @xmath149 . with further increasing field strength the position of this inner minimum decreases and the depth of the corresponding well increases monotonically for @xmath107 . independently of this first inner minimum and the outer minimum there appears for @xmath150 an additional third minimum and corresponding well ( see table 3 and figure 2d ) for small internuclear distances @xmath151 . although this new minimum and well are energetically well below the dissociation limit for @xmath152 they are separated from the other inner minimum only by a tiny barrier . these facts will become better understandable in the context of our discussion of the evolution of the whole spectrum with increasing field strength ( see below ) . the properties of the pec of the @xmath145 state at large internuclear distances are somewhat analogous to that of the @xmath123 state . the outer minimum has its origin in the interaction of the neutral @xmath119 and ionic @xmath153 configurations . starting with @xmath154 and increasing the field strength the depth of the outer well increases . the first change of the dissociation channel from @xmath155 to @xmath156 occurs in the regime @xmath157 . in the regime @xmath158 the position of the outer minimum increases with increasing field strength ( for @xmath133 it is already @xmath159 ) and the depth of the outer well decreases . due to the further increasing binding energy of the hydrogen negative ion @xmath160 state with increasing field strength we encounter a second change of the dissociation channel at @xmath161 to @xmath162 which causes the disappearance of the outer minimum and well . table 3 provides the corresponding data for the @xmath145 state . the pecs of the @xmath163 and @xmath164 states are shown in figures 2e and 2f , respectively . for both states the positions of the maxima and minima as well as the corresponding total energies show an irregular behaviour as a function of the field strength for @xmath165 . we therefore focus on the main features of these states . for certain regimes of the field strength we observe double well structures for the pecs . analogously to the @xmath166 states there exist additional outer minima and wells due to the interaction with the ionic configuration for certain field strength regimes . for @xmath167 the position of the first inner minimum decreases rapidly with increasing field strength whereas the corresponding dissociation energy increases . also we observe the existence of minima whose energies lie above the dissociation energy , i.e. the corresponding wells contain if at all metastable states . we remark that some of the above - discussed features , in particular those associated with small energy scales , might not be visible in the corresponding figures 2 but only in a zoom of the relevant regimes of internuclear distances of the considered pecs . we again emphasize that due to the large amount of data we do not present full pecs or data on the higher excited states @xmath168 which can be obtained from the authors upon request . in the present subsection we focus on the evolution of the complete spectrum of the excited @xmath169 states with increasing field strength . this will give us the complementary information to the evolution of individual states presented above . figure 3a - f shows the corresponding pecs for the field strengths @xmath170 , respectively . the pecs of the five energetical lowest excited states @xmath171 are hereby illustrated with full lines indicating their higher accuracy whereas the pecs of the electronic states @xmath172 are less accurate and illustrated with dotted lines . before we discuss the evolution with increasing field strength some general remarks are in order . the energy gap between the ground state @xmath173 and the first excited state @xmath105 is of the order of @xmath174 in field - free space and increases montonically with increasing field strength . at the same time the total energies of all states @xmath175 are shifted in lowest order proportional to @xmath176 with increasing field strength which is due to the raise of the kinetic energy in the presence of a magnetic field . in field - free space many of the dissocation channels of the pecs of excited @xmath7 states are degenerate due to the degeneracies of the field - free hydrogen atom ( see figure 1 and 4 ) . the major difference of the pecs in field - free space compared to those for weak fields is the removal of these degeneracies ( see , for example , figure 3a for @xmath177 ) . with increasing field strength figures 3a - d ( @xmath178 ) demonstrate the systematic lowering of the diabatic energy curve belonging to the ionic configuration @xmath97 . this diabatic curve passes through the spectrum with increasing field strength thereby causing an intriguing evolution of avoided crossings and corresponding potential wells for the individual states . at @xmath179 the fourth excited @xmath163 state acquires the ionic dissociation channel . the @xmath180 state thereby looses its outer potential well which was very well - pronounced in the absence of the external field . in the same course the @xmath123 state shows a number of avoided crossings with the @xmath105 state : it develops an additional outer minimum and well which is rather deep at @xmath181 accompanied by the flattening of the first inner well and the deepening of the second inner well . furthermore we observe for @xmath181 the appearance of a large number of avoided crossing among the higher excited states @xmath168 at @xmath182 . at @xmath183 the third excited @xmath145 state acquires the ionic dissociation channel . subsequently , i.e. with further increasing field strength , the second excited @xmath123 state ( see figure 3d ) and finally the first excited @xmath105 state acquire ionic character for sufficiently large internuclear distances . in the high field situation ( see figure 3e for @xmath184 ) only the energetically lowest excited state possess a well - pronounced double well structure and the overall picture is dominated by the fact that the pecs of the considered states possess a very similar shape and are energetically very close to each other in particular around the inner minimum at small internuclear distances . figure 3f shows for @xmath184 a zoom of the series of avoided crossings occuring for the higher excited states @xmath185 in the regime @xmath186 . the four energetically lowest states of @xmath187 symmetry at @xmath154 have been investigated in detail and with high accuracy in the literature @xcite . our results @xcite show a relative accuracy of @xmath65 for the energies of the @xmath188 state and of @xmath67 for the first two excited states i.e. the @xmath189 states . the energies of the @xmath190 state are significantly lower than the data presented in @xcite . the pecs for the @xmath191 presented in ref.@xcite for the first time are estimated to possess an accuracy of @xmath67 for the @xmath192 states and @xmath65 for the @xmath193 states . figure 4 shows the pecs of the ground as well as eight excited states of @xmath187 symmetry in the range @xmath194 on a logarithmic scale . the pec of the ground state @xmath188 of ungerade symmetry possesses a minimum at @xmath195 and a corresponding deep well . a closer look at the wave function reveals its ionic character for @xmath196 . with further increasing internuclear distance the ionic character of the wave function decreases and the corresponding dissociation channel is @xmath197 . the pec of the first excited @xmath198 state is similar to that of the ground state @xmath188 : its equilibrium internuclear distance is @xmath199 the dissociation channel is identical to that of the @xmath188 state . the depth of its single well is however only one third of the depth of the well of the @xmath188 state . for the higher excited states we observe a similar behaviour as in the case of the excited electronic states of @xmath200 symmetry . the pecs of the @xmath201 states possess a deep well around a minimum located approximately at @xmath202 . furthermore the @xmath203 states exhibit additional deep outer potential wells at large internuclear distances which arise due to the avoided crossings of the heitler - london configurations with the corresponding ionic configuration . the outer minimum of the @xmath204 state is located at @xmath205 and the corresponding well possesses a remarkable depth of @xmath206 : it is expected to contain a large number of long - lived vibrational states . tables 4 to 6 contain ( among the data in the presence of the magnetic field ) the total and dissociation energies at the equilibrium internuclear distances , the equilibrium internuclear distances and the total energies in the dissociation limit for the first to third excited @xmath207 states in the absence of the magnetic field . first of all we remark that the dissociation channels of the @xmath208 states coincide with those of the @xmath209 states for @xmath210 in the complete regime @xmath211 . the qualitative behaviour of the pecs of the @xmath209 states at large internuclear distances is therefore similar to that of the @xmath208 states discussed in the previous section . in particular many of the explanations and remarks provided there hold also for the present case of the @xmath209 states . before discussing the behaviour of the pecs of the individual excited @xmath209 states with increasing field strength some remarks concerning the lowest , i.e. ground state of @xmath11 symmetry are in order ( for its pec with increasing field strength see figure 6 ) . its dissociation energy increases monotonically with increasing field strength whereas its equilibrium internuclear distance increases slightly for weak fields and decreases significantly for increasingly stronger fields . as indicated above the asymptotic @xmath117 behaviour of the pecs of the @xmath212 and @xmath105 states is very similar . for @xmath184 the pec of the @xmath212 state possesses a peculiar shape which is largely determined by the ionic dissociation channel @xmath213 ( see figure 6f ) . for more details on this state we refer the reader to ref.@xcite . the first excited @xmath214 state possesses in field - free space an equilibrium internuclear distance @xmath215 . figure 5a shows the corresponding pec with increasing field strength for @xmath216 whereas figure 5b illustrates particularly the behaviour at large internuclear distances . in the regime @xmath217 the dissociation energy decreases slightly and the bond length increases . with further increasing field strength the dissociation energy increases drastically and the bond length decreases . for @xmath218 there exists a maximum and a corresponding additional outer minimum at large internuclear distances ( see figure 5b ) whose origin is again the emergence of the ionic configuration for the wave function of the @xmath214 state . figure 5b also demonstrates the similarity of the asymptotic @xmath219 behaviour of the pecs of the @xmath214 state in the regime @xmath220 . the corresponding data for the pecs of the first excited @xmath214 state are given in table 4 . turning to the second excited @xmath221 state we observe that the depth of the potential well located for @xmath124 at @xmath222 decreases for weak fields whereas it increases significantly for strong fields @xmath223 ( see figure 5c ) . the existence of an additional outer minimum for this state can be seen in figure 5d . in many respects a similar behaviour to that of the @xmath214 state is observed although , of course , the regimes of field strength for which the individual phenomena take place are different . table 5 contains the corresponding data of the pecs of the @xmath221 state . finally figures 5e and 5f show the pecs of the @xmath224 states with increasing field strength , respectively . they exhibit a number of maxima and minima most of which can however hardly be seen in figures 5e , f or occur at large internuclear distances . the origin of their existence are again the different ( ionic and neutral ) dissociation channels . these maxima and minima are present only for certain individually different regimes of the field strength . some of them are located above and some of them below the dissociative threshold . as can be seen the bond length ( belonging to the inner minimum ) decreases monotonically and the dissociation energy increases significantly above some critical value @xmath225 . the inner minimum and associated well possesses a remarkably large dissociation energy for strong fields . table 6 provides data on the pecs of the @xmath226 state . to finalize our discussion on the @xmath11 subspace we show in figure 6 the evolution of the spectrum with increasing field strength . figures 6a - f show the pecs for the @xmath227 states for the field strengths @xmath228 , respectively . analogously to the case of the @xmath7 subspace we observe for weak fields the removal of the degeneracies due to the field - free hydrogen atom in the dissociation limit . with increasing field strength we see the lowering of the diabatic energy line belonging to the ionic configuration which causes the appearance and disappearance of outer maxima , minima and corresponding outer potential wells until finally ( @xmath184 ) the @xmath212 state possess the ionic dissociation channel @xmath229 which is the origin of the peculiar shape of its pec . a number of further observations made for the manifold of the @xmath230 states above can also be seen for the @xmath227 states in figure 6 like , for example , the similar shape of the potential wells of the excited states in the high field limit .

excited states of the hydrogen molecule subject to a homogeneous magnetic field are investigated for the parallel configuration in the complete regime of field strengths @xmath0 . up the evolution of the potential energy curves for the individual states with increasing field strength as well as the overall behaviour of the spectrum are discussed in detail .

excited states of the hydrogen molecule subject to a homogeneous magnetic field are investigated for the parallel configuration in the complete regime of field strengths @xmath0 . up to seven excitations are studied for gerade as well as ungerade spin singlet states of @xmath1 symmetry with a high accuracy . the evolution of the potential energy curves for the individual states with increasing field strength as well as the overall behaviour of the spectrum are discussed in detail . a variety of phenomena like for example the sequence of changes for the dissociation channels of excited states and the resulting formation of outer wells are encountered . possible applications of the obtained data to the analysis of magnetic white dwarfs are outlined .

physics0006018

c

the hydrogen molecule is the most fundamental molecular system and of immediate importance in a variety of different physical circumstances . in spite of the fact that it has been investigated over the past decades in great detail and that our knowledge on this system has grown enormously there are plenty of questions and problems to be addressed even for the molecule in field - free space . as an example we mention certain highly excited rydberg states ( @xmath231 ) which , due to the ionic character of the binding for certain regimes of the internuclear distance , possesses a deep outer well at large distances which contains a considerable number of vibrational states . on the other hand the detailed knowledge of hydrogen ( even of highly excited states ) is of utmost importance for our understanding and interpretation of the astrophysically observed interstellar radiation . much less is known about the behaviour of the hydrogen molecule in strong magnetic fields . with increasing field strength the ground state of the molecule undergoes two transitions which are due to a change of the spin and orbital character , respectively . very recently the global ground state configurations have been identified for the parallel configuration ( there are good reasons which lead to the conjecture that the derived results hold for arbitrary angle of the internuclear and magnetic field axis ) both on the hartree - fock level @xcite and via a fully correlated approach @xcite . for low fields the ground state is of spin singlet @xmath7 symmetry , for intermediate fields the spin triplet @xmath15 state represent the ground state whereas in the high field regime the @xmath20 state is the energetically lowest state . the present work goes for the first time beyond the ground state properties and investigates excited states of the hydrogen molecule in the broad regime @xmath101 . we hereby focus on singlet states of both gerade as well as ungerade symmetry : up to seven excited states have been studied for the parallel configuration with a high accuracy of the obtained pecs . a variety of different phenomena have been observed out of which we mention here only the most important ones . double well structures observed in particular for the field - free @xmath232 states are severly modified in the presence of the field thereby showing a coming and going of new maxima and minima as well as corresponding wells . the overall tendency in the strong field limit is the development of deep inner wells containing a large number of vibrational states . in the course of the increasing field strength a fundamental phenomenon occurs which has a strong impact on the overall shape of the pecs . due to the fact that the hydrogen negative ion becomes increasingly bound with increasing field strength we encounter changes in the dissociation channels of individual states from neutral @xmath233 to ionic @xmath234 character . for a certain regime of field strength @xmath235 a certain excited state possesses therefore the ionic dissociation channel thereby modifying the asymptotic behaviour of its pec to an attractive coulombic tail . for weaker fields @xmath236 higher excited states possess this ionic dissociation channel whereas for stronger fields @xmath237 it belongs to increasingly lower excitations . these facts influence the overall appearance of the spectrum thereby creating features like outer potential wells and/or largely changing avoided crossings . the data on the pecs of the excited singlet states obtained here should serve as part of the material to be accumulated for the investigation of quasimolecular absorption features in magnetic white dwarfs . the investigation of excited triplet states of @xmath1 symmetry or of @xmath8 states , which are of equal importance , are left to future investigations .

to seven excitations are studied for gerade as well as ungerade spin singlet states of @xmath1 symmetry with a high accuracy . a variety of phenomena like for example the sequence of changes for the dissociation channels of excited states and the resulting formation of outer wells are encountered . possible applications of the obtained data to the analysis of magnetic white dwarfs are outlined .

excited states of the hydrogen molecule subject to a homogeneous magnetic field are investigated for the parallel configuration in the complete regime of field strengths @xmath0 . up to seven excitations are studied for gerade as well as ungerade spin singlet states of @xmath1 symmetry with a high accuracy . the evolution of the potential energy curves for the individual states with increasing field strength as well as the overall behaviour of the spectrum are discussed in detail . a variety of phenomena like for example the sequence of changes for the dissociation channels of excited states and the resulting formation of outer wells are encountered . possible applications of the obtained data to the analysis of magnetic white dwarfs are outlined .

1603.01994

i

understanding the dynamics of transmission is fundamental for devising effective policies and practical measures that limit the spread of infectious diseases . in recent years , the introduction of affordable whole genome sequencing has provided unprecedented detail on the relatedness of pathogen samples @xcite . as a result , inferring transmission between hosts with accuracy is becoming more and more feasible . however , this requires robust , and computationally efficient methods to infer past transmission events using genetic information . many complications , such as within - host pathogen genetic variation and non - sampled hosts , obscure the relationship between pathogen phylogenies and the history of transmission events , affecting the accuracy of such methods . here , we present a new approach , scotti , that accounts for these complexities in a computationally feasible manner . a number of approaches have been developed that reconstruct transmission from genetic data . one method , based on pathogen genetic data , rules out direct transmission if isolates from different hosts are separated by a number of substitutions above a fixed threshold @xcite . this approach can not generally distinguish direct transmission from transmission through one or more intermediate hosts , or infer its direction . alternatively , the phylogenetic tree of the pathogen samples is often used as a proxy for the transmission history @xcite . while phylogenetic signal can be very informative of transmission , it can also be misleading @xcite . the main cause of this problem is within - host variation that can generate discrepancies between the phylogenetic and epidemiological relatedness of hosts , and can bias estimates of infection times @xcite . one problem arising from within - host diversity is that the pathogen isolates transmitted by a host are not necessarily genetically identical to those sampled from the same host . this phenomenon can be mathematically modelled using population genetics approaches such as the coalescent @xcite , to describe within - host evolution ( figure [ examples]a ) . other factors that can cause disagreement between phylogeny and transmission history are : ( i ) incomplete transmission bottlenecks , where some of the within - host genetic variation is transmitted from donor to recipient through a non - negligibly small inoculum ; this means lineages from the same host may not have shared a common ancestor since long before the time of infection of the host ( figure [ examples]b ) . ( ii ) non - sampled hosts , such that a sampled patient is not necessarily linked by direct transmission to its most closely related sampled patient , but can have a non - sampled intermediate ( figure [ examples]c ) @xcite . ( iii ) multiply infected hosts , that can cause patients to be erroneously excluded from some transmission chains , in particular if multiple samples from the same patient are not collected ( figure [ examples]d ) . in ) , the corresponding transmission history is represented with black beanbags " , and , in red , the phylogenetic tree of the sequences.,title="fig:",scaledwidth=90.0% ] [ examples ] several methods emerged in recent years explicitly modelling both the transmission process and genetic evolution to perform inference of the history of transmission events @xcite . these methods generally make use of epidemiological dating information ( such as the date of sampling , the interval of exposure of a host to an outbreak , or the likely duration of infectiousness ) , but they usually ignore within - host variation and other causes of phylogenetic discordance with transmission history @xcite . the methods of ypma and colleagues @xcite , didelot and colleagues @xcite , and hall and colleagues @xcite account for within - host diversity , but assume that all hosts in the outbreak have been detected and sequenced , which may be incorrect or uncertain in practical settings . here , we propose a new bayesian approach called scotti ( structured coalescent transmission tree inference ) that not only accounts for diversity and evolution within a host , but also for other sources of bias , namely non - sampled hosts and multiple infections of the same host . this new method builds on our recent progress in efficiently modelling migration between populations using an approximation to the structured coalescent @xcite . formally , we model each host as a separate pathogen population , and we model transmission as migration between hosts . scotti has a broad range of applicability as it relaxes the typical assumptions that every host is sampled and that there is no within - host variation ( see figure [ figure1 ] in ) . a limitation of our method is that we do not model transmission bottlenecks . this can be a disadvantage with strong bottlenecks at transmission ( due to small inocula ) , but on the other hand it may be an advantage with large transmission inocula . scotti is implemented as an open - source package for the bayesian phylogenetic software beast2 @xcite , and as such , it can be freely installed and used . we compare the performance of scotti and the popular software outbreaker @xcite ( version 1.1 - 5 ) on simulated data and on real datasets of foot and mouth disease virus ( fmdv @xcite ) and _ klebsiella pneumoniae _ these applications highlight how the two methods usually provide very different interpretations of outbreak dynamics , with scotti showing typically higher accuracy on simulated data . by combining epidemiological and genetic information , and by implementing a general and computationally efficient model , scotti can accurately infer transmission in a broad range of settings , providing important information to understand and limit the spread of infectious disease .

exploiting pathogen genomes to reconstruct transmission represents a powerful tool in the fight against infectious disease . however , their interpretation rests on a number of simplifying assumptions that regularly ignore important complexities of real data , in particular within - host evolution and non - sampled patients . here we propose a new approach to transmission inference called scotti ( structured coalescent transmission tree inference ) . our computationally efficient implementation of this model enables the inference of host - to - host transmission while accommodating within - host evolution and non - sampled hosts . we show that scotti can generally infer transmission events even in the presence of considerable within - host variation , can account for the uncertainty associated with the possible presence of non - sampled hosts , and can efficiently use data from multiple samples of the same host , although there is some reduction in accuracy when samples are collected very close to the infection time . we illustrate the features of our approach by investigating transmission from genetic and epidemiological data in a foot and mouth disease virus ( fmdv ) veterinary outbreak in england and a _ klebsiella pneumoniae _ outbreak in a nepali neonatal unit .

exploiting pathogen genomes to reconstruct transmission represents a powerful tool in the fight against infectious disease . however , their interpretation rests on a number of simplifying assumptions that regularly ignore important complexities of real data , in particular within - host evolution and non - sampled patients . here we propose a new approach to transmission inference called scotti ( structured coalescent transmission tree inference ) . this method is based on a statistical framework that models each host as a distinct population , and transmissions between hosts as migration events . our computationally efficient implementation of this model enables the inference of host - to - host transmission while accommodating within - host evolution and non - sampled hosts . scotti is distributed as an open source package for the phylogenetic software beast2 . we show that scotti can generally infer transmission events even in the presence of considerable within - host variation , can account for the uncertainty associated with the possible presence of non - sampled hosts , and can efficiently use data from multiple samples of the same host , although there is some reduction in accuracy when samples are collected very close to the infection time . we illustrate the features of our approach by investigating transmission from genetic and epidemiological data in a foot and mouth disease virus ( fmdv ) veterinary outbreak in england and a _ klebsiella pneumoniae _ outbreak in a nepali neonatal unit . transmission histories inferred with scotti will be important in devising effective measures to prevent and halt transmission .

1505.00266

i

line emission or absorption is a promising probe of the high - redshift universe . considerable theoretical and instrumental effort has been devoted to the use of the redshifted 21 cm line of neutral hydrogen in such a fashion ( see @xcite for a recent review ) . comparable observations using atomic or molecular lines at far - infrared wavelengths have seen less development . recent advances in far - ir instrumentation , combining sensitive receivers with large collecting area , have led to the detection of far - ir lines in individual sources at cosmological distances , raising the prospects for a future generation of far - ir line surveys as a probe of the high - redshift universe . infrared fine structure lines are important coolants of the neutral and ionized gas phases of normal and starburst galaxies . they are easily excited , arise from the most abundant metals with low ionization potential , and are generally not affected by galactic or intergalactic attenuation . the strongest line is the @xmath3 fine - structure line of singly - ionized carbon at 157.74 @xmath0 m rest wavelength . the ubiquity of carbon in the interstellar medium combined with the relatively low ionization potential and modest excitation temperature make the [ cii ] line bright , with as much as 0.1 1% of the total bolometric luminosity of the host galaxy emitted in this single line @xcite . the intrinsic line brightness and lack of significant attenuation from the galactic or intergalactic medium in the far infrared in turn render the [ cii ] line visible over cosmological distances @xcite . the ability to detect [ cii ] emission to redshifts @xmath4 makes the [ cii ] line a promising candidate for cosmological surveys . [ cii ] emission originates from multiple phases of the interstellar medium . the combined emission from all phases serves as a marker for source redshift for surveys of large - scale structure @xcite . the empirical relation between [ cii ] and the bolometric far - ir luminosity allows the observed [ cii ] intensity to serve as a tracer of star - formation activity @xcite , while the ratio of [ cii ] to other far - ir lines probes physical conditions within different phases of interstellar medium of the host galaxies @xcite . several authors have discussed requirements for [ cii ] surveys at cosmological distances . @xcite estimate that a 500-hour observation of the 2.4 diameter hubble deep field with the atacama large millimeter array could yield 15 [ cii ] detections over the redshift range @xmath5 . the sub - arcsecond angular resolution available for such interferometric observations minimizes confusion from source superposition within each synthesized beam , but the large number of independent pointings needed to map an area comparable to the hdf minimizes the integration time spent on any individual source so that only the brightest sources are detected . observations at coarser angular resolution reduce the need for multiple pointings , at the cost of introducing competing lines from foreground sources . intensity mapping is one such technique , using fluctuations in the spatial and spectral distribution of line emission from a superposition of sources to derive the underlying power spectrum of the individual , unresolved sources ( see , _ e.g. _ , the discussion in @xcite ) . several such surveys have been proposed . for example , @xcite present a concept for [ cii ] intensity mapping using a 25-beam grating spectrometer each with beam width 10 , while @xcite propose a suite of single - beam spectrometers each with 30 beam width . the larger beam size anticipated for such surveys facilitates mapping large areas but requires additional analysis to separate the target line emission from the foreground created by emission from other galaxies along the same line of sight . several authors discuss cross - correlation techniques to minimize foreground confusion in line intensity mapping @xcite . for a given target redshift , the technique defines two observing wavelengths corresponding to emission from two different rest - frame lines . maps of line emission taken at each observing wavelength contain spatially correlated structure corresponding to the two lines emitted by each source galaxy . the contribution from other lines at different rest - frame wavelengths redshifted into the observing wavelengths must originate from sources at different redshifts . spatial correlations from such distant sources will be weaker , so that the cross - correlation traces the power spectrum of the source galaxies at the target redshift . intensity mapping surveys large volumes of the universe to derive statistical estimates of structure formation , but provides little information on individual sources . in this paper , we investigate the complementary technique of direct line identification in narrow - beam spectroscopic surveys . if the [ cii ] line were the only observable far - ir line , redshift identification would be straightforward . in practice , however , the [ cii ] line is merely one of several cooling lines . the problem of sorting through an observed spectrum containing multiple lines from multiple galaxies at different redshifts presents both instrumental and analytical challenges . we use a toy model of far - ir line emission to evaluate a simple algorithm for line identification and estimate relevant instrumental parameters ( angular resolution , sensitivity , and spectroscopic resolution ) required to derive cosmologically interesting results . the results are applicable for spectral cleaning of intensity mapping surveys as well as pencil - beam surveys of more limited cosmological volume . , width=259 ]

far infrared cooling lines are ubiquitous features in the spectra of star forming galaxies the observations require moderate spectral resolution @xmath2 with angular resolution between 20 and 10 , sufficiently narrow to minimize confusion yet sufficiently large to include a statistically meaningful number of sources .

far infrared cooling lines are ubiquitous features in the spectra of star forming galaxies . surveys of redshifted fine - structure lines provide a promising new tool to study structure formation and galactic evolution at redshifts including the epoch of reionization as well as the peak of star formation . unlike neutral hydrogen surveys , where the 21 cm line is the only bright line , surveys of red - shifted fine - structure lines suffer from confusion generated by line broadening , spectral overlap of different lines , and the crowding of sources with redshift . we use simulations to investigate the resulting spectral confusion and derive observing parameters to minimize these effects in pencil - beam surveys of red - shifted far - ir line emission . we generate simulated spectra of the 17 brightest far - ir lines in galaxies , covering the 150 to 1300 @xmath0 m wavelength region corresponding to redshifts @xmath1 , and develop a simple iterative algorithm that successfully identifies the 158@xmath0 m [ cii ] line and other lines . although the [ cii ] line is a principal coolant for the interstellar medium , the assumption that the brightest observed lines in a given line of sight are always [ cii ] lines is a poor approximation to the simulated spectra once other lines are included . blind line identification requires detection of fainter companion lines from the same host galaxies , driving survey sensitivity requirements . the observations require moderate spectral resolution @xmath2 with angular resolution between 20 and 10 , sufficiently narrow to minimize confusion yet sufficiently large to include a statistically meaningful number of sources .

1505.00266

m

we use a simple model of the brightest far - ir lines to simulate the observed line spectra from distant galaxies . we assume that the total luminosity , @xmath6 emitted in a single line at rest frequency @xmath7 may be simply related to the total infrared luminosity , @xmath8 of a galaxy , @xmath9 the observed specific flux of a single line from a set of ir galaxies at redshift @xmath10 is then given by @xmath11 where @xmath12 is the galaxy ir luminosity function , @xmath13 is the luminosity distance , @xmath14 is the redshifted frequency , and @xmath15 is the intrinsic line profile , normalized so that @xmath16 . ignoring the effects of gravitational lensing , the total line intensity emitted from galaxies within a redshift interval @xmath17 to the present ( @xmath18 ) then becomes @xmath19 \nonumber\end{aligned}\ ] ] if the ratio of line intensity to ir luminosity is a constant , eq . ( [ obs_specific_intensity ] ) simplifies to @xmath20\left|{cdt\over dz}\right|{dz\over 1+z}\ ] ] where @xmath21 @xmath22 is the comoving number density of galaxies , and @xmath23 is their average ir luminosity . we simulate the far - ir line spectra using a standard cosmology with @xmath24 , @xmath25 , and @xmath26 @xcite . we divide the comoving volume into redshift bins and compute the total number of galaxies @xmath27 within each bin @xmath28 where @xmath29 is the comoving volume at redshift @xmath10 . we use the resulting number density to generate monte carlo realizations of the far - ir line spectra . the background cosmology fixes the mean number of galaxies within a fixed observing solid angle . we assign each simulated galaxy a redshift and ir luminosity , using the @xcite luminosity function to obtain a representative luminosity distribution within each redshift bin . each galaxy then contributes a set of far - ir lines . figure [ line_fig ] shows the relative intensity of the rest - frame lines used for this study . we include the [ cii ] line at 158 @xmath0 m , [ ci ] at 610 and 371 @xmath0 m , [ oiii ] at 88 and 52 @xmath0 m , [ oi ] at 145 and 63 @xmath0 m , [ niii ] at 57 @xmath0 m , and [ nii ] at 205 and 122 @xmath0 m , as well as the co ( @xmath30 ) series through @xmath31 . the total luminosity in each line is related to that of the host galaxy by the factor @xmath32 ( eq . [ f_def ] ) . we set the mean value of @xmath33 for each line using the ratios of values in table 1 of @xcite . for simplicity , we do not explicitly calculate the star formation rate for each simulated galaxy , but relate the comoving star formation rate @xmath34 to the ir luminosity density @xmath35 as @xmath36 where @xmath37 is the comoving ir luminosity density , @xmath34 is the comoving cosmic star formation rate ( csfr ) in @xmath38 yr@xmath39 mpc@xmath40 , and @xmath41 is a conversion factor for a salpeter stellar initial mass function ( kennicutt 2012 ) . the relative luminosities from different lines within a source are known to vary by roughly a factor of 10 . we account for such variation by multiplying @xmath32 for each line in each host galaxy by a random number drawn uniformly from the range [ 0.3 3 ] . we additionally account for the systematic variation in line luminosity and line ratios due to the increased cmb temperature at higher redshift @xcite . we assume that the host galaxies are not spatially resolved and assign a random rotational linewidth to each galaxy uniformly drawn from the range [ 30 300 ] km s@xmath39 . each galaxy contributes multiple lines ; all lines from a single galaxy have the same rotational line broadening . finally , we accumulate the lines from all source galaxies within the sampled volume and redshift each line to obtain a realization the observed far - ir spectrum . the effects of instrument spectroscopic resolution are discussed in @xmath423.2 . we ignore instrument noise and continuum emission from the superposed host galaxies to focus here on the problem of line identification . for the [ cii ] line . ( top ) individual line flux , shown at the central wavelength before rotational broadening . lines are color - coded by species using the same color coding as figure [ line_fig ] . 48 lines from 48 individual galaxies at @xmath43 fall within the plotted wavelength range . the assumption that the brightest lines are always [ cii ] lines produces a high error rate , with roughly a third of the brightest lines originating from species other than [ cii ] . ( bottom ) the same lines are shown after rotational broadening . the superposition of rotationally broadened lines produces a complicated spectrum ( black curve ) . [ sample_spectrum ] , width=336 ] figure [ sample_spectrum ] shows a typical spectrum with 2 angular resolution at wavelengths corresponding to redshifts @xmath44 for the [ cii ] line . two problems are evident . the first problem is confusion . unlike radio observations , where the redshifted 21 cm line is the only bright line , a number of lines contribute to the observed far - ir spectra . only 16% of the lines within the observed wavelength range correspond to the targeted [ cii ] line , with the remainder consisting of `` interloper '' lines originating at both higher and lower redshifts from species other than [ cii ] . the second problem is blending : the superposition of rotationally broadened lines produces a complicated spectrum . the fainter lines merge to form a near continuum spectrum , further hindering line identification .

. surveys of redshifted fine - structure lines provide a promising new tool to study structure formation and galactic evolution at redshifts including the epoch of reionization as well as the peak of star formation . unlike neutral hydrogen surveys , where the 21 cm line is the only bright line , surveys of red - shifted fine - structure lines suffer from confusion generated by line broadening , spectral overlap of different lines , and the crowding of sources with redshift . we use simulations to investigate the resulting spectral confusion and derive observing parameters to minimize these effects in pencil - beam surveys of red - shifted far - ir line emission . we generate simulated spectra of the 17 brightest far - ir lines in galaxies , covering the 150 to 1300 @xmath0 m wavelength region corresponding to redshifts @xmath1 , and develop a simple iterative algorithm that successfully identifies the 158@xmath0 m [ cii ] line and other lines .

far infrared cooling lines are ubiquitous features in the spectra of star forming galaxies . surveys of redshifted fine - structure lines provide a promising new tool to study structure formation and galactic evolution at redshifts including the epoch of reionization as well as the peak of star formation . unlike neutral hydrogen surveys , where the 21 cm line is the only bright line , surveys of red - shifted fine - structure lines suffer from confusion generated by line broadening , spectral overlap of different lines , and the crowding of sources with redshift . we use simulations to investigate the resulting spectral confusion and derive observing parameters to minimize these effects in pencil - beam surveys of red - shifted far - ir line emission . we generate simulated spectra of the 17 brightest far - ir lines in galaxies , covering the 150 to 1300 @xmath0 m wavelength region corresponding to redshifts @xmath1 , and develop a simple iterative algorithm that successfully identifies the 158@xmath0 m [ cii ] line and other lines . although the [ cii ] line is a principal coolant for the interstellar medium , the assumption that the brightest observed lines in a given line of sight are always [ cii ] lines is a poor approximation to the simulated spectra once other lines are included . blind line identification requires detection of fainter companion lines from the same host galaxies , driving survey sensitivity requirements . the observations require moderate spectral resolution @xmath2 with angular resolution between 20 and 10 , sufficiently narrow to minimize confusion yet sufficiently large to include a statistically meaningful number of sources .

1505.00266

c

the [ cii ] line is a principal coolant of the interstellar medium and is observable at cosmological distances . however , the [ cii ] line is observed against a forest of competing lines from sources at multiple redshifts . we use monte carlo simulations of the galaxy distribution at redshifts @xmath72 to generate realizations of the far - ir spectra including emission from 17 of the brightest far - ir lines . the resulting spectra provide a test bed to evaluate the use of the [ cii ] line as a cosmological probe in blind pencil - beam surveys . the superposition of rotationally - broadened lines from multiple galaxies at different redshifts creates a complex spectrum . the simplest assumption , that the brightest lines are always [ cii ] lines , is at best a coarse approximation to the simulated spectra . the fraction of [ cii ] lines among the brightest 10% of all observed lines falls from 0.8 for observations near 315 @xmath0 m ( @xmath45 ) to 0.4 at 1100 @xmath0 m ( @xmath46 ) . line identification based solely on relative intensity produces a high error rate . a variant of the radio - astronomical clean algorithm yields superior results . the algorithm selects the brightest line from an observed set of spectral lines , tentatively identifies the line as [ cii ] , and uses the resulting source redshift to predict the observed wavelengths for redshifted line emission from other bright far - ir lines from the same source . if the predicted lines are observed , the source identification is confirmed and the [ cii ] line and redshifted companion lines are flagged and removed from the list of unknown lines . if the predicted lines are not observed , the source identification is not confirmed and the bright source line remains on the list of unknown lines for possible later identification as a companion line for a source at a different redshift . the algorithm then proceeds to the next brightest remaining line and iterates until all lines have been processed . a typical spectrum for 2 angular resolution contains some 1600 spectral lines within one octave , originating from 550 different galaxies . the superposition of rotationally broadened lines reduces this to roughly 390 distinct peaks in the observed spectrum , 110 of which result from a single un - blended [ cii ] line . the line identification algorithm correctly identifies 40 of the 110 [ cii ] line peaks for an efficiency of order 36% ( not counting companion lines identified from the same host galaxies ) . chance alignments of lines lead the algorithm to incorrectly identify 3 peaks as [ cii ] lines ; however , the incorrect identifications result almost exclusively from fainter candidate peaks . restricting the algorithm to the brightest third of the observed peaks ( corresponding roughly to threshold 0.3 mjy ) increases the percentage of correct identifications above 90% . correct line identification requires detection of both the targeted `` parent '' line and one or more `` companion '' lines from the same source . survey sensitivity thresholds are thus determined by the expected intensities of the companion lines and not solely by the brighter [ cii ] line . line over one octave in wavelength at spectral resolution @xmath66 . the recovered luminosity distribution ( solid line ) accurately follows the toy model ( dotted curve ) . the dashed line shows the recovered luminosity distribution for a model without luminosity evolution . [ luminosity_evolution ] , width=259 ] the ability to distinguish individual peaks in the superposed spectra depends on the spectral resolution and angular resolution . decreasing the angular resolution increases the number of lines in the observed spectra , requiring higher spectral resolution to minimize blending of neighboring lines . the required resolutions are modest . spectral resolution @xmath59 resolves 90% of the peaks for 20 angular resolution , while @xmath60 resolves 90% of the peaks for 10 angular resolution or coarser . the [ cii ] line is a promising cosmological probe . the large number of potential sources observed within a single pencil beam combined with an efficient and accurate line identification algorithm allow rapid characterization of the galaxy luminosity distribution to redshifts encompassing reionization . a simulated pencil - beam survey demonstrates the ability to distinguish toy models of galaxy evolution within a single angular resolution element . the required angular resolution , sensitivity , wavelength range , and spectroscopic resolution appear achievable , suggesting that far - ir lines may soon provide a new tool to map the large - scale galaxy distribution and evolution for redshifts @xmath73

although the [ cii ] line is a principal coolant for the interstellar medium , the assumption that the brightest observed lines in a given line of sight are always [ cii ] lines is a poor approximation to the simulated spectra once other lines are included . blind line identification requires detection of fainter companion lines from the same host galaxies , driving survey sensitivity requirements .

far infrared cooling lines are ubiquitous features in the spectra of star forming galaxies . surveys of redshifted fine - structure lines provide a promising new tool to study structure formation and galactic evolution at redshifts including the epoch of reionization as well as the peak of star formation . unlike neutral hydrogen surveys , where the 21 cm line is the only bright line , surveys of red - shifted fine - structure lines suffer from confusion generated by line broadening , spectral overlap of different lines , and the crowding of sources with redshift . we use simulations to investigate the resulting spectral confusion and derive observing parameters to minimize these effects in pencil - beam surveys of red - shifted far - ir line emission . we generate simulated spectra of the 17 brightest far - ir lines in galaxies , covering the 150 to 1300 @xmath0 m wavelength region corresponding to redshifts @xmath1 , and develop a simple iterative algorithm that successfully identifies the 158@xmath0 m [ cii ] line and other lines . although the [ cii ] line is a principal coolant for the interstellar medium , the assumption that the brightest observed lines in a given line of sight are always [ cii ] lines is a poor approximation to the simulated spectra once other lines are included . blind line identification requires detection of fainter companion lines from the same host galaxies , driving survey sensitivity requirements . the observations require moderate spectral resolution @xmath2 with angular resolution between 20 and 10 , sufficiently narrow to minimize confusion yet sufficiently large to include a statistically meaningful number of sources .

1602.00208

i

over the real numbers , the classical descartes rule implies that the number of distinct , real roots of a @xmath0-nomial @xmath12 $ ] is less than @xmath13 , regardless of its degree . it is a natural algebraic problem to look for analogous sparsity - dependent bounds over other fields that are not algebraically closed . in @xcite , canetti et al . derive the following analogue of descartes rule for polynomials in @xmath14}$ ] . ( @xcite , lemma 7 ) [ d ] for @xmath15}$ ] ( with @xmath16 nonzero ) , if @xmath17 denotes the number of distinct , nonzero roots of @xmath2 in @xmath18 , then @xmath19 where @xmath20 for @xmath21 , the associated diffie - hellman distribution is defined by the random variable @xmath22 where @xmath23 and @xmath24 are uniformly random over @xmath25 . the diffie - hellman cryptosystem relies on the assumption that an attacker can not easily determine @xmath26 given the values of @xmath27 , @xmath28 , and @xmath29 . in @xcite , canetti et al . showed that diffie - hellman distributions are very nearly uniform ( which is an important property for the security of the cryptosystem ) , and the bound in theorem [ d ] was the central tool which powered their arguments . since then , the bound has been a useful tool for studying various algorithmic and number - theoretic problems : in @xcite it was used to study the complexity of recovering a sparse polynomial from a small number of approximate values ( which is relevant to the security of polynomial pseudorandom number generators ) , in @xcite it was used to study the singularity of generalized vandermonde matrices over @xmath18 , in @xcite it was used to study the solutions of exponential congruences @xmath30 , and in @xcite it was used to study the correlation of linear recurring sequences over @xmath31 . the main result of this paper is a new bound ( theorem [ bound ] of section 2 below ) improving theorem [ d ] by removing the asymptotic term and replacing @xmath32 by a smaller , intrinsic parameter .

additionally , we describe a number - theoretic parameter depending only on @xmath7 and the exponents @xmath8 which provides a general and easily - computable upper bound for @xmath5 . we thus obtain a strict improvement over an earlier bound of canetti et al . which is related to the uniformity of the diffie - hellman distribution .

for a @xmath0-nomial @xmath1 $ ] , we show that the number of distinct , nonzero roots of @xmath2 is bounded above by @xmath3 , where @xmath4 and @xmath5 is the size of the largest coset in @xmath6 on which @xmath2 vanishes completely . additionally , we describe a number - theoretic parameter depending only on @xmath7 and the exponents @xmath8 which provides a general and easily - computable upper bound for @xmath5 . we thus obtain a strict improvement over an earlier bound of canetti et al . which is related to the uniformity of the diffie - hellman distribution . finally , we conjecture that @xmath0-nomials over prime fields have only @xmath9 roots in @xmath10 when @xmath11 .

1212.6595

i

the virtual state wavefunctions are essential for the construction of the multi - indexed laguerre and jacobi polynomials @xcite . they are polynomial type solutions of one - dimensional schrdinger equations for shape - invariant potentials @xcite . they are characterised as having negative energies ( the groundstate has zero energy ) , no zeros in the physical domain and that they and their reciprocals are square non - integrable . by dropping the condition of no zeros and the reciprocals are required to be square - integrable at both boundaries , _ pseudo virtual state wavefunctions _ are obtained . in most cases , the virtual and pseudo virtual state wavefunctions are obtained from the eigenfunctions by twisting the parameter(s ) based on the discrete symmetries of the hamiltonian @xcite . starting from a shape - invariant potential , a darboux transformation @xcite in terms of a nodeless pseudo virtual state wavefunction @xmath3 with energy @xmath4 produces a solvable system with an extra eigenstate below the original groundstate with energy @xmath4 and eigenfunction @xmath5 . this method of generating a solvable system by `` adding an eigenstate '' below the groundstate is known for many years , starting from the simplest harmonic oscillator potential examples @xcite and followed by many authors @xcite@xcite . as remarked by adler @xcite for the harmonic oscillator case and generalised by the present authors @xcite for other potentials , such a system can be derived by special types of krein - adler transformations . that is , the krein - adler transformation for a system with negatively shifted parameters in which the created state will be the groundstate . the transformation use all the eigenstates between the new and the original groundstates . in this paper we present straightforward generalisation of the above result for various shape - invariant potentials listed in section [ sec : exa ] ; coulomb potential with the centrifugal barrier ( c ) , kepler problem in spherical space ( k ) , morse potential ( m ) , soliton potential ( s ) , rosen - morse potential ( rm ) , hyperbolic symmetric top @xmath6 ( hst ) , kepler problem in hyperbolic space ( kh ) , hyperbolic darboux - pschl - teller potential ( hdpt ) , on top of the well - known harmonic oscillator ( h ) , the radial oscillator ( l ) and the darboux - pschl - teller potential ( j ) . they are divided into two groups according to the eigenfunction patterns in [ sec:2group ] . we mainly follow infeld - hull @xcite for the naming of potentials . a darboux - crum transformation in terms of multiple pseudo virtual state wavefunctions is equivalent to a certain krein - adler transformation deleting multiple eigenstates with shifted parameters . in contrast to the use of genuine virtual state wavefunctions @xcite , not all choices of the multiple pseudo virtual states would generate singularity free systems . the singularity free conditions of the obtained system are supplied by the known ones for the krein - adler transformations @xcite . underlying the above equivalence are infinitely many polynomial wronskian identities relating wronskians of polynomials with twisted parameters to those of shifted parameters . these identities imply the equality of the deformed potentials with the twisted and shifted parameters . this in turn guarantees the equivalence of all the other eigenstate wavefunctions . we present the polynomial wronskian identities for group a ; the harmonic oscillator ( h ) , the radial oscillator ( l ) and the darboux - pschl - teller potential ( j ) and some others . for group b , the identities take slightly different forms ; determinants of various polynomials with twisted and shifted parameters . the infinitely many polynomial wronskian identities are the consequences of the fundamental wronskian ( determinant ) identity as demonstrated in section [ sec : main ] . this paper is organised as follows . the essence of darboux - crum transformations for the schrdinger equation in one dimension is recapitulated in [ sec : genstr ] . the definitions of virtual states and pseudo virtual states are given in [ sec : vir ] . in section [ sec : exa ] two groups of eigenfunction patterns are introduced in [ sec:2group ] and related wronskian expressions are explored in [ sec : wro ] . the details of the eleven examples of shape - invariant systems are provided in [ sec : h][sec : hdpt ] . section [ sec : main ] is the main part of the paper . we demonstrate the equivalence of the darboux - crum transformations in terms of multiple pseudo virtual states to krein - adler transformations in terms of multiple eigenstates with shifted parameters . the underlying polynomial wronskian identities are proven with their more general determinant identities . the final section is for a summary and comments .

for eleven examples of one - dimensional quantum mechanics with shape - invariant potentials , the darboux - crum transformations in terms of multiple _ pseudo virtual state wavefunctions _ are shown to be equivalent to krein - adler transformations deleting multiple eigenstates with _ shifted parameters_. these are based upon infinitely many polynomial wronskian identities of classical orthogonal polynomials , _ yukawa institute kyoto + dpsu-12 - 3 + yitp-12 - 85 + * krein - adler transformations for shape - invariant potentials and pseudo virtual states + + * * satoru odake@xmath0 and ryu sasaki@xmath1 * @xmath2 department of physics , shinshu university , + matsumoto 390 - 8621 , japan + @xmath1 yukawa institute for theoretical physics , + kyoto university , kyoto 606 - 8502 , japan + e - mail : ryu@yukawa.kyoto-u.ac.jp

for eleven examples of one - dimensional quantum mechanics with shape - invariant potentials , the darboux - crum transformations in terms of multiple _ pseudo virtual state wavefunctions _ are shown to be equivalent to krein - adler transformations deleting multiple eigenstates with _ shifted parameters_. these are based upon infinitely many polynomial wronskian identities of classical orthogonal polynomials , _ i.e. _ the hermite , laguerre and jacobi polynomials , which constitute the main part of the eigenfunctions of various quantum mechanical systems with shape - invariant potentials . yukawa institute kyoto + dpsu-12 - 3 + yitp-12 - 85 + * krein - adler transformations for shape - invariant potentials and pseudo virtual states + + * * satoru odake@xmath0 and ryu sasaki@xmath1 * @xmath2 department of physics , shinshu university , + matsumoto 390 - 8621 , japan + @xmath1 yukawa institute for theoretical physics , + kyoto university , kyoto 606 - 8502 , japan + e - mail : ryu@yukawa.kyoto-u.ac.jp

1112.2142

i

in @xcite , ap , slovk , and souek construct sequences of invariant differential operators on _ parabolic geometries _ of any type @xmath0 , one for each finite - dimensional representation @xmath1 of @xmath2 . ( here , @xmath2 is a semisimple lie group and @xmath3 a parabolic subgroup . ) these sequences are known as _ bernstein - gelfand - gelfand _ ( bgg ) sequences since , for the homogeneous model @xmath0 of such a geometry , these sequences are complexes , which are dual to a parallel construction due to these authors @xcite on the level of verma modules . in @xcite calderbank and diemer simplify the construction of bgg sequences in @xcite . in addition they provide @xcite , for regular parabolic geometries , alternative bgg sequences , which only coincide with the ones in @xcite if the geometry is _ torsion - free_. the latter sequences not only appear to be more natural , they also have the advantage that if @xmath1 is taken to be the trivial representation , then they form complexes , providing fine resolutions of the locally constant sheaf @xmath4 ( as one sees by suitably modifying ( * ? ? ? * proposition 5.5(iv ) ) ) . for the sequences of @xcite this is only true if the geometry is torsion - free and , in this case , the two sequences are anyway the same . in combination with the construction of canonical cartan connections given in @xcite , this shows that one can find alternatives to the de rham resolution for any parabolic geometry defined in terms of a regular infinitesimal flag structure @xcite . a hallmark of these resolutions is that the ranks of the bundles involved are diminished as compared to the de rham complex . the price one pays is that the operators may be higher than first order . the construction of these resolutions in @xcite , entails firstly constructing the cartan connection as described in @xcite and this is not at all straightforward . in this article we present some examples constructed by a more elementary route . as we show , our method extends to certain non - parabolic geometries , namely arbitrary contact and symplectic geometries . we shall use the spectral sequence of a filtered complex @xcite without comment and merely as a replacement for tedious diagram chasing .

for smooth manifolds equipped with various geometric structures , we construct complexes that replace the de rham complex in providing an alternative fine resolution of the sheaf of locally constant functions . in case , our method extends to contact and symplectic geometries ( beyond the parabolic realm ) .

for smooth manifolds equipped with various geometric structures , we construct complexes that replace the de rham complex in providing an alternative fine resolution of the sheaf of locally constant functions . in case that the geometric structure is that of a parabolic geometry , our complexes coincide with the bernstein - gelfand - gelfand complex associated with the trivial representation . however , at least in the cases we discuss , our constructions are relatively simple and avoid most of the machinery of parabolic geometry . moreover , our method extends to contact and symplectic geometries ( beyond the parabolic realm ) .

1607.04046

i

the standard model ( sm ) of elementary particle physics , which is based on the gauge group @xmath5 is very successful in explaining the fundamental interactions of nature . with the recent discovery of higgs at lhc , the sm seems to be complete . however , it has certain limitations . for example , the muon @xmath1 anomaly , which is a discrepancy between the observation and sm measurement with more than @xmath6 confidence level @xcite . similarly , it does not explain sub - ev masses of active neutrinos as confirmed by long baseline oscillation experiments @xcite . moreover , it does not accommodate any particle candidate of dark matter ( dm ) whose existence is strongly supported by galaxy rotation curve , gravitational lensing and large scale structure of the universe @xcite . in fact , the dm constitutes about @xmath7 of the total energy budget of the universe as precisely measured by the satellite experiments wmap @xcite and planck @xcite . at present lhc is the main energy frontier and is trying to probe many aspects of physics beyond the sm . an attractive way of probing new physics is to search for a @xmath8-gauge boson which will indicate an existence of @xmath9 symmetry . within the sm , we have accidental global symmetries @xmath10 , where @xmath11 is the baryon number , and @xmath12 , where @xmath13 is the total lepton number . note that @xmath10 and @xmath12 are anomalous and can not be gauged without adding any ad hoc fermions to the sm . however , the differences between any two lepton flavours , i.e. , @xmath14 , with @xmath15 , are anomaly free and can be gauged without any addition of extra fermions to the sm . among these extensions the most discussed one is the gauged @xmath16 @xcitethe interactions of corresponding gauge boson @xmath8 are restricted to only @xmath17 and @xmath18 families of leptons and therefore it significantly contribute to muon @xmath1 anomaly , which is a discrepancy between the observation and sm measurement with more than @xmath6 confidence level . moreover , @xmath8 does not have any coupling with the electron family . therefore , it can easily avoid the lep bound : @xmath19 tev @xcite . so , in this scenario a @xmath8- mass can vary from a few mev to tev which can in principle be probed at lhc and at future energy frontiers . in this paper we revisit the gauged @xmath0 model in light of muon @xmath1 anomaly , neutrino mass and dm phenomenology . we augment the sm by including three right handed neutrinos : @xmath20 , @xmath21 and @xmath22 , which are singlets under the sm gauge group , and a vector like colorless neutral fermion @xmath23 . we also add an extra sm singlet scalar @xmath24 . all these particles except @xmath20 , are charged under @xmath0 , though singlet under the sm gauge group . when @xmath24 acquires a vacuum expectation value ( vev ) , the @xmath0 breaks to a remnant @xmath25 symmetry under which @xmath23 is odd while all other particles are even . as a result @xmath23 serves as a candidate of dm . the smallness of neutrino mass is also explained in a type - i see - saw framework with the presence of right handed neutrinos @xmath20 , @xmath21 and @xmath22 whose masses are generated from the vev of scalar field @xmath24 . in this model the relic abundance of dm ( @xmath23 ) is obtained via its annihilation to muon and tauon family of leptons through the exchange of @xmath0 gauge boson @xmath8 . we show that the relic density crucially depends on @xmath0 gauge boson mass @xmath26 and its coupling @xmath27 . in particular , we find that the observed relic density requires @xmath28 for @xmath29 mev . however , if @xmath30 then we get an over abundance of dm , while these couplings are compatible with the observed muon @xmath1 anomaly . we resolve this conflict by adding an extra singlet scalar @xmath31 doubly charged under @xmath0 , which can drain out the large dm abundance via the annihilation process : @xmath32 . as a result , the parameter space of the model satisfying muon @xmath1 anomaly can be reconciled with the observed relic abundance of dm . we further show that the acceptable region of parameter space for observed relic density and muon @xmath1 anomaly is strongly constrained by null detection of dm at xenon-100 @xcite and lux @xcite . moreover , the compatibility of the present framework with indirect detection signals of dm is also checked . in particular , we confront the acceptable parameter space with the latest positron data from pamela @xcite , fermi - lat @xcite and ams-02 @xcite . the paper is arranged as follows . in section - ii , we describe in details the different aspects of the model . section - iii is devoted to show the allowed parameter space from muon @xmath1 anomaly . in section - iv , we estimate the neutrino mass within the allowed parameter space . section v , vi and vii are devoted to obtain constraints on model parameters from the relic density , direct and indirect search of dm . in section - viii , we lay the conclusions with some outlook .

we augment this model with three right - handed neutrinos @xmath3 and a vector - like singlet fermion @xmath4 to explain simultaneously the non - zero neutrino mass and dark matter content of the universe , while satisfying anomalous muon @xmath1 constraints . it is shown that in a large parameter space of this model we can explain positron excess , observed at pamela , fermi - lat and ams-02 , through dark matter annihilation , while satisfying the relic density and direct detection constraints .

gauged @xmath0 model has been advocated for a long time in light of muon @xmath1 anomaly , which is a more than @xmath2 discrepancy between the experimental measurement and the standard model prediction . we augment this model with three right - handed neutrinos @xmath3 and a vector - like singlet fermion @xmath4 to explain simultaneously the non - zero neutrino mass and dark matter content of the universe , while satisfying anomalous muon @xmath1 constraints . it is shown that in a large parameter space of this model we can explain positron excess , observed at pamela , fermi - lat and ams-02 , through dark matter annihilation , while satisfying the relic density and direct detection constraints .

astro-ph9911105

i

stresses developing in the crust of an evolving neutron star could fracture the crust ( a starquake ) , possibly affecting the star s spin evolution and generating high - energy emission . spin down ( , in isolated pulsars ; @xcite ) or spin up ( , in accreting neutron stars ) changes the equilibrium shape of the star , building stresses . in `` magnetars '' , decay of the superstrong field ( @xmath0 g ) could break the crust and produce episodes of intense gamma - ray emission ( @xcite ; @xcite ) . differential rotation between the crust and the interior neutron superfluid may also stress the crust to its breaking point ( @xcite ) . starquake - induced rearrangement of the star s mass distribution changes the star s moment of inertia causing precession and polar wandering ( link , franco & epstein 1998 ; hereafter lfe ) . anomalous spin behavior might therefore signal the occurrence of a starquake . such evidence for crust cracking may already exist in several isolated pulsars . permanent _ offsets _ in period derivative following glitches have been observed in the crab pulsar ( @xcite ) , psr1830 - 08 and probably psr0355 + 54 ( @xcite ) . the observed offsets all have the same sign , and correspond to increases in spin - down rate . in lfe we interpreted these offsets as due to permanent increases in the torque acting on the neutron star . we showed that cracking and readjustment of the stellar crust in response to the star s slow down can increase the angle between the star s spin and magnetic axes , leading to an increase in the spin - down torque in some models of pulsar spin down . other evidence for cracking of the neutron star crust can be found in the soft gamma repeaters , thought to be strongly magnetized neutron stars ( @xmath0 g ) , or _ magnetars_. unlike radio pulsars which have weaker magnetic fields and are powered by rotation , magnetars are thought to be powered by their intense magnetic fields . duncan & thompson ( 1994 ; also thompson & duncan 1995 ; 1996 ) have suggested that sgr outbursts represent cracking of the crust by magnetic stresses . evidence in favor of this hypothesis is the striking statistical similarities between bursts in sgrs and earthquakes ( @xcite ; @xcite ) . for both phenomena the energy released per event obeys similar power - law scalings and the waiting times between events are strongly correlated with one another . the potential importance of violent crust dynamics in neutron star evolution motivates this detailed study of spin - down induced starquakes . the equilibrium shape for a spinning star is an oblate spheroid which becomes more spherical as the star slows down . the liquid core is able to change its shape smoothly as the star slows down . in contrast , the solid crust is strained as it evolves through a continuous series of equilbrium configurations , and eventually will crack if it is brittle . in @xcite , we modeled the neutron star as a homogeneous , self - gravitating , elastic sphere and followed the evolution of strain in its crust as the star spins down . from our calculations we developed the following picture of starquakes . crust cracking occurs as equatorial material shears under the compressive forces arising from the star s decreasing circumference . the star s oblateness suddenly decreases as matter moves to higher latitudes along a slip or _ fault _ plane that is perpendicular to the stellar surface and crosses the equator at an angle of @xmath1 ( see fig . since magnetic stresses suppress shearing near the magnetic poles and across the field lines , starquakes likely originate near the two points on the equator farthest from the magnetic poles and propagate preferentially toward the magnetic poles . the matter redistribution breaks the rotational symmetry of the star , causing the star to precess . damping of the precession eventually restores alignment between the angular velocity and angular momentum , ultimately _ increasing _ the angle between the spin axis and the magnetic moment . in some models of pulsar spin - down ( , the vacuum - dipole model ) an increase in the alignment angle between the rotation and magnetic axes increases the spin - down torque . the magnitude of the starquake - induced changes in the alignment angle are consistent with the changes in the spin - down rates seen in the crab pulsar ( @xcite ) . the observations of spin - down offsets in coincidence with glitches indicates some connection between structural readjustments and glitches . for a recent discussion of this possibility , see link & epstein ( 1996 ) . in this paper we extend the analysis to the more realistic case of a brittle shell floating on a liquid core . we find that the stresses induced by the star s spin down produce similar behavior to that found in lfe . crust cracking associated with other sources of stress , such as magnetic or superfluid stresses , will be considered in future work . the organization of this paper is as follows . section [ phys - pict ] presents a qualitative description of the growth and release of strain in the crust of an idealized , spinning - down neutron star . in [ the - math ] , we calculate the response of the crust s shape as it spins down , treating the star as a homogeneous solid afloat on a liquid core . in [ thickness ] , we explore the cracking and matter flow for a model with realistic crust thickness . in [ b - field ] we discuss the effects of a magnetic field anchored in the crust . section [ summary ] summarizes our results .

gravitational , magnetic and superfluid forces can stress the crust of an evolving neutron star . fracture of the crust under these stresses could affect the star s spin evolution and generate high - energy emission . we study the growth of strain in the crust of a spinning down , magnetized neutron star and examine the initiation of crust cracking ( a _ starquake _ ) . in preliminary work ( link , franco & epstein 1998 ) , we studied a homogeneous model of a neutron star . here we extend this work by considering a more realistic model of a solid , homogeneous crust afloat on a liquid core . in the limits of astrophysical interest thus our previous conclusions concerning the star s spin response still hold ; namely , asymmetric redistribution of matter excites damped precession which could ultimately lead to an increase in the spin - down torque . starquakes associated with glitches could explain the permanent _ offsets _ in period derivative observed to follow glitches in at least three pulsars .

gravitational , magnetic and superfluid forces can stress the crust of an evolving neutron star . fracture of the crust under these stresses could affect the star s spin evolution and generate high - energy emission . we study the growth of strain in the crust of a spinning down , magnetized neutron star and examine the initiation of crust cracking ( a _ starquake _ ) . in preliminary work ( link , franco & epstein 1998 ) , we studied a homogeneous model of a neutron star . here we extend this work by considering a more realistic model of a solid , homogeneous crust afloat on a liquid core . in the limits of astrophysical interest , our new results qualitatively agree with those from the simpler model : the stellar crust fractures under shear stress at the rotational equator , matter moves to higher latitudes and the star s oblateness is reduced . magnetic stresses favor faults directed toward the magnetic poles . thus our previous conclusions concerning the star s spin response still hold ; namely , asymmetric redistribution of matter excites damped precession which could ultimately lead to an increase in the spin - down torque . starquakes associated with glitches could explain the permanent _ offsets _ in period derivative observed to follow glitches in at least three pulsars .

astro-ph9911105

c

we have examined the evolution of strain in the crust of an idealized spinning - down neutron star and the initiation of starquakes as the material reaches critical strain . we modeled the neutron star as a self - gravitating core of incompressible liquid that supports a brittle crust . crust cracking occurs as material shears under the compressive forces arising from the star s decreasing circumference . the star initially cracks near the star s rotational equator , at the base of the crust . the shearing motion along the fault decreases the oblateness of the star and pushes matter to higher latitudes . magnetic stresses suppress shearing near the magnetic poles and across the field lines . starquakes thus originate near the two points on the equator farthest from the magnetic poles and propagate toward the magnetic poles . our conclusion is qualitatively the same as found in our simpler homogeneous spherical model ( @xcite ) . as material slides along a fault directed toward the magnetic poles , the star s principal axis of inertia shifts _ away _ from the magnetic axis , exciting precession . eventually , damping restores alignment between the principal axis of inertia and the angular momentum axis , increasing the angle between the rotation and magnetic axes . in some models of pulsar spin - down , , the magnetic dipole model , this growth in the alignment angle increases the spin - down torque . we might , therefore , expect to see a tendency of alignment angle to increase with age in young pulsars . in older pulsars , however , tauris & manchester ( 1998 ) , find no relationship between magnetic alignment angle and spin - down torque . one possible observational signature from a starquake is a change of the pulse profile . a jump in the alignment angle @xmath132 changes the duration of the line of sight s traverse through the pulse emission cone . in the crab pulsar , the relative change in pulsed flux could be of order 1% ( link & epstein 1997 ) . additionally , the energy released in a starquake could produce an observable enhancement of the star s luminosity . the energy release is of order @xmath133 ergs , where @xmath29 is the average shear modulus along a fault of length @xmath134 and @xmath135 is the strain angle at which fracture occurs . some fraction of the seismic energy will be damped , heating the crust . eventually , a soft x - ray thermal wave will emerge from the star s surface . for localized deposition of @xmath136 ergs at a density of @xmath137 g @xmath138 , tang ( 1999 ) calculates a 5% enhancement of the star s luminosity occurring about 3 yr after the quake for a star with an internal temperature of @xmath139 k and a stiff equation of state . for deposition at @xmath140 g @xmath138 in a star with an internal temperature of @xmath141 k , the enhancement is @xmath142% . the chandra x - ray observatory should be capable of detecting this enhancement in a closer source , such as the vela pulsar . a starquake could drive non - thermal emission as well . seismic energy that reaches the stellar surface couples to alfvn waves which propagate into the magnetosphere . conversion of alfvn waves into @xmath110-rays could occur if the waves are charge - starved or if their amplitudes are comparable to the background field strength of the magnetosphere ( blaes 1989 ) . we thank a. olinto for valuable discussions and c. miller for a critical reading of the manuscript . this work was performed under the auspices of the u.s . department of energy , and was supported in part by nasa epscor grant # 291748 , nasa atp grant # nag 53688 , by igpp at lanl and by the center for thermonuclear flashes at the university of chicago .

, our new results qualitatively agree with those from the simpler model : the stellar crust fractures under shear stress at the rotational equator , matter moves to higher latitudes and the star s oblateness is reduced . magnetic stresses favor faults directed toward the magnetic poles .

gravitational , magnetic and superfluid forces can stress the crust of an evolving neutron star . fracture of the crust under these stresses could affect the star s spin evolution and generate high - energy emission . we study the growth of strain in the crust of a spinning down , magnetized neutron star and examine the initiation of crust cracking ( a _ starquake _ ) . in preliminary work ( link , franco & epstein 1998 ) , we studied a homogeneous model of a neutron star . here we extend this work by considering a more realistic model of a solid , homogeneous crust afloat on a liquid core . in the limits of astrophysical interest , our new results qualitatively agree with those from the simpler model : the stellar crust fractures under shear stress at the rotational equator , matter moves to higher latitudes and the star s oblateness is reduced . magnetic stresses favor faults directed toward the magnetic poles . thus our previous conclusions concerning the star s spin response still hold ; namely , asymmetric redistribution of matter excites damped precession which could ultimately lead to an increase in the spin - down torque . starquakes associated with glitches could explain the permanent _ offsets _ in period derivative observed to follow glitches in at least three pulsars .

1210.6682

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in a short summary , rhic heavy flavor program has achieved many significant results particularly in the past couple of years . it will remain as one of the focuses of rhic heavy ion program in the upcoming rhic ii era . both phenix and star are building significant detector subsystem upgrades now or in the coming years , e.g. phenix vtx and fvtx , star hft and mtd upgrades etc . these are all aiming for precision measurements of both open heavy flavor and quarkonium production at rhic ii . with the lhc experiments ongoing , rhic heavy flavor program will be complementary and remain competitive in many aspects . some of the measurements will be unique at rhic , including : a ) high precision open charm hadron measurements at low @xmath6 to address charm - medium interactions , b ) bottomonium production measurements as bottomonia are expected to be clean at rhic because of negligible contribution from regeneration , c ) heavy quark correlation measurements as heavy quarks are expected to be back - to - back correlated in @xmath2 collisions which allows clean interpretations for results in heavy ion collisions . these systematic study of heavy flavor measurements at rhic and lhc will significantly improve our understanding of the sqgp matter by quantifying its physical properties with controlled accuracy .

i review the latest heavy flavor measurements at rhic experiments . measurements from rhic together with preliminary results from lhc offer us an opportunity to systematically study the sqgp medium properties . in the end , i will outlook a prospective future on precision heavy flavor measurements with detector upgrades at rhic .

i review the latest heavy flavor measurements at rhic experiments . measurements from rhic together with preliminary results from lhc offer us an opportunity to systematically study the sqgp medium properties . in the end , i will outlook a prospective future on precision heavy flavor measurements with detector upgrades at rhic . # 1#2#3#4#1 * # 2 * , # 3 ( # 4 )

hep-ph9611383

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1truecm the partially polarized electron neutrino flux provided by @xmath238 conversions within the sun can give an opportunity to distinguish majorana and dirac neutrinos in the borexino and in the hellaz experiments due to quite different profiles of recoil electron spectra(fig.1 - 3 ) . notice that measurements of @xmath239 and @xmath240 would allow authors of the project@xcite to determine the neutrino energy @xmath203 . the inclusion of other neutrino fluxes with the different @xmath241 is necessary for comparison with real electron spectra although we expect the same qualitative difference of the spectra for the majorana and the dirac cases . really , it is obvious that @xmath242 exceeds @xmath243 in a wide energy region due to additional interaction of right - handed _ active _ majorana neutrinos with electrons in contrast to the _ sterile _ @xmath244 . probably , in the superkamiokande or in the sno detectors this difference can be marked too . in spite of unknown dependence of the survival probability @xmath245 on the incident neutrino energy @xmath203 both the differential @xmath229 and the total @xmath246 cross - sections averaged over the boron neutrino spectrum @xmath247@xcite should have quite different slopes depending on @xmath239 or @xmath233 . one can easily check this statement substituting a fixed probe value of @xmath248 and integrating eq . ( [ weak1 ] ) , eq . ( [ weak2 ] ) over the spectrum @xmath247@xcite . the absolute value of the averages @xmath229 , @xmath246 changes when @xmath249 varies that corresponds to some different levels of the electron neutrino deficit . meanwhile both sets of lines ( for majorana or dirac neutrinos ) conserve different slopes for the two kinds of particles . another model independent way to distinguish majorana and dirac neutrinos was proposed in @xcite . authors @xcite showed that nc events at the sno detector would not oscillate over time for @xmath19 and would oscillate in the case of @xmath20 . the method is based on any active - active transitions @xmath250 in the solar magnetic field for majorana neutrinos and on active - sterile conversions in the dirac case . a changing magnetic field @xmath251 influences neutrino flux variations so that one predicts @xmath252 for @xmath19 and @xmath253 for @xmath20 . in conclusion , without any knowledge of solar magnetic field direction and even for a magnetic moment obeying the astrophysical constraint @xmath257 @xcite one can distinguish majorana and dirac neutrino measuring the recoil electron spectra in the low energy @xmath0-scattering in underground detectors and comparing slopes of their profiles . last remark concerns a possibility to observe some variations of neutrino flux in detectors with large statistics of events . let us assume that the unknown parameter @xmath60 can change somehow in the sun influencing @xmath258 . in this case the spectra @xmath255 will be displaced parallel to the initial one without change of a slope in the contrary to the spectra @xmath256 that should change its slope . this behaviour of spectra would be a strong argument in favour of the mechanism@xcite as solution of the solar neutrino problem . 0.5 cm * acknowledgment * + i acknowledge george zatsepin for useful discussion and for pointing out refs . @xcite , @xcite and correspondence with robert shrock and samoil bilenky regarding the refs . @xcite , @xcite and the ref . i am grateful to i.v . gaidaenko who was first obtaining correct cross - section of the @xmath110-scattering of partially polarized majorana neutrinos and indebted to him for sending of his preprint @xcite that allowed me to improve a wrong previous version of eq . this work was supported in part from rffr under grants n. 95 - 02 - 03724 and n. 97 - 02 - 16501 . bilenky , introduction in feynmann diagrams and physics of the electroweak interaction ( energoatomizdat ( in russian ) , moscow , 1990 ) formula ( d.54 ) . translated in basics of physics , frontiers ( 1994 ) . the differential spectra eqs . ( [ weak1 ] ) and ( [ weak2 ] ) for the beryllium neutrino in the case of the separated @xmath222system ( the normalization parameter a in eq . ( [ normaliz ] ) equals to unity , @xmath259 ) : the lines `` b '' , `` c '' , `` d '' correspond to an incident majorana neutrino with the survival probability @xmath260 correspondingly , and the lines `` e '' , `` f '' describe cross sections for a dirac neutrino in the cases @xmath261 . the line `` a '' is the common one for majorana and dirac fully - polarized left - handed neutrinos with @xmath262 . the same spectra in the case of the equipartition @xmath263 , the parameter @xmath264 : the line `` a '' describes majorana neutrino , the line `` b'' dirac neutrino . the total cross sections for the beryllium neutrino @xmath265 in dependence on the threshold energy @xmath233 . for a liquid scintillator it assumes a low threshold @xmath233 of order @xmath266 a few hundreds kev . the line `` a '' corresponds to the fully polarized left - handed neutrinos ( @xmath267 ) with @xmath268 ( ssm prediction without @xmath269- deficit ) ; lines `` b '' , `` c '' are plotted for majorana neutrino with the survival probabilities @xmath270 and @xmath271 correspondingly ; lines `` d '' , `` e '' are plotted for dirac neutrino with the same @xmath270 and @xmath272 .

if neutrino conversions within the sun result in partial polarization of initial solar neutrino fluxes then a new opportunity to distinguish majorana and dirac neutrinos by measuring the differential @xmath0-scattering cross section in solar neutrino detectors arises . the experiment like hellaz would be preferable in testing of recoil electron spectra differences initiated by majorana and dirac neutrinos since low energy recoil electrons ( @xmath1 ) can be detected and electron energy and direction can be determined with good precision .

if neutrino conversions within the sun result in partial polarization of initial solar neutrino fluxes then a new opportunity to distinguish majorana and dirac neutrinos by measuring the differential @xmath0-scattering cross section in solar neutrino detectors arises . the experiment like hellaz would be preferable in testing of recoil electron spectra differences initiated by majorana and dirac neutrinos since low energy recoil electrons ( @xmath1 ) can be detected and electron energy and direction can be determined with good precision . pacs codes : 13.10.+q ; 13.15.-f ; 13.40.fn ; 14.60.gh ; 96.60.kx . * key words * : neutrino , magnetic moment , magnetic fields , polarization . -1 cm 8.5 in 0.3 cm * can we distinguish majorana and dirac neutrinos in solar neutrino experiments ? * * v.b . semikoz *

astro-ph0401583

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algol ( @xmath5 perseus ) is the eponymous eclipsing binary system which consists of a primary early - type main sequence star and a roche lobe - filling secondary late - type giant or subgiant star . these systems have undergone a period of mass transfer during which material was transferred from the initially more massive present day late - type star to its initially less massive early - type companion . algol is the brightest and nearest example of this type . the primary star ( algol a ) is a b8 v main sequence star , while the secondary ( algol b ) is a k2 iv subgiant that has lost about half of its original mass to the present day primary ( e.g. , * ? ? ? * ) . since algol has a short period orbit of 2.87 days ( e.g. , * ? ? ? * ) the two stars are tidally locked , and their orbital and rotational periods are synchronized . algol was first confirmed as an x - ray source by @xcite , who suggested that the x - ray emission might be explained by a mass - transfer model , where the more massive b star accretes material from the less massive k star , either through roche lobe overflow or a stellar wind . in both cases , the infalling material is shock - heated to x - ray temperatures when it hits the b star . according to this mass - transfer model , we would expect to observe an x - ray eclipse during the optical primary eclipse . however , observations made with the solid state spectrometer ( sss ) of the _ einstein _ observatory revealed no sign of an x - ray eclipse at the time of optical primary eclipse @xcite . at present , it is widely believed that the x - ray emission from algol arises mostly , if not completely , from the corona of algol b @xcite . the two stars are tidally locked and rapidly rotating , and within the rotationally - excited dynamo paradigm , it is expected that the convection zone of the k star would experience increased dynamo activity whose resulting magnetic energy is subsequently dissipated at the stellar surface in the form of a hot , x - ray emitting corona @xcite . however , the nature and structure of this corona remains a topic of debate . more than four orders of magnitude in x - ray luminosity and an order of magnitude in plasma temperature separate the solar corona from coronae of most active stars such as the algol - type secondaries ( e.g. * ? ? ? we currently have very little idea of the physical and spatial characteristics and appearance of these much more active coronae , and whether or not magnetic structures are restricted to the stellar surface or whether significant x - ray emitting plasma resides in larger structures , including inter - binary loops , with magnetic structures linking the two stars @xcite . @xcite analyzed exosat observations of algol and found no clear x - ray eclipse during the optical secondary minimum . if this x - ray emission was indeed from the secondary star , his study suggests that the coronal extent of algol b must be comparable to or greater than the size of the star itself . however , @xcite did detect a secondary x - ray eclipse in rosat observations , and concluded that the scale height of the algol b corona is @xmath6 . similarly , a shallow eclipse at optical secondary minimum was seen by asca @xcite . a dramatic eclipse of a large flare observed by bepposax enabled the size of the flaring structure to be estimated as being less than 0.6 stellar radii and pinpointed the location of the structure to polar regions @xcite . based on these deductions and on observations of flares on algol seen by ginga , exosat , rosat , and xmm - newton , @xcite suggest that the corona is essentially concentrated onto the polar regions of the k star , with a more compact ( smaller than the star ) flaring component and a perhaps somewhat more extended ( comparable in size to the star ) quiescent corona . such a picture of polar - dominated activity has long been suspected based on optical doppler imaging techniques , which consistently see dark polar spots on active stars ( e.g. * ? ? ? @xcite also suggested polar emission was responsible for the lack of rotational modulation in the observed flux in a _ low energy transmission grating spectrograph ( letgs ) observation of algol . however , an xmm - newton observation of an algol flare studied by @xcite was interpreted as lying at lower latitudes . while this interpretation is somewhat subjective , it does suggest that even if polar emission dominates , significant activity at all latitudes is likely present . similar conclusions regarding the corona of the k star might be drawn based on radio detections of algol . in particular , @xcite presents results from 8.4 and 15 ghz observations of algol obtained using the very long baseline array ( vlba ) in 1995 . the vlba maps show a double - lobed structure in the radio corona of the k star , which appear to originate in or near the polar caps . the quiescent radio emission does not show signs of orbital modulation , again suggestive of a corona concentrated on the poles of the k star . caution is warranted in the interpretation of the spatial distributions of radio and x - ray emission , however , since the former is produced by gyrosynchrotron emission from relativistic electrons , and this population might not be co - spatial with the thermal electrons responsible for x - ray emission . direct x - ray observations present the only means to probe the spatial distribution of this thermal population . in this paper , we primarily use the _ chandra _ high energy transmission grating spectrograph ( hetgs ) x - ray spectrum of algol to test this emerging picture of coronal activity . we compare observed doppler shifts with the theoretical orbital velocities of the primary and secondary stars of algol , and compare the observed line widths with theoretical expectations based on instrumental , thermal , and rotational broadening . based on these comparisons , we are able to place the first observational limits on the contribution of the b8 dwarf to the x - ray emission of algol , and to place constraints on the scale height , and any non - thermal motions , characterizing the corona of algol b. finally , we show that lines of o vii seen from quadrature to primary eclipse in a low energy transmission grating spectrograph ( letgs ) observation of algol support our conclusions that the corona of algol b at temperatures of a few @xmath7 k must be radially extended to at least one stellar radius .

we also examine the o vii intercombination and forbidden lines in a low energy transmission grating spectrograph observation and find no change in their relative line fluxes as the system goes from quadrature to primary eclipse . since these lines appear to be strongly affected by uv irradiation from algol a through radiative excitation of the @xmath4 transition , this supports the conjecture that the corona of algol b at temperatures of several million k must be significantly extended and/or located toward the poles to avoid being shadowed from algol a during primary eclipse .

in a study of _ chandra _ high energy transmission grating spectra of algol , we clearly detect doppler shifts caused by the orbital motion of algol b. these data provide the first definitive proof that the x - ray emission of algol is dominated by the secondary , in concordance with expectations that the primary b8 component should be x - ray dark . however , the measured doppler shifts are slightly smaller than might be expected , implying an effective orbital semi - major axis of about @xmath0 instead of @xmath1 for the algol b center of mass . this could be caused by a small contribution of algol a , possibly through accretion , to the observed x - ray flux , in which case such a contribution does not exceed 10 - 15% . we suggest the more likely explanation is an asymmetric corona biased toward the system center of mass by the tidal distortion of the surface of algol b. a detailed analysis of the profiles of the strongest lines indicates the presence of excess line broadening amounting to approximately 150 km s@xmath2 above that expected from thermal motion and surface rotation . possible explanations for this additional broadening include turbulence , flows or explosive events , or rotational broadening from a radially extended corona . we favor the latter scenario and infer that a significant component of the corona at temperatures @xmath3 k has a scale height of order the stellar radius . this interpretation is supported by the shape of the x - ray lightcurve and tentative detection of a shallow dip at secondary eclipse . we also examine the o vii intercombination and forbidden lines in a low energy transmission grating spectrograph observation and find no change in their relative line fluxes as the system goes from quadrature to primary eclipse . since these lines appear to be strongly affected by uv irradiation from algol a through radiative excitation of the @xmath4 transition , this supports the conjecture that the corona of algol b at temperatures of several million k must be significantly extended and/or located toward the poles to avoid being shadowed from algol a during primary eclipse .

astro-ph0401583

c

by modeling observed doppler shifts in terms of orbital motion , we were able to estimate the effective orbital radius of the x - ray emitting material . we found this effective radius to be @xmath60 @xmath30 0.93@xmath39 from the analysis of individual emission lines , and @xmath61 @xmath30 0.29@xmath39 from the cross - correlation analysis ; these results are consistent within @xmath62 uncertainties . the statistical uncertainties in the cross - correlation method are considerably lower because all the information in the spectrum is used , rather than just information in bright lines . the 1@xmath40 error bar of the line - of - sight velocities obtained via the cross - correlation analysis is @xmath88 km s@xmath2 for the meg data and @xmath811 km s@xmath2 for the heg data . however , limitations due to uncertainties in the calibration of the _ chandra _ instruments cause systematic uncertainties which appear somewhat larger than what is implied by the statistical uncertainties . for example , a few of the data points in figure [ f : orbit_crosscor ] show discrepancies between the meg and heg results , by @xmath82@xmath40 . in comparison with the x - ray doppler radius , the orbital radius of algol b around the system center of mass is @xmath63 @xcite . since the effective radius we have derived is smaller than @xmath64 , we can infer that the x - ray emitting material is in fact not perfectly centered on algol b , but is shifted slightly inward toward the primary star . the effective orbital radius of the x - ray emission allows us to place a constraint on the possible contribution from algol a emission that would skew the apparent x - ray doppler radius toward the center of gravity . as mentioned in [ s : intro ] , it has been argued that accretion onto the primary star could be a source of x - rays . if this were true , a small x - ray contribution from the accretion activity of algol a could explain the inward shift of the effective radius of x - ray emitting material . assuming that the emission of the k star corona is centered on the star itself , an effective radius of @xmath65 for the x - ray emission would indicate that @xmath885% of the total x - ray emission is from algol b , and the remaining 15% is from algol a. @xcite considered the issue of accretion - driven x - ray emission in algol - type binaries in their comparison between algols and rs cvn - type binaries . the latter are comprised of two late - type stars in which neither component filled their roche lobes . @xcite found that the algol - type binaries are in fact slightly x - ray deficient relative to their rs cvn cousins , suggesting strongly that the accretion activity of algol - type binaries is not a significant source of x - rays . the 15% effect we are seeking here would , however , be quite inconspicuous in this type of statistical study . the possibility of accretion giving rise to significant x - ray flux in algol was reviewed by @xcite . two key parameters are the shock temperature of the accreting gas , and the mass transfer rate . it seems unlikely that the accretion shock can exceed @xmath66 k , and pustylnik suggests a maximum x - ray luminosity from accretion of about @xmath67 erg s@xmath2 based on a mass transfer estimate of order @xmath68 yr@xmath2 . the x - ray luminosity of algol as measured from the hetg observation analyzed here is about @xmath69 erg s@xmath2 ( * ? ? ? * in preparation ) ; accretion does therefore appear sufficient to account for @xmath70% of the total luminosity . one test of this would be whether or not lines formed only above @xmath71 k lines that could only plausibly originate from coronal emission show the same center of gravity as lines formed at cooler temperatures . unfortunately , our data are of insufficient quality to perform this test since only weaker lines in the spectrum exclusively originate from such hot plasma . the brightest line formed at these higher temperatures is h - like si xiv @xmath726.18 . the line - of - sight velocity as a function of orbital phase indicated by this line is consistent within statistical uncertainties with the velocity seen in the other , cooler lines ( figure [ f : orbit_all ] ) . however , measurement errors are sufficiently large that we can not rule out differences at the 15% level . evidence for plasma associated with accretion and with temperatures of at least @xmath73 k has , however , been found in the algol systems v356 sgr and tt hya from recent fuse observations ( * ? ? ? * ; * ? ? ? * respectively ) . emission detected from o vi appeared to be associated with a bipolar flow that makes a large angle with the orbital plane . however , in order for this plasma to contribute significantly at x - ray wavelengths , it must be comprised of components at least an order of magnitude hotter than the formation temperature of o vi . another possible , and we suggest more likely , explanation for the inward shift of the effective radius is that the corona of algol b is not spherically symmetric or exactly centered on the center of mass of algol b , but rather has some asymmetry and structure on the side facing inward , toward algol a. the surface of algol b itself will be severely distended in this direction by the gravitational field of algol a the roche lobe filling factor for algol b is expected to be very close to unity , such that any equatorial corona could well lie beyond the l1 point and would not be gravitationally bound to algol b. we illustrate the approximate geometry of the system in figure [ f : geom ] . this figure was produced using the _ nightfall _ program by r. wichmann , which accounts for the relative masses of the two stars , the roche lobe filling factors , and inclination of the orbit . we also note that , in the x - ray lightcurve ( figure [ f : lc ] ) , we see a flare just as algol b comes out of eclipse . this flare does not have a sharp rise , but a more gradual one that appears to start before eclipse egress . it is possible that this flaring plasma is located on the hemisphere facing algol a , and that the characteristics of its intensity evolution over time are modulated by the eclipse . if the flaring plasma is indeed located on the hemisphere facing algol a , this could also explain why the effective radius of the x - ray emission during this observation is shifted toward algol a. by comparing observed with theoretical line widths , we have some found evidence for moderate excess line widths that we attribute to the possible presence of non - thermal broadening . while not definitive , this result is supported by recent analyses of far ultraviolet spectra obtained by the hubble space telescope @xcite and the far ultraviolet explorer @xcite . both studies report the need for excess line broadening to understand the profiles of the forbidden lines of fe xxi at 1354 and fe xviii at 976 in the more active stars of their sample with the largest projected rotational velocities ( @xmath74 ) . one source of excess broadening might be turbulence or `` explosive events '' . our line profile analysis ( e.g. , figures [ f : turbulent ] & [ f : profile ] ) suggests that a random velocity component of @xmath75 km s@xmath2 could explain the observed line widths . this is similar to the sound speed at @xmath76 k. such a velocity is reminiscent of the non - thermal broadening of over 100 km s@xmath2 seen in transition region lines of stars of different activity as reviewed by @xcite . it was suggested in this body of work that the broadening might be caused by the acceleration of plasma in magnetic reconnection events associated with microflaring . it is possible that the broadening we see in hot x - ray lines is related to this . other types of flows are also possible . @xcite observed flows with velocities up to 40 km s@xmath2 in solar coronal loops based on detailed transition region and coronal explorer ( _ trace _ ) time - resolved imaging and simultaneous solar and heliospheric observatory ( _ soho _ ) sumer spectra . while the velocities inferred here are three times this , it is not difficult to envisage faster flows when considering that the coronal energy deposition rate of algol b is @xmath77 times that of the sun . however , as pointed out by @xcite , in both the above cases the broadening mechanisms should be ubiquitous among the more active stars and should not be seen only in those with the largest @xmath74 . another possible source of excess line widths is rotational broadening originating in a corona with significantly radially - extended structure . as noted in [ s : intro ] , the evidence from observations of algol during eclipse does not provide an unambiguous picture , with some observations requiring apparently extended coronae @xcite , and others being consistent with scale heights of a stellar radius or less @xcite . the scale height for plasma of mean molecular weight @xmath78 at a temperature @xmath44 on a star of mass @xmath79 and radius @xmath80 is @xmath81 . the parameters for algol b were summarized recently by @xcite , who adopted @xmath82 and @xmath83 ( see also * ? ? ? * ; * ? ? ? * ) . for a coronal temperature @xmath84 k on algol b , the scale height is then about @xmath85 in the absence of strong centrifugal forces . our median scale height and 1@xmath40 upper limit are 3.1@xmath54 and 3.8@xmath54 , respectively . while this is slightly larger than the thermal scale height in the absence of strong centrifugal forces arising from rapid rotation , it is important to keep in mind the following things . firstly , the line profile analysis depends on subtraction of the dominant instrumental and thermal broadening components and is inherently prone to additional systematic error arising as a result of imperfections in the description of these dominant effects . secondly , for a corona on algol b with a radial extent comparable to the stellar radius , the competition between gravitational and centrifugal forces becomes significant : centrifugal acceleration on a single star with the same rotation rate is equivalent to gravitational acceleration at a height of @xmath86 . while the binary nature of algol complicates the picture , it is possible that some regions of an extended corona comprise plasma bound by magnetic fields , as has been discussed in connection with other rapidly rotating stars , such as ab dor ( e.g. * ? ? ? ( see also @xcite who concludes that the 1032 o vi profile of ab dor , observed with orpheus , is not rotationally broadened beyond the photospheric surface @xmath74 value . ) we conclude that , in the interpretation that the tentative evidence for excess line widths is the result of rotational broadening , the extension of the corona would be similar to the expected thermal scale height and comparable to the stellar radius . this interpretation is consistent with that of @xcite based on their fuse analysis of active stars . these authors suggested that their excess line widths could result from coronal structures with heights up to @xmath87 . such a picture would also be consistent with the eclipse studies of @xcite and @xcite . with regard to eclipses , it is important to note that extended structure at the stellar poles would give rise to no obvious x - ray eclipse . however , pole - dominated emission also would not give rise to strong rotational broadening . our results suggest that , if rotational broadening is the correct interpretation for our observed line widths , this emission must be distributed around the star and not concentrated at the poles . the hetg observation does cover the secondary optical eclipse , and there is some evidence that we do indeed see some obscuration of the x - ray corona , despite the complications presented by the flare . we have computed theoretical x - ray lightcurves for algol using a spherically - symmetric , optically - thin emitting shell coronal model . the model assumes that algol a is 100% x - ray dark , and uses the following physical and orbital parameters : @xmath88 , @xmath89 , @xmath90 , @xmath91 , @xmath92 days , and @xmath93 degrees @xcite . theoretical lightcurves were calculated for an array of algol b coronal scale heights , ranging from 0.1 to 4.0 stellar radii . figure [ f : lc ] shows the observed lightcurve of algol with three theoretical lightcurves of various scale heights overplotted . also plotted is a similar curve computed for polar emission restricted to high latitudes corresponding to the scale height predicted by quasi - static loop models ( see below ) . if we assume that the count rate at phase @xmath8 0.5 represents the quiescent level of algol b , as does the level toward the end of the observation , we can see from the overplotted models that scale heights of @xmath94-@xmath95 represent the data reasonably well . the polar emission model clearly does not represent the observed eclipse minimum ; we discuss this further below . a scale height commensurate with the thermal scale height would appear to clash with the recent interpretation of density - sensitive line ratios seen in _ letgs observations of algol by @xcite . the interpretation of helium - like line ratios in terms of plasma density is complicated in the case of algol by the radiation field of algol a , which is sufficiently strong to cause significant radiative excitation of electrons from the upper level of the forbidden line to the upper level of the intercombination line through the transition @xmath4 in the ions c , n and o. nevertheless , @xcite pointed out that , even with densities of order @xmath96 @xmath97similar to those found for other active stars in the extensive survey of ( * ? ? ? * in preparation)simple quasi - static coronal loop model scaling laws ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) that predict that loop peak temperature @xmath44 , pressure @xmath20 and length @xmath98 are related by @xmath99 , suggest maximum loop lengths of order a few @xmath96 cm . this is only a fraction of the radius of algol b. as mentioned in [ s : f / i_analysis ] , there was no detectable orbital modulation of the o vii @xmath55 ratio in the algol letgs data , which was observed during orbital phase @xmath59 - 1.03 . @xcite also found no differences in the @xmath55 ratio of algol spectra which was extracted during the quiescent and flaring phases of an xmm - newton observation . this result has important implications . if we assume that the corona of algol is indeed similar to that of other active stars , such as its `` coronal twin '' hr 1099 @xcite , then we must conclude that _ the bulk of the o vii emission is always illuminated by algol a_. this can be achieved by having a fairly extended corona with a scale height @xmath100 , as our line profile analysis indicates . instead , _ if the o vii emitting coronal structures are compact compared to the stellar radius , then they must reside predominantly at the poles _ where the algol a uv radiation field is not significantly shadowed at primary eclipse . if scale heights are fairly large ( @xmath101 ) , the classical quasi - static loop scaling laws must then be quite inapplicable to these coronal structures . in the case of compact ( by necessity ) quasi - static loops with a plasma density of a few @xmath96 @xmath97 , @xcite estimate a coronal volumetric filling factor of up to 0.3unreasonably large for emission confined to polar regions . as noted earlier in this section , the synthetic lightcurve computed for the case of polar emission with a scale height of @xmath102 , similar to that predicted by quasi - static models , is a very poor match to the observed eclipse minimum light ( figure [ f : lc ] ) . this model predicts very sharp eclipses which have never been observed in x - ray observations of algol . in summary , the combined evidence of a tentative detection of excess line widths , the shape of the x - ray lightcurve , and the lack of orbital modulation of the o vii @xmath55 ratio going into primary eclipse , all point to the plasma source at temperatures up to several @xmath7 k having a scale height of the same order as the stellar radius , and being distributed around the k star . such distributed coronal structure could be responsible for , e.g. , the flaring at lower latitudes , which was inferred by @xcite based on an xmm - newton x - ray lightcurve . unfortunately , the x - ray data alone can not rule out other scenarios involving compact structures , though these would require special and fortuitous placement of dominant active regions in order to remain consistent with past and present observations of the coronal emission of algol . @xcite drew similar conclusions based on the failure to observe a strong x - ray eclipse in the exosat observation , though with the benefit of not having seen data from subsequent observations that have led to strong ambiguities in interpretation . our favored picture of the x - ray emission of algol is also consistent with the picture painted by @xcite , and with the interpretation of excess line widths seen in uv and fuv coronal forbidden lines by @xcite . what we have not tackled in this article , however , is the very hot ( @xmath103 k ) plasma that often flares and seems to be located at the poles . the recent plasma density survey of ( * ? ? ? * in preparation ) indicates that this very hot material is at much higher densities of @xmath104 @xmath97 , and so occupies quite different structures . these are likely to be the structures responsible for pole - dominated flaring activity , such as that highlighted by @xcite .

. however , the measured doppler shifts are slightly smaller than might be expected , implying an effective orbital semi - major axis of about @xmath0 instead of @xmath1 for the algol b center of mass . this could be caused by a small contribution of algol a , possibly through accretion , to the observed x - ray flux , in which case such a contribution does not exceed 10 - 15% . we suggest the more likely explanation is an asymmetric corona biased toward the system center of mass by the tidal distortion of the surface of algol b. a detailed analysis of the profiles of the strongest lines indicates the presence of excess line broadening amounting to approximately 150 km s@xmath2 above that expected from thermal motion and surface rotation . we favor the latter scenario and infer that a significant component of the corona at temperatures @xmath3 k has a scale height of order the stellar radius . this interpretation is supported by the shape of the x - ray lightcurve and tentative detection of a shallow dip at secondary eclipse .

in a study of _ chandra _ high energy transmission grating spectra of algol , we clearly detect doppler shifts caused by the orbital motion of algol b. these data provide the first definitive proof that the x - ray emission of algol is dominated by the secondary , in concordance with expectations that the primary b8 component should be x - ray dark . however , the measured doppler shifts are slightly smaller than might be expected , implying an effective orbital semi - major axis of about @xmath0 instead of @xmath1 for the algol b center of mass . this could be caused by a small contribution of algol a , possibly through accretion , to the observed x - ray flux , in which case such a contribution does not exceed 10 - 15% . we suggest the more likely explanation is an asymmetric corona biased toward the system center of mass by the tidal distortion of the surface of algol b. a detailed analysis of the profiles of the strongest lines indicates the presence of excess line broadening amounting to approximately 150 km s@xmath2 above that expected from thermal motion and surface rotation . possible explanations for this additional broadening include turbulence , flows or explosive events , or rotational broadening from a radially extended corona . we favor the latter scenario and infer that a significant component of the corona at temperatures @xmath3 k has a scale height of order the stellar radius . this interpretation is supported by the shape of the x - ray lightcurve and tentative detection of a shallow dip at secondary eclipse . we also examine the o vii intercombination and forbidden lines in a low energy transmission grating spectrograph observation and find no change in their relative line fluxes as the system goes from quadrature to primary eclipse . since these lines appear to be strongly affected by uv irradiation from algol a through radiative excitation of the @xmath4 transition , this supports the conjecture that the corona of algol b at temperatures of several million k must be significantly extended and/or located toward the poles to avoid being shadowed from algol a during primary eclipse .

1511.03032

i

radio sources constitute an unequally powerful tool to investigate the origin and evolution of our universe . in fact , radio emission is not obscured or attenuated by dust or gas , so deep radio surveys offer a unique opportunity to detect and study sources up to the highest redshifts . it is following this rationale that very ambitious programs like the planned square kilometer array ( ska , carilli et al . , 2004 ) facility , a gigantic radio telescope with a total collective area of 1 square kilometer , or its precursors askap ( australian ska pathfinder , johnston s. et al . 2007 ) and meerkat ( jonas j.l . 2009 ) will soon see their first light . when applied to radio sources , the expected advantages in sensitivity , field - of - view , frequency range and spectral resolution will yield substantial progress in many research fields , from cosmology to astrophysics . extra - galactic radio sources are however a mixed bag of astrophysical objects : amongst the most powerful ones we find radio - loud qsos and frii ( fanaroff & riley 1974 ) galaxies while , moving to weaker sources , the dominant populations become fri , low - excitation galaxies and star - forming galaxies , whose contribution to the total radio counts become predominant at the sub - mjy level ( see e.g. magliocchetti et al . 2000 ; prandoni et al . discerning amongst these objects and their relative weight is an impossible task to carry out only on the basis of radio - continuum data . this is why increasingly more effort was recently put on photometric and spectroscopic follow - up studies of radio sources detected in deep - field surveys ( amongst the many : schinnerer et al . 2004 ; 2007 ; 2010 for the cosmos field ; morrison et al . 2010 for goods - n ; mc alpine et al . 2013 for the video - xmm3 field ; bondi et al . 2003 for the vvds field : simpson et al . 2012 for the subaru / xmm - newton deep field : mao et al . 2011 for the extended chandra deep field ) . investigations of the optical properties of radio sources can then disentangle the different populations and also allow the determination of a number of quantities which influence the source behavior like e.g. the black - hole mass in optical spectra dominated by broad emission lines ( e.g. metcalf & magliocchetti 2006 ) . following the launch of the _ spitzer _ satellite , in recent years radio sources have also been investigated at mid - infrared ( mir ) wavelengths ( e.g. appleton et al . 2004 ; boyle et al . 2007 ; magliocchetti , andreani & zwaan 2008 ; garn et al . 2009 ; leipski et al . 2009 ; de breuck et al . 2010 ; norris et al . 2011 amongst the many ) . these studies proved to be extremely useful for two main reasons : they allowed investigations of the properties and evolution of the sub - population of star - forming galaxies up to @xmath8 , while on the other hand they provided interesting hints on the central engine responsible for radio ( and mir ) agn emission . it is only in these very last few years that the radio community has started to realize the importance of multi - wavelength studies which also include far - infrared ( fir ) information . this growing interest is primarily due to the advent and launch of the _ herschel _ satellite , which for the first time has observed galaxies at fir wavelengths up to very large cosmological ( @xmath9 ) distances ( lutz 2014 ) . earlier fir missions such as iras , iso and _ spitzer_@70@xmath10 m only probed the relatively local ( @xmath11 ) universe , and since agn - powered radio galaxies in the local universe are almost always hosted by massive red galaxies with little or no ongoing star - formation activity ( e.g. magliocchetti et al . 2002 ; 2004 ) , and since fir emission in galaxies is almost entirely due to processes connected with ongoing star formation , it follows that any pre-_herschel _ interest in a joint radio - fir analysis was limited to re - assessing the precision of the tight radio - fir correlation found by early iras - based studies of local star - forming galaxies ( condon et al . 1982 ) . however , when moving to higher redshifts , galaxies undergo dramatic changes . for instance , it is now well established that both the cosmic star - forming activity and agn output steadily increase with look - back time at least up to redshifts @xmath12 ( e.g. gruppioni et al . 2013 : merloni , rudnick & di matteo 2004 ) , and many galaxies are observed to host both an active agn and ongoing star - formation ( e.g. alexander et al . it is then legitimate to wonder whether radio galaxies also follow such a trend and if in the early universe they are also associated with ongoing stellar production . first attempts in this direction were presented by the work of seymour et al . ( 2011 ) which analyses the fir emission as observed by the spire instrument ( griffin et al . 2010 ) on board of the _ herschel _ satellite ( pilbratt et al . 2010 ) for a sample of very powerful , l@xmath13 w hz@xmath5 radio sources selected in the extra - galactic _ first look survey field , and by the work of del moro et al . ( 2013 ) who investigate hidden agn activity in a sample of goods - north sources with deep radio , infrared and x - ray data . magliocchetti et al . ( 2014 ) pushed the seymour et al . ( 2011 ) results further and investigated , for the first time , the fir properties of radio - selected agn of _ all _ radio luminosities and at _ all _ redshifts @xmath14 . this was done by using the very deep radio catalogue obtained at 1.4 ghz in the cosmos field by schinnerer et al . 2004 ; 2007 ; 2010 and bondi et al . ( 2008 ) ; agn were selected solely on the basis of their radio - luminosity and fir information came from the pep survey ( lutz et al . results from this analysis indicate that the probability for a radio - selected agn to be detected at fir wavelengths is both a function of radio power and redshift . powerful sources were found more likely to be fir emitters at earlier epochs because of two distinct effects : 1 ) at all radio luminosities , fir activity monotonically increases with look - back time and 2 ) in the earlier universe , radio activity of agn origin is increasingly less effective at inhibiting fir emission . magliocchetti et al . ( 2014 ) also found that the observed fir ( and mir ) emission was due to processes which were indistinguishable from those which power star - forming galaxies . the above results , although interesting and obtained on a relatively large area , however need the complementarity of deep enough fir observations which can match the depth of the radio data . as a matter of fact , only @xmath15% of the sources identified in the cosmos field as radio - emitting agn possessed a counterpart in the pep catalogues either at 100 @xmath10 m or at 160 @xmath10 m . the present work then overcomes the above limitations and analyses the fir properties of radio - selected agn on three fields where fir observations are the deepest - to - date : goods - north , goods - south and the lockman hole . fir data come from both the pep survey ( lutz et al . 2011 ) and the _ herschel_-goods survey ( elbaz et al . 2011 ) and , in the best - observed areas such as the two goods fields , ensure limiting fir fluxes which are deeper by as much as a factor @xmath16 at 100 @xmath10 m and @xmath17 at 160 @xmath10 m than the pep observations on cosmos . throughout the work we will assume a @xmath18cdm cosmology with @xmath19 ( @xmath20 ) , @xmath21 , @xmath22 and @xmath23 . in all cases , masses for the sources under examination are calculated by using the bruzual & charlot ( 2003 ) templates and adopting a salpeter ( 1955 ) initial mass function ( imf ) .

in order to investigate the fir properties of radio - active agn , we have considered three different fields where both radio and fir observations are the deepest to - date : goods - south , goods - north and the lockman hole . out of a total of 92 radio - selected agn , @xmath0 are found to have a counterpart in _ herschel _ maps . galaxies : evolution - infrared : galaxies - galaxies : starburst - galaxies : active - radio continuum : galaxies - methods : observational

in order to investigate the fir properties of radio - active agn , we have considered three different fields where both radio and fir observations are the deepest to - date : goods - south , goods - north and the lockman hole . out of a total of 92 radio - selected agn , @xmath0 are found to have a counterpart in _ herschel _ maps . the percentage is maximum in the goods - north ( @xmath1% ) and minimum ( @xmath2% ) in the lockman hole , where fir observations are shallower . our study shows that in all cases fir emission is associated to star - forming activity within the host galaxy . such an activity can even be extremely intense , with star - forming rates as high as @xmath3 m@xmath4yr@xmath5 . agn activity does not inhibit star formation in the host galaxy , just as on - site star - formation does not seem to affect agn properties , at least those detected at radio wavelengths and for @xmath6 . given the very high rate of fir detections , we stress that this refers to the majority of the sample : most radio - active agn are associated with intense episodes of star - formation . however , the two processes proceed independently within the same galaxy , at all redshifts but in the local universe , where powerful enough radio activity reaches the necessary strength to switch off the on - site star formation . our data also show that for z @xmath7 the hosts of radio - selected star - forming galaxies and agn are indistinguishable from each other both in terms of mass and ir luminosity distributions . the two populations only differentiate in the very local universe , whereby the few agn which are still fir - active are found in galaxies with much higher masses and luminosities . galaxies : evolution - infrared : galaxies - galaxies : starburst - galaxies : active - radio continuum : galaxies - methods : observational

1511.03032

c

with the aim of providing an analysis as exhaustive as possible of the far infrared properties ( fir ) of radio - selected agn , we have considered three very well studied fields such as the lockman hole , the goods - n and the goods - s . these fields are indeed provided with the deepest radio and fir observations available up - to - date and have also been observed at a large number of other wavelengths , allowing the determination of spectroscopic and photometric redshifts for the overwhelming majority of the sources residing there . + for the primary radio selection , we used data from ibar et al . ( 2009 ) , miller et al . ( 2013 ) and morrison et al . ( 2010 ) . in all cases , these reach depths of @xmath109jy at 1.4 ghz . in order to distinguish between radio emission due to star - formation ongoing in the host galaxy and radio emission of agn origin , we used the method already presented in magliocchetti et al . ( 2014 ) which is based on the radio luminosity of the sources . this marks as an agn all those objects with 1.4 ghz luminosities brighter than a chosen threshold , which roughly corresponds to the break in the radio luminosity function of star - forming galaxies and which positively evolves with look - back time . the number of radio - emitting agn found on the three considered fields with the above method is 92 : 45 in the lockman hole , 15 in the goods - s and 32 in the goods - n . by then relying on the very deep observations provided by the _ herschel _ mission at 100 @xmath10 m and 160 @xmath10 m , we used the pep ( lutz et al . 2011 ) and goods-_herschel _ ( elbaz et al . 2011 ) data to look for fir counterparts to radio - selected agn . thanks to the extreme depth of fir observations , we found that the large majority of radio - emitting agn are indeed fir emitters . the fraction of sources with ongoing fir activity reaches values as high as @xmath60% in the case of goods - n and @xmath2% in the lockman hole , where fir observations are shallower . we found that possibly except for the very local , @xmath70 , universe the chances for fir emission in a radio - active agn do not depend on the redshift of the sources , implying that fir activity is a common event throughout the whole life - time evolution of these objects . as shown in magliocchetti et al . ( 2014 ) , we confirm that fir emission in radio - active agn is entirely due to star - forming activity within the host galaxy . the bolometric luminosities of these sources are extremely high : the peak of their distribution is observed at around l@xmath110 l@xmath4 , with agn reaching l@xmath52 values as high as 10@xmath111 l@xmath4 . converted into star formation rates ( sfr ) , this implies sources with average sfr @xmath112 m@xmath4yr@xmath5 which can even reach values up to @xmath113 m@xmath4yr@xmath5 . recalling that the large majority of radio - active agn are also found to be fir emitters , we can then draw the conclusion that most of the galaxies which host a radio - active agn are also the hosts of extremely intense star - forming activity . this finding confirms and extends to the radio - active case all recent results obtained on the very high star - forming activity observed in the hosts of agn selected in different ways and at various wavelengths ( e.g. hatziminaoglou et al . 2010 ; santini et al . 2012 ; rosario et al . 2013 just to mention a few ) . perhaps more importantly , the data show that neither the spectral slope of the radio emission , nor the radio - luminosity of the sources under examination vary in the presence of fir emission . this is true for the spectral slope at all redshifts , and suggests that the central engine responsible for the agn phenomenon is oblivious , at least at radio wavelengths , to the presence of ongoing star formation within the same galaxy . in other words , fir activity does not seem to influence radio agn activity . this is also true for radio luminosities , at least for redshifts larger than @xmath54 : indeed we find that , irrespective of radio luminosity , in the more distant universe virtually all radio - emitting agn cohabit with a star - forming event . once again , this suggests that radio luminosity , and therefore agn activity at radio wavelengths , is not affected by the nearby star - forming processes . the situation varies in the more local universe , as there is a deficit of fir emitters amongst bright radio agn . this is in accordance with the general view that powerful radio - loud agn reside in old galaxies with little or no ongoing star - forming activity . our results then show that this lack of star - forming activity within the hosts of radio - active agn is only true in the nearby universe , and possibly implies that at some late stage of their evolution , and only for weak enough fir emission , powerful enough agn are capable to swipe off the gas in the surrounding star - forming regions and consequently switch off the on - site star - formation . note that our results are in excellent agreement with those of best et al . ( 2014 ) , which also show a clear positive evolution of radio - loud agn which are in the radiative - mode ( i.e. associated to cold gas and therefore to star - formation ) with respect to those which are in the so - called jet - mode ( radiatively inefficient and generally associated to passive galaxies ) between @xmath114 and @xmath115 . another possible interpretation of the data is provided by recent studies of the mass function of galaxies which show that there is a transition at around @xmath54 between a mass function dominated by late - type galaxies to one dominated by early - type ones ( e.g. pozzetti et al . 2010 ; ilbert et al . the radio - agn behavior might then only mirror this more general trend derived for the whole galaxy population . another relevant result of our analysis is that also the general properties of the galaxies host of radio - selected agn ) , such as their stellar mass or their age , do not vary in the presence of ongoing fir activity . this means that the hosts of radio - active agn all belong to the same population , irrespective of whether or not there is ongoing star - forming activity , i.e. that star - formation is not the dominant ingredient in shaping a galaxy which also hosts a radio - active agn . we stress once again that the above results rely on an extremely high success rate of radio - to - fir associations and therefore that the conclusions we can draw with the present work refer to the majority of radio - active agn . for this class of sources no effect of star - forming origin is observed on agn activity . all the considered properties both of the host galaxy and of the agn itself remain unaltered in the presence of fir emission , showing that star - formation does not influence ( at least radio ) agn activity or shape the physical properties of the hosting galaxies . on the other hand , most of such agn hosts ( virtually the totality for redshifts @xmath6 ) are also found to be the sites of even extremely intense star - forming activity . this indicates that also star formation activity is not affected by the presence of an agn , in all cases except for radio - luminous sources in the local , @xmath11 , universe . we can then conclude that , except for the case of relatively local sources and high radio luminosities , no interaction is observed between the processes of agn emission and star - formation , as they seem to proceed independently of each other . note that no clear evidence for the dominance of agn - feedback in shaping galaxy evolution has also been found by pozzi et al . ( 2015 ) , who use a backward approach capable to reproduce the galaxy k - band and the far - ir luminosity functions across the redshift range @xmath116 . lastly , we have shown that , except for a few cases of sources mainly residing at very high ( z @xmath108 ) redshifts , galaxies hosting radio - selected star - forming events and those hosting radio - selected agn are indistinguishable from each other both in terms of mass and ir luminosity ( or star - forming rate ) at all redshifts larger than @xmath65 . differences only start appearing in the local universe , where radio - active agn start progressively becoming fir - quiet , the more as the higher is their radio luminosity , and at the same time are found associated to much larger galaxies than those which host a star - forming event . why differences in the various radio - selected populations considered here only appear in the local universe is still unclear and will be investigated in a forthcoming paper . + + * acknowledgements * we wish to thank the referee for his / her careful reading of the manuscript and constructive suggestions which helped shaping and improving the paper . pacs has been developed by a consortium of institutes led by mpe ( germany ) and including uvie ( austria ) ; ku leuven , csl , imec ( belgium ) ; cea , lam ( france ) ; mpia ( germany ) ; inaf- ifsi / oaa / oap / oat , lens , sissa ( italy ) ; iac ( spain ) . this development has been supported by the funding agencies bmvit ( austria ) , esa - prodex ( belgium ) , cea / cnes ( france ) , dlr ( germany ) , asi / inaf ( italy ) , and cicyt / mcyt ( spain ) . alexander et al . 2008 , apj , 135 , 1968 appleton p.n . et al . , 2004 , apjs , 154 , 147 berta s. et al . , 2011 , a&a , 532 , 49 best p. n. , ker l. m. , simpson c. , rigby e. e. , sabater j. , 2015 , arxiv:14090263 bondi m. et al . 2003 , a&a , 403 , 857 bondi m. , ciliegi p. , schinnerer e. , smolcic v. , jahke k. , carilli c. , zamorani g. , 2008 , apj , 681 , 1135 boyle b.j . , cornwell t.j . , middleberg e. , norris r.p . , appleton p.n . , smail i. , 2007 , mnras , 385 , 1143 brinhcmann j. , charlot s. , white s.d.m . tremonti c. , kauffmann g. , heckman t. , brinkman j. , 2004 , mnras , 351 , 1151 brunner h. et al . 2008 , a&a , 479 , 283 . bruzual g. , charlot s. , 2003 , mnras , 344 , 1000 carilli c.l . , furlanetto s. , briggs f. , jarvis m. , rawlings s. , falcke h. , 2004 , new astronomy reviews , elsevier , vol . 48 , issue 11 - 12 , 1029 condon j.j . , condon m.a . , gisler g. , pushell j. , 1982 , apj , 252 , 102 condon jj . , 1992 , ara&a , 30 , 575 de breuck c. et al . , 2010 , apj , 725 , 36 del moro a. et al . , 2013 , a&a , 549 , a59 elbaz d. et al . , 2011 , a&a , 533 , a119 fanaroff b.l . , riley j.m . , 1974 , mnras , 167 , 31 fotopoulou s. et al . , 2012 , apjs , 198 , 1 garn t. , green d.a . , riley j.m . alezander p. , 2009 , mnras , 397 , 1101 griffin m.j . et al . , 2010 , a&a , 518 , l3 gruppioni c. et al . 2013 , mnras , 432 , 23 hatziminaoglou e. , et al . 2010 , a&a , 518l , 33 ibar e. , ivison r.j . , biggs a.d . , , best p.n . , green d.a . , 2009 , mnras , 397 , 281 ibar e. , ivison r.j . , best p.n . , coppin k. , pope a. , smail i. , dunlop j.s . , 2010 , mnras , 401 , l53 ilbert o. , 2013 , a&a , 556 , 55 johnston s. et al . , 2007 , pasa , 24 , 174 jonas j.l . , 2009 , ieee proc 97 , 1522 kennicut r.c . jr , 1998 , ara&a , 36 , 189 leipski c. , antonucci r. , ogle p. , whysong d. , 2009 , 701 , 891 lutz d. et al . 2011 , a&a , 532 , 90 lutz d. 2014 , ara&a , 52 , 373 magliocchetti m. , maddox s. j. , wall j. v. , benn c. r. , cotter g. , 2000 , mnras , 318 , 1047 magliocchetti m. et al . ( the 2dfgrs team ) 2002 , mnras , 333 , 100 magliocchetti m. et al . ( the 2dfgrs team ) 2004 , mnras , 350 , 1485 magliocchetti m. , andreani p. , zwaan m.a . , 2008 , mnras , 383 , 479 magliocchetti m. et al . , 2014 , mnras , 442 , 682 magnelli b. et al . 2013 , a&a , 553 , a132 . et al . , 2011 , apj , 731 , 79 mauch t. , sadler e.m . , 2007 , mnras , 375 , 931 mcalpine k. , jarvis m.j . , bonfield d.g . , 2013 , mnras , 436 , 1084 merloni a. , rudnik g. , di matteo t. , 2004 , mnras , 354 , l37 metcalf r.b . , magliocchetti m. , 2006 , mnras , 365 , 101 miller n.a . et al . , 2013 , apjs , 205 , 13 morrison g.e . , owen f.n . , dickinson m. , ivison r.j . , ibar e. , 2010 , apjs , 188 , 178 norris r.p . et al . , 2011 , apj , 736 , 55 peng y.j . et al . , 2010 , apj , 721 , 193 pilbratt g. et al . , 2010 , a&a , 518 , l1 poglitsch a. et al . , 2010 , a&a , 518 , l2 pozzetti l .. et al . , 2010 , a&a , 517 , 11 pozzi f. et al . , 2015 , apj , 803 , 35 prandoni i. , gregorini l. , parma p. , de ruiter h.r . , vettolani g. , zanichelli a. , wieringa m.h . , ekers r.d . , 2001 , a&a , 369 , 787 rodighiero g. et al . 2011 , apj , 739 , l40 randall k.e . , hopkins a.m. , norris r.p . , zinn p .- c . , middleberg e. , mao m.y . , sharp r.g . , 2012 , mnras , 421 , 1644 rosario d. et al . , 2012 , a&a , 545 , 45 rosario d. et al . , 2013 , a&a , 560 , 72 salpeter e. e. , 1955 , apj , 121 , 161 santini p. et al . , 2009 , a&a , 504 , 751 santini p. et al . , 2012 , a&a , 540 , 109 schinnerer e. , et al . , 2004 , aj , 128 , 1974 schinnerer e. et al .. , 2007 , apjs , 172 , 46 schinnerer e. et al .. , 2010 , apjs , 188 , 384 seymour n. et al . , 2011 , mnras , 413 , 1777 simpson c. et al . 2012 , mnras , 421 , 3060

the percentage is maximum in the goods - north ( @xmath1% ) and minimum ( @xmath2% ) in the lockman hole , where fir observations are shallower . our study shows that in all cases fir emission is associated to star - forming activity within the host galaxy . our data also show that for z @xmath7 the hosts of radio - selected star - forming galaxies and agn are indistinguishable from each other both in terms of mass and ir luminosity distributions .

in order to investigate the fir properties of radio - active agn , we have considered three different fields where both radio and fir observations are the deepest to - date : goods - south , goods - north and the lockman hole . out of a total of 92 radio - selected agn , @xmath0 are found to have a counterpart in _ herschel _ maps . the percentage is maximum in the goods - north ( @xmath1% ) and minimum ( @xmath2% ) in the lockman hole , where fir observations are shallower . our study shows that in all cases fir emission is associated to star - forming activity within the host galaxy . such an activity can even be extremely intense , with star - forming rates as high as @xmath3 m@xmath4yr@xmath5 . agn activity does not inhibit star formation in the host galaxy , just as on - site star - formation does not seem to affect agn properties , at least those detected at radio wavelengths and for @xmath6 . given the very high rate of fir detections , we stress that this refers to the majority of the sample : most radio - active agn are associated with intense episodes of star - formation . however , the two processes proceed independently within the same galaxy , at all redshifts but in the local universe , where powerful enough radio activity reaches the necessary strength to switch off the on - site star formation . our data also show that for z @xmath7 the hosts of radio - selected star - forming galaxies and agn are indistinguishable from each other both in terms of mass and ir luminosity distributions . the two populations only differentiate in the very local universe , whereby the few agn which are still fir - active are found in galaxies with much higher masses and luminosities . galaxies : evolution - infrared : galaxies - galaxies : starburst - galaxies : active - radio continuum : galaxies - methods : observational

0808.3785

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the numerical and theoretical study of dynamical systems can resemble observational and experimental situations if the escape of an initial ensemble of trajectories through a leak placed in the otherwise closed phase space is considered . the idea of introducing a leak in a closed chaotic dynamical system to generate transient chaos was first suggested by pianigiani and yorke @xcite . later this problem was discussed in detail in the context of fractal exit boundaries @xcite , of geometrical acoustics @xcite , of quantum chaos @xcite , of controlling chaos @xcite , of resetting in hydrodynamical flows @xcite , of leaked hamiltonian systems @xcite , of astronomy @xcite and of cosmology @xcite . the subject has recently received a renewed attention @xcite . part of this renewed interest comes from recent developments of quantum chaos , that started to consider carefully the effect of measurement devices , absorption , and other forms of leaking both theoretically and experimentally @xcite . it is by now clear that leaking dynamical systems provides a way to peeping at chaos @xcite , and can be used as a kind of chaotic spectroscopy @xcite . from a theoretical point of view , leaking systems provide an interesting bridge between open and closed dynamical systems . in closed systems the phase space coordinates remain confined , and a rigorous mathematical approach based on attractors and ergodic components can be employed @xcite . an important quantity is the distribution @xmath0 of the first poincar recurrence times @xmath1 @xcite to a preselected region of the phase space . as originally proposed by chirikov and shepelyansky @xcite ( see also @xcite ) , @xmath0 is a useful analyser of the entire dynamics . in contrast , in open systems trajectories may leave the region of interest ( e.g. , tend to @xmath2 ) and the method of transient chaos is usually employed @xcite . in this case , the dynamics is characterized by the escape time distribution @xmath3 ( the derivative of the survival probability ) . chaotic dynamics usually leads to an asymptotic exponential decay of both @xmath4 and @xmath5 @xmath6 for large enough @xmath7 . exponentials are the signature of _ strong _ chaotic properties as seen , e.g. , in the divergence of nearby initial conditions , in the decay of correlations , and in the convergence to equilibrium distributions . the exponent @xmath8 is the key quantifier of system specific characteristics and will be considered in detail in this paper . the possibility of comparing a system with leak to its corresponding closed system shows numerous advantages in comparison to naturally opened systems . for instance , the rate @xmath8 in eq . ( [ eq.exp ] ) can be estimated from the probability of escaping or returning . for small leaks , this probability is obtained by computing the closed systems natural measure @xmath9 of a typical leak region @xmath10 , and it follows that @xcite @xmath11 where @xmath12 denotes the mean recurrence or escape times , @xmath13 or @xmath14 . despite its simplicity , relation ( [ eq.smallmu ] ) is of little practical relevance since the limit @xmath15 is never achieved in either numerical or experimental applications @xcite . here we do not restrict ourselves to this limit and find that , apart from being unrealistic , it masks different interesting relations . we perform a formal description through the theory of transient chaos , i.e. , in terms of a nonattracting chaotic set @xcite and the conditionally invariant measure @xcite , and obtain distinct relations for @xmath16 and @xmath17 as a function of the position and size of the region @xmath10 and of the initial ensemble . relation ( [ eq.smallmu ] ) does not hold , but we show that @xmath18 remains valid . this is based on a full correspondence with the recurrence problem obtained for a special initial ensemble and setting the _ leak to be equal to the recurrence region of the closed system_. we have explored the most striking consequences of this unified treatment from the point of view of poincar recurrences in a previous short paper @xcite . here , after describing the relationship between the two problems with additional details , we focus on the escape problem and consider the recurrence problem as a particular , yet important , case . we also use this connection to apply and adapt a method to determine @xmath16 @xcite based only on the escape probabilities for _ short _ times . this is a main advantage over genuine open systems where long - term periodic orbits are needed to determine @xmath19 . in systems showing _ weak _ chaos , as e.g. , hamiltonian systems with mixed phase space , the exponential decay law ( [ eq.exp ] ) experiences a cross - over for longer times towards an asymptotic power - law behavior @xcite . we argue , however , that on intermediate times a decay rate @xmath16 can be well defined @xmath20 we interpret our results based on an effective splitting of the chaotic saddle into hyperbolic and nonhyperbolic components . the paper is organized as follows . in sec . [ sec.recurrence ] we review the main properties of poincar recurrence times . the corresponding results for escape times appear in sec . [ sec.escape ] , together with the dependence of @xmath16 and @xmath12 on @xmath10 . the equivalence between recurrence and escape problems is carefully discussed in sec . [ sec.rec ] . in sec . [ sec.henon ] numerical illustrations of the results are provided for paradigmatic dissipative models . in sec . [ sec.standard ] , the nonhyperbolic case is investigated using an area - preserving map . relations to periodic orbits and an efficient method to determine @xmath16 are described in sec . [ sec.fitting ] . finally , conclusions and discussions appear in sec . [ sec.conclusion ] , where the case of higher order recurrences is also investigated .

in order to simulate observational and experimental situations , we consider a leak in the phase space of a chaotic dynamical system . this expression improves previous estimates based on the properties of the closed system and explains dependencies on the position and size of the leak and on the initial ensemble . with a subtle choice of the initial ensemble

in order to simulate observational and experimental situations , we consider a leak in the phase space of a chaotic dynamical system . we obtain an expression for the escape rate of the survival probability applying the theory of transient chaos . this expression improves previous estimates based on the properties of the closed system and explains dependencies on the position and size of the leak and on the initial ensemble . with a subtle choice of the initial ensemble , we obtain an equivalence to the classical problem of poincar recurrences in closed systems , which is treated in the same framework . finally , we show how our results apply to weakly chaotic systems and justify a split of the invariant saddle in hyperbolic and nonhyperbolic components , related , respectively , to the intermediate exponential and asymptotic power - law decays of the survival probability .

0808.3785

c

experimental and observational measurements often occur through holes or leaks that naturally exist or are deliberately introduced in an otherwise closed dynamical system @xcite . the relevant observable quantity in such systems with leaks is the distribution of escape times from inside the system . in strongly chaotic systems , this distributions decays exponentially . applying the ergodic theory of transient chaos @xcite to chaotic systems with leaks an expression for the escape rate @xmath19 [ eq . ( [ eq.gammamuc ] ) ] is obtained @xcite in terms of the c - measure ( associated to the invariant chaotic saddle ) of the leak @xmath10 . we have provided a theoretical framework to understand the strong dependence of @xmath16 and @xmath238 on the leak size ( fig . [ fig.tmedio ] ) and position ( fig . [ fig.logistic ] ) . in the ( unrealistic ) limit of small leak , the expression of the escape rate converges to a previously known relation [ eqs . ( [ eq.smallmu ] ) ] , based on the invariant measure of the closed system . altogether , our results help to understand previous observations @xcite and set a theoretical framework for future applications . we have shown that the classical problem of poincar recurrences in closed systems can be described as a problem of escape from a system with a leak , once the recurrence region is identified with the leak @xmath10 and the initial density is chosen properly . this allows us to treat both problems in an unified framework and compare previous similar results that were reported independently in both fields ( compare refs . @xcite and @xcite ) , and to adapt ( in sec . [ sec.fitting ] ) a previous method to efficiently obtain @xmath19 . more surprisingly , we show that the relaxation rate of the distribution of poincar recurrences @xmath41 is equal to @xmath19 [ eq . ( [ eq.gamma ] ) ] but that the mean recurrence time @xmath244 given by kac s lemma ( [ eq.kac ] ) differs from the typical mean escape time [ the analog of kac s lemma for leaked systems is ( [ eq.kac2 ] ) ] . these results are summarized in table [ tab.ic ] and provide a more detailed account of the results published in ref . @xcite . in weakly chaotic systems the asymptotic exponential decay is replaced by a power - law decay . we have shown , however , that if the leak region and the initial distribution are away from nonhyperbolic regions , an exponential decay is still well defined for intermediate times . we have obtained the scaling of the cross - over time @xmath197 between the two regimes [ eq . ( [ eq.nc ] ) ] which confirms the importance of the exponential decay for small leaks . altogether , these results justify an effective splitting of the chaotic saddle in a nonhyperbolic component , related to the asymptotic power - law decay , and an hyperbolic component , related to the intermediate exponential decay for which our previous results apply . this splitting is particularly important in the case of hamiltonian systems ( found , e.g. , in fluid dynamics or optical applications ) where the generic phase space shows a mixture of regions of regular and chaotic motion . -th recurrence times ( @xmath245 , from bottom to top ) in the hnon map with parameters as in fig . [ fig.etd ] . the solid lines correspond to the binomial distribution ( [ m ] ) using @xmath246 . for long times , the same decay rate @xmath247 is observed in all curves . the displacement between the distribution and the simulation , as in the @xmath248 case discussed previously , can be related to the short time oscillations that modify the pre - factors of the distribution . ] finally , it is worth considering briefly two extensions of the previous results that have potentially interesting applications . first , consider the case when the leak consists of two or more disjoint components ( of relevance , e.g. , for the problem of resetting in hydrodynamical flows @xcite ) . all our results apply to such cases as well , with the remark that the escape rate is not the mere sum of the escape rates characterizing the components , due to the overlap among pre - images , as pointed out by buljan and paar @xcite and bunimovich and dettmann @xcite . a second extension is to consider the distribution of the second , third , , @xmath249-th recurrence times . in the notation of sec . [ sec.recurrence ] , the @xmath249-th recurrence time is defined as @xmath250 . in view of the analogy to escape presented in sec . [ sec.rec ] , this corresponds to the distribution of escape times taking place only after entering the leak @xmath10 for the @xmath249-th time . the naive ( binomial ) approximation ( [ eq.binomial ] ) can be extended to this case as @xcite @xmath251 and implies that the asymptotic decay rate @xmath252 [ see ( [ eq.gammamu ] ) ] remains valid for any @xmath249 . in fig . [ fig.8 ] we show numerical results for the hnon map . for @xmath253 the distributions take , of course , the value zero for @xmath254 , start growing , and then after a maximum is reached , an exponential decay sets in . the decay rate has been found again to be different from the binomial approximation , but apparently also _ independent of @xmath249 _ , i.e. , to have the value @xmath255 discussed in the context of the first recurrence times [ see eq . ( [ eq.fpe ] ) ] . to understand this result , let us first compare the invariant saddles for @xmath248 ( @xmath256 ) and @xmath257 ( @xmath258 ) . it is easy to see that @xmath259 . trajectories that belong to @xmath258 but _ not _ to @xmath256 must have a point @xmath260 inside @xmath10 that never returns to @xmath10 again . hence , these trajectories necessarily approach @xmath256 for both @xmath261 . to be outside @xmath10 for @xmath262 , @xmath260 has to belong to the unstable manifold of @xmath256 . to be outside @xmath10 for @xmath263 , the image point @xmath264 taken with respect to the closed system s map has to be on the stable manifold of @xmath256 . therefore , points @xmath260 belong to the intersection of the unstable manifold of @xmath256 and the pre - image ( using map @xmath90 ) of the stable manifold of @xmath256 and also approach @xmath256 asymptotically . accordingly , trajectories escaping for long times in the case @xmath257 appear still to be governed by s1 having therefore the escape rate @xmath16 . this argument can be extended straightforwardly to any finite @xmath249 and can also be important for the the case of partial escape in optical systems @xcite . we are indebted to j. brcker , l.a . bunimovich , g. gyrgyi , h. kantz , g. del magno , a. e. motter , and a. pikovsky for useful discussions . we thank the anonymous referees for their valuable inputs . this research was supported by the otka grants t47233 , t72037 . w. bauer and g.f . bertsch , phys . * 65 * , 2213 ( 1990 ) ; o. legrand and d. sornette , _ ibid _ , * 66 * , 2172 ( 1991 ) ; o. legrand and d. sornette , europhys . lett . * 11 * , 538 ( 1990 ) ; o. legrand and d. sornette , physica * d 44 * , 229 ( 1990 ) ; f. mortessagne , o. legrand and d. sornette , chaos * 3 * , 529 ( 1993 ) . , e * 66 * , 066218 ( 2002 ) ; j. schneider and t. tl , ocean dyn . * 53 * 64 - 72 ( 2003 ) ; i. tuval , j. schneider , o. piro , and t. tl , europhys . lett . * 65 * , 633 - 9 ( 2004 ) ; j. schneider , v. fernandez , and e. hernandez - garcia , ices j. marine syst . * 57 * , 111 ( 2005 ) ; j. schneider , j. schmalzl , and t. tl , chaos * 17 * , 033115 ( 2007 ) . lee , s. rim , j. w. ryu , t. y. kwon , m. choi , and c. m. kim , phys . lett . * 93 * 164102 ( 2004 ) . h. g. l. schwefel et al . , j. opt b. * 21 * , 923 ( 2004 ) . j. w. ryu , s. y. lee , c. m. kim , and y. j. park , phys . e * 73 * , 036207 ( 2006 ) . m. hirata , b. saussol , and s. vaienti , comm . math . phys . * 206 * 33 ( 1999 ) ; n. hadyn , j. luevano , g. mantica , and s. vaienti , phys . * 88 * 224502 ( 2002 ) . n. haydn , y. lacroix , and s. vaienti , ann . probab . * 33 * 2043 ( 2005 ) . m. abadi and a. galves , markov process . related fields * 7 * , 97 ( 2001 ) .

we obtain an expression for the escape rate of the survival probability applying the theory of transient chaos . , we obtain an equivalence to the classical problem of poincar recurrences in closed systems , which is treated in the same framework . finally , we show how our results apply to weakly chaotic systems and justify a split of the invariant saddle in hyperbolic and nonhyperbolic components , related , respectively , to the intermediate exponential and asymptotic power - law decays of the survival probability .

in order to simulate observational and experimental situations , we consider a leak in the phase space of a chaotic dynamical system . we obtain an expression for the escape rate of the survival probability applying the theory of transient chaos . this expression improves previous estimates based on the properties of the closed system and explains dependencies on the position and size of the leak and on the initial ensemble . with a subtle choice of the initial ensemble , we obtain an equivalence to the classical problem of poincar recurrences in closed systems , which is treated in the same framework . finally , we show how our results apply to weakly chaotic systems and justify a split of the invariant saddle in hyperbolic and nonhyperbolic components , related , respectively , to the intermediate exponential and asymptotic power - law decays of the survival probability .

hep-ph0501265

i

supersymmetry ( susy ) is one of the most elegant solutions , if not the best , to the gauge hierarchy problem . the fine - tuning argument in the gauge hierarchy problem requires susy particles at work at the tev scale to stabilize the gap between the electroweak scale and the grand unified theory ( gut ) scale or the planck scale . the most recent lower bound on the higgs boson mass has been raised to 114.4 gev @xcite . this in fact puts some stress on the soft susy parameters , known as the little hierarchy problem . since the higgs boson receives radiative corrections dominated by the top squark loop , the mass bound requires the top squark mass to be heavier than 500 gev . from the renormalization - group ( rg ) equation of @xmath2 , the magnitude of @xmath3 . thus , the parameters in the higgs potential are fine - tuned at a level of a few percent in order to obtain a higgs boson mass of @xmath4 gev . recently , arkani - hamed and dimopoulos adopted a rather radical approach to susy @xcite . they essentially discarded the hierarchy problem by accepting the fine - tuning solution to the higgs boson mass . they argued that since the cosmological constant problem needs much more serious fine - tuning that one has to live with , one may as well let go of the much less serious fine - tuning in the gauge hierarchy problem . the only criteria in setting up the scenario are ( i ) the dark matter constraint imposed by the wmap data @xcite : @xmath5 ( @xmath6 range ) , and ( ii ) the gauge - coupling unification . the scenario is coined as `` split susy '' @xcite with the spectrum specified by the feature of the following distinct scales : 1 . all the scalars , except for a cp - even higgs boson , are very heavy . one usually assumes a common mass scale for them at @xmath7 gev to @xmath8 . 2 . the gaugino masses @xmath9 and the higgsino mass parameter @xmath1 are comparatively much lighter and of the order of tev in order to provide an acceptable dark matter candidate . in this work , we propose a further split in the split susy by raising the @xmath1 parameter to a large value which could be about the same as the sfermion mass or the susy breaking scale . we call it the @xmath1-split susy scenario . in this scenario , we do not encounter the notorious @xmath1 problem @xcite . at the same time , our scenario can still achieve the gauge coupling unification and provide a viable dark matter candidate . the gauge coupling unification is satisfied because the rg running of the gauge couplings is mainly determined by the standard model ( sm ) particle and gaugino contributions . whether the higgsinos are very heavy has a milder effect . the dark matter constraint requires @xmath10 to be smaller than @xmath11 ; i.e. , the dark matter is wino - like . we summarize the differences between the split susy and our @xmath1-split susy scenarios as follows . 1 . the higgsino mass parameter @xmath1 is raised to a very high scale in our scenario while in split susy it is at the electroweak scale . 2 . the lightest supersymmetric particle ( lsp ) has to be the wino or gluino instead of the bino in our scenario because the bino would give a too large relic density , whereas the lsp can be the bino with @xmath12 in split susy . 3 . the wino dark matter can reach an interesting level of indirect detection , particularly the monochromatic photon signal , due to strong annihilation cross sections , and similarly for the anti - proton and positron detection . on the other hand , the signal for direct detection is vanishingly small because of the absence of light squarks or higgsino couplings . in split susy both the direct and indirect detection signals are present , depending on the nature of the lsp . 4 . in our @xmath1-split susy scenario , only chargino - pair production ( @xmath13 ) and chargino - neutralino associated production ( @xmath14 ) are possible at hadron colliders . the cross sections are in a certain ratio in terms of gauge couplings . moreover , at @xmath15 colliders only the chargino - pair production is possible . in split susy all pair production channels are possible . 5 . in our @xmath1-split susy scenario , charginos can have long decays . since the mass difference between the chargino and the neutralino can be less than the pion mass , the chargino may travel more than a meter or so before it decays , and therefore producing ionized tracks in central silicon detectors . in split susy , the chargino decays promptly in general . the paper is organized as follows . in the next section , we discuss a few issues in raising the @xmath1 parameter . we discuss the effects on gauge coupling unification in sec . [ sec : coupling ] , dark matter requirements in sec . [ sec : dm ] , and collider phenomenology in sec . [ sec : pheno ] . we summarize our findings in sec . [ sec : summary ] .

we further split the split supersymmetry by taking the higgsino mass parameter @xmath1 to be very large . in this case , the @xmath1 problem is avoided and we keep the wino as a dark matter candidate . a crude gauge coupling unification is still preserved . the associated chargino - neutralino production cross sections have a certain ratio due to gauge couplings , and the chargino has long decays .

in split supersymmetry , the supersymmetric scalar particles are all very heavy , at least at the order of @xmath0 gev , but the gauginos , higgsinos , and one of the neutral higgs bosons remain below a tev . here we further split the split supersymmetry by taking the higgsino mass parameter @xmath1 to be very large . in this case , the @xmath1 problem is avoided and we keep the wino as a dark matter candidate . a crude gauge coupling unification is still preserved . dark matter signals and collider phenomenology are discussed in this @xmath1-split susy scenario . the most interesting dark matter signal is the annihilation into monochromatic photons . in colliders , chargino - pair and the associated chargino - neutralino production cross sections have a certain ratio due to gauge couplings , and the chargino has long decays .

astro-ph9911124

i

dwarf novae ( dn ) are cataclysmic variable binary systems which , every few weeks , exhibit 4 6 mag outbursts , which last for a few days ( see e.g. warner @xcite ) . in several subclasses of dn both the outburst durations and recurrence times can be very different from the values quoted above . it is generally accepted that dn outbursts are due to a thermal - viscous " instability . this instability occurs in the accretion disc in which the viscosity is given by the @xmath0-prescription ( shakura & sunyaev @xcite ) , at temperatures close to 8000 k. hydrogen is then partially ionized and opacities are a steep function of temperature ( see cannizzo @xcite for a review and hameury et al . @xcite for the most recent version of the model ) . modeling dwarf nova lightcurves requires a varying shakura - sunyaev parameter @xmath0 ( smak @xcite ) : it must be of the order of 0.1 0.2 ( 0.2 according to smak 1999b ) in outburst and of the order of 0.01 in quiescence , when the temperature is below the hydrogen ionization temperature . one could therefore expect that the disc instability model ( dim ) might offer useful constraints on mechanisms which generate accretion disc viscosity . this assumes , of course , a successful application of the model to the observed dn outburst cycles . however , despite its success in explaining the overall characteristics of dns , the dim in its standard version faces several serious difficulties when one tries to account for the detailed properties of dwarf nova outbursts . some of these difficulties are the result of an incomplete version of the dim . for example it was believed that a truncation of the inner parts of the disc is necessary to explain the long delay between the rise of optical light and that of uv and euv in systems such as ss cyg . as shown by smak ( @xcite ) , however , when correct outer boundary condition are assumed , the standard dim reproduces the observed delays . on the other hand , observed quiescent x - ray fluxes far exceed the predictions of the model and seem to require an inner ` hole ' in the disk . such a hole can either be due to evaporation of the disc close to the white dwarf ( meyer & meyer - hofmeister @xcite ) , or to the presence of a magnetic field strong enough to disrupt the disc . in addition , systems such as wz sge , which have long recurrence time and large amplitude , long outbursts require very low values of @xmath0 ( @xmath1 ) if interpreted in the framework of the standard dim ( smak @xcite , osaki @xcite , meyer - hofmeister et al . these values , much lower than those of other dns at similar orbital periods , are , however , left unexplained . on the other hand , wz sge systems can be explained with standard values of @xmath0 , provided that the disc is truncated as in other systems so that it is either stable or marginally unstable ( lasota et al . @xcite , warner et al . @xcite ) and the mass transfer from the secondary is significantly increased during the outburst under the influence of illumination by radiation from the accreting matter ( hameury et al . @xcite ) . su uma systems are a subclass of dwarf novae which occasionally show long outbursts during which a lightcurve modulation ( superhump ) is observed at a period slightly longer than the orbital period ; these superoutbursts are , usually , separated by several normal outbursts . the superhump is due to a 3:1 resonance in the disc which causes the disc to become eccentric and to precess ( whitehurst @xcite ) . osaki ( @xcite ) proposed that the related tidal instability is also responsible for the long duration and large amplitude of superoutbursts ( see osaki @xcite for a review of the thermal - tidal instability model ) . in his model , the tidal torques which remove angular momentum from the outer parts of the disc are increased by approximately an order of magnitude when the disc reaches the 3:1 resonance radius ( typically @xmath2 , where @xmath3 is the orbital separation ) until the disc outer radius has shrunk to typically @xmath4 , i.e. by about 30% . this model accounts for many of the properties of su uma systems ; it has , however , difficulties in explaining systems with very short superoutburst cycles such as , for which one must assume that the tidal instability stops when the disc has shrunk by less than 10% ( osaki @xcite ) , i.e. by much less than assumed in the standard case . finally , it must be noted that a number of systems exhibit very bizarre lightcurves : we have already mentioned the case of rz lmi , which has similarities , with systems such as , and . the case of the december 1996 superoutburst of which was followed by 6 closely spaced normal outbursts in 1996 has not been reproduced by simulations , except by osaki ( @xcite ) who assumed that the viscosity parameter @xmath5 in the cold state was increased to 0.1 , almost the value in the hot state , for 70 days after the superoutburst , and then returned to its quiescent value @xmath6 . it is finally worth mentioning that the prototypical classical dwarf nova exhibited an unusually long outburst in 1985 , lasting 45 days , with a shape similar to superoutbursts , but without superhumps ( mattei et al . @xcite ) . since in this system the radius of the 3:1 resonance is larger than the size of the primary s roche lobe , one can conclude that while superhumps can be attributed to the 3:1 resonance , the tidal instability is obviously not the sole cause of very long outbursts . the inability of numerical models to reproduce the large variety of observed light curves may indicate that additional physical effects should be added to the dim . one such effect is the tidal instability . another important class of effects is the illumination of the disc and the secondary star . these effects are usually not included in simulations , and it was suggested by warner ( @xcite ) that irradiation of the secondary star , that gives rise to high and low states of mass transfer , and of the inner disc , that drastically affects the disc instability , account for the light curves of vy scl stars . he also suggested ( warner @xcite ) that the wide spectrum of superoutburst behaviours is generated by the interplay of reactions of the disc and the secondary to irradiation . this suggestion is supported by observations since there is evidence that the mass transfer rate from the secondary star increases during outbursts ( smak @xcite ) in dwarf novae such as or , most probably as a result of illumination of the secondary . recently smak ( @xcite ) argued that properties of outburst cycles of standard " u gem type dwarf novae , which can not be reproduced by the dim ( e.g. the same maximum brightness of narrow and wide outbursts ) , are well explained if _ all _ outbursts are associated with some mass transfer enhancement due to the secondary s irradiation . ( long outbursts would be due to important mass transfer enhancements , making the mass transfer rate larger than the critical value for stability ) . if this is the case the ` pure ' dim would find no application in the real world . it also appears that illumination of the disc itself by the hot white dwarf has strong effects on the stability properties of the disc as soon as the white dwarf temperature exceeds 15,000 k ( king @xcite , hameury at al . @xcite ) . in this paper , we investigate the influence of the combined effects of illumination of the disc , of the secondary star and of evaporation of the inner parts of the disc , on the predictions of the dim in which standard values of viscosity are assumed . our free parameters are the white dwarf mass , the quiescent white dwarf temperature , the mass transfer rate in the absence of illumination , and two parameters describing in a crude manner evaporation effects and the influence of illumination of mass transfer from the secondary . we show that a large variety of light curves are predicted by the models , many of which have an observational counterpart . in section 2 , we show that the long 1985 outburst of u gem requires enhanced mass transfer during the outburst . in section 3 , we describe the model and our assumptions ; in section 4 , we give our results and compare them with lightcurves of observed systems , and we discuss briefly possible extensions of this work .

in the framework of the dwarf nova thermal - viscous disc instability model , we investigate the combined effects on the predicted dwarf nova lightcurves of irradiating the accretion disc and the secondary star and of evaporating the inner parts of the disc . we assume the standard values of viscosity . we confirm the suggestion by warner ( @xcite ) that the large variety of observed outbursts behaviour may result from the interplay of these three effects . we are able to reproduce light curves reminiscent of those of systems such as or .

in the framework of the dwarf nova thermal - viscous disc instability model , we investigate the combined effects on the predicted dwarf nova lightcurves of irradiating the accretion disc and the secondary star and of evaporating the inner parts of the disc . we assume the standard values of viscosity . we confirm the suggestion by warner ( @xcite ) that the large variety of observed outbursts behaviour may result from the interplay of these three effects . we are able to reproduce light curves reminiscent of those of systems such as or . we can obtain long lasting outbursts , very similar to superoutbursts , without assuming the presence of a tidal instability . accretion , accretion discs instabilities ( stars : ) novae , cataclysmic variables ( stars : ) binaries : close

astro-ph9911124

c

we have shown that many types of light curves can be produced by numerical models that include the illumination of both the secondary and the accretion disc , thereby explaining a great variety of observed light curves . these effects account for phenomena such as post - outburst rebrightening ( e.g. ) , long outbursts ( for example ) , or su uma systems with extremely short supercycles . in order to explore further these possibilities , one would need to determine from observations the mass transfer rate from the secondary as a function of the mass accretion rate onto the white dwarf , with a better accuracy than it is available now . despite the fact that our approximations are very crude , in particular the one concerning the response of the secondary to illumination , we can nevertheless draw a number of conclusions . first , the illumination of the disc is important only if the white dwarf is relatively massive , so that it can have a high temperature without contributing too much to the light emitted by the system in outburst , and that the efficiency of accretion is high . rebrightenings also require @xmath0 not to be too low in quiescence . the fact that we can reproduce an alternance of normal and long outbursts when the illumination of the secondary is included does not of course imply that the thermal - tidal instability model for su uma is incorrect ; a tidal instability is most probably required to account for the superhump phenomenon . the question of the precise role of this instability is , however , still open and our results raise some doubt on the validity of the parameters derived when fitting the observations , in particular for systems having a very short supercycle . this also means that the determination of the viscosity from the modeling of light curves is a far more difficult task than previously estimated . we obviously need some progress in the determination of the tidal torque ; we also need to know how the secondary responds to illumination . we finally should include 2d effects in our models . first because the orbits in the outer disc are far from being circular , and second because the presence of a hot spot whose temperature can be of order of 10,000 k could in principle significantly alter the stability properties of the outer disc . augusteijn , t. , kuulkers , e. , shaham , j. , 1993 , a&a 279 , l9 cannizzo , j.k . , 1993 , the limit cycle instability of dwarf nova accretion disks . in : accretion discs in compact stellar systems , wheeler j.c . ( ed . ) , world scientific , singapore , p. 6 dorman , b , nelson , l.a . , chau , w.y . , 1989 , apj 342 , 1003 dubus , g. , lasota , j .- hameury , j .- , charles , p. , 1999 , mnras 303 , 139 hameury , j .- m . , king , a.r . , lasota , j .- , 1986 , a&a 162 , 71 hameury , j .- m . , lasota , j .- p . , king , a.r . , 1988 , a&a 192 , 187 hameury , j .- m . , lasota , j .- hur , j .- m . , 1997 , mnras 287 , 937 hameury , j .- m . , menou , k. , dubus , g. , lasota , j .- hur , j .- m . , 1998 , mnras 298 , 1048 hameury , j .- m . , lasota , j .- p . , dubus , g. , 1999 , mnras 303 , 39 ichikawa , s. , hirose , m. , osaki , y. , 1993 , pasj 45 , 253 kato , s. , nakamura , k.e . , 1998 , pasj 50 , 559 king , a.r . , mnras , 288 , l16 lasota j .- , 1996 , mechanisms for dwarf nova outbursts and soft x - ray transients ( a critical review ) . in : compact stars in binaries , iau symp . 165 , van paradijs , j. , van den heuvel , e.p.j . , kuulkers , e. ( eds . ) , kluwer academic publishers , dordrecht , p. 43 lasota , j .- p . , hameury , j .- m . , hur , j .- m . , 1995 , a&a 302 , 29 lasota , j .- p . , kuulkers , e. , charles , p.a . , 1999 , mnras 1999 , 305 , 473 livio , m. , spruit , h.c . , 1991 , a&a 252 , 189 liu , b.f . , meyer , f. , meyer - hofmeister , e. , 1997 , a&a 328 , 247 lubow , s.h . , shu , f.h . , 1975 , apj 198 , 383 mattei , j.a . , saladyga , m. , waagen , w.o . , jones , c.m . , 1987 , aavso monogr . 2 mccormick , p. , frank , j. , 1998 , apj 500 , 293 mennikent , r.e . , arenas , j. , 1998 , pasj 50 , 333 menou , k. , hameury , j .- m . , stehle , r. , 1999 , mnras , 305 , 79 menou , k. , hameury , j .- m . , lasota , j .- narayan , r. , 1999 , apj , accepted meyer , f. , meyer - hofmeister , e. , 1994 , a&a 288 , 175 meyer - hofmeister , e. , meyer , f. , liu , b. , 1998 , a&a 339 , 507 osaki , y. , 1985 , a&a 144 , 369 osaki , y. , 1989 , pasj 41 , 1005 osaki , y. , 1995a , pasj 47 , 47 osaki , y. , 1995b , pasj 47 , l25 osaki , y. , 1996 , pasp 108 , 39 osaki , y. , 1998 , thermal - tidal instability model for su uma stars . in : wild stars in the old west : proceedings of the 13th north american workshop on cataclysmic variables and related objects , howell , s. , kuulkers , e. , woodward , c. ( eds ) , asp conf . 137 , san francisco , p. 334 osaki , y. , shimizu , s. , tsugawa , m. , 1997 , pasj 49 , l19 patterson , j. , richman , h. , kemp , j. , mukai , k. , 1998 , pasp 110 , 403 ritter , h. , kolb , u. , 1998 , a&as , 129 , 83 shakura , n. i. , sunyaev , r.a . , 1973 , a&a 24 , 337 shaviv , g. , wickramasinghe , d. , wehrse , r. , 1999 , a&a 344 , 639 szkody , p. , mattei , j.a . , 1984 , pasj 96 , 988 smak , j. , 1984 , acta astron . 34 , 161 smak , j. , 1991a , acta astron . 41 , 41 smak , j. , 1991b , acta astron . 41 , 269 smak , j. , 1993 , acta astron . 43 , 101 smak , j. , 1995 , acta astron . 45 , 355 smak , j. , 1998 , acta astron . 48 , 667 smak , j. , 1999a , acta astron . 49 , 383 smak , j. , 1999b , acta astron . 49 , 391 vogt , n. , 1983 , a&a 118 , 95 warner , b. , 1995a , cataclysmic variable stars . cambridge university press , cambridge warner , b. , 1995b , ap&ss 226 , 187 warner , b. , 1995c , ap&ss 230 , 83 warner , b. , 1998 , photometry and the increasing range of cv subtypes . in wild stars in the old west : proceedings of the 13th north american workshop on cataclysmic variables and related objects , howell s. , kuulkers e. , woodward c. ( eds ) , asp conf . 137 , san francisco , p. 2 warner , b. , livio , m. , tout , c.a . , 1995 , mnras 232 , 35 whitehurst , r. , 1988 , mnras 232 , 35

we can obtain long lasting outbursts , very similar to superoutbursts , without assuming the presence of a tidal instability . accretion , accretion discs instabilities ( stars : ) novae , cataclysmic variables ( stars : ) binaries : close

in the framework of the dwarf nova thermal - viscous disc instability model , we investigate the combined effects on the predicted dwarf nova lightcurves of irradiating the accretion disc and the secondary star and of evaporating the inner parts of the disc . we assume the standard values of viscosity . we confirm the suggestion by warner ( @xcite ) that the large variety of observed outbursts behaviour may result from the interplay of these three effects . we are able to reproduce light curves reminiscent of those of systems such as or . we can obtain long lasting outbursts , very similar to superoutbursts , without assuming the presence of a tidal instability . accretion , accretion discs instabilities ( stars : ) novae , cataclysmic variables ( stars : ) binaries : close

1206.5549

i

cosmic relics , such as topological defects and magnetic fields , can be used as probes of the very early universe and extremely high energy particle physics . the formation , evolution , and observational signatures of topological defects have been studied for over three decades , and constraints have been obtained that have guided particle physics model building . the formation of magnetic fields during cosmological phase transitions has also been investigated @xcite . current observational constraints are relatively weak , allowing for intergalactic magnetic field strengths at the nano gauss level ( see for example , @xcite ) . an attractive scenario links the generation of magnetic fields to the generation of the observed matter - antimatter asymmetry @xcite . the produced magnetic field carries magnetic helicity that is directly proportional to the baryon number density @xcite @xmath0 where @xmath1 is the fine structure constant , @xmath2 @xcite , and @xmath3 is the magnetic helicity density and @xmath4 is the baryon number density . the minus sign in the relation ( [ hnb ] ) is a direct cosmological manifestation of cp violation in particle physics that also gives preference to matter over antimatter in the universe . the injection of helical magnetic fields into the plasma can transfer magnetic field power to larger length scales by the `` inverse cascade '' , providing hope that even small scale magnetic fields from phase transitions can grow to astrophysically relevant scales at more recent epochs . _ helical _ magnetic fields can possibly be detected through various cosmological observations @xcite . an external magnetic field tends to align the magnetic moments of the four electron states left - right handedness for electron and positron , denoted in the figure as @xmath5 which implies the shown directionalities of the spin , momenta , and electric current due to each state . if the four states are present in unequal numbers , net electric current may be induced . , scaledwidth=30.0% ] two important chiral effects , called the chiral - vorticity ( @xmath6 ) @xcite and chiral - magnetic ( @xmath7 ) @xcite effects , can also play a role in the early universe @xcite and in qcd @xcite . to understand these effects , consider fig . [ chi - b - scheme ] where we show the effect of a magnetic field on , for example , electrons . the magnetic field couples to the magnetic moments and tends to align them . depending on the electric charge of the carrier , the spins are either aligned or anti - aligned with the magnetic moment . the helicity eigenstates of the fermions then determine the direction of the momentum of the particles , which in turn gives the direction of the electric current due to each species . taking the left- and right - handed electrons and positrons as the four fermion states , which we assume to be massless , we see that the net electric current is @xmath8 - [ n(e^-_r)-n(e^+_l)],\ ] ] where @xmath9 denotes the number density of @xmath10 and similarly for the other particle species . in terms of the chemical potentials for left- and right - handed electrons , the differences within the square brackets are given by @xmath11 and @xmath12 respectively . so @xmath13 . the calculation in ref . @xcite gives @xmath14 similarly , in fig . [ chi - omega - scheme ] , we explain the @xmath15 effect , which occurs if the ambient fluid flow has vorticity ( @xmath16 ) . spin - orbit coupling tends to align the spins of the fermions ; particle helicity then aligns the left - handed states but anti - aligns the right - handed states , which leads to the electric currents as shown . thus , in equilibrium , @xmath17 - [ n(e^-_r)+n(e^+_l)].\ ] ] the presence of non - zero @xmath11 means that @xmath18 and of @xmath12 that @xmath19 . however , if @xmath20 then @xmath21 and @xmath22 , and @xmath23 vanishes . also if @xmath24 then @xmath25 and @xmath26 , and again @xmath27 . so for @xmath23 to be non - vanishing , we need @xmath28 . the exact calculation in ref . @xcite gives @xmath29 where @xmath30 is the fluid vorticity . the above expression for @xmath31 holds when the left- and right - handed particles and antiparticles are in thermal equilibrium at the same temperature . if some of the species are at different temperatures there is an additional contribution per species to @xmath31 proportional to @xmath32 where @xmath33 is the temperature of the particular species @xcite . we will not consider this situation in the present paper , though it may be important for the contribution of left- and right - handed particles , especially neutrinos , to the hypercharge current in the epoch before electroweak symmetry breaking . vortical fluid flow tends to align the spins of the four electron states which implies the shown directionalities of the momenta and electric current due to each state . if the four states are present in unequal numbers , net electric current may be induced . , scaledwidth=30.0% ] the @xmath7 and @xmath15 effects can only lead to a non - zero electric current if there is a disbalance between left- and right - handed particles , that is , @xmath34 . such a disbalance can arise in the early universe from out - of - equilibrium @xmath35-violating decays of massive particles . for example , it could arise due to inflaton decay at the end of inflation . the resulting values of @xmath36 are not generally suppressed by any small couplings , so large values like @xmath37 can easily be achieved @xcite . a right - left asymmetry is also likely to be created during leptogenesis , if it occurs at some energy scale much higher than the electroweak scale . in particular , an asymmetry between left- and right - handed electrons will be created because they carry different charges under the electroweak symmetry group @xmath38 . the chirality - flipping processes due to nonzero electron mass are suppressed at high temperatures , and this asymmetry is preserved until the temperature drops below @xmath39 @xcite . if vorticity develops at any temperature higher than @xmath40 , the @xmath15 effect will operate and create a magnetic field . since the electroweak symmetry is unbroken , this magnetic field will be the @xmath41 hypercharge magnetic field , and will get converted to electromagnetic magnetic field after the electroweak phase transition . it is worth noting that chiral effects induce kinetic and magnetic helicities even if these are not present initially . for the @xmath15 effect , fig . [ chi - omega - scheme ] shows that momenta tend to be aligned along @xmath16 , which means that @xmath42 and so kinetic helicity is induced . in the case of the @xmath7 effect , if the magnetic field is helical , then the induced current , hence velocity , is along the magnetic field and the fluid flow carries kinetic helicity . this fact may be of interest if the kinetic helicity survives until recombination because then it can produce parity odd temperature - polarization correlations @xcite . once a magnetic field is generated , its subsequent evolution may also be influenced by chiral effects . in particular , joyce and shaposhnikov @xcite have shown that @xmath7 currents can induce an exponential growth of the magnetic field on sufficiently large length scales . a helical magnetic field , in turn , back - reacts on the evolution of the left - right disbalance @xmath36 . this is described by the chiral anomaly equation , which relates changes in @xmath36 to changes in magnetic helicity @xcite , @xmath43 here , @xmath44 is the chirality - flipping rate and @xmath45 , @xmath1 is the fine structure constant , and @xmath33 is the temperature at time @xmath46 . boyarsky et al @xcite have shown that as a result the left - right disbalance can survive down to @xmath47 mev if helical magnetic fields are present , for example due to baryogenesis . the plasma equations in the radiation - baryon single fluid approximation are @xmath48 where we have used natural units , @xmath49 . the fluid density is @xmath50 , the pressure is @xmath51 . the displacement current has been ignored , as is done in magnetohydrodynamics ( mhd ) when the flow velocities are small compared to the speed of light . since we are mainly focusing on chiral effects , we have simplified the equations by ignoring the injection of magnetic fields by external sources such as sphalerons @xcite , and the dissipative effects of viscosity . cosmological expansion can be included in the maxwell equations by going to conformal coordinates , as we will do in sec . [ sec : diffevoln ] . the electric current is given by the sum of the ohmic and chiral components @xmath52 the ohmic component is given by @xmath53 where @xmath54 is the electrical conductivity of the plasma . the chiral components , @xmath55 and @xmath31 , are given in eqs . ( [ chibj ] ) and ( [ chiomegaj ] ) , together with the chiral anomaly equation in the form of eq . ( [ dmuevoln ] ) . in eq . ( [ max2 ] ) we can replace @xmath56 by the currents and with a little algebra we find @xmath57 where @xmath58 the terms on the right - hand side of ( [ mhdeq ] ) will be referred to as the advection , diffusion , @xmath15 , and @xmath7 terms respectively . the above set of equations exhibits all the complexities of mhd plus those arising from the chiral anomaly . it is helpful to compare order of magnitudes of the various terms on the right - hand side of eq . ( [ mhdeq ] ) . if @xmath59 denotes a length scale of interest , the advection , diffusion , @xmath15 and @xmath7 terms are estimated as @xmath60 assuming that @xmath61 and using @xmath62 @xcite , the estimates for the four terms become @xmath63 , @xmath64 , @xmath65 , and @xmath66 respectively . now for small flow velocities , @xmath67 , or small magnetic fields , @xmath68 , the advection term is subdominant and can be ignored . the second case we consider is when the length scale is large and the magnetic field is small : @xmath69 , @xmath70 . then the diffusion term can be neglected . we solve the evolution equations in an expanding spacetime , first numerically in sec . [ sec : numerics ] and then analytically in sec . [ analytics ] . throughout this analysis we adopt some simplifications . first of all , we do not attempt to solve the fluid dynamics equations and represent the velocity field by a mode distribution with a kolmogorov spectrum and fixed phases . ( a more realistic representation of turbulent dynamics would include time variation of the phases . ) we also assume negligible advection ; the consistency of the latter assumption is discussed in sec . [ analytics ] . our conclusions are summarized and discussed in sec . [ conclusions ] . in particular , we argue that under certain conditions the magnitude and the spectrum of the magnetic fields produced by our mechanism are not sensitive to the details of the turbulent velocity flow . our estimates should then be valid , despite the oversimplified treatment of turbulent dynamics . in appendix [ app : steady ] we also consider steady - state solutions , _ i.e. _ with @xmath71 , in the regimes of negligible advection and of negligible diffusion in minkowski spacetime .

in the presence of cosmic chiral asymmetry , chiral - vorticity and chiral - magnetic effects can play an important role in the generation and evolution of magnetic fields in the early universe . we include these chiral effects in the magnetic field equations and find solutions under simplifying assumptions .

in the presence of cosmic chiral asymmetry , chiral - vorticity and chiral - magnetic effects can play an important role in the generation and evolution of magnetic fields in the early universe . we include these chiral effects in the magnetic field equations and find solutions under simplifying assumptions . our numerical and analytical results show the presence of an attractor solution in which chiral effects produce a strong , narrow , gaussian peak in the magnetic spectrum and the magnetic field becomes maximally helical . the peak in the spectrum shifts to longer length scales and becomes sharper with evolution . we also find that the dynamics may become non - linear for certain parameters , pointing to the necessity of a more complete analysis .

1410.5767

i

surfaces with constant mean curvature , abbreviated by cmc surfaces , are mathematical models of soap films and soap bubbles and , in general , of interfaces and capillary surfaces . under conditions of homogeneity and in absence of gravity , an interface attains a state of physical equilibrium when minimizes the surface area enclosing a fixed volume , or at least , when it is a critical point for the area under deformations that preserve the volume . the literature on capillarity is extensive and we refer the classical text of finn @xcite ; applications in physics and technological processes appear in @xcite . we will study two physical phenomena . first , a liquid drop @xmath0 deposited on a surface @xmath1 in such way that the wetted region by @xmath0 on @xmath1 is a prescribed domain @xmath2 . then the air - liquid interface @xmath3 is a compact cmc surface whose boundary curve @xmath4 is prescribed to be @xmath5 . the second example appears in contexts of wetting and capillarity . consider a liquid drop @xmath0 deposited on a given support @xmath1 and such that @xmath0 can freely move along @xmath1 . here the curve @xmath4 remains on @xmath1 but now is not prescribed . in equilibrium , the interface @xmath6 is a cmc surface and @xmath6 meets @xmath1 with a constant contact angle @xmath7 , where @xmath7 depends on the materials . both contexts correspond with two mathematical problems . denote by @xmath6 a compact smooth surface with boundary @xmath4 . the first problem is as follows . given a closed smooth curve @xmath8 , study the shape of a compact cmc surface @xmath6 whose boundary is @xmath9 . for example , we ask whether the geometry of @xmath10 imposes restrictions to the possible configurations of @xmath6 , such as , if the symmetries of @xmath10 are inherited by @xmath6 . to be precise , suppose that @xmath11 is an isometry such that @xmath12 and let @xmath6 be a cmc surface spanning @xmath10 . then we ask if @xmath13 . the simplest case of boundary is a circle contained in a plane @xmath1 . this curve is invariant by rotations with respect to the straight line @xmath14 orthogonal to @xmath1 through the center of @xmath10 . if @xmath10 is a circle of radius @xmath15 and @xmath16 , there exist two spherical caps ( the large and the small one ) bounded by @xmath10 and with radius @xmath17 , @xmath18 ( if @xmath19 , then both caps are hemispheres ) . also , the planar disk bounded by @xmath10 is a cmc surface with @xmath20 . all these examples are rotational surfaces where the axis of revolution is @xmath14 . however , it should be noted that kapouleas found non - rotational compact cmc surfaces bounded by a circle @xcite . when the surface is embedded we can apply the so - called alexandrov reflection method ( or the method of moving planes ) based on the maximum principle for elliptic partial differential equations of second order , which consists in a process of reflection about planes , using the very surface as a barrier @xcite . thanks to this technique , given a circle @xmath10 contained in a plane @xmath1 , if @xmath6 is a compact embedded cmc surface with @xmath9 and @xmath6 lies on one side of @xmath1 , then @xmath6 is a spherical cap . recall that kaopuleass examples are non - embedded surfaces and lies on one side of the boundary plane . the lack of examples provides us evidence supporting the next _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ conjecture . a compact embedded cmc surface in @xmath21 spanning a circle is a spherical cap or a planar disk . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ thus , the conjecture reduces to the question under what conditions such a surface lies on one side of @xmath1 . some partial answers have been obtained in @xcite . however it is not known if there exists a cmc surface spanning a circle as in figure [ fig1 ] , left . spanning a circle @xmath10 . this surface is not possible by corollary [ cor1 ] ] the mathematical formulation of the second setting is the following . consider a regular region @xmath22 with @xmath23 . let @xmath6 be a compact surface @xmath6 with @xmath24 and @xmath25 separating a bounded domain @xmath26 with a prescribed volume . the domain @xmath0 is bounded by @xmath6 and by pieces of @xmath1 . let @xmath27 $ ] . we seek a surface @xmath6 which is critical for the energy functional @xmath28 in the space of compact surfaces with boundary contained in @xmath1 and interior contained in @xmath29 and preserving the volume of @xmath0 . in such case , we say that @xmath6 is a stationary surface . a stationary surface is characterized by the fact that its mean curvature @xmath30 is constant and @xmath6 meets @xmath1 in a constant angle @xmath7 along @xmath4 . in this article we shall consider both problems when the supporting surface @xmath1 is a sphere . first in section [ sec2 ] we study compact embedded cmc surfaces with prescribed boundary on a sphere @xmath1 . we give results showing that the surface inherits some symmetries of its boundary , and we prove that the conjecture is true in some special cases . see figure [ fig1 ] , right . in section [ sec3 ] , we study stationary surfaces with boundary on a sphere . in physics , these configurations appear in the context of capillarity , for example , @xcite . in the case that we study here , say , @xmath1 is a sphere , a result of taylor asserts that the boundary of a stationary surface is smooth because of @xmath1 @xcite . with the above notation , if @xmath31 is the closed ball defined by @xmath1 , there are examples of stationary surfaces intersecting @xmath1 with a contact angle : besides the planar disks and spherical caps , whose boundary is a circle contained in @xmath1 , there are pieces of rotational ( non spherical ) cmc surfaces whose boundary is formed by two coaxial circles @xcite . nitsche proved that the only cmc surface homeomorphic to a disk that meets @xmath1 at a contact angle is either a planar disk or a spherical cap ( @xcite ; also @xcite ) . by the physical interest , we also study the case that the mean curvature depends linearly on a spatial coordinate .

we consider the case that the boundary is prescribed or that the surface meets the sphere with a constant angle . our results apply in many scenarios in physics where in absence of gravity a liquid drop is deposited on a round solid ball and the air - liquid interface is a critical point for area under all variations that preserve the enclosed volume .

in this article we study the shape of a compact surface of constant mean curvature of euclidean space whose boundary is contained in a round sphere . we consider the case that the boundary is prescribed or that the surface meets the sphere with a constant angle . we study under what geometric conditions the surface must be spherical . our results apply in many scenarios in physics where in absence of gravity a liquid drop is deposited on a round solid ball and the air - liquid interface is a critical point for area under all variations that preserve the enclosed volume .

1501.01787

i

throughout this paper , @xmath3 is a field or the ring of integers @xmath4 . @xmath5={\mathbf{k}}[v_1,\dots , v_m]$ ] is the graded polynomial algebra on @xmath6 variables , deg@xmath7 . the _ face ring _ ( also known as the _ stanley - reisner ring _ ) of a simplicial complex @xmath0 with @xmath6 vertices is the quotient ring @xmath8/\mathcal { i}_k\ ] ] where @xmath9 is the ideal generated by those square free monomials @xmath10 for which @xmath11 is not a simplex in @xmath0 . for any simple polytope @xmath12 , davis and januszkiewicz @xcite introduced a @xmath13-manifold @xmath14 with orbit space @xmath12 . after that buchstaber and panov @xcite generalized this definition to any simplicial complex @xmath0 with vertex set @xmath15=\{1,2,\dots , m\}$ ] , and named it the _ moment - angle complex _ associated to @xmath0 : @xmath16 where @xmath17 , @xmath18 if @xmath19 and @xmath20 if @xmath21 . the following theorem is proved by buchstaber and panov @xcite for the case over a field by using eilenberg - moore spectral sequence , @xcite for the general case . let k be a simplicial complex with @xmath6 vertices . then the following isomorphism of algebras holds : @xmath22}({\mathbf{k}}(k),{\mathbf{k}}).\ ] ] since @xmath23}({\mathbf{k}}(k),{\mathbf{k}})$ ] has a natural @xmath24-bigrade . so the bigraded cohomology ring can be decomposed as follows : @xmath25}({\mathbf{k}}(k),{\mathbf{k}})=\bigoplus\limits_{i\geq0}\bigoplus\limits_{j\subseteq[m ] } \mathrm{tor}_{i , j}^{{\mathbf{k}}[m]}({\mathbf{k}}(k),{\mathbf{k}}).\ ] ] hochster @xcite gave a combinatorial description of the tor - groups @xmath1}({\mathbf{k}}(k),{\mathbf{k}})$ ] . @xmath26}({\mathbf{k}}(k),{\mathbf{k}})\cong\w{h}^ { |j|-i-1}(k_j;{\mathbf{k}}),\ ] ] where @xmath27 , @xmath28 is the full subcomplex of @xmath0 corresponding to @xmath29 . hochster proved this for the case @xmath3 is a field by analyzing the betti number of both sides . buchstaber and panov ( * ? ? ? * theorem 3.2.9 ) generalize this result to @xmath30 by means of the koszul resolution @xmath31\otimes{\mathbf{k}}[m]$ ] of @xmath3 . recently , wang and zheng @xcite gave another way to calculate @xmath23}({\mathbf{k}}(k),{\mathbf{k}})$ ] by using taylor resolution on the stanley - reisner ring @xmath2 . this method was presented firstly by yuzvinsky in @xcite . in this paper we give a combinatorial description of this method , and then we prove hochster s theorem in a different way . let @xmath0 be a simplicial complex on the set @xmath15 $ ] . a _ missing face _ of @xmath0 is the subset @xmath32 $ ] where @xmath33 and every proper subset of @xmath34 is a simplex of @xmath0 . denote by @xmath35 the missing face set of @xmath0 . clearly @xmath35 is uniquely determined by @xmath0 . a _ simplicial complement _ @xmath36 of @xmath0 is a subset of @xmath37\mid\tau\not\in k\}$ ] so that @xmath38 . usually @xmath36 is not unique . denote by @xmath39 the set of simplicial complements of @xmath0 . given a simplicial complement @xmath36 of @xmath0 , one can define an exterior algebra @xmath40 $ ] generated by all elements of @xmath36 . for a monomial @xmath41 $ ] , let @xmath42 be the _ total set _ of @xmath43 . so @xmath40 $ ] has a natural @xmath24-bigrade , which means @xmath44=\bigoplus\limits_{i\geq 0}\bigoplus\limits_{j\subseteq[m]}\lambda^{i , j}[\mathbb{p}]\ ] ] where @xmath45 $ ] is generated by monomials @xmath43 satisfying @xmath46 and deg@xmath47 . one can make @xmath40 $ ] into a chain complex by defining a differential @xmath48 on it . the differential @xmath49\to \lambda^{n-1,*}[\mathbb{p}]$ ] is generated by @xmath50 where @xmath51 , @xmath52 ( particularly , if @xmath53 , @xmath54 ) , @xmath55 if @xmath56 and zero otherwise . [ thm:1 ] let @xmath0 be a simplicial complex on the set @xmath15 $ ] . given a simplicial complement @xmath57 . then @xmath58}_{i,\,j}({\mathbf{k}}(k),{\mathbf{k}})\cong h_i\big ( \lambda^ { * , j}[\mathbb{p}],d\big).\ ] ] from theorem [ thm:1 ] , we know that the homology groups @xmath59,d\big)$ ] of a simplicial complement @xmath36 is not depend on the choice of @xmath36 . it just depend on the simplicial complex @xmath0 . if we can prove that @xmath60,d\big)\cong\w{h}^{|j|-i-1}(k_j;{\mathbf{k}}),\ ] ] then the hochster theorem is proved . the following theorem ensure these isomorphisms hold . [ thm:3 ] let @xmath0 be a simplicial complex on the set @xmath15 $ ] , and let @xmath36 be one of the simplicial compliments of @xmath0 . then we have the following group isomorphisms : @xmath61}[\mathbb{p}],d\big)\cong\w{h}^{m - i-1}(k;{\mathbf{k}}).\ ] ] let everything be as before . then @xmath62,d\big)\cong\w{h}^{|j|-i-1}(k_j;{\mathbf{k}}).\ ] ]

in this paper , we consider homology groups induced by the exterior algebra generated by a simplicial compliment of a simplicial complex @xmath0 . these homology groups are isomorphic to the tor - groups @xmath1}({\mathbf{k}}(k),{\mathbf{k}})$ ] of the face ring @xmath2 , which is very useful and much studied in toric topology . by using ech homology theory and alexander duality theorem , we prove that these homology groups have dualities with the simplicial cohomology groups of the full subcomplexes of @xmath0 . then we give a new proof of hochster s theorem .

in this paper , we consider homology groups induced by the exterior algebra generated by a simplicial compliment of a simplicial complex @xmath0 . these homology groups are isomorphic to the tor - groups @xmath1}({\mathbf{k}}(k),{\mathbf{k}})$ ] of the face ring @xmath2 , which is very useful and much studied in toric topology . by using ech homology theory and alexander duality theorem , we prove that these homology groups have dualities with the simplicial cohomology groups of the full subcomplexes of @xmath0 . then we give a new proof of hochster s theorem .

1207.2264

i

there are two important phenomena observed in evolutionary dynamical systems of any kind : _ self - organization _ and _ emergence_. both phenomena are the exclusive result of endogenous interactions of the individual elements of an evolutionary dynamical system . emergence characterizes the patterns that are situated at a higher macro level and that arise from interactions taking place at the lower micro level of the system . self - organization , besides departing from the individual micro interactions , implies an increase in order of the system , being usually associated to the promotion of a specific functionality and to the generation of patterns . typically , complex patterns emerge in a system of interacting individuals that participate in a self - organizing process . self - organization is more frequently related to the process itself , while emergence is usually associated to an outcome of the process . although less frequently mentioned , the emergence of patterns from self - organizing processes may be strongly dependent on _ locality_. emergence and self - organization are not enough to distinguish between two important and quite different circumstances : the presence of an influence that impacts the system globally and , conversely , the absence of any global influence and the lack of information about any global property of the system . in the latter case , the system itself is the exclusive result of local interactions . such a global influence ( entity or property ) is often associated with the concept of _ environment_. noteworthy , the latter circumstance may be considered a case of the former : when that global entity does not exist , the environment for each agent is just the set of all the other agents . conversely , when the global entity exists , it is considered part of the environment and may have an inhomogeneous impact on the individual dynamics . regardless of the environmental type , economical , ecological and social environments share as a common feature the fact that the agents operating in these environments usually try to improve some kind of utility , related either to profit , to food , to reproduction or to comfort and power . a general concept that is attached to this improvement attempt is the idea of _ adaptation_. in the economy , adaptation may be concerned with the development of new products to capture a higher market share or with the improvement of the production processes to increase profits : that is , innovation . in ecology , adaptation concerns better ways to achieve security or food intake or reproduction chance and , in the social context , some of the above economical and biological drives plus a few other less survival - oriented needs . in all cases , adaptation aims at finding strategies to better deal with the surrounding environment ( @xcite ) . natural selection through fitness landscapes or geographic barriers are good examples how global influences are considered when modeling adaptation in an evolutionary process . on the other hand , adaptation also operates in many structure generating mechanisms that can be found in both physical and social sciences but that are built on the exclusive occurrence of local interactions . in biology , the ultimate domain of evolution and natural selection , we are confronted with tremendous organic diversity virtually infinite forms and shapes none of which found twice but the distribution is well structured in a way that allows us to order this diversity and to speak of species , families , orders etc . a quite illustrative description is given by the evolutionary geneticist theodusius dobzhanski ( @xcite : p.21 ) : _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ suppose that we make a fairly large collection , say some 10,000 specimens , of birds or butterflies or flowering plants in a small territory , perhaps 100 square kilometers . no two individuals will be exactly alike . let us , however , consider the entire collection . the variations that we find in size , in color , or in other traits among our specimens do not form continuous distributions . instead , arrays of discrete distributions are found . the distributions are separated by gaps , that is , by the absence of specimens with intermediate characteristics . we soon learn to distinguish the arrays of specimens to which the vernacular names english sparrow , chickadee , bluejay , blackbird , cardinal , and the like , are applied . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ if we had to make a visual representation of this description of intra and interspecies variations it would perhaps look like the multi - modal distribution shown in figure [ fig : distribution01 ] . what we call a species , is in fact some norm or mean characteristics of a cluster of individuals . evolutionary theory is ultimately a theory about the history which led to such a pattern . and if the organic diversity we observe nowadays evolved in a way that is characterized by some kind of > > tree of live < < , then there must be events that may lead to the split of a connected set of individuals ( protospecies ) into ( at least ) two sets that are not connected any longer ( see figure [ fig : speciation ] ) . in biology , this is called _ speciation_. as we will see in this article , though , the generation of such a split with simple but well known evolutionary models in which `` natural selection impels and directs evolutionary changes '' ( ibid . p.2 ) is not straightforward . it so happens that constraints on the interaction behavior are required . the phenotype of living beings is not the only domain where patterns of structured diversity as illustrated in figure [ fig : distribution01 ] are observed . phenomena include certain phases of structure formation in physical cosmology , distribution of cultural behavior , languages and dialects , herd behavior in finance , among others . especially for the latter examples in the field of socio - cultural dynamics a variety of models has been proposed which do not rely on the evolutionary concept of ( natural ) selection . they are rather based on the idea of exclusively _ local interactions ( li ) _ implemented in form of a system of agents that interact locally according to simple rules like assimilation or conformity . in these systems , finding strategies to better deal with the surrounding environment ( and thus improving fitness ) is not constrained by any global property . it may , however , be constrained by local ( individual ) rules . as we shall see later in this paper , constraints on the mechanisms of selection , interaction and replacement and the way they are combined in the modeling of an evolutionary process have an important bearing on both adaptation and emergence of speciation . locality operating in each of these mechanisms seems to be the fundamental modeling principle by which emergence of a multi - modal distribution as shown in figure [ fig : distribution01 ] can be explained . on the basis of these observations about the > > modelability < < of speciation with evolutionary and self - organisatory models , we study in this paper the conditions and mechanisms required for speciation and the emergence of a multi - modal distribution . in this analysis , we use computational ( section [ sec : computation ] ) as well as mathematical ( section [ sec : mathematic ] ) arguments . our models simulate how a population of individuals evolves in time in an abstract attribute space @xmath0 that represent phenetic traits , attitudes , verbal behavior , etcetera . modeling agents as points in an attribute space of this kind is of course a highly artificial abstraction from the complexity and multi dimensionality of real agents . for the purposes of this paper , let us conceptualize an _ interaction event _ , defining the system evolution from one time step to the other , by the following three components : 1 . selection of agents , 2 . application of interaction rules , 3 . replacement of agents . any interaction event ( e.g. , mating , communication , ... ) that takes place in the course of a simulation of the model consists of the sequential application of these three steps . the reason to dissect the interaction events in this way is two fold : 1 . we want to look at the dynamical and structural effects of constraints applied to each of the three components independently ; 2 . the scheduling of interaction events may have a crucial effect on the model behavior , and with the distinction between selection and interaction on the one hand , and replacement on the other , we are able to make this effect explicit . the way interaction events are scheduled in the implementation of the models is not always given much importance in existing simulation studies . in the presence of constraints on the selection and interaction mechanisms , however , the outcome as well as the dynamical properties depend in a crucial way on the different choices . on the other hand , there are studies that do analyze the differences between synchronous and asynchronous update ( see , for instance , @xcite ) as well as studies on non overlapping ( nolg ) and respectively overlapping generations ( olg ) in biology and economics ( for instance , @xcite ) . here we show that especially when the interaction is constrained ( as in the case of assortative mating ) there emerges an important qualitative difference between olg and nolg models . namely , speciation is observed in the former , but not in the latter case , whereas adaptation is favored by the latter and hindered by the former . however , by the distinction of selection , interaction and replacement we are able to show that in fact the difference between local and non - local replacement plays the determinant role ( and not the distinction between olg and nolg ) . even though locality also impacts selection and interaction mechanisms , it is on the replacement mode where relies the fundamental difference with respect to the conditions required for either adaptiveness or speciation . this paper is organized as follows : section 2 addresses the main issues of both the fitness landscape and the self - organizing models from a computer simulation framework . in both cases , microscopic implementation rules are tested against their capability of reproducing adaptiveness and speciation . in section 3 , the emergence of speciation is analytically shown to be dependent on the choice of different replacement modes . this is accomplished through a probabilistic description of a minimal model of just three phenetic traits where the transition probabilities between traits follow a markov chain . section 4 is targeted at presenting concluding remarks and a framework that relates interaction events to the emergence of collective structures in adaptive and self - organizing complex systems .

in this paper , we inspect well known population genetics and social dynamics models . in these models , interacting individuals , while participating in a self - organizing process , give rise to the emergence of complex behaviors and patterns . while one main focus in population genetics is on the adaptive behavior of a population , social dynamics is more often concerned with the splitting of a connected array of individuals into a state of global polarization , that is , the emergence of speciation . applying computational and mathematical tools we show that the way the mechanisms of selection , interaction and replacement are constrained and combined in the modeling have an important bearing on both adaptation and the emergence of speciation . differently _ keywords _ : * emergence*,*self - organization*,*agent based models * , * speciation * , * markov chains*. _ msc : _ 37l60 , 37n25 , 05c69 .

in this paper , we inspect well known population genetics and social dynamics models . in these models , interacting individuals , while participating in a self - organizing process , give rise to the emergence of complex behaviors and patterns . while one main focus in population genetics is on the adaptive behavior of a population , social dynamics is more often concerned with the splitting of a connected array of individuals into a state of global polarization , that is , the emergence of speciation . applying computational and mathematical tools we show that the way the mechanisms of selection , interaction and replacement are constrained and combined in the modeling have an important bearing on both adaptation and the emergence of speciation . differently ( un)constraining the mechanism of individual replacement provides the conditions required for either speciation or adaptation , since these features appear as two opposing phenomena , not achieved by one and the same model . even though natural selection , operating as an external , environmental mechanism , is neither necessary nor sufficient for the creation of speciation , our modeling exercises highlight the important role played by natural selection in the interplay of the evolutionary and the self organization modeling methodologies . _ keywords _ : * emergence*,*self - organization*,*agent based models * , * speciation * , * markov chains*. _ msc : _ 37l60 , 37n25 , 05c69 .

1505.02907

c

there is a undetermined parameter @xmath1 , the ionization percent of the blr clouds , in equations ( 3 ) and ( 4 ) . two values of @xmath100 and @xmath101 are assumed to estimate @xmath0 . these assumptions may lead to some unreasonable results . following the strmgren radius of a strmgren sphere of ionized hydrogen around a young star @xcite , an ionization depth of a cloud is defined as the position where the recombination rate equals the ionization rate , and the hydrogen atoms are fully ionized . as the recombination and ionization are in equilibrium , the ionizing photon number arriving at one cloud per unit time equals the recombination line photon number per unit time . the ionizing photon number arriving at the cloud per unit time is @xmath102 , where @xmath103 is the cross - section area of the cloud , @xmath104 is the ionizing photon number emitted by the central engine per unit time ( @xmath105 the mean energy of photons ) , @xmath106 is the ionization parameter of hydrogen , and @xmath58 is the hydrogen number density of the cloud . at the same time , the ionized region of the cloud produces the recombination line photon number per unit time @xmath107 , where @xmath26 is the electron number density in this region , and @xmath108 is the fully ionized volume of the cloud . thus , we have @xmath109 because of the ionization balance . the ionization depth of the cloud is @xmath110 . the cloud has @xmath111 , where @xmath112 and @xmath113 are the volume and thickness of the cloud , respectively . the ionization parameter has @xmath1141 for emission line gas in quasars and seyfert galaxies @xcite . a gas density of @xmath115@xmath116 is required by a very large lyman continuum optical depth ( e.g. * ? ? ? the gas density values are the same as those in @xcite for quasars and seyfert galaxies . @xcite got @xmath117 . a density of @xmath118 is set by the presence of broad semi - forbidden line c iii@xmath119\lambda 1909 $ ] and the absence of broad forbidden lines such as [ o iii@xmath119\lambda \lambda 4363,4959,5007 $ ] @xcite . the typical values are @xmath120 and @xmath114 ( e.g. * ? ? ? * ; * ? ? ? the cloud size of @xmath121@xmath122 was constrained by the smoothness of the emission - line profiles @xcite . @xcite showed a universal ionization parameter @xmath114 in the inner photoionized layer of the blr clouds , independent of luminosity and distance . the radiation pressure confinement of the photoionized layer appears to explain the universality of the blr properties in agns , the similar relative line strength over the vast range of @xmath123@xmath124 @xmath70 in luminosity @xcite . a widely accepted power - law relation has been established between the luminosity @xmath125 and the blr size @xmath14 , as @xmath126 @xcite . this power - law relation spans over a range of @xmath127 in @xmath125 @xcite . so , @xmath129 will be independent of @xmath86 , @xmath34 , and @xmath14 . this independence may lead to a universal ionization parameter as suggested in @xcite . the typical values of @xmath120 and @xmath114 are taken to estimate @xmath130 , and then @xmath1 with @xmath131 and @xmath132@xmath133 . we have @xmath134 @xmath135 , and then @xmath136 0.20.6 . thus , it is basically reasonable to take @xmath75 and 0.5 in the calculations of @xmath0 . so , the masses counteracted by the continuum radiation pressures of the central engines are not negligible compared to , or are comparable to the black hole virial masses at least for some agns ( see figure 1 ) . this counteracting effect of the continuum radiation pressure is significant for quasars at @xmath92 ( see figure 1 ) . j0100 + 2802 at @xmath137 has a bolometric luminosity of @xmath138 and a black hole mass of @xmath139 , and it is the most luminous quasar known at @xmath140 @xcite . it has a @xmath141 as @xmath75 and @xmath142 as @xmath143 . these @xmath0 for this object are comparable to the black hole virial mass @xmath144 . so , j0100 + 2802 will have @xmath145 . this larger black hole mass further gives rise to the most significant challenge to the eddington limit growth of black holes in the early universe @xcite . there are the same cases for the cfhqs quasars as in j0100 + 2802 ( see figure 1 ) . their masses @xmath3 are larger than the virial masses @xmath2 . @xcite suggested for @xmath146 quasars that the supermassive black holes in the early universe likely grew much more quickly than their host galaxies . the larger black hole masses @xmath3 of the quasars at @xmath92 further strengthen this suggestion . thus , it is important to consider the radiation pressure effect on the black hole mass estimates for the agns with the high accretion rates . this importance of the radiation pressure is consistent with that suggested by @xcite who argued for narrow - line seyfert 1 galalxies , and seems to be inconsistent with the suggestions in @xcite and @xcite . an assumption of isotropy in equations ( 3 ) and ( 4 ) is made for the central source luminosity @xmath35 . this assumption might be significantly influence the estimated values of @xmath0 , and then the results of this paper . the anisotropic illumination of a blr by the central radiation was discussed by @xcite , and recently was investigated by @xcite . the central radiation of quasars are anisotropic ( e.g. * ? ? ? @xcite derived bolometric corrections based on the theoretical accretion disk models of @xcite , and obtained an anisotropic correction factor of @xmath147 , where @xmath148 and @xmath149 is the total source luminosity assuming isotropy . @xcite got a factor of @xmath150 for quasars . so , we take @xmath151 , i.e. , @xmath152 to re - estimate @xmath0 , and the re - estimated @xmath0 are compared to @xmath2 in figure 2 . considering the anisotropy of the central source luminosity @xmath35 , the continuum radiation pressure effects on the black hole masses @xmath3 can not be still neglected for the close- and super - eddington limit accretion rate agns . thus , the anisotropy of the central source luminosity could not influence significantly the main results assuming isotropy . @xcite proposed the seambh agns as the most luminous standard candles in the universe . since a part of the seambh agns and the cfhqs quasars have the same behaviors in the plots of @xmath0 versus @xmath2 , the cfhqs quasars likely have the potential to be the most luminous standard candles in the universe . this potential will extend the redshifts of the most luminous standard candles from @xmath153 up to @xmath92 , and will be important to study the universe because of extending significantly the cosmic distance beyond the range explored by type ia supernovae @xcite . an average column density of a cloud is @xmath154 ( @xmath120 and @xmath155@xmath156 ) . the electron thomson scattering optical depth of the cloud is @xmath157 , and the cloud is optically thin , which confirms the fourth assumption of the model . the ionizing optical depth of the cloud is @xmath158 , and the cloud is optically thick to the ionizing photons . the cloud has the strmgren radius smaller than its thickness . so , the cloud is partially ionized , confirming the first assumption of the model , and this is consistent with the constraints set by the reverberation mapping observations . the radiation pressure force ratio of the second to the first term in equation ( 3 ) has averages @xmath1596.3 for agns in table 1 . the first term of the free electron thomson scattering is comparable to the second term of the recombination and re - ionization of the hydrogen ions . the second term becomes more important as @xmath1 increases . the partly ionized clouds will be ionized more as @xmath34 increases , and the second term would be more important as the central engines become brighter . the radiation pressure forces due to absorption of ionizing photons and thomson scattering were used to modify the expression for the black hole virial mass @xmath2 ( see equation 5 in * ? ? ? * ) . as @xmath160@xmath161 , the modified @xmath2 becomes larger by a factor of @xmath162100 for the agns accreting around the eddington limit . in consequence , j0100 + 2802 at @xmath137 will have @xmath3 @xmath163@xmath164 that is nearly impossible to the eddington limit growth of black holes in the early universe because of the larger initial masses of primary black holes . if considering the line - driven radiation pressure force @xcite , the radiation pressure force due to the gas opacity will be @xmath165 times that due to the electron scattering opacity @xcite . this will bring a larger mass @xmath166 @xmath0 @xmath167@xmath168 for j0100 + 2802 . these extremely large corrected masses of the black hole in j0100 + 2802 indicate some problem of their treatments of the radiation pressure forces on the blr clouds in agns , or the model of formation and evolution of black hole , or the model of the universe . in this paper , we investigate the influences of two continuum radiation pressures , usually believed negligible or not considered , of the central engines in agns on the black hole mass estimates with the reverberation mapping method or the descendent methods . the continuum radiation pressure forces are from two origins : the free electron thomson scattering of the central radiation , and the recombination and re - ionization of the ionized hydrogen . the radiation pressures depend on a parameter @xmath1 , the ionized percent of the clouds in a blr . the counteracted black hole masses by the radiation pressures @xmath0 are compared to the black hole virial masses @xmath2 for 40 agns with the high accretion rates . the masses @xmath0 are sensitive to @xmath1 . as @xmath143 , @xmath7 for all the agns in figure 2 . as @xmath75 , the radiation pressures can counteract at least about 3040 percent gravitational forces of the black holes for some agns ( see figure 1 ) . four seambh agns at @xmath169 and five cfhqs quasars at @xmath170 are around the line @xmath171 for @xmath75 ( see figure 1a ) . thus , the continuum radiation pressures of the central engines have to be considered in estimating the black hole masses for the agns accreting around the eddington limit , regardless of the redshifts or the surrounding environments of agns . the most luminous quasar j0100 + 2802 likely has the same case as the nine agns ( see figures 1 and 2 ) . a part of the seambh agns and the cfhqs quasars is blended with the non - seambh and non - cfhqs agns ( see figures 1 and 2 ) . the close- and super - eddington limit accreting agns are not different from the rest of agns . the anisotropy of the central source luminosity could not influence significantly the main results assuming isotropy . the force multiplier , the ratio of gas opacity to electron scattering opacity @xcite , will be needed for the agns with @xmath7 due to the radiation pressures in equation ( 3 ) . though , some extremely large masses are derived from the force multiplier @xmath172 for the black hole in j0100 + 2802 ( @xmath173@xmath168 ) . in future , the force multiplier , due to the photoionization absorption , and the resonance and subordinate line absorption , could be calculated with the spectral simulation code cloudy described by @xcite , and with detailed parameters of the blr structure , the cloud distribution , the gas density of cloud , the chemical abundances of gas , the central continuum , and the observed emission lines , for each high accretion rate agns . thanks the national natural science foundation of china ( nsfc ; grants 11273052 and u1431228 ) for financial support . j.m.b . acknowledges the support of the nsfc ( grant 11133006 ) . thanks the financial supports of the youth innovation promotion association , cas and the project of the training programme for the talents of west light foundation , cas . mrk 335 & 0.026&@xmath174 & @xmath175 & 1 & @xmath176 & @xmath177 + pg 0026 + 129&0.142 & @xmath178 & @xmath179 & 1 & @xmath180 & @xmath181 + pg 0052 + 251&0.155 & @xmath182&@xmath183 & 1 & @xmath184 & @xmath185 + 3c 120 & 0.033&@xmath186&@xmath187 & 1 & @xmath188 & @xmath189 + pg 0844 + 349&0.064&@xmath190&@xmath191 & 1 & @xmath192 & @xmath193 + mrk 110 & 0.035&@xmath194&@xmath195 & 1 & @xmath196 & @xmath197 + pg 0953 + 414&0.234&@xmath198&@xmath199 & 1 & @xmath200 & @xmath201 + pg 1211 + 143&0.081&@xmath202&@xmath203 & 1 & @xmath204 & @xmath205 + pg 1226 + 023&0.158&@xmath206&@xmath207 & 1 & @xmath208 & @xmath209 + pg 1229 + 204&0.063&@xmath210&@xmath211 & 1 & @xmath212 & @xmath213 + ngc 4593 & 0.009 & @xmath214&@xmath215 & 1&@xmath216 & @xmath217 + pg 1307 + 085&0.155&@xmath218&@xmath219 & 1 & @xmath220 & @xmath221 + ic 4329a & 0.016&@xmath222&@xmath223 & 1 & @xmath224&@xmath225 + mrk 279 & 0.030&@xmath226&@xmath227 & 1 & @xmath228&@xmath229 + pg 1613 + 658&0.129 & @xmath230&@xmath231 & 1 & @xmath232 & @xmath233 + pg 1700 + 518&0.292&@xmath234&@xmath235 & 1 & @xmath236 & @xmath237 + ngc 7469 & 0.016 & @xmath238&@xmath239 & 1 & @xmath240 & @xmath241 + @xmath242mrk 335 & 0.026&@xmath243&@xmath244 & 2&@xmath245 & @xmath246 + mrk 1044 & 0.017 & @xmath247&@xmath248 & 2&@xmath249&@xmath250 + mrk 382 & 0.034&@xmath251&@xmath252 & 2&@xmath253&@xmath254 + mrk 142 & 0.045&@xmath255&@xmath256 & 2&@xmath257&@xmath258 + * iras f12397&0.043&@xmath259 & @xmath260 & 2&@xmath261&@xmath262 + mrk 486&0.039&@xmath263&@xmath264 & 2 & @xmath265&@xmath266 + mrk 493&0.031&@xmath267&@xmath268 & 2&@xmath269&@xmath270 + * iras 04416&0.089&@xmath271 & @xmath272 & 2&@xmath273&@xmath274 + sdss j075101&0.121&@xmath275&@xmath276 & 2&@xmath277&@xmath278 + * sdss j080101&0.140&@xmath279&@xmath280 & 2&@xmath281&@xmath282 + sdss j081441&0.163&@xmath283&@xmath284 & 2&@xmath285&@xmath286 + sdss j081456&0.120&@xmath287&@xmath288 & 2&@xmath289&@xmath290 + * sdss j093922&0.186&@xmath291&@xmath292 & 2&@xmath293&@xmath294 + * * * * * j0210 - 0456 & 6.438 & @xmath295@xmath296 & @xmath297 & 3 & @xmath298 & @xmath299 + j2329 - 0301 & 6.417 & @xmath300@xmath296 & @xmath301 & 3 & @xmath302 & @xmath303 + j0050 + 3445 & 6.253 & @xmath304@xmath296&@xmath305 & 3 & @xmath306 & @xmath307 + j0221 - 0802 & 6.161 & @xmath308@xmath296&@xmath309 & 3 & @xmath310 & @xmath311 + * j2229 + 1457 & 6.152 & @xmath312@xmath296&@xmath313 & 3 & @xmath314 & @xmath315 + j1509 - 1749 & 6.121 & @xmath316@xmath296 & @xmath317 & 3 & @xmath318 & @xmath319 + j2100 - 1715 & 6.087 & @xmath320@xmath296 & @xmath321 & 3 & @xmath322 & @xmath323 + * j1641 + 3755 & 6.047 & @xmath324@xmath296 & @xmath325 & 3 & @xmath326 & @xmath327 + j0055 + 0146 & 5.983 & @xmath328@xmath296&@xmath329 & 3 & @xmath330 & @xmath331 + * * *

in this paper , we investigate the influences of two continuum radiation pressures of the central engines on the black hole mass estimates for 40 active galactic nuclei ( agns ) with high accretion rates . the masses counteracted by the two radiation pressures @xmath0 depend sensitively on the percent of ionized hydrogen in the clouds @xmath1 , and are not ignorable compared to the black hole virial masses @xmath2 , estimated from the reverberation mapping method , for these agns . as @xmath1 increases , @xmath0 also does . the black hole masses @xmath3 could be underestimated at least by a factor of 3040 percent for some agns accreting around the eddington limit , regardless of redshifts of sources @xmath4 . some agns at @xmath5 and quasars at @xmath6 have the same behaviors in the plots of @xmath0 versus @xmath2 . the complete radiation pressures will be added as agns match @xmath7 due to the two continuum radiation pressures . compared to @xmath2 , @xmath3 might be extremely underestimated if considering the complete radiation pressures for the agns accreting around the eddington limit .

in this paper , we investigate the influences of two continuum radiation pressures of the central engines on the black hole mass estimates for 40 active galactic nuclei ( agns ) with high accretion rates . the continuum radiation pressure forces , usually believed negligible or not considered , are from two sources : the free electron thomson scattering , and the recombination and re - ionization of hydrogen ions that continue to absorb ionizing photons to compensate for the recombination . the masses counteracted by the two radiation pressures @xmath0 depend sensitively on the percent of ionized hydrogen in the clouds @xmath1 , and are not ignorable compared to the black hole virial masses @xmath2 , estimated from the reverberation mapping method , for these agns . as @xmath1 increases , @xmath0 also does . the black hole masses @xmath3 could be underestimated at least by a factor of 3040 percent for some agns accreting around the eddington limit , regardless of redshifts of sources @xmath4 . some agns at @xmath5 and quasars at @xmath6 have the same behaviors in the plots of @xmath0 versus @xmath2 . the complete radiation pressures will be added as agns match @xmath7 due to the two continuum radiation pressures . compared to @xmath2 , @xmath3 might be extremely underestimated if considering the complete radiation pressures for the agns accreting around the eddington limit .

1504.06805

c

in this paper unlike the analytical solutions for anisotropic matter such as ref . @xcite and ref . @xcite we have used numerical result of isotropic solution and a gaussian perturbation rather than using a totally assumed function . in the following subsections we will discuss the result of adding anisotropy and electric charge to tov equations . our solution indicate that adding positive gaussian anisotropy and electric charge to tov equation increase the maximum mass of neutron star and can predict more massive neutron stars in agreement with ref . @xcite . solving modified tov equation reveals that adding electric charge makes the radial pressure @xmath48 to be increased , as we can see in fig . [ fig : p_re ] . but the sensitivity of tangential pressure @xmath68 to the electric charge is much more , so @xmath6 raises up in charged case as is apparent from fig . [ fig : deltae ] . this behavior is not only the direct result of our speculation about @xmath48 , but also comes from the nature of tov equation . [ fig : mmaxe ] and fig . [ fig : piche ] refer to uncharged and charged isotropic cases . one may expect adding electric charge to tov equation causes an increase in the maximum mass of strange quark star @xmath0 and also in the corresponding radius @xmath1 for obtained @xmath0 . since in gr gravitational mass of star and total energy are proportional , adding charge density @xmath40 increases the total energy and therefore the above result makes sense . however , electrical neutrality condition of stars does not allow a significant growth in maximum masses and their corresponding radii . it is shown in fig . [ fig : mmax ] and fig . [ fig : pich ] that the maximum mass of strange quark star has been raised by adding gaussian perturbation for obtaining @xmath48 . furthermore , according to fig . [ fig : deltae ] the tangential pressure @xmath5 and anisotropy @xmath6 have a maximum and they do not vanish on the surface . in fact our solution indicate that if there is an anisotropy in the star , it should be maximum on the surface . + recent measurements indicate that there exist a pulsar of mass 1.97 @xmath69 0.04 @xmath4 and this mass rules out nearly all currently proposed equations of state@xcite . we have used a trial and error method to get the mentioned mass above . our calculations indicate that an anisotropy amplitude of @xmath2 with a standard deviation of @xmath3 and @xmath70 in eq . ( [ gaussian ] ) can survive sqm equation of state which satisfies boundary and hydrostatic equilibrium conditions by @xmath71 and @xmath72 uncertainties at the origin and on the surface respectively as is depicted in fig . [ fig : p_re ] . for various cases : isotropic uncharged , isotropic charged , and anisotropic uncharged matter with @xmath73 @xmath62 , @xmath2 , @xmath3 and @xmath70 versus radial coordinate @xmath27 , all having the same central density of @xmath74 @xmath30.,title="fig : " ] + for anisotropic charged and uncharged matter with @xmath73 @xmath62 versus radial coordinate @xmath27 with a same central density @xmath74 @xmath30.,title="fig : " ] + in two cases : uncharged ( solid curve ) and charged isotropic ( dashed curve ) matter . , title="fig : " ] + + for uncharged isotropic ( solid curve ) and uncharged anisotropic ( dashed curve ) matter.,title="fig : " ] + +

in this paper for studying the anisotropic strange quark stars , we assume that the radial pressure inside the anisotropic star is a superposition of pressure in an isotropic case plus a gaussian perturbation term . considering a proportionality between electric charge density and the density of matter our results indicate that anisotropy increases the maximum mass @xmath0 and also its corresponding radius @xmath1 for a typical strange quark star . according to our calculations , an anisotropy amplitude of @xmath2 with a standard deviation of @xmath3 leads to a neutron star of 1.97@xmath4 . furthermore , electric charge not only increases the maximum mass and its corresponding radius , but also raises up the anisotropy factor . we can see that the tangential pressure @xmath5 and anisotropy factor @xmath6 unlike the radial pressure @xmath7 have a maximum on the surface and this maximum increases by adding electric charge effect . however , we show that anisotropy can be more effective than electric charge in rasing maximum mass of strange quark stars .

in this paper for studying the anisotropic strange quark stars , we assume that the radial pressure inside the anisotropic star is a superposition of pressure in an isotropic case plus a gaussian perturbation term . considering a proportionality between electric charge density and the density of matter , we solve the tov equation for different cases numerically . our results indicate that anisotropy increases the maximum mass @xmath0 and also its corresponding radius @xmath1 for a typical strange quark star . according to our calculations , an anisotropy amplitude of @xmath2 with a standard deviation of @xmath3 leads to a neutron star of 1.97@xmath4 . furthermore , electric charge not only increases the maximum mass and its corresponding radius , but also raises up the anisotropy factor . we can see that the tangential pressure @xmath5 and anisotropy factor @xmath6 unlike the radial pressure @xmath7 have a maximum on the surface and this maximum increases by adding electric charge effect . however , we show that anisotropy can be more effective than electric charge in rasing maximum mass of strange quark stars .

1507.07719

i

it is widely acknowledged that theoretical research and applications development evolve at different speeds , driven by different aims . research theory investigates new problems and new ideas , taking its time to study different solutions that tackle problems from different points of view . it often happens that while deeply studying one of these solutions , new ideas or entirely new problems emerge , opening the way to entirely new ( sub)theories . the development of applications , instead , is much more oriented towards effective solutions . moreover , the choice between different solutions is often dictated by technology constraints or market constraints such as cost - effectiveness and rapid productivity . the ( relative ) low speed and the wide scope of the theory often result in a ( relative ) lack of integration of results . the theoretical outcomes of research are so abundant that their integration and assimilation is quite hard . nevertheless , incorporating different results under a unifying or coherent view , both formally and epistemologically , would be of great help for the progress of the knowledge . on the other hand , the speedy development of application solutions tends to miss the opportunities offered by theoretical results that have been already established but not yet fully applied . while the percolation of theoretical results into applications intrinsically requires some time , it is helpful to remind taking a look from theory towards applications and from applications to theory every so often . this paper is then written in this spirit . we examine the history of popular programming languages to expose how concurrency has been incorporated into the mainstream programming . this excursus is not meant to be a survey of concurrent languages ; it would be very incomplete in that sense . we aim instead at identifying a number of historical landmarks and crucial concepts that shaped the development of programming languages . moreover , rather than fully describing these major points , we focus on their connection under an evolutionary perspective , using the biological theory of evolution as an instructive metaphor . we then borrow the evolutionary talking from biology , using it as an explanatory tool to more deeply reflect on some concepts and to stimulate the development of meta - knowledge about the history of programming languages . [ [ structure - of - the - paper ] ] structure of the paper + + + + + + + + + + + + + + + + + + + + + + in section 2 we start our excursus of the history of popular programming languages from an evolutionary perspective . we first examine the general development process , and we then deep into some language , trying to uncover evolutionary lineages related to specific programming traits . in section 3 we consider concurrency abstractions : we put forward three different concurrency models used in mainstream programming , emphasizing the fact that they correspond to three different levels of explanation . the evolutionary excursus is then completed in section 4 with a discussion of the impact of the clouds and big data technologies in programming languages . in section 5 we discuss the role of the theoretical research in the evolutionary scenario , putting forward its ability of promoting and testing language mutations . we conclude in section 6 with final comments .

in this paper we examine how concurrency has been embodied in mainstream programming languages . in particular , we rely on the evolutionary talking borrowed from biology to discuss major historical landmarks and crucial concepts that shaped the development of programming languages . we examine the general development process , occasionally deepening into some language , trying to uncover evolutionary lineages related to specific programming traits . we mainly focus on concurrency , discussing the different abstraction levels involved in present - day concurrent programming and emphasizing the fact that they correspond to different levels of explanation . this paper is not meant to be a survey of modern mainstream programming languages : it would be very incomplete in that sense . it aims instead at pointing out a number of remarks and connect them under an evolutionary perspective , in order to grasp a unifying , but not simplistic , view of the programming languages development process .

in this paper we examine how concurrency has been embodied in mainstream programming languages . in particular , we rely on the evolutionary talking borrowed from biology to discuss major historical landmarks and crucial concepts that shaped the development of programming languages . we examine the general development process , occasionally deepening into some language , trying to uncover evolutionary lineages related to specific programming traits . we mainly focus on concurrency , discussing the different abstraction levels involved in present - day concurrent programming and emphasizing the fact that they correspond to different levels of explanation . we then comment on the role of theoretical research on the quest for suitable programming abstractions , recalling the importance of changing the working framework and the way of looking every so often . this paper is not meant to be a survey of modern mainstream programming languages : it would be very incomplete in that sense . it aims instead at pointing out a number of remarks and connect them under an evolutionary perspective , in order to grasp a unifying , but not simplistic , view of the programming languages development process .

0901.4160

i

in this paper we study asymptotic properties of certain extremal sequences of points defined on locally compact metric spaces . we shall refer to them as _ greedy energy sequences_. this terminology was recently introduced in @xcite . these sequences are indeed generated by means of a greedy algorithm at every step of which a certain energy expression is minimized . the notion of energy that we refer to will be specified shortly . the asymptotic properties that we analyze are mainly the following : if @xmath18 denotes the sequence of configurations formed by the first @xmath19 points of a greedy energy sequence , we use potential - theoretic tools to study the behavior of the energy of @xmath20 as @xmath19 approaches infinity and the limiting distributions of these configurations . we remark that in @xcite a number of results about greedy sequences were obtained in a context in which potential theory is no longer applicable . potential theory on locally compact hausdorff ( lch ) spaces is a classical field which was developed , among others , by choquet @xcite , fuglede @xcite and ohtsuka @xcite . in recent years , and also in the context of lch spaces , zorii @xcite has studied solvability properties of the gauss variational problem in the presence of an external field . a similar problem ( we shall also call it gauss variational problem ) is considered below . we next introduce the basic notions necessary to describe our results . let @xmath21 denote a locally compact metric space containing infinitely many points . if @xmath21 is not compact , let @xmath22 denote the one - point compactification of @xmath21 . a _ kernel _ in @xmath21 is , by definition , a lower semicontinuous function ( l.s.c . ) it is called _ positive _ if @xmath24 for all @xmath25 . assume that @xmath26 is a l.s.c . function . for a set @xmath27 of @xmath19 ( @xmath28 ) points in @xmath21 which are not necessarily distinct , we write @xmath29 and define the _ energy _ of @xmath30 by @xmath31 whereas the _ weighted energy _ of @xmath32 is given by @xmath33 in potential theory the function @xmath6 is usually referred to as an _ external field_. if the kernel is _ symmetric _ , i.e. , @xmath34 for all @xmath25 , we may also write @xmath35 for a non - empty set @xmath36 , the _ weighted @xmath19-point energy _ of @xmath5 is given by @xmath37 in case that @xmath38 , we use instead the notation @xmath39 we say that @xmath40 is an _ optimal weighted @xmath19-point configuration _ on @xmath5 if @xmath41 if @xmath5 is compact , the existence of @xmath42 follows from the lower semicontinuity of @xmath43 and @xmath6 . it is necessary to introduce now the continuous counterparts of the above notions . let @xmath44 denote the linear space of all real - valued radon measures that are compactly supported on @xmath36 , and let @xmath45 given a measure @xmath46 , the _ energy _ of @xmath47 is the double integral @xmath48 whereas the function @xmath49 is called the _ potential _ of @xmath47 . the _ weighted energy _ of @xmath47 is defined by @xmath50 since any l.s.c . function is bounded below on compact sets , the above integrals are well - defined , although they may attain the value @xmath51 . the quantity @xmath52 is called the _ wiener energy _ of @xmath5 , and plays an important role in potential theory . the _ capacity _ of @xmath5 is defined as @xmath53@xmath54 if @xmath43 is positive , and otherwise , it is defined as @xmath53@xmath55 . a property is said to hold _ quasi - everywhere _ ( q.e . ) , if the exceptional set has wiener energy @xmath51 . given a net @xmath56 , we say that @xmath57 converges in the _ weak - star topology _ to a measure @xmath58 when @xmath59 where @xmath60 denotes the space of compactly supported continuous functions on @xmath5 . we will use the notation @xmath61 to denote the weak - star convergence of measures . if @xmath62 , a measure @xmath63 satisfying the property @xmath64 is called an _ equilibrium measure_. if @xmath5 is compact , the existence of such a measure is guaranteed by the lower semicontinuity of @xmath43 and the compactness of @xmath65 equipped with the weak - star topology ( cf . * theorem 2.3 ) ) . however , uniqueness does not always hold . the following result is due to g. choquet @xcite , and it is central in this theory . [ choquettheo ] let @xmath43 be an arbitrary kernel and @xmath36 be a compact set . if @xmath66 is a sequence of optimal @xmath19-point configurations on @xmath5 , then @xmath67 the following variation of theorem [ choquettheo ] was obtained by b. farkas and b. nagy @xcite . [ fntheo ] assume that the kernel @xmath43 is positive and is finite on the diagonal , i.e. , @xmath68 for all @xmath69 . then for arbitrary sets @xmath36 , @xmath70 where @xmath71 is defined by @xmath72 . we remark that theorems [ choquettheo ] and [ fntheo ] were proved in the context of lch spaces , but for the sake of uniformity we always assume , unless otherwise stated , that @xmath21 denotes a locally compact metric space . in this paper we are interested in the so - called _ gauss variational problem _ in the presence of an external field @xmath6 . in what follows we assume that @xmath36 is a closed set , and we will refer to @xmath5 as the _ conductor_. the gauss v.p . consists of finding a solution to the minimization problem @xmath73 where @xmath74 denotes the class of measures @xmath75 throughout the rest of the paper we will denote @xmath76 simply as @xmath77 . if @xmath78 then by definition @xmath79 . if @xmath80 and there exists a minimizing measure @xmath81 satisfying @xmath82 , we call @xmath47 an _ equilibrium measure in the presence of the external field _ @xmath6 . in this case we say that the gauss variational problem is _ solvable _ , and observe that @xmath77 is finite . sufficient conditions for the existence and uniqueness of solution for a similar variational problem were provided by n. zorii ( see @xcite ) in the more general context of lch spaces . she assumes that the kernel is positive if @xmath5 is not compact , and allows measures to have non - compact support in this case . we remark that the theory of logarithmic potentials ( @xmath83 for an equilibrium measure @xmath81 . this value is finite . the _ essential support _ of @xmath47 is defined as @xmath84 using lemma 2.3.3 from @xcite and the argument employed in @xcite to prove parts @xmath85 and @xmath86 of theorem i.1.3 , it is easy to see that if @xmath43 is a symmetric kernel and @xmath81 is an equilibrium measure , then @xmath87 holds for all @xmath88 ( i.e. @xmath89 ) and @xmath90 holds q.e . on @xmath5 . we are ready to introduce the following definitions ( see also definitions @xmath91 and @xmath92 in section [ statement ] ) . [ defngreedyprimera ] let @xmath93 be a symmetric kernel on a locally compact metric space @xmath21 , @xmath94 be a closed set , and @xmath95 be an external field . if @xmath21 is not compact , we assume that @xmath6 satisfies the following ` growth ' condition at infinity : for each compactly supported probability measure @xmath96 , @xmath97 ( i.e. given @xmath98 , there exists a compact set @xmath99 such that @xmath100 for all @xmath101 ) . assume that the gauss variational problem is solvable and @xmath81 is an equilibrium measure . a sequence @xmath102 is called a _ weighted greedy @xmath103-energy sequence _ on @xmath5 if it is generated in the following way : * @xmath104 is selected arbitrarily on @xmath105 . * for every @xmath106 , assuming that @xmath107 have been selected , @xmath108 is chosen so that @xmath109 and @xmath110 the set formed by the first @xmath19 points of this sequence is denoted by @xmath111 . we also introduce the following associated function : @xmath112 condition @xmath113 implies in particular that @xmath105 is compact . consequently , for every @xmath106 , the existence of @xmath108 is guaranteed by the lower semicontinuity of @xmath43 and @xmath6 . however , @xmath108 may not be unique . in many practical circumstances it is not possible to determine the support or essential support of an equilibrium measure . for this reason it is of interest to introduce the following : [ defngreedypointsclosed ] let @xmath93 be a symmetric kernel on a locally compact metric space @xmath21 , @xmath94 be a closed set , and @xmath95 be an external field . in case it exists , a sequence @xmath114 is called a _ weighted greedy @xmath6-energy sequence _ on @xmath5 if it is constructed inductively by selecting @xmath104 arbitrarily on @xmath5 such that @xmath115 , and @xmath108 as in @xmath116 but taking the infimum on @xmath5 . we use the notation @xmath117 to indicate the configuration formed by the first @xmath19 points of this sequence . it seems that a. edrei was the first to study in @xcite properties of the configurations @xmath117 under the assumptions @xmath118 , @xmath119 is compact , @xmath120 and @xmath38 . however , in the literature these configurations are often called _ leja points _ in recognition of leja s article @xcite . a very important class of kernels is the so - called _ m. riesz kernels _ in @xmath121 , which depend on a parameter @xmath122 . it is defined as follows : @xmath123 where @xmath124 denotes the euclidean norm and @xmath125 we shall use the notations @xmath126 , @xmath127 and @xmath128 to denote , respectively , the energy ( [ definicionenergia ] ) , weighted energy ( [ defweightedenergy ] ) and potential ( [ defnpotential ] ) of a measure @xmath129 with respect to the riesz @xmath130-kernel . we will also use the symbols @xmath131 and @xmath53@xmath132 to denote the wiener @xmath130-energy and @xmath130-capacity of a set @xmath2 in this setting . the paper is organized as follows . in section [ statement ] we present our results and in section [ proofs ] we provide their proofs . in section [ numerical ] we present some numerical computations .

in this paper we introduce several extremal sequences of points on locally compact metric spaces and study their asymptotic properties . these sequences are defined through a greedy algorithm by minimizing a certain energy functional whose expression involves an external field . we assume here that @xmath17 . an extension of a result due to g. choquet concerning point configurations with minimal energy is obtained in the context of locally compact metric spaces and constitutes a key ingredient in our analysis .

in this paper we introduce several extremal sequences of points on locally compact metric spaces and study their asymptotic properties . these sequences are defined through a greedy algorithm by minimizing a certain energy functional whose expression involves an external field . some results are also obtained in the context of euclidian spaces @xmath0 , @xmath1 . as a particular example , given a closed set @xmath2 , a lower semicontinuous function @xmath3 $ ] and an integer @xmath4 , we investigate ( under suitable conditions on @xmath5 and @xmath6 ) sequences @xmath7 that are constructed inductively by selecting the first @xmath8 points @xmath9 so that the functional @xmath10 attains its minimum on @xmath11 for @xmath12 , @xmath13 , and for every integer @xmath14 , the points @xmath15 are chosen to minimize the expression @xmath16 on @xmath11 . we assume here that @xmath17 . an extension of a result due to g. choquet concerning point configurations with minimal energy is obtained in the context of locally compact metric spaces and constitutes a key ingredient in our analysis .

0901.4160

r

our first result is the following generalization of theorem [ choquettheo ] . [ primer ] let @xmath93 be an arbitrary kernel on a locally compact metric space @xmath21 , @xmath94 be a compact conductor , and @xmath95 be an external field . assume that the gauss variational problem is solvable . if @xmath66 is a sequence of optimal weighted @xmath19-point configurations on @xmath5 , then @xmath133 furthermore , if the gauss variational problem has a unique solution @xmath81 , then @xmath134 where @xmath135 is the unit dirac measure concentrated at @xmath136 . as the proof of theorem [ primer ] shows , without assuming the uniqueness of the equilibrium measure one can deduce that any convergent subsequence of @xmath137 converges weak - star to an equilibrium measure . this observation is also applicable to the following result concerning greedy configurations . [ theoexternalgreedy ] let @xmath93 be a symmetric kernel on a locally compact metric space @xmath21 , @xmath94 be a closed set , and @xmath95 be an external field satisfying @xmath113 in case that @xmath21 is not compact . assume that the gauss variational problem is solvable and @xmath81 is a solution . let @xmath138 be a weighted greedy @xmath103-energy sequence on @xmath5 . then * the following limit @xmath139 holds . * if the equilibrium measure @xmath81 is unique , it follows that @xmath140 @xmath141 where @xmath142 is the @xmath143-th element of the weighted greedy @xmath103-energy sequence . conditions ( [ asympweight])-([eq29 ] ) are related in the following way . [ relationconditions ] let @xmath144 be a real - valued symmetric kernel on a locally compact metric space @xmath21 , @xmath94 be a closed set , and @xmath95 be an external field . assume that the gauss variational problem is solvable and @xmath81 is a solution . suppose that @xmath145 is a sequence of points such that @xmath146 and set @xmath147 if the following limit @xmath148 holds , then @xmath149 theorem [ theoexternalgreedy ] can be extended to the following class of weighted greedy sequences . [ defngreedyprimera2 ] let @xmath4 be a fixed integer . under the same assumptions of definition [ defngreedyprimera ] , suppose that the gauss variational problem is solvable and @xmath81 is an equilibrium measure . a sequence @xmath150 is called a _ weighted greedy @xmath151-energy sequence _ on @xmath5 if it is generated inductively in the following way : * the first @xmath8 points @xmath9 are selected so that @xmath152 is an optimal weighted @xmath8-point configuration on @xmath105 , i.e. @xmath153 for all @xmath154 . * assuming that @xmath155 have been selected , where @xmath14 is an integer , the next set of @xmath8 points @xmath156 are chosen to minimize the energy functional @xmath157 on @xmath158 . for every @xmath159 , the subindices @xmath160 are assigned to the points @xmath15 in an arbitrary order . let @xmath161 denote the configuration formed by the first @xmath162 points of this sequence . in analogy to definition [ defngreedypointsclosed ] , we also introduce the following : [ defngreedypointsclosed2 ] under the same assumptions of definition [ defngreedypointsclosed ] , given an integer @xmath4 , a sequence @xmath163 ( in case it exists ) is called a _ weighted greedy @xmath164-energy sequence _ on @xmath5 if it is obtained inductively as in @xmath165 and @xmath166 but the minimization is taken on @xmath5 . with @xmath167 we denote the configuration @xmath168 . the following result is analogous to theorem [ theoexternalgreedy ] . [ theogreedygeneral ] let @xmath4 . under the same assumptions of theorem @xmath169 , assume that @xmath170 is a weighted greedy @xmath151-energy sequence on @xmath5 , where @xmath81 is an equilibrium measure solving the gauss variational problem . then * the following limit @xmath171 holds . * if the equilibrium measure @xmath81 is unique , it follows that @xmath172 @xmath173 where @xmath174 is the @xmath175-th element of the weighted greedy @xmath151-energy sequence . it is easy to see that @xmath176 implies that @xmath177 let @xmath1 and consider the riesz @xmath130-kernel @xmath178 in @xmath0 ( see @xmath179 ) for @xmath180 . assume that @xmath181 is a closed set and @xmath6 is an external field satisfying the following properties : @xmath182 @xmath183 using the same arguments employed to prove theorem i.1.3 in @xcite ( which concerns the case @xmath184 and @xmath185 ) and the fact that @xmath178 is positive definite ( see ( * ? ? ? * theorem 1.15 ) ) , it is not difficult to see that the gauss variational problem on @xmath5 in the presence of @xmath6 has a unique solution @xmath186 . furthermore , the inequality @xmath187 is valid for all @xmath188 , where @xmath189 denotes the minimal energy constant @xmath190 , and @xmath191 holds q.e . on @xmath5 ( relative to the @xmath130-capacity of sets ) . we remark that if @xmath184 and @xmath185 then these properties hold if @xmath192 is replaced by the condition @xmath193 the following result holds . [ lemanbw ] let @xmath1 and @xmath194 . assume that @xmath2 is closed and @xmath6 satisfies the conditions @xmath195 and @xmath192 @xmath196or @xmath197 in the case @xmath184 , @xmath185@xmath198 . let @xmath199 be the equilibrium measure solving the gauss variational problem on @xmath5 in the presence of @xmath6 . if @xmath200 is an arbitrary collection of points and @xmath201 then for all @xmath202 , @xmath203 where @xmath204 is defined in @xmath205 and @xmath206 is the potential associated to @xmath207 . moreover , @xmath208 implies that @xmath209 the case @xmath184 , @xmath185 of lemma [ lemanbw ] ( the logarithmic kernel is employed in this case ) is known as the _ generalized bernstein - walsh lemma _ and was proved by h. mhaskar and e. saff in @xcite . [ corolario ] assume that all the assumptions of lemma @xmath210 hold . let @xmath211 be a weighted greedy @xmath6-energy sequence on @xmath5 constructed using the riesz kernel @xmath178 for @xmath17 . then this sequence is well - defined and @xmath212 for all @xmath213 . moreover , all the asymptotic properties in theorem @xmath169 are applicable to this sequence @xmath196replacing @xmath111 by @xmath214 and @xmath47 by @xmath207@xmath198 . [ corolario2 ] let @xmath4 and assume that all the assumptions of lemma @xmath210 hold . let @xmath215 be a weighted greedy @xmath164-energy sequence on @xmath5 obtained using the riesz kernel @xmath178 for @xmath17 . then this sequence is well - defined and @xmath216 for all @xmath106 . furthermore , all the asymptotic properties in theorem @xmath217 are applicable to this sequence @xmath196replacing @xmath161 by @xmath218 and @xmath47 by @xmath207@xmath198 . we remark that the problem of finding an explicit representation of the solution of a gauss variational problem in @xmath0 is a difficult task in general . however , there are certain assumptions on @xmath6 that could alleviate the difficulty of this problem , as the following result shows in the case of newtonian potentials . [ propcircweight ] let @xmath219 and @xmath220 . assume that @xmath6 is a radially symmetric function @xmath196i.e . @xmath221 for all @xmath222@xmath198 satisfying @xmath192 . assume further that , as a function of @xmath223 , @xmath6 has an absolutely continuous derivative and obeys one of the following conditions : * @xmath224 is increasing on @xmath225 ; * @xmath6 is convex on @xmath225 . let @xmath226 be the smallest number for which @xmath227 for all @xmath228 , and let @xmath229 be the smallest solution of @xmath230 @xmath196it is easy to see that @xmath231 and @xmath229 is finite@xmath198 . if @xmath232 is the solution of the gauss variational problem on @xmath233 with @xmath6 as the external field , then @xmath234 and @xmath232 is given by @xmath235 where @xmath236 denotes the normalized surface area measure of the unit sphere @xmath237 @xmath238 in @xmath0 . moreover , @xmath239 and @xmath240 the case @xmath184 , @xmath185 was analyzed by mhaskar and saff in @xcite ( see example 3.2 of that paper ) . see also @xcite .

some results are also obtained in the context of euclidian spaces @xmath0 , @xmath1 . as a particular example , given a closed set @xmath2 , a lower semicontinuous function @xmath3 $ ] and an integer @xmath4 , we investigate ( under suitable conditions on @xmath5 and @xmath6 ) sequences @xmath7 that are constructed inductively by selecting the first @xmath8 points @xmath9 so that the functional @xmath10 attains its minimum on @xmath11 for @xmath12 , @xmath13 , and for every integer @xmath14 , the points @xmath15 are chosen to minimize the expression @xmath16 on @xmath11 .

in this paper we introduce several extremal sequences of points on locally compact metric spaces and study their asymptotic properties . these sequences are defined through a greedy algorithm by minimizing a certain energy functional whose expression involves an external field . some results are also obtained in the context of euclidian spaces @xmath0 , @xmath1 . as a particular example , given a closed set @xmath2 , a lower semicontinuous function @xmath3 $ ] and an integer @xmath4 , we investigate ( under suitable conditions on @xmath5 and @xmath6 ) sequences @xmath7 that are constructed inductively by selecting the first @xmath8 points @xmath9 so that the functional @xmath10 attains its minimum on @xmath11 for @xmath12 , @xmath13 , and for every integer @xmath14 , the points @xmath15 are chosen to minimize the expression @xmath16 on @xmath11 . we assume here that @xmath17 . an extension of a result due to g. choquet concerning point configurations with minimal energy is obtained in the context of locally compact metric spaces and constitutes a key ingredient in our analysis .

0809.3187

i

the purpose of this paper is to present a novel approach for efficient estimation via the monte carlo ( mc ) method . the approach is very broadly applicable but here , to present the main ideas , we narrow the focus to ensemble monte carlo where estimation is based on stochastically independent trajectories of a system . to illustrate , we use simulation of time - dependent nonlinear processes for which monte carlo is a particularly general and powerful numerical method compared to available alternatives . time - dependent nonlinear processes are very general models used , among others , in statistical mechanics @xcite , data assimilation in climate , weather and ocean modeling @xcite , financial modeling @xcite , and quantitative biology @xcite . hence developing efficient mc methods may significantly impact a wide range of applications . a known weakness of mc is its slow rate of convergence . assume @xmath0 is a random quantity defined on paths of a process and let @xmath1 denote its standard deviation . the convergence rate of mc for estimating the expected value of @xmath0 is @xmath2 where @xmath3 is the number of independent paths of the process . in general the canonical @xmath4 rate of convergence can not be improved upon , hence , since the inception of the mc method , a number of variance reduction ( vr ) techniques have been devised to reduce @xmath1 ( see , @xcite for an early account and @xcite and @xcite for more recent discussions ) . most vr techniques lead to estimators of the form @xmath5 i.e. , a weighted average of the samples . these techniques prescribe ( i ) a recipe for selecting samples @xmath6 and ( ii ) a set of weights @xmath7 . to arrive at these prescriptions , one must rely on the existence of specific problem features and the ability of the user of the method to discover and effectively exploit such features . this lack of generality has significantly limited the applicability of vr techniques . the point of departure of a new strategy , called database monte carlo ( dbmc ) , is to address this shortcoming and to devise generic vr techniques that can be generically applied @xcite . all vr techniques bring additional information to bear on the estimation problem , however , as mentioned above , this information is problem specific and relies on exploiting special features of the problem at hand . by contrast , as will be clarified in this paper , dbmc adds a generic computational exploration phase to the estimation problem that relies on gathering information at one ( or more ) nominal model parameter(s ) to achieve estimation efficiency at neighboring parameters . the advantage of this approach is its generality and wide applicability : it is quite easy to implement and it can wrap existing ensemble mc codes . on the other hand , the computational exploration phase of the dbmc approach may require extensive simulations and can be computationally costly . therefore , the initial setup cost needs justification . the setup cost may be justified in projects that involve estimations at many model parameters and/or in projects where there is a real - time computational constraint . in the first type of project , the setup cost may lead to efficiency gain for each subsequent estimation , and for a large enough number of subsequent estimations it can be easily justified . in projects with a real - time constraint the setup cost is an off - line `` passive '' cost that can lead to estimates of significantly higher quality ( lower statistical error ) ; the higher quality in many such projects more than justifies the setup cost . in this paper we limit ourselves to presenting the implementation of the vr technique of control variates ( cv ) in the dbmc setting ( see @xcite for discussion of other vr techniques ) . the cv technique , which compared to the vr technique of importance sampling is less utilized in computational physics , requires identifying a number of random variables called _ control variates _ , say @xmath8 , that are correlated with @xmath0 and have _ known _ means . the correlation with @xmath0 implies that @xmath9 s carry information about @xmath0 . the cv technique is a way of utilizing the information included in the controls ( their known means ) to help with the estimation of the mean of variable @xmath0 . in the dbmc setting we assume that @xmath10 depends on a model parameter @xmath11 and use @xmath12 where @xmath13 s are in a neighborhood of @xmath11 ( @xmath14 ) . in a departure from the classical cv technique , we use `` high quality '' estimates of @xmath15 $ ] rather than precise values of @xmath15 $ ] to arrive at the controlled estimator of @xmath16 $ ] . as we argue in this paper ( and elsewhere @xcite ) this departure allows for substantially broader choices of control variates and makes the cv technique significantly more flexible and effective . the dbmc method shares a similar intent as the well - known histogram reweighing method @xcite from the markov chain monte carlo literature ( e.g. @xcite ) , but with a very different setting and implementation , and with broader applicability . for example , it does not rely on having a boltzmann distribution or @xmath17 structure . given its generality , it has potential applications , among others , in ensemble weather prediction , hydrological source location , climate and ocean , optimal control , and stochastic simulations of biological systems . the remainder of the paper is organized as follows . in section [ prel ] we discuss preliminaries , including the details of the example numerical study the time - dependent ginzburg - landau ( tdgl ) equation as well as the method of control variates . estimation of mean outcomes of the tdgl equation over a range of temperatures is of interest , especially considering the large difference in behavior below and above the coexistence curve . in section [ methods ] we describe the dbmc methodology and motivation in a general context . section [ numerical ] discusses the implementation and results of dbmc as applied to estimation of quantities generated by the tdgl equation , and the results of that numerical study . we conclude in section [ conclusions ] .

we present the approach using simulation of paths of a time - dependent nonlinear stochastic equation . the core idea is to extract information at one or more nominal model parameters and use this information to gain estimation efficiency at neighboring parameters . we describe how this strategy can be implemented using the variance reduction technique of control variates ( cv ) . the initial setup cost is justified in projects that require a large number of estimations or in those that are to be performed under real - time constraints .

in this paper we present a new approach to control variates for improving computational efficiency of ensemble monte carlo . we present the approach using simulation of paths of a time - dependent nonlinear stochastic equation . the core idea is to extract information at one or more nominal model parameters and use this information to gain estimation efficiency at neighboring parameters . this idea is the basis of a general strategy , called database monte carlo ( dbmc ) , for improving efficiency of monte carlo . in this paper we describe how this strategy can be implemented using the variance reduction technique of control variates ( cv ) . we show that , once an initial setup cost for extracting information is incurred , this approach can lead to significant gains in computational efficiency . the initial setup cost is justified in projects that require a large number of estimations or in those that are to be performed under real - time constraints . monte carlo , variance reduction , control variates s05.10.ln , 02.70.uu , 02.70.tt

0809.3187

c

in this paper we described a new strategy , database monte carlo ( dbmc ) , for improving computational efficiency of ensemble monte carlo . for a specific time - dependent nonlinear dynamics we showed that the approach can lead to significant efficiency gains for a range of estimation problems . our selection of the controls has been ad - hoc and for illustration purposes . further work is required to better understand the options available and the computational tradeoffs involved . to this end , our current research is focused on ( i ) derivation of more specific guidelines for the selection of effective control variates , ( ii ) implementation of the dbmc strategy in conjunction with other variance reduction techniques , for example , stratification and importance sampling , and ( iii ) application of the method in some specific domains , for example , estimation problems in geophysical fluids and biochemical systems .

in this paper we present a new approach to control variates for improving computational efficiency of ensemble monte carlo . this idea is the basis of a general strategy , called database monte carlo ( dbmc ) , for improving efficiency of monte carlo . in this paper we show that , once an initial setup cost for extracting information is incurred , this approach can lead to significant gains in computational efficiency .

in this paper we present a new approach to control variates for improving computational efficiency of ensemble monte carlo . we present the approach using simulation of paths of a time - dependent nonlinear stochastic equation . the core idea is to extract information at one or more nominal model parameters and use this information to gain estimation efficiency at neighboring parameters . this idea is the basis of a general strategy , called database monte carlo ( dbmc ) , for improving efficiency of monte carlo . in this paper we describe how this strategy can be implemented using the variance reduction technique of control variates ( cv ) . we show that , once an initial setup cost for extracting information is incurred , this approach can lead to significant gains in computational efficiency . the initial setup cost is justified in projects that require a large number of estimations or in those that are to be performed under real - time constraints . monte carlo , variance reduction , control variates s05.10.ln , 02.70.uu , 02.70.tt

q-alg9701024

i

the ordinary schur algebra is of key importance in the study of the representation theory of general linear groups in the describing characteristic , and it provides a link between the general linear groups and the symmetric groups . in @xcite we introduced the @xmath2schur algebra , and demonstrated its usefulness in the representation theory of @xmath3 over a field of non describing characteristic . in @xcite it was shown that the @xmath2schur algebra is given as the dual of a homogeneous part of quantum@xmath4 , or alternatively as the factor of quantum@xmath4 or the corresponding quantum enveloping algebra modulo the kernel of its action on quantum tensor space ( compare @xcite ) . in particular , the representations of @xmath2schur algebras are precisely the homogeneous polynomial representations of quantum@xmath4 in a fixed degree ( compare @xcite ) . the construction of the @xmath2schur algebra involves the hecke algebra of type @xmath5 ; in this paper we use the hecke algebra of type @xmath0 to build an algebra which we call the @xmath6schur algebra . others have devised a version of a schur algebra of type @xmath0 @xcite , but ours is a larger algebra . applications to the representation theory of finite symplectic groups in the non describing characteristic case have already been provided @xcite , and we expect that further applications will ensue , using our larger and more complicated algebra . hecke algebras of type @xmath0 have been studied in @xcite . we begin by recalling and extending some of the notation and results which we used in those papers . the remainder of the paper is then devoted to introducing the @xmath6schur algebra and investigating its main properties . in particular we construct a generic basis of the @xmath6schur algebra and we define @xmath6weyl modules . the weyl modules are labelled by bipartitions and they have unique maximal submodules . the corresponding factor modules are pairwise non isomorphic irreducible representations of the @xmath6schur algebra . we show that the decomposition matrix which describes the composition multiplicities of these irreducible modules in the @xmath6weyl modules is unitriangular , and we construct a `` semistandard basis '' for each @xmath6weyl module . in a forthcoming paper we shall construct a cellular basis of the @xmath6-schur algebra @xmath1 . as a consequence , every irreducible representation of @xmath1 is isomorphic to one of the irreducible representations which we construct here and , in addition , @xmath1 is quasi hereditary . furthermore , we shall generalize some of our results to construct schur algebras of the ariki koike algebras .

in this paper we use the hecke algebra of type @xmath0 to define a new algebra @xmath1 which is an analogue of the @xmath2schur algebra . we construct weyl modules for @xmath1 and obtain , as factor modules , a family of irreducible @xmath1modules over any field . makefnmark

in this paper we use the hecke algebra of type @xmath0 to define a new algebra @xmath1 which is an analogue of the @xmath2schur algebra . we construct weyl modules for @xmath1 and obtain , as factor modules , a family of irreducible @xmath1modules over any field . makefnmark

nucl-th0412035

i

the photo - production of kaons on nucleons has been studied intensively last years [ 1 - 10 ] . analysis of the process contributes to our understanding of dynamics in the strange sector . special attention is payed to investigation of a resonance content of the amplitudes , particularly searching for `` missing resonances '' , the structure of hadrons ( form factors ) , and to better fixing the effective couplings . this is possible especially after copious and good quality data were collected in jlab ( clas ) @xcite , elsa ( saphir ) @xcite , and spring-8 ( leps ) @xcite . the amplitude of the process is also an input information in calculations of excited spectra in the hypernucleus photo - production @xcite . a good quality description of the elementary process can then minimise a theoretical uncertainty of the hypernuclear results . there are several approaches to treat the elementary process . among them the isobaric models based on the effective description utilizing only the hadronic degrees of freedom are suitable for their further use in more complex calculations . other approaches are eligible either for higher energies ( @xmath2 gev ) , the regge model @xcite , or to the threshold region , the chiral perturbation theory @xcite . quark models @xcite are too complicated for their further use in the hypernuclear calculations . while there are many models which provide a satisfactory description of data in the p(@xmath3,k@xmath0)@xmath4 reaction , almost nothing in known about the k@xmath1 photo - production , the only few data being in the p(@xmath3,k@xmath1)@xmath5 channel @xcite . however , the first measurements of the k@xmath1 photo - production from carbon and deuteron in the threshold region were performed at tohoku university @xcite . utilizing these data the simple well known deuteron structure allows one to obtain information on the elementary process , n(@xmath3,k@xmath1)@xmath4 , which is difficult to obtain otherwise .

isobaric models for the photo - production of k@xmath0 are discussed and their predictions are shown in the k@xmath1 photo - production . the models are further used in spectator model calculations of the k@xmath1 photo - production on deuteron . t. takahashi + _ department of physics , tohoku university + sendai , 980 - 8578 , japan _

isobaric models for the photo - production of k@xmath0 are discussed and their predictions are shown in the k@xmath1 photo - production . the models are further used in spectator model calculations of the k@xmath1 photo - production on deuteron . considerable dependence of the inclusive cross section on the elementary amplitude was found . = 15.7 cm * kaon photo - production on the nucleon and deuteron * + p. bydovsk , m. sotona + _ nuclear physics institute , czech academy of sci . + 25068 e near prague , czech republic _ + o. hashimoto , t. takahashi + _ department of physics , tohoku university + sendai , 980 - 8578 , japan _

nucl-th0412035

r

the isobaric models being fitted to the data on the k@xmath0 photo - production on proton are in satisfactory agreement with the data , except for the forward kaon angles , as it is demonstrated in fig . [ figure1 ] for the sla , k - maid , m2 , and h2 models . the sla and k - maid models were fitted to the older data ( triangles ans dots ) whereas the m2 and h2 ones were adjusted only to the latest clas data @xcite . the obvious and most serious , in the view of the hypernuclear calculations , discrepancy of the results is at @xmath36 deg . in this region , however , one observes an inconsistency of the experimental data too , further stressed by the new clas and saphir data . the systematic discrepancy of results for a very small kaon angle is shown in fig . [ figure2 ] . models with hadronic form factors , k - maid , m2 , and h2 , provide much smaller cross sections at @xmath37 gev than the others . in figure [ figure3 ] predictions of the models for the k@xmath1 photo - production on neutron are shown . as mentioned already in sect . [ prdn ] , the only free parameter in this channel is the ratio r@xmath38 . we have used the value of -0.45 , as it was fixed in the k - maid @xcite , in the models m2 and h2 too . in the case of the sla model we have found two values of the ratio , -1.6 ( sla1 ) and -3.4 ( sla2 ) , which provide results very near to those of the k - maid at forward angles , see fig . [ figure3 ] . the models reveal more different results than in the k@xmath0 production . the bump structure is produced by the @xmath39 exchange . in figure [ figure4 ] we demonstrate that the k - maid and sla are much more sensitive to a contribution of the k@xmath14 exchange than the m2 and h2 models . this phenomenon is valid for energies up to 1.5 gev and kaon lab angles up to 50 deg . that makes a choice of values for r@xmath38 less important in the m2 and h2 than in the sla and k - maid models . a sensitivity of the cross section ( [ crs ] ) to the r@xmath38 parameter is shown again for the d(@xmath3,k@xmath1)@xmath4p reaction in fig . [ figure5 ] . the figure shows that the value of r@xmath38 is not too important for the m2 and h2 , so that they provide really predictions in the k@xmath1 channel at the kinematical region assumed here . on the contrary , results of the sla model vary very strongly with values of r@xmath38 ( notice the scale of the appropriate figure ) . predictions of the models for the inclusive cross section ( [ crs ] ) are shown for the k@xmath1 photo - production on the deuteron for small kaon lab angles and photon energies in fig . [ figure6 ] . the results differ significantly in some cases which enable the data from tohoku experiment @xcite to discriminate between the elementary models . to summarise , we showed that the isobaric models still provide different predictions for the cross section of the k@xmath0 photo - production at forward angles which then causes large input uncertainty of the hypernuclear calculations . predictions for the inclusive cross sections of the simple model for the d(@xmath3,k@xmath1)@xmath4p reaction display considerable sensitivity to elementary amplitudes and therefore we expect that the experimental data will allow to discriminate between various elementary amplitudes which otherwise fit the p(@xmath3,k@xmath0)@xmath4 data equally well . one of the authors ( p.b . ) wishes to thank the organisers for their kind invitation to this highly stimulating workshop . we are also very grateful to k. miyagawa and a. salam for very helpful discussions . this work was supported by grant 202/02/0930 of the grant agency of the czech republic . adelseck and b. saghai , _ phys . rev . _ * c42 * , 108 ( 1990 ) . r.a.williams , chueng - ryong ji , s.r.cotanch , _ phys . * c46 * , 1617 ( 1992 ) . david , c. fayard , g .- h . lamot , b. saghai , _ phys . _ * c53 * , 2613 ( 1996 ) ; t. mizutani , c. fayard , g .- h . lamot , b. saghai , _ phys . rev . _ * c58 * , 75 ( 1998 ) . t. mart and c. bennhold , _ phys . _ * c61 * , 012201 ( 2000 ) ; c. bennhold _ et al . _ , nucl - th/9901066 . s. janssen , j. ryckebusch , d. debruyne , and t. van cauteren , _ phys . rev . _ * c65 * , 015201 ( 2001 ) . g. penner and u. mosel , _ phys . rev . _ * c66 * , 055212 ( 2002 ) . chiang , f. tabakin , t .- s.h . lee , b. saghai , _ phys.lett . _ * b517 * , 101 ( 2001 ) . p. bydovsk _ _ , nucl - th/0305039 . p. bydovsk and m. sotona , nucl - th/0408039 . davidson and r. workman , _ phys . _ * c63 * , 025210 ( 2001 ) . _ , _ phys . rev . _ * c69 * , 042201(r ) ( 2004 ) ; nucl - ex/0305028 . _ , _ eur . j. _ * a19 * , 251 ( 2004 ) ; nucl - ex/0308025 . _ , _ phys . lett . _ * 91 * , 092001 ( 2003 ) . t. motoba _ et al . _ , in _ proc . of electrophotoproduction of strangeness on nucleons and nuclei _ , sendai , japan , 16 - 18 june , 2003 , ( eds . k.maeda , h.tamura , s.n.nakamura , o.hashimoto ) . world sci . , 2004 , p.221 . m. guidal , j .- m . laget , m. vanderhaeghen , _ nucl . phys . _ * a627 * , 645 ( 1997 ) . s. steininger and u .- g . meissner , _ phys . lett . _ * b391 * , 446 ( 1997 ) . b. saghai , in _ proc . of electrophotoproduction of strangeness on nucleons and nuclei _ , sendai , japan , 16 - 18 june , 2003 , ( eds . k.maeda , h.tamura , s.n.nakamura , o.hashimoto ) . world sci . , 2004 , p.53 ; nucl - th/0310025 . s. goers _ et al . _ , _ phys . _ * b464 * , 331 ( 1999 ) . t. takahashi _ et al . _ , _ nucl . phys . _ * a691 * , 387c ( 2001 ) ; t. watanabe , in _ these proceedings _ ; k. tsukada , in _ these proceedings_. m.q . _ , _ phys . lett . _ * b445 * , 20 ( 1998 ) . a. bleckmann _ _ , _ z. phys . _ * 239 * , 1 ( 1970 ) . xiaodong li and l.e . g : nucl . part . * 17 * , 1127 ( 1991 ) . darwish , h. arenhvel , m. schwamb , _ eur . phys . j. _ * a16 * , 111 ( 2003 ) . r. machleidt , k. holinde , and ch . elster , _ phys . rep . _ * 149 * , 1 ( 1987 ) . s. eidelman _ et al._(particle data group ) , _ phys . lett . _ * b592 * , 1 ( 2004 ) .

= 15.7 cm * kaon photo - production on the nucleon and deuteron * + p. bydovsk , m. sotona + _ nuclear physics institute , czech academy of sci . + 25068 e near prague , czech republic _ + o. hashimoto ,

isobaric models for the photo - production of k@xmath0 are discussed and their predictions are shown in the k@xmath1 photo - production . the models are further used in spectator model calculations of the k@xmath1 photo - production on deuteron . considerable dependence of the inclusive cross section on the elementary amplitude was found . = 15.7 cm * kaon photo - production on the nucleon and deuteron * + p. bydovsk , m. sotona + _ nuclear physics institute , czech academy of sci . + 25068 e near prague , czech republic _ + o. hashimoto , t. takahashi + _ department of physics , tohoku university + sendai , 980 - 8578 , japan _

physics0403030

c

it is shown that a high energy resolution detector with the radiopurity levels necessary for the operation of borexino , as well as solar neutrino project of kamland , will be sensitive to solar _ pp_neutrinos . the project can compete with other existing proposals ( see table@xmath6[tab : experiments ] ) . 10 k.eguchi , et al , kamland collaboration , phys.rev.lett . 90 ( 2003 ) a.bandyopadhyay , s.choubey , r.gandhi , s.goswami , d.p.roy , phys.lett . * b * 559 ( 2003 ) 121 . e.calabresu , g.fiorentini , and m.lissia , astro - ph/9602045 . j.n.bahcall , proceedings second international workshop on low energy solar neutrinos , university of tokyo , japan , 2000 . s. turck - chieze , the sun : a laboratory for determining neutrino properties , lownu-2003 workshop , may 2003 , paris , http://cdfinfo.in2p3.fr / lownu2003/. r.s.raghavan , lens meeting at lngs , assergi , 28 july 1998 ; + m.fujiwara et al . arxiv : nucl - ex/0006006 . r.s.raghavan , lens . lownu-2003 workshop , may 2003 , paris , http://cdfinfo.in2p3.fr / lownu2003/. h.v.klapdor-kleingrothaus , nucl . b ( proc.suppl . ) * 100 , * 350 , 2001 . + w. hofmann / g . heusser , physics with naked germanium in liquid nitrogen , lownu-2003 workshop , may 2003 , paris , http://cdfinfo.in2p3.fr / lownu2003/. r. lanou , heron , lownu-2003 workshop , may 2003 , paris , http://cdfinfo.in2p3.fr / lownu2003/. m. nakahata , xmass , ibid . a.sarrat ( on behalf of the hellaz collab . ) , nucl . phys . b ( proc.suppl . ) * 95 , * 177 , 2001 . h.ejiri , proc . workshop on low energy solar neutrinos , lownu2 , december 4 and 5 , 2000 , tokyo , japan , ed . by y.suzuki ( world scientific , singapore , 2001 ) , http://www-sk.icrr.u-tokyo.ac.jp/ neutlowe/ 2/ transparency/ index.html c.broggini , ibid . mckinsey , and j.m . doyle , astro - ph/9907314 . j.n.abdurashitov et al . , phys.rev * c60 * , 055801 , 1999 . w.hampel et al . , phys.lett . b * 447 * , 127 , 1999 . smirnov o. , zaimidoroga o. , derbin a. + search for the solar _ pp_neutrinos with an upgrade of ctf detector . + phys.at.nucl . vol 66 , no4 ( 2003 ) 712 - 723 . arpesella c. et al . , borexino at gran sasso , proposal for a real time detector for low energy solar neutrino .. vol . 1 . edited by g.bellini et al . ( dept . of physics of the university of milano , august 1991 ) . alimonti g. et al . , astroparticle physics * 16 * , 205 , 2002 . alimonti g. et al . , nucl.instrum.methods * a 406 , * 411 , 1998 . alimonti g. et al . , astroparticle physics * 8 * , 141 , 1998 . borexino internal report , 2003 . alimonti g. et al . , phys.lett . * b 422 * , 349 , 1998 . o.ju.smirnov , borexino internal note , 02/27/07 . g.ranucci et al . , nucl.instrum.methods a * 333 * , 553 , 1993 . alimonti g. et al . , nucl.instrum.methods * a 440 * , 360 , 1998 . o.ju.smirnov , instruments and experimental techniques , vol 46 , no 3 ( 2003 ) 327 . j.b.birks , proc.phys.soc . a64 ( 1951 ) 874 . j.m.los arcos , f.ortiz , comp.phys.comm . 103 ( 1997 ) 83 . y. kishimoto , kamland solar neutrinos , lownu-2003 workshop , may 2003 , paris , http://cdfinfo.in2p3.fr / lownu2003/. walter r. nelson , hideo hirayama , david w. o. rogers . the egs4 code system . slac-265 , 1985 . private communication . silvia bonetti . private communication . m.morita , beta decay and muon capture ( benjamin , reading , mass . , 1973 ) j.j.simpson , and a.hime , phys.rev . * 39d * , 1825 , 1989 . h.behrens , and j.janecke , numerical tables for beta decay and electron capture ( springer- verlag , berlin , 1969 ) . m.e.rose , phys.rev . * 49 * , 727 , 1936 . e. resconi , doct . thesis , universita degli studi di genova , 2001 ; + s.schoenert , private communication . arpesella c. et al . , astroparticle physics * 18 * , 1 , 2002 . a. ianni , g. korga , g. ranucci , et al . , lngs preprint infn / tc-00/05 . t.hagner , f.von hentig , b.heisinger et al . , astrop.phys . * 14 * , 33 , 2000 . j. n. bahcall , h. pinsonneault , and s. basu , astro - ph/0010346 . j. n. bahcall and r. k. ulrich , rev . phys . * 60 * , 297 , 1988 . bahcall , e. lisi , d.e . alburger et al . , phys . rev . * c 54 * , 411,1996 . bahcall , phys . rev . * c 56 * , 3391 , 1997 . bahcall , krastev , and a.ju.smirnov , phys . d 58 * , 096016 , 1998 . w.d.gunter , jr . , g.r.grant , and s.a.shaw , appl.optics , * 9 * , no.2 , 251 , 1970 . s.harmer , s.hallensleben , and p.d.townsend , nucl.instrum.methods b * 166 - 167 * , 798 , 2000 . s.hallensleben , s.harmer , p.d.townsend , optics comm . * 180 * , 89 , 2000 . i.e. protsenko , v.n . samoilov , o.a . russian patent no 2002107248 with priority from 22/03/2002 .

it is shown that a large volume liquid organic scintillator detector with an energy resolution of 10 kev at 200 kev ( @xmath0 ) will be sensitive to solar _ pp_neutrino , if operated at the target radiopurity levels for the borexino detector , or the solar neutrino project of kamland .

it is shown that a large volume liquid organic scintillator detector with an energy resolution of 10 kev at 200 kev ( @xmath0 ) will be sensitive to solar _ pp_neutrino , if operated at the target radiopurity levels for the borexino detector , or the solar neutrino project of kamland .

1404.7708

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entanglement of formation ( eof)@xcite and relative entropy of entanglement ( ree)@xcite are two major entanglement monotones for bipartite systems . for pure states @xmath0 the eof @xmath1 is defined as a von neumann entropy of its subsystem @xmath2 . on the contrary , ree is defined as minimum value of the relative entropy with separable states ; @xmath3 where @xmath4 is a set of separable states , it is called `` distance entanglement measure '' . another example of the distance entanglement measure is a geometric entanglement measure defined as @xmath5 , where @xmath6 is a maximal overlap of a given state @xmath7 with the nearest product state@xcite . ] . it was shown in ref.@xcite that @xmath8 is a upper bound of the distillable entanglement@xcite . the separable state @xmath9 , which yields a minimum value of the relative entropy is called the closest separable state ( css ) of @xmath10 . surprising fact , at least for us , is that although definitions of eof and ree are completely different , they are exactly same for all pure states@xcite . this fact may indicate that they are related to each other although the exact connection is not revealed yet . the main purpose of this paper is to explore the veiled connection between eof and ree . for mixed states @xmath10 eof is defined via a convex - roof method@xcite ; @xmath11 where the minimum is taken over all possible pure - state decompositions with @xmath12 and @xmath13 . the ensemble that gives the minimum value in eq.([two3 ] ) is called the optimal decomposition of the mixed state @xmath10 . thus , the main task for analytic calculation of eof is derivation of an optimal decomposition of the given mixture . few years ago , the procedure for construction of the optimal decomposition was derived@xcite in the two - qubit system , the simplest bipartite system , by making use of the time - reversal operation of spin-1/2 particles appropriately . in these references the relation @xmath14 is used , where @xmath15 is a binary entropy function @xmath16 and @xmath17 is called the concurrence . this procedure , usually called wootters procedure , was re - examined in ref.@xcite in terms of antilinearity . introduction of antilinearity in quantum information theory makes it possible to derive concurrence - based entanglement monotones for tripartite@xcite and multipartite systems@xcite . due to the discovery of the closed formula for eof in the two - qubit system , eof is recently applied not only to quantum information theory but also to many scientific fields such as life science@xcite . while eof is used in various areas of science , ree is not because of its calculational difficulty . in order to obtain ree analytically for given mixed state @xmath10 one should derive its css , but still we do nt know how to derive css@xcite even in the two - qubit system except very rare cases@xcite . in ref.@xcite ree for bell - diagonal , generalized vedral - plenio@xcite , and generalized horodecki states@xcite were derived analytically through pure geometric arguments@xcite . due to the notorious difficulty some people try to solve the ree problem conversely . let @xmath9 be a two - qubit boundary states in the convex set of the separable states . in ref.@xcite authors derived entangled states , whose css are @xmath9 . this converse procedure is extended to the qudit system@xcite and is generalized as convex optimization problems@xcite . however , as emphasized in ref.@xcite still it is difficult to find a css @xmath9 of given entangled state @xmath10 although the converse procedure may provide some useful information on the css@xcite . in this paper we will try to find a css for given entangled two - qubit state without relying on the converse procedure . as commented , eof and ree are identical for bipartite pure states although they are defined differently . this means that they are somehow related to each other . if this connection is unveiled , probably we can find css for arbitrary two - qubit mixed states because we already know how to compute eof through wootters procedure . to explore this issue is original motivation of this paper . we will show in the following that ree of many mixed symmetric states can be analytically obtained from eof if one follows the following procedure : 1 . for entangled two - qubit state @xmath10 let @xmath18 be an optimal decomposition for calculation of eof . since @xmath19 are pure states , it is possible to obtain their css @xmath20 . thus , it is straight to derive a separable mixture @xmath21 . if @xmath22 is a boundary state in the convex set of separable states , the procedure is terminated with @xmath23 . if @xmath22 is not a boundary state , we consider @xmath24 . by requiring that @xmath25 is a boundary state , one can fix @xmath26 , _ say _ @xmath27 . then we identify @xmath28 . this procedure is schematically represented in fig . 1 . in order to examine the validity of the procedure we have to apply the procedure to the mixed states whose ree are already known . thus , we will choose the bell - diagonal , generalized vedral - plenio and generalized horodecki states , whose ree were computed in ref.@xcite through different methods . also , we will apply the procedure to the less symmetric mixed states such as vedral - plenio - type and horodecki - type states whose ree were computed in ref.@xcite by making use of the the converse procedure introduced in ref.@xcite . the paper is organized as follows . in section ii we show that the procedure generates the correct css for bell - diagonal states . in section iii and section iv we show that the procedure generates the correct css for generalized vedral - plenio and generalized horodecki states , respectively . in section v we consider two less symmetric states , vedral - plenio - type and horodecki - type states . it is shown that while the procedure generates a correct css for the former , it does not give a correct one for the latter . in section vi a brief conclusion is given . in appendix we prove that eof and ree are identical for all pure states by making use of the schmidt decomposition . the schmidt bases derived in this appendix are used in the main body of this paper .

it is well - known that entanglement of formation ( eof ) and relative entropy of entanglement ( ree ) are exactly identical for all two - qubit pure states even though their definitions are completely different . however , it is shown that the procedure does not provide correct ree for arbitrary mixed states .

it is well - known that entanglement of formation ( eof ) and relative entropy of entanglement ( ree ) are exactly identical for all two - qubit pure states even though their definitions are completely different . we think this fact implies that there is a veiled connection between eof and ree . in this context , we suggest a procedure , which enables us to compute ree from eof without relying on the converse procedure . it is shown that the procedure yields correct ree for many symmetric mixed states such as bell - diagonal , generalized vedral - plenino , and generalized horodecki states . it also gives a correct ree for less symmetric vedral - plenio - type state . however , it is shown that the procedure does not provide correct ree for arbitrary mixed states .

1703.02654

i

graphs considered in the paper are finite , without loops or multiple edges . in a graph @xmath13 , @xmath14 and @xmath15 ( @xmath16 and @xmath17 ) denote the vertex set and the edge set of @xmath7 , respectively . for undefined concepts and notation we refer the reader to @xcite . for two vertices @xmath18 and @xmath19 in a graph @xmath7 , a @xmath20-geodesic is a shortest path between @xmath18 and @xmath19 . a set @xmath5 of vertices of @xmath7 is convex if the vertices of every @xmath20-geodesic is contained in @xmath5 for every @xmath21 . according to duchet , convexity in graphs has been studied since the early seventies , when abstract convexity was studied in different contexts ( @xcite is an outdated , but very nice , survey on the subject ) . convexity in graphs has taken many different directions , and different related parameters have been defined and widely studied , e.g. , the hull number @xcite , the geodetic number @xcite , and the convexity number @xcite of a graph . recent papers on this subjects include @xcite , where the decision problem associated with these three parameters are shown to be @xmath10-complete , even when restricted to bipartite graphs , and in the case of the geodetic number , even when restricted to bipartite chordal graphs . chartrand , fink and zhang generalized the concept of convexity to oriented graphs , and defined the convexity number for an oriented graph ; oriented analogues of the hull number and geodetic number are defined in @xcite . we focus on the convexity number of oriented graphs ; although this generalization was introduced in 2002 , and the proof given by gimbel in @xcite on the @xmath10-completeness of determining the convexity number of an arbitrary graph is one of the shortest and neatest @xmath10-completeness proofs ever done , the problem of determining the convexity number of an oriented graph was not known to be @xmath10-complete until now . we prove that determining the convexity number of an oriented graph is @xmath10-complete even when restricted to bipartite graphs of girth @xmath22 , with @xmath23 . an _ oriented graph _ is an orientation of some graph . in an oriented graph @xmath24 , @xmath14 and @xmath15 ( @xmath25 and @xmath26 ) denote the vertex set and the edge set of @xmath0 , respectively . an _ oriented subgraph _ @xmath27 of an oriented graph @xmath24 is an oriented graph with @xmath28 and @xmath29 . an oriented graph is _ connected _ if its underlying graph is connected . a _ directed path _ is a sequence @xmath30 of vertices of an oriented graph @xmath0 such that @xmath31 are distinct and @xmath32 for @xmath33 . an oriented graph is _ strongly connected _ ( or _ strong _ ) if for every pair of distinct vertices @xmath18 and @xmath19 , there exists a directed path from @xmath18 to @xmath19 . the _ girth _ of an oriented graph is the length of a shortest directed cycle . a @xmath20-_geodesic _ in a digraph @xmath0 is a shortest @xmath20-directed path and its length is @xmath34 . a nonempty subset , @xmath5 , of the vertex set of a digraph , @xmath0 , is called a _ convex set _ of @xmath0 if , for every @xmath21 , every vertex lying on a @xmath20- or @xmath35-geodesic belongs to @xmath5 . for a nonempty subset , @xmath36 , of @xmath25 , the _ convex hull _ , @xmath37 $ ] , is the minimal convex set containing @xmath36 . thus @xmath38 = s$ ] if and only if @xmath5 is convex in @xmath0 . the _ convexity number _ , @xmath6 , of a digraph @xmath0 is the maximum cardinality of a proper convex set of @xmath0 . a _ maximum convex set _ @xmath5 , of a digraph @xmath0 , is a convex set with cardinality @xmath6 . since every singleton vertex set is convex in a connected oriented graph @xmath0 , @xmath39 . the _ degree _ , @xmath40 , of a vertex @xmath19 in an oriented graph is the sum of its in - degree and out - degree ; this is , @xmath41 . a vertex , @xmath19 , is an _ end - vertex _ if @xmath42 . a _ source _ is a vertex having positive out - degree and in - degree @xmath43 , while a _ sink _ is a vertex having positive in - degree and out - degree @xmath43 . for a vertex @xmath19 of @xmath0 , the in - neighborhood of @xmath19 , @xmath44 , is the set @xmath45 and the out - neighborhood of @xmath19 , @xmath46 , is the set @xmath47 . a vertex @xmath19 of @xmath0 is a _ transitive vertex _ if @xmath48 , @xmath49 and , for every @xmath50 and @xmath51 , @xmath52 . for graphs @xmath7 and @xmath53 , their _ cartesian product _ , @xmath54 , is the graph with vertex set @xmath55 , and such that two vertices @xmath56 and @xmath57 are adjacent in @xmath54 if either @xmath58 and @xmath59 is an edge in @xmath53 , or @xmath60 and @xmath61 is an edge in @xmath7 . for a vertex @xmath22 of @xmath7 , the subgraph of @xmath54 induced by the set @xmath62 is called an @xmath53-fiber and is denoted by @xmath63 . similarly , for @xmath64 , the @xmath7-fiber , @xmath65 , is the subgraph induced by @xmath66 . we will have occasion to use the fiber notation @xmath65 and @xmath63 to refer instead to the set of vertices in these subgraphs ; the meaning will be clear from the context . it is clear that all @xmath7-fibers are isomorphic to @xmath7 and all @xmath53-fibers are isomorphic to @xmath53 . as mentioned , the concept of convexity number of an oriented graph was first introduced by chartrand , fink and zhang in @xcite , where they proved the following pair of theorems . let @xmath0 be a connected oriented graph of order @xmath67 . then @xmath68 if and only if @xmath0 contains a source , a sink or a transitive vertex . [ no2 ] there is no connected graph of order at least @xmath69 with convexity number @xmath70 . taking an interesting direction for the subject of convexity in oriented graphs , in @xcite , tong , yen and farrugia introduced the concepts of convexity spectrum and strong convexity spectrum of a graph . for a nontrivial connected graph @xmath7 , we define the _ convexity spectrum _ , @xmath71 , of a graph @xmath7 , as the set of convexity numbers of all orientations of @xmath7 , and the _ strong convexity spectrum _ , @xmath72 , of a graph @xmath7 as the set of convexity numbers of all strongly connected orientations of @xmath7 . if @xmath7 has no strongly connected orientation , then @xmath72 is empty . the _ lower orientable convexity number _ , @xmath73 , of @xmath7 is defined to be @xmath74 and the _ upper orientable convexity number _ , @xmath75 , is defined to be @xmath76 . hence , for every nontrivial connected graph @xmath7 of order @xmath77 , @xmath78 . tong , yen and farrugia calculated the convexity and strong convexity spectra of complete graphs and also constructed , for every @xmath79 , a graph @xmath7 with convexity spectrum @xmath80 . it is not very surprising that the strong convexity spectra of @xmath81 for @xmath82 is a `` large '' set , @xmath83 , missing only @xmath84 and @xmath85 . nonetheless , we find very surprising that , in one hand , tong and yen proved in @xcite that @xmath86 for every pair of integers @xmath87 , and , in the other hand , we prove that the strong convexity spectrum of an @xmath88 grid , for any pair of integers @xmath89 , only lacks the set of integers @xmath90 . so , an interesting question arises from the previous observation : what property in a graph determines a large strong convexity spectrum ? we can discard regularity and high degrees ; grids are not regular graphs , and have both small maximum and minimum degree . although we did not find what is so special about grids in terms of convexity , we managed to calculate the strong convexity spectra of all grids . the rest of this paper is ordered as follows . section [ snp ] is devoted to prove the @xmath10-completeness of the problem of determining the convexity number of a given oriented graph ; the problem remains @xmath10-complete even when restricted to bipartite oriented graphs of arbitrarily large girth . in section [ sgrids ] , we prove some basic results on the convexity number of general oriented graphs , and also introduce a concept of main importance to this work : the whirlpool orientation of a grid . using this concept , we prove that @xmath91 for any grid @xmath7 . we finish the section with a result excluding some values from the strong convexity spectra of certain grids . section [ scssg ] is devoted to calculate the strong convexity spectra of @xmath92 and @xmath93 grids for every integer @xmath67 . in section [ smain ] , the strong convexity spectra of @xmath88 grids for every pair of integers @xmath94 is calculated .

let @xmath0 be a connected oriented graph . a set @xmath1 is convex in @xmath0 if , for every pair of vertices @xmath2 , the vertex set of every @xmath3-geodesic , ( @xmath3 shortest directed path ) and every @xmath4-geodesic in @xmath0 is contained in @xmath5 . the convexity number , @xmath6 , of a non - trivial oriented graph , @xmath0 , is the maximum cardinality of a proper convex set of @xmath0 . the strong convexity spectrum of the graph @xmath7 , @xmath8 , is the set @xmath9 . in this paper we prove that the problem of determining the convexity number of an oriented graph is @xmath10-complete , even for bipartite oriented graphs of arbitrary large girth , extending previous known results for graphs . we also determine @xmath11 , for every pair of integers @xmath12 . convexity number , convex set , spectrum , oriented graph , grid 05c 12 , 05c20

let @xmath0 be a connected oriented graph . a set @xmath1 is convex in @xmath0 if , for every pair of vertices @xmath2 , the vertex set of every @xmath3-geodesic , ( @xmath3 shortest directed path ) and every @xmath4-geodesic in @xmath0 is contained in @xmath5 . the convexity number , @xmath6 , of a non - trivial oriented graph , @xmath0 , is the maximum cardinality of a proper convex set of @xmath0 . the strong convexity spectrum of the graph @xmath7 , @xmath8 , is the set @xmath9 . in this paper we prove that the problem of determining the convexity number of an oriented graph is @xmath10-complete , even for bipartite oriented graphs of arbitrary large girth , extending previous known results for graphs . we also determine @xmath11 , for every pair of integers @xmath12 . convexity number , convex set , spectrum , oriented graph , grid 05c 12 , 05c20

1309.0056

i

the study of abelian gauge theory on @xmath6 led string theorists to discover an interesting symmetry , the electric - magnetic duality , which inverts the coupling constant and extends to an action of @xmath7 . this @xmath7 symmetry was later studied over the more general 4-manifolds , some with specific topological twists , where it was called @xmath8-duality , say in the context of @xmath9 supersymmetric yang - mills theories . the @xmath8-duality is roughly saying that certain 4-dimensional gauge theories are modular invariant under the action of the @xmath10 . this modular invariance can be tested by studying the partition function of the theory , roughly speaking , measuring the euler characteristic of the instanton moduli space of that theory . one of interesting results by string theorists in @xcite was to show that the topological quantum field theories obtained by the so - called ( topologically ) twisted super yang - mills theories over the four manifold and their associated partition functions are equivalent to donaldson s theory of four manifolds and the associated partition function of donaldson s invariants . these interesting consequences of s - duality , later set base for much further developments , such as the correspondence between the supersymmetric black hole entropies and @xmath11 super yang - mills theories @xcite . recently the study of the conjectural modular properties of the bps partition functions of the supersymmetric d4-d2-d0 black holes @xcite , @xcite motivated algebraic geometers to construct a mathematical framework for modeling the d4-d2-d0 bps states and prove the modularity properties of their associated partition functions , using purely algebraic - geometric techniques . the current article is the third in the sequel , after @xcite and @xcite , of the authors attempt to achieve this goal where here , the focus of the study is to specifically compute the d4-d2-d0 bps invariants via computing their mathematical counterpart given by the donaldson - thomas invariants of torsion sheaves in an ambient calabi - yau threefold . let @xmath12 be a smooth projective calabi - yau threefold . for a pure sheaf @xmath13 the hilbert polynomial is defined to be @xmath14 , and the reduced hilbert polynomial of @xmath13 is @xmath15 * @xmath13 is called gieseker semistable if for any proper subsheaf @xmath16 we have @xmath17 for @xmath18 . @xmath13 is called gieseker stable if the equality never holds for any proper subsheaf @xmath19 . * @xmath13 is called @xmath20-semistable if for any proper subsheaf @xmath16 we have @xmath21 . @xmath13 is called @xmath20-stable if the equality never holds for any proper subsheaf @xmath19 . * for a fixed @xmath22 , a pair @xmath23 , where @xmath24 is a nonzero section of @xmath25 , is called stable ( ( * ? ? ? * section 12 ) ) if 1 . @xmath13 is gieseker semistable , 2 . if @xmath24 factors through a proper subsheaf @xmath26 then @xmath27 for @xmath18 . @xmath28 the stability of pairs has originated from the stability of the coherent systems defined by le potier @xcite . the reduced hilbert polynomial of the pair @xmath23 is defined to be @xmath29 where and @xmath30 . now if @xmath16 , define @xmath31 to be the restriction of @xmath24 if @xmath24 factors through @xmath26 , and otherwise define @xmath32 . now the pair @xmath23 is stable if and only if for any proper subsheaf @xmath16 , @xmath33 suppose now that @xmath34 is a proper moduli space of gieseker stable sheaves @xmath13 ( or the moduli space of stable pairs @xmath23 ) as above with fixed hilbert polynomial @xmath35 . the moduli space @xmath36 is usually singular and may have several components with different dimensions . to define ( deformation invariant @xmath37-valued ) invariants @xmath38 as _ integration _ over @xmath36 we need to have a _ virtual fundamental class _ of the moduli space constructed by means of a _ perfect obstruction theory _ on @xmath36 . this can be obtained by studying the deformations and obstructions of the stable sheaves or the stable pairs @xcite . moreover , the obstruction theory on @xmath36 is symmetric and the corresponding invariants are expressible as a weighted euler characteristic of the moduli space @xcite . + if the moduli space of gieseker semistable sheaves @xmath34 contains strictly semistable sheaves , then one can not define the invariants @xmath38 by means of the virtual fundamental class . joyce and song @xcite instead define the @xmath39-valued invariants for @xmath36 called the _ generalized dt _ invariants @xmath40 which are given by the `` _ _ stacky _ _ '' weighted euler characteristic of the moduli space of semistable sheaves . joyce - song stable pairs theory @xcite provides a tool to compute the so - called stacky euler characteristics , by using the sophisticated motivic wall - crossing techniques developed by joyce @xcite , as well as kontsevich and soibelman in @xcite . in other words , the main idea is to benefit from the , easier to calculate , joyce song pair invariants to compute the generalized dt invariants . the latter can be done by obtaining a wall - crossing identity between the the elements of the hall algebra of the motivic ring of stack functions of the moduli space of stable pairs and the moduli space of semistable sheaves respectively . after taking the stacky euler characteristics of both sides of this identity , one obtains the wall - crossing identity between the pair invariants and the generalized dt invariants . note that , @xmath40 specializes to @xmath38 if there are no strictly semistable sheaves and moreover , @xmath40 is also deformation invariant . we study the case where @xmath0 is the total space of the canonical bundle of @xmath1 and @xmath41 is the moduli space of semistable sheaves with hilbert polynomial @xmath42 . any semistable sheaf @xmath13 with hilbert polynomial @xmath43 is ( at least set theoretically ) supported on the zero section of @xmath0 , and @xmath44 is equal to @xmath45 times the class of the zero section . we relate @xmath40 to the topological invariants of the moduli space of torsion - free semistable sheaves on @xmath1 . using the wall - crossing formula of joyce - song @xcite and the toric methods of @xcite we find a formula for @xmath40 when @xmath46 in the presence of strictly semistable sheaves . to express the main result , let @xmath47 be the moduli space of rank 2 gieseker semistable sheaves on @xmath1 with hilbert polynomial @xmath43 and let @xmath48 be the open subset of stable sheaves . denote by @xmath49 the hilbert scheme of @xmath50 points on @xmath1 . then we prove [ thm : p2 ] let @xmath51 where @xmath52 , 1 . if @xmath53 is an odd number then @xmath54 . if @xmath53 is an even number then @xmath55 where @xmath56 is a combinatorial expression ( cf . theorem [ thm : ss ] ) taking into account the contribution of indecomposable strictly semistable sheaves . @xmath40 is in general a rational number in the presence of semistable sheaves . joyce and song in ( * ? ? ? * section 6.2 ) define the corresponding bps invariants denoted by @xmath57 by the following formula : @xmath58 joyce and song conjecture that @xmath57 is an integer . in the case that there are no strictly semistable sheaves with hilbert polynomial @xmath43 we have @xmath59 . [ cor : ss]using the notation of theorem [ thm : ss ] , we assume that @xmath53 is an even number then one needs to show that @xmath60 @xmath61

let @xmath0 be the total space of the canonical bundle of @xmath1 . we study the generalized donaldson - thomas invariants defined in @xcite of the moduli spaces of the 2-dimensional gieseker semistable sheaves on @xmath0 with first chern class equal to @xmath2 times the class of the zero section of @xmath0 . when @xmath3 or @xmath4 , and semistability implies stability , we express the invariants in terms of known modular forms . we prove a combinatorial formula for the invariants when @xmath5 in the presence of the strictly semistable sheaves , and verify the bps integrality conjecture of @xcite in some cases .

let @xmath0 be the total space of the canonical bundle of @xmath1 . we study the generalized donaldson - thomas invariants defined in @xcite of the moduli spaces of the 2-dimensional gieseker semistable sheaves on @xmath0 with first chern class equal to @xmath2 times the class of the zero section of @xmath0 . when @xmath3 or @xmath4 , and semistability implies stability , we express the invariants in terms of known modular forms . we prove a combinatorial formula for the invariants when @xmath5 in the presence of the strictly semistable sheaves , and verify the bps integrality conjecture of @xcite in some cases .

1112.0004

i

cryogenic detectors are currently the preferred technology for astronomical observations over most of the electromagnetic spectrum , notably in the far infrared through millimeter ( 0.13 mm ) @xcite , x - ray @xcite , and gamma - ray @xcite wavelength ranges . in the important ultraviolet , optical , and near infrared ( 0.15 @xmath0 m ) wavelength range a variety of detector technologies based on semiconductors , backed by large investment from both consumer and military customers , has resulted in detectors for astronomy with large formats , high quantum efficiency , and low readout noise . however , these detectors are fundamentally limited by the band gap of the semiconductor ( 1.1 ev for silicon ) and thermal noise sources from their high ( @xmath1100 k ) operating temperatures @xcite . cryogenic detectors , with operating temperatures on the order of 100 mk , allow the use of superconductors with gap parameters over 1000 times lower than typical semiconductors . this difference allows new capabilities . a superconducting detector can count single photons with no false counts while determining the energy ( to several percent or better ) and arrival time ( to a microsecond ) of the photon . it can also have much broader wavelength coverage since the photon energy is always much greater than the gap energy . while a ccd is limited to about 0.31 @xmath0 m , the new arrays described here are sensitive from 0.1 @xmath0 m in the uv to greater than 5 @xmath0 m in the mid - ir , enabling observations at infrared wavelengths vital to understanding the high redshift universe . this approach has been pursued in the past with two technologies , superconducting tunnel junctions ( stjs ) @xcite and transition edge sensors ( tess ) @xcite . while both of these technologies produced functional detectors , they are limited to single pixels or small arrays due to the lack of a credible strategy for wiring and multiplexing large numbers of detectors , although recently there have been proposals for larger tes multiplexers @xcite . microwave kinetic inductance detectors , or mkids@xcite , are an alternative cryogenic detector technology that has proven important for millimeter wave astrophysics@xcite due to their sensitivity and the ease with which they can be multiplexed into large arrays . mkids use frequency domain multiplexing @xcite that allows thousands of pixels to be read out over a single microwave cable . while the largest stj array is 120 pixels @xcite and the largest optical tes array is 36 pixels @xcite , the mkid arrays described below are 1024 pixels , with a clear path to megapixel arrays . the ability to easily reach large formats is the primary advantage of mkid arrays . in this paper we describe the first photon - counting , energy - resolving ultraviolet , optical , and near infrared mkid focal plane array . these optical lumped element ( ole ) mkid arrays have significant advantages over semiconductor detectors like charge coupled devices ( ccds ) @xcite . they can count individual photons with essentially no false counts and determine the energy and arrival time of every photon with good quantum efficiency . their physical pixel size and maximum count rate is well matched with large telescopes . these capabilities enable powerful new astrophysical instruments usable from the ground and space .

microwave kinetic inductance detectors , or mkids , have proven to be a powerful cryogenic detector technology due to their sensitivity and the ease with which they can be multiplexed into large arrays . here we describe the first successful effort to create a photon - counting , energy - resolving ultraviolet , optical , and near infrared mkid focal plane array . these new optical lumped element ( ole ) mkid arrays have significant advantages over semiconductor detectors like charge coupled devices ( ccds ) . they can count individual photons with essentially no false counts and determine the energy and arrival time of every photon with good quantum efficiency . their physical pixel size and maximum count rate is well matched with large telescopes . these capabilities enable powerful new astrophysical instruments usable from the ground and space . m. d. niemack , y. zhao , e. wollack , r. thornton , e. r. switzer , d. s. swetz , s. t. staggs , l. page , o. stryzak , h. moseley , t. a. marriage , m. limon , j. m. lau , j. klein , m. kaul , n. jarosik , k. d. irwin , a. d. hincks , g. c. hilton , m. halpern , j. w. fowler , r. p. fisher , r. dnner , w. b. doriese , s. r. dicker , m. j. devlin , j. chervenak , b. burger , e. s. battistelli , j. appel , m. amiri , c. allen , and a. m. aboobaker , `` a kilopixel array of tes bolometers for act : development , testing , and first light , '' j. low temp . den herder , h. hoevers , k. irwin , y. ishisaki , c. a. kilbourne , p. de korte , j. van der kuur , k. mitsuda , t. ohashi , l. piro , f. s. porter , k. sato , k. shinozaki , p. shirron , s. j. smith , y. takei , p. whitehouse , and n. y. yamasaki , `` the x - ray microcalorimeter spectrometer for the international x - ray observatory , '' aip conf m. d. eisaman , j. fan , a. migdall , and s. v. polyakov , `` single - photon sources and detectors , '' rev . r. w. romani , a. j. miller , b. cabrera , s. w. nam , and j. m. martinis , `` phase - resolved crab studies with a cryogenic transition - edge sensor spectrophotometer , '' ap . j. burney , t. j. bay , j. barral , p. l. brink , b. cabrera , j. p. castle , a. j. miller , s. nam , d. rosenberg , r. w. romani , and a. tomada , `` transition - edge sensor arrays for uv - optical - ir astrophysics , '' nucl . p. day , h. leduc , b. mazin , a. vayonakis , and j. zmuidzinas , `` a superconducting detector suitable for use in large arrays , '' nature * 425 * , 817821 ( 2003 ) . j. a. schlaerth , n. g. czakon , p. k. day , t. p. downes , r. duan , j. gao , j. glenn , s. r. golwala , m. i. hollister , h. g. leduc , b. a. mazin , p. r. maloney , o. noroozian , h. t. nguyen , j. sayers , s. siegel , j. e. vaillancourt , a. vayonakis , p. r. wilson , and j. zmuidzinas , `` mkid multicolor array status and results from democam , '' proc . ( c ) 2010 : american institute of physics . m. roesch , a. bideaud , a. benoit , a. cruciani , f. x. dsert , s. doyle , s. leclercq , f. mattiocco , k. f. schuster , l. swenson , and a. monfardini , `` characterization of lumped element kinetic inductance detectors for mm - wave detection , '' proc . b. mazin , p. day , k. irwin , c. reintsema , and j. zmuidzinas , `` digital readouts for large microwave low - temperature detector arrays , '' nucl . s. doyle , p. mauskopf , j. naylon , a. porch , and c. duncombe , `` lumped element kinetic inductance detectors , '' j. low temp . b. a. mazin , `` microwave kinetic inductance detectors , '' , ph.d . l. ma , s. nam , h. xu , b. baek , t. chang , o. slattery , a. mink , and x. tang , `` 1310 nm differential - phase - shift qkd system using superconducting single - photon detectors , '' new j. phys . * 11 * , 045020 ( 2009 ) .

microwave kinetic inductance detectors , or mkids , have proven to be a powerful cryogenic detector technology due to their sensitivity and the ease with which they can be multiplexed into large arrays . a mkid is an energy sensor based on a photon - variable superconducting inductance in a lithographed microresonator , and is capable of functioning as a photon detector across the electromagnetic spectrum as well as a particle detector . here we describe the first successful effort to create a photon - counting , energy - resolving ultraviolet , optical , and near infrared mkid focal plane array . these new optical lumped element ( ole ) mkid arrays have significant advantages over semiconductor detectors like charge coupled devices ( ccds ) . they can count individual photons with essentially no false counts and determine the energy and arrival time of every photon with good quantum efficiency . their physical pixel size and maximum count rate is well matched with large telescopes . these capabilities enable powerful new astrophysical instruments usable from the ground and space . mkids could eventually supplant semiconductor detectors for most astronomical instrumentation , and will be useful for other disciplines such as quantum optics and biological imaging . 10 d. bintley , m. j. macintosh , w. s. holland , p. friberg , c. walther , d. atkinson , d. kelly , x. gao , p. a. r. ade , w. grainger , j. house , l. moncelsi , m. i. hollister , a. woodcraft , c. dunare , w. parkes , a. j. walton , k. d. irwin , g. c. hilton , m. niemack , c. d. reintsema , m. amiri , b. burger , m. halpern , m. hasselfield , j. hill , j. b. kycia , c. g. a. mugford , and l. persaud , `` characterising the scuba-2 superconducting bolometer arrays , '' proc . spie * 7741 * , 2 ( 2010 ) . m. d. niemack , y. zhao , e. wollack , r. thornton , e. r. switzer , d. s. swetz , s. t. staggs , l. page , o. stryzak , h. moseley , t. a. marriage , m. limon , j. m. lau , j. klein , m. kaul , n. jarosik , k. d. irwin , a. d. hincks , g. c. hilton , m. halpern , j. w. fowler , r. p. fisher , r. dnner , w. b. doriese , s. r. dicker , m. j. devlin , j. chervenak , b. burger , e. s. battistelli , j. appel , m. amiri , c. allen , and a. m. aboobaker , `` a kilopixel array of tes bolometers for act : development , testing , and first light , '' j. low temp . phys . * 151 * , 690 ( 2008 ) . j. e. carlstrom , p. a. r. ade , k. a. aird , b. a. benson , l. e. bleem , s. busetti , c. l. chang , e. chauvin , h .- m . cho , t. m. crawford , a. t. crites , m. a. dobbs , n. w. halverson , s. heimsath , w. l. holzapfel , j. d. hrubes , m. joy , r. keisler , t. m. lanting , a. t. lee , e. m. leitch , j. leong , w. lu , m. lueker , d. luong - 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ray microcalorimeters with 47 ev energy resolution at 103 kev , '' appl . . lett . * 90 * , 3508 ( 2007 ) . m. d. eisaman , j. fan , a. migdall , and s. v. polyakov , `` single - photon sources and detectors , '' rev . sci . inst . * 82 * , 071101 ( 2011 ) . d. d. e. martin , p. verhoeve , a. peacock , a. g. kozorezov , j. k. wigmore , h. rogalla , and r. venn , `` resolution limitation due to phonon losses in superconducting tunnel junctions , '' appl . phys . lett . * 88 * , 3510 ( 2006 ) . r. a. hijmering , p. verhoeve , d. d. e. martin , i. jerjen , a. g. kozorezov , and r. venn , `` direct position resolution measurement with droids at optical wavelengths , '' j. low temp . phys . * 151 * , 298 ( 2008 ) . r. w. romani , a. j. miller , b. cabrera , s. w. nam , and j. m. martinis , `` phase - resolved crab studies with a cryogenic transition - edge sensor spectrophotometer , '' ap . j. * 563 * , 221 ( 2001 ) . j. burney , t. j. bay , j. barral , p. l. brink , b. cabrera , j. p. castle , a. j. miller , s. nam , d. rosenberg , r. w. romani , and a. tomada , `` transition - edge sensor arrays for uv - optical - ir astrophysics , '' nucl . instrum . meth . a * 559 * , 525 ( 2006 ) . m. d. niemack , j. beyer , h. m. cho , w. b. doriese , g. c. hilton , k. d. irwin , c. d. reintsema , d. r. schmidt , j. n. ullom , and l. r. vale , `` code - division squid multiplexing , '' appl . . lett . * 96 * , 3509 ( 2010 ) . p. day , h. leduc , b. mazin , a. vayonakis , and j. zmuidzinas , `` a superconducting detector suitable for use in large arrays , '' nature * 425 * , 817821 ( 2003 ) . j. a. schlaerth , n. g. czakon , p. k. day , t. p. downes , r. duan , j. gao , j. glenn , s. r. golwala , m. i. hollister , h. g. leduc , b. a. mazin , p. r. maloney , o. noroozian , h. t. nguyen , j. sayers , s. siegel , j. e. vaillancourt , a. vayonakis , p. r. wilson , and j. zmuidzinas , `` mkid multicolor array status and results from democam , '' proc . spie * 7741 * , 4 ( 2010 ) . ( c ) 2010 : american institute of physics . m. roesch , a. bideaud , a. benoit , a. cruciani , f. x. dsert , s. doyle , s. leclercq , f. mattiocco , k. f. schuster , l. swenson , and a. monfardini , `` characterization of lumped element kinetic inductance detectors for mm - wave detection , '' proc . spie * 7741 * , 16 ( 2010 ) . b. mazin , p. day , k. irwin , c. reintsema , and j. zmuidzinas , `` digital readouts for large microwave low - temperature detector arrays , '' nucl . instrum . meth . a * 559 * , 799801 ( 2006 ) . p. verhoeve , d. d. e. martin , r. a. hijmering , j. verveer , a. van dordrecht , g. sirbi , t. oosterbroek , a. peacock , `` s - cam 3 : optical astronomy with a stj - based imaging spectrophotometer , '' nucl . instrum . meth . a * 559 * , 598 ( 2006 ) . g. e. smith , `` the invention and early history of the ccd , '' app . . lett . * 109 * , 102421 ( 2011 ) . d. c. mattis and j. bardeen , `` theory of the anomalous skin effect in normal and superconducting metals , '' phys . rev . * 111 * , 412417 ( 1958 ) . s. doyle , p. mauskopf , j. naylon , a. porch , and c. duncombe , `` lumped element kinetic inductance detectors , '' j. low temp . phys . * 151 * , 530536 ( 2008 ) . h. g. leduc , b. bumble , p. k. day , b. h. eom , j. gao , s. golwala , b. a. mazin , s. mchugh , a. merrill , d. c. moore , o. noroozian , a. d. turner , and j. zmuidzinas , `` titanium nitride films for ultrasensitive microresonator detectors , '' appl . . lett . * 97 * , 102509 ( 2010 ) . o. noroozian , p. day , b. h. eom , h. leduc , and j. zmuidzinas , `` crosstalk reduction for superconducting microwave resonator arrays , '' ieee trans . microw . theory tech , submitted ( 2011 ) . j. gao , m. daal , a. vayonakis , s. kumar , j. zmuidzinas , b. sadoulet , b. a. mazin , p. k. day , and h. g. leduc , `` experimental evidence for a surface distribution of two - level systems in superconducting lithographed microwave resonators , '' appl . . lett . * 92 * , 152505 ( 2008 ) . b. a. mazin , `` microwave kinetic inductance detectors , '' , ph.d . thesis , california institute of technology ( 2004 ) . a. g. kozorezov , j. k. wigmore , d. martin , p. verhoeve , and a. peacock , `` electron energy down - conversion in thin superconducting films , '' phys . rev . b * 75 * , 094513 ( 2007 ) . u. fano , `` ionization yield of radiations 2 : the fluctuations of the number of ions , '' phys . rev . * 72 * , 2629 ( 1947 ) . j. r. crepp , l. pueyo , d. brenner , b. r. oppenheimer , n. zimmerman , s. hinkley , i. parry , d. king , g. vasisht , c. beichman , l. hillenbrand , r. dekany , m. shao , r. burruss , l. c. roberts , a. bouchez , j. roberts , and r. soummer , `` speckle suppression with the project 1640 integral field spectrograph , '' ap . j. * 729 * , 132 ( 2011 ) . r. j. bouwens , g. d. illingworth , m. franx , and h. ford , `` z 7 - 10 galaxies in the hudf and goods fields : uv luminosity functions , '' ap . j. * 686 * , 230 ( 2008 ) . l. ma , s. nam , h. xu , b. baek , t. chang , o. slattery , a. mink , and x. tang , `` 1310 nm differential - phase - shift qkd system using superconducting single - photon detectors , '' new j. phys . * 11 * , 045020 ( 2009 ) . i. tinoco and r. l. gonzalez , `` biological mechanisms , one molecule at a time , '' gene dev . , * 25 * , 12051231 ( 2011 ) .

1112.0004

r

the device was mounted in a gold - plated copper sample box and wire bonded to duroid transition boards . the sample box was inserted into a mkid testbed based on a dilution refrigerator and cooled to approximately 100 mk . a weinreb microwave hemt amplifier with a noise temperature of approximately 4 kelvin is used to amplify the signal . the testbed allows collimated light fed from an external fiber to illuminate the array while up to 512 resonators are probed with room temperature electronics . the electronics consist of an anritsu signal generators , marki iq mixers , and a national instruments analog to digitial converter . more details on the electronics and cryogenics can be found in @xcite . a mercury argon light source with narrow band filters allows illumination with monochromatic light . . the fall time of the pulse of 50 @xmath0s limits the maximum count to around 2000 counts / pixel / second . the top right panel shows a histogram of the optimally estimated pulse height based on the detection of @xmath150,000 254 nm photons . the solid red curve is the fit of the sum of two gaussian to the histogram , showing an energy resolution r=16 , with a slightly broader shoulder extending to lower energies . the low energy shoulder is likely due to photons that miss the circular microlens and are absorbed in less sensitive areas of the resonator and photons that hit the substrate between the legs of the inductive meander . the bottom panel shows the fourier transform of the average pulse template in black ( arbitrary scale ) as well as the measured phase ( blue dotted line ) and amplitude ( red dashed line ) noise . ] the resonators were illuminated with 254 nm hg line photons , and their response was recorded as shown in figure [ fig : r ] . after processing with a wiener optimal filter an energy resolution r = e/@xmath12e=16 was measured , with @xmath12e being the fwhm . the expected energy resolution based on the measured noise power spectrum and average pulse template was also r=16 , showing good agreement with the actual measurements . as shown in the bottom panel of figure [ fig : r ] , the noise consists of both white amplifier noise and pink tls noise exclusively in the phase direction . most of the signal from the photons comes at frequencies above @xmath13 hz . at these frequencies the phase and amplitude noise are nearly identical , indicating that the dominant noise source is the hemt amplifier the white noise level of -83 dbc / hz at the device readout power of -103 dbm is consistent with an amplifier noise temperature of 4 kelvin assuming 3 db of loss between the mkid and the amplifier . reduction of the amplifier noise temperature or an increase in the maximum usable readout power should immediately improve the energy resolution . in a device with a fixed response ( degrees of phase shift per ev of photon energy ) the energy resolution scales linearly with photon energy , except for a region between 350 and 700 nm where a significant fraction of photons pass through the metal and are absorbed in the silicon substrate . these substrate events occur when a photon is absorbed close to the silicon / tin interface , causing a significant fraction of the phonons ( @xmath1470% ) created in the substrate to diffuse into the tin and break cooper pairs . these substrate events can give quite large signals , and will be discussed in depth in a future paper . simple device changes , such as making the tin film thicker or using a transparent substrate such as sapphire , should eliminate these unwanted substrate events . significant improvements can be made to increase the energy resolution , as the theoretical energy resolution set by the creation statistics of the quasiparticles created during downconversion is @xmath15 , where @xmath16 is the efficiency of creating quasiparticles @xcite , @xmath17 is the energy of the incident photon , @xmath18 is the gap energy of the superconducting absorber , and @xmath19 is the fano factor @xcite . this works out to r=150 at 5 ev for an operating temperature of 100 mk . an operating temperature of 15 mk could allow a theoretical maximum energy resolution of r=400 at 5 ev , although it is likely other noise sources , like two level system noise @xcite , will become more important as future development increases the energy resolution . figure [ fig : meas ] shows data from a typical 32x32 pixel device . in this device , 85% of the resonators were usable . simple number counts showed that at least 95% of the resonators were present , but variations in thickness and t@xmath20 of the tin film caused some resonators to have similar resonant frequencies and overlap in frequency . future improvement to the uniformity of the tin and a more robust algorithm for placement of resonators should significantly decrease the number of overlapping resonators . , was approximately @xmath21 . the bottom right panel is the frequency spacing in mhz between each resonator and its nearest neighbor . most of the missing resonators are too close together in frequency ( @xmath22 khz , noted with a dashed line ) , resulting in only one resonator being included in the plot . ] the quantum efficiency of the device was estimated by depositing a 40 nm tin film on sapphire and measuring the reflection and transmission of the film as a function of wavelength , then subtracting these quantities from unity to give the fraction of photons absorbed in the superconducting film , as shown in the top right panel of figure [ fig : meas ] . this was done with a varian cary 5000 spectrometer with accessories for absolute transmission and absolute specular reflectance . this figure slightly overestimates the quantum efficiency of the final device because it does not account for losses in the microlens array , or the @xmath110% correction due to photons below 0.5 @xmath0 m slipping through the slots in the inductor . the quantum efficiency is extremely good in the uv , but declines to about 30% at 1 @xmath0 m . further development will likely result in significant increases in quantum efficiency .

a mkid is an energy sensor based on a photon - variable superconducting inductance in a lithographed microresonator , and is capable of functioning as a photon detector across the electromagnetic spectrum as well as a particle detector . cho , t. m. crawford , a. t. crites , m. a. dobbs , n. w. halverson , s. heimsath , w. l. holzapfel , j. d. hrubes , m. joy , r. keisler , t. m. lanting , a. t. lee , e. m. leitch , j. leong , w. lu , m. lueker , d. luong - van , j. j. mcmahon , j. mehl , s. s. meyer , j. j. mohr , t. e. montroy , s. padin , t. plagge , c. pryke , j. e. ruhl , k. k. schaffer , d. schwan , e. shirokoff , h. g. spieler , z. staniszewski , a. a. stark , c. tucker , k. vanderlinde , j. d. vieira , and r. williamson , `` the 10 meter south pole telescope , '' pasp * 123 * , 568 ( 2011 ) . r. l. kelley , s. r. bandler , w. b. doriese , y. ezoe , r. fujimoto , l. gottardi , r. den hartog , j .- w . d. d. e. martin , p. verhoeve , a. peacock , a. g. kozorezov , j. k. wigmore , h. rogalla , and r. venn , `` resolution limitation due to phonon losses in superconducting tunnel junctions , '' appl . r. a. hijmering , p. verhoeve , d. d. e. martin , i. jerjen , a. g. kozorezov , and r. venn , `` direct position resolution measurement with droids at optical wavelengths , '' j. low temp . phys . * 151 * , 298 ( 2008 ) . p. verhoeve , d. d. e. martin , r. a. hijmering , j. verveer , a. van dordrecht , g. sirbi , t. oosterbroek , a. peacock , `` s - cam 3 : optical astronomy with a stj - based imaging spectrophotometer , '' nucl . j. gao , m. daal , a. vayonakis , s. kumar , j. zmuidzinas , b. sadoulet , b. a. mazin , p. k. day , and h. g. leduc , `` experimental evidence for a surface distribution of two - level systems in superconducting lithographed microwave resonators , '' appl . a. g. kozorezov , j. k. wigmore , d. martin , p. verhoeve , and a. peacock , `` electron energy down - conversion in thin superconducting films , '' phys . u. fano , `` ionization yield of radiations 2 : the fluctuations of the number of ions , '' phys .

microwave kinetic inductance detectors , or mkids , have proven to be a powerful cryogenic detector technology due to their sensitivity and the ease with which they can be multiplexed into large arrays . a mkid is an energy sensor based on a photon - variable superconducting inductance in a lithographed microresonator , and is capable of functioning as a photon detector across the electromagnetic spectrum as well as a particle detector . here we describe the first successful effort to create a photon - counting , energy - resolving ultraviolet , optical , and near infrared mkid focal plane array . these new optical lumped element ( ole ) mkid arrays have significant advantages over semiconductor detectors like charge coupled devices ( ccds ) . they can count individual photons with essentially no false counts and determine the energy and arrival time of every photon with good quantum efficiency . their physical pixel size and maximum count rate is well matched with large telescopes . these capabilities enable powerful new astrophysical instruments usable from the ground and space . mkids could eventually supplant semiconductor detectors for most astronomical instrumentation , and will be useful for other disciplines such as quantum optics and biological imaging . 10 d. bintley , m. j. macintosh , w. s. holland , p. friberg , c. walther , d. atkinson , d. kelly , x. gao , p. a. r. ade , w. grainger , j. house , l. moncelsi , m. i. hollister , a. woodcraft , c. dunare , w. parkes , a. j. walton , k. d. irwin , g. c. hilton , m. niemack , c. d. reintsema , m. amiri , b. burger , m. halpern , m. hasselfield , j. hill , j. b. kycia , c. g. a. mugford , and l. persaud , `` characterising the scuba-2 superconducting bolometer arrays , '' proc . spie * 7741 * , 2 ( 2010 ) . m. d. niemack , y. zhao , e. wollack , r. thornton , e. r. switzer , d. s. swetz , s. t. staggs , l. page , o. stryzak , h. moseley , t. a. marriage , m. limon , j. m. lau , j. klein , m. kaul , n. jarosik , k. d. irwin , a. d. hincks , g. c. hilton , m. halpern , j. w. fowler , r. p. fisher , r. dnner , w. b. doriese , s. r. dicker , m. j. devlin , j. chervenak , b. burger , e. s. battistelli , j. appel , m. amiri , c. allen , and a. m. aboobaker , `` a kilopixel array of tes bolometers for act : development , testing , and first light , '' j. low temp . phys . * 151 * , 690 ( 2008 ) . j. e. carlstrom , p. a. r. ade , k. a. aird , b. a. benson , l. e. bleem , s. busetti , c. l. chang , e. chauvin , h .- m . cho , t. m. crawford , a. t. crites , m. a. dobbs , n. w. halverson , s. heimsath , w. l. holzapfel , j. d. hrubes , m. joy , r. keisler , t. m. lanting , a. t. lee , e. m. leitch , j. leong , w. lu , m. lueker , d. luong - van , j. j. mcmahon , j. mehl , s. s. meyer , j. j. mohr , t. e. montroy , s. padin , t. plagge , c. pryke , j. e. ruhl , k. k. schaffer , d. schwan , e. shirokoff , h. g. spieler , z. staniszewski , a. a. stark , c. tucker , k. vanderlinde , j. d. vieira , and r. williamson , `` the 10 meter south pole telescope , '' pasp * 123 * , 568 ( 2011 ) . r. l. kelley , s. r. bandler , w. b. doriese , y. ezoe , r. fujimoto , l. gottardi , r. den hartog , j .- w . den herder , h. hoevers , k. irwin , y. ishisaki , c. a. kilbourne , p. de korte , j. van der kuur , k. mitsuda , t. ohashi , l. piro , f. s. porter , k. sato , k. shinozaki , p. shirron , s. j. smith , y. takei , p. whitehouse , and n. y. yamasaki , `` the x - ray microcalorimeter spectrometer for the international x - ray observatory , '' aip conf . proc . * 1185 * , 757 ( 2009 ) . w. b. doriese , j. n. ullom , j. a. beall , w. d. duncan , l. ferreira , g. c. hilton , r. d. horansky , k. d. irwin , j. a. b. mates , c. d. reintsema , l. r. vale , y. xu , b. l. zink , m. w. rabin , a. s. hoover , c. r. rudy , and d. t. vo , `` 14-pixel , multiplexed array of gamma - ray microcalorimeters with 47 ev energy resolution at 103 kev , '' appl . . lett . * 90 * , 3508 ( 2007 ) . m. d. eisaman , j. fan , a. migdall , and s. v. polyakov , `` single - photon sources and detectors , '' rev . sci . inst . * 82 * , 071101 ( 2011 ) . d. d. e. martin , p. verhoeve , a. peacock , a. g. kozorezov , j. k. wigmore , h. rogalla , and r. venn , `` resolution limitation due to phonon losses in superconducting tunnel junctions , '' appl . phys . lett . * 88 * , 3510 ( 2006 ) . r. a. hijmering , p. verhoeve , d. d. e. martin , i. jerjen , a. g. kozorezov , and r. venn , `` direct position resolution measurement with droids at optical wavelengths , '' j. low temp . phys . * 151 * , 298 ( 2008 ) . r. w. romani , a. j. miller , b. cabrera , s. w. nam , and j. m. martinis , `` phase - resolved crab studies with a cryogenic transition - edge sensor spectrophotometer , '' ap . j. * 563 * , 221 ( 2001 ) . j. burney , t. j. bay , j. barral , p. l. brink , b. cabrera , j. p. castle , a. j. miller , s. nam , d. rosenberg , r. w. romani , and a. tomada , `` transition - edge sensor arrays for uv - optical - ir astrophysics , '' nucl . instrum . meth . a * 559 * , 525 ( 2006 ) . m. d. niemack , j. beyer , h. m. cho , w. b. doriese , g. c. hilton , k. d. irwin , c. d. reintsema , d. r. schmidt , j. n. ullom , and l. r. vale , `` code - division squid multiplexing , '' appl . . lett . * 96 * , 3509 ( 2010 ) . p. day , h. leduc , b. mazin , a. vayonakis , and j. zmuidzinas , `` a superconducting detector suitable for use in large arrays , '' nature * 425 * , 817821 ( 2003 ) . j. a. schlaerth , n. g. czakon , p. k. day , t. p. downes , r. duan , j. gao , j. glenn , s. r. golwala , m. i. hollister , h. g. leduc , b. a. mazin , p. r. maloney , o. noroozian , h. t. nguyen , j. sayers , s. siegel , j. e. vaillancourt , a. vayonakis , p. r. wilson , and j. zmuidzinas , `` mkid multicolor array status and results from democam , '' proc . spie * 7741 * , 4 ( 2010 ) . ( c ) 2010 : american institute of physics . m. roesch , a. bideaud , a. benoit , a. cruciani , f. x. dsert , s. doyle , s. leclercq , f. mattiocco , k. f. schuster , l. swenson , and a. monfardini , `` characterization of lumped element kinetic inductance detectors for mm - wave detection , '' proc . spie * 7741 * , 16 ( 2010 ) . b. mazin , p. day , k. irwin , c. reintsema , and j. zmuidzinas , `` digital readouts for large microwave low - temperature detector arrays , '' nucl . instrum . meth . a * 559 * , 799801 ( 2006 ) . p. verhoeve , d. d. e. martin , r. a. hijmering , j. verveer , a. van dordrecht , g. sirbi , t. oosterbroek , a. peacock , `` s - cam 3 : optical astronomy with a stj - based imaging spectrophotometer , '' nucl . instrum . meth . a * 559 * , 598 ( 2006 ) . g. e. smith , `` the invention and early history of the ccd , '' app . . lett . * 109 * , 102421 ( 2011 ) . d. c. mattis and j. bardeen , `` theory of the anomalous skin effect in normal and superconducting metals , '' phys . rev . * 111 * , 412417 ( 1958 ) . s. doyle , p. mauskopf , j. naylon , a. porch , and c. duncombe , `` lumped element kinetic inductance detectors , '' j. low temp . phys . * 151 * , 530536 ( 2008 ) . h. g. leduc , b. bumble , p. k. day , b. h. eom , j. gao , s. golwala , b. a. mazin , s. mchugh , a. merrill , d. c. moore , o. noroozian , a. d. turner , and j. zmuidzinas , `` titanium nitride films for ultrasensitive microresonator detectors , '' appl . . lett . * 97 * , 102509 ( 2010 ) . o. noroozian , p. day , b. h. eom , h. leduc , and j. zmuidzinas , `` crosstalk reduction for superconducting microwave resonator arrays , '' ieee trans . microw . theory tech , submitted ( 2011 ) . j. gao , m. daal , a. vayonakis , s. kumar , j. zmuidzinas , b. sadoulet , b. a. mazin , p. k. day , and h. g. leduc , `` experimental evidence for a surface distribution of two - level systems in superconducting lithographed microwave resonators , '' appl . . lett . * 92 * , 152505 ( 2008 ) . b. a. mazin , `` microwave kinetic inductance detectors , '' , ph.d . thesis , california institute of technology ( 2004 ) . a. g. kozorezov , j. k. wigmore , d. martin , p. verhoeve , and a. peacock , `` electron energy down - conversion in thin superconducting films , '' phys . rev . b * 75 * , 094513 ( 2007 ) . u. fano , `` ionization yield of radiations 2 : the fluctuations of the number of ions , '' phys . rev . * 72 * , 2629 ( 1947 ) . j. r. crepp , l. pueyo , d. brenner , b. r. oppenheimer , n. zimmerman , s. hinkley , i. parry , d. king , g. vasisht , c. beichman , l. hillenbrand , r. dekany , m. shao , r. burruss , l. c. roberts , a. bouchez , j. roberts , and r. soummer , `` speckle suppression with the project 1640 integral field spectrograph , '' ap . j. * 729 * , 132 ( 2011 ) . r. j. bouwens , g. d. illingworth , m. franx , and h. ford , `` z 7 - 10 galaxies in the hudf and goods fields : uv luminosity functions , '' ap . j. * 686 * , 230 ( 2008 ) . l. ma , s. nam , h. xu , b. baek , t. chang , o. slattery , a. mink , and x. tang , `` 1310 nm differential - phase - shift qkd system using superconducting single - photon detectors , '' new j. phys . * 11 * , 045020 ( 2009 ) . i. tinoco and r. l. gonzalez , `` biological mechanisms , one molecule at a time , '' gene dev . , * 25 * , 12051231 ( 2011 ) .

1112.0004

c

improvements in the fabrication of tin films will lead to increased uniformity and fabrication yield . the array size can be grown nearly arbitrarily by adding more resonators per feedline , likely to a maximum of around 10,000 resonators in a 1020 ghz band , and then by adding more microwave feedlines . the primary challenges to growing the array are in the digitization bandwidth and processing power of the room temperature electronics , not the device fabrication . ole mkid arrays have now been proven in the lab , and the first astronomical test at the palomar 200 inch telescope has been conducted with data taken on a variety of astronomical objects . these arrays will bring extreme performance improvements to some of the most exciting areas of astrophysics , such as coronagraphic planet finding @xcite , transient and time variable sources @xcite , and high redshift galaxy evolution @xcite , and will likely also find application in other fields such as quantum optics @xcite and biological imaging @xcite . this material is based upon work supported by the national aeronautics and space administration under grant nnx09ad54 g , issued through the science mission directorate , jet propulsion lab s research & technology development program , and a grant from the w.m . keck institute for space studies . part of the research was carried out at the jet propulsion laboratory , california institute of technology , under a contract with the national aeronautics and space administration . the authors would like to thank rick leduc , jonas zmuidzinas , sunil golwala , david moore , peter day , and omid noroozian for useful insights .

mkids could eventually supplant semiconductor detectors for most astronomical instrumentation , and will be useful for other disciplines such as quantum optics and biological imaging . 10 d. bintley , m. j. macintosh , w. s. holland , p. friberg , c. walther , d. atkinson , d. kelly , x. gao , p. a. r. ade , w. grainger , j. house , l. moncelsi , m. i. hollister , a. woodcraft , c. dunare , w. parkes , a. j. walton , k. d. irwin , g. c. hilton , m. niemack , c. d. reintsema , m. amiri , b. burger , m. halpern , m. hasselfield , j. hill , j. b. kycia , c. g. a. mugford , and l. persaud , `` characterising the scuba-2 superconducting bolometer arrays , '' proc . m . g. e. smith , `` the invention and early history of the ccd , '' app . d. c. mattis and j. bardeen , `` theory of the anomalous skin effect in normal and superconducting metals , '' phys . h. g. leduc , b. bumble , p. k. day , b. h. eom , j. gao , s. golwala , b. a. mazin , s. mchugh , a. merrill , d. c. moore , o. noroozian , a. d. turner , and j. zmuidzinas , `` titanium nitride films for ultrasensitive microresonator detectors , '' appl . thesis , california institute of technology ( 2004 ) . j. r. crepp , l. pueyo , d. brenner , b. r. oppenheimer , n. zimmerman , s. hinkley , i. parry , d. king , g. vasisht , c. beichman , l. hillenbrand , r. dekany , m. shao , r. burruss , l. c. roberts , a. bouchez , j. roberts , and r. soummer , `` speckle suppression with the project 1640 integral field spectrograph , '' ap . j. * 729 * , 132 ( 2011 ) . r. j. bouwens , g. d. illingworth , m. franx , and h. ford , `` z 7 - 10 galaxies in the hudf and goods fields : uv luminosity functions , '' ap . i. tinoco and r. l. gonzalez , `` biological mechanisms , one molecule at a time , '' gene dev . , * 25 * , 12051231 ( 2011 ) .

microwave kinetic inductance detectors , or mkids , have proven to be a powerful cryogenic detector technology due to their sensitivity and the ease with which they can be multiplexed into large arrays . a mkid is an energy sensor based on a photon - variable superconducting inductance in a lithographed microresonator , and is capable of functioning as a photon detector across the electromagnetic spectrum as well as a particle detector . here we describe the first successful effort to create a photon - counting , energy - resolving ultraviolet , optical , and near infrared mkid focal plane array . these new optical lumped element ( ole ) mkid arrays have significant advantages over semiconductor detectors like charge coupled devices ( ccds ) . they can count individual photons with essentially no false counts and determine the energy and arrival time of every photon with good quantum efficiency . their physical pixel size and maximum count rate is well matched with large telescopes . these capabilities enable powerful new astrophysical instruments usable from the ground and space . mkids could eventually supplant semiconductor detectors for most astronomical instrumentation , and will be useful for other disciplines such as quantum optics and biological imaging . 10 d. bintley , m. j. macintosh , w. s. holland , p. friberg , c. walther , d. atkinson , d. kelly , x. gao , p. a. r. ade , w. grainger , j. house , l. moncelsi , m. i. hollister , a. woodcraft , c. dunare , w. parkes , a. j. walton , k. d. irwin , g. c. hilton , m. niemack , c. d. reintsema , m. amiri , b. burger , m. halpern , m. hasselfield , j. hill , j. b. kycia , c. g. a. mugford , and l. persaud , `` characterising the scuba-2 superconducting bolometer arrays , '' proc . spie * 7741 * , 2 ( 2010 ) . m. d. niemack , y. zhao , e. wollack , r. thornton , e. r. switzer , d. s. swetz , s. t. staggs , l. page , o. stryzak , h. moseley , t. a. marriage , m. limon , j. m. lau , j. klein , m. kaul , n. jarosik , k. d. irwin , a. d. hincks , g. c. hilton , m. halpern , j. w. fowler , r. p. fisher , r. dnner , w. b. doriese , s. r. dicker , m. j. devlin , j. chervenak , b. burger , e. s. battistelli , j. appel , m. amiri , c. allen , and a. m. aboobaker , `` a kilopixel array of tes bolometers for act : development , testing , and first light , '' j. low temp . phys . * 151 * , 690 ( 2008 ) . j. e. carlstrom , p. a. r. ade , k. a. aird , b. a. benson , l. e. bleem , s. busetti , c. l. chang , e. chauvin , h .- m . cho , t. m. crawford , a. t. crites , m. a. dobbs , n. w. halverson , s. heimsath , w. l. holzapfel , j. d. hrubes , m. joy , r. keisler , t. m. lanting , a. t. lee , e. m. leitch , j. leong , w. lu , m. lueker , d. luong - van , j. j. mcmahon , j. mehl , s. s. meyer , j. j. mohr , t. e. montroy , s. padin , t. plagge , c. pryke , j. e. ruhl , k. k. schaffer , d. schwan , e. shirokoff , h. g. spieler , z. staniszewski , a. a. stark , c. tucker , k. vanderlinde , j. d. vieira , and r. williamson , `` the 10 meter south pole telescope , '' pasp * 123 * , 568 ( 2011 ) . r. l. kelley , s. r. bandler , w. b. doriese , y. ezoe , r. fujimoto , l. gottardi , r. den hartog , j .- w . den herder , h. hoevers , k. irwin , y. ishisaki , c. a. kilbourne , p. de korte , j. van der kuur , k. mitsuda , t. ohashi , l. piro , f. s. porter , k. sato , k. shinozaki , p. shirron , s. j. smith , y. takei , p. whitehouse , and n. y. yamasaki , `` the x - ray microcalorimeter spectrometer for the international x - ray observatory , '' aip conf . proc . * 1185 * , 757 ( 2009 ) . w. b. doriese , j. n. ullom , j. a. beall , w. d. duncan , l. ferreira , g. c. hilton , r. d. horansky , k. d. irwin , j. a. b. mates , c. d. reintsema , l. r. vale , y. xu , b. l. zink , m. w. rabin , a. s. hoover , c. r. rudy , and d. t. vo , `` 14-pixel , multiplexed array of gamma - ray microcalorimeters with 47 ev energy resolution at 103 kev , '' appl . . lett . * 90 * , 3508 ( 2007 ) . m. d. eisaman , j. fan , a. migdall , and s. v. polyakov , `` single - photon sources and detectors , '' rev . sci . inst . * 82 * , 071101 ( 2011 ) . d. d. e. martin , p. verhoeve , a. peacock , a. g. kozorezov , j. k. wigmore , h. rogalla , and r. venn , `` resolution limitation due to phonon losses in superconducting tunnel junctions , '' appl . phys . lett . * 88 * , 3510 ( 2006 ) . r. a. hijmering , p. verhoeve , d. d. e. martin , i. jerjen , a. g. kozorezov , and r. venn , `` direct position resolution measurement with droids at optical wavelengths , '' j. low temp . phys . * 151 * , 298 ( 2008 ) . r. w. romani , a. j. miller , b. cabrera , s. w. nam , and j. m. martinis , `` phase - resolved crab studies with a cryogenic transition - edge sensor spectrophotometer , '' ap . j. * 563 * , 221 ( 2001 ) . j. burney , t. j. bay , j. barral , p. l. brink , b. cabrera , j. p. castle , a. j. miller , s. nam , d. rosenberg , r. w. romani , and a. tomada , `` transition - edge sensor arrays for uv - optical - ir astrophysics , '' nucl . instrum . meth . a * 559 * , 525 ( 2006 ) . m. d. niemack , j. beyer , h. m. cho , w. b. doriese , g. c. hilton , k. d. irwin , c. d. reintsema , d. r. schmidt , j. n. ullom , and l. r. vale , `` code - division squid multiplexing , '' appl . . lett . * 96 * , 3509 ( 2010 ) . p. day , h. leduc , b. mazin , a. vayonakis , and j. zmuidzinas , `` a superconducting detector suitable for use in large arrays , '' nature * 425 * , 817821 ( 2003 ) . j. a. schlaerth , n. g. czakon , p. k. day , t. p. downes , r. duan , j. gao , j. glenn , s. r. golwala , m. i. hollister , h. g. leduc , b. a. mazin , p. r. maloney , o. noroozian , h. t. nguyen , j. sayers , s. siegel , j. e. vaillancourt , a. vayonakis , p. r. wilson , and j. zmuidzinas , `` mkid multicolor array status and results from democam , '' proc . spie * 7741 * , 4 ( 2010 ) . ( c ) 2010 : american institute of physics . m. roesch , a. bideaud , a. benoit , a. cruciani , f. x. dsert , s. doyle , s. leclercq , f. mattiocco , k. f. schuster , l. swenson , and a. monfardini , `` characterization of lumped element kinetic inductance detectors for mm - wave detection , '' proc . spie * 7741 * , 16 ( 2010 ) . b. mazin , p. day , k. irwin , c. reintsema , and j. zmuidzinas , `` digital readouts for large microwave low - temperature detector arrays , '' nucl . instrum . meth . a * 559 * , 799801 ( 2006 ) . p. verhoeve , d. d. e. martin , r. a. hijmering , j. verveer , a. van dordrecht , g. sirbi , t. oosterbroek , a. peacock , `` s - cam 3 : optical astronomy with a stj - based imaging spectrophotometer , '' nucl . instrum . meth . a * 559 * , 598 ( 2006 ) . g. e. smith , `` the invention and early history of the ccd , '' app . . lett . * 109 * , 102421 ( 2011 ) . d. c. mattis and j. bardeen , `` theory of the anomalous skin effect in normal and superconducting metals , '' phys . rev . * 111 * , 412417 ( 1958 ) . s. doyle , p. mauskopf , j. naylon , a. porch , and c. duncombe , `` lumped element kinetic inductance detectors , '' j. low temp . phys . * 151 * , 530536 ( 2008 ) . h. g. leduc , b. bumble , p. k. day , b. h. eom , j. gao , s. golwala , b. a. mazin , s. mchugh , a. merrill , d. c. moore , o. noroozian , a. d. turner , and j. zmuidzinas , `` titanium nitride films for ultrasensitive microresonator detectors , '' appl . . lett . * 97 * , 102509 ( 2010 ) . o. noroozian , p. day , b. h. eom , h. leduc , and j. zmuidzinas , `` crosstalk reduction for superconducting microwave resonator arrays , '' ieee trans . microw . theory tech , submitted ( 2011 ) . j. gao , m. daal , a. vayonakis , s. kumar , j. zmuidzinas , b. sadoulet , b. a. mazin , p. k. day , and h. g. leduc , `` experimental evidence for a surface distribution of two - level systems in superconducting lithographed microwave resonators , '' appl . . lett . * 92 * , 152505 ( 2008 ) . b. a. mazin , `` microwave kinetic inductance detectors , '' , ph.d . thesis , california institute of technology ( 2004 ) . a. g. kozorezov , j. k. wigmore , d. martin , p. verhoeve , and a. peacock , `` electron energy down - conversion in thin superconducting films , '' phys . rev . b * 75 * , 094513 ( 2007 ) . u. fano , `` ionization yield of radiations 2 : the fluctuations of the number of ions , '' phys . rev . * 72 * , 2629 ( 1947 ) . j. r. crepp , l. pueyo , d. brenner , b. r. oppenheimer , n. zimmerman , s. hinkley , i. parry , d. king , g. vasisht , c. beichman , l. hillenbrand , r. dekany , m. shao , r. burruss , l. c. roberts , a. bouchez , j. roberts , and r. soummer , `` speckle suppression with the project 1640 integral field spectrograph , '' ap . j. * 729 * , 132 ( 2011 ) . r. j. bouwens , g. d. illingworth , m. franx , and h. ford , `` z 7 - 10 galaxies in the hudf and goods fields : uv luminosity functions , '' ap . j. * 686 * , 230 ( 2008 ) . l. ma , s. nam , h. xu , b. baek , t. chang , o. slattery , a. mink , and x. tang , `` 1310 nm differential - phase - shift qkd system using superconducting single - photon detectors , '' new j. phys . * 11 * , 045020 ( 2009 ) . i. tinoco and r. l. gonzalez , `` biological mechanisms , one molecule at a time , '' gene dev . , * 25 * , 12051231 ( 2011 ) .

1111.2877

i

the _ rosat _ all - sky survey ( rass ; @xcite ) showed that our census of cooling , nearby neutron stars was incomplete : it contained not just the known cooling pulsars such as and , but also seven `` isolated neutron stars '' ( inss ) . these are nearby ( @xmath6 ) , young ( @xmath7 ) , cooling neutron stars with thermal x - ray spectra , long periods ( @xmath8 ) , faint optical counterparts , and no detected radio emission ( for reviews , see @xcite ) . the inss are interesting both because of their abundance and because of the promise of inferring neutron - star parameters from their thermal emission . unfortunately , despite large investments of time with _ chandra _ and _ xmm - newton _ , the nature of the emission remains puzzling , and we still understand neither the composition nor state ( gaseous , condensed ) of the surface . a clearer picture has emerged for the origin and abundance of the inss : most likely , they were born with very strong magnetic fields , of @xmath9 , which decayed . empirical evidence for this comes from our x - ray timing efforts @xcite , which showed that the current field strengths of the inss are remarkably similar , in the range 1.0 to @xmath10 g , and that their characteristic ages of several myr are substantially in excess of true ages of @xmath11myr inferred from cooling and kinematics ( @xcite ; @xcite ; @xcite ) . the long periods and characteristic ages follow naturally if the inss initially had much stronger fields and thus faster spindown , and the similar current field strengths can be understood if fields stop decaying at a common value . indeed , this was predicted theoretically by @xcite : for initially weak magnetic fields , field decay leads to only a factor @xmath12 change that is essentially unnoticeable @xcite , while for fields above @xmath13 g field decay becomes increasingly important , with predicted final fields that are always a @xmath14 g , independent of the initial values . the field - decay induced heating may also help explain the observed preponderance of inss compared to `` normal '' middle - aged pulsars @xcite . if the above is correct , the progenitors of the inss would have been neutron stars with fields ranging from @xmath15 to @xmath16 g . the most magnetized would correspond to magnetars , but many would not be so energetic . still , as their fields decay on @xmath17kyr timescales , they should be brighter than expected from simple cooling , and there should be a population of relatively long - period , strong - field sources that are anomalously hot . verifying this might not only confirm the hypothesis for the ins population , but also yield clues to their emission : with the higher temperatures and stronger magnetic fields , one might expect the surface to have a different state and the spectra to show different spectral features that could be contrasted to the inss . checking the @xmath18 diagram for possible ins progenitors ( fig . [ fig : ppdot ] ) , one finds four radio pulsars , one rotating radio transient ( rrat ) , and one relatively low - field anomalous x - ray pulsar ( axp ) ; all have periods longer than 3s and fields in excess of @xmath19 g . of course , the axp ( ) , like other magnetars , is thought to be powered by magnetic field decay ; it certainly is anomalously hot , with @xmath20kev @xcite . of the others , the rrat and one of the pulsars have x - ray counterparts as well , with thermal spectra and inferred temperatures of @xmath21ev ( , @xcite ; , @xcite ) . these temperatures are , as the authors mention , well above expectations from simple cooling ( and also well above the limit of @xmath22ev inferred for @xcite , a young pulsar with a somewhat weaker inferred field ; see fig . [ fig : ppdot ] ) . the best - studied source , , also has a clear absorption feature at 1kev , well above the energies at which absorption is seen in the inss . among the three remaining sources , and have unpublished , reasonably long _ xmm _ observations . we checked these and found no counterparts , but as both pulsars are distant and extincted , this is not unexpected . indeed all of these objects are considerably further than the inss , and while part of this can be explained by their small ages leading to lower space densities , part comes from the narrowly - beamed / intermittent radio emission that is used to detect them ( compared to omni - directional soft x - rays ) . the last source , ( hereafter ) is the subject of this paper . this 3.44s pulsar was discovered in the course of the parkes high - latitude survey @xcite but surprisingly has not seen any x - ray follow - up , despite its inferred magnetic field of @xmath23 g and characteristic age of only @xmath24kyr . yet , it is arguably the most interesting , since it should be the least extincted both because it has the lowest dispersion measure ( dm ) of all ( 70 vs. 200 to @xmath25 for the other four pulsars ) and because it is at what is , for a young pulsar , high galactic latitude ( @xmath26 vs.@xmath27 for the others ) . furthermore , it may well be the closest . from its dispersion measure , combined with a model of the galactic electron distribution @xcite , one infers a rough distance of 3kpc . but at that distance , its height above the galactic plane is 250pc , which is somewhat improbable . a more likely alternative is that it is at @xmath28kpc , situated ( and born ) in the @xcite , which this line of sight passes through ( and which may influence the dispersion measure ) . below , we will scale our distances to @xmath29 . overall , seems a prime candidate for comparison with the inss , being relatively close and unabsorbed , and apparently intermediate between the stronger - field pulsars that look most like ins progenitors and the weak - field normal pulsars that form the bulk of the population . intriguingly , we found a possible counterpart to in the rass : , with @xmath30 . the nominal separation of @xmath31 from the pulsar is relatively large , but in the rass image , the source seemed somewhat extended , encompassing the pulsar . here , we present a _ chandra x - ray observatory _ of that confirms the identification with , and allows a first comparison between and the inss , opening the way for detailed followup .

middle - aged , cooling neutron stars are observed both as relatively rapidly spinning radio pulsars and as more slowly spinning , strongly magnetized isolated neutron stars ( inss ) , which stand out by their thermal x - ray spectra . , we used the _ chandra x - ray observatory _ to observe , a possible x - ray counterpart to , which , with its @xmath0s period and @xmath1 g inferred magnetic field strength , is the nearest and least extincted among the possible slowly - spinning , strong - field ins progenitors ( it likely is in the gould belt , at @xmath2 ) . the properties of strongly resemble those of the inss , except for its much shorter characteristic age of 200kyr ( instead of several myr ) . our results suggest that the long - period , strong - field pulsars and the inss are members of the same class , and open up new opportunities to understand the puzzling x - ray and optical emission of the inss through radio observations of .

middle - aged , cooling neutron stars are observed both as relatively rapidly spinning radio pulsars and as more slowly spinning , strongly magnetized isolated neutron stars ( inss ) , which stand out by their thermal x - ray spectra . the difference between the two classes may be that the inss initially had much stronger magnetic fields , which decayed . to test this , we used the _ chandra x - ray observatory _ to observe , a possible x - ray counterpart to , which , with its @xmath0s period and @xmath1 g inferred magnetic field strength , is the nearest and least extincted among the possible slowly - spinning , strong - field ins progenitors ( it likely is in the gould belt , at @xmath2 ) . we confirm the identification and find that the pulsar has a spectrum consistent with being purely thermal , with blackbody temperature @xmath3ev and radius @xmath4 at a distance of 1kpc . we detect sinusoidal pulsations at twice the radio period with a semi - amplitude of @xmath5 . the properties of strongly resemble those of the inss , except for its much shorter characteristic age of 200kyr ( instead of several myr ) . we conclude that is indeed an example of a young ins , one that started with a magnetic field strength on the low end of those inferred for the inss , and that , therefore , decayed by a relatively small amount . our results suggest that the long - period , strong - field pulsars and the inss are members of the same class , and open up new opportunities to understand the puzzling x - ray and optical emission of the inss through radio observations of .

1111.2877

c

regardless of the path by which and the inss got to their present states , we can examine how closely their current properties resemble each other and whether the unique information from either helps understand the thermal emission from this class of neutron stars as a whole . furthermore , we can see how might help us understand the evolution of high-@xmath75 pulsars and the origin of the inss . we consider these in turn . was selected to be similar to the inss in having a long spin - period , @xmath76s , and strong magnetic field , @xmath77 g . with a thermal spectrum with @xmath78 , and @xmath79 ( at the nominal distance of @xmath28kpc in the ) , its x - ray properties are similar as well ( indeed , it would be classified as an ins based on these ) . its spectrum has no evidence for absorption , unlike , which has strong absorption @xcite while having a very similar magnetic field and a slightly higher temperature ( @xmath80 g , @xcite ; @xmath81ev , @xcite ) . however , , another ins with a similar if slightly lower field ( @xmath82 g , @xcite ) , had weak absorption , with an equivalent width of @xmath83 , which we would not be able to detect , when its temperature was most similar to ( @xmath84 , @xcite ) . intriguingly , this source changed , developing much stronger absorption while becoming hotter ( @xmath85 , @xcite ) . taking our inferred temperature at face value , it is thus possible that emits identically to an ins of the same temperature and dipole magnetic field strength . if so , at higher sensitivity it may show weak absorption at @xmath86 . ( we caution , however , that the dependencies of absorption energy and strength on temperature and magnetic field strength remain puzzling for the inss as a class ; @xcite . ) l c c c c c c blackbody & @xmath87 & @xmath88 & @xmath89 & @xmath90 & @xmath91 & @xmath92 + blackbody & @xmath93 & @xmath94 & @xmath95 & 4.5 & 5.6 & 48.1/68 + blackbody & @xmath96 & @xmath97 & @xmath98 & 3.6 & 33.8 & 55.0/68 + nsa @xmath99 & @xmath100 & @xmath101 & @xmath102 & @xmath103 & @xmath104 & @xmath105 + nsa @xmath106 & @xmath107 & @xmath108 & @xmath109 & @xmath110 & @xmath111 & @xmath105 + power law ( @xmath112 free ) & @xmath113 & @xmath114 & @xmath115 & @xmath103 & @xmath116 & @xmath117 + power law ( @xmath118 ) & @xmath119 & @xmath120 & @xmath121 & @xmath122 & @xmath122 & @xmath123 + + minima & @xmath124 & @xmath125 & @xmath126 & @xmath127 & @xmath128 & @xmath129 + maxima & @xmath124 & @xmath130 & @xmath131 & @xmath132 & @xmath133 & @xmath134 + the inferred luminosity @xmath135 ( 0.321.1kev ) is about half the rotational energy loss rate @xmath136 ( for a moment of inertia @xmath137 ) . this is on the low side of what is seen for the inss ( @xmath138 ) , possibly just a consequence of having a shorter period for the same @xmath75 ( for dipole spin - down , @xmath139 ) . it is much larger than the non - thermal emission typically observed for rotation - powered pulsars ( @xmath140 , @xcite ) , although we can not exclude that has a similar non - thermal component : our 1@xmath73 upper limit of 3% of the 0.321.1kev flux for the contribution of a power - law with @xmath65 ( a value typical for pulsars ) implies @xmath141 . the pulse properties of also echo those of the inss , which show smooth profiles dominated by the fundamental or the first harmonic . the pulse fraction of @xmath142% is a little larger than the @xmath143 to 18% seen for the inss @xcite , but it is not dramatically different . we note that without the radio period , we might have actually identified the pulse period of as half of the true value . the lack of temperature variation is somewhat strange ( cf . up to 10% changes in @xmath144 over the pulse of , for example ; @xcite ) , as , naively , it implies that we are seeing changes in projected area of large regions of similar temperature with anything in between so much colder that it does not contribute . it may be that instead the whole surface emits at more or less a uniform temperature , and that the pulsations reflect anisotropies in the emission , perhaps associated with the strong magnetic field . the same may hold for the inss , which typically also show only modest changes in temperature with pulse phase . a possible difference with the inss is that has an order - of - magnitude smaller characteristic age . this may again be a consequence of its shorter period for the same @xmath75 ( for dipole spin - down , @xmath145 ) , but might also point to an evolutionary difference ( see below ) . another characteristic of inss is that they have faint optical counterparts , but with optical / uv fluxes a factor of 650 above the extrapolation of the x - rays . this is in contrast to middle - aged pulsars such as and , which have ultraviolet fluxes that are more consistent with the x - ray extrapolations @xcite . it will be interesting to see whether has an excess or not . of course , the most glaring difference between and the inss is the radio emission . numerous searches have yet to find confirmed radio emission ( coherent or bursty ) from the inss ( @xcite , and references therein ) . this may be a result of their location near the pulsar `` death line , '' or more simply a consequence of their narrow radio beams : the 50% width of the radio pulse from is @xmath146 of the pulse period ( consistent with general trends for long - period pulsars ) so the chance of missing the radio pulse is large . overall , we conclude that with the exceptions of its radio emission and characteristic age , the properties of agree with those of the inss . based on the compilations of @xcite , @xcite , and references therein , it is the best pulsar analog to the inss to date . in order to look for evolutionary trends , we can compare to sources with similar properties in the @xmath147-@xmath148 diagram , as well as with the evolution expected from the work of @xcite , which seems to explain the origins of the inss ( fig . [ fig : ppdot ] ) . a first comparison is with inss of similar field and temperature , and . as mentioned , the main difference is that the characteristic age of is @xmath149kyr , while those of the inss are @xmath150myr . this could imply that the true age of is closer to its characteristic age than is the case for the inss , and maybe that it has undergone less @xmath75 decay . this is consistent with the models of @xcite : @xmath1 g is near the dividing line where field - decay becomes important , and the true age is expected to be no more than a factor 2 shorter than the characteristic age ( see fig . [ fig : ppdot ] ) . taking the models at face value , one infers that was born with a dipole field of just below @xmath151 g , while most inss would have had a field about a factor 2 stronger . as a second comparison , we can compare with two x - ray - detected objects that have almost the same period : the modest-@xmath75 ins ( @xmath152 g , @xcite ) , and the high-@xmath75 pulsar ( @xmath153 g , @xcite ) . the former is very similar to , with the main difference being that it is cooler ( @xmath154ev ) . from the evolutionary tracks , it seems most likely initially simply had even lower magnetic field strength , which decayed by a factor @xmath12 or so , and that , like , its true age is at most a factor 2 shorter than its characteristic age of 2myr . from the evolutionary tracks , would be a good candidate progenitor for inss like , and indeed it has a largely thermal spectrum consistent with a blackbody with a significantly hotter temperature ( @xmath155ev ) , suggestive of on - going field decay . however , the emitting radius of @xmath156 km and pulsed fraction of @xmath157% differ from those found for the inss ( and ) , and are more reminiscent of even younger high-@xmath75 pulsars like @xcite , which also have high pulsed fractions and smaller radii ( although distance and fitting uncertainties make the radii for all these objects poorly constrained ) . it may be that this reflects some combination of ongoing @xmath75 decay and non - thermal heating ; all these younger , strong - field objects have substantially larger spin - down energy losses . alternatively , the stronger field may lead to more anisotropic emission . overall , it seems that the inss and high-@xmath75 pulsars form a single family ( also see @xcite for further discussion ) , with initial fields that were stronger than their current ones , and that caused rapid initial spin - down . the long periods for the slower spinning objects also imply low rotational energy losses and thus weak non - thermal emission . combined with some additional heating due to field decay , this makes the thermal emission stand out more than it would in normal pulsars . a continuing puzzle , however , is the difference with the magnetars @xcite , which occupy similar parts of the @xmath147-@xmath148 diagram , but are clearly much more strongly affected by magnetic field decay . it may be that those were born with much stronger toroidal components to the field ( which affect the spin - down only indirectly , via the more rapid field decay ) . in any case , there may be a smooth continuum , given objects like ( @xmath158 g ) which exhibited a sudden , magnetar - like x - ray outburst @xcite , the ins that exhibited a possible magnetic reconfiguration @xcite , the transient magnetar that was detected in outburst @xcite but in quiescence appears more like an ins @xcite , or the putative low-@xmath75 magnetar ( @xmath159 g ; @xcite ) .

the difference between the two classes may be that the inss initially had much stronger magnetic fields , which decayed . to test this we confirm the identification and find that the pulsar has a spectrum consistent with being purely thermal , with blackbody temperature @xmath3ev and radius @xmath4 at a distance of 1kpc .

middle - aged , cooling neutron stars are observed both as relatively rapidly spinning radio pulsars and as more slowly spinning , strongly magnetized isolated neutron stars ( inss ) , which stand out by their thermal x - ray spectra . the difference between the two classes may be that the inss initially had much stronger magnetic fields , which decayed . to test this , we used the _ chandra x - ray observatory _ to observe , a possible x - ray counterpart to , which , with its @xmath0s period and @xmath1 g inferred magnetic field strength , is the nearest and least extincted among the possible slowly - spinning , strong - field ins progenitors ( it likely is in the gould belt , at @xmath2 ) . we confirm the identification and find that the pulsar has a spectrum consistent with being purely thermal , with blackbody temperature @xmath3ev and radius @xmath4 at a distance of 1kpc . we detect sinusoidal pulsations at twice the radio period with a semi - amplitude of @xmath5 . the properties of strongly resemble those of the inss , except for its much shorter characteristic age of 200kyr ( instead of several myr ) . we conclude that is indeed an example of a young ins , one that started with a magnetic field strength on the low end of those inferred for the inss , and that , therefore , decayed by a relatively small amount . our results suggest that the long - period , strong - field pulsars and the inss are members of the same class , and open up new opportunities to understand the puzzling x - ray and optical emission of the inss through radio observations of .

cond-mat0601094

i

two - dimensional ( 2d ) materials present some fascinating challenges to condensed - matter theory , with even the most simple 2d systems harboring surprises . one of the most famous problems involves the precise description of melting in 2d solids made up of hard , disk - like particles with short - range repulsive interactions.@xcite specifically , does the fluid undergo a weak first - order transition to the solid , or is there an intermediate hexatic phase linked by two continuous phase transitions ? related avenues of research concern the existence of exotic phases in systems made up of more complex particles , such as ( non)periodic solids of hard - disk dimers,@xcite pentamers and hexamers,@xcite tetratic phases of hard squares@xcite and hard rectangles,@xcite and orientationally ordered solids of hard pentagons and heptagons.@xcite the effects of additional interactions on the phase behavior and dynamics of 2d systems are also of interest , as evidenced by recent studies on dipolar potentials in the context of magnetic colloids.@xcite such models provide an ideal testing ground for condensed - matter theories , and in some cases challenge our most fundamental understanding of the properties of matter . despite their simplicity , 2d models can provide reliable descriptions of some real , and rather complex , experimental situations . for example , in a number of recent studies , 2d models have been employed to help interpret and understand the clustering and crystallization of proteins at interfaces . the conformations and interactions of proteins are central to biological activity , and ideally one would like to investigate these properties _ in vivo_. unfortunately , structural information is most commonly obtained from x - ray diffraction studies on crystals . there is a class of proteins , however , that can be studied under conditions resembling those _ in vivo_. membrane proteins constitute a large class of molecules found within the lipid bilayers that constitute cell walls . they fulfill a variety of roles , such as controlling the selective transport of ions and molecules across cell membranes , or providing binding sites for other molecules on to the membrane . the structures of membrane proteins can be studied by deposition on to a surface , alongside lipids , to form either low surface - coverages or 2d crystals ; the hydrophobic lipids help to mimic the interior of the membrane . electron microscopy or atomic - force microscopy can then be used to image directly the clustering and packing of proteins at the solid - air interface.@xcite in many cases , the ordering of proteins can be rationalized on the basis of their gross shapes ( the way in which those shapes would ` tile the plane ' ) and the presence of specific binding interactions between domains on different molecules . for example , the surface structure of bacteriorhodopsin ( a transmembrane protein ) is comprised of a close - packed array of trimers , each made up of monomers that resemble @xmath0 sectors of a circle . monte carlo ( mc ) simulations of hard sectors with an additional attractive square - well potential to mimic specific binding interactions yield insight on the self - assembly and subsequent crystallization processes.@xcite in another application , the ordering in 2d crystals of annexin v another ` triangular ' membrane protein was reproduced in simulations of a hard - disk model decorated with an appropriate orientation - dependent potential to mimic the locations of the specific binding sites on the protein . experimentally observed honeycomb and triangular structures were captured by the molecular model . these examples show that the basic physics of large - scale structural order in 2d protein crystals can be studied with simple models , and without resorting to atomistically detailed and hence very expensive computer simulations . there are a large number of proteins which are either inherently triangular in shape , or otherwise form trimeric structures . for example , rotavirus inner capsid protein v6 forms trimers resembling equililateral triangles , which pack in 2d crystals ( space group @xmath1).@xcite specific fragments of prion proteins found _ in vivo _ form trimeric units that crystallize in to a 2d structure ( space group @xmath2).@xcite finally , we highlight an example in which a membrane fusion protein ( from the semiliki forest virus ) is seen to form pentagons of trimers , with the center of the pentagon raised slightly out of the plane.@xcite some semblance of local five - fold coordination can also been seen in teta a roughly triangular transporter protein at moderate surface coverages.@xcite motivated by the diversity of 2d crystal structures exhibited by trimeric protein units , and also by the observation of five - fold coordination,@xcite we have investigated the structure and phase behavior of model trimeric molecules made up of hard disks . in order to mimic specific binding interactions , such as those that might give rise to local five - fold coordination , we focus on an equililateral triangle of three hard disks at contact , in which one disk can interact with the corresponding disks on other molecules _ via _ a short - range attractive square - well potential . as we will show below , this raises the possibility of generating orientational order within simple close - packed structures , and also offers the opportunity of forming clusters at low surface coverages . using mc simulations , we map out the phase diagram of the model system , and characterize the structures of the low - density clustered fluid and high - density solids which are formed at low temperature . the remainder of the article is organized as follows . in section [ sec : model ] we describe the molecular model , and summarize the simulation methods . the results are presented in section [ sec : results ] , and section [ sec : discussion ] concludes the paper .

motivated by the diversity and complexity of two - dimensional crystals formed by triangular proteins and protein trimers , we have investigated the structures and phase behavior of hard - disk trimers . in order to mimic specific binding interactions , each trimer possesses on ` attractive ' disk which can interact with similar disks on other trimers _ via _ an attractive square - well potential . at low density and low temperature , the fluid phase mainly consists of tetramers , pentamers , or hexamers .

motivated by the diversity and complexity of two - dimensional crystals formed by triangular proteins and protein trimers , we have investigated the structures and phase behavior of hard - disk trimers . in order to mimic specific binding interactions , each trimer possesses on ` attractive ' disk which can interact with similar disks on other trimers _ via _ an attractive square - well potential . at low density and low temperature , the fluid phase mainly consists of tetramers , pentamers , or hexamers . hexamers provide the structural motif for a high - density , low - temperature periodic solid phase , but we also identify a metastable periodic structure based on a tetramer motif . at high density there is a transition between orientationally ordered and disordered solid phases . the connections between simulated structures and those of 2d protein crystals as seen in electron microscopy are briefly discussed .

1209.5480

i

rough set theory , proposed by pawlak @xcite , is an extension of set theory for the study of intelligent systems characterized by insufficient and incomplete information . in theory , rough sets have been connected with matroids @xcite , lattices @xcite , hyperstructure theory @xcite , topology @xcite , fuzzy sets @xcite , and so on . rough set theory is built on an equivalence relation , or to say , on a partition . but equivalence relation or partition is still restrictive for many applications . to address this issue , several meaningful extensions to equivalence relation have been proposed . among them , zakowski has used coverings of a universe for establishing the covering based rough set theory @xcite . many scholars have done deep researches on this theory @xcite , and some basic results have been presented . neighborhood is an important concept in covering based rough set theory . many scholars have studied it from different perspectives . lin augmented the relational database with neighborhood @xcite . yao presented a framework for the formulation , interpretation , and comparison of neighborhood systems and rough set approximations @xcite . by means of consistent function based on the concept of neighborhood , wang et al . @xcite dealt with information systems through covering based rough sets . furthermore , the concept of neighborhood itself has produced lots of meaningful issues as well , and under what condition neighborhoods form a partition is one of them . many scholars have focused on this issue and conducted some researches on it @xcite . different scholars provided different sufficient and necessary conditions respectively . however , there is a common trait among these necessary and sufficient conditions , that is the neighborhoods had been calculated out before the necessary and sufficient condition was presented . for example , yun et al . @xcite studied the conditions for neighborhoods to form a partition from the viewpoint of operators , while the operators were defined by all neighborhoods . if all the neighborhoods have been calculated out , then whether or not the neighborhoods form a partition is already clear . so it is necessary to seek condition for neighborhoods to form a partition directly based on the covering itself . in this paper , we provide a necessary and sufficient condition directly based on the covering itself . first , we investigate the influence of that there are reducible elements in the covering on neighborhoods . we prove that the reducible elements in the covering have no influence on the neighborhoods induced by the covering . second , we propose the definition of uniform block and obtain a sufficient condition from it . we also give a counter - example to prove the condition is not necessary . third , we propose the definitions of repeat degree and excluded number , and obtain some properties of them . by means of the two concepts and their properties , we obtain a necessary and sufficient condition for neighborhoods to form a partition . this necessary and sufficient condition for neighborhoods to form a partition does not involve in any lower or upper approximations , but the covering itself . the remainder of this paper is organized as follows . in section [ s : basic definitions ] , we review the relevant concepts and introduce some existing results . in section [ s : two sufficient conditions ] , we give two sufficient conditions for neighborhoods to form a partition . in section [ s : the main theorem in this paper ] , we present a sufficient and necessary condition . section [ s : conclusions ] concludes this paper and points out further works .

many scholars have paid attention to this issue and presented some necessary and sufficient conditions . however , there exists one common trait among these conditions , that is they are established on the basis of all neighborhoods have been obtained . in this paper , we provide a necessary and sufficient condition directly based on the covering itself . first , we investigate the influence of that there are reducible elements in the covering on neighborhoods . second , we propose the definition of uniform block and obtain a sufficient condition from it . third , we propose the definitions of repeat degree and excluded number . by means of the two concepts , we obtain a necessary and sufficient condition for neighborhoods to form a partition . in a word , we have gained a deeper and more direct understanding of the essence over that neighborhoods form a partition . neighborhood ; reducible element ; membership repeat degree ; excluded number .

neighborhood is an important concept in covering based rough sets . that under what condition neighborhoods form a partition is a meaningful issue induced by this concept . many scholars have paid attention to this issue and presented some necessary and sufficient conditions . however , there exists one common trait among these conditions , that is they are established on the basis of all neighborhoods have been obtained . in this paper , we provide a necessary and sufficient condition directly based on the covering itself . first , we investigate the influence of that there are reducible elements in the covering on neighborhoods . second , we propose the definition of uniform block and obtain a sufficient condition from it . third , we propose the definitions of repeat degree and excluded number . by means of the two concepts , we obtain a necessary and sufficient condition for neighborhoods to form a partition . in a word , we have gained a deeper and more direct understanding of the essence over that neighborhoods form a partition . neighborhood ; reducible element ; membership repeat degree ; excluded number .

1603.02755

i

together with gravity neutrinos drive the evolution of several stellar phenomena such as supernovae , binary mergers , and black hole accretion disks . they are also a key ingredient in the synthesis of heavy elements @xcite , the production of gamma ray bursts @xcite and kilonova @xcite . despite the numerous efforts to fully understand these phenomena there are still puzzles to address . unrevealing the missing pieces requires complex and computationally expensive simulations of the system under study that bring together details of nuclear physics and gravity . furthermore , due to the complexity of the problem , it is necessary to post - process the results to shed light on other derived aspects such as the element abundances and neutrino detection . the strong gravitational field generated by a binary neutron star merger changes the spectral properties of the emerging neutrinos . this will affect any physical quantity related to them . for example , the emitted neutrinos can interact with matter outflowing the merger . via weak interactions neutrinos will change the neutron to proton ratio ( electron fraction ) of the outflow setting the path that a nuclear reaction chain follows . however , strong gravity effects , such as redshifts and bending of neutrino trajectories , affect the neutrino fluxes altering the electron fraction . as a consequence the final abundances differ from those obtained in the absence of the gravitational field @xcite . on another hand , if the merger occurs in the milky way or in the local galaxy group chances are that we will able to detect those neutrinos with current and future facilities @xcite . it is therefore interesting to study the behavior of neutrinos emitted from binary systems . in this proceedings we present post - processed neutrino emission results from state of the art 3d fully relativistic binary neutron star simulations with magnetic fields , neutrino cooling and different equations of state . the original simulation results of the coalescence have been presented in reference @xcite . there , the evolution of the matter in connection to the equation of state ( eos ) is discussed , as well as the gravitational wave emission and neutrino detection rates . here , we expand our discussion of neutrino emission focusing on the evolution of the neutrino surface and its relation to the eos .

neutron - star mergers are interesting for several reasons : they are proposed as the progenitors of short gamma - ray bursts , they have been speculated to be a site for the synthesis of heavy elements , and they emit gravitational waves possibly detectable at terrestrial facilities . we present some aspects of neutrino emission from binary neutron star mergers showing the impact that the equation of state has on neutrinos and discuss some spectral quantities relevant to their detection such as energies and luminosities far from the source .

neutron - star mergers are interesting for several reasons : they are proposed as the progenitors of short gamma - ray bursts , they have been speculated to be a site for the synthesis of heavy elements , and they emit gravitational waves possibly detectable at terrestrial facilities . the understanding of the merger process , from the pre - merger stage to the final compact object - accreting system involves detailed knowledge of numerical relativity and nuclear physics . in particular , key ingredients for the evolution of the merger are neutrino physics and the matter equation of state . we present some aspects of neutrino emission from binary neutron star mergers showing the impact that the equation of state has on neutrinos and discuss some spectral quantities relevant to their detection such as energies and luminosities far from the source .

0711.1052

i

quasi - one - dimensional transition - metal ( @xmath1 ) complexes with bridging halogens ( @xmath0 ) @xcite have been attracting much interest for several decades and significant efforts are still devoted to fabricating their new varieties . conventional platinum - halide chains exhibit a peierls - distorted mixed - valent ground state , @xcite while their nickel analogs have a mott - insulating monovalent regular - chain structure . @xcite palladium - halide chains are intermediates with a ground state tunable optically @xcite and electrochemically . @xcite the charge - density - wave ( cdw ) ground state can be tuned by halogen doping @xcite and pressure application @xcite as well . metal binucleation leads to a wider variety of electronic states . @xcite a diplatinum - iodide chain compound , [ ( c@xmath5h@xmath18)@xmath5nh@xmath5]@xmath4[pt@xmath5(p@xmath5o@xmath18h@xmath5)@xmath4i ] , exhibits photo- and pressure - induced phase transitions , @xcite whereas its analog without any counter ion , pt@xmath5(ch@xmath12cs@xmath5)@xmath4i , is of metallic conduction at room temperature and undergoes successive phase transitions @xcite with decreasing temperature . there are further attempts @xcite to bridge polynuclear and/or heterometallic units by halogens . more than three hundred @xmath14 compounds have thus been synthesized so far , but their crystal structures are all based on @xmath14 single chains . in such circumstances , several authors @xcite have recently succeeded in assembling @xmath14 complexes within a ladder lattice . metal - oxide ladders are generally remarkable for their strongly correlated @xmath15 electrons . srcu@xmath5o@xmath12 behaves as a @xmath15-@xmath16 ladder of the hubbard type , @xcite whereas nav@xmath5o@xmath18 is well describable within a single - band holstein - hubbard hamiltonian . @xcite on the other hand , the newly synthesized metal - halide ladders are double - featured with competing electron - electron and electron - phonon interactions @xcite and are possibly of @xmath15-@xmath16-@xmath17-mixed character . such a multicolored stage potentially exhibits a variety of electronic states and it is highly interesting to control them chemically and physically . thus motivated , we make a model study of ladder - shaped @xmath14 compounds , ( @xmath20-bpym)[pt(en)@xmath0]@xmath7(clo@xmath4)@xmath21h@xmath5o ( @xmath22br , cl ; en@xmath23ethylendiamine@xmath23c@xmath5h@xmath2n@xmath5 ; @xmath20-bpym@xmath24-bipyrimidine@xmath23c@xmath2h@xmath3n@xmath4 ) and ( bpy)[pt(dien)br]@xmath5br@xmath13h@xmath5o ( dien@xmath23diethylentriamine@xmath23c@xmath4h@xmath11n@xmath12 ; bpy@xmath25-bipyridyl@xmath23c@xmath10h@xmath2n@xmath5 ) , which are hereafter referred to as ( bpym)[pt(en)@xmath0]@xmath5 and ( bpy)[pt(dien)br]@xmath5 , respectively . ladders , where @xmath26 ; @xmath9 ; @xmath27 . an electron with spin @xmath28 is created on the @xmath29 and @xmath30 orbitals on the @xmath31th leg in the @xmath32th unit by @xmath33 and @xmath34 , respectively , and on the @xmath32th - rung @xmath35 orbital by @xmath36 . the resultant electron density is given by @xmath37 , @xmath38 , and @xmath39 . the on - site energies ( electron affinities ) of isolated atoms and molecules are given by @xmath40 ( @xmath41 ) and the electron hoppings between these levels are modeled by @xmath42 [ @xmath43 ; @xmath44 . @xmath45 and @xmath46 ( @xmath47 ) describe the on - site and different - site coulomb interactions , respectively . the halogen - ion displacements @xmath48 affect electrons through intersite ( @xmath49 ) and intrasite ( @xmath50 ) coupling constants , accompanied by elastic energy @xmath51.,width=321 ] ladders , where @xmath26 ; @xmath9 ; @xmath27 . an electron with spin @xmath28 is created on the @xmath29 and @xmath30 orbitals on the @xmath31th leg in the @xmath32th unit by @xmath33 and @xmath34 , respectively , and on the @xmath32th - rung @xmath35 orbital by @xmath36 . the resultant electron density is given by @xmath37 , @xmath38 , and @xmath39 . the on - site energies ( electron affinities ) of isolated atoms and molecules are given by @xmath40 ( @xmath41 ) and the electron hoppings between these levels are modeled by @xmath42 [ @xmath43 ; @xmath44 . @xmath45 and @xmath46 ( @xmath47 ) describe the on - site and different - site coulomb interactions , respectively . the halogen - ion displacements @xmath48 affect electrons through intersite ( @xmath49 ) and intrasite ( @xmath50 ) coupling constants , accompanied by elastic energy @xmath51.,width=321 ]

new varieties of quasi - one - dimensional halogen ( @xmath0)-bridged transition - metal ( @xmath1 ) complexes , ( c@xmath2h@xmath3n@xmath4)[pt(c@xmath5h@xmath2n@xmath5)@xmath0]@xmath7(clo@xmath4)@xmath8h@xmath5o ( @xmath9 ) and ( c@xmath10h@xmath2n@xmath5)[pt(c@xmath4h@xmath11n@xmath12)br]@xmath5br@xmath13h@xmath5o , comprising two - leg ladders of mixed - valent platinum ions , are described in terms of a multiband extended peierls - hubbard hamiltonian .

new varieties of quasi - one - dimensional halogen ( @xmath0)-bridged transition - metal ( @xmath1 ) complexes , ( c@xmath2h@xmath3n@xmath4)[pt(c@xmath5h@xmath2n@xmath5)@xmath0]@xmath7(clo@xmath4)@xmath8h@xmath5o ( @xmath9 ) and ( c@xmath10h@xmath2n@xmath5)[pt(c@xmath4h@xmath11n@xmath12)br]@xmath5br@xmath13h@xmath5o , comprising two - leg ladders of mixed - valent platinum ions , are described in terms of a multiband extended peierls - hubbard hamiltonian . the polarized optical conductivity spectra are theoretically reproduced and the ground - state valence distributions are reasonably determined . the latter variety , whose interchain valence arrangement is out of phase , is reminiscent of conventional @xmath14 single - chain compounds , while the former variety , whose interchain valence arrangement is in phase , reveals itself as a novel @xmath15-@xmath16-@xmath17-hybridized multiband ladder material .

1603.07098

i

it is expected that results obtained in one renormalisation scheme will be related to those obtained in another by a ( finite ) redefinition of the couplings and fields of the theory . the required redefinition may be easily constructed by considering the finite differences between the bare quantities in the two schemes . in particular , the @xmath1-function in one scheme may be derived from the @xmath1-function in the other , in a well - known manner . the most widely - used scheme is of course minimal subtraction within dimensional regularisation , or more precisely its variant @xmath0 . in this paper we discuss the issues involved in relating a general non - minimal scheme to @xmath0 in two cases : a general theory of fermions and scalars with multiple fields and couplings in four dimensions , and a general scalar theory with multiple fields and couplings in six dimensions . the procedure is implicit in the standard literature@xcite in general terms , but the detailed implementation for a theory of multiple fields and couplings presents some problems , especially in connection with one - particle reducible ( 1pr ) 2-point function contributions , which we elucidate here . our results apply to any non - minimal scheme ; however at appropriate points we shall emphasise especially the application to the most widely - used non - minimal scheme , namely momentum subtraction ( mom ) . the mom scheme was first introduced in ref . @xcite for a three - loop computation in six - dimensional @xmath2 theory one of the theories we shall consider in detail later . however it was used more widely following its independent development for qcd in ref . the renormalisation constants of the mom scheme are defined such that all the green s functions are set to their tree values at the subtraction point@xcite . variations ( called `` hybrid '' mom schemes ) have also been discussed where the renormalisation constants associated with @xmath3-point functions are defined in a different way to the coupling - constant renormalisations@xcite ( see refs . @xcite for further computations in this scheme ) . motivated by this , we shall consider similar `` hybrid '' schemes in the general non - minimal case . we shall describe our results here in a little more detail , before presenting the full calculation in the following sections . the coupling redefinition which takes us from @xmath0 to a non - minimal scheme may readily be derived . when we implement it , we find a non - zero prediction at three - loop order for certain @xmath1-function terms corresponding to 1pr contributions to the anomalous dimension @xmath4 . more precisely , these terms depend on the antisymmetric part of a certain 1pr contribution to @xmath4 . one s natural expectation might be that such terms should vanish ; but when one reviews the complications involved in performing an explicit computation , it becomes clear that intuition may not be a reliable guide . for a non - minimal subtraction scheme such as mom , the process of computing the @xmath1-function from the bare couplings of the theory is non - trivial , and an additional complexity is introduced when one recalls that the computation of the two - point function in fact only determines the symmetric part . we resort to an indirect argument to obtain the antisymmetric part , based upon working back from the anomalous dimension as obtained by scheme change from @xmath0 . finally , it is important to recall that the coupling redefinition which effects the scheme change is accompanied by a corresponding field redefinition . this has no effect on the prediction for the @xmath1-function , but crucially it does affect the anomalous dimension and thereby our indirect method of computation of the @xmath1-function in the non - minimal scheme . the layout of the paper is as follows . we consider first a scalar - fermion theory in four dimensions in sect . 2 , and then a scalar theory in six dimensions in sect . the renormalisation of these theories is familiar in the literature , at least as far as 1pi contributions are concerned . we therefore try to present only as much background is needed to follow the arguments . we finish with conclusions in sect . 4 and list some explicit diagrammatic results in appendix a , and basic general results from renormalisation theory in appendix b.

non - minimal renormalisation schemes such as the momentum subtraction scheme ( mom ) have frequently been used for physical computations . we discuss the implementation of this procedure in detail for a general theory and show how to construct the relevant redefinition up to three - loop order , for the case of a general theory of fermions and scalars in four dimensions and a general scalar theory in six dimensions . university of liverpool , liverpool l69 3bx , uk +

non - minimal renormalisation schemes such as the momentum subtraction scheme ( mom ) have frequently been used for physical computations . the consistency of such a scheme relies on the existence of a coupling redefinition linking it to @xmath0 . we discuss the implementation of this procedure in detail for a general theory and show how to construct the relevant redefinition up to three - loop order , for the case of a general theory of fermions and scalars in four dimensions and a general scalar theory in six dimensions . lth1080 + consistency of non - minimal renormalisation schemes + * i. jack and c. poole * + dept . of mathematical sciences , university of liverpool , liverpool l69 3bx , uk +

1603.07098

c

we have shown that starting at three loop order the @xmath1-function derived using a non - minimal renormalisation scheme contains terms corresponding to 1pr contributions to the two - point function , using as examples the cases of theories with general couplings in both four and six dimensions . we were unable to perform a full explicit three - loop computation of the relevant terms , since the computation of the two - point function yields only the symmetrised part . we therefore relied on a scheme redefinition from @xmath0 to provide further information on the asymmetric part . therefore the most we can say is that the scheme redefinition results are consistent with those obtained explicitly . we have considered a general non - minimal scheme in which the two - point function is renormalised differently from the three point function ; i.e. 1pr three point diagrams with divergent two - point subdiagrams are assigned different finite parts ( via @xmath24 ) to those appearing in the corresponding two - point renormalisation constant for @xmath23 ; this is a somewhat different philosophy from the `` hybrid mom '' schemes@xcite , where @xmath173 but the 1pi three - point diagrams are renormalised by a different prescription . in both the four - dimensional and six - dimensional case we have only carried out a partial computation of the 1pr2 terms in which we are interested ; in four dimensions we focussed on mixed fermion scalar terms for simplicity , since in this case the relevant two - loop contribution to @xmath23 had only a simple pole ; and in six dimensions we omitted a two - loop simple pole contribution to @xmath23 precisely so that we coould focus on the double pole contribution which displayed new features . it is now clear that we easily obtain the general results simply by incorporating extra finite contributions analogous to @xmath62 and @xmath56 for each relevant one and two loop tensor structure ; in the four - dimensional case this would involve consideration of @xmath20 in addition to @xmath23 . an interesting special case is where we set @xmath174 , i.e. renormalise the two - point function minimally ( note that this is not @xmath0 , since the counterterms are those computed in the non - minimal scheme).in this case we have @xmath175 and no field redefinition is required ; we also find @xmath176 in section 2 and @xmath177 in section 3 , indicating that in this case the contributions to @xmath136 are predicted to be symmetric . our own interest in this issue was inspired though the consistency conditions on @xmath1-function coefficients , derived from gradient flow equations which were obtained during the investigation of a six - dimensional @xmath178-theorem@xcite . specifically , the appearance of potential 1pr @xmath1-function contributions was noticed during the demonstration of the scheme independence of these consisteny conditions . there are still unresolved issues here connected with the scheme dependence of extra terms arising in the conformal anomaly for theories with an @xmath179 symmetry , and it would be interesting to return to this with our better understanding of the general issue of scheme dependence , particularly the role of the field redefinition in this case . we are very grateful to john gracey and tim jones for useful conversations . this work was supported in part by the stfc under contract st / g00062x/1 , and cp was supported by an stfc studentship .

the consistency of such a scheme relies on the existence of a coupling redefinition linking it to @xmath0 . lth1080 + consistency of non - minimal renormalisation schemes + * i. jack and c. poole * + dept . of mathematical sciences ,

non - minimal renormalisation schemes such as the momentum subtraction scheme ( mom ) have frequently been used for physical computations . the consistency of such a scheme relies on the existence of a coupling redefinition linking it to @xmath0 . we discuss the implementation of this procedure in detail for a general theory and show how to construct the relevant redefinition up to three - loop order , for the case of a general theory of fermions and scalars in four dimensions and a general scalar theory in six dimensions . lth1080 + consistency of non - minimal renormalisation schemes + * i. jack and c. poole * + dept . of mathematical sciences , university of liverpool , liverpool l69 3bx , uk +

1105.3304

i

the 50 years old quark mixing @xcite is the key for strange particles to decay and for the weak cp violation to be realized in the standard model ( sm ) @xcite . existence of cp violation is one key element for baryon number generation , the baryogenesis . at present , however , we can not relate the weak cp violation , satisfying ` baryon number conservation ' , to the cp violation needed for the baryogenesis employing ` baryon number violation ' . nevertheless , the weak cp violation study might hints physics far above the electroweak scale and hopefully to the cp phase appearing in the baryogenesis . this may come by observing a deviation from the sm prediction or completion of the weak cp violation in an ultraviolet completed theory beyond the sm . in any case , completing the sm is achieved by the complete determination of the quark and lepton mixing matrices , and hence determining the mixing matrices in terms of an exact form is of fundamental importance . the original kobayashi - maskawa ( km ) model for weak cp violation in the sm is represented by the km unitary matrix @xmath7 . the cabibbo angle @xmath8 , the @xmath9 element of @xmath7 , is known to be small but not too small , @xmath10 , and hence can be a good expansion parameter . a decade after the km matrix , wolfenstein expressed the matrix elements in terms of powers of @xmath11 @xcite . the wolfenstein parametrization introduces four parameters as required : three real parameters @xmath12 , and an imaginary parameter @xmath13 , @xmath14 which is very useful in fitting the weak cp violation data @xcite . even though the imaginary number @xmath13 is introduced , it is not a phase . if any parametrization is introducing an invariant phase , a unitary transformation should not change its determinant . the determinant of the original km matrix has a phase @xcite , while the chau - keung - maiani form does not have a phase @xcite . if the phase is present , it is related to the phase of the quark mass matrix , arg.det.@xmath15 . this can be rotated away if there exists the peccei - quinn symmetry @xcite . if there is no peccei - quinn symmetry , one may resort to calculable vacuum angle ( @xmath16 ) models @xcite where one starts with arg.det.@xmath17 . therefore , the determinant of a well - defined quark mixing matrix better does not have a phase . a posteriori , the ( 13 ) and ( 31 ) elements are known to be very small @xmath18 . also , it is known that the third generation is needed to have the weak cp violation . in addition , specifically , if either the ( 13 ) or ( 31 ) element is zero , there is no cp violation . in general , if any one element among nine elements of the ckm matrix is zero , then there is no weak cp violation since one can find an appropriate phase redefinition such that all the ckm elements become real . in the wolfenstein form , the product of ( 13 ) , ( 22 ) and ( 31 ) elements , appearing among six terms of the determinant , is a barometer of cp violation , @xmath19 where @xmath20 and @xmath21 . but in the wolfenstein form , the case ( 13 ) or ( 31 ) element vanishing is not parametrized by one parameter . therefore , there is a need to parametrize the weak cp violation in a better form where vanishing of one parameter makes either ( 13 ) or ( 31 ) element vanishing . in fact , qin and ma ( qm ) realizes this scheme which is identical to the wolfenstein form with the qm phase interpreted by those of eq . ( [ eq : wolfdetphase ] ) , @xmath22 @xcite . in these @xmath23 expanded forms , the weak cp violation occurs at order @xmath24 .

is defined from the product of the first row elements , @xmath5 , and the angle between two sides at the origin is defined to be the phase @xmath6 . this is a useful definition since every jarlskog triangle has the angle @xmath6 at the origin , defined directly from the unitarity condition .

noting the hierarchy between three mixing angles , @xmath0 , we present an exact form of the quark mixing matrix , replacing wolfenstein s approximate form . in addition , we suggest to rotate the unitarity triangle , using the weak cp phase convention where the phase is located at the ( 31 ) element @xmath1 while the ( 13 ) element @xmath2 is real . for the @xmath3 unitarity triangle , the base line ( @xmath4-axis ) is defined from the product of the first row elements , @xmath5 , and the angle between two sides at the origin is defined to be the phase @xmath6 . this is a useful definition since every jarlskog triangle has the angle @xmath6 at the origin , defined directly from the unitarity condition . it is argued that @xmath6 represents the barometer of the weak cp violation , which can be used to relate it to possible yukawa textures .

quant-ph0009085

i

recent years brought about spectacular successes in the study of dilute bosonic quantum gases confined to atomic traps at extremely low temperatures . these and the experimental details are reviewed in @xcite . the next stage of investigations will incorporate fermionic quantum gases . fermi degeneracy of potassium atoms ( @xmath4 ) has recently been observed in @xcite . the effects of interactions between the neutral atoms are of particular interest . they can give rise to collective ground states like superfluid phases . another development regards the construction of highly anisotropic traps , e.g. , the microtraps in @xcite . the magnetic trapping fields can be taylored so as to make the confining potential harmonic . if the longitudinal confinement frequency @xmath5 is smaller than the radial frequency @xmath6 by a factor @xmath7 it is possible to fill the first @xmath8 longitudinal states while the radial wave functions of the fermions are still that of the ground state provided @xmath9 holds . from semi classical theory or local density approximation ( lda ) it is well known ( cf . e.g. @xcite ) , that a fermi wave number @xmath10 can be associated with the one dimensional fermi gas of atomic mass @xmath11 in a harmonic trap . it is noted that the condition @xmath9 is roughly in line with the standard estimate @xmath12 for a fermi system which is confined to a transverse width @xmath13 to be quasi one dimensional provided the length @xmath13 is identified with the extension @xmath14 of the radial ground state wave function in the trap . non interacting fermions in anisotropic harmonic traps have been studied recently @xcite using exact and semi classical methods . the thermodynamics of harmonically confined spin polarized fermions in any spatial dimension including a harmonic two particle interaction has been studied in @xcite using the general approach @xcite . the latter results are not available in closed form and require numerical evaluation . a finite series representation for the free energy of one dimensional non interacting spin polarized fermions confined by a harmonic potential has been given in @xcite . in view of the feasibility to realize one dimensional fermions at ultra low temperatures it seems worthwhile to supplement these works by studying the strictly one dimensional case of non interacting fermions at zero temperature when a number of exact explicit results can be obtained . interactions between spin polarized identical fermions are weak because the pauli principle forbids s wave scattering . on the other hand the theory of luttinger liquids ( cf . e.g. , @xcite for a review ) shows that even small interactions change a one dimensional fermi system substantially . nevertheless , it is useful to have results for the non interacting case to compare the effect of interactions with them . the results that we present below show features specific for one spatial dimension . in existing micro traps magnetic gradients of up to @xmath15 t / cm has already been realized @xcite resulting in a periodic motion of the trapped atoms on a time scale of micro seconds . novel versions of micro traps based on micro fabricated current conductors achieve even higher gradients with an expected radial atomic oscillation frequency of above @xmath16 mhz @xcite . for the longitudinal oscillation frequency @xmath16 hz appears to be a reasonable lower limit because time scales longer than a second gives rise to experimental difficulties due to seismic and acoustic noise . thus , the maximum value which is currently feasible for @xmath7 is @xmath17 and would limit the number of atoms inside the trap to about one million . the main experimental difficulty , however , is to fill the @xmath18 states of the micro trap with a substantial number of atoms . starting from an optically cooled sample of atoms with a phase space density of typically @xmath17 @xcite a phase space compression of six orders of magnitude is required to completely fill up the wave guide . such compression is possible with state of the art techniques of evaporative cooling @xcite . thus , a conservative estimation for realistic experimental conditions would assume a one component fully spin polarized fermi gas with a radial frequency inside the micro trap of @xmath19 hz . the longitudinal frequency can be set at @xmath20 hz giving @xmath21 . thus @xmath22 quasi one dimensional fermions can be accommodated inside the trap . assuming @xmath23 atoms ( in the hyperfine state @xmath24 ) the inverse harmonic oscillator length @xmath25 according to @xmath26 is estimated as @xmath27 leading to a fermi wave number @xmath28 . obviously the quasi one dimensional fermi energy @xmath29 , i.e. , the energy of the highest occupied state without the radial contribution is @xmath30 under the above assumptions @xmath29 corresponds to about @xmath31k and this temperature must be larger than the physical temperature in order to achieve degeneracy of the fermi gas . another relevant quantity is the spatial extension of the inhomogeneous fermi gas . the appropriate measure is twice that later given in equation ( [ 2.1 ] ) and leads to a characteristic extension of @xmath32 cm and to an average fermion density of about @xmath33 atoms per cm . the radial width @xmath34 is about @xmath35 cm . thus the tonks gas limit @xcite is avoided and the fermionic atoms can be treated as point particles . the exact quantum mechanical results usually give only small corrections to the corresponding lda predictions . some of them are , however , of qualitative nature and worth to point out . among them are diverging density oscillations near the classical boundary of the trap for large fermion numbers and the general feature of friedel oscillations @xcite of the density . the paper is organized as follows . ii presents the basic theory . iii discusses the relevant lengths and energy scales of the one dimensional fermi gas in the harmonic trap . in sec . iv we compile the results for the zero temperature one particle density distribution . v is concerned with the fourier transform of the density distribution . vi discusses momentum distributions and in the final sec . vii we calculate the expansion of the particle density distribution when the trap is suddenly switched off . an appendix summarizes mathematical formulae used in our calculations .

the fourier transform of the density distribution is calculated exactly . dependent one particle problem we calculate exactly the evolution of the particle density when the trap is suddenly switched off and find a simple scaling behaviour in agreement with recent general results . pacs nos . 05.30fk , 71.10.pm , 0375.fi 2

one particle properties of non interacting fermions in a one dimensional harmonic trap and at zero temperature are studied . exact expressions and asymptotic results for large fermion number @xmath0 are given for the particle density distribution @xmath1 . for large @xmath0 and near the classical boundary at the fermi energy the density displays increasing fluctuations . a simple scaling of these tails of the density distribution with respect to @xmath0 is established . the fourier transform of the density distribution is calculated exactly . it displays a small but characteristic hump near @xmath2 with @xmath3 being a properly defined fermi wave number . this is due to friedel oscillations which are identified and discussed . these quantum effects are missing in the semi classical approximation . momentum distributions are also evaluated and discussed . as an example of a time dependent one particle problem we calculate exactly the evolution of the particle density when the trap is suddenly switched off and find a simple scaling behaviour in agreement with recent general results . pacs nos . 05.30fk , 71.10.pm , 0375.fi 2

1609.05268

i

many data analysis tasks can be facilitated by high - dimensional data visualization . for example , it is often helpful to know what sets of dimensions in the data are correlated or have a significant impact in processes such as clustering , sampling , or labeling . another important task is the discovery of hidden relationships between labels and numeric values in the analysis of labeled high - dimensional datasets . several machine learning techniques such as deep neural networks or association rule mining are useful for this purpose but may require significant computational time when discovering relationships between labels and large arbitrary combinations of numeric dimensions . moreover , in many application domains , high - dimensional data analysis requires interactive analysis and decision making by a domain expert to specify the rules between the labels and the numeric values . such circumstances arise in important application domains such as biomedicine , finance , and social media analysis , where the a priori characterization and detection of interesting patterns is difficult and limited due to a lack of domain - specific knowledge as well as the complexity and dynamic nature of the data . the application of a data visualization framework is often helpful for these types of problems . high - dimensional data visualization continues to be an important and active research field with several survey papers dedicated to this area @xcite @xcite . one of these surveys @xcite divided the available multi - dimensional data visualization techniques into three categories : animations , two - variate displays , and multivariate displays . animation techniques facilitate the dynamic display of multiple configurations of the high - dimensional data and are commonly applied to both two - variate and multivariate techniques . two - variate techniques only visualize the relationships between two variables ; an example of such a technique is the well - known scatterplot ( sp ) . multivariate visualization techniques attempt to represent the distribution of all the dimensions in a given dataset on a single display space . the increasing dimensionality of modern datasets is spurring the use of multivariate visualization techniques , such as sp matrices and parallel coordinate plots ( pcps ) @xcite . a sp matrix consists of multiple adjacent sps in a grid - like arrangement , with each sp being identified by its row and column index . the greatest advantage of sp matrices is the high level of familiarity that non - expert users have with it . however , this visualization technique suffers from few major drawbacks . firstly , individual sps within the display space may be very small if the number of dimensions of the dataset is very large . in addition , it can be difficult for humans to visually compare arbitrary pairs of sps that are distantly placed in the display space . several studies aimed at selecting meaningful sets of sps and effectively arrange them onto the display spaces @xcite @xcite @xcite @xcite @xcite ; however , these studies often had difficulty to visually compare large number of sps . pcps are an alternative multivariate visualization technique that display high - dimensional datasets as a set of polylines that intersect with parallel axes ; this visualization better enables the observation of correlations between pairs of dimensions . specifically , the existence of parallel polylines between two axes indicates positive correlation . conversely , polylines crossing between axes are indicative of negative correlation . while pcps have been well studied for high - dimensional data visualization and are a valuable tool for the analysis of multidimensional data , they have some shortcomings in practice . pcps may require a large horizontal display space even for a modest number of dimensions . within this horizontal display space the ordering of the dimensions is relevant for the detection of pairwise correlations . moreover , it is difficult to visually represent the correlation of a particular dimension with three or more different dimensions . an example of this situation can be illustrated given a dataset which has four dimensions @xmath0 , @xmath1 , @xmath2 , and @xmath3 , which are visualized by a single pcp . the correlations between @xmath0 and @xmath1 , or @xmath1 and @xmath2 , can be easily observed if the dimensions are arranged in the order @xmath0 , @xmath1 , @xmath2 , and @xmath3 . however , the correlation between @xmath1 and @xmath3 can not be easily observed within this visualization . several techniques @xcite @xcite have attempted to address this last issue by only displaying pcps for subsets of the dimensions that are highly correlated . given the example dataset and situation specified above , these techniques would construct two pcps : one displaying @xmath0 , @xmath1 , and @xmath2 , and the other displaying @xmath1 and @xmath3 . this enables users to view correlations between @xmath1 and all of the other dimensions . however , adjusting the optimal visualization parameters ( subset of dimensions to display ) is a challenging issue that often requires interactive input by an expert user . we hypothesize that new high - dimensional data visualization capabilities can be enabled by combining multivariate visualization techniques ( e.g. pcps ) with an innovative coupling to interactive dimension selection techniques @xcite @xcite @xcite @xcite . this paper presents a new technique for high - dimensional data visualization in which a set of low - dimensional pcps are interactively constructed . figure [ fig : snapshot0 ] shows a snapshot of our proposed technique , which features two visualization components : _ low - dimensional pcps _ and a _ dimension graph_. the low - dimensional pcps display the values of the selected dimensions . we provide two approaches to interactive dimension selection , derived from the correlation between numeric dimensions or from data mined association rules between numeric dimensions and categorical labels . the dimension graph displays the relationships between the numeric dimensions and allows interactive dimension selection . this representation is visually similar to correlation map proposed by zhang et al . @xcite ; however , our technique differs in the application of the dimension graph where we enabled simultaneous extraction of a set of low - dimensional subspaces with a simple threshold adjustment operation , thus offering an interactive mechanism that is more intuitive , when compared with existing techniques . we allow duplication in the selection of dimensions and the consequent display across multiple low - dimensional pcps . this enables visualization of relationships between a particular dimension and three or more other dimensions , which can be often difficult to understand when all dimensions are shown in a single pcp . at the same time , our method flexibly saves display space because many unnecessary dimensions can be removed from the visualization results . the rest of this paper is organized as follows . we introduce related work in section 2 . in section 3 , we present the framework that describes our new high - dimensional visualization technique . we present an experimental validation of our technique in section 4 and draw conclusions from the outcomes in section 5 .

they are especially useful for the representation of correlations among the dimensions , which identify relationships and interdependencies between variables . however , within these high - dimensional spaces , pcps face difficulties in displaying the correlation between combinations of dimensions and generally require additional display space as the number of dimensions increases . in this paper , we present a new technique for high - dimensional data visualization in which a set of low - dimensional pcps are interactively constructed by sampling user - selected subsets of the high - dimensional data space . in our technique , we first construct a graph visualization of sets of well - correlated dimensions .

parallel coordinate plots ( pcps ) are among the most useful techniques for the visualization and exploration of high - dimensional data spaces . they are especially useful for the representation of correlations among the dimensions , which identify relationships and interdependencies between variables . however , within these high - dimensional spaces , pcps face difficulties in displaying the correlation between combinations of dimensions and generally require additional display space as the number of dimensions increases . in this paper , we present a new technique for high - dimensional data visualization in which a set of low - dimensional pcps are interactively constructed by sampling user - selected subsets of the high - dimensional data space . in our technique , we first construct a graph visualization of sets of well - correlated dimensions . users observe this graph and are able to interactively select the dimensions by sampling from its cliques , thereby dynamically specifying the most relevant lower dimensional data to be used for the construction of focused pcps . our interactive sampling overcomes the shortcomings of the pcps by enabling the visualization of the most meaningful dimensions ( i.e. , the most relevant information ) from high - dimensional spaces . we demonstrate the effectiveness of our technique through two case studies , where we show that the proposed interactive low - dimensional space constructions were pivotal for visualizing the high - dimensional data and discovering new patterns . visualization , high - dimensional data , parallel coordinate plots .

1609.05268

l

in this section , we survey pcps and interactive dimension selection techniques . our visualization technique builds upon a combination of these approaches . as mentioned previously , pcps @xcite display high - dimensional datasets as polylines intersecting with parallel axes . the improvement of pcps is a very active research topic and one of the well - known challenges in this domain is that of polyline cluttering , i.e. , a reduction of line crossings and overlaps for visual comprehensibility . several techniques have attempted to improve the comprehensibility of the results obtained by pcps by applying clustering or sampling of the polylines @xcite @xcite @xcite @xcite . in addition , the effectiveness of pcps are highly dependent on the order of the dimensions and various dimension ordering techniques have recently been proposed to address this issue @xcite @xcite @xcite @xcite . the last major challenge is the difficulty in representing all correlations in one display space , especially when a particular dimension is strongly correlated with many other dimensions . in these circumstances , pcps can represent only a subset of all possible relationships between the dimensions . when a multi - dimensional dataset contains a very large number of dimensions , existing visualization techniques ( e.g. , pcps or sps ) may need very large display spaces to represent them completely . this problem can be solved by dividing the high - dimensional data space into smaller subsets . ten caat et al . applied multiple pcps to represent time - varying multidimensional data @xcite . suematsu et al . @xcite also converted high - dimensional datasets into low - dimensional subsets and visualized these subsets using multiple pcps arranged on display spaces based upon their similarity and correlation . using similar ideas , zheng et al . @xcite selected sps based upon the meaningfulness of the dimensions being displayed and adjusted their layout based upon their similarity . claessen et al . @xcite presented a technique to visualize high - dimensional datasets by selecting sets of low - dimensional subspaces and representing them as a combination of pcps and sps . these techniques provide static results by the decomposition of high - dimensional spaces into multiple pre - selected low - dimensional spaces . however , the lack of any interactive mechanisms to select the sets of dimensions denies domain experts the ability to use their prior experience and knowledge to specify rules about the data . several studies have demonstrated that subsets or subspaces of high - dimensional spaces can be effectively visualized by a user s interactive selection of the subspace ( subset of dimensions ) . elmqvist et al . @xcite presented an interactive mechanism to select pairs of dimensions and to smoothly switch between the sps , which was effective in preserving users mental maps of the high - dimensional spaces . lee et al . @xcite and liu et al . @xcite applied dimension reduction schemes to interactively select subsets of the high - dimensional data . nohno et al . @xcite presented a technique to interactively contract highly - correlated dimensions to adjust the number of axes displayed in pcps . several recent studies have applied sps for the representation of _ dimension spaces _ in which each dot in the sp represents a single dimension in the space . turkay et al . @xcite @xcite presented a dual sp model to visualize both the items and dimensions spaces . similarly , yuan et al . @xcite presented a interactive mechanism to select low - dimensional subspaces on the sp display in which each dot corresponds to a different dimension . we also represent the relationships among the dimensions in a 2d space ; however , our technique applies a graph rather than a sp . the technique recently proposed by zhang et al . @xcite uses a similar representation to that applied by our technique . they construct a `` correlation map '' in which the dataset dimensions are represented by dots where the connection between the dots is derived from pairwise correlations . our technique includes two characteristics that differ fundamentally from the method of zhang et al . firstly , the dimension graph in our technique is used as an interactive mechanism to simultaneously control the dimensionality of the set of pcps , thereby allowing the pcps to act as a visual representation of a set of low - dimensional subspaces ; in contrast , users need to find interesting dimensions and select them individually while using the method of zhang et al . in addition , our technique uses association rule mining to extract low - dimensional subspaces in contrast with the correlation - based technique used by zhang et al . our technique can therefore extract complex multi - variate relationships in comparison to pairwise correlations .

users observe this graph and are able to interactively select the dimensions by sampling from its cliques , thereby dynamically specifying the most relevant lower dimensional data to be used for the construction of focused pcps . our interactive sampling overcomes the shortcomings of the pcps by enabling the visualization of the most meaningful dimensions ( i.e. , the most relevant information ) from high - dimensional spaces .

parallel coordinate plots ( pcps ) are among the most useful techniques for the visualization and exploration of high - dimensional data spaces . they are especially useful for the representation of correlations among the dimensions , which identify relationships and interdependencies between variables . however , within these high - dimensional spaces , pcps face difficulties in displaying the correlation between combinations of dimensions and generally require additional display space as the number of dimensions increases . in this paper , we present a new technique for high - dimensional data visualization in which a set of low - dimensional pcps are interactively constructed by sampling user - selected subsets of the high - dimensional data space . in our technique , we first construct a graph visualization of sets of well - correlated dimensions . users observe this graph and are able to interactively select the dimensions by sampling from its cliques , thereby dynamically specifying the most relevant lower dimensional data to be used for the construction of focused pcps . our interactive sampling overcomes the shortcomings of the pcps by enabling the visualization of the most meaningful dimensions ( i.e. , the most relevant information ) from high - dimensional spaces . we demonstrate the effectiveness of our technique through two case studies , where we show that the proposed interactive low - dimensional space constructions were pivotal for visualizing the high - dimensional data and discovering new patterns . visualization , high - dimensional data , parallel coordinate plots .

1609.05268

c

we presented an interactive technique for the visualization of high - dimensional data spaces . our technique displays numeric values of the selected sets of dimensions by a set of pcps , while the dimension graph component displays the relations between the numeric dimensions and provides interactive dimension selection mechanisms . our technique features two types of dimension selection criteria : distances among dimensions , and separateness of labels . the former is used to visualize highly correlated sets of dimensions while the latter is used to visualize the sets of dimensions which sufficiently separate items with specific labels . we demonstrated the effectiveness of our technique using two case studies . we discovered important knowledge about unknown relations among design variables of airplane wing shape and objective functions , and about relations between image feature values derived from ct images and nodule - level diagnosis .

parallel coordinate plots ( pcps ) are among the most useful techniques for the visualization and exploration of high - dimensional data spaces . we demonstrate the effectiveness of our technique through two case studies , where we show that the proposed interactive low - dimensional space constructions were pivotal for visualizing the high - dimensional data and discovering new patterns .

parallel coordinate plots ( pcps ) are among the most useful techniques for the visualization and exploration of high - dimensional data spaces . they are especially useful for the representation of correlations among the dimensions , which identify relationships and interdependencies between variables . however , within these high - dimensional spaces , pcps face difficulties in displaying the correlation between combinations of dimensions and generally require additional display space as the number of dimensions increases . in this paper , we present a new technique for high - dimensional data visualization in which a set of low - dimensional pcps are interactively constructed by sampling user - selected subsets of the high - dimensional data space . in our technique , we first construct a graph visualization of sets of well - correlated dimensions . users observe this graph and are able to interactively select the dimensions by sampling from its cliques , thereby dynamically specifying the most relevant lower dimensional data to be used for the construction of focused pcps . our interactive sampling overcomes the shortcomings of the pcps by enabling the visualization of the most meaningful dimensions ( i.e. , the most relevant information ) from high - dimensional spaces . we demonstrate the effectiveness of our technique through two case studies , where we show that the proposed interactive low - dimensional space constructions were pivotal for visualizing the high - dimensional data and discovering new patterns . visualization , high - dimensional data , parallel coordinate plots .

1401.5954

i

proteins are fascinating molecules due to their ability to play many roles in biological systems . their functions often involve complex configurational changes . therefore the familiar aphorism that `` form is function '' should rather be replaced by a view of the `` dynamic personalities of proteins''@xcite . this is why proteins are also intriguing for theoreticians because they provide a variety of yet unsolved questions . besides the dynamics of protein folding , the rise in the time averaged mean square fluctuation @xmath0 occurring at temperatures around @xmath1 , sometimes called the `` protein dynamic transition '' @xcite is arguably the most considerable candidate in the search of unifying principles in protein dynamics . protein studies lead to the concept of _ energy landscape _ @xcite . according to this viewpoint a protein is a system which explores a complex landscape in a highly multidimensional space and some of its properties can be related to an incomplete exploration of the phase space . the protein glass transition , in which the protein appears to `` freeze '' when it is cooled down to about @xmath2k is among them . protein folding too can be related to this energy landscape . the famous kinetic limitation known as the levinthal paradox , associated to the difficulty to find the native state among a huge number of possible configurations , is partly solved by the concept of a funneled landscape which provides a bias towards the native state . these considerations suggest that the dynamics of the exploration of protein phase space deserves investigation , particularly at low temperature where the dynamic transition occurs . but , in spite of remarkable experimental progress which allows to `` watch protein in action in real time at atomic resolution '' @xcite , experimental studies at this level of detail are nevertheless extremely difficult . further understanding from models can help in analyzing the observations and developing new concepts . however , studies involving computer modeling to study the dynamics of protein fluctuations are not trivial either because the range of time scales involved is very large . this is why many meso - scale models , which describe the protein at scales that are larger than the atom , have been proposed . yet , their validity to adequately describe the qualitative features of a real protein glass remains to be tested . in this paper we examine a model with an intermediate level of complexity . this frustrated g model @xcite is an off - lattice model showing fluctuations at a large range of time scales . it is though simple enough to allow the investigation of time scales which can be up to @xmath3 times larger than the time scales of small amplitude vibrations at the atomic level . the model , which includes a slight frustration in the dihedral angle potential which does not assume a minimum for the positions of the experimentally determined structure , exhibits a much richer behavior than a standard g model . besides folding one observes a rise of fluctuations above a specific temperature , analogous to a dynamical transition @xcite , and the coexistence of two folded states . this model has been widely used and it is therefore important to assess to what extent it can describe the qualitative features of protein dynamics beyond the analysis of folding for which it was originally designed . this is why we focus our attention on its low - temperature properties in an attempt to determine if a fairly simple model can provide some insight on the protein dynamical transition . the purpose of the present article is to clarify the origin of the transition in the computer model , and to determine similarities and differences with respect to experimental observations . although the calculations are performed with a specific model , the methods are more general and even raise some questions for experiments , especially concerning the non - equilibrium properties . this article is organized as follows . the numerical findings relating to the dynamical transitionfrom previous studies @xcite are presented in sec . [ sec : model ] . as a very large body of experimental studies of protein dynamics emanates from neutron scattering experiments , it is rational to seek a connection between theory and experiment by studying the most relevant experimental observable for dynamics , the incoherent structure factor ( isf ) . we calculate the isf from molecular dynamics simulations of the model in sec . [ sec : strfact ] . we show that its main features can be well reproduced by a theoretical analysis based on the one - phonon approximation , which indicates that , at low temperature , the dynamics of the protein within this model takes place in a single minimum of the energy landscape . [ sec : is ] proceeds to an inherent structure analysis to examine how the transitions among energy states start to play a role when temperature increases . as the freezing of the protein dynamics at low temperature is often called a `` glass transition '' , this raises the question of the properties of the model protein in non - equilibrium situations . in sec . [ sec : fdt ] we examine the violation of the fluctuation dissipation theorem after a sudden cooling of the protein . we find that the effective temperature of the quenched protein , deduced from the fluctuation - dissipation theorem ( fdt ) deviates from the temperature of the thermostat , however it relaxes towards the actual temperature with an an arrhenius behavior as the waiting time increases . this would imply that the dynamics of the protein model is very slow but not actually glassy . this method could be useful to distinguish very slow dynamics from glassy dynamics , in experimental cases as well as in molecular dynamics simulations . finally sec . [ sec : discussion ] summarizes and discusses our results .

prompted by results that showed that a simple protein model , the frustrated g model , appears to exhibit a transition reminiscent of the protein dynamical transition , we examine the validity of this model to describe the low - temperature properties of proteins . first , we examine equilibrium fluctuations . we calculate its incoherent neutron - scattering structure factor and show that it can be well described by a theory using the one - phonon approximation . by performing an inherent structure analysis , we assess the transitions among energy states at low temperatures . then , we examine non - equilibrium fluctuations after a sudden cooling of the protein . we investigate the violation of the fluctuation dissipation theorem in order to analyze the protein glass transition . we find that the effective temperature of the quenched protein deviates from the temperature of the thermostat , however it relaxes towards the actual temperature with an arrhenius behavior as the waiting time increases .

prompted by results that showed that a simple protein model , the frustrated g model , appears to exhibit a transition reminiscent of the protein dynamical transition , we examine the validity of this model to describe the low - temperature properties of proteins . first , we examine equilibrium fluctuations . we calculate its incoherent neutron - scattering structure factor and show that it can be well described by a theory using the one - phonon approximation . by performing an inherent structure analysis , we assess the transitions among energy states at low temperatures . then , we examine non - equilibrium fluctuations after a sudden cooling of the protein . we investigate the violation of the fluctuation dissipation theorem in order to analyze the protein glass transition . we find that the effective temperature of the quenched protein deviates from the temperature of the thermostat , however it relaxes towards the actual temperature with an arrhenius behavior as the waiting time increases . these results of the equilibrium and non - equilibrium studies converge to the conclusion that the apparent dynamical transition of this coarse - grained model can not be attributed to a glassy behavior .

1002.4659

i

quantum information science incorporates quantum principles into information processing and communication . amongst the most spectacular discoveries and conjectures , we know that quantum cryptography could enable information - theoretic secure communication through public channels @xcite , and quantum computing would efficiently solve certain computational problems that are believed to be intractable by conventional computing @xcite . furthermore quantum dynamics becomes efficiently simulatable on a quantum computer @xcite . the prototypical model of quantum information processing represents information as strings of qubits , and processing is effected by unitary quantum gates . the qubit is a single - particle state in a two - dimensional hilbert space . if the particle is a single photon , then the qubit can be encoded in several ways . for example , in polarization encoding the logical zero state @xmath0 can correspond to a single photon being left - circularly polarized and @xmath1 to right - circularly polarized . other examples include path @xcite , photon - number @xcite , and time - bin encodings @xcite . a general qubit state can be expressed as a superposition of @xmath0 and @xmath1 , and general states of quantum information are superpositions of strings of qubits . quantum memory needs to store qubit strings or parts thereof faithfully and to release them on demand . storage of a quantum state need not be perfect . fault - tolerant quantum error correction can be employed to make an imperfect memory sufficient as long as the fidelity of the memory ` gate ' exceeds a particular performance threshold @xcite . next we study the specific requirements for optical quantum memory to be effective for quantum information tasks . in general quantum memory stores a pure or mixed state represented by density matrix @xmath2 and outputs a state @xmath3 , which should be close to @xmath2 . the ultimate performance criterion for quantum memory is the _ worst - case fidelity _ with respect to the set of input states where the fidelity for a specific state is given by @xmath4 . there exists a threshold worst - case fidelity beyond which fault - tolerant quantum error correction methods can overcome memory imperfection @xcite . the fidelity of quantum - optical memory for an arbitrary set of input states can be determined by subjecting it to complete quantum process tomography @xcite . however , this procedure is relatively bulky , so in practical experimental implementations , other performance criteria are used . for example the term ` fidelity ' sometimes refers to state overlap @xmath5 ( possibly after post - selection ) , which is the square of @xmath6 for the case that @xmath7 is a pure state . _ average fidelity _ is often used , where the average is taken over all input states with respect to an assumed prior distribution @xcite . another popular criterion is _ efficiency _ @xmath8 , which is the ratio between the energies of the stored and retrieved pulses . efficiency , while easy to determine experimentally , does not account for possible detrimental effects such as contamination of the retrieved state by the excess noise from the storage medium . in continuous - variable implementations , memory can be characterized by the _ transfer coefficient _ and _ conditional variance _ these quantities are convenient for characterizing quantum memory for single - mode fields provided that input and retrieved states are gaussian . the _ multimode capacity _ of quantum memory determines the number of optical modes that can be stored in the memory cell with the requisite performance threshold or better . the multimode capacity strongly depends on the memory mechanism @xcite . quantum memory needs to be able to store the state long enough to perform the task at hand so _ storage time _ is another essential memory performance criterion . for many applications , an appropriate figure of merit would be the _ delay - bandwidth product _ , i.e the ratio between storage time and duration of the stored pulse . in _ optical quantum computation _ the role of quantum memory is to store quantum bits so that operations can be timed appropriately . many qubits are being processed in parallel with each other at each step in time , and these processing steps must be synchronized @xcite . _ quantum communication _ suffers from imperfect transmission channels , resulting , for example , in quantum key distribution being possible only over finite distances . the _ quantum repeater _ @xcite solves this problem and permits quantum communication over arbitrary distances with a polynomial cost function . a necessary component of the quantum repeater is quantum memory , which , similar to quantum computation , allows synchronization between entangled resources distributed over adjacent sections of the transmission link . in addition , quantum memory for light finds applications in _ precision measurements _ based on quantum interference of atomic ensembles . by transferring quantum properties of an optical state to the atoms one can reduce the quantum noise level of the observable measured , thereby improving the precision of magnetometry , clocks , and spectroscopy @xcite . finally , quantum optical memory can be used as a component of _ single - photon sources_. if a single - photon detector is placed in one of the emission channels of non - degenerate spontaneous parametric down - conversion , a detection event indicates emission of a photon pair , and thus the presence of a single photon in the other channel @xcite . such a heralded photon is emitted at an arbitrary time , in the following , we review recent theoretical and experimental work related to different approaches to quantum memory .

quantum memory is important to quantum information processing in many ways : a synchronization device to match various processes within a quantum computer , an identity quantum gate that leaves any state unchanged , and a tool to convert heralded photons to photons - on - demand . in addition to quantum computing , quantum memory would be instrumental for the implementation of long - distance quantum communication using quantum repeaters . the importance of this basic quantum gate is exemplified by the multitude of optical quantum memory mechanisms being studied : optical delay lines , cavities , electromagnetically - induced transparency , photon - echo , and off - resonant faraday interaction . here we report on the state - of - the - art in the field of optical quantum memory , including criteria for successful quantum memory and current performance levels .

quantum memory is important to quantum information processing in many ways : a synchronization device to match various processes within a quantum computer , an identity quantum gate that leaves any state unchanged , and a tool to convert heralded photons to photons - on - demand . in addition to quantum computing , quantum memory would be instrumental for the implementation of long - distance quantum communication using quantum repeaters . the importance of this basic quantum gate is exemplified by the multitude of optical quantum memory mechanisms being studied : optical delay lines , cavities , electromagnetically - induced transparency , photon - echo , and off - resonant faraday interaction . here we report on the state - of - the - art in the field of optical quantum memory , including criteria for successful quantum memory and current performance levels .

hep-ex0201042

i

hera is an @xmath0 collider which has especially high sensitivity to new particles coupling to lepton - quark pairs . in 1994 - 97 hera collided 27.5 gev positrons on 820 gev protons . in 1998 the proton energy was raised to 920 gev increasing the center - of - mass energy @xmath1 from 300 gev to 318 gev . in 1998 and in the first months of 1999 , hera ran with electrons . in may 1999 hera switched back to @xmath2 collisions . the three main colliding periods as well as the corresponding luminosities for each experiment are summarized in table [ tab : lumit ] . * * . _ _ luminosities collected by h1 and zeus for each colliding period . _ _ [ cols="^,^,^,^,^",options="header " , ] hera resulting limits on @xmath3 coupling are the following : * h1 : @xmath4 * zeus : @xmath5 figure [ fig : final ] summarizes the limits on the anomalous coulings @xmath6 ( @xmath7 vectorial coupling ) and @xmath8 ( @xmath3 magnetic coupling ) obtained at hera , lep and tevatron . hera sensitivity to @xmath8 is competitive with other colliders .

recent results on searches for physics beyond the standard model obtained by the h1 and zeus experiments are reported here . * search for new particles at hera * + mireille schneider + cppm , 163 , avenue de luminy , case 907 , + 13288 marseille cedex 9 , france

recent results on searches for physics beyond the standard model obtained by the h1 and zeus experiments are reported here . after a brief introduction to the hera collider , indirect searches for contact interactions and extra - dimensions are presented as well as direct searches for new physics including leptoquarks , lepton - flavour violation , squarks produced by r - parity violation and excited fermions . new results from isolated lepton events and single top searches are also presented . finally the future prospects of hera-2 are shown . * search for new particles at hera * + mireille schneider + cppm , 163 , avenue de luminy , case 907 , + 13288 marseille cedex 9 , france

hep-ex0201042

c

hera is the unique collider to test direct @xmath10 interactions . about @xmath11 of @xmath2 data and @xmath12 of @xmath13 data have been collected per experiment at hera-1 . no evidence of new physics has been observed in various models in inclusive analyses ( contact interactions , extra - dimensions , leptoquarks ) and exclusive analyses ( lepton - flavour violation , @xmath14-violating susy , excited fermions ) , therefore new constraints have been set . hera limits are seen to be competitive with and complementary to the lep and tevatron searches . the status of isolated lepton events with missing @xmath15 is still intriguing and will become clearer with the new hera-2 data . hera has been shutdown since fall 2000 for a general upgrade : new focussing magnets have been installed in order to increase the luminosity and many improvements have been performed in the detectors in order to increase their sensitivity . moreover , the lepton beam will be longitudinally polarised in the h1 and zeus interaction regions . the first luminosity runs are predicted for beginning 2002 and hera-2 is expected to accumulate 1 @xmath16 in the next 5 years . the anticipated factor of ten increase in the integrated luminosity will give an outstanding discovery potential for hera .

after a brief introduction to the hera collider , indirect searches for contact interactions and extra - dimensions are presented as well as direct searches for new physics including leptoquarks , lepton - flavour violation , squarks produced by r - parity violation and excited fermions . new results from isolated lepton events and single top searches are also presented . finally the future prospects of hera-2 are shown .

recent results on searches for physics beyond the standard model obtained by the h1 and zeus experiments are reported here . after a brief introduction to the hera collider , indirect searches for contact interactions and extra - dimensions are presented as well as direct searches for new physics including leptoquarks , lepton - flavour violation , squarks produced by r - parity violation and excited fermions . new results from isolated lepton events and single top searches are also presented . finally the future prospects of hera-2 are shown . * search for new particles at hera * + mireille schneider + cppm , 163 , avenue de luminy , case 907 , + 13288 marseille cedex 9 , france

astro-ph0506597

i

stars more massive than @xmath4 25 @xmath5 form a black hole at the end of their evolution . stars with non - rotating black holes are likely to collapse `` quietly '' ejecting a small amount of heavy elements ( faint supernovae ) . in contrast , stars with rotating black holes are likely to give rise to very energetic supernovae ( hypernovae ) . we present distinct nucleosynthesis features of these two classes of `` black - hole - forming '' supernovae . nucleosynthesis in hypernovae is characterized by larger abundance ratios ( zn , co , v , ti)/fe and smaller ( mn , cr)/fe than normal supernovae , which can explain the observed trend of these ratios in extremely metal - poor stars . nucleosynthesis in faint supernovae is characterized by a large amount of fall - back . we show that the abundance pattern of the recently discovered most fe - poor star , he0107 - 5240 , and other extremely metal - poor stars are in good accord with those of black - hole - forming supernovae , but not pair - instability supernovae . this suggests that black - hole - forming supernovae made important contributions to the early galactic ( and cosmic ) chemical evolution . finally we discuss the nature of first ( pop iii ) stars .

these two classes of supernovae are likely to be `` black - hole - forming '' supernovae with rotating or non - rotating black holes . we compare their nucleosynthesis yields with the abundances of extremely metal - poor ( emp ) stars to identify the pop iii ( or first ) supernovae . we show that the emp stars , especially the c - rich type , are likely to be enriched by black - hole - forming supernovae .

recent studies of core - collapse supernovae have revealed the existence of two distinct classes of massive supernovae ( sne ) : 1 ) very energetic sne ( hypernovae ) , whose kinetic energy ( ke ) exceeds @xmath0erg , about 10 times the ke of normal core - collapse sne , and 2 ) very faint and low energy sne ( @xmath1 0.5 @xmath2 @xmath3erg ; faint supernovae ) . these two classes of supernovae are likely to be `` black - hole - forming '' supernovae with rotating or non - rotating black holes . we compare their nucleosynthesis yields with the abundances of extremely metal - poor ( emp ) stars to identify the pop iii ( or first ) supernovae . we show that the emp stars , especially the c - rich type , are likely to be enriched by black - hole - forming supernovae .

1609.05828

i

a divergence - free vector field frequently appears in various mathematical and engineering problems such as an incompressible flow in the navier - stokes equation or a solenoidal magnetic induction in the maxwell equations or the limit of displacements in elasticity equations when poisson s ratio goes to 1/2 . an incompressible stokes problem can be reduced to an elliptic problem for the velocity only in the divergence - free space @xcite . the locally divergence - free subspace of @xmath1 ^ 2 $ ] was used for finite element methods to solve that elliptic problem @xcite , where @xmath2 is the crouzeix - raviart @xmath0-nonconforming finite element space on triangular meshes . it have also been adopted for the time - harmonic maxwell equations @xcite . it is equipped with sufficient interpolants for continuous divergence - free functions in @xmath3 ^ 2 $ ] , since it can be interpreted as the curls of the morley element . if the domain is simply connected in @xmath4 , its dimension is the number of interior vertices and edges @xcite , which is about two third of that of @xmath1 ^ 2 $ ] . a conforming locally divergence - free space whose elements are piecewise linear can be constructed with the curls of @xmath5-powell - sabin elements on triangular meshes for biharmonic problems @xcite . instead of working with divergence - free spaces , some researchers have developed finite element methods for stokes equations whose velocity solutions are resulted divergence - free @xcite as well as locally divergence - free discontinuous galerkin methods @xcite . in this paper , we are interested in the locally divergence - free subspace of @xmath6 ^ 2 $ ] , the @xmath0-nonconforming finite element space on square meshes . the space @xmath7 consists of functions which are linear in each square and continuous on each midpoint of edge @xcite . recently , it has been proved that @xmath6 ^ 2 $ ] is stable to solve stokes equations with the piecewise constant space for velocity and pressure , respectively @xcite . we will apply the locally divergence - free subspace to solve the elliptic problem for the velocity only , reduced from the incompressible stokes problem . the concerning system of linear equations is much smaller than that of the stokes equation . furthermore , it is split into two smaller ones for the red and black squares . after solving the velocity first , the pressure in the stokes problem will be obtained by an explicit method very rapidly . the paper is organized as follows . in the next section the @xmath0-nonconforming finite element space on quadrilateral meshes will be briefly reviewed . then , restricted on square meshes , we will devote section [ sec : divfree ] to characterizing its locally divergence - free subspace as well as a basis . in section [ sec : stokes ] , the reduced elliptic problem for the velocity and an explicit method for the pressure in the stokes problem are stated , respectively . finally , some numerical tests will be presented in the last section . throughout the paper , @xmath8 is a generic notation for a constant which depends only on @xmath9 .

recently , the @xmath0-nonconforming finite element space over square meshes has been proved stable to solve stokes equations with the piecewise constant space for velocity and pressure , respectively . in this paper , we will introduce its locally divergence - free subspace to solve the elliptic problem for the velocity only decoupled from the stokes equation . the concerning system of linear equations is much smaller compared to the stokes equations . furthermore , it is split into two smaller ones . after solving the velocity first , the pressure in the stokes problem can be obtained by an explicit method very rapidly .

recently , the @xmath0-nonconforming finite element space over square meshes has been proved stable to solve stokes equations with the piecewise constant space for velocity and pressure , respectively . in this paper , we will introduce its locally divergence - free subspace to solve the elliptic problem for the velocity only decoupled from the stokes equation . the concerning system of linear equations is much smaller compared to the stokes equations . furthermore , it is split into two smaller ones . after solving the velocity first , the pressure in the stokes problem can be obtained by an explicit method very rapidly . [ section ] [ theorem]remark [ theorem]lemma [ theorem]proposition [ theorem]definition [ section ] 2h_2h u v c

0901.1537

r

mf structures , indicative of a dynamo , were detected for 6 of the 7 giants ( exception : hd233517 ) , see ( incl . s index and @xmath2 ) table 1 . we determined the evolutionary status and masses of these 6 giants , using hipparcos parallaxes , @xmath3 from the wright catalogue ( 2003 ) , and matching evolutionary tracks from schrder et al . ( 1997 ) , see figure [ fig : hr ] . all 6 giants with mf - detection have masses @xmath41.5 @xmath5 and their convective zones are currently deepening while the stars are evolving . their evolutionary stages reach from the hertzsprung gap to the agb . while the particular reasons for the fast rotation could be different , depending on mass and evolutionary history , an @xmath0@xmath1 dynamo presents a likely reason for the detected magnetic activity .

early results include 6 mf - detections with fast rotating giants , and for the first time a magnetic field was detected directly in an evolved m - giant : ek boo . our results could be explained in the terms of @xmath0@xmath1 dynamo operating in these giants .

red giants offer a good opportunity to study the interplay of magnetic fields and stellar evolution . using the spectro - polarimeter narval of the telescope bernard lyot ( tbl ) , pic du midi , france and the lsd technique we began a survey of magnetic fields in single g - k - m giants . early results include 6 mf - detections with fast rotating giants , and for the first time a magnetic field was detected directly in an evolved m - giant : ek boo . our results could be explained in the terms of @xmath0@xmath1 dynamo operating in these giants .

1510.06515

r

our aim is to evaluate relativistic effects on dynamical behavior of parameter quantum estimation for an accelerated atom . in experiments , the observation of a phase difference between two energy states plays a great role in quantum information technology @xcite . in this scenario , we consider phase estimation for atoms in relativistic motions . for a measuring device in the same motion as a uniformly accelerated atom , the observation of quantum estimation should be presented in the non - inertial frame . different from quantum estimation in the non - inertial frame , the results are established in the inertial frame when the measuring device is in a motion with uniform velocity . an selected initial state for the atom at @xmath22 involves a phase parameter and has the form of @xmath46 represent a phase difference between the excited state @xmath47 and ground state @xmath48 . @xmath49 describes the relative occurrence possibility of the energy states . it is easily found that the phase quantum estimation is dependent on the evolution of the parameterized states . to evaluate the true value of a phase parameter @xmath50 as precisely as possible , we need an unbiased estimator @xmath51 whose expectation holds that @xmath52 . the precision of quantum estimation satisfies the quantum cramr - rao ( @xmath53 ) inequality @xcite , i.e. , @xmath54 , where @xmath55 is the number of independent measurements and @xmath56 is the @xmath2 with respect to phase parameter @xmath50 . the @xmath53 inequality shows that the high precision of phase estimation is attained when the value of @xmath2 is large . the standard calculation procedure @xcite starts by the construction of a symmetric logarithmic derivative @xmath57 which is defined as @xmath58 the @xmath2 which is not dependent on the choice of @xmath57 is generally written as @xmath59.\ ] ] the evolution state @xmath60 of the atom in the non - inertial frame is written as @xmath61 for the density matrix of @xmath62 , the elements of @xmath57 are calculated as @xmath63,\ ] ] where the eigenvalues and eigenstates of the density matrix are given by @xmath64 and @xmath65 . as a result , we accomplish the analytical expression of @xmath2 as @xmath66 when the parameter @xmath67 , the value of @xmath2 reaches a maximal one , i.e. , @xmath68 . it is seen that the dynamical behavior of @xmath2 are determined by the decay rates and proper time . to discover some controllable conditions that contribute to the @xmath2 , we reasonably take into account boundary effects of the scalar field . boundaries can modify the fluctuations of quantum fields . it leads to a lot of novel effects , such as casimir effects@xcite , entanglement generation @xcite and the modification for the radiative properties of uniformly accelerated atoms @xcite . in our scheme , two perfectly reflecting plane boundaries that are perpendicular to each other locate at @xmath69 and @xmath70 in the space , respectively . from fig . ( 1 ) , it is shown that @xmath71 denotes the distance between the trajectory of the accelerated atom and the cross of the two boundaries . the angle @xmath72 represents the relative position of the atom between the two boundaries . in this simple case , the boundary conditions holds that @xmath73 and @xmath74 . according to the method of images , the correlation function for the vacuum field is expressed as @xmath75 } - \dfrac 1{\sinh^2\left [ \frac { a(\tau-\tau^{\prime}}{2 } -i\epsilon \right]-a^2r^2\cos^2\alpha } \right . \nonumber \\ & \left . + \dfrac 1{\sinh^2\left [ \frac { a(\tau-\tau^{\prime}}{2 } -i\epsilon \right]-a^2r^2 } - \dfrac 1{\sinh^2\left [ \frac { a(\tau-\tau^{\prime}}{2 } -i\epsilon \right]-a^2r^2\sin^2\alpha } \right\}.\end{aligned}\ ] ] the fourier transformation of the correlation function @xmath31 is also calculated as @xmath76,\ ] ] where the special function @xmath77 is defined as @xmath78}{2r\sqrt{1+a^2r^2}\omega}$ ] . the unruh temperature @xmath79 is involved in the above equation . and in the limit of @xmath80 , the parameter @xmath81 $ ] where the function @xmath82 . consequently , the analytical expression of the maximal @xmath2 in the non - inertial frame is given by @xmath83 \right . \nonumber \\ & - \left . \frac { \lambda^2 a \tau}{\pi^2}\left [ 1-f_2(r\cos\alpha)-f_2(r\sin\alpha)+f_2(r ) \right ] \right\}.\end{aligned}\ ] ] to clearly demonstrate the effects of the relativistic motions and boundaries on the dynamics of the @xmath2 , we carry out the numerical calculation of @xmath2 which are plotted in figs . ( 2)-(4 ) provide the observation results of the maximal @xmath2 in the non - inertial frame . the observation is achieved by a measuring device in the same motion as the acceleration atom . it is clearly seen that the values of the maximal @xmath2 are always monotonically decreased with the proper time @xmath84 in fig . besides it , the values in the low acceleration condition are larger than those in the high acceleration condition . this means that the relativistic motion of the measuring device can suppress the precision of parameter quantum estimation for the accelerated atom . the boundary effects on the @xmath2 are shown in fig . ( 3 ) . in the region of @xmath85 , the values of @xmath2 can keep high in the short time interval . when the trajectory of the accelerated atom is far away from the boundaries , i.e. , @xmath86 , the boundary effects are trivial and even neglected . we also notice that the apparent oscillation of the @xmath2 will happen if the accelerated atom is close to the boundaries . this phenomena is induced by the relativistic motion . from fig . ( 4 ) , we also see that the values of @xmath2 are symmetrical to the boundaries . in the case of @xmath87 , the value of @xmath2 arrives at the minimal one . meanwhile , the high values of @xmath2 can be reached under the condition of @xmath88 or @xmath89 . the fact is that the precision of phase quantum estimation is enhanced when the accelerated atom is near to the boundaries .

the quantum fisher information is used to estimate the phase sensitivity of atoms in non - inertial motions or in gravitational fields . it is found out that monotonic decrease in phase sensitivity is characteristic of dynamics of relativistic quantum estimation . to improve relativistic quantum metrology , we reasonably take into account two reflecting plane boundaries perpendicular to each other .

relativistic effects on the precision of quantum metrology for particle detectors , such as two - level atoms are studied . the quantum fisher information is used to estimate the phase sensitivity of atoms in non - inertial motions or in gravitational fields . the unruh - dewitt model is applicable to the investigation of the dynamics of a uniformly accelerated atom weakly coupled to a massless scalar vacuum field . when a measuring device is in the same relativistic motion as the atom , the dynamical behavior of quantum fisher information as a function of rindler proper time are obtained . it is found out that monotonic decrease in phase sensitivity is characteristic of dynamics of relativistic quantum estimation . to improve relativistic quantum metrology , we reasonably take into account two reflecting plane boundaries perpendicular to each other . keywords : phase quantum estimation , relativistic effects , unruh - dewitt model , quantum fisher information pacs : 03.67.-a , 03.65.yz , 42.50.ex

1510.06515

c

by means of the @xmath0 model , we study the dynamical behavior of phase quantum estimation for a uniformly accelerated atom weakly coupled to a massless quantum scalar field . the dynamics of quantum states of the atom can be obtained in the non - inertial frame . the calculation of the @xmath2 provides an efficient way to estimate the measuring precision . when a measuring device is accelerated in the same motion as the atom , the monotonic decrease of the @xmath2 is manifest in the high acceleration limit . this means that the relativistic motion of the measuring device restrains the precision of phase quantum estimation . it is found out that the obvious oscillation of @xmath2 occur under the condition that the trajectory of the atom is close to the boundaries . this provides us a possible way to enhance the precision of phase quantum estimation in the relativistic situation . let us examine the magnitudes involved in some possible experiments . the natural scale of units is fixed by fixing units for the energy gap @xmath6 of the atom , namely @xmath90 . for atomic gaps of @xmath91 , one natural unit of acceleration corresponds to @xmath92 ( @xmath93 is the earth surface gravitation acceleration ) @xcite . the acceleration required in our scenario can be reduced by the use of qubits with smaller gaps . for example , for special qubits defined by nuclear spins , energy gaps can be limited to the order of @xmath94 , which can reduce the acceleration to almost @xmath95 @xcite . the scale of acceleration can be realized in @xmath96 setups . in addition , qubits with stark shifted atomic levels or zenner - induced transition nearly have energy gaps of the order of @xmath97 . for these qubits , the acceleration can reach @xmath98 @xcite . those accelerations are indeed experimentally achieved for short time intervals . current technology of ion trapping and superconducting circuits allows for experiments where relativistic effects can be observed . the work was supported by the @xmath99 talents project of jiangsu province , by jiangsu government scholarship for study abroad , and by nserc of canada and templeton foundation , grant no . we would like to thank bill unruh for the discussions on related work . a. peres and d. r. terno , rev . phys . * 76 * , 93(2004 ) . n. friis , m. huber , i. fuentes , d. e. bruschi , phys . d * 86 * , 105003(2012 ) . d. e. bruschi , a. dragan , a. r. lee , i. fuentes , j. louko , phys . lett . * 111 * , 090504(2013 ) . e. martn - martnez , d. aasen , a. kempf , phys . lett . * 110 * , 160501(2013 ) . e. e. martn - martnez and c. sutherland , phys . b * 739 * , 74(2014 ) . a. g. s. landulfo and g. e. a. matsas , phys . a * 80 * , 032315 ( 2009 ) . l. c. cleri , a. g. s. landulfo , r. m. serra , and g. e. a. matsas , phys . a * 81 * , 062130 ( 2010 ) . j. wang , j. jing , and h. fan , phys . d * 90 * , 025032(2014 ) . grant salton , robert b mann , and nicolas c menicucci , new j. phys . * 17 * , 035001(2015 ) d. su and t. c. ralph , phys . d 90 084022 ( 2014 ) w. g. unruh , phys . d * 14 * , 870(1976 ) . l. c. b. crispino , a. higuchi , and g. e. a. matsas , rev . mod . phys . * 80 * , 787(2008 ) . b. s. dewitt , phys . rev . * 160 * , 1113(1967 ) . e. g. brown , e. martn - martnez , n. c. menicucci , r. b. mann , phys d * 87*,084062(2013 ) . m. o. scully , m. s. zubairy , quantum optics , cambridge university press(1997 ) . h. yu , phys . 106 , 061101(2011 ) . j. feng , y. z. zhang , m. d. gould , and h. fan , phys . b * 743 * , 198(2015 ) p. d. nation , m. p. blencowe , a. j. rimberg , and e. buks , phys . lett . * 103 * , 087004(2009 ) . c. m. wilson , g. johansson , a. pourkabirian , m. simoen , j. r. johansson , t. duty , f. nori , and p. delsing , nature(london ) * 479 * , 376(2011 ) . s. l. braunstein and c. m. caves , phys . lett . * 72 * , 3439(1994 ) . d. petz , linear algebra appl . * 244 * , 81(1996 ) . s. luo , lett . 53 * , 243(2000 ) . p. gibilisco , d. imparato , and t. isola , j. math . phys . * 48 * , 072109(2007 ) . m. m. taddei , b. m. escher , l. davidovich , and r. l. de matos filho , phys . lett . * 110 * , 050402(2013 ) . c. invernizzi , m. korbman , l. c. venuti , and m. g. a. paris , phys . a * 78 * , 042106(2008 ) . s. boixo and a. monras , phys . 100 , 100503(2008 ) . m. aspachs , g. adesso , and i. fuentes , phys . lett . * 105 * , 151301(2010 ) . y. yao , x. xiao , l. ge , x. wang , and c. sun , phys . rev . a * 89 * , 042336(2014 ) . d. hosler and p. kok , phys . a * 88 * , 052112(2013 ) . m. ahmadi , d. e. bruschi , n. friis , c. sabn , g. adesso , and i. fuentes , sci . rep . * 4 * , 4996(2014 ) . z. tian , j. wang , h. fan and j. jing , sci . * 5 * , 7946(2015 ) . f. benatti , r. floreanini , and m. piani , phys . lett . * 91 * , 070402 ( 2003 ) . f. benatti and r. floreanini , phys . a * 70 * , 012112 ( 2004 ) . v. giovanetti , s. lloyd , and l. maccone , science * 306 * , 1330(2004 ) . c. w. helstrom , quantum detection and estimation theory , academic , new york(1976 ) . a. s. holevo , probabilistic and statistical aspects of quantum theory , north - holland , amsterdam(1982 ) . h. b. g. casimir , proc . akad . wet . * 51 * , 793(1948 ) . j. zhang , h. yu , phys . rev . a * 75 * , 012101(2007 ) . h. yu and s. lu , phys . d * 72 * , 064022 ( 2005 ) . e. arimondo , m. inguscio , and p. violino , rev . * 49 * , 31(1977 ) . ( atlas collaboration ) , phys . lett . * 105 * , 161801 ( 2010 ) . the effects of the acceleration on the dynamics of @xmath2 as a function of the proper time @xmath84 are shown when the measuring device is in the same relativistic motion as the atom . the observation results are obtained under the conditions that @xmath100 in the non - inertial frame . the boundary effects on the dynamics of @xmath2 as a function of the proper time @xmath84 are shown when the measuring device is in the same relativistic motion as the atom . the observation results are obtained under the conditions that @xmath101 in the non - inertial frame . the effects of the relative position of the atom between the boundaries are shown at some proper time when the measuring device is in the same relativistic motion as the atom . the observation results are obtained under the conditions that @xmath102 in the non - inertial frame .

the unruh - dewitt model is applicable to the investigation of the dynamics of a uniformly accelerated atom weakly coupled to a massless scalar vacuum field . when a measuring device is in the same relativistic motion as the atom , the dynamical behavior of quantum fisher information as a function of rindler proper time are obtained .

relativistic effects on the precision of quantum metrology for particle detectors , such as two - level atoms are studied . the quantum fisher information is used to estimate the phase sensitivity of atoms in non - inertial motions or in gravitational fields . the unruh - dewitt model is applicable to the investigation of the dynamics of a uniformly accelerated atom weakly coupled to a massless scalar vacuum field . when a measuring device is in the same relativistic motion as the atom , the dynamical behavior of quantum fisher information as a function of rindler proper time are obtained . it is found out that monotonic decrease in phase sensitivity is characteristic of dynamics of relativistic quantum estimation . to improve relativistic quantum metrology , we reasonably take into account two reflecting plane boundaries perpendicular to each other . keywords : phase quantum estimation , relativistic effects , unruh - dewitt model , quantum fisher information pacs : 03.67.-a , 03.65.yz , 42.50.ex

astro-ph0604618

i

is a symbiotic recurrent nova ( rn ) which had previously undergone recorded outbursts in 1898 , 1933 , 1958 , 1967 and 1985 ( see * ? ? ? * ; * ? ? ? * ) , with a possible additional outburst in 1907 @xcite . on 2006 february 12.83ut it was observed to be undergoing a further eruption @xcite , reaching magnitude v=4.5 at this time . for the purposes of this paper , we define this as @xmath6 . the optical light curve then continued a rapid decline , consistent with that seen in previous outbursts ( @xcite , aavso ) . the rs oph binary system comprises a red giant star in a @xmath7 day orbit with a white dwarf ( wd ) of mass near the chandrasekhar limit ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? accretion of hydrogen - rich material from the red giant onto the wd surface leads to the conditions for a thermonuclear runaway ( tnr ) in a similar fashion to that for classical novae ( cne ) . the much shorter inter - outburst period for this type of rn compared to cne is thought to be due to a combination of the high wd mass and a supposed high accretion rate ( e.g. * ? ? ? * ; * ? ? ? such models lead to the ejection of somewhat lower masses at higher velocities than those for cn models ( typically 5000 km s@xmath8 and @xmath9m@xmath10 respectively for rne ) . spectroscopy of rs oph has indeed shown h@xmath11 line emission with fwhm @xmath12 km s@xmath8 and fwzi @xmath13 km s@xmath8 on 2006 february 14.2 ( @xmath14 days , @xcite ) . superimposed on the broad line is an intense and narrow double - peaked structure . unlike cne , where the mass donor is a low - mass main - sequence star , the presence of the red giant in the rs oph system means that the high velocity ejecta run into a dense circumstellar medium in the form of the red giant wind , setting up a shock system with gas temperatures @xmath15k for @xmath16 km s@xmath8 , where @xmath17 is the velocity of the forward shock running into the pre - existing wind ( see below ) . evidence for the presence of such high temperature material in outbursts prior to 1985 came from observations of coronal lines in optical spectra @xcite and the expected deceleration was evidenced by the narrowing of the initially broad emission lines @xcite . the superimposed narrow lines are then from emission and absorption in the red giant wind ahead of the forward shock . the interstellar absorbing column , @xmath18 @xmath19 , was determined from hi 21 cm measurements @xcite and is consistent with the visual extinction ( @xmath20 ) determined from iue observations in 1985 @xcite . these quantities , together with the observed versus theoretical bolometric luminosity and apparent brightness of the red giant , are all consistent with a distance to rs oph of @xmath21 kpc @xcite . exosat observations in 1985 @xcite from @xmath22 days post - outburst showed that rs oph was initially an intense , then a rapidly declining soft x - ray source . @xcite formulated an analytical model of the evolution of the outburst based on the x - ray emission observed by exosat at 55 days , the rapidly increasing radio emission from @xmath23 days @xcite and parameters of the red giant wind derived from optical observations . they concluded that rs oph evolved like a supernova remnant ( snr ) , but on timescales around @xmath24 times faster ( see below ) . subsequently , @xcite and @xcite constructed detailed analytical and numerical models of the interaction of the ejecta with the circumstellar medium which led to consistent estimates of the outburst energy and ejected mass of @xmath25 erg and @xmath26 m@xmath10 respectively , with the ratio of mass loss rate to outflow speed in the red giant wind being estimated as @xmath27 g cm@xmath8 , compatible with that from isolated red giants . perhaps not surprisingly , this relatively simple model failed to agree fully with the observed spectral evolution of the x - ray emission . in particular , it was difficult to reconcile both the low - energy and higher energy behaviour of the emission ( see also @xcite who primarily explored the interaction of shells from two separate outbursts ) .

rs ophiuchi began its latest outburst on 2006 february 12 . previous outbursts have indicated that high velocity ejecta interact with a pre - existing red giant wind , setting up shock systems analogous to those seen in supernova remnants . however , in the previous outburst in 1985 , x - ray observations did not commence until @xmath0 days after the initial explosion . here similarly , @xmath3_w$ ] is in accord with that expected from the red giant wind ahead of the forward shock .

rs ophiuchi began its latest outburst on 2006 february 12 . previous outbursts have indicated that high velocity ejecta interact with a pre - existing red giant wind , setting up shock systems analogous to those seen in supernova remnants . however , in the previous outburst in 1985 , x - ray observations did not commence until @xmath0 days after the initial explosion . here we report on _ swift _ observations covering the first month of the 2006 outburst with the burst alert ( bat ) and x - ray telescope ( xrt ) instruments . rs oph was clearly detected in the bat 14 - 25 kev band from @xmath1 to @xmath2 days . xrt observationsfrom 0.3 - 10 kev , started at 3.17 days after outburst . the rapidly evolving xrt spectra clearly show the presence of both line and continuum emission which can be fitted by thermal emission from hot gas whose characteristic temperature , overlying absorbing column , @xmath3_w$ ] , and resulting unabsorbed total flux decline monotonically after the first few days . derived shock velocities are in good agreement with those found from observations at other wavelengths . similarly , @xmath3_w$ ] is in accord with that expected from the red giant wind ahead of the forward shock . we confirm the basic models of the 1985 outburst and conclude that standard phase i remnant evolution terminated by @xmath4 days and the remnant then rapidly evolved to display behaviour characteristic of phase iii . around @xmath5 days however , a new , luminous and highly variable soft x - ray source began to appear whose origin will be explored in a subsequent paper .

1404.6343

i

in physics , the boundary condition is often treated as a secondary issue . similar to the term itself , boundary conditions remain peripheral , never central . in string theory , however , the boundary condition plays a fundamental role . certain boundary conditions of the worldsheet exhibit non - perturbative aspects of string theory through d - branes . they also distinguish between open and closed strings , which correspond to gauge theories and gravity , respectively . this short note concerns the boundary conditions in string theory . in recent studies of a certain class of quantum systems , systems with closed and open boundary conditions were found to have identical vacua provided that the coupling constants of the open - boundary system are modulated in a way called _ sine - square deformation _ ( ssd ) @xcite . in particular , ssd works for two - dimensional conformal field theories , which describe the worldsheets of string theory @xcite . therefore , the implications of this discovery to string theory are potentially vast . the spatial modulation of the coupling constant is seldom investigated in condensed matter physics . however , such modulation may correspond to introducing a metric with non - trivial curvature . in this sense , the above - mentioned uncovering can be interpreted as an effect caused by the worldsheet metric . thus , by investigating the effect of the ssd on the worldsheet , we may better understand the non - perturbative aspects of string theory such as d - branes or open / closed duality through interchanges of the boundary condition caused by the worldsheet metric . specifically , if certain worldsheet metrics can alter the boundary condition , resulting in d - brane emission or transitions between open and closed strings , then non - perturbative aspects of string theory can be understood from the dynamics of the worldsheet through its condensation . although , the worldsheet metric can be gauged away in the perturbative treatment of string theory , the metric may couple to the dynamics when non - perturbative effects are incorporated . the boundary condition , by nature , stipulates the development of a system , not the other way around . once set up , a system only evolves within its pre - determined boundary . therefore , if non - perturbative effects of string theory are depicted in terms of boundary conditions , they remain unaltered throughout the system development . here we explore a possibility that the condensation of the worldsheet metric effectively alter the boundary condition , thereby exhibiting non - perturbative effects of string dynamics . if this is the case , non - perturbative aspects of string theory can be understood in terms of worldsheet metric dynamics . in fact , one could argue that this has been somewhat achieved by the research through matrix models @xcite , in which the effects of d - branes were identified . noting that the matrix models are nothing but the statistical mechanics of the discretized worldsheet , here we rather seek a continuum treatment of the world sheet based on the ssd . in this note , we attempt to clarify the role of the world sheet metric in the non - perturabative dynamics of string theory . to this end , we explore the consequences of the ssd on the worldsheet . ssd is briefly overviewed in section [ sec : ssd ] , and it is applied to conformal field theory in subsection [ sec : sl2cvac ] . in subsection [ subsec : nont ] , we verify that the ssd is actually a non - trivial transformation . a novel state in the deformed system is presented in subsection [ sec : anovac ] . we examine the ssd in the lagrangian formalism in section [ sec : ssdstring ] . here , we reveal large divergence of the worldsheet metric . we conclude with notes and future perspectives in section [ sec : sum ] .

sine - square deformation , a recently found modulation of the coupling strength in certain statistical models , is discussed in the context of two - dimensional conformal field theories , with particular attention to open / closed string duality . this deformation is shown to be non - trivial and leads to a divergence in the worldsheet metric . the approach advocated here may provide an understanding of string duality through the worldsheet dynamics .

sine - square deformation , a recently found modulation of the coupling strength in certain statistical models , is discussed in the context of two - dimensional conformal field theories , with particular attention to open / closed string duality . this deformation is shown to be non - trivial and leads to a divergence in the worldsheet metric . the structure of the vacua of the deformed theory is also investigated . the approach advocated here may provide an understanding of string duality through the worldsheet dynamics . [ cols= " < " , ] * sine - square deformation and its relevance to string theory * tsukasa tada _ riken nishina center for accelerator - based science , + wako , saitama 351 - 0198 , japan _ _ version published as mod . phys . lett . a , vol . 30 , no . 19 ( 2015 ) 1550092 . _

cond-mat9905355

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titin , a giant protein molecule responsible for elasticity of muscles , is comprised of a few hundred immunoglobulin ( ig ) and fibronectin - iii repeats aligned in tandem @xcite . recently , through nanomanipulation of single protein molecules , there has been direct evidence for sequential unfolding of individual domains upon stretching @xcite . these remarkable experiments and others on dna @xcite have made it possible to unearth the microscopic underpinnings of the unusual elastic behavior in biological molecules . in two experiments @xcite individual titin molecules were tethered to a plastic bead and optical tweezers were used to stretch the molecule . direct measurement of the forces required to stretch titin were used to infer that tension leads to unfolding of individual ig - like domains @xcite . perhaps , the clearest evidence for domain unraveling was presented by rief _ _ @xcite who used atomic force microscopy ( afm ) to pull on titin molecules adsorbed onto a gold surface . the afm experiments , on both the model recombinant titin molecules consisting only of ig ( ig@xmath2 and ig@xmath3 ) domains and the native titin , showed clear saw - tooth patterns in the force - extension curves indicating sequential unfolding of domains . the constant periodicity of the saw - tooth pattern ( @xmath4 ) is nearly coincident with the dimensions of the fully unfolded ig domain ( @xmath5 ) and is very similar to the contour length inferred from fitting the force - extension curves obtained from the optical tweezer experiments @xcite ( see also related experiments on tenascin @xcite ) . all the experiments conclude that sequential unraveling of the domains results upon mechanically stretching titin . inspired by these experiments , we report the results of force - induced unfolding of single domain proteins using simple lattice models which have been useful in the search for general principles of protein folding @xcite . because the primary mechanism of stretching titin involves unraveling of individual ig - like domains , which fold spontaneously in the absence of tension @xcite , our calculations provide microscopic origins of force induced unfolding . we show that the response of proteins to force depends primarily on their topology in the absence of force . by computing the phase diagram and kinetics of a number of model proteins subject to tension we show that the folding free energy landscape @xcite in the absence of force can be deciphered using single molecule manipulation techniques .

single molecule force spectroscopy reveals unfolding of domains in titin upon stretching . we provide a theoretical framework for these experiments by computing the phase diagrams for force - induced unfolding of single domain proteins using lattice models . the stretching rates of individual molecules show great variations reflecting the heterogeneity of force - induced unfolding pathways . unfolding dynamics depends sensitively on topology . a mapping of these results to proteins shows qualitative agreement with force - induced unfolding of ig - like domains in titin . we show that single molecule force spectroscopy can be used to map the folding free energy landscape of proteins in the absence of denaturants .

single molecule force spectroscopy reveals unfolding of domains in titin upon stretching . we provide a theoretical framework for these experiments by computing the phase diagrams for force - induced unfolding of single domain proteins using lattice models . the results show that two - state folders ( at zero force ) unravel cooperatively whereas stretching of non - two - state folders occurs through intermediates . the stretching rates of individual molecules show great variations reflecting the heterogeneity of force - induced unfolding pathways . the approach to the stretched state occurs in a step - wise `` quantized '' manner . unfolding dynamics depends sensitively on topology . the unfolding rates increase exponentially with force @xmath0 till an optimum value which is determined by the barrier to unfolding when @xmath1 . a mapping of these results to proteins shows qualitative agreement with force - induced unfolding of ig - like domains in titin . we show that single molecule force spectroscopy can be used to map the folding free energy landscape of proteins in the absence of denaturants .

1502.01228

i

human action detection at real - time has become a topic of increasing interest due to its wide practical use . applications like human - machine interaction , surveillance and gaming , all require accurate and low - latency action detection . action detection on raw videos is difficult because it is first needed to localize a person in a scene full of objects and clutter , then try to recognize the type of action being performed . on the other hand , the recent low - cost depth sensors , like microsoft kinect , provided a more convenient way for data capture . the 3d positions of body joints can be estimated from depth maps at low - latency and with acceptable accuracy . filtering out background clutter , it is now more adequate to perform action detection based on skeleton data . recently , skeleton - based approaches to action recognition and detection have been widely adopted . while action recognition focuses on identifying the action label of pre - segmented video sequences , action detection tackles the more challenging problem of temporally localizing the action in an unsegmented stream of frames . the main contribution of this paper is a novel approach for action detection from skeleton data , that we refer to as efficient linear search ( els ) . we show that a combination of simple components and specializing them towards skeleton - based action detection can achieve state - of - the - art results and overcome the limitations of similar approaches . the proposed approach is flexible : it can be used with a wide class of classifier functions and with different types of action local descriptors . as a byproduct contribution , we propose a simple skeleton - based local descriptor that , when used in a simple bag - of - features model , produces state - of - the - art results on different datasets . the proposed framework works online and is suitable for real - time applications . moreover , it can be used for real - time video segmentation , since it specifies both the start and end frames of the action . the rest of this paper is organized as follows : section [ sec : relwork ] gives an overview about recent related work in the literature . we show the used action representation and our proposed descriptor in section [ sec : mainidea ] . we , then , explain our efficient linear search approach in section [ sec : els ] . experimental evaluation is presented in [ sec : experiments ] . and finally , we conclude in [ sec : conclusion ] .

sliding window is one direct way to extend a successful recognition system to handle the more challenging detection problem . while action recognition decides only whether or not an action is present in a pre - segmented video sequence , action detection identifies the time interval where the action occurred in an unsegmented video stream . , we propose a novel approach for online action detection based on 3d skeleton sequences extracted from depth data . furthermore , it is suitable for real - time applications with low latency .

sliding window is one direct way to extend a successful recognition system to handle the more challenging detection problem . while action recognition decides only whether or not an action is present in a pre - segmented video sequence , action detection identifies the time interval where the action occurred in an unsegmented video stream . sliding window approaches can however be slow as they maximize a classifier score over all possible sub - intervals . even though new schemes utilize dynamic programming to speed up the search for the optimal sub - interval , they require offline processing on the whole video sequence . in this paper , we propose a novel approach for online action detection based on 3d skeleton sequences extracted from depth data . it identifies the sub - interval with the maximum classifier score in linear time . furthermore , it is suitable for real - time applications with low latency .

1407.2188

c

we have proposed a quantitative mathematical model of the social spreading of smoking that is derived from basic principles well - documented in the sociology and social psychology literature . the model appears to match real - world smoking prevalence data from a variety of countries well ( to our knowledge , the largest historical data set of this type ever compiled ) , and all predictions of the model appear to be supported by the data . in particular , the model predicts that the level of individualism or collectivism of a society may significantly affect the temporal dynamics of smoking prevalence : the strong influence of the personal utility of smoking ( and its decrease due to increased awareness of adverse health effects ) is predicted to lead to faster adoption and cessation of smoking in individualistic societies than in more collectivistic societies . it has previously been argued that social support mechanisms in collectivistic societies make it more likely that a person will stop smoking @xcite based on findings that social support ( supportive counselors ) can help people to adhere to decisions to quit smoking @xcite . we find that , to the contrary , cessation of smoking occurs more slowly in collectivistic societies . our model suggests that this is so because social inertia will inhibit decisions to stop smoking more strongly in collectivistic societies than in individualistic societies . these results have significant implications for combating the ongoing smoking epidemic . for example , they imply that interventions designed to discourage smoking should be tailored differently in societies or social groups whose cultures differ in how they value individualism versus collectivism @xcite . more broadly , these results demonstrate that differences in culture can measurably affect the dynamics of a social spreading process , and that a mathematical model can help to illuminate this phenomenon . despite the good match between model predictions and data , a number of limitations remain . we have made an implicit `` mean - field '' approximation in taking social utility to be a function of the overall smoking prevalence @xmath17 , rather than the local smoking prevalence among contacts in an individual s social network . similarly , we have taken individual utility to be uniform across the population ( though not in time ) , whereas a more detailed model might allow for individual variation . as a mild justification for these assumptions , we point out that analysis of a similar model in another context @xcite suggests that inclusion of more detail will not change qualitative predictions . we claim that the correlation of individualism with faster societal change results from a causative influence as predicted by our model . other factors such as income levels also correlate with individualism , and it s possible that what we observe is ultimately also related to gdp or other variables . we certainly can not exclude that there may be other causative factors . for example , our model in its current form is incapable of explaining differences in smoking prevalence between genders and why these inter - gender differences vary between countries @xcite . nevertheless , we remark that many previously proposed causative factors for differences in observed inter - country smoking dynamics can be accounted for within our modelling framework . in particular , beliefs about the harmful effects of smoking , the price of cigarettes , socioeconomic status and inequality , and government regulation have all been cited as potential factors affecting the differences observed in inter - country smoking dynamics @xcite . each of these factors can be interpreted within our modelling framework . for example , beliefs about the harmful effects of smoking , as well as the price of cigarettes , both likely contribute directly to individual utility derived from smoking ( @xmath16 ) and from non - smoking ( @xmath21 ) . moreover , socioeconomic status may affect individual utility from smoking indirectly by affecting an individual s tolerance for risk and/or how they discount future rewards and costs ( i.e. how they discount their future health status ) @xcite . addressing the model s inability to account for gender differences in smoking prevalence and quantifying the relationship between other causative factors and model parameters are potential areas for future work . we also welcome future work comparing a variety of social contagion phenomena across societies . our model suggests that the increased cultural inertia in collectivistic societies would lead to slower change across a wide spectrum of spreading processes ( those where important changes occur in personal utility ) , a hypothesis that could be supported or rejected by further study .

responding effectively to this epidemic requires a thorough understanding of how smoking behaviour is transmitted and modified . here , we present a new mathematical model of the social dynamics that cause cigarette smoking to spread in a population . our model predicts that more individualistic societies will show faster adoption and cessation of smoking . evidence from a new century - long composite data set on smoking prevalence in 25 countries supports the model , with direct implications for public health interventions around the world . our results suggest that differences in culture between societies can measurably affect the temporal dynamics of a social spreading process , and that these effects can be understood via a quantitative mathematical model matched to observations . [ [ keywords ] ] keywords : + + + + + + + + + smoking prevalence , individualism , mathematical modelling

smoking of tobacco is predicted to cause approximately six million deaths worldwide in 2014 . responding effectively to this epidemic requires a thorough understanding of how smoking behaviour is transmitted and modified . here , we present a new mathematical model of the social dynamics that cause cigarette smoking to spread in a population . our model predicts that more individualistic societies will show faster adoption and cessation of smoking . evidence from a new century - long composite data set on smoking prevalence in 25 countries supports the model , with direct implications for public health interventions around the world . our results suggest that differences in culture between societies can measurably affect the temporal dynamics of a social spreading process , and that these effects can be understood via a quantitative mathematical model matched to observations . [ [ keywords ] ] keywords : + + + + + + + + + smoking prevalence , individualism , mathematical modelling

cond-mat0003012

i

as soon as kuhn understood the flexibility of polymer chains , and the origin of rubber elasticity , his student a. katchalsky thought about the possibility of transforming chemical energy into mechanical energy , using gels swollen by water . his first idea is explained on fig.[fig1 ] . starting from chains which carry acid groups @xmath0 and adding @xmath1 ions , one obtains a charged network @xmath2 where the chains stretch by electrostatic repulsions . if one then adds @xmath3 , the system returns to neutral , and the gel contracts . [ h ] pgg1nov.eps this system , however , does not allow for many cycles . adding @xmath1 really means adding soda @xmath4 and adding @xmath3 means adding hydrochloric acid @xmath5 . at each cycle , one thus adds one mole of @xmath6 , and this ionic solute screens out the electrostatic interactions : the system dies out fast . katchalsky solved this problem by an intelligent trick : he used ion exchange @xmath7 against @xmath8 where @xmath9 binds two @xmath2 groups and contracts the gel . his group produced active fibers of this type@xcite @xmath10 however , the process did not gave rise to useful applications , for a number of reasons : \1 ) time constants : what is implied here is diffusion of ions from a bath to a fiber , and diffusion is always very slow . and even if the ions were injected locally ( by highly divided electrodes , or , by conducting polymers ) the diffusion of water remains necessary to swell or deswell . \2 ) fatigue : if we swell a gel by water , the swelling process starts at the outer surface , and creates huge mechanical tensions in a thin region : buckling instabilities occur@xmath11 and fractures show up . there is little hope for an artificial muscle which breaks locally at each cycle . in the following section , we present two attempts where these difficulties are taken into account . it may well be that none of them gives a durable answer , but the trends are interesting .

solid state actuators ( piezoelectric , ferroelectric , ... ) deform under an external field , and have found many applications . there is a need for soft actuators , giving larger responses , but necessarily less fast . this paper describes the early attempts by katchalsky and others , and the problems which showed up -related to time constants , and , most importantly , to fatigue . two current attempts are reviewed . _ key words _ : actuators , artificial muscles , nematic polymers , electro osmosis . _ pacs numbers _ : 64.70 md , 65.70 + y , 66.30 qa .

solid state actuators ( piezoelectric , ferroelectric , ... ) deform under an external field , and have found many applications . they respond fast , but their mechanical deformations are very small . there is a need for soft actuators , giving larger responses , but necessarily less fast . this paper describes the early attempts by katchalsky and others , and the problems which showed up -related to time constants , and , most importantly , to fatigue . two current attempts are reviewed . _ key words _ : actuators , artificial muscles , nematic polymers , electro osmosis . _ pacs numbers _ : 64.70 md , 65.70 + y , 66.30 qa .

1611.07909

i

image segmentation can be thought as a signal decomposition problem , where the goal is to decompose the signal into several components such that each one represents the same content or semantic information . one special case is the background - foreground segmentation , which tries to decompose an image into two components , background and foreground . foreground - background segmentation has many applications in image processing such as separate coding of background and foreground in video compression , organ detection in medical images , text extraction , and medical image analysis @xcite-@xcite . different algorithms have been proposed in the past for foreground - background segmentation , including k - means clustering in djvu @xcite , shape primitive extraction and coding ( spec ) @xcite , least absolute deviation fitting @xcite , and sparse - smooth decomposition @xcite . the hierarchical k - means clustering applies the k - means clustering algorithm with k=2 on blocks in multi - resolution . it first applies the k - means clustering algorithm on a large block to obtain foreground and background colors and then uses them as the initial foreground and background colors for the smaller blocks in the next stages . it also applies some post - processing at the end to refine the results . this algorithm has difficulty for the regions where background and foreground color intensities overlap and some part of the background will be detected as foreground . in the shape primitive extraction and coding ( spec ) method , a two - step segmentation algorithm is proposed . in the first step the algorithm classifies each block of size @xmath0 into either pictorial block or text / graphics , by comparing the number of colors with the threshold 32 . in the second step , segmentation result of pictorial blocks is refined by extracting shape primitives . because of variations in image content , it is hard to find a fixed threshold on the number of colors that can robustly separate pictorial blocks and text / graphics blocks . one problem with clustering - based segmentation techniques is that if the intensity of background pixels has a large dynamic range , some part of the background could be segmented as foreground . one such example is shown in fig . 1 , where the foreground mask ( a binary mask showing the location of foreground pixels ) for a sample image by hierarchical clustering and the proposed algorithm are shown . to overcome this problem , in a previous work we proposed a least absolute deviation fitting method , which fits a smooth model to the image and classifies regions in the image based on their smoothness @xcite . it uses the @xmath1 norm on the fitting error to enforce the sparsity of the error term . although this algorithm achieved significantly better segmentation than both djvu and spec , it suffers from two problems . first , it does not impose any connectivity on the pixels in the foreground layer , which could result in many isolated points in the foreground . second , it uses a fixed set of smooth basis functions and does not impose any restrictions on the smooth model parameters , which could result in overfitting the smooth model to the image . in this work we propose a sparse decomposition based segmentation , which tries to resolve these problems . sparse representation has been used for various applications in recent years , including face recognition , super - resolution , morphological component analysis , image restoration , image denoising and sparse coding @xcite-@xcite . within our sparse decomposition framework , we also impose suitable priors on each layer , in particular smoothness on the background , and connectivity on the foreground . to promote the connectivity of the foreground component , the group - sparsity of the foreground pixels is added to the cost function . it is worth mentioning that total - variation can also be used to promote connectivity , and it is used in some of our previous works @xcite-@xcite . this algorithm is tested on an image segmentation dataset and is shown to be very successful . the structure of the rest of this paper is as follows : section ii presents the main idea of the proposed segmentation algorithm . section iii describes the admm formulation for solving the proposed optimization problem . section iv provides the experimental results for the proposed algorithm , and the paper is concluded in section v.

sparse decomposition has been widely used for different applications , such as source separation , image classification and image denoising . this paper presents a new algorithm for segmentation of an image into background and foreground text and graphics using sparse decomposition . then the background and foreground are separated using a sparse decomposition framework and imposing some prior information , which promote the smoothness of background , and the sparsity and connectivity of foreground pixels .

sparse decomposition has been widely used for different applications , such as source separation , image classification and image denoising . this paper presents a new algorithm for segmentation of an image into background and foreground text and graphics using sparse decomposition . first , the background is represented using a suitable smooth model , which is a linear combination of a few smoothly varying basis functions , and the foreground text and graphics are modeled as a sparse component overlaid on the smooth background . then the background and foreground are separated using a sparse decomposition framework and imposing some prior information , which promote the smoothness of background , and the sparsity and connectivity of foreground pixels . this algorithm has been tested on a dataset of images extracted from hevc standard test sequences for screen content coding , and is shown to outperform prior methods , including least absolute deviation fitting , k - means clustering based segmentation in djvu , and shape primitive extraction and coding algorithm .

1611.07909

r

to evaluate the performance of our algorithm , we have tested the proposed algorithm on the same screen content image segmentation dataset provided in @xcite , which consist of 332 image blocks of size 64x64 , extracted from sample frames of hevc test sequences for screen content coding @xcite , @xcite . in our implementation , the block size is chosen to be @xmath63=64 . the number of dct basis functions , @xmath9 , is chosen to be 10 . the weight parameters in the objective function are tuned by testing on a validation set and are set to be @xmath64 and @xmath65 . the admm algorithm described in algorithm 1 is implemented in matlab and is publicly available in @xcite . the number of iterations for admm is chosen to be 50 and the parameters @xmath46 are all set to 1 . we compare the proposed algorithm with three previous algorithms ; hierarchical k - means clustering in djvu , spec , and lad . for spec , we have adapted the color number threshold and the shape primitive size threshold from the default value given in @xcite when necessary to give a more satisfactory result . to provide a numerical comparison , we report the average precision , recall and f1 score @xcite achieved by different algorithms over this dataset . the average precision , recall and f1 score by different algorithms are given in table 1 . recall & f1 score + spec @xcite & 50% & 64% & 56.1% + hierarchical clustering @xcite & 64% & 69% & 66.4% + least absolute deviation @xcite & 91.4% & 87% & 89.1% + the proposed algorithm & 93.7% & 86.7% & 90% + [ tblcomp ] the precision and recall are defined as in eq . ( 8) , where tp , fp and fn denote true positive , false positive and false negative respectively . in our evaluation , we treat a foreground pixel as positive . a pixel that is correctly identified as foreground ( compared to the manual segmentation ) is considered true positive . the same holds for false negative and false positive . the balanced f1 score is defined as the harmonic mean of precision and recall , as it is shown in eq 9 . @xmath66 @xmath67 0.18 0.18 0.18 0.18 0.18 + 0.18 0.18 0.18 0.18 0.18 + 0.18 0.18 0.18 0.18 0.18 + 0.18 0.18 0.18 0.18 0.18 + 0.18 0.18 0.18 0.18 0.18 as it can be seen , the proposed scheme achieves much higher precision and recall than hierarchical k - means clustering and spec algorithms . compared to the least absolute deviation fitting , the proposed formulation yields significant improvement in terms of precision , while also having a slightly higher recall rate . to see the visual quality of the segmentation , the results for 5 test images ( each consisting of multiple 64@xmath6864 blocks ) are shown in fig . it can be seen that the proposed algorithm gives superior performance over djvu and spec in all cases . there are also noticeable improvement over our prior approach using least absolute deviation fitting . we would like to note that , this dataset mainly consists of challenging images where the background and foreground have overlapping color ranges . for simpler cases where the background has a narrow color range that is quite different from the foreground , both djvu and least absolute deviation fitting will work well . on the other hand , spec does not work well when the background is fairly homogeneous within a block and the foreground text / lines have varying colors . to illustrate the smoothness of the background layer and its suitability for being coded with transform - based coding , the filled background layer of a sample image is presented in fig . the background holes ( pixels belonging to the foreground layer ) are filled by the predicted value using the smooth model , which is obtained using the least squares fitting to the detected background pixels . as we can see , the background layer is very smooth and does not contain any text and graphics . to show the application of the proposed algorithm for medical image segmentation , we present its result for the task of blood vessel segmentation . the result for a sample image is shown in fig . 4 . as it can be seen the blood vessels have a very low contrast with background , makes it difficult to be segment them from background .

this algorithm has been tested on a dataset of images extracted from hevc standard test sequences for screen content coding , and is shown to outperform prior methods , including least absolute deviation fitting , k - means clustering based segmentation in djvu , and shape primitive extraction and coding algorithm .

sparse decomposition has been widely used for different applications , such as source separation , image classification and image denoising . this paper presents a new algorithm for segmentation of an image into background and foreground text and graphics using sparse decomposition . first , the background is represented using a suitable smooth model , which is a linear combination of a few smoothly varying basis functions , and the foreground text and graphics are modeled as a sparse component overlaid on the smooth background . then the background and foreground are separated using a sparse decomposition framework and imposing some prior information , which promote the smoothness of background , and the sparsity and connectivity of foreground pixels . this algorithm has been tested on a dataset of images extracted from hevc standard test sequences for screen content coding , and is shown to outperform prior methods , including least absolute deviation fitting , k - means clustering based segmentation in djvu , and shape primitive extraction and coding algorithm .

cond-mat9809428

i

size segregation of granular mixtures @xcite is known to occur when mixtures are exposed to external periodic perturbations . a much - studied size segregation phenomenon is known as the `` brazil nut effect '' @xcite and occurs when , upon vibration , larger grains rise on a bed of finer grains . axial size segregation in alternating bands consisting of small and large grains occurs when a mixture of grains is placed in a horizontal rotating cylinder @xcite . it is also known that even in the absence of external perturbations mixtures of grains of different sizes can spontaneously segregate . for example , when a mixture of spherical grains of different sizes is poured onto a heap , the large grains are more likely to be found near the base , while the small grains are more likely to be near the top . another type of segregation , called spontaneous stratification , arises when the grains composing the mixture differ not only in size but also in shape ( or friction properties ) . when a mixture of large grains that are more faceted and small grains that are less faceted is poured in a `` granular hele - shaw cell '' ( two vertical slabs separated by a gap of typically 510 mm ) , the mixture spontaneously stratifies into alternating layers of larger faceted grains and smaller rounded grains @xcite . figure [ strat]a shows an example of such stratification . a mixture of large cubic sugar grains ( typical diameter 0.8 mm ) and smaller spherical glass beads ( diameter 0.19 mm ) is poured in the cell . we notice the striped pattern with approximately constant wavelength . in contrast , when the mixture is composed of larger less faceted grains and smaller more faceted grains , the mixture only segregates i.e . , the small more - faceted grains are found preferentially at the top of the cell , while the large less - faceted grains are found near the bottom @xcite . figure [ strat]b shows an example of such segregation , when a mixture of small faceted sand grains ( typical size 0.3 mm ) and large spherical glass beads ( typical size 0.8 mm ) is poured in the cell . the dynamical process leading to spontaneous stratification was recently studied theoretically @xcite using discrete models , and a set of continuum equations for surfaces flows of granular mixtures developed in refs . @xcite . in this theoretical formalism , the grains are considered to belong to one of two phases : a _ static or bulk phase _ if the grain is part of the solid sandpile , and a _ rolling or liquid phase _ if the grain is not part of the sandpile but rolls downward on top of the static phase . in ref . @xcite the dynamics of spontaneous stratification was found to be governed by the existence of a `` kink '' at which the grains are stopped during an avalanche . in this paper , we study experimentally the dynamical processes leading to spontaneous stratification . using a high speed video camera to study the motion of the grains in great detail , we divide the dynamical process of stratification into three stages ( see fig . [ stages ] ) : * the avalanche of grains down the slope , and size segregation of grains in the rolling phase due to `` percolation '' . * the formation of the `` kink''an uphill wave at which grains are stopped . * the uphill motion of the kink and formation of a pair of layers . we study a well - developed flow regime where the rolling grains segregate during the flow . in this regime the thickness of the layer of rolling grains is larger than the typical size of a grain @xmath0 ( typically 5@xmath0 ) , and the smaller rolling grains are found to percolate downward in the rolling phase to form a sublayer of smaller rolling grains underneath the sublayer of larger rolling grains . this dynamical size segregation process , known as `` percolation '' or `` kinematic sieving '' @xcite , contributes to the stratification of grains . stratification is an instability developed due to a competition between size segregation and shape segregation @xcite . in the case of thin flows , size segregation occurs since the smaller grains are captured more easily than larger grains . in the case of thick flow regimes study here , the kinematic sieving in the rolling phase is mainly responsible for the size segregation of the grains . since the larger grains are on top of the rolling phase , they are convected further down than the smaller grains , producing the size segregation effect , which together with the segregation due to different shape of the grains , gives rise to the instability leading the system to spontaneously stratify @xcite . it is important to note that percolation in the rolling phase is not sufficient condition to obtain stratification . for thick flows and when the large grains are smoother , segregation in the rolling phase still occurs , and yet we do not get stratification but only the sharp segregation pattern of fig . [ strat]b . a large difference in size is also a condition for the percolation effect to take place usually @xmath1 , where @xmath2 is the ratio of the size of the large grains to the size of the small grains . we performed a series of experiments with mixtures of glass beads and sand with @xmath3 and found continuos segregation patterns ( as opposed to the sharp segregation pattern with a separation zone of a few centimeters of fig . [ strat]b obtained for @xmath1 ) no matter the shape of the grains . this is because , when @xmath3 the effect of size segregation is very weak . the limiting case in which both species of grains are spherical was first studied by williams @xcite ; his results ( showing segregation plus a hint of stratification ) differ from our results for this case ( showing only segregation ) . we believe that the reason is that the grains used by williams were not quite spherical , inducing some shape segregation as well . according to the above interpretation , we note that experiments with mixtures of perfect spherical beads differing only in size should not show stratification since the shape segregation effect is not present and size segregation alone ( even due to percolation ) is not able to produce stratification and our work confirms these expectations . however some oscillations might still be present around the stable segregation profile , as seen in previous experiments using mixtures of spherical beads @xcite . here we focus on the regime where segregation in the rolling phase takes place . we characterize the kinematic percolation process , and measure the velocity gradient of the grains during the avalanche . we find a linear velocity profile of the rolling grains , and that the mean velocity of the rolling grains is the same as the velocity of the kink . we also study the shape and size of the kink and thereby measure the wavelength of the layers . we find that the wavelength increases linearly with the flux of grains , a result in agreement with recent theoretical predictions @xcite . we also measure the profiles of the rolling grains and static phases of the pile , and the values of several phenomenological coefficients which appear in the theory for surface flows of granular mixtures . our results are valid for flow rates of the order of gr / sec ( which gives rise to a rolling phase less than 1 cm thick ) . we also comment on the applicability of our results , and on the deviations that may occur for smaller and larger flow regimes .

spontaneous stratification in granular mixtures i.e . the formation of alternating layers of small - rounded and large - faceted grains when one pours a random mixture of the two types of grains into a quasi - two dimensional vertical hele - shaw cell has been recently reported by h. a. makse et al . here we study experimentally the dynamical processes leading to spontaneous stratification . we divide the process in three stages : ( a ) avalanche of grains and segregation in the rolling phase , ( b ) formation of the `` kink''an uphill wave at which grains are stopped at the bottom substrate , and ( c ) uphill motion of the kink and formation of a pair of layers . using a high - speed video camera , we study a rapid flow regime where the rolling grains size segregate during the avalanche due to the fact that small grains move downward in the rolling phase to form a sublayer of small rolling grains underneath a sublayer of large rolling grains . this dynamical segregation process known as `` kinematic sieving '' , `` free surface segregation '' or simple `` percolation'' contributes to the spontaneous stratification of grains in the case of thick flows .

spontaneous stratification in granular mixtures i.e . the formation of alternating layers of small - rounded and large - faceted grains when one pours a random mixture of the two types of grains into a quasi - two dimensional vertical hele - shaw cell has been recently reported by h. a. makse et al . [ nature * 386 * , 379 ( 1997 ) ] . here we study experimentally the dynamical processes leading to spontaneous stratification . we divide the process in three stages : ( a ) avalanche of grains and segregation in the rolling phase , ( b ) formation of the `` kink''an uphill wave at which grains are stopped at the bottom substrate , and ( c ) uphill motion of the kink and formation of a pair of layers . using a high - speed video camera , we study a rapid flow regime where the rolling grains size segregate during the avalanche due to the fact that small grains move downward in the rolling phase to form a sublayer of small rolling grains underneath a sublayer of large rolling grains . this dynamical segregation process known as `` kinematic sieving '' , `` free surface segregation '' or simple `` percolation'' contributes to the spontaneous stratification of grains in the case of thick flows . we characterize the dynamical process of stratification by measuring all relevant quantities : the velocity of the rolling grains , the velocity of the kink , and the wavelength of the layers . we also measure other phenomenological constants such as the rate of collision between rolling and static grains , and all the angles of repose characterizing the mixture . the wavelength of the layers behaves linearly with the thickness of the layer of rolling grains ( i.e. , with the flow rate ) , in agreement with theoretical predictions . the velocity profile of the grains in the rolling phase is a linear function of the position of the grains along the moving layer , which implies a linear relation between the mean velocity and the thickness of the rolling phase . we also find that the speed of the upward - moving kink has the same value as the mean speed of the downward - moving grains . we measure the shape and size of the kink , as well as the profiles of the rolling and static phases of grains , and find agreement with recent theoretical predictions . 2

cond-mat9809428

c

in summary , we tested experimentally the main assumptions of the theory of surface flows of granular materials . we measured the profile of the static and rolling phases , in order to study the profile of the kink and the effects of percolation in the rolling phase and compared with analytical predictions . we characterized the dynamical process of stratification by measuring all the relevant quantities . we measured the velocity of the rolling grains , the velocity of the kink , the wavelength of the layers , and also the rate of collisions @xmath50 , and all four angles of repose @xmath34 characterizing the mixture . the velocity of the kink and the wavelength of the layers both vary linearly with the grain flux . the velocity profile of the grains in the rolling phase is a linear function of the position of the grains along the moving layer , which implies a linear relation between the mean velocity and the thickness of the rolling phase . we find the mean velocity of the rolling grains is the same as the velocity of the kink . our results apply to the moderate flow rates used in this work of the order of 1 gr / sec . for sufficiently larger or smaller flow rates , deviations might appear as discussed in the text . for larger fluxes , nonlinear terms may modify eq . ( [ lambda ] ) . for even larger fluxes the kink may not support the incoming grains turning stratification into the mixing of grains or to weak segregation . for smaller fluxes than the ones used in this study , the percolation effect does not take place . however , when the size ratio is large enough @xmath1 strong segregation occurs anyway at the shear surface between the fluid and solid phase : the large grains are not trapped in the holes of the surface , and they are convected further . thus stratification is also observed for small fluxes , but the size segregation mechanism is different from the one studied here . the sharp segregation profiles with a separation zone of a few cm observed in the experiment shown in fig . [ strat]b is also a consequence of strong segregation effects . when @xmath3 , size segregation has a weak effect , resulting in a weak continuos segregation of the mixture no matter the shapes of the grains . theoretically the case @xmath3 is treated in @xcite , and the case @xmath1 in @xcite . our results might be also applicable to other systems . size and shape segregation in rotating drums may be analized in analogy to the regimes found here . further experimental results may include qualitative studies of the other flows regimes mentioned above . it would be also appropriate to have an estimation of the angles of repose of the grains independently of the theoretical calculations used here . for instance , by gluing grains of one species to an inclined plane and pouring grains of the other species is a way to obtain a direct estimation of the cross angles of repose . since we are considering the limit of high flux , the percolation effect takes place , so the interaction between rolling and static grains ( at least in the center of the pile where we measure the profiles ) is almost entirely between small grains . this fact makes difficult the identification of the boundary since small grains are difficult to track at the resolution of the video camera . nevertheless we are able to identify the two phases . j. baxter , u. tzn , d. heyes , i. hayati , and p. fredlund , nature * 391 * , 136 ( 1998 ) . the experiments reported by baxter _ et al . _ were done in a rather special situation . instead of using a bimodal distribution of grains size differing also in shape as reported in @xcite , they used a continuos distribution of size of the grains and they colored half of them to distinguish from the other half . under these circumstances the shape of both `` species '' should be the same and no stratification should occur , since there is no competition between size and shape segregation . however , due to this special way of preparing a `` two species '' system , some shape or surface - properties induced segregation might appear as well leading to an irregular stratification pattern . an increase in the flux then destroy the weak kink formed in such conditions .

the velocity profile of the grains in the rolling phase is a linear function of the position of the grains along the moving layer , which implies a linear relation between the mean velocity and the thickness of the rolling phase . we measure the shape and size of the kink , as well as the profiles of the rolling and static phases of grains , and find agreement with recent theoretical predictions . 2

spontaneous stratification in granular mixtures i.e . the formation of alternating layers of small - rounded and large - faceted grains when one pours a random mixture of the two types of grains into a quasi - two dimensional vertical hele - shaw cell has been recently reported by h. a. makse et al . [ nature * 386 * , 379 ( 1997 ) ] . here we study experimentally the dynamical processes leading to spontaneous stratification . we divide the process in three stages : ( a ) avalanche of grains and segregation in the rolling phase , ( b ) formation of the `` kink''an uphill wave at which grains are stopped at the bottom substrate , and ( c ) uphill motion of the kink and formation of a pair of layers . using a high - speed video camera , we study a rapid flow regime where the rolling grains size segregate during the avalanche due to the fact that small grains move downward in the rolling phase to form a sublayer of small rolling grains underneath a sublayer of large rolling grains . this dynamical segregation process known as `` kinematic sieving '' , `` free surface segregation '' or simple `` percolation'' contributes to the spontaneous stratification of grains in the case of thick flows . we characterize the dynamical process of stratification by measuring all relevant quantities : the velocity of the rolling grains , the velocity of the kink , and the wavelength of the layers . we also measure other phenomenological constants such as the rate of collision between rolling and static grains , and all the angles of repose characterizing the mixture . the wavelength of the layers behaves linearly with the thickness of the layer of rolling grains ( i.e. , with the flow rate ) , in agreement with theoretical predictions . the velocity profile of the grains in the rolling phase is a linear function of the position of the grains along the moving layer , which implies a linear relation between the mean velocity and the thickness of the rolling phase . we also find that the speed of the upward - moving kink has the same value as the mean speed of the downward - moving grains . we measure the shape and size of the kink , as well as the profiles of the rolling and static phases of grains , and find agreement with recent theoretical predictions . 2

cond-mat0110195

i

suppose that a system is placed at a certain metastable state surrounded by local potential minimum , the system would be unstable to decay to a global minimum assisted by either quantum or thermal fluctuations . such processes are called false - vacuum decay and metastability relaxation , and they are considered to be non - perturbative in nature . hence , in order to calculate the decay rate ( life time ) , ingenious treatments have been invented so far @xcite . those treatments rely on semi - classical approximation . that is , the treatments take into account quadratic fluctuations around the field configuration which extremizes the euclidean action . such field configurations are called instanton , bounce and ( critical ) droplet . therefore , those treatments , just like the wkb approximation in wave mechanics , are not justified for strong fluctuations ( namely , short life time ) . in addition , it is quite cumbersome to improve the approximation systematically . in order to compensate the above drawback , first - principle calculation scheme free from any biased errors would be desirable . as for discrete variable model ( kinetic ising model ) , actually , remarkable _ tour de force _ scheme was invented by gnther _ they introduced the so - called constrained - transfer - matrix method , which meets nonequilibrium situation . then , they carried out extensive numerical calculations of the transfer matrix . in consequence , they extracted imaginary part of the free energy , which is to be identified as the decay rate . to the best of our knowledge , it is the first _ ab initio _ approach to the decay rate in the presence of many - body correlations . their result supports the aforementioned analytic theory based on the droplet picture . ( besides this , monte - carlo simulation has been utilized to evolve the relaxation processes @xcite , where the number of monte - carlo steps is interpreted as time progression . though the interpretation is , in a strict sense , not fully justified , the simulation result is fairly in accordance with the droplet picture actually . ) on the contrary , as for continuous - variable model such as the @xmath0 model , the above approach does not apply , and so far , no attempt at _ ab initio _ calculation has been reported . for quantum - mechanics level ( @xmath2 dimension ) , however , a number of substantial progresses are made @xcite : suzuki and yasuta obtained a compact expression for the decay ( tunnelling ) rate based on the weak - coupling expansion and succeeding borel resummation @xcite . they succeeded in calculating the tunnelling rate beyond instanton calculus . alternatively , from the weak coupling expansion , karrlein and kleinert obtained , remarkably enough , strong - coupling series by means of the so - called variational perturbation @xcite . both approaches pursue first - principle calculation scheme beyond instanton calculus . as a consequence , these theories clarified how the instanton description fails for low potential barrier ; true decay rate is suppressed owing to inter - instanton interaction . at present , extension to many - body case appears to be unsuccessful @xcite . the aim of this paper is to investigate the false - vacuum decay rate for many - body system through series expansion . we studied the lattice @xmath0 model in @xmath1 dimensions , @xmath3 with the canonical commutation relations @xmath4= { \rm i } \delta_{ij}$ ] , @xmath5=0 $ ] and @xmath6=0 $ ] . note that for @xmath7 , the potential is not bounded below , and renders the state @xmath8 unstable ( false vacuum ) . the decay rate due to the quantum fluctuations is our concern . we will show that in contrast to @xmath2 dimension mentioned above , the decay rate is _ enhanced _ owing to inter - instanton interaction . the present paper is organized as follows . in the next section , we calculate the decay rate by means of strong - coupling expansion . we explain methodological details , and check the validity by means of an alternative simulation . in the last section , we summarize the present study .

strong - coupling expansion is performed for the lattice @xmath0 model in @xmath1 dimensions . because the strong - coupling limit itself is not solvable , we employed numerical calculations so as to set up unperturbed eigensystems . restricting the number of hilbert - space bases , we performed linked - cluster expansion up to eleventh order . thereby , we confirmed that our series - expansion data with a convergence - acceleration trick are in good agreement with the simulation result . through the analytic continuation to the domain of negative biquadratic interaction , we obtain the false - vacuum decay rate .

strong - coupling expansion is performed for the lattice @xmath0 model in @xmath1 dimensions . because the strong - coupling limit itself is not solvable , we employed numerical calculations so as to set up unperturbed eigensystems . restricting the number of hilbert - space bases , we performed linked - cluster expansion up to eleventh order . we carried out alternative simulation by means of the density - matrix renormalization group . thereby , we confirmed that our series - expansion data with a convergence - acceleration trick are in good agreement with the simulation result . through the analytic continuation to the domain of negative biquadratic interaction , we obtain the false - vacuum decay rate . contrary to common belief that tunnelling phenomenon lies out of perturbative treatments , our series expansion reproduces the instanton - theory behaviour for high potential barrier . for shallow barrier , on the contrary , our result tells that the relaxation is no more described by instanton , but the decay rate acquires notable enhancement .

1611.06809

i

massive stars with an initial mass greater than @xmath28 are expected to end their lives with the gravitational collapse of their degenerate core . if a successful explosion follows , an h - rich progenitor leads to a type ii supernova ( sn ) , the most frequently observed type of core - collapse sne @xcite . these sne are characterised by the presence of strong hydrogen balmer lines in their optical spectra . their high - brightness phase , which also coincides with the photospheric phase , lasts about one hundred days . early simulations of such type ii sne ( @xcite , @xcite ) suggest a progenitor star with a massive and extended h - rich envelope , as typically found in red - supergiant ( rsg ) stars . the physics underlying the evolution of a sn ii - plateau ( ii - p ) has been extensively discussed by , for example , @xcite or more recently @xcite . the association between type ii - p sne and rsg stars has also been more directly made through the identification of the progenitor star on pre - explosion images ( see @xcite for a review ) . type ii sne exhibit a broad range in @xmath5-band absolute magnitude , spanning about 5 mag during the photospheric phase and the nebular phase @xcite . the latter suggests a range of @xmath610 in the mass of ni ejected . the ejecta expansion rate inferred from p - cygni profile widths halfway through the plateau also spans a range from 1000 to 8000 @xcite , suggestive of a large scatter in the ratio of ejecta kinetic energy @xmath7 and ejecta mass @xmath8 . more recent surveys document this diversity further @xcite , and also emphasize , for example , the range in photospheric phase durations , the @xmath4-band decline rate after maximum , how various radiative properties correlate . the existence of low - luminosity ( i.e. , intrinsically faint ) sne ii was well established in the 90s . sn1997d was one of the first type ii to exhibit abnormally narrow p - cygni profiles ( of the order of 1000 ) and a low optical brightness during the photospheric phase ( always fainter than @xmath914.65mag in the @xmath4-band ; @xcite ) , both suggestive of a low energy explosion in an extended h - rich star . the sample of low - luminosity type ii sne now includes a handful of objects @xcite , with an absolute @xmath4-band magnitude that covers from @xmath914 to @xmath915.5mag around 50d after explosion , thus 2@xmath93mag fainter than the prototypical type ii - p sn1999em @xcite . the fraction of low - luminosity sne could be @xmath25% of all type ii sne @xcite . numerous radiation - hydrodynamic simulations of low - luminosity type ii sne have been carried out . constraints on the progenitor star and the ejecta ( explosion energy , ni mass ) are obtained through iteration until a good match to the bolometric light curve and the photospheric velocity evolution . @xcite modelled the low - luminosity sn2003z and obtained an ejecta mass of 14 , an ejecta kinetic energy of 2.45@xmath010@xmath1erg , 0.006 of ni , and a progenitor radius of 230 . @xcite used a similar approach and proposed progenitor masses in the range 1015 for the whole sample of low - luminosity sne ii . these results suggest that low - luminosity type ii sne are intrinsically under - energetic and synthesize little ni . other studies have argued that these low - luminosity type ii sne are the result of weak explosions in higher mass rsg stars . in this context , the low ni mass arises from the significant fallback of material onto the proto - neutron star , associated potentially with the subsequent formation of a black hole . @xcite propose this scenario with a 26 progenitor star for sn1997d @xcite , and argue against the possibility of a lower mass progenitor . later work by @xcite , using a semi - analytic modelling of the light curve , give support to the association with higher mass progenitors , in which the explosion is followed by fallback . the situation is therefore unsettled . for sn1997d , @xcite proposes a 14 progenitor , which disagrees with @xcite . for the low - luminosity sne ii - p 2005cs and 2008bk , a progenitor detection exists and suggests a low / moderate mass massive star ( in the range 913 on the zero - age main - sequence , zams ; @xcite ; @xcite ; @xcite ; @xcite ; @xcite ) . even when an ejecta mass is inferred from light - curve modelling , estimating the corresponding progenitor mass on the main sequence is subject to error because of the uncertain mass loss history . furthermore , the light curve modelling above is primarily sensitive to the h - rich ejecta mass , not the total ejecta mass . the helium core mass can only be estimated by modelling nebular phase spectra and the helium core dynamics @xcite . in this work , we model the low - luminosity sn2008bk because it is the best observed sn of this class of event , with a good photometric monitoring in the optical that started about a week after explosion @xcite . based on pre - explosion images and evidence of the disappearance of a source on post - explosion images , inferences have been made to constrain the nature of the progenitor star and its mass . the consensus is that it is a rsg star , although its inferred zams mass differs somewhat between studies , with 88.5 ( @xcite ; see also @xcite ) and 11.114.5 @xcite . in contrast , there has been little analysis of the sn spectroscopic and photometric data . a preliminary analysis is presented in @xcite , who proposes an ejecta with @xmath102.5@xmath010@xmath1erg , a total mass of 12 , and a ni mass of 0.009 , together with a progenitor radius of 550 , @xcite present an analysis of a nebular - phase spectrum at 547d after explosion and propose a progenitor star with a main - sequence mass of 12 . the simulations presented here are based on models of the progenitor evolution from the main - sequence until core collapse , together with the subsequent simulation of the piston - driven explosion including explosive nucleosynthesis . the bulk of the work lies , however , in the non - local - thermodynamic - equilibrium ( nlte ) time - dependent radiative - transfer modelling of the photometric and spectroscopic evolution of sn2008bk . since a low / moderate mass progenitor has been proposed by all former studies on sn2008bk , we limit our investigation to a progenitor star of 12 on the main sequence . in a forthcoming study , we will investigate the properties of the whole sample of low - luminosity type ii sne , and consider progenitors from both low and high mass rsg stars . in the next section , we summarise the source of observational data for sn2008bk . in section [ sect_model ] , we present our numerical approach for the modelling of the pre - sn evolution with @xcite , the explosion with 1d @xcite , and the modelling of the sn radiation from 10d after explosion until nebular times with @xcite . our best match model to the photometric and spectroscopic observations of sn2008bk is presented in section [ sect_x ] . in section [ sect_dep ] , we discuss the sensitivity of our results to changes in progenitor / ejecta radius ( section [ sect_rad ] ) , progenitor mass ( section [ sect_mass ] ) , and chemical mixing ( section [ sect_mixing ] ) . we conclude in section [ sect_conclusion ] .

we model the subsequent evolution of the ejecta with non - local - thermodynamic - equilibrium time - dependent radiative transfer . we discuss the sensitivity of our results to changes in progenitor radius and mass , as well as chemical mixing . [ firstpage ] radiative transfer - hydrodynamics - supernovae : general - supernovae : individual : sn2008bk

supernova ( sn ) 2008bk is a well observed low - luminosity type ii event visually associated with a low - mass red - supergiant progenitor . to model sn2008bk , we evolve a 12 star from the main sequence until core collapse , when it has a total mass of 9.88 , a he - core mass of 3.22 , and a radius of 502 . we then artificially trigger an explosion that produces 8.29 of ejecta with a total energy of 2.5@xmath010@xmath1erg and @xmath20.009 of ni . we model the subsequent evolution of the ejecta with non - local - thermodynamic - equilibrium time - dependent radiative transfer . although somewhat too luminous and energetic , this model reproduces satisfactorily the multi - band light curves and multi - epoch spectra of sn2008bk , confirming the suitability of a low - mass massive star progenitor . as in other low - luminosity sne ii , the structured h@xmath3 profile at the end of the plateau phase is probably caused by ba6496.9 rather than asphericity . we discuss the sensitivity of our results to changes in progenitor radius and mass , as well as chemical mixing . a 15% increase in progenitor radius causes a 15% increase in luminosity and a 0.2mag @xmath4-band brightening of the plateau but leaves its length unaffected . an increase in ejecta mass by 10% lengthens the plateau by @xmath210d . chemical mixing introduces slight changes to the bolometric light curve , limited to the end of the plateau , but has a large impact on colours and spectra at nebular times . [ firstpage ] radiative transfer - hydrodynamics - supernovae : general - supernovae : individual : sn2008bk

1611.06809

c

we have presented the results of numerical simulations that aim at understanding the properties of the ejecta / radiation associated with sn2008bk , as well as the progenitor star at its origin . we have focused on a single mass of 12 for the progenitor , and have evolved this model with at solar metallicity but with different parameterisations for mass loss and convection in order to produce rsg stars at death that cover a range of final masses and surface radii . these models were then exploded with the radiation hydrodynamics code 1d to produce ejecta with various explosion energies and ni mass . finally , starting at a post - explosion time of 10d , we have evolved these ejecta with the nlte radiative transfer code , building multi - band light curves and multi - epoch spectra that can be directly compared to observations . our model x , which closely matches sn2008bk , corresponds to a star with an initial mass of 12 , a final mass of 9.88 , an h - rich envelope mass of 6.7 a final surface radius of 502 . the associated ejecta has a mass of 8.29 , a kinetic energy of 2.5@xmath010@xmath1erg and 0.0086 of ni . provided we introduce a 0.5mag offset , model x follows closely the multi - band optical and near - ir light curves of sn2008bk , including the colour evolution ( e.g. , the sharp drop in the @xmath34 band and the near - constant evolution of the @xmath35band magnitude ) and the plateau duration . model x reproduces well the spectral evolution of sn2008bk ( provided we renormalise the spectra to cancel the 0.5mag offset in brightness ) , the progressive reddening of the spectra as the photospheric temperature drops and line blanketing strengthens , the reduction in line widths as the photosphere recedes to deeper / slower ejecta layers . the early colour evolution and reddening of the spectra is best matched with an explosion date of mjd54546.0 . we find that model x yields lines that are 10 - 20% too broad it typically overestimates the expansion rate by 1020% . our model x is therefore somewhat too energetic for sn2008bk . a lower explosion energy could reduce the offset in line widths and brightness . the offset in luminosity could be reduced by invoking a larger reddening ( perhaps up to @xmath110.1mag ) to sn2008bk . the uncertainty in the cepheid - based distance to the host of sn2008bk is probably small . given all the uncertainties involved , these offsets are reasonably small to suggest that model x is a sensible representation of sn2008bk . our model of sn2008bk is a low - energy counterpart of the models for standard " sne ii - p like 1999em . the mechanisms that control their evolution are the same for both in our approach we merely reduce the energy injection to produce a model for sn2008bk rather than one for sn1999em . however , the lower expansion rate in sn2008bk allows a much better inspection of the line profile fits . interestingly , in low - luminosity sne ii , the h@xmath3 line systematically develops a complex structure at the end of the plateau phase . this structure is most likely not a signature of asymmetry , but instead caused by overlap with the strong ba6496.9 line . this conclusion is reinforced by the good match obtained to the isolated line of ba6141.7 in sn2008bk . we have performed additional models to gauge the sensitivity of our results to changes in progenitor / explosion parameters . a 15% increase in the progenitor surface radius leads to a @xmath215% increase in plateau luminosity and a 0.2mag brightening of the @xmath4-band magnitude , but does not affect the length of the photospheric phase . an increase in ejecta mass of 1 hardly affects the results for model x , except for the lengthening of the photospheric phase by 10.0d . in our simplistic approach , chemical mixing has little impact on the sn radiation throughout most of the plateau phase . early on , increased mixing causes extra line blanketing and produces redder optical colours . in our models where only ni is mixed outwards ( but no mixing is applied to h and he ) , the light curve develops a 15-d long ledge before dropping from the plateau . mixing of h with he smoothes that transition , most likely because it allows a much smoother evolution of the electron - scattering optical depth , which controls the release of radiative energy stored in the ejecta ( and the rate of recession of the photosphere ) . however , the most drastic impact of mixing in our models is seen at the nebular times . depending on how we perform the mixing , we can completely quench h@xmath3 , boost ca7300 , or mitigate the temperature and ionisation state of the gas to alter the sn colours . because of all these complications , we defer the modelling of the nebular - phase spectra of sn2008bk .

supernova ( sn ) 2008bk is a well observed low - luminosity type ii event visually associated with a low - mass red - supergiant progenitor . to model sn2008bk , we evolve a 12 star from the main sequence until core collapse , when it has a total mass of 9.88 , a he - core mass of 3.22 , and a radius of 502 . we then artificially trigger an explosion that produces 8.29 of ejecta with a total energy of 2.5@xmath010@xmath1erg and @xmath20.009 of ni . a 15% increase in progenitor radius causes a 15% increase in luminosity and a 0.2mag @xmath4-band brightening of the plateau but leaves its length unaffected . an increase in ejecta mass by 10% lengthens the plateau by @xmath210d .

supernova ( sn ) 2008bk is a well observed low - luminosity type ii event visually associated with a low - mass red - supergiant progenitor . to model sn2008bk , we evolve a 12 star from the main sequence until core collapse , when it has a total mass of 9.88 , a he - core mass of 3.22 , and a radius of 502 . we then artificially trigger an explosion that produces 8.29 of ejecta with a total energy of 2.5@xmath010@xmath1erg and @xmath20.009 of ni . we model the subsequent evolution of the ejecta with non - local - thermodynamic - equilibrium time - dependent radiative transfer . although somewhat too luminous and energetic , this model reproduces satisfactorily the multi - band light curves and multi - epoch spectra of sn2008bk , confirming the suitability of a low - mass massive star progenitor . as in other low - luminosity sne ii , the structured h@xmath3 profile at the end of the plateau phase is probably caused by ba6496.9 rather than asphericity . we discuss the sensitivity of our results to changes in progenitor radius and mass , as well as chemical mixing . a 15% increase in progenitor radius causes a 15% increase in luminosity and a 0.2mag @xmath4-band brightening of the plateau but leaves its length unaffected . an increase in ejecta mass by 10% lengthens the plateau by @xmath210d . chemical mixing introduces slight changes to the bolometric light curve , limited to the end of the plateau , but has a large impact on colours and spectra at nebular times . [ firstpage ] radiative transfer - hydrodynamics - supernovae : general - supernovae : individual : sn2008bk

1007.1434

i

testing whether a subset of covariates have any linear relationship with a quantitative response has been a staple of statistical analysis since fisher introduced the analysis of variance ( anova ) in the 1920s @xcite . fisher developed anova in the context of agricultural trials and the test has since then been one of the central tools in the statistical analysis of experiments @xcite . as a consequence , there are countless situations in which it is routinely used , in particular , in the analysis of clinical trials @xcite or in that of cdna microarray experiments @xcite , to name just two important areas of biostatistics . to begin with , consider the simplest design known as the one - way layout , @xmath9 where @xmath10 is the @xmath11th observation in group @xmath12 , @xmath13 is the main effect for the @xmath12th treatment , and the @xmath14 s are measurement errors assumed to be i.i.d . zero - mean normal variables . the goal is of course to determine whether there is any difference between the treatments . formally , assuming there are @xmath0 groups , the testing problem is @xmath15 the classical one - way analysis of variance is based on the well - known @xmath16-test calculated by all statistical software packages . a characteristic of anova is that it tests for a _ global _ null and does not result in the identification of which @xmath13 s are nonzero . taking within - group averages reduces the model to @xmath17 where @xmath18 and the @xmath19 s are independent zero - mean gaussian variables . if we suppose that the grand mean has been removed , so that the overall mean effect vanishes , that is , @xmath20 , then the testing problem becomes @xmath21 in order to discuss the power of anova in this setting , assume for simplicity that the variances of the error terms in ( [ eqbeta+z ] ) are known and identical , so that anova reduces to a chi - square test that rejects for large values of @xmath22 . as explained before , this test does not identify which of the @xmath23 s are nonzero , but it has great power in the sense that it maximizes the minimum power against alternatives of the form @xmath24 where @xmath25 . such an appealing property may be shown via invariance considerations ; see @xcite and @xcite , chapters 7 and 8 . a different approach to the same testing problem is to test each individual hypothesis @xmath26 versus @xmath27 , and combine these tests by applying a bonferroni - type correction . one way to implement this idea is by computing the minimum @xmath28-value and comparing it with a threshold adjusted to achieve a desired significance level . when the variances of the @xmath19 s are identical , this is equivalent to rejecting the null when @xmath29 exceeds a given threshold . from now on , we will refer to this procedure as the max test . because anova is such a well established method , it might surprise the reader but not the specialist to learn that there are situations where the max test , though apparently naive , outperforms anova by a wide margin . suppose indeed that @xmath30 in ( [ eqbeta+z ] ) and consider an alternative of the form @xmath31 where @xmath32 . in this setting , anova requires @xmath33 to be at least as large as @xmath34 to provide small error probabilities , whereas the max test only requires @xmath33 to be on the order of @xmath35 . when @xmath0 is large , the difference is very substantial . later in the paper , we shall prove that in an asymptotic sense , the max test maximizes the minimum power against alternatives of this form . the key difference between these two different classes of alternatives resides in the kind of configurations of parameter values which make the likelihoods under @xmath36 and @xmath37 very close . for the alternative @xmath38 , the likelihood functions are hard to distinguish when the entries of @xmath39 are of about the same size ( in absolute value ) . for the other , namely , @xmath40 , the likelihood functions are hard to distinguish when there is a single nonzero coefficient equal to @xmath41 . multiple hypothesis testing with sparse alternatives is now commonplace , in particular , in computational biology where the data is high - dimensional and we typically expect that only a few of the many measured variables actually contribute to the response only a few assayed treatments may have a positive effect . for instance , dna microarrays allow the monitoring of expression levels in cells for thousands of genes simultaneously . an important question is to decide whether some genes are differentially expressed , that is , whether or not there are genes whose expression levels are associated with a response such as the absence / presence of prostate cancer . a typical setup is that the data for the @xmath11th individual consists of a response or covariate @xmath42 ( indicating whether this individual has a specific disease or not ) and a gene expression profile @xmath43 , @xmath44 . a standard approach consists in computing , for each gene @xmath12 , a statistic @xmath45 for testing the null hypothesis of equal mean expression levels and combining them with some multiple hypothesis procedure @xcite . a possible and simple model in this situation may assume @xmath46 under the null while @xmath47 under the alternative . hence , we are in our sparse detection setup since one typically expects only a few genes to be differentially expressed . despite the form of the alternative , anova is still a popular method for testing the global null in such problems . our exposition has thus far concerned simple designs , namely , the one - way layout or sparse mean model . this paper , however , is concerned with a much more general problem : we wish to decide whether or not a response depends linearly upon a few covariates . we thus consider the standard linear model @xmath48 with an @xmath49-dimensional response @xmath50 , a data matrix @xmath51 ( assumed to have full rank ) and a noise vector , assumed to be i.i.d . . the decision problem ( [ eqtest ] ) is whether all the @xmath52 s are zero or not . we briefly pause to remark that statistical practitioners are familiar with the anova derived @xmath16-statistic also known as the model adequacy test that software packages routinely provide for testing @xmath36 . our concern , however , is not at all model adequacy but rather we view the test of the global null as a detection problem . in plain english , we would like to know whether there is signal or whether the data is just noise . a more general problem is to test whether a subset of coordinates of @xmath39 are all zero or not , and , as is well known , anova is in this setup the most popular tool for comparing nested models . we emphasize that our results also apply to such general model comparisons , as we shall see later . there are many applications of high - dimensional setups in which a response may depend upon only a few covariates . we give a few examples in the life sciences and in engineering ; there are , of course , many others : * _ genetics . _ a single nucleotide polymorphism ( snp ) is a form of dna variation that occurs when at a single position in the genome , multiple ( typically two ) different nucleotides are found with positive frequency in the population of reference . one then collects information about allele counts at polymorphic locations . almost all common snps have only two alleles so that one records a variable @xmath53 on individual @xmath11 taking values in @xmath54 depending upon how many copies of , say , the rare allele one individual has at location @xmath12 . one also records a quantitative trait @xmath42 . then the problem is to decide whether or not this quantitative trait has a genetic background . in order to scan the entire genome for a signal , one needs to screen between 300,000 and 1,000,000 snps . however , if the trait being measured has a genetic background , it will be typically regulated by a small number of genes . in this example , @xmath49 is typically in the thousands while @xmath0 is in the hundreds of thousands . the standard approach is to test each hypothesis @xmath55 by using a statistic depending on the least - squares estimate @xmath56 obtained by fitting the simple linear regression model @xmath57 the global null is then tested by adjusting the significance level to account for the multiple comparisons , effectively implementing a max test ; see @xcite , for example . * _ communications . _ a multi - user detection problem typically assumes a linear model of the form ( [ setting ] ) , where the @xmath12th column of @xmath58 , denoted @xmath59 , is the channel impulse response for user @xmath12 so that the received signal from the @xmath12th user is @xmath60 ( we have @xmath26 in case user @xmath12 is not sending any message ) . note that the mixing matrix @xmath58 is often modeled as random with i.i.d . entries . in a strong noise environment , we might be interested in knowing whether information is being transmitted ( some @xmath23 s are not zero ) or not . in some applications , it is reasonable to assume that only a few users are transmitting information at any given time . standard methods include the matched filter detector , which corresponds to the max test applied to @xmath61 , and linear detectors , which correspond to variations of the anova @xmath16-test @xcite . * _ signal detection . _ the most basic problem in signal processing concerns the detection of a signal @xmath62 from the data @xmath63 where @xmath64 is white noise . when the signal is nonparametric , a popular approach consists in modeling @xmath62 as a ( nearly ) sparse superposition of waveforms taken from a dictionary @xmath58 , which leads to our linear model ( [ setting ] ) ( the columns of @xmath58 are elements from this dictionary ) . for instance , to detect a multi - tone signal , one would employ a dictionary of sinusoids ; to detect a superposition of radar pulses , one would employ a time - frequency dictionary @xcite ; and to detect oscillatory signals , one would employ a dictionary of chirping signals . in most cases , these dictionaries are massively overcomplete so that we have more candidate waveforms than the number of samples , that is , @xmath65 . sparse signal detection problems abound , for example the detection of cracks in materials @xcite , of hydrocarbon from seismic data @xcite and of tumors in medical imaging @xcite . * _ compressive sensing . _ the sparse detection model may also arise in the area of compressive sensing @xcite , a novel theory which asserts that it is possible to accurately recover a ( nearly ) sparse signal and by extension , a signal that happens to be sparse in some fixed basis or dictionary from the knowledge of only a few of its random projections . in this context , the @xmath66 matrix @xmath58 with @xmath67 may be a random projection such as a partial fourier matrix or a matrix with i.i.d . entries . before reconstructing the signal , we might be interested in testing whether there is any signal at all in the first place . all these examples motivate the study of two classes of sparse alternatives : _ sparse fixed effects model _ ( _ sfem _ ) . under the alternative , the regression vector @xmath39 has at least @xmath68 nonzero coefficients exceeding @xmath33 in absolute value . _ sparse random effects model _ ( _ srem _ ) . under the alternative , the regression vector @xmath39 has at least @xmath68 nonzero coefficients assumed to be i.i.d . normal with zero mean and variance @xmath69 . in both models , we set @xmath70 , where @xmath71 is the sparsity exponent . our purpose is to study the performance of various test statistics for detecting such alternatives . and on the signs of its nonzero entries in sfem . ] to introduce our results and those of others , we need to recall a few familiar concepts from statistical decision theory . from now on , @xmath72 denotes a set of alternatives , namely , a subset of @xmath73 and @xmath74 is a prior on @xmath72 . the bayes risk of a test @xmath75 for testing @xmath76 versus @xmath77 when @xmath36 and @xmath37 occur with the same probability is defined as the sum of its probability of type i error ( false alarm ) and its average probability of type ii error ( missed detection ) . mathematically , @xmath78,\ ] ] where @xmath79 is the probability distribution of @xmath80 given by the model ( [ setting ] ) and @xmath81 $ ] is the expectation with respect to the prior @xmath74 . if we consider the linear model in the limit of large dimensions , that is , @xmath82 and @xmath83 , and a sequence of priors @xmath84 , then we say that a sequence of tests @xmath85 is asymptotically _ powerful _ if @xmath86 . we say that it is asymptotically _ powerless _ if @xmath87 . when no prior is specified , the risk is understood as the worst - case risk defined as @xmath88 with our modeling assumptions , anova for testing @xmath76 versus @xmath89 reduces to the chi - square test that rejects for large values of @xmath90 , where @xmath91 is the orthogonal projection onto the range of @xmath58 . since under the alternative , @xmath90 has the chi - square distribution with @xmath92 degrees of freedom and noncentrality parameter @xmath93 , a simple argument shows that anova is asymptotically powerless when @xmath94 and asymptotically powerful if the same quantity tends to infinity . this is congruent with the performance of anova in a standard one - way layout ; see @xcite , who obtain the weak limit of the anova @xmath16-ratio under various settings . consider the sparse fixed effects alternative now . we prove that anova is still essentially optimal under mild levels of sparsity corresponding to @xmath95 $ ] but not under strong sparsity where @xmath96 $ ] . in the sparse mean model ( [ eqbeta+z ] ) where @xmath58 is the identity , anova is suboptimal , requiring @xmath33 to grow as a power of @xmath0 ; this is simply because ( [ anova ] ) becomes @xmath97 when all the nonzero coefficients are equal to @xmath33 in absolute value . in contrast , the max test is asymptotically powerful when @xmath33 is on the order of @xmath98 but is only optimal under very strong sparsity , namely , for @xmath99 $ ] . it is possible to improve on the max test in the range @xmath100 and we now review the literature which only concerns the sparse mean model , @xmath101 . set @xmath102 then ingster @xcite showed that if @xmath103 with @xmath104 fixed as @xmath82 , then all sequences of tests are asymptotically powerless . in the other direction , he showed that there is an asymptotically powerful sequence of tests if @xmath105 . see also the work of jin @xcite . donoho and jin @xcite analyzed a number of testing procedures in this setting , and , in particular , the higher criticism of tukey which rejects for large values of @xmath106 where @xmath107 denotes the survival function of a standard normal random variable . they showed that the higher criticism is powerful within the detection region established by ingster . hall and jin @xcite have recently explored the case where the noise may be correlated , that is , @xmath108 and the covariance matrix @xmath109 is known and has full rank . letting @xmath110 be a cholesky factorization of the covariance matrix , one can whiten the noise in @xmath111 by multiplying both sides by @xmath112 , which yields @xmath113 ; @xmath114 is now white noise , and this is a special case of the linear model ( [ setting ] ) . when the design matrix is triangular with coefficients decaying polynomially fast away from the diagonal , @xcite proves that the detection threshold remains unchanged , and that a form of higher criticism still achieves asymptotic optimality . there are few other theoretical results in the literature , among which @xcite develops a locally most powerful ( score ) test in a setting similar to srem ; here , `` locally '' means that this property only holds for values of @xmath115 sufficiently close to zero . the authors do not provide any minimal value of @xmath115 that would guarantee the optimality of their method . however , since their score test resembles the anova @xmath16-test , we suggest that it is only optimal for very small values of @xmath115 corresponding to mild levels of sparsity , that is , @xmath116 . since the submission of our paper , a manuscript by ingster , tsybakov and verzelen @xcite , also considering the detection of a sparse vector in the linear regression model , has become publicly available . we comment on differences in section [ secsparse ] . in the signal processing literature , a number of applied papers consider the problem of detecting a signal expressed as a linear combination in a dictionary @xcite . however , the extraction of the salient signal is often the end goal of real signal processing applications so that research has focused on estimation rather than pure detection . as a consequence , one finds a literature entirely focused on estimation rather than on testing whether the data is just white noise or not . examples of pure detection papers include @xcite . in @xcite , the authors consider detection by matched filtering , which corresponds to the max test , and perform simulations to assess its power . the authors in @xcite assume that @xmath39 is approximately known and examine the performance of the corresponding matched filter . finally , the paper @xcite proposes a bayesian approach for the detection of sparse signals in a sensor network for which the design matrix is assumed to have some polynomial decay in terms of the distance between sensors . we show that if the predictor variables are not too correlated , there is a sharp detection threshold in the sense that no test is essentially better than a coin toss when the signal strength is below this threshold , and that there are statistics which are asymptotically powerful when the signal strength is above this threshold . this threshold is the same as that one gets for the sparse mean problem . therefore , this work extends the earlier results and methodologies cited above @xcite , and is applicable to the modern high - dimensional situation where the number of predictors may greatly exceed the number of observations . a simple condition under which our results hold is a low - coherence assumption . setup , our results apply _ regardless _ of the values of @xmath0 and @xmath49 . ] let @xmath117 be the column vectors of @xmath58 , assumed to be normalized ; this assumption is merely for convenience since it simplifies the exposition , and is not essential . then if a large majority of all pairs of predictors have correlation less than @xmath118 with @xmath119 for each @xmath120 ( the real condition is weaker ) , then the results for the sparse mean model ( [ eqbeta+z ] ) apply almost unchanged . interestingly , this is true even when the ratio between the number of observations and the number of variables is negligible , that is , @xmath121 . in particular , @xmath122 is the sharp detection threshold for sfem ( sparse fixed effects model ) . moreover , applying the higher criticism , not to the values of @xmath80 , but to those of @xmath61 is asymptotically powerful as soon as the nonzero entries of @xmath39 are above this threshold ; this is true for all @xmath123 $ ] . in contrast , the max test applied to @xmath61 is only optimal in the region @xmath124 $ ] . we derive the sharp threshold for srem as well , which is at @xmath125 . we show that the max tests and the higher criticism are essentially optimal in this setting as well for all @xmath123 $ ] , that is , they are both asymptotically powerful as soon as the signal - to - noise ratio permits . before continuing , it may be a good idea to give a few examples of designs obeying the low - coherence assumption ( weak correlations between most of the predictor variables ) since it plays an important role in our analysis : * _ orthogonal designs . _ this is the situation where the columns of @xmath58 are orthogonal so that @xmath126 is the @xmath127 identity matrix ( necessarily , @xmath128 ) . here the coherence is of course the lowest since @xmath129 . * _ balanced , one - way designs . _ as in a clinical trial comparing @xmath0 treatments , assume a balanced , one - way design with @xmath130 replicates per treatment group and with the grand mean already removed . this corresponds to the linear model ( [ setting ] ) with @xmath131 and , since we assume the predictors to have norm @xmath132 , @xmath133 \in{\mathbb{r}}^{n \times p},\ ] ] where each vector in this block representation is @xmath130-dimensional . this is in fact an example of orthogonal design . note that our results apply even under the standard constraint @xmath134 . * _ concatenation of orthonormal bases . _ suppose that @xmath135 and that @xmath58 is the concatenation of @xmath130 orthonormal bases in @xmath136 jointly used as to provide an efficient signal representation . then our result applies provided that @xmath137 and that our bases are mutually incoherent so that @xmath118 is sufficiently small ( for examples of incoherent bases see , e.g. , @xcite ) . * _ random designs . _ as in some compressive sensing and communications applications , assume that @xmath58 has i.i.d . normal entries with columns subsequently normalized ( the column vectors are sampled independently and uniformly at random on the unit sphere ) . such a design is close to orthogonal since @xmath138 with high probability . this fact follows from a well - known concentration inequality for the uniform distribution on the sphere @xcite . the exact same bound applies if the entries of @xmath58 are instead i.i.d . rademacher random variables . we return to the discussion of our statistics and note that the higher criticism and the max test applied to @xmath61 are exceedingly simple methods with a straightforward implementation running in @xmath139 flops . this brings us to two important points : in the classical sparse mean model , bonferroni - type multiple testing ( the max test ) is not optimal when the sparsity level is moderately strong , that is , when @xmath140 @xcite . this has direct implications in the fields of genetics and genomics where this is the prevalent method . the same is true in our more general model and it implies , for example , that the matched filter detector in wireless multi - user detection is suboptimal in the same sparsity regime . we elaborate on this point because this carries an important message . when the sparsity level is moderately strong , the higher criticism method we propose is powerful in situations where the signal amplitude is so weak that the max test is powerless . _ this says that one can detect a linear relationship between a response @xmath80 and a few covariates even though those covariates that are most correlated with @xmath80 are not even in the model . _ put differently , if we assign a @xmath28-value to each hypothesis @xmath26 ( computed from a simple linear regression as discussed earlier ) , then _ the case against the null is not in the tail of these @xmath28-values but in the bulk _ , that is , the smallest @xmath28-values may not carry any information about the presence of a signal . in the situation we describe , the smallest @xmath28-values most often correspond to true null hypotheses , sometimes in such a way that the false discovery rate ( fdr ) can not be controlled at any level below 1 ; and yet , the higher criticism has full power . though we developed the idea independently , the higher criticism applied to @xmath61 is similar to the innovated higher criticism of hall and jin @xcite , which is specifically designed for time series . not surprisingly , our results and arguments bear some resemblance with those of hall and jin @xcite . we have already explained how their results apply when the design matrix is triangular ( and , in particular , square ) and has sufficiently rapidly decaying coefficients away from the diagonal . our results go much further in the sense that ( 1 ) they include designs that are far from being triangular or even square , and ( 2 ) they include designs with coefficients that do not necessarily follow any ordered decay pattern . on the technical side , hall and jin astutely reduce matters to the case where the design matrix is banded , which greatly simplifies the analysis . in the general linear model , it is not clear how a similar reduction would operate especially when @xmath141at the very least , we do not see a way and one must deal with more intricate dependencies in the noise term @xmath142 . as we have remarked earlier , we have discussed testing the global null @xmath76 , whereas some settings obviously involve nuisance parameters as in the comparison of nested models . examples of nuisance parameters include the grand mean in a balanced , one - way design or , more generally , the main effects or lower - order interactions in a multi - way layout . in signal processing , the nuisance term may represent clutter as opposed to noise . in general , we have @xmath143 where @xmath144 is the vector of nuisance parameters , and @xmath145 the vector we wish to test . our results concerning the performance of anova , the higher criticism or the max test apply provided that the column spaces of @xmath146 and @xmath147 be sufficiently far apart . this occurs in lots of applications of interest . in the case of the balanced , multi - way design , these spaces are actually orthogonal . in signal processing , these spaces will also be orthogonal if the column space of @xmath146 spans the low - frequencies while we wish to detect the presence of a high - frequency signal . the general mechanism which allows us to automatically apply our results is to simply assume that @xmath148 , where @xmath149 is the orthogonal projector with the range of @xmath146 as null space , obeys the conditions we have for @xmath58 . the paper is organized as follows . in section [ secortho ] we consider orthogonal designs and state results for the classical setting where no sparsity assumption is made on the regression vector @xmath39 , and the setting where @xmath39 is mildly sparse . in section [ secsparse ] we study designs in which _ most _ pairs of predictor variables are only weakly correlated ; this part contains our main results . in section [ secfull ] we focus on some examples of designs with full correlation structure , in particular , multi - way layouts with embedded constraints . section [ secnumerics ] complements our study with some numerical experiments , and we close the paper with a short discussion , namely , section [ secdiscussion ] . finally , the proofs are gathered in a supplementary file @xcite . we provide a brief summary of the notation used in the paper . set @xmath150 = \{1,\ldots , p\}$ ] and for a subset @xmath151 $ ] , let @xmath152 be its cardinality . bold upper ( resp . , lower ) case letters denote matrices ( resp . , vectors ) , and the same letter not bold represents its coefficients , for example , @xmath153 denotes the @xmath12th entry of @xmath154 . for an @xmath66 matrix @xmath155 with column vectors @xmath156 , and a subset @xmath151 $ ] , @xmath157 denotes the @xmath49-by-@xmath152 matrix with column vectors @xmath158 . likewise , @xmath159 denotes the vector @xmath160 . the euclidean norm of a vector is @xmath161 and the sup - norm @xmath162 . for a matrix @xmath163 , @xmath164 , and this needs to be distinguished from @xmath165 , which is the operator norm induced by the sup norm , @xmath166 . the frobenius ( euclidean ) norm of @xmath155 is @xmath167 . @xmath168 ( resp . , @xmath169 ) denotes the cumulative distribution ( resp . , density ) function of a standard normal random variable , and @xmath107 its survival function . for brevity , we say that @xmath39 is @xmath68-sparse if @xmath39 has exactly @xmath68 nonzero coefficients . finally , we say that a random variable @xmath170 is stochastically smaller than @xmath171 , denoted @xmath172 , if @xmath173 for all scalar @xmath174 .

testing for the significance of a subset of regression coefficients in a linear model , a staple of statistical analysis , goes back at least to the work of fisher who introduced the analysis of variance ( anova ) . we study this problem under the assumption that the coefficient vector is sparse , a common situation in modern high - dimensional settings . suppose we have @xmath0 covariates and that under the alternative , the response only depends upon the order of @xmath1 of those , @xmath2 . under moderate sparsity levels , that is , @xmath3 , we show that anova is essentially optimal under some conditions on the design . a multiple comparison procedure is often preferred and we establish its optimality when @xmath5 . we suggest a method based on the higher criticism that is powerful in the whole range @xmath7 . this optimality property is true for a variety of designs , including the classical ( balanced ) multi - way designs and more modern `` @xmath8 '' designs arising in genetics and signal processing . in addition to the standard fixed effects model , we establish similar results for a random effects model where the nonzero coefficients of the regression vector are normally distributed . , .

testing for the significance of a subset of regression coefficients in a linear model , a staple of statistical analysis , goes back at least to the work of fisher who introduced the analysis of variance ( anova ) . we study this problem under the assumption that the coefficient vector is sparse , a common situation in modern high - dimensional settings . suppose we have @xmath0 covariates and that under the alternative , the response only depends upon the order of @xmath1 of those , @xmath2 . under moderate sparsity levels , that is , @xmath3 , we show that anova is essentially optimal under some conditions on the design . this is no longer the case under strong sparsity constraints , that is , @xmath4 . in such settings , a multiple comparison procedure is often preferred and we establish its optimality when @xmath5 . however , these two very popular methods are suboptimal , and sometimes powerless , under moderately strong sparsity where @xmath6 . we suggest a method based on the higher criticism that is powerful in the whole range @xmath7 . this optimality property is true for a variety of designs , including the classical ( balanced ) multi - way designs and more modern `` @xmath8 '' designs arising in genetics and signal processing . in addition to the standard fixed effects model , we establish similar results for a random effects model where the nonzero coefficients of the regression vector are normally distributed . , .

hep-th9902154

i

since their introduction @xcite , topological field theories have been responsible for many applications @xcite and are object of continuous investigations . nowadays they represent an important chapter of quantum field theory . the original motivation was related to the possibility of describing topological invariants by means of standard field - theory techniques @xcite . in order to give an idea of this framework , let us briefly present here the field - theory characterization of one of the most simple and familiar topological invariants , namely , the linking number @xmath3 of two nonintersecting smooth closed oriented curves in @xmath4@xcite : as is well known , the linking number @xmath5 is an integer which counts the number of times that one curve winds around the other . it is independent from the shape of the curves and can be represented by the gauss integral @xmath6 expression ( [ g - int ] ) is in fact easily seen to be an integer by use of the stokes theorem @xcite . taking a field theory point of view , the linking number @xmath5 may be obtained by introducing the topological abelian chern simons action @xcite @xmath7 and by evaluating the correlation function of two loop variables @xmath8 , _ i .. e . , _ @xmath9 that expression ( [ l - cs ] ) reproduces the linking number follows from the observation that the propagator of the gauge field @xmath10 obtained from the chern simons action ( [ c - s ] ) upon quantization in the landau gauge is precisely the kernel of the gauss integral ( [ g - int ] ) , _ i.e. , _ @xmath11 the correlator ( [ l - cs ] ) may thus be regarded as a field - theory description of the linking @xmath12 the action ( [ c - s ] ) can be suitably extended to higher dimensions , providing a field - theory characterization of the generalizations of the linking number @xcite . moreover , the nonabelian version of the three - dimensional chern simons action ( [ c - s ] ) has been proven to play a very relevant role in knot theory @xcite . although the topological field theories possess their own interests and applications , it is worth underlining here that topological terms appear frequently as parts of more general effective actions useful for the theoretical description of a large number of phenomena in different space - time dimensions . for instance , the effective action corresponding to the bosonization @xcite of relativistic three - dimensional massive fermionic systems at @xmath13 can be written as the sum of the chern - simons term ( [ c - s ] ) and of an infinite series of higher - order terms in the curvature @xmath14 and its derivatives , _ @xmath15 with @xmath16 being a combination of terms of the type @xmath17 this kind of action turns out to be useful in order to study several three - dimensional phenomena such as the fermi bose transmutation @xcite and the quantum hall effect @xcite . a second interesting example is provided by the five - dimensional generalization of ( [ eff - cs ] ) , obtained from the ads / cft _ _ _ _ correspondence @xcite , which relates the conformal @xmath18 super - yang - mills theory to type - iib superstring on ads@xmath19 . in fact , in the conformal case , the dual supergravity on @xmath20 possesses a chern simons term obtained from a @xmath21 doublet of two - forms @xmath22 @xmath23 . in this case , the relevant effective action for @xmath22 @xmath23 looks like @xcite @xmath24 where the term @xmath25 collects all the higher - order terms in the curvatures @xmath26 . the correlation function ( [ l - cs ] ) generalizes now to @xmath27 where @xmath28 @xmath29 are appropriate two - surfaces . in view of these applications , it seems natural to ask ourselves what is the response of a correlator of the type ( [ l - cs ] ) when the corresponding topological field theory is perturbed by the introduction of a nontopological interaction term depending on the curvature . this is the aim of the present paper . more precisely , we shall report on the four - loop computation of the correlator @xmath30 when the three - dimensional chern simons action ( [ c - s ] ) is perturbed by a nontopological interaction term of the kind @xmath31 namely _ _ , _ _ expression ( [ p - c ] ) will be evaluated with an effective action @xmath32 given by @xmath33 with @xmath34 and @xmath35 being an arbitrary parameter with negative mass dimension , reflecting the power - counting nonrenormalizability of the perturbation . in particular , we shall be able to prove that the correlation function ( [ p - c ] ) turns out to be independent from @xmath35 , yielding the linking number @xmath5 of the two curves @xmath1 , @xmath36 although the loop analysis will be worked out only up to the fourth order , this conclusion holds to all orders of perturbation theory and may be easily generalized to any local nontopological interaction term containing arbitrary powers of the curvature @xmath14 as well as to the higher - dimensional cases @xcite as , for instance , the effective action of eq.([ads ] ) . this result means that the loop correlator ( [ p - c ] ) is stable with respect to the perturbations which can be added to the starting topological action . in other words , the expression ( [ p - c ] ) will give the linking number of the two curves @xmath1 , @xmath2 , regardless of any @xmath37-dependent perturbation term that can be introduced and of their power - counting nonrenormalizability character . two remarks are now in order . first , we will limit here ourselves only to effective actions which are abelian . second , we shall consider only @xmath37-dependent terms which can be treated as true perturbations . therefore , we shall avoid in the effective action ( [ seff ] ) the inclusion of a term of the maxwell type @xmath38 where @xmath39 is a mass parameter . the presence of this term would completely modify the original properties of the model . in fact , being expression ( [ max ] ) quadratic in the gauge fields , it can not be considered as a perturbation term , as it will be responsible for the presence of massive excitations in the spectrum of the theory @xcite . rather , the presence of the maxwell term in the effective action ( [ seff ] ) will give rise to the existence of two distinct regimes corresponding to the long and short distance behaviours , respectively . for distances larger than the inverse of the mass parameter @xmath39 ( _ i.e. _ , the low - energy regime ) , the topological term will prevail , _ _ _ _ while the maxwell term will become the relevant one at short distances ( _ i.e. , _ the high - energy regime ) . it is worth mentioning here that these two regimes can be accessed in a very simple way by means of suitable gauge - invariant field redefinitions of the gauge connection @xmath10 @xcite . however , their full understanding is a difficult and delicate task , which is beyond the aim of the present paper , being under investigation . we should also underline here that , in the abelian case , the loop variable @xmath8 is gauge invariant for closed curves , and so there is no need to take into account its exponentiation @xmath40 , as it would be required in the nonabelian case . this feature has a useful consequence . it allows indeed to avoid the case in which the double - line integral ( [ p - c ] ) has to be taken along the same curve . this case , usually referred to as the self - linking , would be automatically generated by the perturbative taylor expansion of the exponential @xmath41 . in other words , as far as the abelian case is concerned , the loop variables in eq.([p - c ] ) do not need to be exponentiated . therefore , the two curves @xmath1 and @xmath2 will always refer to two distinct curves which do not intersect each other . as we shall see in the following , this point will be relevant in order to establish the independence from the parameter @xmath35 of the expression ( [ p - c ] ) .

the abelian chern simons theory is perturbed by introducing local gauge - invariant interaction terms depending on the curvature . the computation of the correlation function @xmath0 for two smooth closed nonintersecting curves @xmath1 , @xmath2 is reported up to four loops and is shown to be unaffected by radiative corrections . this result ensures the stability of the linking number of @xmath1 and @xmath2 with respect to the local perturbations which may be added to the chern simons action .

the abelian chern simons theory is perturbed by introducing local gauge - invariant interaction terms depending on the curvature . the computation of the correlation function @xmath0 for two smooth closed nonintersecting curves @xmath1 , @xmath2 is reported up to four loops and is shown to be unaffected by radiative corrections . this result ensures the stability of the linking number of @xmath1 and @xmath2 with respect to the local perturbations which may be added to the chern simons action .

0904.0953

i

the research about the cosmological scale factor has attracted intense attention during the last years as well as the investigation about the connection between the cosmological constant and the dark energy issue . as the vacuum has a non - trivial role in the early universe , a @xmath0-term in the einstein field equations is generated . this @xmath0-term leads to the inflationary phase @xcite . based on the inflationary cosmology we can say that during an early exponential phase , the vacuum energy was a large cosmological constant . however , the current observed small value of the cosmological constant makes us to assume that @xmath0 , representing the energy density of the vacuum , is a variable dynamic degree of freedom which being initially very large went down to its small present value in an expanding universe @xcite . the last one can be measured through the discrepancies between the infinitesimal value that the cosmological constant has for the present universe ( it is very small in planck units ) and the values expected by the standard model @xcite . there is an extensive literature that show examples of phenomenological @xmath0-decay laws . to mention some ideas , the studies comprise a @xmath0 depending on temperature , time , hubble parameter and scale factor @xcite . a dynamically decaying cosmological constant with cosmic expansion has been considered by several authors @xcite . the importance of the subject resides in the fact that any nonzero value of @xmath0 introduces a length scale and a time scale into the theory of general relativity @xcite . the cosmological constant perturbs spacetime dynamics , although the general relativity works on scales much larger than the planck scales . however , vacuum quantum fluctuations of the standard model rekindle the theory of the cosmological constant problem . moreover , the cosmological constant is one of the candidates to be a de model , namely , with the equation of state @xmath1 . a plaudible de model is very important to explain the observations introduced by supernovae ( sne ) type ia @xcite . other candidates are scalar fields models such as quintessence , k - essence , tachion , phantom and etc .. for a review see @xcite . albeit there are many references about a scale factor inverse - square law for the cosmological constant there is a lack of information about the explicit form of the function of the scale factor that obeys this requirement . in reference @xcite there are some analytical solutions . however , those were obtained for a perfect - fluid matter energy - momentum tensor . besides , it is our opinion that there is not an appropriate analysis in the literature that includes the scale factor analytical solutions in a de approach . the underlying motivation to carry out these solutions is the fact that the time variation of @xmath0 can lead to a creation of matter ( i.e. , @xmath0(t)cdm models ) and/or radiation such as to help us in the investigation of the age of the universe . in this work we will use the requirement of the energy - momentum tensor conservation in order to introduce some new analytical solutions for the scale factor different from the published and unpublished @xcite literature . while the current observations clearly pinpoint to a flat universe , in the name of generalization , we will find solutions that have different curvatures , @xmath2 as parameters , i.e. , for flat , open and closed universes respectively . the obvious interest in a flat @xmath3 cosmological constant model has its motivation rooted in the fact that a @xmath0-term helps to connect inflation with observations . moreover , with @xmath0 , it is possible to obtain , for flat universes , a theoretical age in the observed range , even for a high value of the hubble parameter @xcite , but it is not the objective of this work . with these parameters we analyze some de models in the background of these analytical calculations . in this paper we also assume , as will be said below , that the parameter of the de equation of state , @xmath4 , is constant . this parame4ter measures the ratio between the dark energy pressure and its energyh density and is its precse value is one of the main tarets in general relativistic cosmology . in the next section we will depict the field equations and the differential form of the scale factor equation . in section iii we will present some motivations about the reasons to study this specific form for the cosmological constant . we present some possible analytical solutions for the scale equation in section iv . in section v we carry out a very brief review about de and we analyze its connection with the obtained results . the final discussions are left for the final section .

the extreme smallness of the cosmological constant expressed in either planck , or even atomic units means only that its origin is not related to strong , electromagnetic and weak interactions . despite the fact that this general expression is well known , in this work we introduce families of analytical solutions for the scale factor different from the current literature .

the accelerated expansion of the universe has now been confirmed by several independent observations including those of high redshift type ia supernovae , and the cosmic microwave background combined with the large scale structure of the universe . another way of presenting this kinematic property of the universe is to postulate the existence of a new and exotic entity , with negative pressure , the dark energy ( de ) . in spite of observationally well established , no single theoretical model provides an entirely compelling framework within which cosmic acceleration or de can be understood . at present all existing observational data are in agreement with the simplest possibility of the cosmological constant to be a candidate for de . this case is internally self - consistent and non - contradictory . the extreme smallness of the cosmological constant expressed in either planck , or even atomic units means only that its origin is not related to strong , electromagnetic and weak interactions . although in this case de reduces to only a single fundamental constant we still have no derivation from any underlying quantum field theory for its small value . from the principles of quantum cosmologies , it is possible to obtain the reason for an inverse - square law for the cosmological constant with no conflict with observations . despite the fact that this general expression is well known , in this work we introduce families of analytical solutions for the scale factor different from the current literature . the knowledge of the scale factor behavior might shed some light on these questions since the entire evolution of a homogeneous isotropic universe is contained in the scale factor . we use different parameters for these solutions and with these parameters we stablish a connection with the equation of state for different dark energy scenarios . .2 in

0901.0670

i

the broad emission iron lines are well - known features found in about two dozens of spectra of active galactic nuclei and black hole binaries . they are supposed to originate close to the black hole by the reflection of the primary radiation on the accretion disc . the spin of the black hole plays an important role in the forming of the line shape . especially , it determines the position of the marginally stable orbit which is supposed to confine the inner edge of the accretion disc ( see figure [ intro ] ) . the innermost stable orbit occurs closer to a black hole with a higher spin value . however , the spin affects also the overall shape of the line . over almost two decades the most widely used model of the relativistic disc spectral line has been the one by , which includes the effects of a maximally rotating kerr black hole . in other words , the laor model sets the dimensionless angular momentum @xmath1 to the canonical value of @xmath0 so that it can not be subject of the data fitting procedure . have relaxed this limitation and allowed @xmath1 to be fitted in the suite of ky models . other numerical codes have been developed independently by several groups ( , , ) and equipped with similar functionality . however , the laor model can still be used for evaluation of the spin if one identifies the inner edge of the disc with the marginally stable orbit . in this case the spin is actually estimated from the lower boundary of the broad line . the comparison of the laor and model is shown in the right panel of figure [ intro ] . the other parameters of the relativistic line models are inclination angle @xmath2 , rest energy of the line @xmath3 , inner radius of the disc @xmath4 , outer radius of the disc @xmath5 , emissivity parameters @xmath6 , @xmath7 with the break radius @xmath8 . the emissivity of the line is given by @xmath9 for @xmath10 and @xmath11 for @xmath12 . the angular dependence of the emissivity is characterized by limb darkening profile @xmath13 in the laor model . the model enables to switch between different emission laws . we used further two extreme cases , the with the same limb - darkening law as in the laor model and * with the limb - brightening law @xmath14 . the aim of this paper is to compare the two models applied to the current data provided by the xmm - newton satellite , and to the artificial data generated for the on - coming x - ray mission . for this purpose we have chosen two sources , mcg-6 - 30 - 15 and gx 339 - 4 , which exhibit an extremely skewed iron line according to recently published papers ( ) . and marginally stable orbit @xmath15 . right : comparison of the laor ( black , solid ) and ( red , dashed ) model for two values of the spin @xmath16 ( top ) and @xmath17 ( bottom ) . the other parameters of the line are @xmath18kev , @xmath19 , @xmath20.,scaledwidth=98.0% ] and marginally stable orbit @xmath15 . right : comparison of the laor ( black , solid ) and ( red , dashed ) model for two values of the spin @xmath16 ( top ) and @xmath17 ( bottom ) . the other parameters of the line are @xmath18kev , @xmath19 , @xmath20.,title="fig:",scaledwidth=98.0% ] + and marginally stable orbit @xmath15 . right : comparison of the laor ( black , solid ) and ( red , dashed ) model for two values of the spin @xmath16 ( top ) and @xmath17 ( bottom ) . the other parameters of the line are @xmath18kev , @xmath19 , @xmath20.,title="fig:",scaledwidth=98.0% ]

the analysis of the broad iron line profile in the x - ray spectra of active galactic nuclei and black hole x - ray binaries allows us to constrain the spin parameter of the black hole . we compare the constraints on the spin value for two x - ray sources , mcg-6 - 30 - 15 and gx 339 - 4 , with a broad iron line using present relativistic line models in xspec laor and . the laor model has the spin value set to the extremal value @xmath0 , while the model enables direct fitting of the spin parameter . the spin value is constrained mainly by the lower boundary of the broad line , which depends on the inner boundary of the disc emission where the gravitational redshift is maximal . the position of the inner disc boundary is usually identified with the marginally stable orbit which is related to the spin value . in this way the laor model can be used to estimate the spin value . we investigate the consistency of the laor and models .

the analysis of the broad iron line profile in the x - ray spectra of active galactic nuclei and black hole x - ray binaries allows us to constrain the spin parameter of the black hole . we compare the constraints on the spin value for two x - ray sources , mcg-6 - 30 - 15 and gx 339 - 4 , with a broad iron line using present relativistic line models in xspec laor and . the laor model has the spin value set to the extremal value @xmath0 , while the model enables direct fitting of the spin parameter . the spin value is constrained mainly by the lower boundary of the broad line , which depends on the inner boundary of the disc emission where the gravitational redshift is maximal . the position of the inner disc boundary is usually identified with the marginally stable orbit which is related to the spin value . in this way the laor model can be used to estimate the spin value . we investigate the consistency of the laor and models . we find that the spin values evaluated by both models agree within the general uncertainties when applied on the current data . however , the results are apparently distinguishable for higher quality data , such as those simulated for the international x - ray observatory ( ixo ) mission . we find that the laor model tends to overestimate the spin value and furthermore , it has insufficient resolution which affects the correct determination of the high - energy edge of the broad line . +

0901.0670

c

we investigated the iron line band for two representative sources mcg-6 - 30 - 15 ( active galaxy ) and gx 339 - 4 ( x - ray binary ) . the iron line is statistically better constrained for the active galaxy mcg-6 - 30 - 15 due to a significantly longer exposure time of the available observations for comparison of count rates of the sources see table 3 . the spectra of both sources are well described by a continuum model plus a broad iron line model . we compared modeling of the broad iron line by the two relativistic models , laor and . the model leads to a better defined minimum of @xmath29 for the best fit value . the confidence contour plots for @xmath30 versus other model parameters are more regularly shaped . this indicates that the model has a smoother adjustment between the different points in the parameter space allowing for more reliable constraints on @xmath30 . the laor model has a less accurate grid and is strictly limited to the extreme kerr metric . the discrepancies between the and laor results are within the general uncertainties of the spin determination using the skewed line profile when applied to the current data . however , the results are apparently distinguishable for higher quality data , as those simulated for the xeus mission . we find that the laor model tends to overestimate the spin value and furthermore , it has insufficient energy resolution which affects the correct determination of the high - energy edge of the broad line . the discrepancies in the overall shape of the line are more visible especially for lower values of the spin @xmath30 . as a side - product , we have found that the correct re - binning of the data with respect to the instrumental energy resolution is crucial to obtain statistically the most relevant results . arnaud , m. , barcons , x. , barret , d. , bautz , m. , bellazzini , r. , xeus : the physics of the hot evolving universe , _ experimental astronomy _ , tmp , 24a , 2008 beckwith , k. , done , c. , iron line profiles in strong gravity , _ monthly notices of royal astronomical society _ , 352 , 353 , 2004 brenneman , l. w. , reynolds , c. s. , constraining black hole spin via x - ray spectroscopy , _ astrophysical journal _ , 652 , 1028 , 2006 ade , a. , calvani , m. , relativistic emission lines from accretion discs around black holes , _ monthly notices of royal astronomical society _ , 363 , 177 , 2005 doviak , m. , karas , v. , yaqoob , t. , an extended scheme for fitting x - ray data with accretion disc spectra in the strong gravity regime , _ astrophysical journal supplements _ , 153 , 205 , 2004 fabian , a. c. , vaughan , s. nandra , k. , iwasawa , k. , ballantyne , d. r. et al . , a long hard look at mcg-6 - 30 - 15 with xmm - newton , _ monthly notices of royal astronomical society _ , 335 , l1 , 2002 gallo e. , corbel s. , fender r. p. , a transient large - scale relativistic radio jet from gx 339 - 4 , _ monthly notices of royal astronomical society _ , 347l , 52 g , 2004 laor , a. , line profiles from a disk around a rotating black hole , _ astrophysical journal _ , 376 , 90 , 1991 miller , j. m. , fabian , a. c. , reynolds , c. s. , nowak , m. a. , homan , j. et al . , evidence of black hole spin in gx 339 - 4 : xmm - newton / epic - pn and rxte spectroscopy of the very high state , _ astrophysical journal _ , 606 , l131 , 2004 miller , j. m. , homan , j. , steeghs , d. , rupen , m. , hunstead , r. w. et al . , a long , hard look at the low / hard state in accreting black holes , _ astrophysical journal _ , 653 , 525 , 2006 miller , l. , turner , t. j. , reeves , j. n. , an absorption origin for the x - ray spectral variability of mcg-6 - 30 - 15 , _ astronomy & astrophysics _ , 483 , 437 , 2008 reis , r. c. , fabian , a. c. , ross , r. , miniutti , g. , miller , j. m. , reynolds , c. s. , a systematic look at the very high and low / hard state of gx 339 - 4 : constraining the black hole spin with a new reflection model , _ arxiv:0804.0238 _ , 2008 remillard , r. a. and mcclintock , j. e. , x - ray properties of black hole binaries , _ annual review of astronomy & astrophysics _ , 49 , 2006 vaughan , s. , fabian , a. c. , a long hard look at mcg-6 - 30 - 15 with xmm - newton - ii . detailed epic analysis and modelling , _ monthly notices of royal astronomical society _ , 348 , 1415 , 2004

we find that the spin values evaluated by both models agree within the general uncertainties when applied on the current data . however , the results are apparently distinguishable for higher quality data , such as those simulated for the international x - ray observatory ( ixo ) mission . we find that the laor model tends to overestimate the spin value and furthermore , it has insufficient resolution which affects the correct determination of the high - energy edge of the broad line . +

the analysis of the broad iron line profile in the x - ray spectra of active galactic nuclei and black hole x - ray binaries allows us to constrain the spin parameter of the black hole . we compare the constraints on the spin value for two x - ray sources , mcg-6 - 30 - 15 and gx 339 - 4 , with a broad iron line using present relativistic line models in xspec laor and . the laor model has the spin value set to the extremal value @xmath0 , while the model enables direct fitting of the spin parameter . the spin value is constrained mainly by the lower boundary of the broad line , which depends on the inner boundary of the disc emission where the gravitational redshift is maximal . the position of the inner disc boundary is usually identified with the marginally stable orbit which is related to the spin value . in this way the laor model can be used to estimate the spin value . we investigate the consistency of the laor and models . we find that the spin values evaluated by both models agree within the general uncertainties when applied on the current data . however , the results are apparently distinguishable for higher quality data , such as those simulated for the international x - ray observatory ( ixo ) mission . we find that the laor model tends to overestimate the spin value and furthermore , it has insufficient resolution which affects the correct determination of the high - energy edge of the broad line . +

1411.0003

i

the recently discovered brown dwarf binary wisej104915.57@xmath0531906.1 @xcite , hereafter luhman16ab , is one of only a few known spatially resolved binaries where both components are located at the transition of l to t spectral type ( l7.5 and t0.5 , * ? ? ? * ; * ? ? ? its very large parallax of @xmath10 mas @xcite puts it at a distance of only @xmath11 pc , making it the third closest known system from the sun after @xmath12 cen and barnard s star . because of that proximity , they are by far the brightest brown dwarfs of their spectral type , allowing studies not previously possible for fainter objects . for example , @xcite were able to use time - resolved very high resolution spectroscopy to create a surface map by applying doppler imaging for the first time to a brown dwarf . the map showed a heterogeneous surface structure for luhman16b that may be linked to patchy cloud cover . heterogeneous cloud cover has already been inferred for other early t dwarfs ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) as well as for luhman16b @xcite from measurements of photometric and/or spectroscopic variability . the removal of cloud opacity is the dominant driver of the spectral changes happening between late l to mid t type dwarfs ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? the change in near - infrared colors from red to blue and the brightening of the j band suggest that the clouds , likely composed of silicates and iron , that form opaque layers in late l dwarfs are fully removed from the visible photosphere by spectral type of @xmath2t5 @xcite . these changes happen at nearly constant effective temperatures of t@xmath13k . one mechanism proposed to explain the color evolution , the re - emergence of the feh feature from early to mid t dwarfs @xcite , and the photometric variability is the appearance and growth of holes in the clouds @xcite , where flux can then emerge from deeper , hotter regions . cloud thinning through growth of particle size , increased sedimentation efficiency and rapid rain out may also remove the clouds @xcite . the multi - wavelength variability of the two early t dwarfs 2massj21392676 + 0220226 ( hereafter 2m2139 ) and simpj013656.57 + 093347.3 ( hereafter simp0136 ) are not compatible with fully cleared holes in clouds . instead , models that are a combination of varying covering fraction of thin and thick clouds over one rotation period can reproduce many of the characteristics of the variability @xcite . with luhman16b , a third early t dwarf with multiple percent variability is now available to test whether the two - component thin / thick cloud model can represent the cloud structure at the beginning of the l / t transition . the luhman16 system offers many additional benefits to significantly increase our understanding of cloud structure at the l / t transition . its brightness offers the possibility for studies over a very broad wavelength range , even in the optical @xcite , and a very good signal to noise ratio at intermediate @xcite or very high resolution @xcite . the distance is already known very precisely and the orbital motion will eventually lead to a measurement of the dynamical mass ; the orbital time scale is @xmath14 years at a separation of @xmath23 au . finally , the a component is most likely co - eval with the b component , implying that their age and metallicity are equal . the a component is brighter overall , but fainter in the y and j bands @xcite . this flux reversal suggests that cloud evolution has progressed less far than for the b component and it therefore provides a comparison point before the onset of the l / t transition . many characteristics of the luhman16ab binary have already been constrained . the discovery of lithium in both objects points to an age between 0.1 and 3 gyr @xcite . their masses are therefore in the range of 20 - 65 m@xmath15 . from their bolometric luminosities , their effective temperatures are very similar with @xmath16k for a and @xmath17k for b , while the brightness temperature is about 50 k higher for b in regions that are dominated by condensate grain scattering @xcite . the @xmath18 measurements indicate that the inclination of luhman16b is @xmath19 from equator - on @xcite . the rotation period has been determined as close to 5 hours , with formal measurements @xmath20 @xcite or @xmath21 h @xcite . precise determination of the rotation period is difficult because the light curve shape evolves on time scales of only one rotation period . in this paper , we present spatially resolved spectroscopic time series obtained with the hubble space telescope ( hst ) for both luhman16 a and b. this allows a study of their variability amplitudes independently and with high precision , and gives access to features such as the 1.4 @xmath1 m water band that are not obtainable from the ground but are an important tracer of the vertical extension of the cloud . in section 2 we describe the observations and data reduction . in section 3 we present and analyze the measured spectroscopic variability and its evolution over one rotation period . we also provide an update on the binary separation . in section 4 we model the observations with patchy cloud models and in section 5 we discuss and compare to previous results . our conclusions are presented in section 6 .

the binary brown dwarf wisej104915.57@xmath0531906.1 ( also luhman16ab ) , composed of a late l and early t dwarf , is a prototypical l / t transition flux reversal binary located at only 2pc distance . luhman16b is a known variable whose light curves evolve rapidly . the amplitude and light curve shape changes over only one rotation period .

the binary brown dwarf wisej104915.57@xmath0531906.1 ( also luhman16ab ) , composed of a late l and early t dwarf , is a prototypical l / t transition flux reversal binary located at only 2pc distance . luhman16b is a known variable whose light curves evolve rapidly . we present spatially resolved spectroscopic time - series of luhman16a and b covering 6.5h using hst / wfc3 at 1.1 to 1.66@xmath1 m . the small , count - dependent variability of luhman16a at the beginning of the observations likely stems from instrumental systematics ; luhman16a appears non - variable above @xmath20.4% . its spectrum is well fit by a single cloud layer with intermediate cloud thickness ( @xmath3 , t@xmath4k ) . luhman16b varies at all wavelengths with peak - to - valley amplitudes of 7 - 11% . the amplitude and light curve shape changes over only one rotation period . the lowest relative amplitude is found in the deep water absorption band at 1.4 @xmath1 m , otherwise it mostly decreases gradually from the blue to the red edge of the spectrum . this is very similar to the other two known highly variable early t dwarfs . a two - component cloud model accounts for most of the variability , although small deviations are seen in the water absorption band . we fit the mean spectrum and relative amplitudes with a linear combination of two models of a warm , thinner cloud ( t@xmath5k , @xmath6 ) and a cooler , thicker cloud ( t@xmath7k , @xmath8 ) , assuming out - of - equilibrium atmospheric chemistry . a cloud as for luhman16a but with holes can not reproduce the variability of luhman16b , indicating more complex cloud evolution through the l / t transition . the projected separation of the binary has decreased by @xmath9 in 8 months .

1411.0003

c

as our nearest brown dwarf neighbors , the luhman16ab system offers unprecedented opportunities to further our understanding of the l / t transition . we have obtained very high signal - to - noise , spatially resolved spectroscopic time series of both objects with hst that reveal a highly patchy cloud structure for luhman16b . * luhman16a is not variable at 1.1 - 1.66 @xmath1 m above our instrumental systematics of @xmath20.2 - 0.4% depending on wavelength . a model with a single , homogeneous cloud layer with t@xmath105 = 1200 k , @xmath83 , @xmath106 and out - of - equilibrium chemistry with @xmath70@xmath67s@xmath25 provides a good fit to the spectrum . * luhman16b varies with a maximum peak - to - peak amplitude of more than 10% in the near - ir , but the relative amplitude is lower in the deep water absorption band at 1.4 @xmath1 m . outside the absorption band there is also a small decrease in the relative amplitude with increasing wavelength . * a two - component cloud model can explain most , but not all , of the variability of luhman 16b , with the primary differences seen in the water absorption band . a combination of a warmer , thinner cloud with t@xmath107k and @xmath108 and a cooler , thicker cloud with t@xmath109 k and @xmath62 provide a decent fit to both the spectrum and relative amplitude as a function of wavelength , but the covering fraction of each cloud is degenerate with other model parameters . the relative covering fraction varies by 5 - 10% between the two hemispheres . out - of - equilibrium chemistry ( @xmath70@xmath67s@xmath25 ) is also required to fit the spectrum . * we can firmly exclude the existence of areas without cloud opacity , suggesting that the primary difference in the color and the variability between a co - eval late l and early t dwarf is not caused by the opening and clearing of deep holes . instead , we find a difference in the cloud structure before the l / t transition ( overall intermediate cloud thickness ) to within the transition ( patchy coverage with thicker and thinner clouds ) . * the relative amplitude shows very similar wavelength dependent behavior for the three known highly variable early t dwarfs , suggesting similar underlying cloud structure that may be typical for these objects . * the light curve shape and amplitude of luhman16b evolves significantly on the time scale of only one rotation period . between epochs , the wavelength dependence of the variability may also change significantly , although it is unclear what mechanism could cause these changes . * the projected separation of luhman16a and b has decreased by 03 within a time - span of 8 months . further monitoring of the orbital evolution with hst ( program # 13748 ) , gaia , and from the ground will eventually result in a dynamical mass measurement , a crucial input for the constraint of atmospheric models . combined with continuing monitoring of the variability of luhman16b across a wide wavelength range and the direct comparison to its companion luhman16a , it will be possible to put together a comprehensive model of its atmosphere and weather patterns that can not be obtained for any other substellar object . we thank the staff at space telescope science institute ( stsci ) , in particular amber armstrong , for the coordination and scheduling of the observations . we also thank jay anderson for providing information and routines regarding the distortion correction for wfc3 . we thank adam burgasser , alexei kniazev and jackie faherty for providing their published spectra of luhman16ab in electronic form . based on observations made with the nasa / esa hubble space telescope , obtained at the space telescope science institute , which is operated by the association of universities for research in astronomy , inc . , under nasa contract nas 5 - 26555 . these observations are associated with program # 13280 . support for program # 13280 was provided by nasa through a grant from the space telescope science institute . eb was supported by the swiss national science foundation ( snsf ) . this research has made use of the simbad database , operated at cds , strasbourg , france , and of nasa s astrophysics data system bibliographic services .

we present spatially resolved spectroscopic time - series of luhman16a and b covering 6.5h using hst / wfc3 at 1.1 to 1.66@xmath1 m . its spectrum is well fit by a single cloud layer with intermediate cloud thickness ( @xmath3 , t@xmath4k ) . luhman16b varies at all wavelengths with peak - to - valley amplitudes of 7 - 11% . the lowest relative amplitude is found in the deep water absorption band at 1.4 @xmath1 m , otherwise it mostly decreases gradually from the blue to the red edge of the spectrum . a two - component cloud model accounts for most of the variability , although small deviations are seen in the water absorption band . we fit the mean spectrum and relative amplitudes with a linear combination of two models of a warm , thinner cloud ( t@xmath5k , @xmath6 ) and a cooler , thicker cloud ( t@xmath7k , @xmath8 ) , assuming out - of - equilibrium atmospheric chemistry . a cloud as for luhman16a but with holes can not reproduce the variability of luhman16b , indicating more complex cloud evolution through the l / t transition . the projected separation of the binary has decreased by @xmath9 in 8 months .

the binary brown dwarf wisej104915.57@xmath0531906.1 ( also luhman16ab ) , composed of a late l and early t dwarf , is a prototypical l / t transition flux reversal binary located at only 2pc distance . luhman16b is a known variable whose light curves evolve rapidly . we present spatially resolved spectroscopic time - series of luhman16a and b covering 6.5h using hst / wfc3 at 1.1 to 1.66@xmath1 m . the small , count - dependent variability of luhman16a at the beginning of the observations likely stems from instrumental systematics ; luhman16a appears non - variable above @xmath20.4% . its spectrum is well fit by a single cloud layer with intermediate cloud thickness ( @xmath3 , t@xmath4k ) . luhman16b varies at all wavelengths with peak - to - valley amplitudes of 7 - 11% . the amplitude and light curve shape changes over only one rotation period . the lowest relative amplitude is found in the deep water absorption band at 1.4 @xmath1 m , otherwise it mostly decreases gradually from the blue to the red edge of the spectrum . this is very similar to the other two known highly variable early t dwarfs . a two - component cloud model accounts for most of the variability , although small deviations are seen in the water absorption band . we fit the mean spectrum and relative amplitudes with a linear combination of two models of a warm , thinner cloud ( t@xmath5k , @xmath6 ) and a cooler , thicker cloud ( t@xmath7k , @xmath8 ) , assuming out - of - equilibrium atmospheric chemistry . a cloud as for luhman16a but with holes can not reproduce the variability of luhman16b , indicating more complex cloud evolution through the l / t transition . the projected separation of the binary has decreased by @xmath9 in 8 months .

0808.0137

i

within the context of ao systems pyramid wavefront sensors ( pwfs ) are a relatively novel concept . the special interest in this concept arises from the prediction of a gain in sensitivity and thus in limiting magnitude for a nonmodulated pwfs over a shack - hartmann sensor ( shs ) @xcite in closed - loop conditions for a well - corrected point source . the definition of this gain is that in order to achieve the same correction quality the pwfs needs less signal than the shs . this gain in sensitivity results basically from the fact that the accuracy of the measurement and the resulting reconstruction error @xmath0 of the shs depends on @xmath1 with @xmath2 = sensing wavelength , @xmath3 = subaperture size typically chosen on the order of the fried - parameter @xmath4 for typical site seeing at science wave - length . in the case of the pwfs the measurement error @xmath5 depends on @xmath6 with @xmath7 being the telescope diameter ( @xmath8 ) . from these formulas the difference in stellar magnitudes that are needed to achieve the same strehl ratio for the exemplary case of tip - tilt only can be derived for both sensors as @xmath9 . simulations show , for instance , @xcite that the gain in sensitivity for a 4 m class telescope and a seeing of @xmath10 ( @xmath11 cm ) is predicted to be 2 magnitudes . wavefront sensing based on the pyramid principle has its origin in the foucault knife - edge test . the historical development of the pwfs is described in @xcite . the optical setup of a pyramid sensor is shown in figure [ im : f1 ] . the transmissive , four - sided pyramid prism is placed in the focal plane . the focus is placed on the tip of the pyramid . after the pyramid , a relay lens images the pupils onto the detector.the signal a four - sided ao pwfs system uses are the intensities inside four pupil images . the illumination of these images depends on the aberrations of the wavefront . the signal @xmath12 one extracts is the difference in intensities @xmath13 between corresponding pixels in the four pupils , i.e. , the pixels at the same optical position in the pupils as shown in fig.[im : f1 ] : @xmath14}\over{i_1(x , y)+i_2(x , y)+i_3(x , y)+i_4(x , y)}}\ ] ] @xmath15}\over{i_1(x , y)+i_2(x , y)+i_3(x , y)+i_4(x , y)}}\ ] ] for the x- and y - direction , respectively . these signals @xmath12 are what we will refer to as gradients , even if they might not exactly represent wavefront gradients . in the limit of small perturbations and a telescope with infinite aperture the frequency spectrum of the signal @xmath16 of our sensor is given by @xmath17 here @xmath18 means fourier transform , @xmath19 the phase of the electromagnetic wave with @xmath20 and @xmath21 the coordinates in fourier space , and sgn the sign - function ( see @xcite ) . thus the sensor is working as a phase sensor in this regime . the principle of the pwfs implies some limitations that either do not occur in other sensor types , or have a much more `` dramatic '' impact on pwfss than on other sensor types . in this class fall the structure of the pyramid edges that cause both diffraction and scattering , the read out noise of the system , the goodness of centering the beam on the pyramid tip , noncommon - path aberrations , and the homogeneity of the pupil illumination , the latter being important especially during calibration . it is these limitations , that may ultimately influence the choice of this or another sensor type , that will be examined in the course of this article . the structure in the remaining part of the article is as follows : in the next section , the pyramir system is described in detail . the optical path and the possible detector read out modes are explained . section 3 accounts for the calibration procedure of the system . the peculiarities of tip - tilt calibration and flattening the wavefront are presented . section 4 shows fundamental limitations to the performance of a pyramid system . `` fundamental '' in this case is not meant to be based on natural laws and constants , but on always - present aberrations and nonideal conditions . thus , the fundamental limitations discussed here can be eased by careful alignment and set up of the system , but they can never entirely be removed . in this context , we explore the effect of static aberrations , different calibration light sources , and diffraction and scattering on the pyramid edges to the response of the system . in the next section the implications of the modal cross talk of the system aliasing and measurement error to the number of modes to be calibrated , and the residual wavefront error are calculated . we end the section with a prediction of the on - sky performance under different seeing conditions . the last section concludes the results of our measurements and the implications for any pyramid wavefront sensor.on-sky results will be presented in a following paper @xcite .

the concept of pyramid wavefront sensors ( pwfs ) has been around about a decade by now . the intrinsic errors include diffraction effects on the pyramid edges and detector read out noise . we investigated the effect of three differently sized reference sources on the calibration of the pwfs . we also calculate the total wavefront error arising from aliasing , modal cross talk , measurement error , and fitting error in order to optimize the number of calibrated modes for on - sky operations . these measurements result in a prediction of on - sky performance for various conditions . *

the concept of pyramid wavefront sensors ( pwfs ) has been around about a decade by now . however there is still a great lack of characterizing measurements that allow the best operation of such a system under real life conditions at an astronomical telescope.in this article we , therefore , investigate the behavior and robustness of the pyramid infrared wavefront sensor pyramir mounted at the 3.5 m telescope at the calar alto observatory under the influence of different error sources both intrinsic to the sensor , and arising in the preceding optical system . the intrinsic errors include diffraction effects on the pyramid edges and detector read out noise . the external imperfections consist of a gaussian profile in the intensity distribution in the pupil plane during calibration , the effect of an optically resolved reference source , and noncommon - path aberrations . we investigated the effect of three differently sized reference sources on the calibration of the pwfs . for the noncommon - path aberrations the quality of the response of the system is quantified in terms of modal cross talk and aliasing . we investigate the special behavior of the system regarding tip - tilt control . from our measurements we derive the method to optimize the calibration procedure and the setup of a pwfs adaptive optics ( ao ) system . we also calculate the total wavefront error arising from aliasing , modal cross talk , measurement error , and fitting error in order to optimize the number of calibrated modes for on - sky operations . these measurements result in a prediction of on - sky performance for various conditions . * d. peter , m. feldt , b. dorner , t. henning , s. hippler , j. aceituno *

1509.03403

i

the corot space mission @xcite was operating for almost 6 years , producing thousands of continuous photometric light curves . the readout of each ccd exposure transfers simultaneously the flux of 6,000 stars . the temporal series of exposures are processed by the production pipeline , correcting the data for known instrumental effects , such as gain , background , jitter , emi , saa discarding , time corrections @xcite . but even after these model - based corrections , some collective trends are still visible in the light curves ( fig . [ guterman : fig1 ] ) . the flux gradually decreases with unknown shape and a different slope for each star . previous work to correct these effects has been suggested , including magzep @xcite , that uses a zero - point magnitude correction , associated with the sysrem systematics algorithm @xcite . + algorithms for removing systematics consist of two parts : 1 ) identify the _ effects _ among a set of stars by combining all light curves like sysrem @xcite , see also @xcite , finding combination of a few representative stars @xcite or fitting a model for each exposure based on observational @xcite or instrumental quantities @xcite , then 2 ) remove them by properly adapting them to each light curve . an effect is a pattern that appears among a large set of independent stars . effects can be additive , multiplicative or follow any law that needs to be determined . in the common techniques , the effects are derived from a training set of stars using correlation methods like the iterative sysrem @xcite . the training set can be a properly selected subset of stars or even the whole set itself . + after their global determination , the effects need to be scaled and subtracted from each of the light curves . classical fitting techniques like least square are not satisfactory because the resulting coefficient is partly pulled by the light curve s natural shape and disturbs the scientific signal . for example , the gradual loss of sensitivity visible in fig . [ guterman : fig1 ] correlates with any long - period stellar variability , resulting in removing some real signal . to avoid this critical drawback we propose here a technique similar to magzep @xcite that fits the instrumental effects to each exposure independently . the effect of each exposure is a function of only two instrumental stellar parameters , position on the ccd and photometric aperture . the advantage is that the effect is not a function of the stellar flux , and therefore much more robust . + this paper is structured as follows : section [ sectmethod ] describes the systematics removal method and its application to corot , section [ sectresult ] reviews the derived effects and the performances of the method and section [ sectsummary ] summarizes and concludes this work .

the corot space mission was operating for almost 6 years , producing thousands of continuous photometric light curves . the temporal series of exposures are processed by the production pipeline , correcting the data for known instrumental effects . but even after these model - based corrections , some collective trends are still visible in the light curves . we propose here a simple exposure - based algorithm to remove instrumental effects . the effect of each exposure is a function of only two instrumental stellar parameters , position on the ccd and photometric aperture . techniques : photometric , methods : data analysis

the corot space mission was operating for almost 6 years , producing thousands of continuous photometric light curves . the temporal series of exposures are processed by the production pipeline , correcting the data for known instrumental effects . but even after these model - based corrections , some collective trends are still visible in the light curves . we propose here a simple exposure - based algorithm to remove instrumental effects . the effect of each exposure is a function of only two instrumental stellar parameters , position on the ccd and photometric aperture . the effect is not a function of the stellar flux , and therefore much more robust . as an example , we show that the @xmath0 long - term variation of the early run _ lrc01 _ is nicely detrended on average . this systematics removal process is part of the corot _ legacy _ data pipeline . techniques : photometric , methods : data analysis

1509.03403

i

we present a simple method to remove systematics from the light curves of the corot satellite without altering the scientific information . we apply a 3 parameter linear model per exposure to identify and correct most long - term systematics . the robust estimation algorithm allows to use the full information of the corot sample of a run without selecting a training subset . the derived systematics only depend on the stellar position and mask area and not on the corresponding light curve . consequently , no fitting based on the light curve itself can modify the real stellar variation , even when it resembles the systematics profile . as an example , we show that the @xmath0 long - term variation of the early _ lrc01 _ is nicely detrended on average , and the spread of stars variations is reduced . this systematics removal process is part of the corot _ legacy _ data pipeline .

the effect is not a function of the stellar flux , and therefore much more robust . as an example , we show that the @xmath0 long - term variation of the early run _ lrc01 _ is nicely detrended on average . this systematics removal process is part of the corot _ legacy _ data pipeline .

the corot space mission was operating for almost 6 years , producing thousands of continuous photometric light curves . the temporal series of exposures are processed by the production pipeline , correcting the data for known instrumental effects . but even after these model - based corrections , some collective trends are still visible in the light curves . we propose here a simple exposure - based algorithm to remove instrumental effects . the effect of each exposure is a function of only two instrumental stellar parameters , position on the ccd and photometric aperture . the effect is not a function of the stellar flux , and therefore much more robust . as an example , we show that the @xmath0 long - term variation of the early run _ lrc01 _ is nicely detrended on average . this systematics removal process is part of the corot _ legacy _ data pipeline . techniques : photometric , methods : data analysis

nucl-th9804074

i

the particle - hole state densities are basic quantities for the description of preequilibrium emission ( pe ) in semiclassical models as well as quantum - statistical theories ( e.g. , @xcite ) involving a series of particle - hole excitations caused by two - body interactions . the nuclear excitation in the equilibrium processes concerns the single - particle levels ( s.p.l . ) within an energy range of the order of the nuclear temperature around the fermi level . this explains the basic role of the s.p.l . equidistant spacing model ( esm ) @xcite in the analysis of the equilibrium emission ( see also @xcite ) . however , much higher and lower single - particle energies are involved in pe reactions so that one should consider the reduced suitability of the esm partial - state density ( psd ) formula of williams @xcite . moreover , the inconsistency between the phenomenological s.p.l . density @xmath0 mev@xmath1 and the number _ a _ of nucleons in the nucleus has come under increasing criticism @xcite . on the other hand , combinatorial calculations performed in the space of realistic shell model s.p.l . @xcite have other inherent shortcomings ( e.g. , the strong dependence on the basic set of s.p.l . ) @xcite . this accounts for the continued use of the williams - type formula with various corrections @xcite or exact calculation @xcite for additional pauli blocking and the pairing interaction . in fact , there have been early attempts at considering the single - particle energy dependence of the s.p.l . density @xmath2 within pe formalisms @xcite . next , kalbach @xcite discussed different forms of this dependence and found it tied to pe surface effects due to the interdependence of the respective assumptions . @xcite obtained an indication for the energy dependence nearly as that given by the fermi - gas model ( fgm ) below the fermi energy @xmath3 , but linear above @xmath3 . chadwick and reffo @xcite found the use of either the fgm prescription or the equidistant parametrization @xmath4=@xmath5 more accurate than the phenomenological one . the fgm s.p.l . density has also been involved in the development of the partial level densities with linear momentum @xcite . at the same time , the esm accuracy has been discussed in connection with the non - uniform s.p.l . density effect @xcite provided by the harmonic oscillator model . the analysis of the energy - dependent s.p.l . density in the vicinity of the fermi energy @xcite provided a more general form and a good approximation of the effect for low energies , where the influence of the finite depth of the potential well can be neglected . various @xmath2 have been obtained within both the semiclassical thomas - fermi approximation @xcite and the exact quantum mechanical calculations @xcite which are also applicable at the high excitations located in the continuum region . the psd including distinct energy - dependences for the excited - particle and hole level densities has recently been used in semiclassical @xcite or quantum - statistical @xcite cross - section calculations . the valid use of energy - dependent s.p.l . densities within the esm particle - hole state density formula , even when corrected for the finite depth of the real nuclear potential well @xcite , has not yet been proved . proving it is one aim of this work . first , the particle - hole state density is obtained in sec . ii by means of recursive relations particularly using the fgm s.p.l . density . next , these are compared in sec . iii with the results of the esm formula modified by using s.p.l . densities different for excited particles and holes , obtained from the fgm at the respective average - excitation energies @xcite ( the average energy - dependent esm formalism ) . the analysis is also carried out for the density of particle - hole bound states , with single - particle excitations not exceeding the nucleon binding energy @xcite . the advanced pairing correction @xcite is taken into account while the comparison of various effects includes the exact correction for the pauli exclusion principle @xcite . the importance of distinct corrections in the average energy - dependent esm formalism is further discussed in sec . iv . at the same time the subtraction of the free - gas contribution @xcite is analysed within this formalism , thus making no use of arbitrary truncation @xcite . the respective results are compared with the semiclassical and quantum - mechanical calculations of the continuum effect . since the actual quantum - statistical analyses of the multistep reactions still involve the rough esm , the respective results could be altered following consideration of the effective @xmath6-interaction strength as the only free parameter . the conclusions are drawn in sec .

the correct use of energy - dependent single - particle level ( s.p.l . ) densities within particle - hole state densities based on the equidistant spacing model ( esm ) is analysed . first , an analytical expression is obtained following the convolution of energy - dependent excited - particle and hole densities . densities for the excited particles and holes , respectively . the fermi - gas model ( fgm ) s.p.l . densities calculated at the corresponding average excitation energies are used in both cases . the analysis concerns also the density of particle - hole bound states . the pairing correlations are taken into account while the comparison of various effects includes the exact correction for the pauli exclusion principle . quantum - mechanical s.p.l .

the correct use of energy - dependent single - particle level ( s.p.l . ) densities within particle - hole state densities based on the equidistant spacing model ( esm ) is analysed . first , an analytical expression is obtained following the convolution of energy - dependent excited - particle and hole densities . next , a comparison is made with results of the esm formula using average s.p.l . densities for the excited particles and holes , respectively . the fermi - gas model ( fgm ) s.p.l . densities calculated at the corresponding average excitation energies are used in both cases . the analysis concerns also the density of particle - hole bound states . the pairing correlations are taken into account while the comparison of various effects includes the exact correction for the pauli exclusion principle . quantum - mechanical s.p.l . densities and the _ continuum effect _ can also match a corresponding fgm formula , suitable for use within the average energy - dependent partial state density in multistep reaction models .