Datasets:

tomekkorbak

/

pii-pile-chunk3-1100000-1150000

like 0

[ "Prabhanjan Sanket\n\nPrabhanjan Sanket is a popular Urdu language newspaper serving major cities in the region of Western Uttar Pradesh in India, including the cities of Agra, Aligarh, Mathura, and Firozabad.", "The paper is available in print Newspaper.", "\n\nSee also\nList of newspapers in India\n\nReferences \n\nCategory:Daily newspapers published in India\nCategory:Urdu-language newspapers\nCategory:Media in Uttar Pradesh\nCategory:Urdu-language newspapers published in India" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.014563106796116505, 0.023809523809523808, 0.004629629629629629 ]

[ "Background {#Sec1}\n==========\n\nObesity, commonly defined as a body mass index (BMI) of ≥ 30 kg/m^2^ in adults \\[[@CR1]\\], is the result of a complex multifactorial relationship (e.g. genetic, socioeconomic, and cultural factors) \\[[@CR2]\\]. ", "The prevalence of obesity is affected by lifestyle habits, consumption patterns as well as the urban development \\[[@CR2]\\]. ", "Since the 1980s, the prevalence of obesity has risen considerably and doubled in many countries \\[[@CR3]\\]. ", "Furthermore, a high BMI seems to be associated with a significant proportion of mortality and disability cases \\[[@CR4], [@CR5]\\]. ", "Obesity is therefore recognized as a serious worldwide epidemic.", "\n\nA number of severe health conditions are correlated with being very overweight, e.g. cardiovascular disease and hypertension, but in particular type 2 diabetes mellitus (T2DM) \\[[@CR6]\\], which is the second leading cause of BMI-related deaths in 2015 \\[[@CR4]\\]. ", "Furthermore, obesity and overweight are the single most relevant predictors for T2DM \\[[@CR7]\\]. ", "Because some studies revealed the simultaneous spread of obesity and diabetes, the term 'diabesity' has been used in the literature in order to illustrate the close connectedness \\[[@CR8]\\].", "\n\nThe built environment, comprising buildings, spaces and products generated or influenced by humans, has a strong influence on promoting or preventing diseases \\[[@CR9], [@CR10]\\]. ", "The built environment can act on three different scales: the macro level describes the sprawl or the compactness of a region on a higher aggregated level, e.g. at the nationwide level, whereas the meso level is concerned with the community or neighbourhood environment, in which the access to certain facilities is of major interest. ", "The micro level constitutes a person-related perspective, for example regarding qualities of urban design, and is often connected with the concept of walkability \\[[@CR11]\\]. ", "Factors of the built environment may contribute to obesity, for example via the availability of unhealthy food or the absence of green spaces \\[[@CR12]\\], and consequently create obesogenic environments. ", "Following Swinburn and colleagues \\[[@CR13]\\], obesogenic environments can be described as 'the sum of influences that the surroundings, opportunities, or conditions of life have on promoting obesity in individuals or populations'.", "\n\nIn order to evaluate features of the built environment, tools based on the use of geographic information systems (GIS) have been developed using remote sensing techniques applicable as desk-based approaches \\[[@CR14]\\]. ", "In the past, researchers have shown great interest in commercial data within GIS-based analyses \\[[@CR15], [@CR16]\\]. ", "Recently, freely available data from online geocoding services such as Google Maps and OpenStreetMap (OSM) have become increasingly popular \\[[@CR17], [@CR18]\\]. ", "These services are often accessed via embedded application programming interfaces (APIs) to search data within the geographical databases, e.g. for food-related data \\[[@CR19]\\]. ", "These freely available data can be further applied to assess the environmental risk of the development of obesity by describing high- and low-risk geographical areas originating from the accumulation of obesogenic and protective environmental factors \\[[@CR20]\\]. ", "Further applications of such data could refer to environmental pollution or geographical access to primary health care \\[[@CR21], [@CR22]\\].", "\n\nThe aim of our study was to examine the feasibility of integrating information from online geocoding services into the assessment of environmental obesogenic factors which could potentially be used for diabetes surveillance. ", "Diabetes risk has often been estimated e.g. using data from national surveys, but also from administrative data \\[[@CR23]\\]. ", "Thus secondary data from online geocoding services could be a potential complementary data source for diabetes surveillance. ", "Considering this, two steps were required: First, we checked whether obesogenic and protective factors can be derived from the literature and translated into variables from online geocoding services. ", "Second, we compared Google Maps and OSM regarding their validity and reliability of queried data.", "\n\nMethods {#Sec2}\n=======\n\nDesign of the validation process {#Sec3}\n--------------------------------\n\nTo prepare subsequent validations, we initially identified environmental factors correlated with obesity from the literature. ", "Based on these results and on expert discussions, we have chosen variables from Google Maps and OSM and downloaded these for four regions in Bavaria, Germany. ", "Subsequently, these downloaded data points were validated in the field and by using search engines. ", "An overview of the methods applied during the two phases of preparation and validation is shown in Fig.", " [1](#Fig1){ref-type=\"fig\"}, and further details are provided below.", "Fig.", " 1Flow chart of the validation process\n\nLiterature search and extraction of variables {#Sec4}\n---------------------------------------------\n\nWe applied a search strategy within PubMed using the search terms 'obesogenic', 'environmental factors', 'systematic' and 'review'. ", "After screening the results, two reviews were determined to be relevant for our analysis. ", "The first review by Mackenbach and colleagues \\[[@CR24]\\] provided a systematic search strategy and identified correlates of environmental factors with obesity. ", "The second publication was a review of GIS methods by Jia and colleagues \\[[@CR25]\\], in which correlations of variables with weight status and obesity were described. ", "Following Mackenbach et al. ", "\\[[@CR24]\\], we created a table in order to summarize the factors from our literature search. ", "In a first step, we extracted environmental factors from the studies covered by the two reviews. ", "In a second step, we grouped the publications describing these environmental factors and extracted and summarized information from these publications in order to determine their correlation with obesity.", "\n\nSubsequently, we extended the systematic search strategy provided by Mackenbach et al. ", "in order to identify recent additional studies within PubMed, EMBASE, Web of Science, Cochrane Library, PsychInfo and Google Scholar. ", "We completed the variable table with the additionally identified publications, and information from these studies was used to update the correlations of the environmental factors.", "\n\nDefinition of correlation {#Sec5}\n-------------------------\n\nFor each given environmental factor, we summed up the numbers of studies describing a positive and significant correlation with obesity. ", "Analogously, we counted the numbers of studies describing negative and significant correlations with obesity for the same given factor. ", "Subsequently, we defined this factor as overall positively correlated if at least three publications could be found and if the ratio of the number of positive correlations for the factor divided by the number of negative correlations for the same factor was 2 or higher. ", "Dividing by 0 in this sense can be interpreted as causing infinity. ", "Studies showing no significant correlation were not taken into account. ", "Analogously, if the number of negative correlations divided by the number of positive correlations equals 2 or more, we assumed the factor to be overall negatively correlated. ", "Otherwise, we supposed that no association existed. ", "For example, if a factor was described with a positive correlation in five publications and with a negative correlation in 12 publications, an overall negative correlation was assumed as 12/5 ≥ 2. ", "This calculation procedure was performed for each extracted environmental factor.", "\n\nDetermining the variables from the geocoding services {#Sec6}\n-----------------------------------------------------\n\nWe checked environmental factors identified within the literature search regarding mapping possibilities with variables from Google Maps and OSM. ", "Google Maps data, among other sources, are derived from official registries, e.g. from the Agency for Digitisation, High-Speed Internet and Surveying in Bavaria \\[[@CR26], [@CR27]\\]. ", "OpenStreetMap, in contrast, is based on volunteered geographical information (VGI), i.e. it is based on user-generated content \\[[@CR28]\\]. ", "We have chosen both geocoding services because their data were freely available at low cost. ", "Furthermore, their accuracy has been investigated for Germany in the past. ", "Apparently, Google Maps showed higher completeness and higher precision of coordinates than OSM \\[[@CR17]\\]. ", "Besides environmental obesogenic factors, additional variables concerning the regional healthcare structure were taken into account. ", "Four researchers in our team independently rated the relevance of the variables from the geocoding services with respect to the results of the literature search. ", "After discussion, the variables best operationalizing the identified factors from the literature were determined and downloaded from Google Maps and OSM. ", "We focused our analysis on single points of interest (POIs). ", "Therefore, complex variable constructs, such as 'neighbourhood walkability' and 'land use mix', were not considered, as these compound measures are based e.g. on residential density or numbers of developed hectares which cannot be directly derived from online geocoding services. ", "For an overview on the composites of these variables see Feng et al. ", "\\[[@CR29]\\]. ", "Furthermore, six broader categories, 'food', 'doctor', 'sport', 'education', 'transport' and 'other', were determined via expert discussions within our team, and each operationalized variable, for which POIs were returned by at least one geocoding service, was assigned to one of those categories. ", "Based on this approach, it was possible to visualize the distribution of environmental factors on a higher aggregated level and improve interpretability of the field validation results.", "\n\nChoosing locations for the validation process {#Sec7}\n---------------------------------------------\n\nWe have chosen four pilot areas in the German federal state of Bavaria for the validation process. ", "Our aim was to investigate the data quality of the geocoding services within regions of different population density and urbanization level. ", "Size and population count of each area were derived from the German Federal Statistical Office and the statistical offices of the German Länder (federal states) \\[[@CR30]\\]. ", "The first region was a sparsely populated municipality in the south-west of Bavaria with fewer than 2000 inhabitants encompassing an area of about 36.31 km^2^. This area constituted a rural region containing few amenities (Area A). ", "The second area was a street in a medium-sized major district town near Munich, the capital of Bavaria, with fewer than 45,000 inhabitants and a size of around 34.96 km^2^ (Area B). ", "Finally, the densely populated city of Munich (about 1.5 million inhabitants, total area 310.71 km^2^) was selected for the validation. ", "From the whole city of Munich, both a denser area close to the city centre and an area with a relatively lower density of amenities was chosen (Areas C and D).", "\n\nDatabase extraction and processing of data {#Sec8}\n------------------------------------------\n\nGoogle Maps data were downloaded using queries in uniform resource locator (URL) format targeting the Google Places API. ", "Furthermore, OSM queries were performed using a web interface and an OSM-based R package. ", "The geographical database returns data in JavaScript Object Notation (JSON), GeoJSON or osmar ('OpenStreetMap and R') format, which are standard representations for geographical data. ", "Based on the structure of these data formats, information for each of the single POIs can be accessed efficiently via a hierarchical structure and subsequently processed. ", "For the Google Maps results, each entry had to be queried again in order to get additional relevant information, e.g. on names, addresses and categorizations. ", "Using the downloaded OSM data, additional information could be extracted directly from the previously described data formats without any additional query. ", "An overview of the data formats and query possibilities is shown in Fig.", " [2](#Fig2){ref-type=\"fig\"}. ", "The return of the spatial databases was checked regarding consistency and plausibility. ", "Important examinations were identifying POIs that were counted twice or more because of being listed within different categories and checking whether the return of the database lies completely within the pre-specified search area. ", "Additionally, spatial POIs were visualized on maps in order to check coherence. ", "The geographical data points were marked according to their factor category, and the search area was also plotted. ", "An example of visualization of some factors for Area D can be found in Fig.", " [3](#Fig3){ref-type=\"fig\"} for OSM. ", "The underlying code and the other codes regarding Area D are available on github \\[<https://github.com/MAPraeger/GOcode>. ", "Accessed 23 April 2019\\].Fig.", " 2Overview on the data and query structure. *", "JSON* JavaScript Object Notation, *API* application programming interface, *POI* point of interest Fig.", " 3Example of visualization of OpenStreetMap data points (Area D)\n\nSearch area and download capacity {#Sec9}\n---------------------------------\n\nThe shape of the downloaded regions was predefined by the geocoding services. ", "OSM areas were rectangular, whereas Google Maps areas were circular. ", "In order to make the shapes of OSM and Google Maps queries more comparable, we defined OSM search regions as quadratic. ", "Further differences between the geocoding services affected the maximum downloadable data size. ", "At the time of data download in 2017, Google Maps allowed up to 200 results per query and 1000 queries per day per person at zero costs \\[[@CR31]\\], whereas OSM had fewer restrictions \\[[@CR32]\\]. ", "Depending on the API and the download tools used, areas of arbitrary size, whole so-called 'planet files' \\[[@CR33]\\] or nearly arbitrary data sizes caused by memory overload within the statistical software, could be downloaded. ", "Therefore, areas for the validation process were determined such that none of the above-mentioned restrictions took effect. ", "Owing to the lower number of spatial POIs within the rural region (Area A), a wider area containing the whole municipality was chosen compared with the more urban areas (Areas B--D), for which the diameters of the circles and the edges of the squares were set to 200 metres.", "\n\nValidation process {#Sec10}\n------------------\n\nFour researchers in our team locally scanned the predefined validation areas looking for the existence of the downloaded POIs of Google Maps and OSM. ", "We designed a template to standardize the recording process and used maps containing the data points to improve efficiency. ", "The number of returned POIs of a database was called 'hits'. ", "Each researcher documented the validation date, confirmation (true positive hit) or rejection (false positive hit) of existence of the POIs and new record of false negatives, i.e. data points discovered in the field that were not covered by Google Maps or OSM or both. ", "After completion, the templates were digitalized.", "\n\nIf uncertainties regarding the existence of a POI were present during validation in the field, the researchers recorded their comments. ", "If these notes indicated restrictions, e.g. regarding access to certain facilities during in-field validations, several online search engines were used to resolve these uncertainties. ", "Further examples were incorrect categorization or implausible numbers of false positives at a certain place. ", "To overcome these issues, we visited the home pages of the affected amenities and considered business directories (yellow pages).", "\n\nCommon summary statistics for the validation of geographical data points were calculated. ", "For the quality assessment of the performance of a geocoding service for a given area, sensitivities, i.e. true positives divided by the sum of true positives and false negatives, and positive predictive values (PPVs), i.e. true positives divided by the sum of true positives and false positives, were calculated \\[[@CR34], [@CR35]\\].", "\n\nSoftware {#Sec11}\n--------\n\nWe used the free software environment R, version 3.3.2, to implement code targeting the Google Places API via embedded URL query and for processing of the query results \\[[@CR36]\\]. ", "In order to download data from OSM, we applied an online tool for data filtering (Overpass Turbo) and the R package 'osmar' \\[[@CR37], [@CR38]\\]. ", "For data processing, we used the packages 'geojsonR', 'jsonlite' and 'rgdal' and, for data visualization, the R packages 'ggmap' and 'ggplot2' \\[[@CR39]--[@CR43]\\].", "\n\nResults {#Sec12}\n=======\n\nLiterature search {#Sec13}\n-----------------\n\nAn extensive list of environmental factors and the corresponding references (N = 256) can be found within Additional file [1](#MOESM1){ref-type=\"media\"}: Table S1. ", "The table contains the numbers of studies describing positive correlations, negative correlations and studies without significant associations for a given environmental factor. ", "According to the definition of correlation within the methods section, overall positive correlations with weight status were discovered for the variables 'fast food', 'food retail', 'unhealthy food outlets', 'convenience store', 'rural areas', 'urban sprawl', 'county sprawl', 'traffic', 'transport' and 'poverty'. ", "Overall negative correlations were found for the variables '(healthy) food outlets', 'restaurants', 'supermarkets', 'tree cover', 'fitness or physical activity facilities', 'forests', 'greenspace', 'longer way to school', 'open space', 'outdoor recreation', 'park', 'recreation centre', 'walkability', 'aesthetics', 'intersection density', 'land use mix', 'population density', 'safety', 'sidewalk completeness', 'street connectivity', 'education' and 'physician supply'.", "\n\nChosen variables from Google Maps and OSM {#Sec14}\n-----------------------------------------\n\nTables [1](#Tab1){ref-type=\"table\"} and [2](#Tab2){ref-type=\"table\"} show the factors from Google Maps (N = 25 in total) and OSM (N = 126 in total) chosen for the validation process. ", "Owing to the extent of the OSM variable pool, the relevant factors in the category 'amenity' are shown within Table [2](#Tab2){ref-type=\"table\"} (N = 42). ", "The full list of OSM variables is shown in Additional file [2](#MOESM2){ref-type=\"media\"}: Table S2. ", "Table 1Selected variables from the Google Maps poolBakeryBarBus stationCafeConvenience storeDentistDoctorFoodGrocery or supermarketGymHospitalMeal deliveryMeal takeawayParkPharmacyPhysiotherapistRestaurantSchoolSpaStadiumSubway stationTaxi standTrain stationTransit stationUniversity Table 2Selected OpenStreetMap (OSM) variables in the category 'amenity'BarBbqBiergartenCafeFast foodFood courtIce creamPubRestaurantCollegeSchoolBicycle parkingBicycle rentalBoat sharingBus stationTaxiClinicDentistDoctorsHospitalNursing homePharmacyDive centreDojoRanger stationBeach resortDanceFishingFitness centreGardenGolf courseIce rinkNature reserveParkPitchPlaygroundSports centreStadiumSwimming areaSwimming poolTrackWater park\n\nDistribution of database results across categories {#Sec15}\n--------------------------------------------------\n\nBar charts are shown for Google Maps (Fig.", " [4](#Fig4){ref-type=\"fig\"}) and OSM (Fig.", " [5](#Fig5){ref-type=\"fig\"}) in order to visualize the distribution of the database hits, i.e. the distribution of the sum of true-positive and false-positive entries of the geocoding services, across the six categories of 'doctor', 'education', 'food', 'sport', 'transport' and 'other' for the validation areas. ", "Within the medium-sized populated Area B and the densely populated Area C, predominantly entries in the categories 'doctor' and 'food' account for most of the database hits in Google Maps. ", "For the remaining areas, using Google Maps, 'food' was the most relevant category. ", "Regarding OSM, the category 'food' was the most frequent category within Areas C and D of the city of Munich.", "Fig.", " 4Distribution of hits across variable categories using Google Maps. ", "Area A: sparsely populated municipality in the south-west of Bavaria. ", "Area B: street in a medium-sized populated major district town near Munich. ", "Area C: area close to the centre within the densely populated city of Munich. ", "Area D: area with a lower density of amenities within the densely populated city of Munich Fig.", " 5Distribution of hits across variable categories using OpenStreetMap. ", "Area A: sparsely populated municipality in the south-west of Bavaria. ", "Area B: street in a medium-sized populated major district town near Munich. ", "Area C: area close to the centre within the densely populated city of Munich. ", "Area D: area with a lower density of amenities within the densely populated city of Munich\n\nValidations {#Sec16}\n-----------\n\nTables [3](#Tab3){ref-type=\"table\"} and [4](#Tab4){ref-type=\"table\"} show the numbers of true positives and false positives, PPVs, numbers of false negatives and sensitivity values for each validation area. ", "As shown in the table, absolute numbers of true hits were higher for Google Maps than the corresponding numbers for OSM, irrespective of the validation area under consideration. ", "Furthermore, false positives were also higher for Google Maps compared with OSM. ", "The PPVs of OSM hits, ranging between 81 and 100%, were higher than the PPVs of Google Maps hits, which were found to be between 65 and 89%. ", "In contrast, sensitivities were higher in Google Maps (between 59 and 98%) than in OSM (between 20 and 64%). ", "False negatives were higher for OSM within three of the four validation areas. ", "An overall comparison between the four areas showed that Area C within the city of Munich had the highest numbers of false negatives for both geocoding services. ", "For OSM, high numbers of false negatives were also discovered for Area B, i.e. for the major district town. ", "Predominantly during the validation within Area C, it became evident that the data quality regarding the variable category 'doctor' had a fundamental influence on the validation results. ", "Therefore, we recalculated Table [3](#Tab3){ref-type=\"table\"} without the POIs belonging to this category. ", "The results of this recalculation process can be found within Table [4](#Tab4){ref-type=\"table\"}. ", "Having omitted the category 'doctor', sensitivities of OSM improved for Area B and Area C. Within Area D, sensitivities of OSM were higher than sensitivities of Google Maps.", "Table 3Results of the field validationAreaGeocoding serviceTrue positives: N (% positive)^a^False positives: N (% positive)False negatives: NSensitivity^b^: %AGoogle Maps19 (63.33)11 (36.67)1359.38AOpenStreetMap15 (88.24)2 (11.76)1746.88BGoogle Maps58 (89.23)7 (10.77)198.31BOpenStreetMap12 (100)0 (0)4720.34CGoogle Maps144 (71.64)57 (28.36)6369.57COpenStreetMap41 (87.23)6 (12.77)16619.81DGoogle Maps22 (64.71)12 (35.29)1166.67DOpenStreetMap21 (80.77)5 (19.23)1263.64Area A: sparsely populated municipality in the south-west of BavariaArea B: area in a medium-sized populated major district town near MunichArea C: area close to the centre within the densely populated city of MunichArea D: area with a lower density of amenities within the densely populated city of Munich^a^The percentage of true positives is the positive predictive value (PPV) \\[PPV = true positives/(true positives + false positives)\\]^b^Sensitivity = true positives/(true positives + false negatives) Table 4Results of the field validation without the category 'doctor'AreaGeocoding serviceTrue positives: N (% positive)^a^False positives: N (% positive)False negatives: NSensitivity^b^: %AGoogle Maps18 (62.07)11 (37.93)1358.06AOpenStreetMap15 (88.24)2 (11.76)1648.39BGoogle Maps29 (90.63)3 (9.38)196.67BOpenStreetMap10 (100)0 (0)2033.33CGoogle Maps48 (69.57)21 (30.43)3061.54COpenStreetMap36 (85.71)6 (14.29)4246.15DGoogle Maps19 (67.86)9 (32.14)676.00DOpenStreetMap21 (80.77)5 (19.23)484.00Area A: sparsely populated municipality in the south-west of BavariaArea B: area in a medium-sized populated major district town near MunichArea C: area close to the centre within the densely populated city of MunichArea D: area with a lower density of amenities within the densely populated city of Munich^a^The percentage of true positives is the positive predictive value (PPV) \\[PPV = true positives/(true positives + false positives)\\]^b^Sensitivity = true positives/(true positives + false negatives)\n\nDiscussion {#Sec17}\n==========\n\nThe aim of our study was to examine the feasibility of integrating information from online geocoding services for the assessment of environmental obesogenic factors that could potentially be used for diabetes surveillance. ", "First, we identified variables correlated with obesogenic environments from the literature. ", "Subsequently, we tested whether these variables could be reproduced using data from the online geocoding services Google Maps and OpenStreetMap (OSM). ", "The results showed that this was possible given some restrictions, predominantly the diversity of the variable pools of the geocoding services and the complexity of the environmental factor to be projected. ", "Maps created from the obesogenic and from protective data showed the geographical distribution of the environmental factors and were used within subsequent field validations. ", "On the one hand, Google Maps showed greater completeness, i.e. lower proportion of false negatives, regarding POIs subsequently discovered in the field and the additional information assigned to them. ", "Furthermore, the sensitivity of Google Maps was higher than the sensitivity of OSM. ", "On the other hand, a higher PPV was seen for OSM in each of the validation areas.", "\n\nRecently, the validity of the geocoding service Google Maps was tested using geoprocessing information \\[[@CR18]\\]. ", "Instead of using single geographical data points from the spatial databases of Google Maps and OSM, the authors compared virtual audit via Google Street View. ", "Additionally, local field inspections were performed as the gold standard. ", "It was shown that the validity and reliability of using Google Maps for the assessment of the built environment was high (Kappa of 78% and 80% respectively). ", "Considering the German context, field inspections concerning the obesogenic environment have been performed in the past in order to record POIs \\[[@CR44]\\]. ", "Therefore, it was an important step within our study to inspect the database results of Google Maps and OSM locally.", "\n\nPPVs of Google Maps and OSM found during our validation process were compared with each other. ", "It became evident that the PPV of OSM was higher than the PPV for Google Maps in each region, because Google Maps showed considerably more false positives. ", "Considering sensitivity, OSM showed lower values than Google Maps. ", "Most influential variables regarding these comparisons were found within the category 'doctor'. ", "The data quality regarding physicians was better for Google Maps compared to OSM. ", "Therefore, within areas with a higher share of doctors (Area B and Area C) the differences in sensitivities between Google Maps and OSM were large. ", "Deleting the category 'doctor' from the analysis thus moderated this difference. ", "False positives of Google Maps within the densely populated Area C were also mainly caused by the category 'doctor'. ", "The same category also contributed to the number of false negatives in OSM within this area and the sensitivity of OSM improved considerably after omitting POIs belonging to this category (see Table [4](#Tab4){ref-type=\"table\"}). ", "To highlight the different influences of certain variable groups, it was an important step in our validation process to look for suitable stratification structures, such as the six categories 'doctor', 'food', 'sport', 'transport', 'education' and 'other'.", "\n\nIn our study, we calculated the sensitivities and PPVs of Google Maps and OSM hits. ", "They can be compared with the PPVs of other POI databases that we found in the existing literature. ", "For example, Clary and colleagues \\[[@CR34]\\] validated a Canadian food outlet database in the field. ", "Comparing their database results with the actual occurrences in the field, the authors found sensitivities between 54.5 and 65.5% as well as PPVs between 64.4 and 77.3%. ", "Within our study, the PPV for OSM was markedly higher (between 81 and 100%), whereas Google Maps had a more similar PPV compared with the Canadian database (between 63 and 89%). ", "Regarding sensitivity, OSM showed lower values within three of the four validation areas (between 20 and 64%), whereas Google Maps sensitivities were at least comparable (between 59 and 98%) with the food outlet database.", "\n\nTo evaluate features of the obesogenic environment, Bethlehem and colleagues \\[[@CR14]\\] performed a virtual audit based on Google Earth (GE) and Google Street View (GSV). ", "They assessed the aspects walking, cycling, public transport, aesthetics, land use mix, grocery stores, food outlets and recreational facilities using observers. ", "Virtual audit was found to be a valid and reliable approach. ", "Within our study, we used Google Maps and OSM APIs for the programmed download of POIs, which does not need individual assessment for data collection.", "\n\nWithin our analyses, it also became evident that new variable entries appear more frequently, but old entries were deleted with time lag within the Google Maps database. ", "The more specific variables in the OSM pool made it possible to identify some POIs that could not be precisely queried by Google. ", "For example, OSM made it possible to extract 'fast food' instead of the broader category 'food'. ", "This feature nevertheless required taking into account all relevant specific factors describing a variable at a higher level in order to exhaust the OSM database completely.", "\n\nStrengths and limitations {#Sec18}\n-------------------------\n\nOur study is based on an extensive literature search extracting factors of obesogenic environments. ", "We used freely available data from global geocoding services Google Maps and OSM and applied various methods for downloading and processing geographical data using new query codes in the R programming environment. ", "Finally, we validated our results with in-field inspections. ", "To evaluate both physical activity and food-related environmental factors, composite approaches are required, which have been performed rather infrequently in the past \\[[@CR12]\\]. ", "Within our approach, we combined the food environment and the physical activity environment into a single layer containing POIs of the obesogenic factors and POIs of the protective factors.", "\n\nSome limitations of our study have to be mentioned. ", "First, it is focused on evidence from the literature based on an energy imbalance model \\[[@CR45]\\]. ", "However, according to the recent literature, other etiological causes for the development of obesity have to be considered to fully understand the underlying mechanisms, e.g. the carbohydrate-insulin model of obesity (beyond 'calories in, calories out') \\[[@CR46]\\] or dietary behaviour ('ultra-processed food vs unprocessed food') \\[[@CR47]\\]. ", "Second, the literature search had a broad scope by updating and complementing a systematic review; however, a large number of the identified studies originated from the US. ", "Structural differences regarding the built environment in US and European cities may influence direct transferability to the European context. ", "For example, cities in the US are much more car dependent than European cities, which results in expected different health effects of environmental factors associated with physical activity \\[[@CR48]\\]. ", "Furthermore, instead of unhealthy corner stores in the US, in European countries, healthy stores selling fresh fruit and vegetables exist more often and are more evenly distributed across the cities \\[[@CR49]\\]. ", "A third drawback regarding our literature search could be publication bias, which would influence the assessment of the overall correlation of an environmental factor \\[[@CR50], [@CR51]\\]. ", "Fourth, a significant proportion of the environmental factors was not correlated with obesity in the same direction across studies. ", "Given this restriction, we have summarized the correlations found in the literature based on expert decision. ", "Fifth, the precision and feasibility of variable extraction fundamentally depend on the variable pool structure of the geocoding service. ", "Differences in the definition of a variable across geocoding services hamper direct comparisons of variables. ", "Within our study, we found that the variable pool of OSM contains many more variables than Google Maps for a large number of environmental factors. ", "Finding broader categories for environmental factors within our analysis made it easier to compare variables across geocoding services. ", "Sixth, our study was limited to a German environment; therefore, generalization of our findings needs further assessment in other countries. ", "Seventh, we have downloaded spatial POIs at a certain point in time; thus, we cannot make inferences on time effects. ", "However, this cross-section offers an important starting point for future analyses. ", "Eighth, each geographical area was validated by a different researcher; therefore, interobserver variability could have appeared during validation. ", "In order to counteract this kind of bias, prior instructions were defined as precisely as possible, and discussions between the observers took place both before and after the validations. ", "Finally, some restrictions regarding access to certain facilities appeared during validations in the field, mostly concerning database hits of the category 'doctor'. ", "Results of the validation process without this category are shown in Table [4](#Tab4){ref-type=\"table\"}. ", "Within the analysis including the category 'doctor', this generated some uncertainties; therefore, we used the best available evidence, i.e. the home pages of these amenities and business directories (yellow pages). ", "However, these uncertainties occurred only in a small number of cases and were discussed in detail during processing of the validation results.", "\n\nThe aim of our study was to examine the feasibility of using data from online geocoding services for diabetes surveillance. ", "We were able to integrate information from these services by downloading, processing and visualizing their data on maps. ", "The reliability of these variables was assessed within field validations and by search engines. ", "Future examinations could test further types of variables from other research areas.", "\n\nConclusions {#Sec19}\n===========\n\nBased on an extensive literature search, environmental factors could be identified that are associated with obesity. ", "These factors could be partly operationalized through the variables and data available from the online geocoding services Google Maps and OSM. ", "Using APIs, spatial data points could be identified and subsequently visualized on maps. ", "Our findings showed that the validity of data from online geocoding services was reasonable. ", "Consequently, environmental obesogenic factors could be described with our methodology and potentially used within diabetes surveillance. ", "Further validation studies are needed to investigate the importance of environmental obesogenic factors.", "\n\nAdditional files\n================\n\n {#Sec20}\n\n**Additional file 1: Table S1.** ", "Factors determined by literature search. **", "Additional file 2: Table S2.** ", "Complete list of chosen OSM variables.", "\n\nAPI\n\n: application programming interface\n\nBMI\n\n: body mass index\n\nGE\n\n: Google Earth\n\nGIS\n\n: geographic information system\n\nGSV\n\n: Google Street View\n\nJSON\n\n: JavaScript Object Notation\n\nOSM\n\n: OpenStreetMap\n\nPOI\n\n: point of interest\n\nPPV\n\n: positive predictive value\n\nT2DM\n\n: type 2 diabetes mellitus\n\nURL\n\n: uniform resource locator\n\nVGI\n\n: volunteered geographical information\n\n**Publisher\\'s Note**\n\nSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.", "\n\nNot applicable.", "\n\nWM initiated the cooperation and supervised the project. ", "MP and JB were responsible for the literature search and extraction of environmental factors. ", "MP programmed the database queries, processed the data and visualized the results on maps. ", "CK provided statistical input. ", "ML and WM provided health scientific input. ", "MP, JB, CK and ML performed field validations. ", "MP wrote the manuscript. ", "All authors read previous versions of the manuscript, commented on and approved the final version of the manuscript for submission. ", "All authors read and approved the final manuscript.", "\n\nThe study was supported by the Federal Ministry of Health, Germany (FKZ: GE20160324) as part of the German Diabetes Surveillance Project conducted by the Robert Koch Institute, Berlin.", "\n\nThe data generated for this study were downloaded from Google Maps and OSM and the exemplary code is available on github \\[<https://github.com/MAPraeger/GOcode>. ", "Accessed 23 April 2019\\] as described in the methods section.", "\n\nNot applicable.", "\n\nNot applicable.", "\n\nThe authors declare that they have no competing interests.", "\n" ]

{ "pile_set_name": "PubMed Central" }

[ 0.012448132780082987, 0.008, 0.009259259259259259, 0.022900763358778626, 0, 0.011278195488721804, 0.010309278350515464, 0.005263157894736842, 0.01098901098901099, 0, 0.005714285714285714, 0.004901960784313725, 0.008658008658008658, 0.0045045045045045045, 0.025423728813559324, 0.018518518518518517, 0.00558659217877095, 0.003787878787878788, 0.014285714285714285, 0, 0.008, 0, 0, 0.010309278350515464, 0, 0.006289308176100629, 0, 0.009708737864077669, 0, 0.25, 0, 0, 0.012422360248447204, 0.011904761904761904, 0, 0.010638297872340425, 0, 0, 0.011235955056179775, 0.029850746268656716, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0037735849056603774, 0.01639344262295082, 0.014285714285714285, 0, 0, 0.027522935779816515, 0, 0, 0.006493506493506494, 0, 0, 0.014492753623188406, 0.07692307692307693, 0, 0, 0, 0, 0.011494252873563218, 0, 0, 0, 0, 0, 0.022222222222222223, 0.010869565217391304, 0, 0, 0.0064516129032258064, 0.013888888888888888, 0, 0, 0, 0, 0, 0.013333333333333334, 0.02702702702702703, 0.00819672131147541, 0, 0, 0.019417475728155338, 0, 0.014492753623188406, 0.016666666666666666, 0, 0.015228426395939087, 0.008733624454148471, 0, 0, 0.01, 0, 0, 0.0037174721189591076, 0, 0.007246376811594203, 0, 0, 0, 0, 0.005988023952095809, 0.0047169811320754715, 0.0273972602739726, 0.012195121951219513, 0, 0, 0, 0, 0.007168458781362007, 0.0064516129032258064, 0.009900990099009901, 0.004571428571428572, 0.047619047619047616, 0, 0, 0, 0.009174311926605505, 0.25, 0, 0, 0, 0, 0.010526315789473684, 0, 0, 0, 0, 0, 0.0056179775280898875, 0.012345679012345678, 0.014184397163120567, 0.009174311926605505, 0.012658227848101266, 0, 0.009259259259259259, 0.0053475935828877, 0, 0, 0.017341040462427744, 0.0013452914798206279, 0, 0.006622516556291391, 0, 0, 0, 0.011904761904761904, 0.024691358024691357, 0.00847457627118644, 0.012578616352201259, 0, 0, 0.006369426751592357, 0.008620689655172414, 0.020618556701030927, 0.00641025641025641, 0.014925373134328358, 0, 0.012195121951219513, 0.013513513513513514, 0, 0, 0.013043478260869565, 0, 0.011627906976744186, 0.01, 0.00980392156862745, 0, 0.016853932584269662, 0.004524886877828055, 0.022988505747126436, 0, 0, 0.006666666666666667, 0, 0.015384615384615385, 0.010309278350515464, 0.005780346820809248, 0, 0.004672897196261682, 0, 0.0055248618784530384, 0, 0, 0.009900990099009901, 0.005797101449275362, 0, 0, 0.0049261083743842365, 0.0047169811320754715, 0.010582010582010581, 0, 0, 0, 0, 0.006756756756756757, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.006993006993006993, 0, 0, 0, 0, 0, 0, 0, 0.02631578947368421, 0.0072992700729927005, 0, 0, 0, 0, 0.03225806451612903, 0.045454545454545456, 0.0425531914893617, 0, 0, 0, 0.016129032258064516, 0.012195121951219513, 0, 0, 0, 0, 0 ]

[ "In my business, many times the customers forget the appointments, which results in loses for me. ", "Is there a web service that can help me organize my appointments and it notifies my customers (maybe 2 ...\n\nI'm creating an hostable start page in the spirit of Opera Web Dial, as example. ", "For this service, I would like to show site logo (and NOT favicon, for which i already have a posisble implementation).", "\n...\n\nI currently am using a macro-enabled Excel sheet that gives me an output based on several input fields with client specific information. ", "I want to automate the process of entering the input values, by ...\n\nSeveral days ago somebody steal my account (from mail.ru), after that they are steal my premium EA account and several accounts for different MMORPG. ", "fortunately I restore access to all accounts, but ...\n\nFeedler and Mobile RSS have served me well in browsing my RSS subscription content that I added in Google Reader. ", "What API are these apps using to get the list of subscriptions?", "\nI want to create my ...\n\nIs there any web service that provides something to make phone calls?", "\nLet say I want to build one site where people can make phonepranks. ", "I enter the number of my friend and when I submit the form, ...\n\nI am looking for a web application that will store project metadata. ", "I work on a wide variety of different projects (software, product demo videos, websites, etc) and am looking for a system with a ...\n\nIt's my first question, so sorry if something is not right.", "\nPlease, suggest sites or programs that allow the user to save a web page. ", "It does not matter on the Internet or on user's computer, or it is ...\n\nI wanted try Amazon SNS, so I clicked the Sign Up button on its tab on the managament console. ", "Amazon approved my signup and in my account under \"Services You're Signed Up For\" I see almost all Amazon ...\n\nI know Google Trends/Zeitgeist. ", "But what I'm looking for is a service where you can enter, for example \"Politics\", and then the service gives out the most popular queries containing \"Politics\"-keyword ...\n\nIs there an app that some way can track the times I go to sleep and more importantly log the times at which I (assumably) awake every day?", "\nFor instance, install a small script to Ubuntu or a webapp ...\n\nLarger context: we're working on an Intranet portal's search engine, which needs to be able to search within ALL office types: .doc, .docx, .xls, .xlsx, .ppt, and .pptx. ", "Having the search also already ...\n\nI'm looking for a reliable (paid) service which snaps screenshots from sites and delivers the images. ", "I know that there's quite a few out there, but the quality seems to vary wildly and the sites seem ..." ]

{ "pile_set_name": "Pile-CC" }

[ 0, 0.005291005291005291, 0, 0, 0.0045662100456621, 0.01775147928994083, 0.015873015873015872, 0, 0, 0, 0, 0, 0.005988023952095809, 0.013986013986013986, 0.003205128205128205, 0, 0, 0 ]

[ "The present invention relates to a system and method for determining the time interval (\"dead time\") between adjustment of a parameter in a process and detection of the effect of such adjustment on the product of the process. ", "The present invention also relates to control of a process using a dead time compensated control loop.", "\nIn a typical manufacturing process, there may be a number of actuators at a particular processing station which can be utilized to vary process parameters, such as temperature, pressure, flow rate, etc., ", "to thereby effect changes in the process. ", "In addition, in some processes, there are also a number of sensors which are used to detect the effects of varying the process parameters on the resulting product. ", "Some of these processes make use of feed-back signals from the sensors to control the actuators and thereby control the manufacturing process in accordance with particular process specifications.", "\nFIG. ", "1 shows a schematic arrangement of a simple product manufacturing process. ", "In the process, a particular product 6 is being processed by a processing station 4. ", "The product is carried by a conveyor belt 3 in a direction indicated by arrow 7 to a sensor 2. ", "The sensor 2 determines if the processing station 4 has processed the product 6 in a manner meeting a desired specification, e.g., a target weight or dimension. ", "The sensor 2 transmits feedback signals, corresponding to the sensed characteristic of the product 6, along line 8 to a controller 5. ", "If the controller 5 determines that the product 6 does not meet the desired specification, it outputs a control signal along line 9, to the processing station 4 so as to adjust one or more parameters such that products subsequently processed by the processing station 4 will meet the desired specification.", "\nIt can be seen from FIG. ", "1 that there is a time interval, T, between the change in parameter at the processing station 4 and the detection of such change by the sensor 2. ", "The interval T is present due to the physical characteristics of the system, i.e. in this example, the speed V of the conveyor belt 3 and the distance D between the processing station 4 and the sensor 2 (T=D/V). ", "This interval T represents the time between when the processing station 4 has processed the product 6 and when the sensor 2 can detect the effects of the processing station 4 on the product. ", "This time interval T is often referred to as \"dead time\". ", "The term \"dead\" is used instead of \"delay\" to describe the time interval T because the interval T is neither a delay in the response of the sensor 2 nor a delay in the response time of the processing station 4 or controller 5. ", "Rather, the dead time interval T is a waiting period during which the particular product 6 cannot be sensed by the sensor 2 during the movement of the product 6 from the processing station 4 to the sensor 2.", "\nIt has been found that for certain applications it is critical to be able to accurately determine the dead time T. In the process shown in FIG. ", "1, for example, assume that the controller 5 effects a change in the processing parameters of the processing station 4 at the time that the product 6 is under the station 4. ", "If the controller 5 reacts to signals from the sensor 2 after a time interval less than the actual dead time T since the change in the process parameter, then the process will be over-corrected. ", "This is because the feed-back signal from the sensor 2 would not correspond to the product 6 which was actually processed by the processing station 4 during the change in the process parameter. ", "Instead, the sensor would have detected a different product 6' which is in front of the product 6 on the conveyor belt 3. ", "Product 6' was, however, not affected by the change in the process parameter and therefore does not correspond to the current state of the process at the instant the sensor 2 detects product 6'. ", "As a result, the feed-back signal from the sensor 2 will erroneously indicate to the controller 5 that further corrections of the process parameter are required in order to make the subsequent products meet the desired specification. ", "Consequently, an additional, and possibly unnecessary correction of the process parameter is triggered by the controller 5, which will thus over-correct the process. ", "Such over-correction may result in oscillations in the control process.", "\nOn the other hand, if the controller 5 reacts to the feed-back signal from the sensor 2 at a time interval which is longer than the actual dead time T since the preceding change in the process parameter, the controller 5 would thus control the processing station based upon sensor feed-back signals which correspond to the physical characteristics of a product 6'\" that was processed by the processing station long after product 6 had been processed. ", "As a result, an unnecessarily large number of products 6\" may have passed from the processing station 4 to the sensor without the controller 5 making corrections to the processing characteristics of the processing station 4. ", "In the interim, the process parameter affected by the processing station 4 may have drifted out of the specification limits.", "\nReferring to FIG. ", "2, a previously known method of determining dead time in a paper manufacturing process will now be described. ", "In particular, FIG. ", "2 illustrates a system in a papermaking process for controlling the mass per unit area (\"basis weight\") of a sheet of paper 13. ", "Typically, in a papermaking process, a slurry of wood fibers and water is fed into a tank called a \"headbox\" 10, and the slurry then flows continuously through an opening 12 defined by the slice lip 16. ", "The slurry is deposited onto a continuous conveyor belt 14. ", "The conveyor belt 14 moves in a direction away from the headbox 10 as shown by arrow 15. ", "The slurry thus forms a continuous sheet 13 on the conveyor belt 14. ", "The sheet of paper slurry 13 drains some of its water content as it is being transported by the conveyor belt 14, and thereafter the sheet 13 is pressed by rollers 20 to remove additional moisture from the sheet 13. ", "The basis weight of the sheet 13 is then measured using the basis weight sensor 24.", "\nThe vertical position of the slice lip 16 is related to the size of the opening 12 and hence to the amount of slurry deposited on the conveyor belt and ultimately to the basis weight of the sheet 13. ", "The vertical position of the slice lip 16 is controlled by a plurality of actuators 18 which are connected to the slice lip 16 and to the headbox 10. ", "Information from the sensor 24 is transmitted to a controller 26 which in turn controls the actuators 18 to obtain the desired basis weight of the sheet 13.", "\nA previously known method of determining the dead time with respect to the slice lip 16 and the sensor 24 includes the steps of manually perturbing the control of the actuators 18 and determining the elapsed time from such a single perturbation before the effect of the perturbation on the basis weight can be detected by the sensor 24. ", "Specifically, the perturbation effects a sudden change in width of the opening 12 from its nominal width, thereby changing the basis weight of the sheet 13. ", "The local change in basis weight serves as a marker to be detected by the sensor 24 after dead time T. The magnitude of the perturbation is set to be substantially larger than the magnitude of the noise in the control signals 28 from the controller 26 to ensure that the sensor 24 is able to distinguish the marker, which is caused by the manual perturbation, from the variations in basis weight caused by noise in the control signals 28.", "\nThe above described method of determining dead time has a number of shortcomings. ", "Firstly, the method requires a relatively large local change in basis weight from the steady state basis weight to ensure that the marker can be clearly distinguished from the variations in basis weight caused by noise in the control signals. ", "As a result, considerable time may be required after the change for the process to regain a steady state.", "\nSecondly, the above described method destroys the uniformity of the finished product. ", "The presence of the marker sets the upper limit on the length of sheet that can be produced of uniform basis weight. ", "Moreover, when the sheet is cut to size for conversion into finished paper products, the local basis weight variation may be located in the middle of a cut portion. ", "Such portion has to be discarded, thus leading to waste. ", "Also, additional inspection steps are required to identify such marked portion in the finished product.", "\nAnother method previously used to determine dead time involves determining the speed of the sheet 13 by simply determining the speed of the rollers 20. ", "However, the dead time determined by this method is not reliable. ", "This is because there may be slippage between the rollers 20 and the paper sheet 13, which slippage may vary with time. ", "In addition, the sheet 13 changes length as it is stretched and/or pressed by the rollers 20. ", "The speed of the rollers 20 thus does not directly correspond to the speed of the sheet 13. ", "Consequently, dead time cannot be accurately determined by this method." ]

{ "pile_set_name": "USPTO Backgrounds" }

[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.038461538461538464, 0, 0, 0, 0, 0, 0, 0.006896551724137931, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.05263157894736842, 0, 0.05, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]

[ "##\n# This file is part of WhatWeb and may be subject to\n# redistribution and commercial restrictions. ", "Please see the WhatWeb\n# web site for more information on licensing and terms of use.", "\n# http://www.morningstarsecurity.com/research/whatweb\n##\n# Version 0.5 # 2011-05-14 # Brendan Coles <bcoles@gmail.com>\n# Changed @cookies to @headers[\"set-cookie\"] to support recursive mode\n##\n# Version 0.4 # 2011-04-08 # Brendan Coles <bcoles@gmail.com>\n# Added username and localfile path detection for cookies containing public_html\n##\n# Version 0.3 # 2011-01-30 # Brendan Coles <bcoles@gmail.com>\n# Fixed regex bug # Cookies were always split by \"=\" even when it wasn't present\n##\n# Version 0.2\n# removed :certainty=>100\n##\nPlugin.define \"Cookies\" do\nauthor \"Andrew Horton\"\nversion \"0.5\"\ndescription \"Display the names of cookies in the HTTP headers. ", "The values are not returned to save on space.\"", "\n\n# ShodanHQ results as at 2011-04-08 #\n# 2,527,334 for set-cookie\n# 37 for set-cookie path home public_html\n# 17 for set-cookie path=/home/ /public_html\n\n# Passive #\ndef passive\n\tm=[]\n\n\tunless @headers[\"set-cookie\"].nil? ", "or @headers[\"set-cookie\"].empty?", "\n\n\t\t# Extract cookie names\n\t\t@headers[\"set-cookie\"].split(\"\\n\").each do |cookie|\n\t\t\tm << { :string=>cookie.split(\"=\")[0] } if cookie =~ /=/\n\t\tend\n\n\t\t# Detect local file paths containing public_html\n\t\tif @headers[\"set-cookie\"].to_s =~ /path=\\/home[\\d]*\\/([^\\/]+)\\/public_html\\//\n\t\t\tm << { :account=>@headers[\"set-cookie\"].to_s.scan(/path=\\/home[\\d]*\\/([^\\/]+)\\/public_html\\//).flatten }\n\t\t\tm << { :filepath=>@headers[\"set-cookie\"].to_s.scan(/path=(\\/home[\\d]*\\/[^\\/]+\\/public_html\\/)/).flatten }\n\t\tend\n\n\tend\n\n\t# Return passive match\n\tm\nend\n\nend\n\n" ]

{ "pile_set_name": "Github" }

[ 0.00980392156862745, 0.011764705882352941, 0.01524390243902439, 0, 0.009009009009009009, 0.03125, 0.009174311926605505 ]

[ "Q:\n\nIs it good to have model mapping and more logics in a MVC controller?", "\n\nIm doing a .NET solution and i have to architect this. ", "So my architecture is like below.", "\n\nDLL(data logic layer) (Where i have all my repositories to access data)\nModels(In a schema wise)\nViewModels(Separately as class library )\nServices Layer (Where manipulate data and sends to controller)\n\nHere DLL will sent the data by accessing DB. ", "Then Service layer will use these Repositories (etc. ", "UserRepository) and manipulate the data as i want to send it to controller. ", "In this case controller will return the ViewModels to views.", "\nSo what i wanna know is, when mapping data to ViewModels ,Should my service layer do mappings and return ViewModels to Controller ??", "\nOR\nService Layer return as Models and in controller we do the mapping and create view models ?", "\nWhat i feels is it is not good to have so many operations in the controller. ", "So my service should return ViewModels ,So the controller have less work. ", "\nI would like to hear best practices and ideas ??", "\n\nA:\n\nI would do mapping in the controller. ", "Because there can be some instances we need to map the same service output to different view models. ", "Otherwise, we have to write multiple service methods for each view model type. ", "\nYou can simplify mapping by using AutoMapper.", "\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0.0136986301369863, 0, 0, 0.004016064257028112, 0.018867924528301886, 0, 0, 0.007518796992481203, 0, 0, 0, 0, 0, 0, 0, 0.021739130434782608, 0 ]

[ "Scientists at the National Aeronautics and Space Administration (NASA) — the US space agency — have apparently created a \"rogue\" Twitter account to tweet science facts in an effort to stick it to US President Donald Trump- a climate change denier under whose regime the White House has removed pages on the topic from its official website.", "\n\nAlso read: NASA is close to figuring out how to put space crews in cryostasis on long space journeys\n\nTrump has often been criticised for his stance on climate change, especially after he called climate change phenomenon a Chinese propaganda to hurt American business prospects. ", "Meanwhile, the US National Park Service (NPS) has been banned from tweeting after it posted some content that the Trump administration took offence to. ", "The NPS has since created an alternate Twitter account, to relay climate information.", "\n\n'Rogue NASA'\n\nThe alternate NASA account seems to serve the same purpose. ", "In its third tweet, the Twitter handle @RogueNASA, says: \"We cannot allow Mr. Trump to silence the scientific community. ", "We need peer-reviewed, evidence-based research MORE THAN EVER now. [", "sic]\"\n\nIt goes on to add: \"How sad is it that government employees have to create rogue Twitter accounts just to communicate FACTS to the American public?\" ", "It also says: \"If posting facts and news to Twitter from a rogue account is what we have to do for the next four years, count us in. #", "resist [sic]\"\n\nAdvocating science and climate change\n\nThe Rogue NASA Twitter account has gone on to post a number of other tweets, promoting science and slamming those who deny climate change. ", "One tweet says: \"Science deniers are dangerous. ", "The impact of climate change is real. ", "There are consequences for infrastructure and human life.\" ", "Another goes on to say: \"Advocating for climate science and environmental protection is the most pro-life you can be. ", "The future of the planet depends on it.\"", "\n\nThe last of the 26 tweets from the account so far — which have already gathered it more than a quarter of a million followers on the micro-blogging site — says: \"Science is not a partisan issue. ", "Science is the foundation of our society — we owe so much to peer-reviewed scientific research.\"" ]

{ "pile_set_name": "OpenWebText2" }

[ 0.011799410029498525, 0.0035587188612099642, 0.019736842105263157, 0.011764705882352941, 0.02631578947368421, 0.01652892561983471, 0.014705882352941176, 0.00641025641025641, 0, 0.0051813471502590676, 0, 0, 0, 0, 0, 0, 0 ]

[ "FROM ubuntu:xenial\nMAINTAINER Joel Martin <github@martintribe.org>\n\n##########################################################\n# General requirements for testing or common across many\n# implementations\n##########################################################\n\nRUN apt-get -y update\n\n# Required for running tests\nRUN apt-get -y install make python\n\n# Some typical implementation and test requirements\nRUN apt-get -y install curl libreadline-dev libedit-dev\n\nRUN mkdir -p /mal\nWORKDIR /mal\n\n##########################################################\n# Specific implementation requirements\n##########################################################\n\n# Java and maven\nRUN apt-get -y install openjdk-8-jdk\n#RUN apt-get -y install maven2\n#ENV MAVEN_OPTS -Duser.home=/mal\n\n# Scala\nRUN echo \"deb http://dl.bintray.com/sbt/debian /\" > /etc/apt/sources.list.d/sbt.list\nRUN apt-get -y update\n\nRUN apt-get -y --force-yes install sbt\nRUN apt-get -y install scala\nENV SBT_OPTS -Duser.home=/mal\n\n" ]

{ "pile_set_name": "Github" }

[ 0.006103763987792472 ]

[ "Karl Albert Buehr\n\nKarl Albert Buehr (1866–1952) was a painter born in Germany.", "\n\nBuehr was born in Feuerbach - near Stuttgart. ", "He was the son of Frederick Buehr and Henrietta Doh (Dohna?). ", " He moved to Chicago with his parents and siblings in the 1880s. ", " In Chicago, young Karl worked at various jobs until he was employed by a lithograph company near the Art Institute of Chicago. ", "Introduced to art at work, Karl paid regular visits to the Art Institute, where he found part-time employment, enabling him to enroll in night classes. ", "Later, working at the Institute as a night watchman, he had a unique opportunity to study the masters and actually posted sketchings that blended in favorably with student's work. ", "Having studied under John H. Vanderpoel, Buehr graduated with honors, while his work aroused such admiration that he was offered a teaching post there, which he maintained for many years thereafter. ", "He graduated from the Art Inst. ", "of Chicago and served in the IL Cav in the Spanish–American War. ", "Mary Hess became Karl's wife—she was a student of his and an accomplished artist in her own right. ", "In 1922, he was elected into the National Academy of Design as an Associate member.", "\n\nArt Studies in Europe\nIn 1904, Buehr received a bronze medal at the St. Louis Universal Exposition, then, in 1905, Buehr and his family moved to France, thanks to a wealthy Chicago patron, and they spent the following year in Taormina, Sicily, where the artist painted local subjects, executing both genre subjects and landscapes as well as time in Venice. ", "Buehr spent at least some time in Paris, where he worked with Raphaël Collin at the Académie Julian.", "\n\nGiverny and American Impressionism\nPrior to this time, Buehr had developed a quasi-impressionistic style, but after 1909, when he began spending summers near Monet in Giverny, his work became decidedly characteristic of that plein-air style but he began focusing on female subjects posed out-of-doors. ", "He remained for some time in Giverny, and here he became well-acquainted with other well known expatriate America impressionists such as Richard Miller, Theodore Earl Butler, Frederick Frieseke, and Lawton Parker. ", "It seems likely that Buehr met Monet, since his own daughter Kathleen and Monet’s granddaughter, Lili Butler, were playmates, according to George Buehr, the painter’s son. ", "His other daughter Lydia died before adulthood due to diabetes. ", "He returned to Chicago at the onset of World War I and taught at The Art Inst for many years. ", "One of his noted pupils at the Art Institute was Archibald Motley, Jr. the famous African American \"Harlem\" Renaissance painters. ", "Motley credits Buehr with being one of his finest teachers and one who encouraged his style.", "\n\nTeaching Career in Chicago\nBuehr remained an expressive colorist, but broadened his brushwork somewhat in later years when impressionism waned. ", "Back in America, he was immediately successful. ", "He won a silver medal at the Panama-Pacific International Exposition in San Francisco and the Purchase Prize of the Chicago Municipal Art Commission in the following year. ", "So famed was Buehr that had a one-man exhibition at the Century of Progress Fair in Chicago in 1934.", "\n\nAfter a long and exceedingly productive career, Karl Buehr died in Chicago at the age of eighty-six.", "\n\nWalter Buehr\nHis nephew Walter Buehr was the author and illustrator of many children's books. ", " Walter Franklin Buehr May 14, 1897 - January 2, 1971\nWalter Buehr was born in Chicago on May 14, 1897. ", "After high school he attended several different art schools including the Art Students League of New York (where he later taught), the Detroit School of Design, the Philadelphia School of Industrial Arts, the Art Students League, and he also studied art in Europe.", "\nHe began a first sergeant in the first camouflage section of the U.S. Army Engineers during World War I and was awarded the active service medal.", "\nHe married Camilla Goodwyn, a portrait artist and fashion illustrator, in 1938. ", "The two had three daughters, and at least five grandchildren. ", "Two of his grandchildren lived in France & couldn't speak English, which made it very hard on a grandfather who spoke very little French!", "\nBuehr had varied talents and interests. ", "He designed furniture, was interested in ceramics, like to tinker with high fidelity systems, and loved sailing. ", "He even lived on his boat during the summers and cruised both the Atlantic coast and the Mediterranean. ", "This hobby led to the writing of his first book - Ships and Life Afloat. ", "He wanted children in the Midwest to be able to understand the terms used in stories about the sea, how the ships were rigged, how they operated, what the life of a sailor was like, etc.", "\nHis over fifty-six books, including four for adults, reflect his wide variety of interests, including sailing and the sea, medieval history, exploration, transportation, electricity, and more. ", "His history books dealt with romantic eras full of knights, castles, galleys, and galleons. (", "This should be moved to its own entry if he is notable enough.)", "\n\nNotable Works include but are not limited to:\n1812: The War and the World, 1967 - TruthQuest \nAutomobiles, Past and Present, 1968 \nBirth of a Liner, 1961 \nBread, the Staff of Life, 1959 \nCargoes in the Sky, 1958 \nChivalry and the Mailed Knight, 1963 - TruthQuest \nCloth, from Fiber to Fabric, 1965 \nThe Crusades, 1959 - TruthQuest \nFamous Small Boat Voyages, 1967 \nFirearms, 1967 \nFirst Book of Machines, 1962 \nFood, From Farm to Home, 1970 \nFreight Trains of the Sky, 1969 \nFrench Explorers in America, 1961 - TruthQuest \nGalleys and Galleons, 1964 - TruthQuest \nGenie and the Word: Electricity and Communication, 1959 \nHarbors and Cargoes, 1955 \nHarvest of the Sea, 1955 - TruthQuest \nHeraldry: The Story of Armorial Bearing, 1964 - TruthQuest \nHome Sweet Home in the Nineteenth Century, 1965 \nKeeping Time, 1960 \nKnights and Castles and Feudal Life, 1957 - TruthQuest \nMagic of Paper, 1966 \nMarvel of Glass, 1963 \nMeat, From Ranch to Table, 1956 \nOil, Today’s Black Magic, 1957 \nPlastics, The Man-made Miracle, 1967 \nThe Portuguese Explorers, 1966 - TruthQuest \nRailroads, Today and Yesterday, 1958 \nRubber, Natural and Synthetic, 1964 \nSalt, Sugar, and Spice, 1969 \nSea Monsters, 1966 \nSending the Word, The Story of Communication, 1959 \nShips and Life Afloat: From Galley to Turbine, 1953 \nShips of the Great Lakes, 1956 \nThe Spanish Armada, 1962 - TruthQuest \nThe Spanish Conquistadores in North America, 1962 - TruthQuest \nStorm Warning, 1972 \nThe Story of Locks, 1953 \nStory of the Wheel, 1960 \nStrange Craft, 1963 \nThrough the Locks: Canals Today and Yesterday, 1954 \nTimber! ", "Farming Our Forests, 1960 \nTreasure: The Story of Money and Its Safeguarding, 1955 \nTrucks and Trucking, 1957 \nUnderground Riches, The Story of Mining, 1958 \nThe Viking Explorers, 1968 - TruthQuest \nVolcano!, ", "1962 \nWarriors Weapons (adult), 1963 \nWater, Our Vital Need, 1967 \nWestward with American Explorers, 1963 - TruthQuest \nWhen Towns Had Walls, Life in a Medieval English Town, 1970 \nWonder Worker, The Story of Electricity, 1961 \nWorld Beneath the Waves, 1964 \nThe World of Marco Polo, 1961 - TruthQuest \nBooks Illustrated by Walter Buehr: \nAdventures on the Cloud 9, by Adelaide Field \nThe First Book of the Ocean, by Sam & Beryl Epstein \nMary, Queen of Scots, by Emily Hahn (Landmark series) - TruthQuest \nMoon Base, by William Nephew\n\nSee also\nDecorative Impressionism\nFrench Impressionism\nAmerican Impressionism\nCalifornia Plein-Air Painting\nRichard E. Miller\nTheodore Lukits\nChristian von Schenidau\nList of German painters\n\nExternal links\n Buehr family papers at the Smithsonian Archives of American Art\nCatalog Karl Albert Buehr, Richard Norton Gallery, LLC, 2002.", "\nhttp://richardnortongallery.com/artists/karl-albert-buehr\n\nCategory:1866 births\nCategory:1952 deaths\nCategory:19th-century German painters\nCategory:German male painters\nCategory:20th-century German painters\nCategory:School of the Art Institute of Chicago alumni" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.02531645569620253, 0, 0.04838709677419355, 0, 0.015384615384615385, 0.013157894736842105, 0.005555555555555556, 0.010050251256281407, 0, 0.015384615384615385, 0.020202020202020204, 0.012048192771084338, 0.008356545961002786, 0.01, 0.006578947368421052, 0.018691588785046728, 0.03488372093023256, 0.015625, 0, 0.022900763358778626, 0, 0, 0, 0.011627906976744186, 0, 0.00980392156862745, 0.020833333333333332, 0.019230769230769232, 0.015151515151515152, 0.00684931506849315, 0.012345679012345678, 0, 0.0072992700729927005, 0, 0, 0, 0.0136986301369863, 0, 0, 0, 0, 0.01575299306868305, 0, 0.02304147465437788, 0.007633587786259542 ]

[ "Sequestration Could Be Left To Lame-Duck U.S. Congress\n\nApr. 7, 2012 - 10:33AM\n|\n\n(Blair Tomlinson / Staff)\n\nBetween now and Jan. 2, when automatic spending cuts are set to slash up to $54 billion from the Pentagon’s 2013 budget, there is only one date that truly matters: Nov. 6, Election Day.", "\n\nThat is practically the only thing that people watching the U.S. government’s budget battle can agree on.", "\n\n“Barring an earth-changing event, it’s hard to see any political agreement before the election,” said David Berteau of the Center for Strategic and International Studies.", "\n\nHow Democrats and Republicans fare at the polls will determine whether some kind of deal on deficit reduction and a slew of other issues can be achieved during the final weeks of the 112th Congress.", "\n\nFor people with a stake in defense spending, sequestration — the process by which automatic spending cuts will take place — is the most significant problem that needs to be solved. ", "However, it is just one of several divisive issues that will be on Congress’ plate in December.", "\n\nAround that time, the U.S. Treasury is expected to ask for another extension of the debt ceiling or risk defaulting on U.S. debt. ", "The tax cuts that were first signed into law by President George W. Bush are set to expire at midnight on New Year’s Eve. ", "Appropriations bills for fiscal 2013 will need to be passed, or at the very least a temporary spending bill to avert a government shutdown. ", "Reauthorization is needed for the farm bill and transportation funding. ", "Plus, the so-called “doc fix,” a temporary measure by which doctors are paid by Medicare, will also require legislative action.", "\n\nWhile the number of items is astounding, the fact that so many are on the table could mean a grand bargain is within reach, according to former budget officials and defense analysts.", "\n\nWith months to go and so much at stake, speculation is running rampant in Washington: What are the chances a lame-duck Congress will solve any of these problems?", "\n\nIn the meantime, the Pentagon and other federal agencies under the sequester gun are beginning to consider their options as they begin building their 2014 budget requests.", "\n\nLooking Ahead\n\nWhen Congress returns to work after the November elections, some members will have lost their re-election bids and will know that come January, when the 113th Congress begins, they will not be returning to Capitol Hill. ", "This is what’s called a lame-duck Congress.", "\n\nSpeaking March 27 in Washington, Rep. Barney Frank, D-Mass., predicted this December would be the most powerful lame-duck session in history, with the results of the November elections shaping everything.", "\n\nWhile a decisive win for either party would remove any incentive to tackle these big problems in December, the consensus is that divided government is here to stay.", "\n\nThe likelihood that either side will receive a mandate to act from the election is very low, said Mackenzie Eaglen, a fellow at the American Enterprise Institute.", "\n\nWhile the White House or one of the congressional chambers could flip, the government will likely remain divided between the two parties, she said.", "\n\nFor that reason, the results of the election may not matter all that much, Berteau said.", "\n\n“I have cautious optimism that the lame duck might be able to solve this, almost regardless of the outcome of the election,” he said.", "\n\nFor now, Berteau is not alone in his optimism.", "\n\n“There is a genuine desire on the part of members of both parties for a deal that goes big,” Eaglen said.", "\n\nA large-scale debt deal was within reach last summer before negotiations between the White House and House Speaker John Boehner, R-Ohio, collapsed.", "\n\nIt was also the goal of the bipartisan congressional supercommittee before it announced it had failed to reach an agreement on deficit reduction in November.", "\n\nThe list of issues that are up in the air until after the election is getting long. ", "That could be a recipe for a train wreck or the opportunity to make a deal, said Gordon Adams, who oversaw national defense budgeting at the Office of Management and Budget (OMB) during the Clinton administration.", "\n\n“It’s not definitive, but the opportunity for a deal is enormous when you get to November and December,” Gordon said.", "\n\nAccording to an April 2 report by Credit Suisse, the items that are realistically going to be in play in December are the upper-income Bush tax cuts; the lower payroll tax rates and unemployment benefits; and sequestration cuts.", "\n\nIt is an unlikely scenario, but if the automatic cuts to discretionary spending go forward and all of the Bush tax cuts are allowed to expire, the U.S. Gross Domestic Product (GDP) will take a 4 percent hit, according to the analysis. “", "Until Congress acts, the economy will still technically be on a collision course with the largest fiscal hit in modern times.”", "\n\nThat could serve as impetus to act. ", "Or, Congress could choose to avert the crisis and kick the can down the road with some kind of temporary fix, “as there won’t be enough time or political will to deal with big changes to policy,” according to the Credit Suisse report.", "\n\nTodd Harrison, an analyst at the Center for Strategic and Budgetary Assessments (CSBA), said he agrees. “", "I think the most likely outcome is that the lame-duck Congress punts on the big issues and lets the next Congress deal with it.”", "\n\nPentagon Choices\n\nWhile full-blown sequestration remains an unlikely outcome, the pressure is on the Pentagon to consider its options if further cuts to defense spending are called for.", "\n\nFor now, DoD officials maintain they are not planning for sequestration. ", "However, Defense Secretary Leon Panetta has told Congress that the Defense Department will begin planning this summer if there is still no deal within sight.", "\n\nTo do so, DoD will need to know the baseline from which sequester cuts will be made and the amount of flexibility it will have in administering those cuts.", "\n\nBerteau said there is “vigorous internal debate” over what the baseline would be in the case of sequestration.", "\n\nThe Budget Control Act mandates that roughly $500 billion be cut from the defense budget over the next decade if Congress fails to identify $1.2 trillion in deficit reduction.", "\n\nAccording to analysis by CSBA, sequestration would take an extra $54 billion from the 2013 budget, dropping the base budget to $472 billion from the Pentagon’s request of $525 billion.", "\n\nHowever, the Budget Control Act (and the 1980s Gramm-Rudman-Hollings legislation on which it is based) is ambiguous about what the baseline should be.", "\n\nDepending on the baseline, the Pentagon may have to ax anywhere from $30 billion to $55 billion, Berteau said.", "\n\nAdams said he doesn’t think it is quite that uncertain.", "\n\n“My understanding is that the baseline will be whatever action has been taken by the appropriators at that point in time,” he said\n\nBefore the Pentagon or the rest of the government can plan for sequestration, it needs guidance from OMB about how these cuts will be administered.", "\n\nThe cuts could hit at the title level — for example, DoD-wide procurement. ", "Or they could target the account level, the sub-account level or the program element level, which would be the most restrictive.", "\n\nMany expect OMB to issue guidance to plan for the most painful, least flexible cuts possible in an effort to spur Congress to act.", "\n\nGiving the Pentagon flexibility to administer the cuts makes sequestration more acceptable, and that was never the point, Berteau said.", "\n\nThere is no incentive for OMB to announce that decision now, without seeing what the cards will look like when they are dealt in November, Adams said.", "\n\nIn the meantime, it is possible the Pentagon will start drafting alternative budget scenarios like it did last summer in preparation for the Budget Control Act, Berteau said.", "\n\nThis type of planning has become the norm inside the Pentagon. ", "However, under sequestration, it’s not an alternative budget that will be needed, but a brand new strategy, Eaglen said.", "\n\nTestifying before the House Armed Services Committee in February, Panetta said, “If you take another $500 billion out of this defense budget, the strategy I just presented you, I’d have to throw out the window.”" ]

{ "pile_set_name": "Pile-CC" }

[ 0.003401360544217687, 0, 0.011627906976744186, 0.005, 0, 0.010526315789473684, 0.007575757575757576, 0.00819672131147541, 0, 0, 0.007874015748031496, 0, 0.006134969325153374, 0.005780346820809248, 0.012658227848101266, 0.023255813953488372, 0.0048543689320388345, 0, 0.012195121951219513, 0.006711409395973154, 0.011111111111111112, 0, 0.020833333333333332, 0, 0.020134228187919462, 0, 0, 0.014084507042253521, 0.008403361344537815, 0.008695652173913044, 0.004201680672268907, 0.007936507936507936, 0, 0.008547008547008548, 0.018691588785046728, 0.015625, 0.0106951871657754, 0, 0.025477707006369428, 0, 0, 0.005649717514124294, 0.010752688172043012, 0.006578947368421052, 0.017857142857142856, 0, 0.0035587188612099642, 0, 0, 0.007575757575757576, 0.014598540145985401, 0.006578947368421052, 0.017045454545454544, 0.015384615384615385, 0.008333333333333333, 0.009389671361502348 ]

[ "Dario Šarić\n\nDario Šarić (; born 8 April 1994) is a Croatian professional basketball player for the Phoenix Suns of the National Basketball Association (NBA). ", "He was selected with the 12th overall pick in the 2014 NBA draft. ", "He also represents the senior Croatia national team.", "\n\nProfessional career\n\nEarly years\nŠarić began his professional career in 2009 with Zrinjevac. ", "After joining Zagreb mid-way through the 2009–10 season, and spending much of the 2010–11 season on loan with Dubrava, Šarić won the Città di Roma EuroLeague (IJT) in May 2011, alongside teammates, Mario Hezonja and Dominik Mavra, and progressed to the Final Four of the tournament, where his team eventually won. ", "After he had registered a triple-double in the final game with 19 points, 14 rebounds and 10 assists, in addition to 10 drawn fouls, he was named the MVP of the tournament.", "\n\nIn 2010 and 2011, Šarić was nominated for the FIBA Europe Young Player of the Year Award.", "\n\nIn 2012, he was selected to play for the World Team, for the second year in a row, at the Nike Hoop Summit in Portland, Oregon. ", "In the all-star game, the international players of the World Team beat the US team, with Šarić scoring 13 points and leading in rebounds (14) and assists (5).", "\n\nHe signed with Bilbao Basket and was loaned to Split in 2012. ", "However, due to a sanction by FIBA, forcing the Spanish team to pay a buyout of €550,000, he didn't sign with Bilbao. ", "After that, he trained with Split, but was not playing games with them.", "\n\nCibona Zagreb (2012–2014)\n\nIn November 2012, he signed a four-year contract with the Croatian club Cibona.", "\n\nAgain, in 2012, he was nominated for the FIBA Europe Young Men's Player of the Year Award, finishing second.", "\n\nŠarić had initially decided to declare for the 2013 NBA draft on April 4, 2013. ", "However, two days after the initial declaration, he decided not to participate in it and had planned to play for KK Cibona for at least one more season. ", "Šarić would, however, officially declare himself for the draft once again on April 14, 2013. ", "Finally, Šarić withdrew from the draft altogether, because of his desire to stay in Europe for another year, to gain experience.", "\n\nIn 2013, he won the Croatian National Cup and Croatian League championship with Cibona, and won the MVP award for the Croatian finals.", "\n\nHe was named the 2013 FIBA Europe Young Player of the Year in February 2014. ", "In April 2014, he was selected into the ideal team and also named the MVP of the Adriatic League, averaging 16.7 points, 9.7 rebounds and 3.2 assists in the regular season. ", "In the Final Four of the competition, Cibona eventually won the league championship, and Šarić was also proclaimed the MVP of the final four. ", "He was also named the ABA League Top Prospect for the 2013–14 season.", "\n\nAnadolu Efes (2014–2016)\nOn June 24, 2014, he signed a 2+1 contract with the Turkish team Anadolu Efes. ", "Cibona also received US$1.2 million in the name of buyout from Anadolu Efes, as Šarić was still under contract with them. ", "He signed the offer days before the 2014 NBA draft commenced. ", "The Orlando Magic selected Šarić 12th overall in the 2014 draft, but his rights were traded to the Philadelphia 76ers for Elfrid Payton on draft night. ", "After the draft, Šarić stated that he planned on playing in Europe for at least one more year, but promised that he would eventually play in the NBA.", "\n\nAt the beginning of the 2014–15 season, Šarić's father criticized Efes's head coach, Dušan Ivković, for not putting Dario in the roster for the Turkish Super League games, openly threatening possible termination of the player's contract, if the situation didn't improve. ", "He was named the EuroLeague 2014–15 season's MVP of the Month for the month of November, becoming the youngest player in EuroLeague history to win the monthly MVP award. ", "Over 4 EuroLeague games in November, he averaged 15.5 points and 7.8 rebounds per game.", "\n\nIn January 2015, he was named the 2014 FIBA Europe Young Men's Player of the Year, his second consecutive award.", "\n\nAnadolu Efes finished their participation in the EuroLeague season, after they lost their quarterfinal playoffs series to Real Madrid, by a 3–1 series result. ", "Over 27 EuroLeague games played in 2014–15 season, Šarić averaged 9.9 points, 6.4 rebounds, and 2.3 assists per game. ", "In May 2016, he finished second, for the second straight season, in the EuroLeague Rising Star voting.", "\n\nPhiladelphia 76ers (2016–2018)\nOn 15 July 2016, Šarić signed with the Philadelphia 76ers. ", "In just his third NBA game on 1 November 2016, Šarić scored 21 points in a 103–101 loss to the Orlando Magic. ", "On 3 December 2016, he had a second 21-point game in a 107–106 loss to the Boston Celtics. ", "On 9 February 2017, he had a 26-point effort in a 112–111 win over Orlando. ", "On 17 February 2017, he participated in the Rising Stars Challenge during the All-Star Weekend. ", "On March 2, 2017, he was named Eastern Conference Rookie of the Month for games played in February, after his injured teammate, Joel Embiid, had won each month prior. ", "On 9 March 2017, he had a 28-point effort in a 114–108 overtime loss to the Portland Trail Blazers. ", "Three days later, he scored a career-high 29 points in a 118–116 win over the Los Angeles Lakers. ", "He surpassed that mark on 24 March 2017, scoring 32 points in a 117–107 win over the Chicago Bulls. ", "On 3 April 2017, he was named Eastern Conference Rookie of the Month for the second straight month. ", "Following the season, he was named to the NBA All-Rookie First Team and finished second in NBA Rookie of the Year voting, behind Malcolm Brogdon.", "\n\nOn 7 November 2017, Šarić scored a then season-high 25 points in a 104–97 win over the Utah Jazz. ", "It was the 76ers' fifth straight win, their longest since the 2011–12 season. ", "On 18 December 2017, he scored 20 of his 27 points in the second half of the 76ers' 117–115 loss to the Chicago Bulls. ", "Three days later, he had a near triple-double with 18 points, 10 rebounds and nine assists in a 114–109 loss to the Toronto Raptors. ", "On 31 December 2017, he tied a season high with 27 points in a 123–110 win over the Phoenix Suns. ", "In Game 4 of the 76ers' second-round playoff series against the Celtics, Šarić scored a game-high 25 points in a 103–92 win, helping Philadelphia cut the series deficit to 3–1. ", "The 76ers went on to lose to the Celtics in Game 5, despite Šarić's 27 points and 10 rebounds in a 114–112 loss.", "\n\nMinnesota Timberwolves (2018–19)\nOn 12 November 2018, Šarić was traded to the Minnesota Timberwolves, along with Jerryd Bayless, Robert Covington and a 2022 second-round pick, in exchange for Jimmy Butler and Justin Patton. ", "He made his debut for the Timberwolves two days later, scoring nine points in 20 minutes off the bench in a 107–100 win over the New Orleans Pelicans. ", "On 24 November, he had 19 points and 14 rebounds in a 111–96 win over the Chicago Bulls.", "\n\nPhoenix Suns (2019–present)\nOn July 6, 2019, Šarić, along with the draft rights to Cameron Johnson, was traded to the Phoenix Suns, in exchange for the draft rights to Jarrett Culver, completing a draft day trade. ", "On November 24, Šarić scored 18 points and grabbed a career-high 17 rebounds in a 116–104 loss to the Denver Nuggets. ", "He later matched his career-high of 17 rebounds, scoring 19 points this time around, in a 121–119 overtime loss to the San Antonio Spurs on December 14 in Mexico City.", "\n\nNational team career\n\nWhile playing with Croatia's Under-16 national team, Šarić was named the Most Valuable Player of the 2010 FIBA Europe Under-16 Championship in a unanimous vote, after leading the tournament in scoring (24.3 ppg) and rebounding (11.5 rpg), and finishing second in assists (5.8 apg). ", "He registered a triple-double (30 points, 11 rebounds, 11 assists) in the final, becoming only the second player to do so (after Ricky Rubio in 2006).", "\n\nHe won a gold medal with Croatia's Under-18 national team in the 2012 FIBA Europe Under-18 Championship, where he finished first in scoring (25.6 ppg) and second in rebounds (10.1 rpg). ", "Soon after scoring 39 points to lead Croatia to victory in the gold medal game against Lithuania, Šarić was voted unanimously as tournament MVP.", "\n\nŠarić also played with Croatia's Under-19 national team in the 2011 FIBA Under-19 World Cup, where he finished fourth in scoring (18.1 ppg) and third in rebounds (10.1 rpg), despite being one of the youngest participants at 17 years of age. ", "He also played at the 2013 FIBA Under-19 World Cup, where he averaged 20.3 points, 11.2 rebounds, 4.9 assists per game, and was named to the All-Tournament Team.", "\n\nŠarić represented the senior men's Croatia men's national basketball team at a major FIBA tournament for the first time at EuroBasket 2013, where he averaged 5.5 points, 3.2 rebounds, and 0.9 assists per game. ", "He then played with Croatia's senior men's team at the 2014 FIBA World Cup, where he averaged 11.7 points, 6.7 rebounds, and 2.3 assists per game.", "\n\nHe also played with Croatia at the EuroBasket 2015, where they were eliminated in the eighth finals by Czech Republic. ", "Over 6 tournament games, he averaged 9.7 points, 6.3 rebounds, and 2.7 assists per game, on 44.7% shooting from the field.", "\n\nŠarić played with Croatia at the 2016 Olympic games, where they were eliminated in the quarter-finals by Serbia. ", "Over 6 tournament games, he averaged 33.1 minutes, 11.8 points, 6.7 rebounds and 3.2 assists per game, on 43.1% shooting from the field.", "\n\nŠarić represented Croatia at the EuroBasket 2017. ", "Croatia was eliminated in the round of 16 by Russia. ", "Over 5 tournament games, he averaged 32.4 minutes, 14.8 points, 6.7 rebounds, and 2.5 assists per game, on 37.4% field goal shooting.", "\n\nPersonal life\nŠarić is the son of basketball-playing parents, Predrag and Veselinka. ", "His nicknames include \"The Homie\", \"Super Dario\" or \"Šiši\" (pronounced \"she-she\").", "\n\nCareer statistics\n\nNBA\n\nRegular season\n\n|-\n| style=\"text-align:left;\"| \n| style=\"text-align:left;\"| Philadelphia\n| 81 || 36 || 26.3 || .411 || .311 || .782 || 6.3 || 2.2 || .4 || .7 || 12.8\n|-\n| style=\"text-align:left;\"| \n| style=\"text-align:left;\"| Philadelphia\n| 78 || 73 || 29.6 || .453 || .393 || .860 || 6.7 || 2.6 || .3 || .7 || 14.6\n|-\n| style=\"text-align:left;\"| \n| style=\"text-align:left;\"| Philadelphia\n| 13 || 13 || 30.5 || .364 || .300 || .900 || 6.6 || 2.0 || .2 || .3 || 11.1\n|-\n| style=\"text-align:left;\"| \n| style=\"text-align:left;\"| Minnesota\n| 68 || 28 || 23.9 || .454 || .383 || .875 || 5.5 || 1.5 || .6 || .1 || 10.5\n|- class=\"sortbottom\"\n| style=\"text-align:center;\" colspan=\"2\"| Career\n| 240 || 150 || 26.9 || .433 || .358 || .835 || 6.2 || 2.1 || .6 || .2 || 12.7\n\nPlayoffs\n\n|-\n| style=\"text-align:left;\"| 2018\n| style=\"text-align:left;\"| Philadelphia\n| 10 || 10 || 32.9 || .421 || .385 || .850 || 7.3 || 3.5 || 1.0 || .4 || 17.2\n|- class\"sortbottom\"\n| style=\"text-align:center;\" colspan=\"2\"| Career\n| 10 || 10 || 32.9 || .421 || .385 || .850 || 7.3 || 3.5 || 1.0 || .4 || 17.2\n\nEuroLeague\n\n|-\n| style=\"text-align:left;\"| 2011–12\n| style=\"text-align:left;\"| Zagreb\n| 4 || 3 || 15.0 || .200 || .167 || .500 || 4.5 || .5 || .3 || .3 || 2.0 || .8\n|-\n| style=\"text-align:left;\"| 2014–15\n| style=\"text-align:left;\"| Anadolu Efes\n| 27 || 22 || 24.4 || .433 || .306 || .707 || 6.4 || 2.3 || .7 || .4 || 9.9 || 12.6\n|-\n| style=\"text-align:left;\"| 2015–16\n| style=\"text-align:left;\"| Anadolu Efes\n| 24 || 18 || 22.4 || .500 || .403 || .939 || 5.8 || 1.5 || .5 || .5 || 11.7 || 13.5\n|- class=\"sortbottom\"\n| style=\"text-align:center;\" colspan=\"2\"| Career\n| 55 || 43 || 22.9 || .457 || .350 || .783 || 6.0 || 1.8 || .6 || .4 || 10.1 || 12.1\n\nAwards and accomplishments\n\nClub honours\nJunior club honours\n Città di Roma Tournament (2010, 2011)\n EuroLeague Junior Tournament (2011)\nSenior club honours\n Croatian League Champion (2013)\n Croatian Cup Winner (2013)\n Adriatic League Champion (2014)\n Turkish Cup Winner (2015)\n Turkish President's Cup Winner (2015)\n\nIndividual\nJunior honours \n 2010 Albert Schweitzer Tournament: Burkhard Wildermuth-Award\n 2010 FIBA Europe Under-16 Championship: All-Tournament Team, MVP\n Città di Roma Tournament: All-Tournament Team, MVP (2010, 2011)\n 2011 EuroLeague Junior Tournament: All-Tournament Team, MVP\n 2012 FIBA Europe Under-18 Championship: All-Tournament Team, MVP\n 2013 FIBA Under-19 World Cup: All-Tournament Team\nSenior honours\n Croatian League Finals MVP (2013)\n Adriatic League: First Team, Season MVP, Final Four MVP (2014)\n Adriatic League Top Scorer (2014)\n Adriatic League Top Prospect (2014)\n FIBA European Young Player of the Year (2013, 2014)\n NBA Eastern Conference Rookie of the Month (February, March 2017)\n NBA All-Rookie First Team (2017)\n\nSee also\n\n List of European basketball players in the United States\n\nReferences\n\nExternal links\n\nDario Šarić at euroleague.net\nDario Šarić at tblstat.net\n\nCategory:1994 births\nCategory:Living people\nCategory:ABA League players\nCategory:Anadolu Efes S.K. players\nCategory:Basketball players at the 2016 Summer Olympics\nCategory:Croatian men's basketball players\nCategory:Croatian expatriate basketball people in the United States\nCategory:Croatian expatriates in Turkey\nCategory:Expatriate basketball players in Turkey\nCategory:KK Cibona players\nCategory:KK Zagreb players\nCategory:KK Zrinjevac players\nCategory:Minnesota Timberwolves players\nCategory:National Basketball Association players from Croatia\nCategory:Olympic basketball players of Croatia\nCategory:Orlando Magic draft picks\nCategory:Philadelphia 76ers players\nCategory:Phoenix Suns players\nCategory:Power forwards (basketball)\nCategory:Sportspeople from Šibenik\nCategory:2014 FIBA Basketball World Cup players" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.031446540880503145, 0.015151515151515152, 0, 0, 0.009554140127388535, 0.005813953488372093, 0.01098901098901099, 0.015384615384615385, 0.006329113924050633, 0.015625, 0, 0.014084507042253521, 0, 0.00909090909090909, 0, 0.006535947712418301, 0, 0, 0.029411764705882353, 0, 0.011560693641618497, 0.014084507042253521, 0.014492753623188406, 0, 0.00819672131147541, 0.016129032258064516, 0.013157894736842105, 0.006711409395973154, 0.014652014652014652, 0.01764705882352941, 0.011494252873563218, 0, 0.006211180124223602, 0.00847457627118644, 0.00980392156862745, 0, 0.00909090909090909, 0.01098901098901099, 0, 0.010416666666666666, 0.005988023952095809, 0.01, 0.01020408163265306, 0.01, 0, 0.020689655172413793, 0.01, 0, 0.008403361344537815, 0, 0.01020408163265306, 0, 0, 0.017699115044247787, 0.006622516556291391, 0.011363636363636364, 0.013888888888888888, 0.01694915254237288, 0.005988023952095809, 0.0032679738562091504, 0.006666666666666667, 0.005319148936170213, 0.006944444444444444, 0.00411522633744856, 0.006211180124223602, 0.0047169811320754715, 0.00684931506849315, 0.008264462809917356, 0, 0, 0, 0, 0, 0, 0.011494252873563218, 0, 0.005815490351572826 ]

[ "The Institute for Environmental Science and Policy (IESP) at the University of Illinois at Chicago advances cooperative research, scholarship, and service that support a sustainable environment. ", "We facilitate interdisciplinary collaboration by teaming scholars with their counterparts in the public and private sectors to devise workable solutions for complex environmental challenges." ]

{ "pile_set_name": "OpenWebText2" }

[ 0.010256410256410256, 0 ]

[ "Bundesliga: Bayern hammer Werden Bremen 6-1 to extend unbeaten run\n\nAmongst the key changes, Germany striker Mario Gomez, who scored twice, came in for Mario Mandzukic, Dutch wing Arjen Robben, who opened the scoring, started for Thomas Mueller while Swiss midfielder Xherdan Shaqiri took Toni Kroos' place.", "\n\nBerlin: Bayern Munich rested half a dozen stars but still romped to a 6-1 win at home to 10-man Werder Bremen on Saturday to go 18 points clear at the top of the Bundesliga.", "\n\nBayern boss Jupp Heynckes celebrated his 1000th Bundesliga game as a player and coach by making six changes from the team which won 3-1 at Arsenal in the Champions League on Tuesday.", "\n\nBut they still extended their unbeaten run to 20 matches since their last defeat at home to Bayer Leverkusen at the end of October.", "\n\nAmongst the key changes, Germany striker Mario Gomez, who scored twice, came in for Mario Mandzukic, Dutch wing Arjen Robben, who opened the scoring, started for Thomas Mueller while Swiss midfielder Xherdan Shaqiri took Toni Kroos' place.", "\n\nMunich were ahead after 25 minutes when Robben won the race with Franck Ribery to convert Philipp Lahm's cross for the opener.", "\n\nThe next goal came just four minutes later when Robben's free-kick was headed home by Javi Martinez.", "\n\nTo make matters worse for Bremen, centre-back Sebastian Proedl was shown a straight red card for bringing down Gomez, who was through on goal, a minute before the break.", "\n\nThings did not improve in the second half when Bremen's left-back Theodor Gebre Selassie turned the ball into his own net on 49 minutes, then Gomez grabbed his first and Bayern's fourth just two minutes later.", "\n\nBelgium midfielder Kevin de Bruyne, on loan at Bremen from Chelsea, pulled a goal back for Werder approaching the hour mark, but Bremen's defence capitulated late on as Ribery, then Gomez, added goals in the last five minutes.", "\n\nThe two teams closest to Bayern, Borussia Dortmund, who are at Moenchengladbach, and Bayer Leverkusen, at bottom side Greuther Fuerth, need to pick up wins on Sunday to cut Bayern's huge lead.", "\n\nSouth Korean striker Ji Dong-Won scored his first goal in six appearances for strugglers Augsburg since joining from Sunderland in January in his team's 2-1 win at home to Hoffenheim.", "\n\nStriker Sascha Moelders added a second on 79 minutes to seal only Augsburg's third win of the season and they move up to 16th in the league, nine points from safety, while Hoffenheim drop to 17th and deeper in the relegation mire.", "\n\nHanover bounced back from their midweek Europa League exit at the hands of Russia's Anzhi Makhachkala with a 5-1 win over guests Hamburg to move up to seventh.", "\n\nIvory Coast's Didier Ya Konan, playing on the right wing, scored twice including a superb volley from 20 metres out just before the break.", "\n\nWolfsburg earned a 1-1 draw at Mainz 05 despite playing with 10 men for 60 minutes after centre-back Alexander Madlung was shown an early red card for pulling back Mainz's Nicolai Muelle.", "\n\nNuremberg earned a 1-1 draw at Stuttgart to stay 14th and just above the relegation place, while on Saturday night, Schalke 04, fresh from Wednesday's 1-1 Champions League draw at Galatasaray, host Fortuna Duesseldorf." ]

{ "pile_set_name": "Pile-CC" }

[ 0.019543973941368076, 0.011428571428571429, 0.010869565217391304, 0.007518796992481203, 0.024896265560165973, 0.0234375, 0.0196078431372549, 0.011695906432748537, 0.014218009478672985, 0.017543859649122806, 0.02577319587628866, 0.005405405405405406, 0, 0.012422360248447204, 0.007142857142857143, 0.021164021164021163, 0.00909090909090909 ]

[ "[Investigation of quantitative detection of water quality using spectral fluorescence signature].", "\nA method of spectral analysis, which can simultaneously detect dissolved organic matter (DOM) and chlorophyll a (Chl-a) in natural water, was developed in the present paper with the intention of monitoring water quality fast and quantitatively. ", "Firstly, the total luminescence spectra (TLS) of water sample from East Lake in Wuhan city were measured by the use of laser (532 nm) induced fluorescence (LIF). ", "There were obvious peaks of relative intensity at the wavelength value of 580, 651 and 687 nm in the TLS of the sample, which correspond respectively to spectra of DOM, and the Raman scattering of water and Chl-a in the water. ", "Then the spectral fluorescence signature (SFS) technique was adopted to analyze and distinguish spectral characteristics of DOM and Chl-a in natural water. ", "The calibration curves and function expressions, which indicate the relation between the normalized fluorescence intensities of DOM and Chl-a in water and their concentrations, were obtained respectively under the condition of low concentration(< 40 mg x L(-1))by using normalization of Raman scattering spectrum of water. ", "The curves have a high linearity. ", "When the concentration of the solution with humic acid is large (> 40 mg x L(-1)), the Raman scattering signal is totally absorbed by the molecules of humic acid being on the ground state, so the normalization technique can not be adopted. ", "However the function expression between the concentration of the solution with humic acid and its relative fluorescence peak intensity can be acquired directly with the aid of experiment of fluorescence spectrum. ", "It is concluded that although the expression is non-linearity as a whole, there is a excellent linear relation between the fluorescence intensity and concentration of DOM when the concentration is less than 200 mg x L(-1). ", "The method of measurement based on spectral fluorescence signature technique and the calibration curves gained will have prospects of broad application. ", "It can recognize fast what pollutants are and detect quantitatively their contents in water. ", "It is realizable to monitor the quality of natural water with real time, dynamics and inlarge area." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0.0040650406504065045, 0.012345679012345678, 0.013215859030837005, 0.01282051282051282, 0.009287925696594427, 0, 0.004166666666666667, 0, 0, 0, 0, 0 ]

[ "For applications that require quality of service (QoS) assurances, the best effort service model commonly used to transmit information over the Internet is proving inadequate. ", "In general, assuring QoS entails providing differentiated services for certain packet-level or session-level treatment; that is, some users receive higher priority treatment or have a greater bandwidth allocation than other users.", "\nApproaches to managing data traffic for providing differential services fall into two categories, those with network-wide reservations that include explicit signaling and those without such network-wide reservations. ", "Reservation-based traffic management explicitly identifies and reserves network resources. ", "Network nodes categorize data traffic into classes and provide QoS using the network resources reserved for the particular class associated with incoming data traffic. ", "One example of network-wide reservation-based traffic management is the Integrated Services (IntServ) model, which uses the per-flow approach to provide guarantees to individual data streams and makes reservations of resources at intermediate routers.", "\nIn traffic management that does not use network-wide reservations, but can use local reservations at a router, the network nodes classify data traffic into a set of classes and use the classes to grant priority-based treatment to the traffic. ", "An example of such traffic management is the Differentiated Services (DiffServ) model. ", "DiffServ provides aggregate assurances for a group of applications.", "\nToday, many of the communication links between the various communications entities in networks are wire-line; that is, client and server systems are typically connected to other server and client systems by wires, such as twisted-pair wires, coaxial cables, fiber optic cables, and the like. ", "Notwithstanding this wired infrastructure, wireless networks such as cellular and Personal Communication Systems (PCS) and wireless local area networks, microwave links, infrared (IR) links, and satellite links are becoming more prevalent. ", "Wireless devices connected to such networks are typically mobile. ", "Such mobility creates frequent, dynamic changes to the network topology. ", "Moreover, the peculiarities of signal propagation over wireless links cause frequent changes to the state of such communication links between the devices on the network. ", "Consequently, nodes in wireless networks need to deal with higher data losses and frequent bandwidth reallocations.", "\nThe initial designs of the IntServ and DiffServ models, however, contemplated wired networks only and are not suited for the various characteristics of wireless networks. ", "Thus, there remains a need for a system and a method that can manage traffic in a wireless network to provide QoS assurances despite the aforementioned difficulties associated with the mobility of the communication devices and propagation conditions encountered in the wireless networks." ]

{ "pile_set_name": "USPTO Backgrounds" }

[ 0, 0, 0, 0, 0, 0.00398406374501992, 0, 0.011494252873563218, 0.014925373134328358, 0, 0.004166666666666667, 0, 0, 0, 0, 0.011627906976744186, 0 ]

[ "Igabi\n\nIgabi is a Local Government Area (LGA) of Kaduna State, Nigeria. ", "It is one of 774 local government areas (LGAs) in Nigeria. ", "Rigasa ward is under Igabi LGA, one of the Largest ward in terms of population in Nigeria. ", "The first confirmed H5N1 (bird flu) outbreak in an African country was on February 8, 2006 on a commercial chicken farm in Jaji, a village in Igabi.", "\n\nReferences \n\nCategory:Local Government Areas in Kaduna State\nCategory:Kaduna State\nCategory:Populated places in Kaduna State" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.027777777777777776, 0, 0.01098901098901099, 0.006756756756756757, 0 ]

[ "14-4647\nBanner Industries of N.E., Inc. v. Wicks\n\n\n\n UNITED STATES COURT OF APPEALS\n FOR THE SECOND CIRCUIT\n\n SUMMARY ORDER\n\nRULINGS BY SUMMARY ORDER DO NOT HAVE PRECEDENTIAL EFFECT. ", "CITATION TO A\nSUMMARY ORDER FILED ON OR AFTER JANUARY 1, 2007, IS PERMITTED AND IS GOVERNED\nBY FEDERAL RULE OF APPELLATE PROCEDURE 32.1 AND THIS COURT’S LOCAL RULE 32.1.1.", "\nWHEN CITING A SUMMARY ORDER IN A DOCUMENT FILED WITH THIS COURT, A PARTY\nMUST CITE EITHER THE FEDERAL APPENDIX OR AN ELECTRONIC DATABASE (WITH THE\nNOTATION “SUMMARY ORDER”). ", "A PARTY CITING A SUMMARY ORDER MUST SERVE A COPY\nOF IT ON ANY PARTY NOT REPRESENTED BY COUNSEL.", "\n\n\n\n At a stated Term of the United States Court of Appeals for the Second Circuit, held at the\nThurgood Marshall United States Courthouse, 40 Foley Square, in the City of New York on the\n25th day of January, two thousand sixteen.", "\n\nPresent: ROSEMARY S. POOLER,\n PETER W. HALL,\n SUSAN L. CARNEY,\n Circuit Judges.", "\n_____________________________________________________\n\nBANNER INDUSTRIES OF N.E., INC.,", "\n\n Plaintiff-Appellant,\n\n v. 14-4647-cv\n\nKENNETH L. WICKS, HARRINGTON INDUSTRIAL PLASTICS LLC,\n\n Defendants-Appellees.", "\n_____________________________________________________\n\nAppearing for Appellant: Seth H. Hochbaum, Regnante, Sterio & Osborne LLP, Wakefield,\n MA.", "\n\nAppearing for Appellees: Andrew Marks, Littler Mendelson, P.C. (Stephen T. Melnick, on\n the brief), New York, NY.", "\n\nAppeal from the United States District Court for the Northern District of New York (Mordue, J.).", "\n\n ON CONSIDERATION WHEREOF, IT IS HEREBY ORDERED, ADJUDGED,\nAND DECREED that the order of said District Court be and it hereby is AFFIRMED.", "\n\f Banner Industries of N.E., Inc. appeals from the December 1, 2014 memorandum-\ndecision and order of the United States District Court for the Northern District of New York\n(Mordue, J.) granting the motion for summary judgment made by Kenneth L. Wicks and\nHarrington Industrial Plastics, LLC. ", "Banner Industries of N.E., Inc. v. Wicks, 71 F. Supp. ", "3d 284\n(N.D.N.Y. 2014). ", "We assume the parties’ familiarity with the underlying facts, procedural\nhistory, and specification of issues for review.", "\n\n We affirm for the reasons set forth in the district court’s thorough and well-reasoned\nopinion. ", "In order for a party to succeed on a claim for misappropriation of trade secrets, the\nparty must show “(1) that it possessed a trade secret and (2) that the defendants used that trade\nsecret in breach of an agreement, [a] confidential relationship or duty, or as a result of discovery\nby improper means.” ", "N. Atl. ", "Instruments, Inc. v. Haber, 188 F.3d 38, 43–44 (2d Cir. ", "1999)\n(citing Hudson Hotels Corp. v. Choice Hotels Int'l, 995 F.2d 1173, 1176 (2d Cir. ", "1993)\n(abrogated on other grounds )). ", "Banner argues that the record contains sufficient circumstantial\nevidence from which a fact finder can infer that Wicks misappropriated Banner’s confidential\ninformation. ", "The district court properly determined that Banner failed to raise a question of\nmaterial fact on this issue. ", "The fact that Wicks had information belonging to Banner does not\ngive rise to an inference that Wicks misappropriated the information, because even assuming\nWicks possessed Banner’s trade secrets, nothing in the record supports an inference that Wicks\nused those trade secrets.", "\n\n Further, the district court properly declined to enforce the restrictive covenant as\noverbroad. ", "As a general rule, “New York courts disfavor restrictive covenants in the employment\ncontext and will generally enforce them only to the extent they are reasonable and necessary to\nprotect valid business interests.” ", "Lucente v. Int’l Bus. ", "Mach. ", "Corp., 310 F.3d 243, 254 (2d Cir.", "\n2002). (", "citing BDO Seidman v. Hirshberg, 93 N.Y.2d 382, 388 (1999)). ", "New York “require[s]\nrestrictive covenants to be reasonably limited in time, scope and geographical area, and to be\ngrounded in a legitimate business purpose.” ", "Brown & Brown, Inc. v. Johnson, 25 N.Y.3d 364,\n369 (2015). ", "We find no error with the district court’s analysis.", "\n\n We have considered the remainder of Banner’s arguments and find them to be without\nmerit. ", "Accordingly, the order of the district court hereby is AFFIRMED.", "\n\n FOR THE COURT:\n Catherine O’Hagan Wolfe, Clerk\n\n\n\n\n 2\n\f" ]

{ "pile_set_name": "FreeLaw" }

[ 0.01718213058419244, 0, 0.005714285714285714, 0, 0.01694915254237288, 0.023255813953488372, 0, 0.00823045267489712, 0.015625, 0.024844720496894408, 0.01020408163265306, 0.013888888888888888, 0.016611295681063124, 0.037037037037037035, 0, 0, 0, 0, 0.125, 0.03571428571428571, 0.011494252873563218, 0, 0.017543859649122806, 0.00909090909090909, 0.018050541516245487, 0, 0, 0.045454545454545456, 0, 0, 0, 0.01639344262295082, 0.00625, 0.03389830508474576, 0, 0.010101010101010102, 0, 0.009389671361502348 ]

[ "Drop in transforming growth factor-alpha and osteoprotegerin level in gingival crevicular fluid from patients with gingivitis.", "\nInflammatory mediators, especially cytokine, play a central role in the pathogenesis of gingivitis. ", "The aim of this study was to identify and quantify the various growth factors, and cytokines in the gingival crevicular fluid (GCF) of patients with gingivitis, as compared with those of control subjects. ", "The levels of cytokine in the samples were determined by their respective ELISAs. ", "The transforming growth factor (TGF)-alpha and osteoprotegerin (OPG) level were significantly lower in patients with gingivitis than in the controls (p < 0.05). ", "Also, there was a positive correlation between TGF-alpha and OPG levels (r = 0.761). ", "These results suggest that the decrease in growth factor TGF-alpha is associated with the pathophysiology and/or the progress of gingivitis." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0, 0, 0, 0.006211180124223602, 0.023529411764705882, 0.007142857142857143 ]

[ "Summary of conclusions from a consensus panel of experts on health attributes of lactic cultures: significance to fluid milk products containing cultures.", "\nA panel of experts sponsored by the California Dairy Research Foundation was convened on January 31, 1992 to discuss the effect of the consumption of lactic cultures on human health. ", "The panel was composed of 10 scientists with diverse applicable specialties. ", "Topics discussed included lactose digestion, diarrheal diseases, chronic kidney disease, cancer, adherence, immune system stimulation, cholesterol reduction, constipation, and safety. ", "Legitimacy of health claims and research needs for these areas were determined. ", "The panel noted the promising results in the areas of positive effects of ingestion of lactic cultures on lactose digestion, some diarrheal illnesses, small bowel overgrowth associated with chronic kidney disease, and reduction of fecal enzymes that may play a role in colon cancer. ", "However, additional research is necessary to confirm the effects in all of these areas. ", "A coordinated research effort between microbiologists and clinicians is essential for the most effective research to ensure the choice of best available strains, the best conditions of analysis, and the best clinical models." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0.005434782608695652, 0, 0, 0, 0, 0, 0 ]

[ "all: presentation.pdf\n\npresentation.pdf: presentation.tex pics/f_optimized.png pics/logreg_pydotprint_prediction.png\n# pics/f_unoptimized.png pics/logreg_pydotprint_predic.png pics/logreg_pydotprint_train.png\n\tpdflatex presentation.tex\n\npics/f_optimized.png: simple_example.py\n\tpython simple_example.py\n\npics/logreg_pydotprint_prediction.png: logreg_example.py\n\tpython logreg_example.py\n#pics/f_unoptimized.png: simple_example.py\n#\tpython simple_example.py\n\n" ]

{ "pile_set_name": "Github" }

[ 0.004366812227074236 ]

[ "Nat Butcher\n\nNat Butcher (born 25 July 1997) is an Australian professional rugby league footballer who plays as a and forward for the Sydney Roosters in the NRL.", "\n\nBackground\nButcher was born in Sydney, New South Wales, Australia. ", "He is the son of former Rabbitohs' player Blake Butcher.", "\n\nButcher played his junior rugby league for the South Eastern Seagulls, before being signed by the South Sydney Rabbitohs. ", "Butcher is of New Zealand Europe descent\n\nPlaying career\n\nEarly career\nIn November and December 2014, Butcher played for the Australian Schoolboys. ", "After playing in the lower grades at the South Sydney Rabbitohs, he joined the Sydney Roosters in 2015. ", "In 2015 and 2016, he played for the Roosters' NYC team.", "\n\n2016\nIn round 26 of the 2016 NRL season, Butcher made his NRL debut for the Roosters against the Brisbane Broncos. ", "In September, he was named at lock in the 2016 NYC Team of the Year. ", "In October, he captained the Roosters' NYC team to a premiership win, defeating the Penrith Panthers 30-28 at ANZ Stadium.", "\n\n2017\nButcher made 2 appearances for Easts in 2017 but did not feature for the club in their finals campaign.", "\n\n2018\nButcher made 13 appearances for Eastern Suburbs in 2018 but made no appearances for the club in the finals and did not play in Easts 21-6 grand final victory over Melbourne.", "\n\n2019\nButcher made a total of 23 appearances for the Sydney Roosters in the 2019 NRL season. ", " Butcher played from the bench in the club's 2019 NRL Grand Final victory over Canberra at ANZ Stadium.", "\n\nOn 7 October 2019, Butcher was named on the bench for the U23 Junior Australian side.", "\n\nReferences\n\nExternal links\n\nSydney Roosters profile\nRoosters profile\nNRL profile\n\nCategory:1997 births\nCategory:Australian rugby league players\nCategory:Sydney Roosters players\nCategory:Rugby league locks\nCategory:Rugby league second-rows\nCategory:Living people\nCategory:Rugby league players from Sydney" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.024539877300613498, 0, 0.03571428571428571, 0, 0.006756756756756757, 0.019230769230769232, 0.01818181818181818, 0.017094017094017096, 0, 0.00819672131147541, 0, 0.005555555555555556, 0.010638297872340425, 0, 0.022988505747126436, 0.006557377049180328 ]

[ "Lost in Space’s Mina Sundwall talks Penny Robinson, drooling pterodactyls and future seasons.", "\n\nMina Sundwall plays Penny Robinson, the emotionally precocious middle child of the Robinson family. ", "She often serves as the show’s spontaneous muse or its pulse. ", "After a successful first season, Lost in Space is prepped to provide more and more of Penny and her family in future seasons.", "\n\nHidden Remote sat down with Mina to get a little personal information about her portrayal, Penny’s relationships, and future seasons of Lost in Space.", "\n\nMina: Hi! ", "How are you?", "\n\nHidden Remote: Hi Mina! ", "I’m doing great. ", "How are you?", "\n\nMina: I’m doing really well, thank you.", "\n\nHidden Remote: I appreciate the opportunity. ", "I’m ready to go if you are.", "\n\nMina: Yeah! ", "I’m ready to go, whenever.", "\n\nHidden Remote: First and foremost, what drew you to Penny as a character?", "\n\nMina: Well, I think I – I think about this now, especially – when I was reading the script, the first scene I ever read was the scene between Penny and Judy on the ice. ", "Where they’re reading Moby Dick. ", "That as a whole, just the fact that she’s reading Moby Dick, on the ice, on the glacier, in the middle of a lost planet, and she’s the only one to think to bring her phone, or the only one who is a non-science person in a science family, being non-sciency is definitely something I can relate to. ", "So there is immediately that kind of connection.", "\n\nAnd, then, when I read more of the script, and felt the character even more, I saw that she’s very genuine. ", "She’s very true to herself. ", "And she doesn’t necessarily fit into every situation. ", "No matter what, she never hides behind a mask or puts up a fake face. ", "She’s always who she is, and proud of it. ", "And that’s something I feel really good to get to play. ", "She has a lot of qualities I aspire to be more like, and it’s what continues to draw me to her every day.", "\n\nHidden Remote: You sort of derailed me! ", "I wanted to keep it light, so Penny ruined Moby Dick without a spoiler alert because it was written in 1851. ", "How old does something need to be before the spoiler alert is off the table in Penny’s mind?", "\n\nMina: Ha! ", "Well, I think one of the lines is, “It was written in 1851. ", "You had your shot.” ", "I think, you know, I’m gonna give it a good, let’s say 50 years. ", "When something has been around for 50 years, we can talk about it without a spoiler warning.", "\n\nHidden Remote: Since Penny is the literature lover, what do you think her top three books of all time are?", "\n\nMina: I would definitely say she’s probably into Shakespeare. ", "I think about this all the time. ", "I would definitely say Hamlet, because it’s so complicated. ", "Also, I’m actually reading it for my English class right now. ", "I think that she would be into David Foster Wallace as a writer because he’s witty, and sarcastic, and very cynical, and that’s a lot of her personality. ", "So, probably “Consider the Lobster” by David Foster Wallace. ", "Maybe “Catcher in the Rye,” because it’s a kind of teenage rebellion. ", "Very angsty.", "\n\nHidden Remote: It fits her personality really, really well. ", "So, how much did you know about Lost in Space before reading the script?", "\n\nMina: I ummm, [clears throat], I aaaaahhh…\n\nHidden Remote: [laughing] Noted.", "\n\nMina: Not so much, actually. ", "Neither one of my parents are American. ", "They both are from Europe. ", "So it was never really this kind of novelty in my household. ", "I had heard of the phrase, “Danger Will Robinson” from difference references and TV shows. ", "Max talks about Family Guy all the time. ", "I heard it on Gilmore Girls. ", "But, I never really connected it with a show until I read the new script. ", "Then, of course, I did my research.", "\n\nHidden Remote: Given you didn’t know a lot about it, you were surprised about a lot of what happened?", "\n\nMina: Definitely! ", "I mean, reading the first script, it was like this is the premise of our show. [", "excited laughing] And I went with it!", "\n\nHidden Remote: Sounds good. ", "Let’s get into some specifics. ", "Judy is a doctor, Will is an engineer, Maureen is an aerospace engineer and mission commander, John is a Navy SEAL and a pilot. ", "Aside from sarcasm and a sense of comedic timing, what’s Penny’s special skill? ", "We know she’s true to herself and speaks her mind. ", "Does she have a special skill we haven’t seen yet?", "\n\nMina: Well, I think because she’s philosophical, and very into literature as a person, when you are that kind of person in such an important space, life or death mission, then you become, she became the head of communications. ", "I guess that’s Penny’s “job” inside the spaceship.", "\n\nHidden Remote: Excellent! ", "That’s the first I’ve heard that. ", "Hypothetically, what did Penny have planned at the waterfall?", "\n\nMina: [laughs] Well, listen, I mean, you can never go wrong with a little smooching action. ", "She got it in the end, so I don’t know why she was complaining.", "\n\nHidden Remote: First date kind of stuff, yeah?", "\n\nMina: Yeah, yeah, yeah. ", "You know, the cute. ", "The innocent. ", "The cute fun.", "\n\nHidden Remote: You just don’t know! ", "She’s so wild and prone to exaggerated and spontaneous things, like yanking the bar on the vehicle, so you just don’t know what she’s going to do.", "\n\nMina: I guess not. ", "I guess not.", "\n\nHidden Remote: Along that same line, that spontaneous nature, why does Penny cheat at cards?", "\n\nMina: Because, especially being the middle child that’s always kind of…she always feels like she’s cheated out of every situation. ", "You know what I mean?", "\n\nHidden Remote: Yeah.", "\n\nMina: She feels gets the shorter end of the stick, and any little advantage, she’ll take it. ", "Even if it’s cheating in a card game.", "\n\nHidden Remote: That’s a great answer. ", "I expected you to really pause on that one because it’s random. ", "You know, there has to be a reason why they put in the cheating at cards, and making her the middle child does make sense.", "\n\nMina: Yeah, it gives her the one-up. ", "At least in one situation.", "\n\nHidden Remote: And using the reflection. ", "I mean, who doesn’t cheat at cards some?", "\n\nMina: Yeah.", "\n\nhttps://www.instagram.com/p/Bfgcsy3FVoU/?hl=en&taken-by=minasundwall\n\nHidden Remote: In one scene you’re putting together a model with Will and you eat a little piece of food that is supposed to represent him. ", "He called you a cannibal. ", "Do you think cannibalism is a possibility if stranded in space?", "\n\nMina: [laughing] I think anything is possible stranded in space. ", "Thankfully enough we did not resort to cannibalism on our show.", "\n\nHidden Remote: Yet.", "\n\nMina: But, you know, desperate times call for desperate measures. [", "laughing] Yeah, you never know. ", "I’m hoping the writers don’t resort to cannibalism on our show. ", "It is not something that I personally see for the future of Lost in Space. ", "But, desperate times call for desperate measures. ", "Whatever it takes.", "\n\nHidden Remote: If the writers do go that direction, do you eat your mother first because you compared her to steak?", "\n\nMina: [laughing] I didn’t even think of that. ", "That’s very funny. ", "Well, where would we be without Maureen. ", "So, no, Maureen can’t go first.", "\n\nHidden Remote: It’s on your Instagram page. ", "I had to do a little research. ", "So, what do you think started the rivalry with Judy? ", "Is it just the middle child syndrome?", "\n\nMina: I think it’s partially the middle child syndrome, but I also think it’s just this idea of some underlying insecurity that comes with being the younger sister. ", "Especially having her be so close in age, because it’s like always being undermined without knowing what to do to get out of that position. ", "There is nothing you can do to get out of the position of being younger, right? ", "Then this mix of wanting to be useful, but not being useful in the sense she doesn’t understand the science like everyone else does.", "\n\nI think we see throughout the season, she finds her own tasks, and how she can contribute what she can do. ", "At the same time, there’s that internal struggle of wanting to be something she’s not.", "\n\nHidden Remote: Do you think scientific alienation would lead her towards a connection to Dr. Smith?", "\n\nMina: I think it depends. ", "Dr. Smith has done a lot of very bad things to her family. ", "When we find out what is really behind the mask of Dr. Smith, it is harder to connect, at least from Penny’s part, because family always comes first, right? ", "So I think on some level, there might be a kind of similarity between the two personalities, but at the same time, I feel like Penny is more like that genuine, innocent air, that stays true to what she thinks is right. ", "And that is her family.", "\n\nHidden Remote: On a scale of 1 to OMG, how cute is Maxwell Jenkins?", "\n\nMina: OMG times 100,000.", "\n\n[both laughing]\n\nHidden Remote: I wanted to stay on focus with you, but I had to ask a question about Maxwell. ", "He’s adorable.", "\n\nMina: Yes, of course. ", "Oh my goodness, he’s an amazing kid.", "\n\nHidden Remote: When the pterodactyl looking thing drooled into Penny’s face from a few inches away, why did she keep her mouth open? ", "That’s what I really want to know.", "\n\nMina: Because she was so in shock! ", "I don’t know what to do. ", "What are you gonna do when a pterodactyl looking thing starts drooling in your face?", "\n\nHidden Remote: I don’t know. ", "I close my mouth.", "\n\nMina: I was watching that scene and I thought that exact thought. ", "My mind went, “Why is my mouth open?” ", "And then I closed it at one point and I went, “Thank God,” because that could have gone really badly.", "\n\nHidden Remote: Well, if you’ve watched that movie The Descent, you know to turn around.", "\n\nMina: [relenting] Yeah.", "\n\nHidden Remote: Well alright, I’m glad I’m not the only one that noticed.", "\n\nMina: Oooh no. ", "I noticed them all.", "\n\nHidden Remote: What do you want to see in the inevitable future seasons of Lost in Space? ", "What do you want to see from Penny and the show?", "\n\nMina: Well, firstly, I like the use of the word inevitable. ", "That is a word I like to hear when talking about future seasons. ", "I know from one side we’ll see more from Dr. Smith. ", "I think we’ll be in a new world. ", "Whether it’s one or more we’ll see. ", "But, we’ll see both Penny and Will grow in their teenage years, and the changes and the challenges that relate to that.", "\n\nFor Penny in particular, I would like to see her come into herself a little more, and find her space within the family, but still with that rebellious, creative mindset. ", "So you never really know what that means exactly. ", "I definitely do not expect her to sit back and enjoy the ride. ", "She always has an opinion on everything.", "\n\nHidden Remote: There wouldn’t be a better way than that. ", "I think keeping her that way keeps everybody else on their toes.", "\n\nMina: Yeah, I mean, I hope so. ", "It’s a lot more fun to play than sitting back and enjoying the ride.", "\n\nHidden Remote: This is a small add-on to that. ", "Do you think she’ll miss her love interest, or will she find a new one?", "\n\nMina: I think Vijay deserves a slap in the face. ", "And HE knows it. ", "And Penny knows it. ", "It’s been fully established that Vijay will get a slap in the face. ", "And if Vijay doesn’t get a slap in the face, I will give Ajay a slap in the face personally.", "\n\nHidden Remote: On-screen or off-screen it’s going to happen.", "\n\nMina: All of the above, yep!", "\n\nHidden Remote: Do you have any other projects you’d like to talk about?", "\n\nMina: Right now, I’m finishing high school. ", "That’s the most difficult project there is. ", "I just took the ACTs, so my whole world has been very academic focused.", "\n\nHidden Remote: A 30, right?", "\n\nMina: Sorry?", "\n\nHidden Remote: You got a 30 at least, right?", "\n\nMina: Liiiiiisten, we’ll talk about it. ", "No, I actually haven’t seen my score yet.", "\n\nHidden Remote: So you probably did really well in English, and had trouble in science. ", "Is that it?", "\n\nMina: I would not be surprised.", "\n\nHidden Remote: Perfect for the character.", "\n\nMina: Exactly. ", "What can I say? ", "I relate to her on very private levels. ", "But, I have a couple of things in mind, but nothing that is ready to be released yet.", "\n\nHidden Remote: Alright, I was hoping for a tidbit, some inside info, but it’ll have to be a quiet end.", "\n\nMina: I can’t spill the tea quite yet.", "\n\nHidden Remote: Sounds good. ", "Well, I really appreciate the time, Mina, and here’s to future seasons of Lost in Space.", "\n\nMina: Thank you so much. ", "I really appreciate it.", "\n\nLost in Space Season 2 has been officially confirmed." ]

{ "pile_set_name": "OpenWebText2" }

[ 0.010752688172043012, 0.0196078431372549, 0, 0, 0.013157894736842105, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.013333333333333334, 0.005847953216374269, 0.030303030303030304, 0.003367003367003367, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01834862385321101, 0, 0, 0, 0, 0, 0, 0, 0.015625, 0, 0, 0, 0.006493506493506494, 0.01639344262295082, 0, 0, 0, 0, 0.01282051282051282, 0, 0, 0, 0, 0, 0.04878048780487805, 0.034482758620689655, 0, 0, 0, 0, 0, 0, 0, 0, 0.03125, 0, 0, 0, 0, 0, 0, 0, 0.01639344262295082, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.010638297872340425, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0047169811320754715, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.024390243902439025, 0.03225806451612903, 0.021739130434782608, 0, 0.018867924528301886, 0, 0, 0, 0, 0, 0, 0, 0.009900990099009901, 0, 0.01694915254237288, 0.012738853503184714, 0.0045662100456621, 0, 0.014492753623188406, 0, 0.008849557522123894, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.019230769230769232, 0, 0, 0, 0.005813953488372093, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0196078431372549, 0, 0.05, 0.014705882352941176, 0.021739130434782608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.011363636363636364, 0, 0, 0 ]

[ "Reddit Flip Pin 14 Shares\n\nAndrew Newton on the video games we were playing back in February 1990…\n\nJust like this month, February 1990 was plagued with storms with trees being uprooted, roof tiles being removed, flooding and worse. ", "The weather may have been making the country down in the mouth but on the gaming front things were doing much better and giving gamers a reason to smile. ", "Some of the cracking games that were keeping us occupied during these storms were…..\n\nX-Out – Rainbow Arts\n\nX-Out was a cracking good shoot ’em up available on all major home computers of the time from the Spectrum to Amiga and provided gamers with a lot more choice than the standard fare of this genre. ", "At the start of the game players got a certain amount of in-game money they could use straight away in the shop (manned by a creepy alien looking chap) to kit out their fighter submarines, these credits could also be used to purchase extra subs which served as lives. ", "The initial sub players started with was the cheapest and could carry 3 different weapons but as the game progressed more credits could be collected and used to purchase better subs that could carry more weaponry with the most expensive being able to carry a whopping 12 weapons. ", "Talking about weaponry, the game had masses of different weapons, including various missiles, three way weapons, lasers, orbiting auto turrets and the ever popular smart bombs.", "\n\nEnemies came thick and fast with squadrons of puny one shot kills flying onto the screen quickly, less weak ships coming singularly or in very small units and a rock hard, screen filling boss at the end. ", "But why were we fighting them I hear you cry, well apart from shooting enemies being great fun the plot was simple, alien invasion. ", "Aliens had traveled to Earth from Alpha Centauri and made their base in the depths of our oceans and only the single pilot hired by Earth’s Project Deep Star could stop them.", "\n\nX-Out earned a worthy 78% in Amiga Format and 90% in Sinclair User. ", "Look it up if you ever get an emulator.", "\n\nTurbo Outrun – US Gold\n\nRacing games were to 8 and 16-bit gamers what first person shooters are to today’s gamers, and it was an unwritten rule to own at least one. ", "In fact, in many cases a racing game magically appeared in your collection as if planted there by a little gaming elf. ", "Racing games were all over the place but perhaps none stood out so much as the Outrun franchise, and in-particular Turbo Outrun. ", "These conversions of the arcade classics were beloved by all…..well…. ", "most gamers.", "\n\nTurbo Outrun took players on a thrilling race across the United States in a lovely Ferrari F40 convertible. ", "The race, against an overly cocky Porsche 959 driver, took players from New York to L.A through several different environments including snowy mountains, sun-baked deserts and rainy city-scapes, and no the roof dis not go up on the convertible when it rained. ", "As well as a race against the clock, players had to put up with policemen and speed bumps and other nuisances on the road, but if things got to tough there was always the turbo boost!", "\n\nPlayers must have enjoyed racing in this red Ferrari (or monochrome Ferrari on the Spectrum) as there were several more titles afterwards. ", "Turbo Outrun race results were 70% in Your Sinclair and Amiga Format, and 79% in Crash.", "\n\nWatch Steve Benway play Turbo Outrun (badly) on the Sega Megadrive in the video below.", "\n\nAxel’s Magic Hammer – Gremlin Graphics\n\nThis wonderful little platformer was released on the dominating 16-bit machines and follows our young hero, Axel, as he sets out on a quest to rescue his kidnapped girlfriend from the dreaded Dragon King. ", "Armed only with a hammer, Axel must navigate his way through a hazardous world, fight his way past numerous nasties and rescue his girl.", "\n\nAlthough many folk thought Axel’s Magic Hammer was just a standard platformer, for me it was much better than most. ", "Enemies could be clobbered with the hammer but discover a power-up hidden behind some destructible blocks and the hammer could be thrown across the screen.", "\n\nDespite a thoroughly entertaining platforming romp, the reviewers just didn’t feel it broke any boundaries and awarded it average scores, 56% Amiga Action and 67% from Amiga Format.", "\n\nWizard Willy – Codemasters Cartoon Time\n\nOn the old 8-bit computers like the Spectrum and Commodore 64 there were a lot of publishing houses churning out budget games for £1.99 or £2.99. ", "Now, you may think that at such a cheap price the games wouldn’t be that good but there were so many absolute classics with Codemasters (responsible for the iconic Dizzy series) being one such publisher. ", "One of Cartoon Time’s (A label of Codemasters) entertaining little platformers arriving in newsagents back in the day was Wizard Willy.", "\n\nTaking control of the titular Wizard Willy, players had to guide him through enchanted forests, dark and damp dungeons, and crazy battlements to rescue Fifi the Fairy from the Emperors fortress. ", "Along the way, players would have to collect a number of magical eyes which they would then use in the final battle.", "\n\nThe game featured cute big sprites and was pretty easy to play, it certainly came across as a game intended for younger players rather than for older teens but there was certainly worse games out to spend £2.99 on. ", "Gaming magazines awarded it very average scores with Crash giving it a below average score of 42%, Your Sinclair awarding it 68% and Zzap!64 giving it 53%.", "\n\nChase H.Q. – Ocean Software\n\nChase H.Q. was a conversion of the arcade game and it had gamers on nearly all the main home computers hooked (except the C64, as that version is rubbish). ", "Unlike several of my friends though, I wasn’t addicted to its racing charms and ramming delights, in fact I found some aspects downright frustrating.", "\n\nPlayers take control of a police interceptor and have to track down a suspect among the multitude of other cars on the road, racing down motorways and weaving in and out of cars until you locate them. ", "Once found a few more precious seconds are added to the timer and it is up to the player to ram them repeatedly until their car stops and they give up. ", "Any collisions with other road users or objects at side of the road (and trust me you can’t help but collide with others) will cost valuable seconds and may even lead to running out of time before reaching the suspect.", "\n\nThere is also a choice of routes, although I use the word ‘choice’ loosely because if you miss the recommended route (recommended by a big yellow arrow) then you have to use all three turbo boosts to stand a chance of catching up. ", "Gameplay aside, the graphics on all platforms were well done and it did provide a good impression of speed.", "\n\nChase H.Q. made me tear my hair out but the reviewers seemed to like it with Amiga Format giving it 82%, Zero Magazine giving it 79% on the Amiga and ST, and Computer & Video Games awarding it hit status on the Spectrum with 97% and the Amiga and ST with 93%. ", "I tend to agree more with Zzap!64 who awarded it an average 53%.", "\n\nYou can see what Mr Benway thought of the Commodore 64 version in the video below.", "\n\nSo there you have it my friends, 5 games that UK gamers were enjoying in February 1990. ", "Of course, the year was only to get better but we will look at those next month.", "\n\nSEE ALSO: Back in the Day: The Video Games We Were Playing in February 1980\n\nAs usual, a big thank you to Steve Benway for allowing us to use his videos, he has hundreds more gameplay videos and system reviews for a whole host of systems so subscribe to his channel and be edu-tained.", "\n\nAndrew Newton" ]

{ "pile_set_name": "OpenWebText2" }

[ 0.004291845493562232, 0, 0.003278688524590164, 0, 0, 0, 0, 0, 0.017241379310344827, 0.014285714285714285, 0, 0, 0, 0.015503875968992248, 0, 0, 0.00909090909090909, 0.007692307692307693, 0, 0, 0.011494252873563218, 0.03409090909090909, 0.016194331983805668, 0.007352941176470588, 0.01694915254237288, 0, 0.00546448087431694, 0.010582010582010581, 0.00980392156862745, 0.014814814814814815, 0.015228426395939087, 0, 0, 0, 0.0106951871657754, 0, 0, 0, 0, 0, 0, 0.022900763358778626, 0, 0.023809523809523808, 0, 0, 0.0034965034965034965, 0.06666666666666667 ]

[ "Source: Xinhua| 2017-12-28 21:23:01|Editor: Liangyu\n\nVideo Player Close\n\nChinese President Xi Jinping speaks as he meets with Chinese diplomatic envoys to foreign countries in Beijing, capital of China, Dec. 28, 2017. (", "Xinhua/Ding Lin)\n\nBEIJING, Dec. 28 (Xinhua) -- Chinese President Xi Jinping on Thursday met with Chinese diplomatic envoys to foreign countries, calling for more efforts to advance the major-country diplomacy with Chinese characteristics.", "\n\nOn behalf of the Communist Party of China (CPC) Central Committee, Xi extended his sincere greetings to the diplomatic envoys for their hard work and lauded the great accomplishments that their diplomatic work has achieved in the past five years.", "\n\nAs socialism with Chinese characteristics has entered a new era, Xi urged the diplomats to comprehend the spirit of the 19th CPC National Congress and correctly understand the trend of the times and the international situation.", "\n\nDiplomats should be absolutely loyal to the Party, to the country and to the people, said Xi, who is also general secretary of the CPC Central Committee.", "\n\nDiplomatic envoys should resolutely safeguard national interests and national dignity, make their contributions to the country and serve the people wholeheartedly, he said.", "\n\nHe asked the diplomats to promote the building of a new type of international relations with win-win cooperation at the core, as well as the building of a community with a shared future for mankind.", "\n\nHe called for more efforts in expanding the diplomatic layout, building the global partnership network and advancing the Belt and Road construction.", "\n\nThe president called on the diplomats to actively participate in global governance and multilateral affairs.", "\n\nHe hoped that Chinese diplomatic envoys could continue to boost understanding and friendship between China and foreign countries.", "\n\nXi said the diplomatic team should enhance capacity building and acquire the ability to learn more and keep their knowledge up to date.", "\n\nHe also demanded strict compliance with political discipline for diplomats." ]

{ "pile_set_name": "OpenWebText2" }

[ 0.0045662100456621, 0.012605042016806723, 0.012096774193548387, 0.008733624454148471, 0.01935483870967742, 0, 0, 0, 0, 0, 0, 0 ]

[ "Q:\n\nSQL Server: Select hierarchically related items from one table\n\nSay, I have an organizational structure that is 5 levels deep:\nCEO -> DeptHead -> Supervisor -> Foreman -> Worker\n\nThe hierarchy is stored in a table Position like this:\nPositionId | PositionCode | ManagerId\n 1 | CEO | NULL\n 2 | DEPT01 | 1\n 3 | DEPT02 | 1\n 4 | SPRV01 | 2\n 5 | SPRV02 | 2\n 6 | SPRV03 | 3\n 7 | SPRV04 | 3\n ... | ... | ...\n\nPositionId is uniqueidentifier. ", "ManagerId is the ID of employee's manager, referring PositionId from the same table.", "\nI need a SQL query to get the hierarchy tree going down from a position, provided as parameter, including the position itself. ", "I managed to develop this:\n-- Select the original position itself\nSELECT\n'Rank' = 0,\nPosition.", "PositionCode\nFROM Position\nWHERE Position.", "PositionCode = 'CEO' -- Parameter\n-- Select the subordinates\nUNION\nSELECT DISTINCT\n'Rank' =\n CASE WHEN Pos2.PositionCode IS NULL THEN 0 ELSE 1+\n CASE WHEN Pos3.PositionCode IS NULL THEN 0 ELSE 1+\n CASE WHEN Pos4.PositionCode IS NULL THEN 0 ELSE 1+\n CASE WHEN Pos5.PositionCode IS NULL THEN 0 ELSE 1\n END\n END\n END\n END,\n'PositionCode' = RTRIM(ISNULL(Pos5.PositionCode, ISNULL(Pos4.PositionCode, ISNULL(Pos3.PositionCode, Pos2.PositionCode)))),\nFROM Position Pos1\nLEFT JOIN Position Pos2\nON Pos1.PositionId = Pos2.ManagerId\nLEFT JOIN Position Pos3\nON Pos2.PositionId = Pos3.ManagerId\nLEFT JOIN Position Pos4\nON Pos3.PositionId = Pos4.ManagerId\nLEFT JOIN Position Pos5\nON Pos4.PositionId = Pos5.ManagerId\nWHERE Pos1.PositionCode = 'CEO' -- Parameter\nORDER BY Rank ASC\n\nIt works not only for 'CEO' but for any position, displaying its subordinates. ", "Which gives me the following output:\nRank | PositionCode\n 0 | CEO\n ... | ...\n 2 | SPRV55\n 2 | SPRV68\n ... | ...\n 3 | FRMN10\n 3 | FRMN12\n ... | ...\n 4 | WRKR01\n 4 | WRKR02\n 4 | WRKR03\n 4 | WRKR04\n\nMy problems are:\nThe output does not include intermediate nodes - it will only output end nodes, i.e. workers and intermediate managers which have no subordinates. ", "I need all intermediate managers as well.", "\nI have to manually UNION the row with original position on top of the output. ", "I there any more elegant way to do this?", "\nI want the output to be sorted in hieararchical tree order. ", "Not all DeptHeads, then all Supervisors, then all Foremen then all workers, but like this:\nRank | PositionCode\n 0 | CEO\n 1 | DEPT01\n 2 | SPRV01\n 3 | FRMN01\n 4 | WRKR01\n 4 | WRKR02\n ... | ...\n 3 | FRMN02\n 4 | WRKR03\n 4 | WRKR04\n ... | ...\n\nAny help would be greatly appreciated.", "\n\nA:\n\nTry a recursive CTE, the example on TechNet is almost identical to your problem I believe:\nhttp://technet.microsoft.com/en-us/library/ms186243(v=sql.105).aspx\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0.0016313213703099511, 0.023809523809523808, 0.0078125, 0.010638297872340425, 0, 0.0054466230936819175, 0.0021645021645021645, 0, 0, 0, 0, 0, 0.012048192771084338 ]

[ "CHICAGO, April 19, 2013 /PRNewswire/ -- Boeing (NYSE: BA) honored 16 companies and one university last night with its Supplier of the Year awards, recognizing those organizations' exceptional performance and contributions to Boeing's success during 2012.", "\n\nThe awards are based on meeting or exceeding quality, on-time delivery, post-delivery support and affordability goals, and demonstrating the ability to anticipate and respond to changing requirements.", "\n\n\"We count on these important partners to help us deliver market-leading products and services that satisfy our customers,\" said Jim McNerney, Boeing chairman, president and CEO. \"", "They represent the best of a high-performing, global supply chain that keeps us at the forefront of technology and innovation.\"", "\n\nEach year, Boeing buys more than $50 billion in goods and services from more than 23,000 suppliers around the world.", "\n\n\"These partners are critical to helping Boeing provide our customers the most affordable, highest-quality products and services possible,\" said Jack House, leader of Boeing's Supplier Management program. ", "He added Boeing must have a global supply chain that is capable of recognizing and reducing risk, while demonstrating a strong commitment to customer service and consistent performance excellence.", "\n\nIn 2012, Boeing's global supply chain contributed more than 60 percent of the value of its products, helping the company recapture market share leadership in commercial aerospace. ", "Boeing delivered 601 airplanes – the most in more than a decade – including a single-year record of 415 737s and the 1,000th 777. ", "Suppliers also supported delivery of 144 production military aircraft, including the first Block C V-22 Osprey and P-8A Poseidon for the U.S. Navy and 10 satellites.", "\n\nThe list of award categories and recipients follows below. ", "For more information on each supplier, click on the link. ", "Each supplier is also profiled in this video gallery." ]

{ "pile_set_name": "Pile-CC" }

[ 0.015748031496062992, 0, 0.011049723756906077, 0, 0.00847457627118644, 0.014563106796116505, 0.00510204081632653, 0.005494505494505495, 0.007692307692307693, 0.006060606060606061, 0, 0, 0 ]

[ "owner = ITA\r\ncontroller = ITA\r\nadd_core = ITA\r\nadd_core = AUS\r\n\r\ninfra = 8\r\n1943.9.23 = {\r\n\towner = RSI\r\n\r\n\tcontroller = RSI\r\n\r\n\tadd_core = RSI\r\n\r\n}\r\n" ]

{ "pile_set_name": "Github" }

[ 0.04666666666666667 ]

[ "Threading in C++\n\nThis is a discussion on Threading in C++ within the C++ Programming forums, part of the General Programming Boards category; A quick search was not pulling up anything I could use as a starting point. ", "If I wanted to learn ...\n\nManasij Mukherjee | gcc-4.9.2 @Arch Linux Slow and Steady wins the race... if and only if :1.None of the other participants are fast and steady.", "\n2.The fast and unsteady suddenly falls asleep while running !", "\n\n[Edit]Sorry for the needlessly aggressive original. ", "I've rewritten the post with more context.[/Edit]\n\nConst correct code is thread safe in c++11\n\nYog Sothoth!", "\n\nWill you please never repeat only half of that discussion again? ", "It is hard enough to teach `const' and `mutable'.", "\n\nYour statement lacks crucial context.", "\n\nFor that to be true, `const' operations MUST be composed of only read operations across threads or be made thread-safe using measures internal to the operation.", "\n\nIf neither of those holds true for a given class, it is, in fact, trivial to write a class that is `const'-correct and `mutable'-correct. ", "Consider a class that caches to a `mutable' variable being read from a `const' method: from the point of view of the `const' `this' the `mutable' variable is a read operation even though a second thread, with a reference to the same `this', may use an operation that writes to the `mutable' variable. ", "For the standard library guarantees to hold, the reads and writes to that `mutable' variable must be internally atomic so that they outside world really does get to assume that such operations are thread-safe making the implementation, of the standard library, thread-safe by virtue.", "\n\nThere is no magic to this \"new\" situation; if you write internals of a class such that they aren't thread-safe with respect to `const' and `mutable' using those keywords correctly will do nothing for you. ", "The standard library implementation in question will probably choke on your class." ]

{ "pile_set_name": "Pile-CC" }

[ 0.0091324200913242, 0.011764705882352941, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]

[ "\"Marrying the Mafia\" \"Executive Producer JUNG Tae-won\" \"JUNG Joon-ho\" \"KIM Jung-eun\" \"YOO Dong-geun\" \"SUNG Ji-roo\" \"PARK Sang-wook\" \"PARK Keun-young LEE Ki-young\" \"LEE Seo-yeon RYU Hae-jung\" \"Special Guest JIN Hee-kyung\" \"Original Screenplay / Director JUNG Heung-soon\" \" Who are you?\" \" ", "Who are you?\" \"", "Those are mine, you know.\" \" ", "Who are you, and where am I?\" \" ", "This would be my house.\" \" ", "What did you do to me?\" \" ", "What are you talking about?\" \"", "What are you?\" \"", "Are you a kidnapper?\" \" ", "What the...\" \" Wait!\" \"", "For crying out loud, will you let me speak?\" \"", "Just be quiet.\" \"", "I don't need this now.\" \"", "Oh my god... what do I do now?\" \"", "My god... what am I gonna do now...\" \" My god...\" \" I don't know.\" \"", "Hey, miss...\" \"I think you're seriously mistaken.\" \"", "Please just calm down and let's think.\" \"", "Take it easy now.\" \"", "I swear, I didn't do anything.\" \"", "Hey, miss...\" \"What's wrong?\" \"", "Miss!\" \"", "Hello?\" \"", "Ummm... miss?\" \"", "Dad, I think this is it!\" \"", "Miss!\" \"", "Miss!\" \"", "Wait.\" \"", "Get your hands off of me!\" \" ", "What the hell are you doing?\" \" ", "Get your hands off of me!\" \" ", "Please just let go.\" \" ", "Miss.\" \"Hey!\" \"", "Take my name card here.\" \"", "I don't need it.\" \"", "And don't worry...\" \"I'm not gonna ask you to take responsibility for this.\" \"", "No...\" \"I just need my clothes back.\" \"", "I wouldn't take these even if you gave these to me for free.\" \"", "Just in case, can I get yours?\" \"", "Hey, Yoo-jin...\" \"Here!\" \"", "Here's my card.\" \"", "Wait...\" \"I can explain this.\" \"", "So that's why you left me so early last night.\" \"", "Whatever.\" \"", "It doesn't really matter to me.\" \"", "It's just that...\" \"I thought you could do better than that.\" \"", "So you picked up a prostitute on your way home, huh?\" \"", "See you later.\" \"", "Wait...\" \"A prostitute?\" \"", "How am I a prostitute?\" \"", "Member database security, more so than ever is increasingly becoming a major issue in maintaining a company's market share.\" \"", "Accordingly, Rio Web Solution Corp.\" \"developed the best security system\" \"Cyber Protector 7.7 with world renown\" \"Webpia Corp. In a strategic partnership.\" \"", "Hi.\" \"", "Hi.\" \"", "Hey, Mr. Park!\" \"", "Absolute home-run.\" \"", "Thanks to you.\" \"", "Dinner's on me tonight.\" \"", "Oh wait, I think someone's waiting for you at the rooftop.\" \" ", "At the rooftop?\" \" ", "Yeah.\" \"", "Did you gentlemen look for me?\" \" ", "Piss ass.\" \" ", "What are you doing?\" \"", "Take it easy guys.\" \"", "Why are you hitting me?\" \"", "Please let me go.\" \"", "I'm sorry.\" \"", "Whatever I did to you, I won't ever do it again.\" \"", "What are you sorry for?\" \"", "I'm not exactly sure.\" \"", "What?\" \"", "Say that again bitch.\" \"", "Why don't I take care of him?\" \"", "Alright.\" \"", "Look down bitch!\" \"", "PARK Dae-suh.\" \" ", "This is him alright.\" \" ", "Is that right?\" \"", "Then let's get him.\" \"", "Okay.\" \"", "Okay.\" \"", "Can you at least tell me what you have against me?\" \"", "Okay... if you must know...\" \"Hey, Kyung-tae.\" \"", "What are you a girl?\" \"", "Don't pee in your pants or anything.\" \"", "Just listen.\" \"", "Uhh...\" \"Over here is our father, JANG Jung-jong.\" \"", "And this over here, would be me.\" \"", "Next to me would be JANG Seok-tae.\" \"", "Followed by JANG Kyung-tae.\" \"", "And this over here is our princess you decided to get on with last night.\" \"", "We'll get into that later.\" \"", "So anyway, all of us put together is what you would call a family.\" \"", "Okay...\" \"I think I know what you're talking about, but...\" \"Here, I got it.\" \"", "Look at this kiss ass.\" \"", "You're alright boy.\" \"", "Get up for a sec.\" \"", "Here.\" \"", "Take a puff.\" \"", "Alright that's enough.\" \"", "So what are you gonna do about Jin-kyung?\" \"", "A man's gotta take responsibility for his actions, right?\" \"", "What responsibility?\" \"", "I didn't do anything.\" \"", "Hey, you slept with my sister so you'll take responsibility.\" \"", "We did sleep together, but never actually did it.\" \" ", "Never actually did it.\" \" ", "Motherfucker!\" \"", "I'm sorry.\" \"", "Please help me.\" \" ", "Down more, down more.\" \" ", "Please help me.\" \" ", "Down more boys.\" \" ", "Okay, I did it once.\" \"", "Drop!\" \"", "Memorandum PARK Dae-suh\" \"Motherfucker.\" \"", "Who told you to use SAT words on a memorandum?\" \"", "Here, give it to me.\" \"", "Memorandum.\" \"", "It looks just fine.\" \"", "What's wrong with you boys?\" \"", "Didn't you study at the pen?\" \"", "What did you do in school?\" \"", "Considering the circumstances involving the night of May 2nd.\" \"", "the alleged attempt at having sexual intercourse with Ms. JANG Jin-kyung seems rather probable.\" \"", "However, valid evidence seems to be lacking...\" \"This is the problem with educated motherfuckers.\" \"", "Hey, Mr. Law School.\" \"", "We ain't no brain surgeons.\" \"", "So make it simple.\" \"\"", "I got jiggy with Jin-kyung late that night\"\" \"\"so I will take full responsibility.\" ", "Somewhere along those lines, okay?\" \"", "Stupid.\" \"", "You ain't no Will Smith.\" \"", "Just say you did boom boom.\" \"", "Getting jiggy and boom boom... same shit.\" \"", "What's so hard about writing a memorandum?\" \"", "Make it simple.\" \"", "Just say, on the night of May 2nd,\" \"I did it with Jin-kyung three to five times.\" \"", "You got that?\" \"", "Do you want to go back up to the rooftop?\" \"", "Isn't this one of those...\" \"Oh my god!\" \"", "You did it.\" \"", "No!\" \"", "I don't know maybe.\" \"", "You're such a girl.\" \"", "Why didn't you tell me?\" \"", "So who's the lucky guy?\" \"", "Is he cute?\" \"", "Come on, I'm serious.\" \"", "Is it no period?\" \"", "When did you do it?\" \"", "Yesterday.\" \"", "And you're doing this today?\" \"", "Relax... you're not a rabbit.\" \"", "Hey, are all your brothers gangsters?\" \" ", "I'm sorry.\" \" ", "Sorry's all you got?\" \"", "Who the hell do they think they are?\" \"", "With this kind of beating, we're talking at least a four week diagnosis.\" \"", "That's strange... guess they were tired.\" \"", "What?\" \"", "Usually, it's an easy eight to twelve weeks.\" \"", "That's real funny.\" \"", "So you're telling me that boy and Jin-kyung spent a night together?\" \"", "Yes, father.\" \"", "Forgive me for saying this... but they sort of got it on all night.\" \"", "You know...\" \"They what?\" \"", "Who is this boy?\" \"", "He went to Seoul National University's Law School.\" \"", "He must be smart as hell.\" \"", "That's right.\" \"", "For real?\" \"", "Seoul National?\" \"", "Isn't that like the best school in the nation?\" \"", "Now we can finally have an elite family member after all.\" \"", "Marvelous.\" \"", "We could definitely use some brain in our family.\" \"", "But isn't that like nearly impossible to get into?\" \"", "Yeah, pop.\" \"", "That school's got all the smart people in this country.\" \"", "Then go get him for our family honor.\" \"", "Don't worry about it father.\" \"", "I'll make sure he gets married to Jin-kyung.\" \"", "Even if that means breaking his legs.\" \"", "Marvelous.\" \"", "Marriage?\" \"", "That's nonsense.\" \"", "Marriage?\" \"...", "all because of a one night stand?\" \"", "What are you talking about?\" \"", "I didn't sleep with her.\" \"", "You just said you did.\" \"", "We did sleep together, but we never did it.\" \"", "Don't you believe me?\" \"", "I believe you.\" \"", "And even if you did it,\" \"I can let it go for once.\" \"", "I really didn't.\" \"", "Well...\" \"I'm not sure but I just don't think we did...\" \"Forget about it.\" \"", "You can go now.\" \"", "Okay.\" \"", "Hello?\" \" ", "Hey, brother!\" \" ", "What?\" \"", "Forgot my voice already?\" \"", "It's me, JANG In-tae.\" \"", "Jin-kyung's brother.\" \"", "My father wants to see you.\" \"", "So if you'll come down to Yeo-soo...\" \"Guess got disconnected.\" \"", "Anyway, I said some nice things about you.\" \"", "So my father is eager to meet you.\" \"", "So why don't you come down to Yeo-soo?\" \"", "It should be fun.\" \"", "I'll talk to you later.\" \"", "And if you hung up on purpose before, don't do it again.\" \"", "We're like brothers now.\" \"", "You're the man, Later.\" \"", "So you're here.\" \"", "You have something to say to me?\" \"", "Why don't we go outside?\" \"", "I can't.\" \"", "I'm working.\" \"", "Need to get back in soon.\" \"", "Okay, we'll talk here then.\" \"", "Have a seat.\" \"", "I really gave this some thought.\" \"", "Perhaps we can... go to the hospital and take a test you know, since we don't remember much.\" \"", "Are you...?\" \"", "What is that you want to test?\" \"", "Uhhh... you know, your hymen.\" \"", "What are you doing?\" \"", "Is that so important to you?\" \"", "Of course it is.\" \"", "Isn't it important to you?\" \"", "You were going to kill yourself.\" \"", "It wasn't about keeping my virginity.\" \"", "I just felt terrible that I had done this with someone I didn't even know.\" \"", "Did what?\" \"", "Christ.\" \"", "Your brothers are telling me to take responsibility for sleeping with you.\" \"", "I'll talk to my father about that and see what I can do.\" \"", "Talking to your father won't solve anything.\" \"", "You think I'm taking all this shit because I don't know how to fight?\" \"", "Your nose is bleeding.\" \"", "Have a good day.\" \"", "Hey, Jin-kyung!\" \"", "Jin-kyung!\" \"", "Bang!\" \"", "What brings you here?\" \"", "Your clothes...\" \"I had them dry cleaned.\" \" ", "Thanks.\" \" ", "Wait...\" \"Can I speak to you for a minute?\" \" ", "Have a seat.\" \" ", "Okay.\" \"", "Are you scorpio?\" \"", "Know anything about stars?\" \"", "Well... we have stars at home.\" \"", "Oh...\" \"You're missing a star.\" \"", "My girlfriend took that.\" \"", "Yeah...\" \"About what you asked last time...\" \"Yeah...\" \"I thought about it for a while and decided to do it.\" \"", "Really?\" \"", "That's great.\" \"", "Thank you so much.\" \"", "I'll never forget this.\" \"", "I'm gonna go now.\" \"", "Why already?\" \"", "Have some juice at least.\" \"", "One, two, three, four.\" \"", "One, two... three, four.\" \"", "So everything's okay?\" \"", "Play soccer from now on.\" \" ", "Master Albong's secret text...\" \" Albongrok.\" \"", "This is the Albongrok.\" \" ", "So did you look him up?\" \" ", "Yes, father.\" \"", "First and foremost his private life seems real clean.\" \"", "And he's got good connections from his SNU Law School alumni.\" \"", "His father was a colonel for the army and is now some executive.\" \"", "Most importantly, the kid stood on his own through hard work.\" \"", "Is that right?\" \"", "That's great.\" \"", "So what's that web thing he's doing?\" \"", "It's called web solution.\" \"", "So I think he brings solutions for problems on the internet.\" \"", "So he's a problem solver.\" \"", "Sure, father.\" \"", "I'm counting on you to get the kid for our family honor.\" \"", "I'll die happy if Jin-kyung can find a decent man to marry.\" \"", "Okay father.\" \"", "I'll get started on it right away.\" \" ", "Right on.\" \" ", "Yeah.\" \" ", "Wait!\" \" ", "Yes.\" \"", "But aren't you going to play this with me?\" \"", "Alright then.\" \"", "Hundred bucks minimum.\" \"", "You got it.\" \"", "I shouldn't be doing this.\" \"", "I got things to take care of.\" \"", "Your turn.\" \" ", "Wow.\" \" ", "What the hell...\" \" Give me a beer.\" \" ", "Yes.\" \" ", "Here you go.\" \" ", "Thanks.\" \"", "Guess you really like eggs...\" \"No.\" \"", "It's just that... you can't go without boiled eggs on a train.\" \" ", "You want some?\" \" ", "No, I don't eat boiled eggs.\" \"", "It's good.\" \"", "You should try.\" \"", "Do you know how many you've had?\" \"", "Are you sure you went to Seoul National?\" \"", "What does boiled eggs have to do with SNU Law School?\" \"", "They taste good and that's all that matters.\" \"\"", "WALCOME TO YEO-SOO.\"\" \"\"", "JANG'S FAMILY'S TO-BE BROTHER IN-LAW.\"\" \"", "Good to see you again.\" \"", "This ride costs about a hundred grand, you know.\" \"", "We should take this to Seoul and drive around Apku-jong.\" \"", "For what?\" \"", "You know, we can pickup some nice broads there.\" \"", "And rip 'em naked.\" \"", "Hey, hey.\" \"", "Do you have to use that Kind of language right now?\" \"", "What would our to-be brother in law think of our family?\" \"", "Be Quiet.\" \"", "Why do you always pick on me?\" \"", "Ain't there no love for us anymore?\" \"", "I mean...\" \"I wanted to go to Seoul National too.\" \"", "But you know, I ain't that smart and figured it was too far from home.\" \"", "So I gave up the dream.\" \"", "We're not getting no love no more.\" \"", "Dae-suh is four years older than you, so just shut the fuck up.\" \"", "I'm sorry.\" \"", "Please be understanding.\" \"", "PARK Dae-suh here.\" \"", "Very nice meeting you, sir.\" \"", "Is this what I think it is?\" \"", "Yes, father.\" \"", "It's a proof that says my body is all well.\" \"", "Okay.\" \"", "Then, let's set a date now.\" \"", "What date, father?\" \"", "Date for the wedding, of course.\" \"", "What?\" \"", "Sir, I think you're going over the line.\" \"", "What did you say?\" \"", "You have here a proof that says she's a virgin, and you're not satisfied with that?\" \"", "That's not what I mean, sir.\" \"", "I just don't think that marriage is something you can take that lightly.\" \"", "It has to be based on a profound foundation of love.\" \"", "What did you say?\" \"", "I beg to differ.\" \"", "Marriage is about destiny.\" \"", "And for you, sleeping with my daughter was destiny.\" \"", "Do you hear what I'm saying?\" \"", "But, sir... just like you don't marry women you randomly meet at bars,\" \" What?\" \" ", "What are you doing?\" \"", "You think my daughter's just some random girl?\" \"", "That's not what I said.\" \"", "If you have eyes, look at my daughter here.\" \"", "She's beautiful and smart.\" \"", "And she's a hospital approved virgin.\" \"", "You spend a night with my virgin daughter and this is what I get?\" \"", "How do you call yourself a man?\" \" ", "How irresponsible...\" \" Father.\" \" ", "Father, please.\" \" ", "Off of me.\" \"", "You don't know how hard it was to raise my princess on my own.\" \"", "You would never know.\" \"", "Raising her without her mother... my dear...\" \"I feel so lonely.\" \"", "Father!\" \"", "Dae-suh please have some food.\" \"", "How is this possible?\" \"", "Well... if we don't give into the situation, we're both dead.\" \"", "Just relax and enjoy the food.\" \"", "How can I relax?\" \"", "Looking good you two.\" \"", "Beautiful!\" \"", "Take it slow for now though.\" \"", "Hey Dae-suh, that's my wife.\" \"", "She's from Wanwol village.\" \"", "I don't know if you've been there.\" \"", "Nice meeting you.\" \"", "I'm PARK Dae-suh.\" \"", "I didn't expect you to be so naughty miss.\" \"", "I mean...\" \"I never imagined you would spend a night with a total stranger.\" \"", "Was it good?\" \"", "They just literally slept together.\" \"", "Just stay out of it.\" \"", "You actually want me to believe that nothing happened between two naked people of opposing sex in their twenties?\" \"", "What would you have done?\" \"", "I would've just done it, of course.\" \"", "You see?\" \"", "What about you?\" \"", "What do you think I'm crazy?\" \"", "How do you not do it?\" \"", "Plus, I wouldn't even have made it to bed.\" \"", "What about you?\" \"", "A man's gotta do what's necessary.\" \"", "You see... you're lying...\" \"Lying to me.\" \"", "I'm thinking they did it.\" \"", "Honestly, we didn't.\" \"", "I even brought you the doctor's note.\" \"", "Oh yeah, forgot about that.\" \"", "How do you know if that's real?\" \"", "Anyway, did you use protection?\" \"", "What the hell is wrong with you today Mi-soon?\" \"", "You stay out.\" \"", "Jin-kyung can be very naive sometimes, you know.\" \"", "Okay, let's just go have some drinks... just us men.\" \"", "Sounds good.\" \"", "Why don't you just stay... home for a change?\" \"", "Our future brother in law is here.\" \"", "It would be rude not to treat him.\" \"", "You're gonna go to that bar with whore hostesses again, aren't you?\" \"", "Relax.\" \"", "I won't go to the one in Wanwol.\" \"", "Stupid bitch.\" \"", "So I'm from Wanwol, what are you gonna do?\" \"", "Hope you die!\" \"", "What did you say to your husband?\" \"", "Here, take one.\" \"", "And just make yourself at home, ok?\" \"", "You better fuck the shit out of your partner tonight.\" \"", "Our baby here looks so innocent.\" \"", "Of course, he went to Seoul National.\" \"", "Really?\" \"", "I love intelligent men.\" \"", "I always hated nerds back in school.\" \"", "I think pretty much every one in the top 10%% % got their asses beat by me.\" \"", "Just because they were smart.\" \"", "For our future brother in law!\" \"", "You too, Kyung-tae.\" \"", "Let's drink.\" \"", "Hey, fuckface!\" \"", "Idiot, wake up!\" \"", "What a piece of scum.\" \" ", "For Dae-suh!\" \" ", "Cheers!\" \"", "Dae-suh!\" \"", "Are you awake?\" \"", "Yes, I'm awake.\" \"", "I brought you some honey tea.\" \"", "I'll put in by the door.\" \" ", "Jin-kyung, I want to talk to you.\" \" ", "I know what it is.\" \"", "We'll talk on our way back.\" \"", "Tea's always good for hangovers.\" \"", "Have some.\" \"", "It's not much... but take this.\" \"", "It should be enough to take Jin-kyung out on dates.\" \"", "I couldn't possibly.\" \"", "It's unnecessary, sir.\" \"", "It's not a big deal.\" \"", "Just take it.\" \"", "It's his order.\" \"", "It's really okay.\" \"", "Take it.\" \"", "Make sure to set a date for a formal bow before the wedding.\" \"", "I'm thrilled about Jin-kyung getting married.\" \"", "Finally...\" \"That thrilled, huh?\" \"\"", "Attorney at Law KIM Do-hyung.\"\" \"", "Wait here for a minute.\" \"", "I just want to say hi to a brother from my fraternity.\" \"", "Okay, just don't take too long.\" \"", "We don't want to miss the train.\" \"", "It'll be quick.\" \"", "You came to the right place.\" \"", "I specialize in threat counseling.\" \"", "So who is it that's threatening you?\" \"", "Do you know who JANG Jung-jong is?\" \"", "JANG Jung-jong?\" \"", "Yeah.\" \"", "What are you kidding?\" \"", "Everyone knows Triple J.\" \"Triple J?\" \"", "Triple J is a legend.\" \"", "Supposedly, he once took on more than ten members of the...\" \"Dolsan family all by himself.\" \"", "Some say it was more than that.\" \"", "Just him and them.\" \"", "JANG Jung-jong.\" \"", "J, J, J Triple J...\" \"People once compared him to Robin Hood.\" \"", "He was poor fishermen's hero.\" \"", "The Dolsan family's boss left Yeo-soo ever since.\" \"", "And the two families became enemies.\" \"", "Let's assume that Triple J has a daughter.\" \"", "And some guy spent a night with her by accident.\" \"", "And Triple J wants the two of them to get married.\" \"", "But the guy refuses.\" \"", "What do you think will happen to the guy?\" \"", "That guy will disappear, and nobody will ever find out.\" \"", "because, he was buried in the ground.\" \"", "Holy god.\" \"", "Then what do you think the guy should do?\" \"", "There's only one answer.\" \"", "He should get married, or commit suicide.\" \"", "What?\" \"", "Suicide?\" \"", "Think you can do it, kid?\" \"", "Yes, sir.\" \"", "She's pretty hot too.\" \"", "It's not gonna be easy though.\" \"", "Considering she's a designer and all.\" \"", "If you take care of this,\" \"I'll see about that commercial you wanted.\" \"", "I'm not kidding you.\" \"", "You know my connections...\" \"Let's just leave it at that.\" \"", "Thank you, sir.\" \"", "I would've done it myself, if it weren't for a family matter.\" \"", "But need to stay out this time.\" \"", "I'm counting on you, okay?\" \"", "I'll keep that in mind, sir.\" \" ", "Did you have lunch?\" \" ", "Mi-soon.\" \"", "What brings you here?\" \"", "Just stopping by.\" \"", "Who is he?\" \"", "He'll be working with us.\" \"", "Really?\" \"", "Nice meeting you.\" \"", "I'm Mi-soon.\" \"", "Jesus.\" \"", "She's Mr. Jang's wife.\" \"", "YEO Min-seok here.\" \"", "Pleasure meeting you.\" \"", "My pleasure.\" \"", "So you're the rookie model, YEO Min-seok, right?\" \"", "What an honor...\" \"so what brings you here?\" \"", "Hey.\" \"", "Stop embarrassing me, and just sit.\" \"", "Do you always have to do that in front of other people?\" \"", "We're gonna go now.\" \"", "Okay.\" \"", "He had a really... cute butt.\" \"", "Why don't you go date him then.\" \"", "Dirty whore.\" \"", "You have a husband to serve.\" \"", "You're one to speak.\" \"", "You're the one that sleeps around with hostess sluts all the time.\" \"", "What the...\" \"Are you starting with me?\" \"", "I didn't come here to see you.\" \"", "I came to talk about our son.\" \"", "Like father like son.\" \"", "I'm ashamed to visit his teacher.\" \"", "Can I help you?\" \"", "Are you...\" \"Ms. WON Hae-sook?\" \"", "I'm Young-min's father.\" \"", "Oh yeah, please come in.\" \"", "Yes.\" \"", "Thought you were going to marry Yoo-jin.\" \"", "What happened?\" \"", "It's a long story.\" \"", "Just go along with me.\" \"", "A mob family?\" \"", "This is just so preposterous.\" \"", "Please just bear with me today.\" \"", "Or else, we're all dead.\" \"", "What are you so scared of?\" \"", "I maybe a retired colonel, but I can take 'em.\" \"", "Don't worry about it.\" \"", "I'll take care of it.\" \"", "Dad, I don't think it'll be that easy.\" \"", "You don't think I can take them?\" \"", "Oh lord.\" \"", "Dad, there they are.\" \"", "Good to see you, sir.\" \"", "It's a pleasure meeting the in-laws.\" \"", "Pardon?\" \" ", "Please have a seat.\" \" ", "Okay.\" \"", "Cheers again!\" \"", "To our family honor,\" \"What is this a beauty pageant?\" \"", "I know that you're all a little surprised by the whole thing...\" \"But please be understanding as I always like things done fast.\" \"", "Why don't we set a date for the wedding while we're at it?\" \"", "Sir, marriage I think should be thought over more carefully.\" \"", "Listen to him.\" \"", "We were informed of this matter just recently... so if you'll just let us think over this with some time...\" \"Do you not like my daughter?\" \"", "No, sir.\" \"", "That's not what we meant.\" \"", "What's with the knife?\" \"", "You got anything better?\" \"", "What are you a sissy?\" \"", "Carry a bigger knife.\" \"", "You see... this works.\" \"", "This is a good knife.\" \"", "You are right on, father.\" \"", "Are you okay there?\" \"", "Would you like to try this?\" \"", "Father.\" \"", "Okay.\" \"", "Her family was a little rough, but she seemed very nice, right?\" \"", "That's right, Dae-suh.\" \"", "I think you should give this some thought.\" \"", "I'm not getting married to no mafia.\" \"", "We could all get hurt though.\" \"", "I was so scared,\" \"I couldn't tell where the food was going.\" \"", "What's wrong with you?\" \"", "I'm not marrying her regardless.\" \"", "Hey, Dae-suh.\" \"", "Please think again.\" \"", "I think it could really be something.\" \"", "On the bright side, it could bring us wealth.\" \"", "Dad, what happened to your\" \"\"I'll take care of everything\" speech?\" \"", "Hi.\" \"", "Why are you making a big fuss over a one night stand?\" \"", "Excuse me?\" \"", "I understand that your family's a bunch of thugs.\" \"", "No wonder.\" \"", "But don't you think that this is too much?\" \"", "I think you're crossing the line.\" \"", "Why is your family going all out to get your married to Dae-suh?\" \"", "I've been going out with him for six years.\" \"", "Six god damn years.\" \"", "Do you know what we went through during all that time?\" \"", "How long did you know him?\" \"", "About two weeks.\" \"", "And of course, you probably slept with him way more times.\" \"", "Bitch.\" \"", "If you measure love by the number you've had sex with the person,\" \"Why would there ever be divorced couples?\" \"", "Whatever.\" \"", "That's enough.\" \"", "That's right, my family members are all thugs you got a problem with that?\" \"", "Just shut the fuck up before I rip your mouth.\" \"", "You know Dae-suh would never just randomly sleep around.\" \"", "Who do you think you are?\" \"", "You wanna die, bitch?\" \"", "Need to calm down now.\" \"", "You see...\" \"I never gave two shits about your boyfriend to tell you the truth.\" \"", "But just because you're a little slut,\" \"I just might as well take him from you.\" \"", "So I don't ever want to see you again.\" \"", "You don't think this is too much?\" \"", "I mean... couldn't you find a man on your own?\" \"", "Stop pretending like you're a goodie goodie.\" \"", "Here in democracy,\" \"I mean... what's up with all the violence?\" \"", "If not smart, you should at least be nice.\" \"", "If they use violence again,\" \"I'm telling the police...\" \"What was that for?\" \"", "That's right, my family's a bunch of low-life gangsters.\" \"", "But they're still my family.\" \"", "They raised me with love and devotion.\" \"", "They may be gangsters, but they're my father and brothers.\" \"", "Even if people point fingers at them, they're my loving family.\" \"", "Who are you to talk bad about them?\" \"", "Why are you crying?\" \"", "Why are you talking like that about my family?\" \"", "Stop crying.\" \"", "You just degraded my family.\" \" ", "When did I...\" \" You did.\" \"", "That's not what I...\" \"Man... that's some touching shit.\" \"", "It's like a god damn movie.\" \"", "They're looking real good.\" \"", "Hey, Yoo-jin!\" \"", "What brings you here?\" \"", "Yoo-jin, YEO Min-seok.\" \"", "Min-seok, LEE Yoo-jin.\" \"", "You know him, right?\" \"", "Of course I've seen you on magazines, but it's my first time in person.\" \"", "Nice meeting you.\" \"", "LEE Yoo-jin here.\" \"", "Pleasure meeting you too.\" \"", "She studied in France.\" \"", "We all have huge expectations of her.\" \"", "Looking forward to working with you.\" \"", "Don't mention it.\" \"", "I should be the one to thank you.\" \"", "Let's get to business.\" \"", "They're going to the chick's house.\" \"", "My parents went abroad.\" \"", "My sister studies in England, so they made a trip out of it.\" \"", "Yeah...\" \"I like your house.\" \"", "So what's your intention?\" \"", "What do you mean?\" \"", "You're being too nice to me.\" \"", "When you really have no reason to be.\" \" ", "I have a work to do.\" \" ", "What are you talking about?\" \"", "I just want to get to know you a little bit better, that's all.\" \"", "Oh yeah?\" \"", "Right on then.\" \"", "Let's.\" \"", "I sort of needed this lately, because of heavy stress.\" \"", "I'll shower first.\" \"", "Sir, you need to pay.\" \"", "Look at the check please.\" \"", "C'mon get up sir.\" \"", "Check please.\" \"", "376 grand?\" \"", "Are you nuts?\" \"", "What are you crazy?\" \"", "What the...\" \"You expect me to pay this?\" \"", "This is a fuckin' scam.\" \" ", "Call the manager.\" \" ", "Sir...\" \"What?\" \"", "What?\" \" ", "Are you the manager?\" \" ", "Yeah, what?\" \"", "What the hell is wrong with you people?\" \"", "You drink, you pay.\" \"", "When the hell did we drink that much?\" \"", "Look at all these bottles you drank.\" \"", "What the hell...\" \"Who drank this?\" \"", "You're underestimating me.\" \"", "Out of my way!\" \"", "Do you know who I am?\" \" ", "Fuckin' assholes.\" \" ", "Motherfucker...\" \"Hey!\" \"", "Hey!\" \"", "Hey!\" \"", "Alright.\" \"", "Let's see what a big shot he is.\" \"", "Who is he?\" \"", "Oh lord, I'm sorry sir.\" \"", "Please forgive us, sir.\" \"", "You get who I am now?\" \"", "Thought I would do this, right?\" \"", "In your dreams fuckheads!\" \"", "Take out their wallets.\" \"", "What the... poor bastards.\" \"", "What the...\" \"Hey, try this one.\" \"", "Mr. Manager, no need for credit cards.\" \"", "I'll make a call.\" \"", "Okay.\" \"", "Hey, Dae-suh.\" \"", "Who did you call?\" \"", "I got it.\" \"", "What the hell?\" \"", "Where's our brother in-law?\" \"", "Here.\" \"", "You okay, brother?\" \"", "Yeah.\" \"", "On your knees asshole.\" \"", "Fuck.\" \"", "Don't be stupid.\" \"", "Be nice boys, okay?\" \"", "Fuckin' assholes.\" \"", "Hey, keep it straight!\" \"", "Dae-suh!\" \"", "You got a problem, bitch?\" \"", "Fuckin' assholes.\" \"", "Be nice, okay?\" \"", "What?\" \"", "Who did?\" \"", "Fuck.\" \"", "Boss!\" \"", "Who the fuck was it?\" \"", "I'm thinking it had to have been triple J's boys.\" \"", "Hang the fuck up.\" \"", "Are you stupid?\" \"", "How did they invade our territory?\" \"", "Boss, you're getting wet.\" \"", "I don't give a shit stupid.\" \"", "Just go get triple J you shmuck.\" \"", "Hey, brother.\" \"", "How come you're not picking up the phone?\" \"", "Jin-kyung's been kidnapped.\" \"", "Give me a call when you get this message.\" \"", "The message has been deleted.\" \"", "What?\" \"", "How did that happen?\" \"", "Press the star button.\" \"", "I did, moron.\" \"", "For AT T wireless, you have to press the pound key.\" \"", "Why is everything so damn complicated?\" \"", "Hey, I'm sorry.\" \" ", "Wait a moment...\" \" Let's go!\" \"", "I got that.\" \"", "Take care.\" \"", "Hey, Dae-suh.\" \"", "Jin-kyung's all yours.\" \"", "So remember, you're gonna have to save Jin-kyung, okay?\" \"", "Okay!\" \"", "You boys crossed our territory, huh?\" \"", "Just shut up and get down here.\" \"", "Nice move kidnapping my sister.\" \"", "What the...\" \"Off of me!\" \"", "Take it easy... jesus.\" \"", "Dae-suh's really something that kid.\" \"", "I just thought he was a well educated geek.\" \"", "But today, he showed us his bravery by saving Jin-kyung.\" \"", "As he should.\" \"", "He'll be a part of our family soon.\" \"", "Jin-kyung, how do you feel about Dae-suh?\" \"", "You can talk to us.\" \"", "What do you think?\" \"", "I don't know...\" \"Don't mention it.\" \"", "Relationships... should come natural.\" \"", "He has a girlfriend he's been dating.\" \"", "No need to worry about that.\" \"", "You're right.\" \"", "We don't want to force anything between you two.\" \"", "I understand what you and father are trying to do.\" \"", "I just want someone nice and warm like you guys.\" \"", "Except for all the fighting.\" \"", "Let's go to sleep now.\" \"", "We all have to go to work.\" \"", "I'm really in no mood to drink.\" \"", "I have an important meeting tomorrow morning.\" \"", "We'll just have a beer or two.\" \"", "This place isn't bad.\" \"", "Let's go.\" \" ", "Let's go.\" \" ", "I...\" \"Take this.\" \"", "Bottoms up.\" \"", "You know her?\" \"", "No...\" \"How was your day Mr. Park?\" \"", "Some lady left this here.\" \"\"", "Try not to skip meals.\" \"", "Jin-kyung\"\" \"Man... this is some expensive dog.\" \"", "Yeah man...\" \"Can't get no dogs anymore these days if you're not rich.\" \"\"", "My name is Mr. Dae-suh.\" \"", "Dae-suh.\"\" \"", "I never ate breakfast before...\" \"But I've been eating it everyday, thanks to you.\" \"", "Have you been taking cooking classes?\" \"", "How did you know?\" \"", "I only went twice.\" \"", "I can tell by the taste.\" \"", "You can always tell one's cooking if you taste the food, but did you?\" \"", "Do you want to hear a funny story?\" \"", "Dae-suh snoars during sleep.\" \" ", "I snoar?\" \" ", "Yes.\" \"", "And he also grinds his teeth.\" \"", "Oh... you mean when I drank with your brothers and got really drunk...\" \"You first.\" \"", "Dae-suh drinks a lot of water it seems.\" \"", "Not really.\" \"", "Only when I eat salty food.\" \"", "But there's always pee on the floor.\" \"", "I was busy cleaning it for a while.\" \"", "What?\" \"", "Watch out.\" \"", "The elevator needs repair.\" \"", "Please use the stairs.\" \"", "What do we do?\" \"", "Don't worry.\" \"", "I'm with you.\" \"", "There should be an emergency switch over here somewhere.\" \" ", "Here...\" \" Get your hands off!\" \"", "Sorry.\" \"", "Thought the switch was too big.\" \"", "Your hands are still on me.\" \"", "Where is it then?\" \"", "Maybe it's this one.\" \"", "That's mine too.\" \"", "Sorry.\" \"", "Thought I saw it somewhere.\" \"", "What's wrong?\" \"", "Dae-suh!\" \"", "Move that over for a sec.\" \"", "That surprised me big time.\" \"", "The phone's not working either.\" \"", "This is 'apple juice'.\" \"", "We're at the destination, over.\" \"", "This is 'viagra'.\" \"", "Got it, over.\" \"", "That was quick.\" \"", "Don't move.\" \"", "Dae-suh!\" \"", "Dae-suh!\" \"", "Dae-suh!\" \"", "Dae-suh!\" \"", "Dae-suh!\" \"", "Dae-suh!\" \"", "Dae-suh!\" \"", "The star you're looking at right now is a virgo named Spica.\" \"", "That doesn't look like a virgin to me.\" \"", "Use your imagination.\" \"", "How about that?\" \"", "Yeah.\" \"", "Now it does.\" \"", "It's resistance to a compromise with reality is what makes it so beautiful.\" \"", "Thanks for laying out my personality so nicely.\" \"", "I'm not done yet.\" \"", "As the virgin went up to create the stars, she shed ears on the way.\" \"", "Do you know what those turned into?\" \"", "No.\" \"", "The milky way.\" \"", "Orpheus played the harp in front of Hades to revive his dead wife.\" \"", "Touched by Orpheus' spirit, Hades revived Orpheus' dead wife and told Orpheus not to look back until she was completely out of hell.\" \"", "But then he looked back.\" \"", "How did you know?\" \"", "Hmm, Usually...\" \"That's what happens.\" \"", "You said you were interested in astrology.\" \"", "Out of the Harpe constellation, Vega stands out the most.\" \"", "Like you, Jin-kyung.\" \"", "Why did you call me?\" \"", "I'm busy as all hell.\" \"", "I came 'cause I missed you.\" \"", "How old is your teacher, Young-min?\" \"", "I don't know.\" \"", "You don't know your teacher's age?\" \"", "Is she married yet?\" \"", "I think she's single.\" \" ", "Are you sure?\" \" ", "Yeah.\" \"", "Really?\" \"", "You're doing okay in school?\" \"", "Well... there's this kid named KIM Dong-suk.\" \"", "He keeps writing stuff on my clothes.\" \"", "Take a look at this.\" \"", "Man...\" \"Crazy kid... so did you just let him do this to you?\" \"", "You should've stabbed him with a pencil.\" \"", "What if he gets seriously hurt?\" \"", "You see, bothering a quiet person is wrong.\" \"", "But it's okay to stab someone with a pencil if that person kept bothering you.\" \" ", "For real?\" \" ", "Of course.\" \"", "And as a man, you should always keep on eye out for yourself.\" \"", "What's up?\" \"", "I've had enough now.\" \"", "What's wrong?\" \"", "Young-min beat up a kid again.\" \"", "Who?\" \"", "KIM Dong-suk?\" \"", "How do you know him?\" \"", "Well... if you look at Young-min's diary, it says that Dong-suk's a bad kid.\" \"", "It said he wanted to hurt Dong-suk.\" \"", "Do we have to go to school?\" \"", "I don't even have time for it.\" \"", "Okay.\" \"", "Don't go.\" \"", "I'll go.\" \"", "Besides, only man can solve a man's problem.\" \"", "You okay, honey?\" \"", "Why don't you go get your hair done again?\" \"", "What a bad boy.\" \"", "Bad boy.\" \"", "Let's ban school violence!\" \"", "Let's stop school violence.\" \"", "How are you doing?\" \"", "School violence should really be stopped, don't you think?\" \"", "Sure.\" \"", "Taking my kid for instance.\" \"", "This naughty kid that sat in front of him just took out a pencil and stabbed him.\" \"", "The injury could've been quite serious.\" \"", "You can't be serious.\" \"", "That's not all.\" \"", "Excuse me for a sec.\" \"", "It's me.\" \"", "What?\" \"", "Sang-pal?\" \"", "Motherfucker.\" \"", "What the...\" \"Kill the motherfucker!\" \"", "What are you looking at?\" \"", "Ms. Won...\" \"How are you?\" \"", "So... 8 o'clock's good?\" \"", "Yeah, 8 o'clock.\" \"", "Let's ban school violence.\" \"", "So do you like the clothes?\" \"", "Yes.\" \"", "Put them on and think about me from time to time.\" \"", "I don't think we should do this.\" \"", "We didn't even do anything.\" \"", "Well...\" \"I guess you could say that.\" \"", "Don't you love me, Ms. Won?\" \"", "Man...\" \"Look at me in the eyes and talk...\" \"Don't you love me?\" \"", "Christ.\" \"", "To tell you the truth,\" \"I'm married.\" \"", "What are you talking about?\" \"", "I didn't mean to hide it from the beginning.\" \"", "I'm sorry.\" \"", "Ms. Won, settle down.\" \"", "I know you're single.\" \"", "What are you talking about?\" \"", "Are you for real?\" \"", "You sure?\" \"", "Yes.\" \"", "Oh lord...\" \"Go get some coffee.\" \"", "I said coffee!\" \"", "Okay, okay.\" \"", "What a fuckin' shame.\" \"", "What a perfect night for couples.\" \"", "Stars shining upon the sky.\" \"", "Coming up is TAE Jin-ah.\" \"", "I think she's single.\" \" ", "Are you sure?\" \" ", "Yeah.\" \"", "Providing false information is not allowed in our family.\" \"", "You fuckin' whore!\" \"", "How do you call yourself a teacher when you sleep around like that?\" \"", "Wait!\" \"", "What are you doing?\" \"", "I didn't do anything.\" \"", "What did you do that for?\" \"", "You bitch!\" \"", "Love is for lovers.\" \"", "Love is for lovers.\" \"", "What...\" \"Ms. Won!\" \"", "What happened?\" \"", "Ms. Won get ride in.\" \"", "Who did this to you?\" \"", "Who did this to Ms. Won?\" \"", "That's...\" \"Mi-soon.\" \"", "Bitches!\" \"", "Ms. Won, I'll see you later.\" \"", "I'm out.\" \"", "Sir, you have a delivery.\" \"", "Just leave it there.\" \"", "You don't wear them...\" \"Oh my panties?\" \"", "Tae-woo's taste changed.\" \"", "Fantastic.\" \"", "I told Tae-woo that I loved him last night.\" \"", "The funny thing is, as soon as I said it, I actually started falling in love.\" \"", "You?\" \"", "Love?\" \"", "Whatever.\" \"", "Jin-kyung, I'm telling you it just sort of happened.\" \"", "It comes natural.\" \"", "I was surprised myself.\" \"", "I'll see you later.\" \"", "I come here whenever I feel lonesome.\" \"", "It just makes everything better.\" \"", "Random people would just come and sing, or play music.\" \"", "I feel alive here.\" \"", "Frankly, I don't like crowded places.\" \"", "I feel more comfortable on my own.\" \"", "I think you're great except, you have this self defensive shield.\" \"", "Guess you're quite conservative.\" \"", "You should open up your mind a bit by meeting lots of people.\" \"", "It's my personality, you know.\" \"", "I'm trying... but it takes time.\" \" ", "Pleasure having you here sir.\" \" ", "Oh, yes.\" \"", "Why don't you come down and sing?\" \"", "You know I can't sing.\" \"", "It's our bar's 5th anniversary.\" \"", "If you win, you get two tickets to Saipan.\" \" ", "Really?\" \" ", "Yes.\" \"", "You're going down?\" \"", "Yeah, to the bathroom.\" \"", "I always miss you\" \"But you're not as close as you are in my mind.\" \"", "Looking at a worn out picture of you makes me miss you again.\" \"", "I always miss you.\" \"", "Where did you go?\" \"", "Come back to me.\" \"", "I'm always thinking of you.\" \"", "Dae-suh!\" \"", "What brings you here Yoo-jin?\" \"", "Thought I might see you here.\" \" ", "So I came.\" \" ", "You had too much to drink.\" \"", "I'm sorry, I have a party.\" \"", "Sure.\" \"", "I always miss you.\" \"", "Yoo-jin!\" \"", "Are you okay, Yoo-jin?\" \"", "Come back to me.\" \"", "I'm always thinking of you.\" \"", "Come back to me darling.\" \"", "Let's light up our fire.\" \"", "Dae-suh.\" \"", "I'm not feeling well.\" \"", "Stop the car please.\" \"", "Wake up, Yoo-jin!\" \"", "Why did you drink so much?\" \"", "Let's start all over Dae-suh.\" \"", "I missed you so much.\" \"", "You're too drunk.\" \"", "I'll get you something to drink.\" \"", "Hello?\" \"", "It's Jin-kyung.\" \"", "Who's calling... my boyfriend at this hour?\" \"", "She left a while ago.\" \"", "Jin-kyung!\" \"", "Jin-kyung!\" \"", "It's me, Dae-suh!\" \"", "Dae-suh, It's me.\" \"", "Jin-kyung.\" \"", "First, I want to say that I'm sorry.\" \"", "My family bothered you too much, didn't they?\" \"", "I thank you for putting up with me and feel sorry at the same time.\" \"", "But, don't think of my father and my brothers so negatively.\" \"", "If anything, it's because they love me too much.\" \"", "I'm going to see my father now.\" \"", "I'll tell them that if they bother you again,\" \"I'll run away.\" \"", "Don't worry and hope you find the right person.\" \"", "Be happy...\" \"Jin-kyung!\" \"", "Jin-kyung!\" \"", "One sec.\" \"", "Jin-kyung.\" \"", "Hey Mr., stop the car.\" \"", "Please, stop the car.\" \"", "C'mon.\" \"", "Stop the car.\" \"", "What do you want to do?\" \"", "Just keep driving.\" \"", "Hey, Jin-kyung!\" \"", "You look so beautiful.\" \"", "Thanks.\" \"", "Man... it's good to have Phil Jackson's blessing.\" \"", "Florist?\" \"", "We're missing Michael Jordan.\" \"", "Oh, and we're missing Shaq too.\" \"", "Hurry up.\" \"", "Mother...\" \"Jin-kyung's finally getting married.\" \"", "The groom is an SNU educated elite.\" \"", "He's a great guy.\" \"", "Very nice, the kid.\" \"", "Guess we're finally an elite family after all, huh?\" \"", "You would've loved this.\" \"", "Boss, you got a call.\" \"", "What is it?\" \"", "What, Sang-pal is?\" \"", "Ladies and gentlemen, the bride and groom.\" \"", "An educated man who owns and manages a respected business...\" \"My sister's getting married today.\" \"", "Please let go.\" \"", "Motherfucker...\" \"I don't think so, asshole!\" \"", "You okay?\" \"", "In-tae!\" \" ", "Are you okay?\" \" ", "What happened?\" \"", "Are you okay?\" \"", "What's going on?\" \"", "Is the wedding over yet?\" \"", "Yes, it's over.\" \"", "Get up In-tae.\" \"", "Come on, let's go.\" \"", "So you two are a couple now, huh?\" \"", "Yes, sir.\" \"", "Boys, they say the wedding's over.\" \"", "Fuckin' A.\" \"Have some respect for yourselves.\" \"", "Father, these motherfuckers...\" \"You fuck.\" \"", "How do you do?\" \"", "Just wanted to stop by and send my regards.\" \"", "You fuckin' assholes...\" \"Dae-suh, chill out.\" \"", "You need to save your energy for our honeymoon.\" \"", "Yeah, you do that.\" \"", "Are you Sang-pal?\" \"", "Good thing you came.\" \"", "I'll show you today what an excellent shape I'm in.\" \"", "Boys, let's rock and roll.\" \"", "For our family honor!\" \"", "These two are wasted.\" \"", "Taking you people home now.\" \"", "Heads!\" \"", "Watch your legs.\" \"", "You did good.\"" ]

{ "pile_set_name": "OpenSubtitles" }

[ 0.024305555555555556, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.038461538461538464, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.012658227848101266, 0, 0, 0.058823529411764705, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.058823529411764705, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.019230769230769232, 0, 0, 0.03333333333333333, 0, 0, 0, 0, 0, 0, 0.05, 0, 0, 0, 0.022727272727272728, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01020408163265306, 0, 0.043478260869565216, 0, 0, 0.011904761904761904, 0, 0, 0.037037037037037035, 0, 0, 0, 0, 0.011904761904761904, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.014285714285714285, 0, 0, 0, 0, 0.018867924528301886, 0, 0, 0, 0.05555555555555555, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.02127659574468085, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.043478260869565216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.05555555555555555, 0.07692307692307693, 0.125, 0, 0, 0, 0, 0, 0, 0, 0, 0.030303030303030304, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.03571428571428571, 0, 0, 0, 0, 0.02127659574468085, 0, 0, 0, 0, 0.015625, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.016129032258064516, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.023255813953488372, 0.017857142857142856, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.019230769230769232, 0, 0, 0, 0, 0, 0, 0.047619047619047616, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.05, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0196078431372549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.025, 0, 0, 0, 0, 0, 0, 0.045454545454545456, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.02702702702702703, 0, 0, 0.02857142857142857, 0, 0, 0.018518518518518517, 0, 0, 0, 0, 0, 0, 0, 0, 0.020833333333333332, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.010638297872340425, 0, 0, 0.05555555555555555, 0.015625, 0, 0.019230769230769232, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.016666666666666666, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.04, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.030303030303030304, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.09090909090909091, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.04, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0625, 0, 0.04, 0.04, 0, 0, 0, 0.05, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.024390243902439025, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.03333333333333333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.04, 0.017241379310344827, 0, 0, 0, 0, 0, 0, 0, 0, 0.01694915254237288, 0, 0, 0.045454545454545456, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.02702702702702703, 0, 0, 0.02, 0, 0.038461538461538464, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.03571428571428571, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.015873015873015872, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.007407407407407408, 0, 0, 0.024390243902439025, 0, 0.016666666666666666, 0.043478260869565216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.02127659574468085, 0, 0.043478260869565216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0625, 0, 0.02531645569620253, 0.02631578947368421, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.043478260869565216, 0, 0, 0, 0, 0, 0, 0.03571428571428571, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.03333333333333333, 0, 0, 0, 0, 0, 0, 0.041666666666666664, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.047619047619047616, 0, 0.043478260869565216, 0, 0.037037037037037035, 0, 0, 0.03225806451612903, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01818181818181818, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.021739130434782608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.03125, 0, 0, 0, 0, 0, 0, 0.09090909090909091, 0.04, 0, 0, 0, 0, 0, 0, 0, 0.05, 0, 0.03125, 0, 0, 0, 0, 0.05555555555555555, 0, 0, 0.07692307692307693, 0.07692307692307693, 0, 0, 0.07692307692307693, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.07692307692307693, 0.09090909090909091, 0.07692307692307693, 0, 0, 0, 0, 0, 0, 0.05555555555555555, 0, 0, 0.019230769230769232, 0, 0.03125, 0, 0, 0.0196078431372549, 0.02631578947368421, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]

[ "Dallas Cowboys quarterback Tony Romo went through a full practice Friday and is listed as probable for Sunday's game against the Jacksonville Jaguars. ", "He should be a lock to play in London.", "\nHe had no issues with his back on the plane ride to London and had no problems with his back during practice.", "\nHead Coach Jason Garrett stated that he still hasn't made a decision yet on who will start, but I think we all know that if Romo is available, he is starting.", "\nThe Jag's record is (1-8) but expect them to come hard and play a competitive game. ", "I fully expect them to bring the pressure on Romo and test how healthy he is. ", "Cowboys should get all they can handle." ]

{ "pile_set_name": "Pile-CC" }

[ 0.006622516556291391, 0, 0, 0.012578616352201259, 0, 0.01282051282051282, 0 ]

[ "Q:\n\nPreload Webpage with jQuery\n\nI found the below script here but wanted to know if it is posible to preload multiple pages with the same script. ", " The reason is I want to preload some forms that will be hold in fancybox and it takes too long to load. ", " Using this script help load the form much faster (it works) but I don't know how to make it work for multiple pages.", "\n<script src=\"//ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js\"></script>\n<script type=\"text/javascript\">\n jQuery().ready(function () {\n $.get('index2.html', function(data) {\n jQuery(\"#index2content\").html(data);\n });\n });\n</script>\n\n<div id=\"index2content\"></div>\n\nA:\n\nThis script loads the page \"index2.html\" and puts its content into the div#index2content when the DOM is ready.", "\nSo, if you want to load multiple pages, you can do the following:\n<script src=\"//ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js\"></script>\n<script type=\"text/javascript\">\n jQuery().ready(function () {\n $.get('index2.html', function(data) {\n jQuery(\"#index2content\").html(data);\n });\n\n $.get('index3.html', function(data) {\n jQuery(\"#index3content\").html(data);\n });\n\n $.get('index4.html', function(data) {\n jQuery(\"#index4content\").html(data);\n });\n });\n</script>\n\n<div id=\"index2content\"></div>\n<div id=\"index3content\"></div>\n<div id=\"index4content\"></div>\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0, 0, 0, 0.0024813895781637717, 0.0049833887043189366 ]

[ "/*\n * Mesa 3-D graphics library\n *\n * Copyright (C) 1999-2008 Brian Paul All Rights Reserved.", "\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included\n * in all copies or substantial portions of the Software.", "\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS\n * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. ", " IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR\n * OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,\n * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR\n * OTHER DEALINGS IN THE SOFTWARE.", "\n */\n\n\n#ifndef _M_XFORM_H\n#define _M_XFORM_H\n\n\n#include \"main/compiler.h\"\n#include \"main/glheader.h\"\n#include \"math/m_matrix.h\"\n#include \"math/m_vector.h\"\n\n#ifdef USE_X86_ASM\n#define _XFORMAPI _ASMAPI\n#define _XFORMAPIP _ASMAPIP\n#else\n#define _XFORMAPI\n#define _XFORMAPIP *\n#endif\n\n\nextern void\n_math_init_transformation(void);\nextern void\ninit_c_cliptest(void);\n\n/* KW: Clip functions now do projective divide as well. ", " The projected\n * coordinates are very useful to us because they let us cull\n * backfaces and eliminate vertices from lighting, fogging, etc\n * calculations. ", " Despite the fact that this divide could be done one\n * day in hardware, we would still have a reason to want to do it here\n * as long as those other calculations remain in software.", "\n *\n * Clipping is a convenient place to do the divide on x86 as it should be\n * possible to overlap with integer outcode calculations.", "\n *\n * There are two cases where we wouldn't want to do the divide in cliptest:\n * - When we aren't clipping. ", " We still might want to cull backfaces\n * so the divide should be done elsewhere. ", " This currently never\n * happens.", "\n *\n * - When culling isn't likely to help us, such as when the GL culling\n * is disabled and we not lighting or are only lighting\n * one-sided. ", " In this situation, backface determination provides\n * us with no useful information. ", " A tricky case to detect is when\n * all input data is already culled, although hopefully the\n * application wouldn't turn on culling in such cases.", "\n *\n * We supply a buffer to hold the [x/w,y/w,z/w,1/w] values which\n * are the result of the projection. ", " This is only used in the\n * 4-vector case - in other cases, we just use the clip coordinates\n * as the projected coordinates - they are identical.", "\n *\n * This is doubly convenient because it means the Win[] array is now\n * of the same stride as all the others, so I can now turn map_vertices\n * into a straight-forward matrix transformation, with asm acceleration\n * automatically available.", "\n */\n\n/* Vertex buffer clipping flags\n */\n#define CLIP_RIGHT_SHIFT \t0\n#define CLIP_LEFT_SHIFT \t1\n#define CLIP_TOP_SHIFT \t2\n#define CLIP_BOTTOM_SHIFT 3\n#define CLIP_NEAR_SHIFT \t4\n#define CLIP_FAR_SHIFT \t5\n\n#define CLIP_RIGHT_BIT 0x01\n#define CLIP_LEFT_BIT 0x02\n#define CLIP_TOP_BIT 0x04\n#define CLIP_BOTTOM_BIT 0x08\n#define CLIP_NEAR_BIT 0x10\n#define CLIP_FAR_BIT 0x20\n#define CLIP_USER_BIT 0x40\n#define CLIP_CULL_BIT 0x80\n#define CLIP_FRUSTUM_BITS 0x3f\n\n\ntypedef GLvector4f * (_XFORMAPIP clip_func)( GLvector4f *vClip,\n\t\t\t\t\t GLvector4f *vProj,\n\t\t\t\t\t GLubyte clipMask[],\n\t\t\t\t\t GLubyte *orMask,\n\t\t\t\t\t GLubyte *andMask,\n\t\t\t\t\t GLboolean viewport_z_clip );\n\ntypedef void (*dotprod_func)( GLfloat *out,\n\t\t\t GLuint out_stride,\n\t\t\t const GLvector4f *coord_vec,\n\t\t\t const GLfloat plane[4] );\n\ntypedef void (*vec_copy_func)( GLvector4f *to,\n\t\t\t const GLvector4f *from );\n\n\n\n/*\n * Functions for transformation of normals in the VB.", "\n */\ntypedef void (_NORMAPIP normal_func)( const GLmatrix *mat,\n\t\t\t\t GLfloat scale,\n\t\t\t\t const GLvector4f *in,\n\t\t\t\t const GLfloat lengths[],\n\t\t\t\t GLvector4f *dest );\n\n\n/* Flags for selecting a normal transformation function.", "\n */\n#define NORM_RESCALE 0x1\t\t/* apply the scale factor */\n#define NORM_NORMALIZE 0x2\t\t/* normalize */\n#define NORM_TRANSFORM 0x4\t\t/* apply the transformation matrix */\n#define NORM_TRANSFORM_NO_ROT 0x8\t/* apply the transformation matrix */\n\n\n\n\n/* KW: New versions of the transform function allow a mask array\n * specifying that individual vector transform should be skipped\n * when the mask byte is zero. ", " This is always present as a\n * parameter, to allow a unified interface.", "\n */\ntypedef void (_XFORMAPIP transform_func)( GLvector4f *to_vec,\n\t\t\t\t\t const GLfloat m[16],\n\t\t\t\t\t const GLvector4f *from_vec );\n\n\nextern dotprod_func _mesa_dotprod_tab[5];\nextern vec_copy_func _mesa_copy_tab[0x10];\nextern vec_copy_func _mesa_copy_clean_tab[5];\nextern clip_func _mesa_clip_tab[5];\nextern clip_func _mesa_clip_np_tab[5];\nextern normal_func _mesa_normal_tab[0xf];\n\n/* Use of 2 layers of linked 1-dimensional arrays to reduce\n * cost of lookup.", "\n */\nextern transform_func *_mesa_transform_tab[5];\n\n\n\n#define TransformRaw( to, mat, from ) \\\n ( _mesa_transform_tab[(from)->size][(mat)->type]( to, (mat)->m, from ), \\\n (to) )\n\n\n#endif\n" ]

{ "pile_set_name": "Github" }

[ 0, 0.005084745762711864, 0, 0.0036900369003690036, 0.014285714285714285, 0, 0, 0, 0, 0, 0, 0.006329113924050633, 0, 0, 0, 0, 0, 0.0050200803212851405, 0, 0.002398081534772182, 0, 0, 0.02072538860103627 ]

[ "// CodeMirror, copyright (c) by Marijn Haverbeke and others\n// Distributed under an MIT license: http://codemirror.net/LICENSE\n\n// Depends on csslint.js from https://github.com/stubbornella/csslint\n\n// declare global: CSSLint\n\n(function(mod) {\n if (typeof exports == \"object\" && typeof module == \"object\") // CommonJS\n mod(require(\"../../lib/codemirror\"));\n else if (typeof define == \"function\" && define.amd) // AMD\n define([\"../../lib/codemirror\"], mod);\n else // Plain browser env\n mod(CodeMirror);\n})(function(CodeMirror) {\n\"use strict\";\n\nCodeMirror.registerHelper(\"lint\", \"css\", function(text) {\n var found = [];\n if (!", "window.", "CSSLint) return found;\n var results = CSSLint.verify(text), messages = results.messages, message = null;\n for ( var i = 0; i < messages.length; i++) {\n message = messages[i];\n var startLine = message.line -1, endLine = message.line -1, startCol = message.col -1, endCol = message.col;\n found.push({\n from: CodeMirror.", "Pos(startLine, startCol),\n to: CodeMirror.", "Pos(endLine, endCol),\n message: message.message,\n severity : message.type\n });\n }\n return found;\n});\n\n});\n" ]

{ "pile_set_name": "Github" }

[ 0.007836990595611285, 0, 0.012012012012012012, 0.02127659574468085, 0 ]

[ "A strategy to optimise the performance of the mouth-to-bag resuscitator using small tidal volumes: effects on lung and gastric ventilation in a bench model of an unprotected airway.", "\nWhen ventilating an unintubated patient with a standard adult self-inflating bag, high peak inspiratory flow rates may result in high peak airway pressures with subsequent stomach inflation. ", "In a previous study we have tested a newly developed mouth-to-bag-resuscitator (max. ", "volume, 1500 ml) that limits peak inspiratory flow, but the possible advantages were masked by excessive tidal volumes. ", "The mouth-to-bag-resuscitator requires blowing up a balloon inside the self-inflating bag that subsequently displaces air, which then flows into the patient's airway. ", "Due to this mechanism, gas flow and peak airway pressures are reduced during inspiration when compared with a standard bag-valve-mask-device. ", "In addition, the device allows the rescuer to use two hands instead of one to seal the mask on the patient's face. ", "The purpose of the present study was to assess the effects of the mouth-to-bag-resuscitator, which was modified to produce a maximum tidal volume of 500 ml, compared with a paediatric self-inflating bag (max. ", "volume, 380 ml), and a standard adult self-inflating bag (max. ", "volume, 1500 ml) in an established bench model simulating an unintubated patient with respiratory arrest. ", "The bench model consisted of a face mask, manikin head, training lung (lung compliance, 100 ml/0.098 kPa (100ml/cm H2O); airway resistance, 0.39 kPa/(l s) (4 cm H2O/(l s)), and a valve simulating lower oesophageal sphincter pressure, 1.47 kPa (15 cm H2O). ", "Twenty critical care nurses volunteered for the study and ventilated the manikin for 1 min with a respiratory rate of 20 min(-1) with each ventilation device in random order. ", "The mouth-to-bag-resuscitator versus paediatric self-inflating bag resulted in significantly (P < 0.05) higher lung tidal volumes (302 +/- 41 ml versus 233 +/- 22 ml), and peak airway pressure (10 +/- 1 cm H2O versus 9 +/- 1 cm H2O), but comparable inspiratory time fraction (28 +/- 5% versus 27 +/- 5%, Ti/Ttot), peak inspiratory flow rate (0.6 +/- .01 l/s versus 0.6 +/- 0.2 l/s), and stomach inflation (149 +/- 495 ml/min versus 128 +/- 278 ml/min). ", "In comparison with the adult self-inflating bag, there was significantly (P < 0.05) less gastric inflation (3943 +/- 4896 ml/min versus 149 +/- 495 ml/min versus 128 +/- 278 ml/min, respectively) with both devices, but the standard adult self-inflating bag had significantly higher lung tidal volumes (566 +/- 77 ml), peak airway pressure (13 +/- 1 cm H2O), and peak inspiratory flow rate (0.8 +/- 0.11 l/s). ", "In conclusion, comparing the mouth-to-bag-resuscitator with small tidal volumes versus the paediatric self-inflating-bag during simulated ventilation of an unintubated patient in respiratory arrest resulted in comparable marginal stomach inflation, but significantly reduced the likelihood of gastric inflation compared to the adult self-inflating-bag. ", "Lung tidal volumes were improved from approximately 250 ml with the paediatric self-inflating-bag to approximately 300 ml with the mouth-to-bag-resuscitator." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0, 0.011764705882352941, 0, 0, 0, 0, 0.004784688995215311, 0.015873015873015872, 0, 0.0078125, 0, 0.004415011037527594, 0, 0, 0.006369426751592357 ]

[ " 1 This memorandum opinion was not selected for publication in the New Mexico Reports. ", "Please\n 2 see Rule 12-405 NMRA for restrictions on the citation of unpublished memorandum opinions.", "\n 3 Please also note that this electronic memorandum opinion may contain computer-generated\n 4 errors or other deviations from the official paper version filed by the Court of Appeals and does\n 5 not include the filing date.", "\n 6 IN THE COURT OF APPEALS OF THE STATE OF NEW MEXICO\n\n 7 STATE OF NEW MEXICO,\n\n 8 Plaintiff-Appellee,\n\n 9 v. NO. ", "28,662\n\n10 LEROY ROYBAL,\n\n11 Defendant-Appellant.", "\n\n12 APPEAL FROM THE DISTRICT COURT OF SANTA FE COUNTY\n13 Timothy L. Garcia, District Judge\n\n14 Gary K. King, Attorney General\n15 Santa Fe, NM\n16 Max Shepherd, Assistant Attorney General\n17 Albuquerque, NM\n\n18 for Appellee\n\n19 Robert E. Tangora, L.L.C.\n20 Robert E. Tangora\n21 Santa Fe, NM\n\n22 for Appellant\n\n23 MEMORANDUM OPINION\n\n24 KENNEDY, Judge.", "\n\n25 Defendant Leroy Roybal appeals the district court’s denial of his motion to\n\f 1 dismiss. ", "He contends the State failed to file a timely request for extension under the\n\n 2 six-month rule and, as a result, his case should have been dismissed with prejudice.", "\n\n 3 See Rule 5-604 NMRA. ", "We agree. ", "We reverse the district court and remand for\n\n 4 proceedings consistent with this opinion.", "\n\n 5 BACKGROUND\n\n 6 A grand jury indicted Defendant on January 11, 2007, for possession of a\n\n 7 controlled substance in violation of NMSA 1978, Section 30-31-23(D) (2005), and\n\n 8 possession of drug paraphernalia in violation of NMSA 1978, Section 30-31-25.1\n\n 9 (2001). ", "His arraignment occurred on February 16, 2007, before Judge Stephen\n\n10 Pfeffer. ", "Defendant entered a plea of not guilty. ", "Defendant then filed a motion to\n\n11 excuse Judge Pfeffer on February 27, 2007, and the case was reassigned to Judge\n\n12 Michael Vigil. ", "Defendant’s trial was set for July 5, 2007, and then reset to August 14,\n\n13 2007, less than a week short of six months from the date of his arraignment.", "\n\n14 On July 20, 2007, Defendant, in a separate case before Judge Vigil, requested\n\n15 Judge Vigil recuse himself because he had previously represented Defendant in\n\n16 another matter. ", "Judge Vigil did so, and at the July 23, 2007, hearing in the instant\n\n17 case, he also recused himself. ", "During that hearing, the State orally requested an\n\n18 extension under Rule 5-604, and Judge Vigil, having recused himself, stated he could\n\n19 not rule on the issue and advised the State to seek a ruling from another judge. ", "After\n\n\n 2\n\f 1 this exchange, the record does not contain an order of recusal for Judge Vigil and is\n\n 2 silent with regard to any actions for more than five months prior to December 13,\n\n 3 2007, when Defendant filed a motion to dismiss for failure to comply with Rule 5-\n\n 4 604. ", "On December 19, 2007, the State filed a petition for extension under Rule 5-604,\n\n 5 indicating that the six-month rule ran on August 17, 2007, more than four months\n\n 6 prior to the filing of the petition. ", "Defendant opposed the extension.", "\n\n 7 The matter was eventually assigned to Judge Timothy Garcia, who granted the\n\n 8 State’s extension without a hearing in an order dated January 23, 2008. ", " At\n\n 9 Defendant’s request, a hearing was later held on February 8, 2008, at which time the\n\n10 court concluded that under State v. Dominguez, 2007-NMCA-132, 142 N.M. 631, 168\n\n11 P.3d 761, equity weighed against dismissal under Rule 5-604. ", "The court reasoned that\n\n12 because Defendant requested recusal of Judge Vigil and then benefited from Judge\n\n13 Vigil’s inability to rule on the State’s oral extension request, Defendant was\n\n14 responsible for the delay and failed in his duty to ask the court to relinquish its\n\n15 jurisdiction and refer the matter to another judge. ", "On February 19, 2008, Defendant\n\n16 entered a no contest plea to the charges against him, reserving his right to appeal the\n\n17 court’s denial of his motion to dismiss.", "\n\n18 On appeal, Defendant argues the district court improperly ignored a clear, four-\n\n19 month violation of Rule 5-604 and reached the equities of the case. ", "Even assuming\n\n\n 3\n\f 1 it properly reached such equitable considerations, Defendant contends that those\n\n 2 nonetheless weigh in favor of dismissal. ", "The State has filed no responsive pleadings\n\n 3 in this matter. ", "We therefore consider these issues on the basis of Defendant’s brief\n\n 4 alone. ", "See Lozano v. GTE Lenkurt, Inc., 1996-NMCA-074, ¶ 30, 122 N.M. 103, 920\n\n 5 P.2d 1057 (“Our Rules of Appellate Procedure do not require an answer brief to be\n\n 6 filed; instead, where no brief is filed, the cause may be submitted upon the brief of the\n\n 7 appellant.”); ", "Cobb v. Otero County Assessor, 100 N.M. 207, 210, 668 P.2d 323, 326\n\n 8 (Ct. ", "App. ", "1983) (affirming a lower court’s decision in the absence of an answer brief).", "\n\n 9 DISCUSSION\n\n10 The six-month rule requires the commencement of a defendant’s trial within six\n\n11 months of his arraignment or other triggering event. ", "Rule 5-604(B)(1)-(8); see Rule\n\n12 5-104(A) (computation of time). ", "Upon a showing of “good cause,” the district court\n\n13 may grant an extension of this requirement, so long as the party seeking the extension\n\n14 files a petition with the court during the six-month limit. ", "Rule 5-604(C), (D). ", "But in\n\n15 the event of “exceptional circumstances,” the party seeking the extension may have\n\n16 ten additional days in which to file its petition. ", "Rule 5-604(D). ", "If not brought to trial\n\n17 in accordance with the requirements of Rule 5-604, the case against a defendant “shall\n\n18 be dismissed with prejudice.” ", "Rule 5-604(E)(2). ", "A defendant’s right to a speedy trial\n\n19 under the six-month rule is not contingent; it “is a criminal defendant’s right, not that\n\n\n 4\n\f 1 of the State, the courts, or any other party[.]” ", "State v. Savedra, 2010-NMSC-025, ¶\n\n 2 8, ___ N.M. ___, 236 P.3d 20, cert. ", "denied, 2010-NMCERT-___, ___ N.M. ___, ___\n\n 3 P.3d __ (No. ", "31,288, June 24, 2010).1 Our courts have described the six-month rule\n\n 4 as a bright-line rule, meant to insure the timely disposition of criminal cases.", "\n\n 5 Dominguez, 2007-NMCA-132, ¶ 6. ", "Even so, we have cautioned that the rule should\n\n 6 not be interpreted so as to defy common sense or effect hypertechnical dismissal. ", "Id.;\n\n 7 State v. Jaramillo, 2004-NMCA-041, ¶ 13, 135 N.M. 322, 88 P.3d 264 (Vigil, J.,\n\n 8 specially concurring); State v. Eden, 108 N.M. 737, 741-42, 779 P.2d 114, 118-19 (Ct.", "\n\n 9 App. ", "1989); see State v. Lobato, 2006-NMCA-051, ¶¶ 28-30, 139 N.M. 431, 134 P.3d\n\n10 122 (discussing various considerations to assist in determining when dismissal would\n\n11 be unreasonable or hypertechnical). ", "Courts therefore must strike a balance between\n\n12 enforcing the rule as written and preventing unreasonable applications that defy\n\n13 common sense.", "\n\n14 In Lobato, for example, this Court held that under “the common sense\n\n15 approach,” a court may ignore a technical violation of the six-month rule where “(1)\n\n16 the delay inures to the benefit of the defendant or (2) the defendant acquiesces in the\n\n17 delay or fails to raise the issue of the . . . ", "rule in a timely manner.” ", "2006-NMCA-051,\n\n 1\n18 In Savedra, our Supreme Court withdrew Rule 5-604(B)-(E) and made its\n19 holding effective for all cases pending as of May 12, 2010. ", "Savedra, 2010-NMSC-\n20 025, ¶ 9. ", "We note that those changes do not apply in the instant case, which was\n21 already on appeal as of May 12, 2010.", "\n\n 5\n\f 1 ¶ 28 (citing State v. Mendoza, 108 N.M. 446, 449-50, 774 P.2d 440, 443-44 (1989);\n\n 2 State v. Sanchez, 109 N.M. 313, 316-17, 785 P.2d 224, 227-28 (1989); and Jaramillo,\n\n 3 2004-NMCA-041, ¶ 15). ", "In deciding whether to relax the standard, courts may also\n\n 4 consider whether the defendant “took affirmative action . . . ", "that could have further\n\n 5 delayed his trial.” ", "Id. ¶ 29; see Dominguez, 2007-NMCA-132, ¶ 21 (observing that\n\n 6 defendant “neither benefited from, caused, nor stipulated to any delay in bringing him\n\n 7 to trial” and did not “wait until the last moment or take an unreasonably lingering\n\n 8 amount of time to move for dismissal”). ", "We apply a de novo standard of review to\n\n 9 a district court’s interpretation of the six-month rule. ", "Id. ¶ 8.", "\n\n10 Applying these principles, we hold the district court improperly granted the\n\n11 State’s untimely petition for an extension under the six-month rule. ", "Although the\n\n12 record indicates the State did make an oral request to Judge Vigil within the required\n\n13 time limit, Judge Vigil made it clear he was unable to rule on the matter due to his\n\n14 recusal. ", "He instructed the State to seek a ruling elsewhere, but the State never\n\n15 followed through. ", "Instead, it waited more than four months, long after the expiration\n\n16 of the six-month rule, to seek a valid extension; and it did so only after Defendant had\n\n17 already moved for dismissal under the rule. ", "It is well-established that an “accused has\n\n18 no duty to bring on his trial.” ", "State v. Mascarenas, 84 N.M. 153, 155, 500 P.2d 438,\n\n19 440 (Ct. ", "App. ", "1972). ", " As this case aptly illustrates, the State must bear the\n\n\n 6\n\f 1 responsibility “to get on with the prosecution, both out of fairness to the accused and\n\n 2 to protect the community interests in a speedy trial.” ", "Id. In this case, the State was\n\n 3 well-aware of its failure to receive an extension from Judge Vigil and never sought a\n\n 4 ruling from another judge. ", "It did so only as a reaction to Defendant’s motion for\n\n 5 dismissal more than four months later. ", " “The crux of the six-month rule is\n\n 6 promptness.” ", "Dominguez, 2007-NMCA-132, ¶ 22. ", "We hold on these facts that the\n\n 7 district court improperly granted the State’s late request.", "\n\n 8 Furthermore, we disagree with the district court’s conclusion that the equities\n\n 9 favor the State because Defendant caused and/or benefited from the delay. ", "While true\n\n10 that Defendant sought Judge Vigil’s recusal, it does not follow that he was responsible\n\n11 for the State’s failure to seek a ruling on its motion. ", "It was the State, not Defendant,\n\n12 that waited to seek an extension after four additional months, and Defendant can bear\n\n13 no responsibility for that tardiness. ", "Nor do we see any benefit, besides the mere fact\n\n14 of the delay itself, inuring to Defendant. ", "Also, while true that Defendant himself\n\n15 waited four months to file a motion to dismiss under Rule 5-604, such a period is not\n\n16 per se untimely.", "\n\n17 CONCLUSION\n\n18 We reverse the district court’s denial of Defendant’s motion to dismiss, and\n\n19 we remand this case for proceedings consistent with this opinion.", "\n\n\n 7\n\f1 IT IS SO ORDERED.", "\n\n\n2 ______________________________\n3 RODERICK T. KENNEDY, Judge\n\n4 WE CONCUR:\n\n\n\n5 _________________________________\n6 MICHAEL D. BUSTAMANTE, Judge\n\n\n\n7 _________________________________\n8 LINDA M. VANZI, Judge\n\n\n\n\n 8\n\f" ]

{ "pile_set_name": "FreeLaw" }

[ 0.011235955056179775, 0, 0.004347826086956522, 0, 0, 0.03076923076923077, 0.009708737864077669, 0.006024096385542169, 0, 0, 0, 0.007168458781362007, 0.012345679012345678, 0, 0.014705882352941176, 0, 0.010416666666666666, 0.009615384615384616, 0.017777777777777778, 0.003048780487804878, 0.004830917874396135, 0, 0.012195121951219513, 0.011857707509881422, 0.008928571428571428, 0, 0, 0, 0.015625, 0.0125, 0.007407407407407408, 0.012987012987012988, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.00423728813559322, 0.013333333333333334, 0, 0, 0, 0, 0.03389830508474576, 0, 0.004878048780487805, 0, 0.003194888178913738, 0, 0.011695906432748537, 0, 0, 0.016, 0, 0, 0.0035211267605633804, 0, 0, 0.006172839506172839, 0.014563106796116505, 0.02127659574468085, 0, 0, 0, 0, 0, 0.003787878787878788, 0.013071895424836602, 0, 0, 0, 0.010526315789473684, 0.0058823529411764705, 0.012269938650306749, 0.006060606060606061, 0, 0.006666666666666667, 0.005780346820809248, 0, 0.009230769230769232 ]

[ "What people wore in the early 1900s\n\n“Men, alas! ", "cannot dress prettily nowadays — at one\ntime they had the best of it there, too — and that is\ncertainly a source of diversion and consolation in a\ntroublesome world. ", "To many women, new dresses form\nthe chief novelty of their existence; and well do the\narbiters of fashion take care that variety shall be provided for us in that direction. — ", "1902 Illustrated London News" ]

{ "pile_set_name": "Pile-CC" }

[ 0, 0, 0, 0.03571428571428571 ]

[ "This update is provided for media and general public.", "\n\nThe SMM observed that the Donetsk railway station was open. ", "In Shakhtarsk running water is available for only two hours per day, and gas and electricity has been unavailable since 27 July.", "\n\nThe SMM in Donetsk city saw that the railway station was open. ", "Tickets from Donetsk to Kyiv were, however, unavailable for the next couple of days. ", "At banks which were still operational, people were queuing at ATMs.", "\n\nThe SMM went to Shakhtarsk (57km east of Donetsk city, 21km northwest of Torez). ", "The town appeared deserted. ", "Shops were closed. ", "Residents told the SMM that running water was available for only two hours per day. ", "Gas and electricity had been cut since 27 July. ", "The SMM observed in the town damage, which appeared have been caused by shelling on the night of 7 and 8 August. ", "On one street a number of apartments had been destroyed in two residential blocks; on another street, in another residential block, two apartments had been completely destroyed; and a two-metre-deep crater was observed.", "\n\nThe lack of electricity and Internet coverage in the Luhansk region prevented the SMM from sending its report. ", "Reporting will be resumed as soon as possible.", "\n\nIn Dergachi (16km north of Kharkiv city) the SMM observed in front of the military recruitment centre a group of 60 people protesting against mobilisation. ", "No incidents were reported.", "\n\nIn Pokrovske (130km southeast of Dnipropetrovsk city) the SMM observed a protest against mobilisation. ", "Approximately 50 women gathered in front of the district administration building. ", "The protestors dispersed after two hours. ", "No incidents were reported. ", "The women said that they on 6 August had met representatives of the military recruitment office, the district council and the prosecutor’s office to discuss the issue of mobilisation.", "\n\nIn Kherson the SMM met the deputy head of the State Migration Service, who said that either a Ukrainian ID or Ukrainian passport was sufficient to cross the administrative boundary line (ABL) from Crimea. ", "According to him no invitation was required for Ukrainian citizens.", "\n\nThe situation in Odessa was calm.", "\n\nIn Hertsa (30km south of Chernivtsi) representatives of the Regional Administration told the SMM that Russian-speaking children displaced from Crimea could not receive education in the town in Russian. ", "He explained that the town had a large ethnic Romanian population and so the language of instruction in local schools was either Romanian or Ukrainian. ", "The nearest Russian-language school, he said, was 30km away.", "\n\nThe situation in Ivano-Frankivsk and Lviv was calm.", "\n\nFollowing the recent events in Kyiv on the Maidan (see Latest SMM update of 8 August 2014) the SMM observed several newly established barricades, reinforced with tyres, timber and paving stones. ", "Many cases of ready-to-use Molotov cocktails, and containers of engine-oil-like fluid were seen on Khreshchatyk Street, close to the Maidan. ", "Several gatherings of up to 120 people were monitored. ", "The SMM observed several tents that had been put up again." ]

{ "pile_set_name": "OpenWebText2" }

[ 0, 0, 0.0078125, 0, 0, 0.014925373134328358, 0.012048192771084338, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.00546448087431694, 0.00966183574879227, 0, 0.02857142857142857, 0.00980392156862745, 0, 0, 0, 0.005076142131979695, 0.0070921985815602835, 0, 0 ]

[ "Heterotopic heart transplantation: mid-term hemodynamic and echocardiographic analysis--the concern of arteriovenous-valve incompetence.", "\nTo assess the hemodynamic contribution of both hearts after heterotopic heart transplantation, we examined recipients by cardiac catheterization and Doppler echocardiography. ", "Since September 1984, immunosuppression consisted of cyclosporine, azathioprine, methylprednisolone, and antithymocyte globulin. ", "In this time interval, 55 orthotopic and 14 heterotopic transplants have been performed. ", "The indications for heterotopic transplant were elevated pulmonary vascular resistance (greater than 4 Wood units), in 10 patients, or gross (greater than 20%) donor-recipient weight mismatch, in six patients. ", "Two patients belonged to both groups. ", "The 1-year survival rate was 63%; currently seven of the 14 patients are alive. ", "Cardiac output (as measured by dye dilution curves and by the Fick method) increased from 4.2 L/min preoperatively to 6.1 L/min in both groups postoperatively (mean follow up, 5.3 months; p less than 0.0005); the transpulmonary gradient fell from 18.5 to 12.3 mm Hg, the pulmonary vascular resistance from 4.4 to 2.4 Wood units (p less than 0.01). ", "The echocardiographic findings were as follows: left ventricular end-diastolic diameter (mm) in the recipient heart was 67.4 +/- 12 and in the donor heart, 42.6 +/- 8.7. ", "Fractional shortening (%) in the recipient heart was 7.1 +/- 2.9 and in the donor heart, 30.4 +/- 10.4. ", "The Doppler technique revealed a cardiac output contribution-ratio (CO donor/CO recipient) of 3.0 +/- 0.61 on average. ", "In all recipient hearts mild and moderate mitral and tricuspid regurgitation was discovered. ", "In the donor heart all mitral and tricuspid valves were found to be incompetent; this was severe in 66% and 11% of the mitral and tricuspid valves, respectively.(ABSTRACT TRUNCATED AT 250 WORDS)" ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0.005681818181818182, 0, 0, 0, 0, 0, 0.005747126436781609, 0.0058823529411764705, 0, 0.01680672268907563, 0, 0 ]

[ "Seasonal volatility dependence of ambient particle phase amines.", "\nDuring the summer and fall of 2005 in Riverside, California, the seasonal volatility behavior of submicrometer aerosol particles was investigated by coupling an automated thermodenuder system to an online single-particle mass spectrometer. ", "A strong seasonal dependence was observed for the gas/particle partitioning of alkylamines within individual ambient submicrometer aged organic carbon particles internally mixed with ammonium, nitrate, and sulfate. ", "In the summer, the amines were strongly correlated with nitrate and sulfate, suggesting the presence of aminium nitrate and sulfate salts which were nonvolatile and comprised approximately 6-9% of the average particle mass at 230 degrees C. In the fall, 86 +/- 1% of the amines volatilized below 113 degrees C with aminium nitrate and sulfate salts representing less than 1% of the particle mass at 230 degrees C. In the summer, a more acidic particle core led to protonation of the amines and subsequent formation of aminium sulfate and nitrate salts; whereas, in the fall, the particles contained more ammonium and thus were less acidic, causing fewer aminium salts to form. ", "Therefore, the acidity of individual particles can greatly affect gas/particle partitioning of organic species in the atmosphere, and the concentrations of amines, as strong bases, should be included in estimations of aerosol pH." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0, 0, 0, 0 ]

[ "---\nauthor:\n- Kazumasa Nomura and Paul Terwilliger\ntitle: 'Leonard pairs, spin models, and distance-regular graphs'\n---\n\n> [**Abstract**]{}\n>\n> A Leonard pair is an ordered pair of diagonalizable linear maps on a finite-dimensional vector space, that each act on an eigenbasis for the other one in an irreducible tridiagonal fashion. ", "In the present paper we consider a type of Leonard pair, said to have spin. ", "The notion of a spin model was introduced by V.F.R. Jones to construct link invariants. ", "A spin model is a symmetric matrix over ${\\mathbb{C}}$ that satisfies two conditions, called the type II and type III conditions. ", "It is known that a spin model ${{\\sf W}}$ is contained in a certain finite-dimensional algebra $N({{\\sf W}})$, called the Nomura algebra. ", "It often happens that a spin model ${{\\sf W}}$ satisfies ${{\\sf W}}\\in {{\\sf M}}\\subseteq N({{\\sf W}})$, where ${{\\sf M}}$ is the Bose-Mesner algebra of a distance-regular graph $\\Gamma$; in this case we say that $\\Gamma$ affords ${{\\sf W}}$. If $\\Gamma$ affords a spin model, then each irreducible module for every Terwilliger algebra of $\\Gamma$ takes a certain form, recently described by Caughman, Curtin, Nomura, and Wolff. ", "In the present paper we show that the converse is true; if each irreducible module for every Terwilliger algebra of $\\Gamma$ takes this form, then $\\Gamma$ affords a spin model. ", "We explicitly construct this spin model when $\\Gamma$ has $q$-Racah type. ", "The proof of our main result relies heavily on the theory of spin Leonard pairs.", "\n\nIntroduction {#sec:intro}\n============\n\nThe notion of a Leonard pair was introduced by the second author in [@T:Leonard]. ", "A Leonard pair is roughly described as follows. ", "Let $V$ denote a vector space with finite positive dimension. ", "A Leonard pair on $V$ is an ordered pair of diagonalizable linear maps $A: V \\to V$ and $A^* : V \\to V$ that each act on an eigenbasis for the other one in an irreducible tridiagonal fashion. ", "The Leonard pairs were classified up to isomorphism in [@T:Leonard]; the isomorphism classes correspond to a family of orthogonal polynomials consisting of the $q$-Racah polynomials and their relatives in the terminating branch of the Askey scheme [@T:survey]. ", "See [@T:survey; @T:Leonard; @T:qRacah; @NT:affine; @NT:lineartrans] for more information about Leonard pairs.", "\n\nIn the present paper we will consider a type of Leonard pair, said to have spin [@C:spinLP]. ", "The spin condition is described as follows. ", "Let $A, A^*$ denote a Leonard pair on $V$. A Boltzmann pair for $A,A^*$ is an ordered pair of invertible linear maps $W : V \\to V$ and $W^* : V \\to V$ such that $W A = A W$ and $W^* A^* = A^* W^*$ and $W A^* W^{-1} = (W^*)^{-1} A W^*$. The Leonard pair $A,A^*$ is said to have spin whenever there exists a Boltzmann pair for $A,A^*$. In [@C:spinLP] the spin Leonard pairs are classified up to isomorphism and their Boltzmann pairs are described.", "\n\nNext we summarize how Leonard pairs come up in algebraic graph theory. ", "Let $\\Gamma$ denote a distance-regular graph [@BCN p. 126] with vertex set $X$ and adjacency matrix ${{\\sf A}}\\in {\\text{\\rm Mat}_X({\\mathbb{C}})}$. Let ${{\\sf M}}$ denote the subalgebra of ${\\text{\\rm Mat}_X({\\mathbb{C}})}$ generated by ${{\\sf A}}$. By [@BCN Theorem 2.6.1] the algebra ${{\\sf M}}$ has a basis $\\{{{\\sf A}}_i\\}_{i=0}^D$ where $D$ is the diameter of $\\Gamma$ [@BCN p. 432] and ${{\\sf A}}_i$ is the $i^\\text{th}$ distance-matrix of $\\Gamma$ [@BCN p. 127] for $0 \\leq i \\leq D$. The algebra ${{\\sf M}}$ is called the Bose-Mesner algebra of $\\Gamma$; it is a useful tool in the study of $\\Gamma$ [@BI; @BCN]. ", "To carry out this study in more detail, it is helpful to bring in another algebra called the subconstituent algebra or Terwilliger algebra. ", "This algebra is described as follows. ", "For $x \\in X$ and $0 \\leq i \\leq D$, the diagonal matrix ${{\\sf E}}^*_i = {{\\sf E}}^*_i (x) \\in {\\text{\\rm Mat}_X({\\mathbb{C}})}$ is the projection onto the $i^\\text{th}$ subconstituent of $\\Gamma$ with respect to $x$ [@BCN p. 434]. ", "The matrices $\\{{{\\sf E}}^*_i\\}_{i=0}^D$ form a basis for a commutative subalgebra ${{\\sf M}}^* = {{\\sf M}}^*(x)$ of ${\\text{\\rm Mat}_X({\\mathbb{C}})}$, called the dual Bose-Mesner algebra of $\\Gamma$ with respect to $x$. The Terwilliger algebra ${{\\sf T}}= {{\\sf T}}(x)$ is the subalgebra of ${\\text{\\rm Mat}_X({\\mathbb{C}})}$ generated by ${{\\sf M}}$ and ${{\\sf M}}^*$ [@T:subconst1]. ", "The algebra ${{\\sf T}}$ is semi-simple [@T:subconst1 Lemma 3.4], so it is natural to investigate the irreducible ${{\\sf T}}$-modules. ", "For an irreducible ${{\\sf T}}$-module $U$, there is a condition called thin; this means that for the action of ${{\\sf M}}$ and ${{\\sf M}}^*$ on $U$ the eigenspaces all have dimension $1$. Most of the known distance-regular graphs with large diameter satisfy an algebraic condition called $Q$-polynomial [@BCN Section 4.1.E]; if $\\Gamma$ is $Q$-polynomial then ${{\\sf M}}^*$ contains a certain matrix ${{\\sf A}}^*$ called the dual adjacency matrix of $\\Gamma$ with respect to $x$ [@T:subconst1 p. 379]. ", "In this case ${{\\sf A}}, {{\\sf A}}^*$ acts on each thin irreducible ${{\\sf T}}$-module as a Leonard pair [@T:subconst1 Lemmas 3.9, 3.12].", "\n\nMotivated by state models in statistical mechanics, V.F.R. Jones [@Jones] introduced the notion of a spin model to construct link invariants. ", "The construction is roughly described as follows. ", "A link is a finite collection of mutually disjoint closed curves in $3$-dimensional Euclidean space. ", "A link diagram is a projection of a link onto a plane. ", "For a link diagram $L$ and a square matrix ${{\\sf W}}$ over ${\\mathbb{C}}$ with all entries nonzero, Jones defined a scalar $Z_{{\\sf W}}(L) \\in {\\mathbb{C}}$. The function $Z_{{\\sf W}}$ from the set of all link diagrams to ${\\mathbb{C}}$ gives a link invariant, provided that ${{\\sf W}}$ satisfies two conditions called type II and type III; these are given in [@Jones] and , below. ", "The matrix ${{\\sf W}}$ is called a spin model whenever it is type II and type III.", "\n\nIn [@Jones] Jones gave three examples of spin models; the Potts model, the square model, and the odd cyclic model. ", "In [@Jaeger1] F. Jaeger observed that each of these examples is contained in the Bose-Mesner algebra of a distance-regular graph $\\Gamma$. Specifically, for the Potts model $\\Gamma$ is a complete graph, for the square model $\\Gamma$ is the $4$-cycle, and for the odd cyclic model $\\Gamma$ is an odd cycle. ", "Jaeger then found a new spin model contained in the Bose-Mesner algebra of the Higman-Sims graph [@Jaeger1]. ", "Motivated by this result, other authors found new spin models contained in the Bose-Mesner algebra of the even cycle [@BB], the Hadamard graph [@N:Hadamard], and the double cover of the Higman-Sims graph [@Mune].", "\n\nFor the rest of this section let $\\Gamma$ denote a distance-regular graph with vertex set $X$ and Bose-Mesner algebra ${{\\sf M}}$. For a spin model ${{\\sf W}}$ contained in ${{\\sf M}}$, it often happens that ${{\\sf W}}$ and ${{\\sf M}}$ are related by the following condition. ", "For $b,c \\in X$ let $\\text{\\bf u}_{b,c}$ denote the column vector with entries indexed by $X$ and $y$-entry ${{\\sf W}}(b,y) {{\\sf W}}(c,y)^{-1}$ for $y \\in X$. The condition is that $\\text{\\bf u}_{b,c}$ is a common eigenvector of ${{\\sf M}}$ for all $b,c \\in X$. In this case we say that [*$\\Gamma$ affords ${{\\sf W}}$*]{}. ", "Each of the above mentioned spin models [@Jones; @Jaeger1; @BB; @N:Hadamard; @Mune] is afforded by the associated distance-regular graph; this will be demonstrated in Section \\[sec:example\\] below.", "\n\nNext we describe how spin models are related to spin Leonard pairs. ", "Assume that $\\Gamma$ affords a spin model ${{\\sf W}}$. It was shown in [@CN:hyper Lemma 5.1] that $\\Gamma$ satisfies a condition called formally self-dual, which implies that $\\Gamma$ is $Q$-polynomial [@BCN p. 49]. ", "Pick $x \\in X$ and write ${{\\sf A}}^*={{\\sf A}}^*(x)$, ${{\\sf M}}^* = {{\\sf M}}^*(x)$, ${{\\sf T}}= {{\\sf T}}(x)$. Define ${{\\sf W}}^* \\in {{\\sf M}}^*$ that has $(y,y)$-entry $|X|^{1/2} {{\\sf W}}(x,y)^{-1}$ for $y \\in X$. Let $U$ denote a thin irreducible ${{\\sf T}}$-module. ", "Then ${{\\sf A}}, {{\\sf A}}^*$ act on $U$ as a spin Leonard pair, and ${{\\sf W}},{{\\sf W}}^*$ act on $U$ as a Boltzmann pair for this Leonard pair; see Proposition \\[prop:C2\\] and Lemma \\[lem:spinLP3\\] below. ", "Consequently the intersection numbers of $U$ [@T:survey Definition 11.1] are given by the formulas in [@CW Theorem 8.5]. ", "Another consequence for $U$ is that its endpoint [@T:subconst1 Lemma 3.12] is equal to its dual endpoint [@T:subconst1 Lemma 3.9].", "\n\nNow we describe our main result. ", "Assume that our distance-regular graph $\\Gamma$ is formally self-dual and has $q$-Racah type [@TZ Definition 5.1]. ", "Assume that for all $x \\in X$ each irreducible ${{\\sf T}}(x)$-module $U$ is thin with matching endpoint and dual-endpoint, and the intersection numbers of $U$ are given by the formulas in [@CW Theorem 8.5]. ", "Then there exists a spin model afforded by $\\Gamma$; this spin model is explicitly constructed. ", "Our main result is Theorem \\[thm:main3\\]. ", "We comment on the nature of this result. ", "We have not discovered any new spin model to date. ", "What we have shown, is that a new spin model would result from the discovery of a distance-regular graph with the right sort of irreducible ${{\\sf T}}$-modules.", "\n\nThe proof of our main result relies heavily on the theory of spin Leonard pairs. ", "In the first half of the paper we develop this theory, and obtain several new results that may be of independent interest; for instance Theorem \\[thm:WtiinvAi\\] and Lemmas \\[lem:spinLP0\\], \\[lem:new\\]. ", "The paper is organized as follows.", "\n\nCONTENTS\n\n> 1\\. Introduction $\\; 1$\\\n> 2. ", "Leonard pairs and Leonard systems $\\; 3$\\\n> 3. ", "The map $\\pi$ $\\; 8$\\\n> 4. ", "The map $\\rho$ $\\; 11$\\\n> 5. ", "Boltzmann pairs and spin Leonard pairs $\\; 18$\\\n> 6. ", "Leonard pairs of $q$-Racah type $\\; 24$\\\n> 7. ", "Type II matrices and spin models $\\; 29$\\\n> 8. ", "Hadamard matrices and spin models $\\, 30$\\\n> 9. ", "Distance-regular graphs $\\; 31$\\\n> 10. ", "Formally self-dual distance-regular graphs $\\; 39$\\\n> 11. ", "From a spin model to spin Leonard pairs $\\; 41$\\\n> 12. ", "From a spin model to spin Leonard pairs; the $q$-Racah case $\\; 44$\\\n> 13. ", "From spin Leonard pairs to a spin model $\\; 48$\\\n> 14. ", "From spin Leonard pairs to a spin model; the $q$-Racah case $\\; 51$\\\n> 15. ", "Examples $\\; 54$\\\n> References $\\; 55$\n\nLeonard pairs and Leonard systems {#sec:LP}\n=================================\n\nWe now begin our formal argument. ", "In this section we recall the notion of a Leonard pair. ", "We use the following terms. ", "A square matrix is said to be [*tridiagonal*]{} whenever each nonzero entry lies on either the diagonal, the subdiagonal, or the superdiagonal. ", "A tridiagonal matrix is said to be [*irreducible*]{} whenever each entry on the subdiagonal is nonzero and each entry on the superdiagonal is nonzero. ", "Let ${\\mathbb{F}}$ denote a field.", "\n\n[@T:Leonard Definition 1.1] \\[def:LP\\] . ", "Let $V$ denote a vector space over ${\\mathbb{F}}$ with finite positive dimension. ", "By a [*Leonard pair*]{} on $V$ we mean an ordered pair of ${\\mathbb{F}}$-linear maps $A: V \\to V$ and $A^* : V \\to V$ that satisfy the following [(i), (ii)]{}.", "\n\n- There exists a basis for $V$ with respect to which the matrix representing $A$ is irreducible tridiagonal and the matrix representing $A^*$ is diagonal.", "\n\n- There exists a basis for $V$ with respect to which the matrix representing $A^*$ is irreducible tridiagonal and the matrix representing $A$ is diagonal.", "\n\nAccording to a common notational convention, for a matrix $A$ its conjugate-transpose is denoted by $A^*$. We are not using this convention. ", "In a Leonard pair $A,A^*$ the linear maps $A,A^*$ are arbitrary subject to (i) and (ii) above.", "\n\nReferring to Definition \\[def:LP\\], let $A,A^*$ denote a Leonard pair on $V$. Then $A^*,A$ is a Leonard pair on $V$.\n\nWe refer the reader to [@T:survey] for background on Leonard pairs.", "\n\nFrom now until the end of Section \\[sec:qRacah\\], fix an integer $d \\geq 0$ and let $V$ denote a vector space over ${\\mathbb{F}}$ with dimension $d+1$. Let $\\text{\\rm End}(V)$ denote the ${\\mathbb{F}}$-algebra consisting of the ${\\mathbb{F}}$-linear maps $V \\to V$. We denote by $I$ the identity element of $\\text{\\rm End}(V)$. For $A \\in \\text{\\rm End}(V)$ let ${\\langle A \\rangle}$ denote the subalgebra of $\\text{\\rm End}(V)$ generated by $A$. ", "By [@Rot Corollary 2.133] the center of $\\text{\\rm End}(V)$ consists of the elements $\\alpha I$ $(\\alpha \\in {\\mathbb{F}})$.\n\n[[@T:survey Corollary 5.6]]{} \\[lem:generate\\] . ", "Let $A,A^*$ denote a Leonard pair on $V$. Then $A$, $A^*$ together generate the algebra $\\text{\\rm End}(V)$.\n\nFor an ${\\mathbb{F}}$-algebra $\\cal A$, by an [*automorphism*]{} of $\\cal A$ we mean an ${\\mathbb{F}}$-algebra isomorphism ${\\cal A} \\to {\\cal A}$. By an [*antiautomorphism*]{} of $\\cal A$ we mean an ${\\mathbb{F}}$-linear bijection $\\tau : {\\cal A} \\to {\\cal A}$ such that $(Y Z)^\\tau = Z^\\tau Y^\\tau$ for all $Y, Z \\in {\\cal A}$.\n\n[[@Rot Corollary 7.126] (Skolem-Noether) ]{} \\[lem:SN\\] . ", "A map $\\sigma : \\text{\\rm End}(V) \\to \\text{\\rm End}(V)$ is an automorphism of $\\text{\\rm End}(V)$ if and only if there exists an invertible $K \\in \\text{\\rm End}(V)$ such that $Y^\\sigma = K Y K^{-1}$ for all $Y \\in \\text{\\rm End}(V)$.\n\n[[@T:survey Theorem 6.1] ]{} \\[lem:dagger\\] . ", "Let $A,A^*$ denote a Leonard pair on $V$. Then there exists a unique antiautomorphism $\\dagger$ of $\\text{\\rm End}(V)$ such that $A^\\dagger = A$ and $A^{* \\dagger} = A^*$. Moreover $(Y^\\dagger)^\\dagger = Y$ for all $Y \\in \\text{\\rm End}(V)$. The map $\\dagger$ fixes every element in ${\\langle A \\rangle}$ and every element in ${\\langle A^* \\rangle}$.\n\nWe recall the notion of an isomorphism for Leonard pairs. ", "Let $A,A^*$ denote a Leonard pair on $V$. Let $V'$ denote a vector space over ${\\mathbb{F}}$ with dimension $d+1$, and let $A', A^{*\\prime}$ denote a Leonard pair on $V'$. By an [*isomorphism of Leonard pairs*]{} from $A,A^*$ to $A', A^{*\\prime}$ we mean an ${\\mathbb{F}}$-algebra isomorphism $\\text{\\rm End}(V) \\to \\text{\\rm End}(V')$ that sends $A \\mapsto A'$ and $A^* \\mapsto A^{* \\prime}$. The Leonard pairs $A,A^*$ and $A',A^{*\\prime}$ are said to be [*isomorphic*]{} whenever there exits an isomorphism of Leonard pairs from $A,A^*$ to $A', A^{*\\prime}$. In this case the isomorphism is unique by Lemma \\[lem:generate\\].", "\n\nWe recall the self-dual Leonard pairs. ", "A Leonard pair $A,A^*$ is said to be [*self-dual*]{} whenever $A,A^*$ is isomorphic to $A^*,A$. In this case, the isomorphism of Leonard pairs from $A,A^*$ to $A^*,A$ is called the [*duality*]{} of $A,A^*$.\n\n\\[lem:s2\\] . ", "Assume that $A,A^*$ is self-dual with duality $\\sigma$. Then $\\sigma^2 = 1$.\n\nBy construction $\\sigma^2$ fixes each of $A,A^*$. By this and Lemma \\[lem:generate\\], $\\sigma^2$ fixes every element of $\\text{\\rm End}(V)$. The result follows.", "\n\nWhen working with a Leonard pair, it is convenient to consider a closely related object called a Leonard system [@T:Leonard]. ", "Before we define a Leonard system, we recall a few concepts from linear algebra.", "\n\nLet $\\text{\\rm Mat}_{d+1}({\\mathbb{F}})$ denote the ${\\mathbb{F}}$-algebra consisting of the $d+1$ by $d+1$ matrices that have all entries in ${\\mathbb{F}}$. We index the rows and columns by $0,1,\\ldots,d$. Let $\\{v_i\\}_{i=0}^d$ denote a basis for $V$. For $A \\in \\text{\\rm End}(V)$ and $M \\in \\text{\\rm Mat}_{d+1}({\\mathbb{F}})$, we say that [*$M$ represents $A$ with respect to $\\{v_i\\}_{i=0}^d$*]{} whenever $A v_j = \\sum_{i=0}^d M_{i,j} v_i$ for $0 \\leq j \\leq d$. Let $A \\in \\text{End}(V)$. For ${\\theta}\\in {\\mathbb{F}}$ define $V({\\theta}) = \\{ v \\in V \\,|\\, A v = {\\theta}v\\}$. Observe that $V({\\theta})$ is a subspace of $V$. The scalar ${\\theta}$ is called an [*eigenvalue*]{} of $A$ whenever $V({\\theta}) \\neq 0$. In this case, $V({\\theta})$ is called the [*eigenspace*]{} of $A$ corresponding to ${\\theta}$. We say that $A$ is [*diagonalizable*]{} whenever $V$ is spanned by the eigenspaces of $A$. ", "We say that $A$ is [*multiplicity-free*]{} whenever $A$ is diagonalizable, and each eigenspace of $A$ has dimension one. ", "Assume that $A$ is multiplicity-free, and let $\\{V_i\\}_{i=0}^d$ denote an ordering of the eigenspaces of $A$. ", "Then $V = \\sum_{i=0}^d V_i$ (direct sum). ", "For $0 \\leq i \\leq d$ let ${\\theta}_i$ denote the eigenvalue of $A$ corresponding to $V_i$. For $0 \\leq i \\leq d$ define $E_i \\in \\text{End}(V)$ such that $(E_i - I)V_i = 0$ and $E_i V_j = 0$ if $j \\neq i$ $(0 \\leq j \\leq d)$. Thus $E_i$ is the projection onto $V_i$. Observe that (i) $V_i = E_i V$ $(0 \\leq i \\leq d)$; (ii) $E_i E_j = \\delta_{i,j} E_i$ $(0 \\leq i,j \\leq d)$; (iii) $I = \\sum_{i=0}^d E_i$; (iv) $A = \\sum_{i=0}^d {\\theta}_i E_i$. Also $$\\begin{aligned}\n E_i &= \\prod_{\\begin{smallmatrix} 0 \\leq j \\leq d \\\\ j \\neq i \\end{smallmatrix} }\n \\frac{A-{\\theta}_j I}{{\\theta}_i - {\\theta}_j} \n \\qquad\\qquad (0 \\leq i \\leq d). ", " \\label{eq:Ei0}\\end{aligned}$$ We call $E_i$ the [*primitive idempotent*]{} of $A$ for ${\\theta}_i$ $(0 \\leq i \\leq d)$. Observe that $\\{A^i\\}_{i=0}^d$ is a basis for the ${\\mathbb{F}}$-vector space ${\\langle A \\rangle}$, and $\\prod_{i=0}^d (A-{\\theta}_i I) =0$. Also observe that $\\{E_i\\}_{i=0}^d$ is a basis for the ${\\mathbb{F}}$-vector space ${\\langle A \\rangle}$.\n\nLet $A,A^*$ denote a Leonard pair on $V$. By [@T:Leonard Lemma 1.3] each of $A$, $A^*$ is multiplicity-free. ", "Let $\\{E_i\\}_{i=0}^d$ denote an ordering of the primitive idempotents of $A$. ", "For $0 \\leq i \\leq d$ pick $0 \\neq v_i \\in E_i V$. Then $\\{v_i\\}_{i=0}^d$ is a basis for $V$. The ordering $\\{E_i\\}_{i=0}^d$ is said to be [*standard*]{} whenever the basis $\\{v_i\\}_{i=0}^d$ satisfies Definition \\[def:LP\\](ii). ", "A standard ordering of the primitive idempotents of $A^*$ is similarly defined.", "\n\n[[@T:Leonard Definition 1.4] ]{} \\[def:LS\\] . ", "By a [*Leonard system*]{} on $V$ we mean a sequence $$\\Phi = (A; \\{E_i\\}_{i=0}^d; A^*; \\{E^*_i\\}_{i=0}^d) \\label{eq:Phi}$$ of elements in $\\text{\\rm End}(V)$ that satisfy the following (i)–(iii):\n\n- $A,A^*$ is a Leonard pair on $V$;\n\n- $\\{E_i\\}_{i=0}^d$ is a standard ordering of the primitive idempotents of $A$;\n\n- $\\{E^*_i\\}_{i=0}^d$ is a standard ordering of the primitive idempotents of $A^*$.\n\nFor the rest of this section, we fix a Leonard system $\\Phi$ as in .", "\n\n\\[lem:dagger2\\] . ", "The antiautomorphism $\\dagger$ from Lemma \\[lem:dagger\\] fixes each of $E_i$, $E^*_i$ for $0 \\leq i \\leq d$.\n\nBy Lemma \\[lem:dagger\\].", "\n\nWe recall the notion of isomorphism for Leonard systems. ", "Let $V'$ denote a vector space over ${\\mathbb{F}}$ with dimension $d+1$, and let $\\Phi' = (A'; \\{E'_i\\}_{i=0}^d; A^{*\\prime}; \\{E^{* \\prime}_i\\}_{i=0}^d)$ denote a Leonard system on $V'$. By an [*isomorphism of Leonard systems*]{} from $\\Phi$ to $\\Phi'$ we mean an ${\\mathbb{F}}$-algebra isomorphism $\\text{\\rm End}(V) \\to \\text{\\rm End}(V')$ that sends $A \\mapsto A'$, $A^* \\mapsto A^{* \\prime}$ and $E_i \\mapsto E'_i$, $E^*_i \\mapsto E^{* \\prime}_i$ for $0 \\leq i \\leq d$. The Leonard systems $\\Phi$ and $\\Phi'$ are said to be [*isomorphic*]{} whenever there exits an isomorphism of Leonard systems from $\\Phi$ to $\\Phi'$. In this case the isomorphism is unique.", "\n\nEach of the following is a Leonard system on $V$: $$\\begin{aligned}\n \\Phi^* &= (A^*; \\{E^*_i\\}_{i=0}^d; A; \\{E_i\\}_{i=0}^d),\n\\\\\n \\Phi^{\\downarrow} &= (A; \\{E_i\\}_{i=0}^d; A^*; \\{E^*_{d-i}\\}_{i=0}^d),\n\\\\\n \\Phi^{\\Downarrow} &= (A; \\{E_{d-i}\\}_{i=0}^d; A^*; \\{E^*_i\\}_{i=0}^d).\\end{aligned}$$ Moreover, for $\\alpha, \\beta, \\alpha^*, \\beta^* \\in {\\mathbb{F}}$ with $\\alpha \\alpha^* \\neq 0$, the sequence $$( \\alpha A + \\beta I; \\{E_i\\}_{i=0}^d; \\alpha^* A^* + \\beta^* I ; \\{E^*_i\\}_{i=0}^d)$$ is a Leonard system on $V$. We call this Leonard system [*an affine transformation of $\\Phi$*]{}.", "\n\nFor $0 \\leq i \\leq d$ let ${\\theta}_i$ (resp.", " ${\\theta}^*_i$) denote the eigenvalue of $A$ (resp.", " $A^*$) corresponding to $E_i$ (resp.", " $E^*_i$). ", "We call $\\{{\\theta}_i\\}_{i=0}^d$ (resp.", " $\\{{\\theta}^*_i\\}_{i=0}^d$) the [*eigenvalue sequence*]{} (resp.", " [*dual eigenvalue sequence*]{}) of $\\Phi$. Throughout this paper we often discuss the Leonard system $\\Phi^*$ as well as $\\Phi$. The following notational convention will simplify this discussion.", "\n\n\\[def:star\\] . ", "Referring to our Leonard system $\\Phi$, for any object $\\omega$ associated with $\\Phi$, let $\\omega^*$ denote the corresponding object for $\\Phi^*$.\n\nWe recall the $\\Phi$-standard basis. ", "Pick $0 \\neq u \\in E_0 V$. By [@T:survey Lemma 10.2] the vectors $\\{E^*_i u\\}_{i=0}^d$ form a basis for $V$, said to be [*$\\Phi$-standard*]{}. ", "With respect to this basis the matrix representing $A$ is irreducible tridiagonal, and the matrix representing $A^*$ is diagonal with $(i,i)$-entry ${\\theta}^*_i$ for $0 \\leq i \\leq d$. So with respect to the basis $\\{E^*_i u\\}_{i=0}^d$ the matrices representing $A,A^*$ are $$\\begin{aligned}\nA &:\n \\begin{pmatrix}\n a_0 & b_0 & & & & \\bf{0} \\\\\n c_1 & a_1 & b_1 \\\\\n & c_2 & \\cdot & \\cdot \\\\\n && \\cdot & \\cdot & \\cdot\\\\\n &&& \\cdot & \\cdot & b_{d-1} \\\\\n \\bf{0} & & & & c_d & a_d\n \\end{pmatrix},\n&\nA^* &:\n \\begin{pmatrix}\n {\\theta}^*_0 & & & & & \\bf{0} \\\\\n & {\\theta}^*_1 \\\\\n && {\\theta}^*_2 \\\\\n & & & \\cdot \\\\\n & & & & \\cdot \\\\\n \\bf{0} & & & & & {\\theta}^*_d\n \\end{pmatrix}, \\label{eq:matrixAAs}\\end{aligned}$$ where $\\{c_i\\}_{i=1}^d$, $\\{a_i\\}_{i=0}^d$, $\\{b_i\\}_{i=0}^{d-1}$ are scalars in ${\\mathbb{F}}$ such that $b_{i-1} c_i \\neq 0$ for $1 \\leq i \\leq d$. The scalars $\\{c_i\\}_{i=1}^d$, $\\{a_i\\}_{i=0}^d$, $\\{b_i\\}_{i=0}^{d-1}$ are uniquely determined by $\\Phi$, and called the [*intersection numbers of $\\Phi$*]{}. ", "The sum of the vectors in a $\\Phi$-standard basis is contained in $E_0 V$, and therefore an eigenvector for $A$ with eigenvalue ${\\theta}_0$. Consequently $$\\begin{aligned}\n {\\theta}_0 &= c_i + a_i + b_i && (0 \\leq i \\leq d), $$ where $c_0 = 0$ and $b_d = 0$.\n\nWe define some polynomials. ", "Let $\\lambda$ denote an indeterminate, and let ${\\mathbb{F}}[\\lambda]$ denote the ${\\mathbb{F}}$-algebra consisting of the polynomials in $\\lambda$ with all coefficients in ${\\mathbb{F}}$. For $0 \\leq i \\leq d$ define the following polynomials in ${\\mathbb{F}}[\\lambda]$: $$\\begin{aligned}\n\\tau_i (\\lambda) &= (\\lambda-{\\theta}_0)(\\lambda-{\\theta}_1) \\cdots (\\lambda-{\\theta}_{i-1}),\n\\\\\n\\eta_i (\\lambda) &= (\\lambda-{\\theta}_d)(\\lambda-{\\theta}_{d-1}) \\cdots (\\lambda-{\\theta}_{d-i+1}).\\end{aligned}$$\n\nFor a nonzero $u \\in E^*_0 V$, consider the vectors $\\{\\tau_i (A) u\\}_{i=0}^d$. By [@T:survey Section 21] these vectors form a basis for $V$. This basis is called a [*$\\Phi$-split basis*]{} for $V$.\n\n[[@T:Leonard Theorem 3.2] ]{} \\[lem:split\\] . ", "There exist scalars $\\{{\\varphi}_i\\}_{i=1}^d$ in ${\\mathbb{F}}$ such that with respect to a $\\Phi$-split basis for $V$ the matrices representing $A$ and $A^*$ are $$\\begin{aligned}\nA &:\\:\n \\begin{pmatrix}\n {\\theta}_0 & & & & & \\bf{0} \\\\\n 1 & {\\theta}_1 \\\\\n & 1 & {\\theta}_2 \\\\\n && \\cdot & \\cdot \\\\\n &&& \\cdot & \\cdot \\\\\n \\bf{0} & & & & 1 & {\\theta}_d\n \\end{pmatrix},\n&\nA^* &:\n \\begin{pmatrix}\n {\\theta}^*_0 & {\\varphi}_1 & & & & \\bf{0} \\\\\n & {\\theta}^*_1 & {\\varphi}_2 \\\\\n && {\\theta}^*_2 & \\cdot \\\\\n & & & \\cdot & \\cdot \\\\\n & & & & \\cdot & {\\varphi}_d \\\\\n \\bf{0} & & & & & {\\theta}^*_d\n \\end{pmatrix}.\\end{aligned}$$ The sequence $\\{{\\varphi}_i\\}_{i=1}^d$ is uniquely determined by $\\Phi$. Moreover ${\\varphi}_i \\neq 0$ for $1 \\leq i \\leq d$.\n\nReferring to Lemma \\[lem:split\\], the sequence $\\{{\\varphi}_i\\}_{i=1}^d$ is called the [*first split sequence of $\\Phi$*]{}. ", "Let $\\{\\phi_i\\}_{i=1}^d$ denote the first split sequence of $\\Phi^\\Downarrow$. We call $\\{\\phi_i\\}_{i=1}^d$ the [*second split sequence of $\\Phi$*]{}. ", "By the [*parameter array*]{} of $\\Phi$ we mean the sequence $$(\\{{\\theta}_i\\}_{i=0}^d; \\{{\\theta}^*_i\\}_{i=0}^d; \\{{\\varphi}_i\\}_{i=1}^d; \\{\\phi_i\\}_{i=1}^d). ", " \\label{eq:parray}$$\n\n[[@T:Leonard Theorem 1.9]]{} \\[lem:isomorphic\\] . ", "A Leonard system is uniquely determined up to isomorphism by its parameter array.", "\n\n[[@T:survey Theorem 23.5] ]{} \\[lem:intersection\\] . ", "The intersection numbers $\\{c_i\\}_{i=1}^d$, $\\{b_i\\}_{i=0}^{d-1}$ of $\\Phi$ are determined by the parameter array in the following way: $$\\begin{aligned}\n c_i &= \\phi_i \\frac{\\eta^*_{d-i} ({\\theta}^*_i) } { \\eta^*_{d-i+1} ({\\theta}^*_{i-1}) } \n && (1 \\leq i \\leq d), \\label{eq:ci0}\n\\\\\n b_i &= {\\varphi}_{i+1} \\frac{ \\tau^*_i ({\\theta}^*_i) } { \\tau^*_{i+1}({\\theta}^*_{i+1}) }\n && (0 \\leq i \\leq d-1). ", " \\label{eq:bi0}\\end{aligned}$$\n\n\\[lem:parray\\] . ", "The parameter array of $\\Phi$ is determined by the eigenvalue sequence, dual eigenvalue sequence, and the $\\{c_i\\}_{i=1}^d$, $\\{b_i\\}_{i=0}^{d-1}$.\n\nBy Lemma \\[lem:intersection\\].", "\n\nWe recall the the self-dual Leonard systems. ", "The Leonard system $\\Phi$ is said to be [*self-dual*]{} whenever $\\Phi$ is isomorphic to $\\Phi^*$. In this case, the isomorphism of Leonard systems from $\\Phi$ to $\\Phi^*$ is called the [*duality*]{} of $\\Phi$. We remark that if $\\Phi$ is self-dual then so is the Leonard pair $A,A^*$, and in this case the duality of $\\Phi$ is the duality of $A,A^*$.\n\n[[@NT:affine Lemma 8.6, Proposition 8.7] ]{} \\[lem:selfdualparam\\] . ", "The Leonard system $\\Phi$ is self-dual if and only if ${\\theta}_i = {\\theta}^*_i$ for $0 \\leq i \\leq d$. In this case, $\\phi_i = \\phi_{d-i+1}$ for $1 \\leq i \\leq d$.\n\nThe map $\\pi$ {#sec:pi}\n=============\n\nIn this section, we introduce a certain map $\\pi : \\text{\\rm End}(V) \\to {\\mathbb{F}}$ attached to a Leonard system. ", "Before defining this map, we briefly recall some basis facts about the trace function $\\text{\\rm tr} \\! : ", " \\text{\\rm End}(V) \\to {\\mathbb{F}}$. We have $\\text{\\rm tr} (Y Z) = \\text{tr} (Z Y)$ for $Y$, $Z \\in \\text{\\rm End}(V)$.\n\n\\[lem:trYsigma\\] . ", "Let $\\sigma$ denote an automorphism of $\\text{\\rm End}(V)$. Then $\\text{\\rm tr}(Y^\\sigma) = \\text{\\rm tr}(Y)$ for all $Y \\in \\text{\\rm End}(V)$.\n\nBy Lemma \\[lem:SN\\] there exists an invertible $K \\in \\text{\\rm End}(V)$ such that $Y^\\sigma = K Y K^{-1}$ for all $Y \\in \\text{\\rm End}(V)$. We have $\\text{\\rm tr}(K Y K^{-1}) = \\text{\\rm tr}(K^{-1} K Y) = \\text{\\rm tr}(Y)$. The result follows.", "\n\n\\[lem:trYgamma\\] . ", "Let $\\tau$ denote an antiautomorphism of $\\text{\\rm End}(V)$. Then $\\text{\\rm tr}(Y^\\tau) = \\text{\\rm tr}(Y)$ for all $Y \\in \\text{\\rm End}(V)$.\n\nWithout loss we may identify $\\text{\\rm End}(V)$ with $\\text{\\rm Mat}_{d+1}({\\mathbb{F}})$. The transpose map is an antiautomorphism of the algebra $\\text{\\rm Mat}_{d+1}({\\mathbb{F}})$. So the composition of $\\tau$ and the transpose map is an automorphism of $\\text{\\rm Mat}_{d+1}({\\mathbb{F}})$. The result follows in view of Lemma \\[lem:trYsigma\\] and the fact that a matrix and its transpose have the same trace.", "\n\nWe now define the map $\\pi$. Let $\\Phi = (A; \\{E_i\\}_{i=0}^d; A^*; \\{E^*_i\\}_{i=0}^d)$ denote a Leonard system on $V$ with parameter array as in .", "\n\n\\[def:pipis\\] . ", "Define the map $$\\pi \\; : \\;\n \\begin{array}{ccc}\n \\text{\\rm End}(V) & \\longrightarrow & {\\mathbb{F}}\\\\\n Y & \\longmapsto & \\text{\\rm tr} (Y E_0)\n \\end{array}$$ Observe that $\\pi$ is ${\\mathbb{F}}$-linear.", "\n\n\\[lem:E0YE0\\] . ", "For $Y \\in \\text{\\rm End}(V)$, $$\\begin{aligned}\n E_0 Y E_0 &= \\pi(Y) E_0. ", " $$\n\nAbbreviate ${\\cal A} = \\text{\\rm End}(V)$. The primitive idempotent $E_0$ is a basis for the subspace $E_0 {\\cal A} E_0$. This subspace contains $E_0 Y E_0$, so there exists $\\alpha \\in {\\mathbb{F}}$ such that $E_0 Y E_0 = \\alpha E_0$. In this equation, take the trace of each side to get $\\text{\\rm tr} (E_0 Y E_0) =\\alpha \\text{\\rm tr}(E_0)$. We have $\\text{\\rm tr}(E_0 Y E_0) = \\text{\\rm tr}(Y E_0) = \\pi(Y)$. Also $\\text{\\rm tr}(E_0) = 1$ since $E_0$ is a primitive idempotent. ", "By these comments, $\\alpha = \\pi (Y)$. The result follows.", "\n\n\\[lem:piY\\] . ", "For $0 \\leq i \\leq d$, $$\\begin{aligned}\n \\pi (E_i) &= \\delta_{i,0}. ", " \\label{eq:piEi}\\end{aligned}$$\n\nWe have $\\text{\\rm tr}(E_0)= 1$. For $1 \\leq i \\leq d$ we have $E_i E_0=0$. By these comments and Definition \\[def:pipis\\] we obtain .", "\n\n\\[lem:piA\\] . ", "We have $$\\begin{aligned}\n \\pi (I) &= 1, &\n \\pi (A) &= {\\theta}_0.\\end{aligned}$$\n\nWe have $\\pi(I)=1$ since $\\text{\\rm tr}(E_0)=1$. In $A = \\sum_{i=0}^d {\\theta}_i E_i$, apply $\\pi$ to each side and use to get $\\pi(A)={\\theta}_0$.\n\n\\[lem:piYZ\\] . ", "For $Y \\in {\\langle A \\rangle}$ and $Z \\in \\text{\\rm End}(V)$, $$\\pi (Y Z) = \\pi (Z Y) = \\pi (Y) \\pi (Z). ", " $$\n\nWrite $Y = \\sum_{i=0}^d \\alpha_i E_i$. We have $$\\pi (Y Z) = \\text{\\rm tr}(Y Z E_0) = \\text{\\rm tr}(Z E_0 Y)\n = \\alpha_0 \\text{\\rm tr} (Z E_0) = \\alpha_0 \\pi (Z).$$ Similarly $\\pi (Z Y) = \\alpha_0 \\pi (Z)$. The result follows since $\\alpha_0 = \\pi (Y)$ by Lemma \\[lem:piY\\].", "\n\n\\[lem:pihom\\] . ", "The restriction of $\\pi$ to ${\\langle A \\rangle}$ is an ${\\mathbb{F}}$-algebra homomorphism ${\\langle A \\rangle} \\to {\\mathbb{F}}$.\n\nBy Lemma \\[lem:piYZ\\].", "\n\nRecall the antiautomorphism $\\dagger$ from Lemma \\[lem:dagger\\].", "\n\n\\[lem:dagger3\\] . ", "The map $\\pi$ makes the following diagram commute. ", "$$\\begin{diagram}\n\\node{ \\text{\\rm End}(V) } \\arrow{e,t}{\\dagger} \\arrow{s,l}{ \\pi}\n\\node{ \\text{\\rm End}(V) } \\arrow{s,r}{ \\pi}\n\\\\\n\\node{{\\mathbb{F}}} \\arrow{e,b}{\\text{\\rm id}} \\node{{\\mathbb{F}}}\n\\end{diagram}$$\n\nPick any $Y \\in \\text{\\rm End}(V)$. Using Lemma \\[lem:trYgamma\\] we argue $$\\pi (Y^\\dagger)\n = \\text{\\rm tr}(Y^\\dagger E_0)\n = \\text{\\rm tr}(Y^\\dagger E_0^\\dagger)\n = \\text{\\rm tr}((E_0 Y)^\\dagger)\n = \\text{\\rm tr}(E_0 Y)\n = \\text{\\rm tr}(Y E_0)\n = \\pi (Y).$$ The result follows.", "\n\n\\[lem:piYsigma\\] . ", "Assume that $\\Phi$ is self-dual with duality $\\sigma$. Then the following diagram commutes. ", "$$\\begin{diagram}\n\\node{ \\text{\\rm End}(V) } \\arrow{e,t}{\\sigma} \\arrow{s,l}{ \\pi^*}\n\\node{ \\text{\\rm End}(V) } \\arrow{s,r}{ \\pi}\n\\\\\n\\node{{\\mathbb{F}}} \\arrow{e,b}{\\text{\\rm id}} \\node{{\\mathbb{F}}}\n\\end{diagram}$$\n\nFor $Z \\in \\text{\\rm End}(V)$ we have $\\text{\\rm tr}(Z^\\sigma) = \\text{\\rm tr}(Z)$. For $Y \\in \\text{\\rm End}(V)$ we have $Y^\\sigma E_0 = Y^\\sigma (E^*_0)^\\sigma = (Y E^*_0)^\\sigma$. By these comments $\\text{\\rm tr}(Y^\\sigma E_0) = \\text{\\rm tr}(Y E^*_0)$. Thus $\\pi (Y^\\sigma) = \\pi^* (Y)$. The result follows.", "\n\n[[@T:survey Lemma 9.4] ]{} \\[lem:nuE0Es0E0\\] . ", "There exists $0 \\neq \\nu \\in {\\mathbb{F}}$ such that $$\\begin{aligned}\n \\nu E_0 E^*_0 E_0 &= E_0, &\n \\nu E^*_0 E_0 E^*_0 &= E^*_0. ", " \\label{eq:nu}\\end{aligned}$$\n\nNote that $\\nu = \\nu^*$. By and Lemma \\[lem:E0YE0\\], $$\\nu^{-1} = \\pi (E^*_0). ", " \\label{eq:defnu}$$\n\n[[@T:survey Theorem 23.8] ]{} \\[lem:nu\\] . ", "We have $$\\nu = \\frac{\\eta_d({\\theta}_0) \\eta^*_d ({\\theta}^*_0) } {\\phi_1 \\phi_2 \\cdots \\phi_d}. ", " \\label{eq:nu2}$$\n\n\\[def:ki\\] . ", "For $0 \\leq i \\leq d$ define $$\\begin{aligned}\n k_i &= \\nu \\pi (E^*_i). ", " \\label{eq:defki}\\end{aligned}$$\n\n\\[lem:ki0\\] . ", "We have $$\\begin{aligned}\n k_0 &= 1, & \\sum_{i=0}^d k_i &= \\nu. ", " \\label{eq:k0}\\end{aligned}$$\n\nUse and to get $k_0 = 1$. In $\\sum_{i=0}^d E^*_i = I$, apply $\\pi$ to each side, and simplify the result using and Lemma \\[lem:piA\\]. ", "This gives the equation on the right in .", "\n\nIn Lemma \\[lem:ki2\\] the scalars $k_i$ are expressed in terms of the parameter array.", "\n\n\\[lem:E0EsiE0\\] . ", "For $0 \\leq i \\leq d$, $$E_0 E^*_i E_0 = \\nu^{-1} k_i E_0. ", " $$\n\nUse Lemma \\[lem:E0YE0\\] (with $Y=E^*_i$) and .", "\n\nThe map $\\rho$ {#sec:rho}\n==============\n\nLet $\\Phi = (A; \\{E_i\\}_{i=0}^d; A^*; \\{E^*_i\\}_{i=0}^d)$ denote a Leonard system on $V$. In this section we introduce a certain map $\\rho : {\\langle A \\rangle} \\to {\\langle A^* \\rangle}$. We abbreviate ${\\cal A} = \\text{\\rm End}(V)$.\n\n\\[lem:AcalAEs0\\] . ", "The map ${\\langle A \\rangle} \\to {\\cal A} E^*_0$, $Y \\mapsto Y E^*_0$ is an ${\\mathbb{F}}$-linear bijection.", "\n\nThe map is clearly ${\\mathbb{F}}$-linear. ", "By [@T:survey Corollary 5.8] the elements $\\{E_i E^*_0\\}_{i=0}^d$ form a basis for ${\\cal A} E^*_0$. The map $Y \\mapsto Y E^*_0$ sends the basis $\\{E_i\\}_{i=0}^d$ for ${\\langle A \\rangle}$ to the basis $\\{E_i E^*_0\\}_{i=0}^d$ for ${\\cal A} E^*_0$, so it is bijective.", "\n\n\\[lem:rho\\] . ", "There exists a unique ${\\mathbb{F}}$-linear map $\\rho : {\\langle A \\rangle} \\to {\\langle A^* \\rangle}$ such that for $Y \\in {\\langle A \\rangle}$, $$\\begin{aligned}\n Y E^*_0 E_0 &= Y^\\rho E_0. ", " \\label{eq:defrho}\\end{aligned}$$\n\nConcerning existence, consider the ${\\mathbb{F}}$-linear map $g : {\\langle A \\rangle} \\to {\\cal A} E_0$, $Y \\mapsto Y E^*_0 E_0$. By Lemma \\[lem:AcalAEs0\\] applied to $\\Phi^*$, the map $\\mu : {\\langle A^* \\rangle} \\to {\\cal A} E_0$, $Y \\mapsto Y E_0$ is an ${\\mathbb{F}}$-linear bijection. ", "The composition $$\\rho : {\\langle A \\rangle} \\xrightarrow{\\;\\;\\;\\; g\\;\\;\\;\\; } {\\cal A} E_0 \n \\xrightarrow{\\;\\;\\;\\; \\mu^{-1}\\;\\;} {\\langle A^* \\rangle}$$ satisfies . ", "We have shown that $\\rho$ exists. ", "The map $\\rho$ is unique by Lemma \\[lem:AcalAEs0\\].", "\n\nRecall the scalar $\\nu$ from .", "\n\n\\[lem:rhorhospre\\] . ", "The maps $\\rho$ and $\\nu \\rho^*$ are inverses. ", "In particular, the maps $\\rho$, $\\rho^*$ are bijective.", "\n\nPick $Y \\in {\\langle A \\rangle}$. Using in order for $\\Phi^*$, , we obtain $$(Y^\\rho)^{\\rho^*} E^*_0\n = Y^\\rho E_0 E^*_0\n = Y E^*_0 E_0 E^*_0\n = \\nu^{-1} Y E^*_0.$$ By this and Lemma \\[lem:AcalAEs0\\] we get $(Y^\\rho)^{\\rho^*} = \\nu^{-1} Y$. Similarly, for $Z \\in {\\langle A^* \\rangle}$ we get $(Z^{\\rho^*})^\\rho = \\nu^{-1} Z$. Thus the maps $\\rho$ and $\\nu \\rho^*$ are inverses.", "\n\n\\[def:Ai\\] . ", "For $0 \\leq i \\leq d$ define $$A_i = \\nu (E^*_i)^{\\rho^*}. ", " \\label{eq:defAiAsi}$$\n\n\\[lem:rhorhos\\] . ", "For $0 \\leq i \\leq d$, $\\rho$ sends $A_i \\mapsto E^*_i$ and $E_i \\mapsto \\nu^{-1} A^*_i$.\n\nBy Lemma \\[lem:rhorhospre\\] and Definition \\[def:Ai\\].", "\n\n\\[lem:rhorhos2\\] . ", "For $0 \\leq i \\leq d$, $$\\begin{aligned}\n A_i E^*_0 E_0 &= E^*_i E_0, & \n E_i E^*_0 E_0 &= \\nu^{-1} A^*_i E_0, \\label{eq:AiEs0E0}\n\\\\\n A^*_i E_0 E^*_0 &= E_i E^*_0, &\n E^*_i E_0 E^*_0 &= \\nu^{-1} A_i E^*_0. ", " \\label{eq:AsiE0Es0}\\end{aligned}$$\n\nTo get , use Lemmas \\[lem:rho\\], \\[lem:rhorhos\\]. ", "Applying to $\\Phi^*$ we obtain .", "\n\n\\[lem:selfdualAi\\] . ", "Assume that $\\Phi$ is self-dual with duality $\\sigma$. Then $\\sigma$ sends $A_i \\leftrightarrow A^*_i$ $(0 \\leq i \\leq d)$.\n\nBy Lemmas \\[lem:rho\\] and \\[lem:rhorhos2\\], $A_i$ is the unique element in ${\\langle A \\rangle}$ such that $$A_i E^*_0 E_0 = E^*_i E_0. ", " \\label{eq:rhorhos2aux1}$$ Applying this to $\\Phi^*$, we find that for $0 \\leq i \\leq d$, $A^*_i$ is the unique element in ${\\langle A^* \\rangle}$ such that $$A^*_i E_0 E^*_0 = E_i E^*_0. ", " \\label{eq:rhorhos2aux2}$$ Apply $\\sigma$ to , and compare the result with to find that $\\sigma$ sends $A_i \\mapsto A^*_i$. Applying this fact to $\\Phi^*$, we find that $\\sigma$ sends $A^*_i \\mapsto A_i$.\n\n\\[lem:A0As0\\] . ", "We have $A_0 = I$.\n\nFor the equation on the right in , set $i=0$ and apply to obtain $E^*_0 = A_0 E^*_0$. By this and Lemma \\[lem:AcalAEs0\\] we get $A_0 = I$.\n\n\\[lem:rhoI\\] . ", "The map $\\rho$ sends $I \\mapsto E^*_0$ and $E_0 \\mapsto \\nu^{-1} I$.\n\nSet $i=0$ in Lemma \\[lem:rhorhos\\] and use Lemma \\[lem:A0As0\\].", "\n\n\\[lem:sumAi\\] . ", "We have $$\\begin{aligned}\n \\sum_{i=0}^d A_i &= \\nu E_0. ", " $$\n\nApply $\\rho^*$ to each side of the equation $\\sum_{i=0}^d E^*_i = I$, and evaluate the result using Lemmas \\[lem:rhorhos\\], \\[lem:rhoI\\] applied to $\\Phi^*$.\n\n\\[lem:AiAsi\\] . ", "The elements $\\{A_i\\}_{i=0}^d$ form a basis for the ${\\mathbb{F}}$-vector space ${\\langle A \\rangle}$.\n\nBy Lemmas \\[lem:rhorhospre\\], \\[lem:rhorhos\\], and since $\\{E^*_i\\}_{i=0}^d$ form a basis for the ${\\mathbb{F}}$-vector space ${\\langle A^* \\rangle}$.\n\nRecall the antiautomorphism $\\dagger$ from Lemma \\[lem:dagger\\].", "\n\n\\[lem:dagger4\\] . ", "The antiautomorphism $\\dagger$ fixes each of $A_i$, $A^*_i$ for $0 \\leq i \\leq d$.\n\nBy Lemma \\[lem:dagger\\] and since $A_i \\in {\\langle A \\rangle}$, $A^*_i \\in {\\langle A^* \\rangle}$ for $0 \\leq i \\leq d$.\n\n\\[lem::rhodagger\\] . ", "The map $\\rho$ from Lemma \\[lem:rho\\] makes the following diagram commute. ", "$$\\begin{diagram}\n \\node{{\\langle A \\rangle}} \\arrow{e,t}{\\rho} \\arrow{s,l}{\\dagger}\n \\node{{\\langle A^* \\rangle}} \\arrow{s,r}{\\dagger}\n\\\\\n \\node{{\\langle A \\rangle}} \\arrow{e,b}{\\rho}\n \\node{{\\langle A^* \\rangle}}\n\\end{diagram}$$\n\nBy Lemma \\[lem:dagger2\\].", "\n\nRecall the ${\\mathbb{F}}$-linear map $\\pi$ from Definition \\[def:pipis\\].", "\n\n\\[lem:rhopi\\] . ", "For $Y \\in {\\langle A \\rangle}$, $$\\pi (Y^\\rho) = \\nu^{-1} \\pi (Y). ", " \\label{eq:pirho}$$\n\nBy Definition \\[def:pipis\\], $\\pi (Y^\\rho) = \\text{tr} (Y^\\rho E_0)$. By Lemma \\[lem:rho\\], $Y^\\rho E_0 = Y E^*_0 E_0$. By these comments and Definition \\[def:pipis\\], $\\pi(Y^\\rho) = \\pi(Y E^*_0)$. By this and Lemma \\[lem:piYZ\\], $\\pi(Y^\\rho) = \\pi(Y) \\pi (E^*_0)$. By , $\\pi(E^*_0) = \\nu^{-1}$. Thus holds.", "\n\n\\[lem:AiE0\\] . ", "For $0 \\leq i \\leq d$, $$\\begin{aligned}\n A_i E_0 &= k_i E_0. ", " \\label{eq:AiE0}\\end{aligned}$$\n\nSince $A_i \\in {\\langle A \\rangle}$ there exists $\\alpha_i \\in {\\mathbb{F}}$ such that $A_i E_0 = \\alpha_i E_0$. In the first equation of Lemma \\[lem:rhorhos2\\], take the trace of each side and use , to obtain $\\alpha_i = k_i$ after a routine computation. ", "The result follows.", "\n\n\\[lem:piAi\\] . ", "For $0 \\leq i \\leq d$, $$\\begin{aligned}\n \\pi (A_i) &= k_i, & \\pi(A^*_i) &= \\delta_{i,0}. ", " \\label{eq:piAi}\\end{aligned}$$\n\nIn , take the trace of each side and use $\\text{tr}(E_0) = 1$ to get the equation on the left in . ", "Next we obtain the equation on the right in . ", "By , $A^*_i = \\nu E_i^\\rho$. By Lemma \\[lem:rhopi\\], $\\pi(E_i^\\rho) = \\nu^{-1} \\pi (E_i)$. By these comments, $\\pi (A^*_i) = \\pi (E_i)$. By this and Lemma \\[lem:piY\\] we obtain the equation on the right in .", "\n\nRecall from the intersection numbers $\\{c_i\\}_{i=1}^d$, $\\{a_i\\}_{i=0}^d$, $\\{b_i\\}_{i=0}^{d-1}$ of $\\Phi$.\n\n\\[lem:AAi\\] . ", "Assume that $d \\geq 1$. Then $$\\begin{aligned}\n A A_0 &= c_1 A_1 + a_0 A_0, \\label{eq:AA0}\n\\\\\n A A_i &= c_{i+1} A_{i+1} + a_i A_i + b_{i-1} A_{i-1} \n && (1 \\leq i \\leq d-1), \\label{eq:AAi}\n\\\\\n A A_d &= a_d A_d + b_{d-1} A_{d-1}. ", " \\label{eq:AAd}\\end{aligned}$$\n\nPick $0 \\neq u \\in E_0 V$ and consider the $\\Phi$-standard basis $\\{E^*_i u\\}_{i=0}^d$ for $V$. By , $$\\begin{aligned}\n A E^*_i u &= c_{i+1} E^*_{i+1} u + a_i E^*_i u + b_{i-1} E^*_{i-1} u\n && (0 \\leq i \\leq d), \\end{aligned}$$ where $b_{-1}=0$, $c_{d+1}=0$ and $E^*_{-1}=0$, $E^*_{d+1}=0$. By this and since $u$ is basis for $E_0 V$, $$\\begin{aligned}\n A E^*_i E_0 &= c_{i+1} E^*_{i+1} E_0 + a_i E^*_i E_0 + b_{i-1} E^*_{i-1} E_0\n && (0 \\leq i \\leq d). ", " \\end{aligned}$$ By this and the first equation in Lemma \\[lem:rhorhos2\\], $$\\begin{aligned}\n (A A_i - c_{i+1} A_{i+1} - a_i A_i - b_{i-1} A_{i-1} ) E^*_0 E_0 &= 0 && (0 \\leq i \\leq d),\\end{aligned}$$ where $A_{-1}=0$, $A_{d+1}=0$. The map ${\\langle A \\rangle} \\to {\\cal A} E_0$, $Y \\mapsto Y E^*_0 E_0$ is an ${\\mathbb{F}}$-linear bijection, since this map is the composition of $\\rho$ and the bijection ${\\langle A^* \\rangle} \\to {\\cal A} E_0$, $Y \\mapsto Y E_0$ from Lemma \\[lem:AcalAEs0\\]. ", "By these comments we obtain the result.", "\n\n\\[lem:AA1\\] . ", "Assume that $d \\geq 1$. Then $A = c_1 A_1 + a_0 I$.\n\nBy Lemma \\[lem:A0As0\\] and .", "\n\n\\[lem:defp\\] . ", "There exist scalars $p^h_{i j}$ $(0 \\leq h,i,j \\leq d)$ in ${\\mathbb{F}}$ such that $$\\begin{aligned}\n A_i A_j &= \\sum_{h=0}^d p^h_{i j} A_h && (0 \\leq i,j \\leq d). ", " \\label{eq:AiAj}\\end{aligned}$$\n\nBy Lemma \\[lem:AiAsi\\].", "\n\nFor notational convenience, define $$\\begin{aligned}\n q^h_{i j} &= (p^h_{i j})^* && (0 \\leq h,i,j \\leq d). ", " $$ Applying to $\\Phi^*$, $$\\begin{aligned}\n A^*_i A^*_j &= \\sum_{h=0}^d q^h_{i j} A^*_h && (0 \\leq i,j \\leq d). ", " \\label{eq:AsiAsj2}\\end{aligned}$$\n\n\\[lem:phijphji\\] . ", "The following hold:\n\n- $p^h_{i j} = p^h_{j i} \\qquad (0 \\leq h,i,j \\leq d)$;\n\n- $\\sum_{r=0}^d p^t_{h r} p^r_{i j} = \\sum_{s=0}^d p^t_{s j} p^s_{h i} \\qquad (0 \\leq h,i,j, t \\leq d)$.\n\n\\(i) Since the algebra ${\\langle A \\rangle}$ is commutative.", "\n\n\\(ii) Expand $A_h (A_i A_j) = (A_h A_i) A_j$ in two ways using , and compare the coefficients.", "\n\n\\[lem:kip0ii\\] . ", "We have $p^0_{i j} = \\delta_{i,j} k_i$ for $0 \\leq i,j \\leq d$.\n\nIn , multiply each side on the left by $E_0 E^*_0$ and on the right by $E^*_0 E_0$. Simplify the result using the equation on the left in and the equation obtained from it by applying $\\dagger$. This gives $$E_0 E^*_i E^*_j E_0 = \\sum_{h=0}^d p^h_{i j} E_0 E^*_0 E^*_h E_0.$$ Thus $$\\delta_{i,j} E_0 E^*_i E_0 = p^0_{i j} E_0 E^*_0 E_0.$$ In this line, take the trace of each side and use Definition \\[def:pipis\\] along with , to get the result.", "\n\n\\[lem:khphij\\] . ", "For $0 \\leq h,i,j \\leq d$, $$k_h p^h_{i j} = k_i p^i_{h j} = k_j p^j_{h i}. ", " $$\n\nIn view of Lemma \\[lem:phijphji\\](i), it suffices to show that $k_h p^h_{i j} = k_j p^j_{h i}$. To obtain this equation, set $t=0$ in Lemma \\[lem:phijphji\\](ii), and evaluate the result using Lemma \\[lem:kip0ii\\].", "\n\n\\[lem:phij\\] . ", "Assume that $d \\geq 1$. Then $$\\begin{aligned}\n c_i &= c_1 p^i_{1,i-1} && (1 \\leq i \\leq d),\n\\\\\n a_i &= c_1 p^i_{1i} + a_0 && (0 \\leq i \\leq d),\n\\\\\n b_i &= c_1 p^i_{1,i+1} && (0 \\leq i \\leq d-1).\\end{aligned}$$\n\nCompare Lemma \\[lem:AAi\\] and in light of Lemma \\[lem:AA1\\].", "\n\nIn view of Lemma \\[lem:AAi\\] we consider the following polynomials.", "\n\n[[@T:survey Lemma 13.3] ]{} \\[def:vi\\] . ", "Define polynomials $\\{v_i\\}_{i=0}^d$ in ${\\mathbb{F}}[\\lambda]$ such that $v_0 =1$ and for $d \\geq 1$, $$\\begin{aligned}\n \\lambda v_0 &= c_1 v_1 + a_0, \n\\\\\n \\lambda v_i &= c_{i+1} v_{i+1} + a_i v_i + b_{i-1} v_{i-1} && (1 \\leq i \\leq d-1).\\end{aligned}$$\n\n\\[lem:viA\\] . ", "Referring to Definition \\[def:vi\\], the following hold for $0 \\leq i \\leq d$:\n\n- $v_i$ has degree $i$ and leading coefficient $(c_1 c_2 \\cdots c_i)^{-1}$;\n\n- $A_i = v_i (A)$;\n\n- $A_i = \\sum_{j=0}^d v_i ({\\theta}_j) E_j$;\n\n- $E_i = \\nu^{-1} \\sum_{j=0}^d v^*_i ({\\theta}^*_j) A_j$.\n\n\\(i) By Definition \\[def:vi\\].", "\n\n\\(ii) By Lemma \\[lem:AAi\\] and Definition \\[def:vi\\].", "\n\n\\(iii) We have $A_i E_j = v_i (A) E_j = v_i ({\\theta}_j) E_j$ for $0 \\leq i,j \\leq d$. We have $A_i = A_i I = \\sum_{j=0}^d A_i E_j$. The result follows.", "\n\n\\(iv) Applying (iii) to $\\Phi^*$ we obtain $A^*_i = \\sum_{j=0}^d v^*_i ({\\theta}^*_j) E^*_j$. In this equation, apply $\\rho^*$ to each side. ", "Simplify the result using Lemma \\[lem:rhorhos\\] (applied to $\\Phi^*$) to get the result.", "\n\nThe following lemma is from [@T:survey Theorem 12.4]; we give a short proof for the sake of completeness.", "\n\n\\[lem:ki\\] . ", "For $0 \\leq i \\leq d$, $$\\begin{aligned}\n k_i &= \\frac{b_0 b_1 \\cdots b_{i-1} } {c_1 c_2 \\ldots c_i}. ", " \\label{eq:kibici}\\end{aligned}$$\n\nWe have $k_0=1$ by . ", "By Lemma \\[lem:khphij\\] (with $h=1$, $j=i-1$) and Lemma \\[lem:phij\\], $$\\begin{aligned}\n c_i k_i &= b_{i-1} k_{i-1} && (1 \\leq i \\leq d). ", "\\end{aligned}$$ The result follows.", "\n\n\\[lem:kinonzero\\] . ", "We have $k_i \\neq 0$ for $0 \\leq i \\leq d$.\n\nBy Lemma \\[lem:ki\\].", "\n\n\\[lem:phij2\\] . ", "For $0 \\leq h,i,j \\leq d$ the scalar $p^h_{i j}$ is zero (resp.", " nonzero) if one of $h,i,j$ is greater than (resp.", " equal to) the sum of the other two.", "\n\nBy Lemmas \\[lem:khphij\\] and \\[lem:kinonzero\\], it suffices to consider the case $h \\geq i+j$. For this case the result follows from and the observation that for $0 \\leq r \\leq d$ the elements $I, A, A^2, \\ldots, A^r$ and $A_0, A_1, \\ldots, A_r$ form a basis for the same vector space.", "\n\n\\[lem:kivith0\\] . ", "We have $$\\begin{aligned}\n k_i &= v_i ({\\theta}_0) && (0 \\leq i \\leq d).\\end{aligned}$$\n\nFor the equation in Lemma \\[lem:viA\\](iii), multiply each side by $E_0$ to get $A_i E_0 = v_i ({\\theta}_0) E_0$. The result follows from this and Lemma \\[lem:AiE0\\].", "\n\n[[@T:survey Theorem 23.9] ]{} \\[lem:ki2\\] . ", "For $0 \\leq i \\leq d$, $$\\begin{aligned}\n k_i &= \\frac{{\\varphi}_1 {\\varphi}_2 \\cdots {\\varphi}_i} {\\phi_1 \\phi_2 \\cdots \\phi_i}\n \\frac{\\eta^*_d({\\theta}^*_0)} {\\tau^*_i({\\theta}^*_i) \\eta^*_{d-i}({\\theta}^*_i) }\n && (0 \\leq i \\leq d). ", " \\label{eq:kiparam}\\end{aligned}$$\n\nBy and Lemma \\[lem:intersection\\].", "\n\nThe following lemma is from [@T:survey Theorem 16.2]. ", "We give a short proof for the sake of completeness.", "\n\n\\[lem:AWduality\\] . ", "Referring to Definition \\[def:vi\\], $$\\begin{aligned}\n v_i ({\\theta}_j) / k_i &= v^*_j ({\\theta}^*_i) / k^*_j && (0 \\leq i,j \\leq d). ", " \\label{eq:AWduality}\\end{aligned}$$\n\nWe evaluate $E^*_0 A_i A^*_j E_0$ in two ways. ", "By the equation on the right in , $$A^*_j E_0 = \\nu E_j E^*_0 E_0. ", " \\label{eq:AWaux1}$$ By Lemma \\[lem:viA\\](iii), $$A_i E_j = v_i ({\\theta}_j) E_j. ", " \\label{eq:AWaux2}$$ By Lemma \\[lem:E0EsiE0\\] (applied to $\\Phi^*$), $$\\begin{aligned}\n E^*_0 E_j E^*_0 = \\nu^{-1} k^*_j E^*_0. ", " \\label{eq:AWaux3}\\end{aligned}$$ Evaluating $E^*_0 A_i A^*_j E_0$ using – we obtain $$E^*_0 A_i A^*_j E_0 = v_i ({\\theta}_j) k^*_j E^*_0 E_0. ", " \\label{eq:AWaux6}$$ Apply this to $\\Phi^*$, then interchange $i$, $j$ and apply $\\dagger$ to get $$E^*_0 A_i A^*_j E_0 = v^*_j ({\\theta}^*_i) k_i E^*_0 E_0. ", " \\label{eq:AWaux11}$$ We have $E_0 E^*_0 \\neq 0$ by . ", "Now comparing and we obtain .", "\n\nBoltzmann pairs and Spin Leonard pairs {#sec:spinLP}\n======================================\n\nThe notions of a Boltzmann pair and a spin Leonard pair were introduced by Curtin [@C:spinLP]. ", "In this section we first recall these notions, and then prove a theorem about these topics.", "\n\n\\[lem:AsWWs\\] . ", "Let $A,A^*$ denote a Leonard pair on $V$. For invertible $W \\in {\\langle A \\rangle}$ and invertible $W^* \\in {\\langle A^* \\rangle}$ the following are equivalent: $$\\begin{aligned}\n W A^* W^{-1} &= (W^*)^{-1} A W^*, \\label{eq:WAsWinv} \n\\\\\n W^{-1} A^* W &= W^* A (W^*)^{-1}, \\label{eq:WinvAsW}\n\\\\\n W^* W A^* &= A W^* W, \\label{eq:AWsW}\n\\\\\n A^* W W^* &= W W^* A. \\label{eq:WWsA}\\end{aligned}$$\n\nBy linear algebra is equivalent to , and is equivalent to . ", "The equations , are equivalent since each is obtained from the other by applying $\\dagger$.\n\n[@C:spinLP Definition1.2] \\[def:spinLP\\] . ", "Let $A,A^*$ denote a Leonard pair on $V$. By a [*Boltzmann pair for $A,A^*$*]{} we mean an ordered pair $W, W^*$ such that\n\n- $W$ is an invertible element of ${\\langle A \\rangle}$;\n\n- $W^*$ is an invertible element of ${\\langle A^* \\rangle}$;\n\n- $W$, $W^*$ satisfy the four equivalent conditions in Lemma \\[lem:AsWWs\\].", "\n\nThe Leonard pair $A,A^*$ is called a [*spin Leonard pair*]{} whenever there exists a Boltzmann pair for $A,A^*$.\n\nFor the rest of this section, let $A,A^*$ denote a spin Leonard pair on $V$ and let $W,W^*$ denote a Boltzmann pair for $A,A^*$.\n\n\\[lem:AW\\] . ", "We have $$\\begin{aligned}\n A W &= W A, &\n A^* W^* &= W^* A^*. ", " $$\n\nSince $W \\in {\\langle A \\rangle}$ and $W^* \\in {\\langle A^* \\rangle}$.\n\n\\[lem:affine\\] . ", "For $\\alpha$, $\\beta \\in {\\mathbb{F}}$ with $\\alpha \\neq 0$, consider the Leonard pair $\\alpha A + \\beta I$, $\\alpha A^* + \\beta I$. Then $W,W^*$ is a Boltzmann pair for this Leonard pair.", "\n\nBy Definition \\[def:spinLP\\].", "\n\n[[@C:spinLP Lemma 3.3] ]{} \\[lem:WinvWsinv\\] . ", "The following hold.", "\n\n- For nonzero $\\alpha, \\alpha^* \\in {\\mathbb{F}}$ the pair $\\alpha W, \\alpha^* W^*$ is a Boltzmann pair for $A,A^*$.\n\n- The pair $W^{-1}, (W^*)^{-1}$ is a Boltzmann pair for $A,A^*$.\n\n\\(i) By Definition \\[def:spinLP\\].", "\n\n\\(ii) Compare lines and .", "\n\n\\[lem:AsA\\] . ", "The pair $W^*,W$ is a Boltzmann pair for the Leonard pair $A^*,A$.\n\nBy Lemma \\[lem:AsWWs\\].", "\n\n\\[lem:AWWsW\\] . ", "We have $$\\begin{aligned}\n A W W^* W &= W W^* W A^*,\n&\n A^* W W^* W &= W W^* W A, \\label{eq:AWWsW}\n\\\\\n A W^* W W^* &= W^* W W^* A^*,\n&\n A^* W^* W W^* &= W^* W W^* A. \\label{eq:AsWswWs}\\end{aligned}$$\n\nBy Lemmas \\[lem:AsWWs\\], \\[lem:AW\\].", "\n\n[[@C:spinLP Lemma 5.1] ]{} \\[lem:WWsWprepre\\] . ", "The following agree up to a nonzero scalar factor in ${\\mathbb{F}}$: $$W W^* W, \\qquad\\qquad\\qquad W^* W W^*.$$\n\nSet $Z = W W^* W (W^*)^{-1} W^{-1} (W^*)^{-1}$. By Lemma \\[lem:AWWsW\\], $Z$ commutes with $A$ and $A^*$. By this and Lemma \\[lem:generate\\], $Z$ commutes with everything in $\\text{\\rm End}(V)$. So $Z$ is contained in the center of $\\text{\\rm End}(V)$. Thus there exists $\\alpha \\in {\\mathbb{F}}$ such that $Z = \\alpha I$. The result follows.", "\n\nUsing $W$ and $W^*$ we obtain an action of the modular group $\\text{\\rm PSL}_2(\\mathbb{Z})$ on $\\text{\\rm End}(V)$ as a group of automorphisms. ", "Recall from [@Alperin] that $\\text{PSL}_2(\\mathbb{Z})$ has a presentation by generators $\\psi$, $\\sigma$ and relations $\\psi^3=1$, $\\sigma^2=1$. The next result is a variation on [@C:spinLP Lemma 5.2].", "\n\n\\[lem:PSL\\] . ", "The group $\\text{\\rm PSL}_2(\\mathbb{Z})$ acts on $\\text{\\rm End}(V)$ such that $\\psi$ sends $Y \\mapsto (W W^*)^{-1} Y W W^*$ and $\\sigma$ sends $Y \\mapsto (W W^* W)^{-1} Y W W^* W$ for $Y \\in \\text{\\rm End}(V)$.\n\nThe automorphism $\\sigma$ swaps $A$, $A^*$ by . ", "Therefore $A,A^*$ is self-dual with duality $\\sigma$. Thus $\\sigma^2 = 1$ by Lemma \\[lem:s2\\]. ", "By Lemma \\[lem:WWsWprepre\\], there exists $\\alpha \\in {\\mathbb{F}}$ such that $W^* W W^* = \\alpha W W^* W$. So $$(W W^*)^3 = W W^* W W^* W W^* = \\alpha (W W^* W)^2.$$ Thus $\\sigma^2 = \\psi^3$. The result follows.", "\n\nFor the rest of this section, we identify $\\sigma$ with the automorphism of $\\text{\\rm End}(V)$ from Lemma \\[lem:PSL\\]. ", "We record a result from the proof of Lemma \\[lem:PSL\\].", "\n\n\\[lem:PSL2\\] . ", "The spin Leonard pair $A,A^*$ is self-dual with duality $\\sigma$.\n\nThe following definition is motivated by Lemma \\[lem:WWsWprepre\\].", "\n\n\\[def:balanced\\] . ", "The Boltzmann pair $W,W^*$ is said to be [*balanced*]{} whenever $$W W^* W = W^* W W^*. ", " \\label{eq:WWsWpre}$$\n\n\\[lem:balanced\\] . ", "The following [(i)–(iii)]{} hold.", "\n\n- There exists a nonzero $\\alpha \\in {\\mathbb{F}}$ such that the Boltzmann pair $\\alpha W, W^*$ is balanced.", "\n\n- There exists a nonzero $\\alpha^* \\in {\\mathbb{F}}$ such that the Boltzmann pair $W, \\alpha^* W^*$ is balanced.", "\n\n- Assume that $W,W^*$ is balanced. ", "Then for any nonzero $\\xi \\in {\\mathbb{F}}$, the Boltzmann pair $\\xi W, \\xi W^*$ is balanced.", "\n\n\\(i) By Lemma \\[lem:WWsWprepre\\] there exists a nonzero $\\alpha \\in {\\mathbb{F}}$ such that $\\alpha W W^* W = W^* W W^*$. Thus the pair $\\alpha W, W^*$ is balanced.", "\n\n\\(ii) Similar.", "\n\n\\(iii) By Definition \\[def:balanced\\].", "\n\nFor the rest of this section, assume that $W,W^*$ is balanced.", "\n\n\\[lem:sigma\\] . ", "The automorphism $\\sigma$ swaps $W$ and $W^*$.\n\nIn , multiply each side on the left by $W$ to get $$W W W^* W = W W^* W W^*.$$ In this line, multiply each side on the left by $(W W^* W)^{-1}$ to find that $\\sigma$ sends $W \\mapsto W^*$. By this and Lemma \\[lem:s2\\], $\\sigma$ sends $W^* \\mapsto W$.\n\nLet $\\{E_i\\}_{i=0}^d$ denote a standard ordering of the primitive idempotents of $A$. ", "Define $$\\begin{aligned}\n E^*_i &= E_i^\\sigma && (0 \\leq i \\leq d). ", " \\label{eq:defEsi}\\end{aligned}$$ Observe that the sequence $$\\Phi = (A; \\{E_i\\}_{i=0}^d; A^*; \\{E^*_i\\}_{i=0}^d) \\label{eq:Phi2}$$ is a Leonard system on $V$.\n\n\\[lem:Phisd\\] . ", "The Leonard system $\\Phi$ is self-dual with duality $\\sigma$.\n\nBy Lemma \\[lem:PSL2\\], $\\sigma$ swaps $A$ and $A^*$. By and Lemma \\[lem:s2\\], $\\sigma$ swaps $E_i$ and $E^*_i$ for $0 \\leq i \\leq d$. The result follows.", "\n\n\\[lem:EiWsW\\] . ", "For $0 \\leq i \\leq d$, $$\\begin{aligned}\n W^* W E^*_i &= E_i W^* W, &\n W W^* E_i &= E^*_i W W^*. ", " \\label{eq:EiWsW}\\end{aligned}$$\n\nFirst we obtain the equation on the left in . ", "By Lemma \\[lem:PSL\\] and , $$W W^* W E^*_i = E_i W W^* W.$$ In this line, multiply each side on the left by $W^{-1}$. Simplify the result using $E_i \\in {\\langle A \\rangle}$ and Lemma \\[lem:AW\\] to get the equation on the left in . ", "In this equation, apply $\\dagger$ to each side to get the equation on the right in .", "\n\n\\[lem:WtiEi\\] . ", "There exist nonzero scalars $f$, $\\{\\tau_i\\}_{i=0}^d$ in ${\\mathbb{F}}$ such that $\\tau_0=1$ and $$\\begin{aligned}\n W &= f \\sum_{i=0}^d \\tau_i E_i, &\n W^* &= f \\sum_{i=0}^d \\tau_i E^*_i. ", " \\label{eq:WtiEi}\\end{aligned}$$\n\nFirst we obtain the equation on the left in . ", "By $W \\in {\\langle A \\rangle}$ and since $\\{E_i\\}_{i=0}^d$ is a basis for ${\\langle A \\rangle}$, there exist scalars $\\{\\alpha_i\\}_{i=0}^d$ in ${\\mathbb{F}}$ such that $W = \\sum_{i=0}^d \\alpha_i E_i$. The scalars $\\{\\alpha_i\\}_{i=0}^d$ are nonzero since $W$ is invertible. ", "Define $f=\\alpha_0$ and $\\tau_i = \\alpha_0^{-1} \\alpha_i$ for $0 \\leq i \\leq d$. Then the equation on the left in holds. ", "By construction the scalars $f$, $\\{\\tau_i\\}_{i=0}^d$ are all nonzero and $\\tau_0 = 1$. In the equation on the left in , apply $\\sigma$ to each side, and use Lemma \\[lem:sigma\\] and to get the equation on the right in .", "\n\nThe scalars $\\{\\tau_i\\}_{i=0}^d$ do not change under the adjustments of Lemma \\[lem:balanced\\](iii), but $f$ can be adjusted to have any nonzero value.", "\n\n\\[lem:Winv\\] . ", "We have $$\\begin{aligned}\n W^{-1} &= f^{-1} \\sum_{i=0}^d \\tau_i^{-1} E_i, &\n (W^*)^{-1} &= f^{-1} \\sum_{i=0}^d \\tau_i^{-1} E^*_i. ", " \\label{eq:WinvtiinvEi}\\end{aligned}$$\n\nFollows from .", "\n\nRecall the map $\\pi$ from Definition \\[def:pipis\\].", "\n\n\\[lem:piWf\\] . ", "We have $$\\begin{aligned}\n \\pi (W) &= f, \\qquad\\qquad\\qquad \\pi^* (W^*) = f. \\label{eq:piWf}\\end{aligned}$$\n\nApply $\\pi$ to the equation on the left in and use Lemma \\[lem:piY\\] to get the equation on the left in . ", "The equation on the right in is similarly obtained.", "\n\n\\[lem:defgamma\\] . ", "There exists $\\gamma \\in {\\mathbb{F}}$ such that $$\\pi(W^*) = f \\gamma, \\qquad\\qquad\\qquad\n \\pi^*(W) = f \\gamma. ", " \\label{eq:fgamma}$$\n\nDefine $\\gamma = f^{-1} \\pi(W^*)$. Then the equation on the left in holds. ", "By Lemma \\[lem:sigma\\], $W^\\sigma = W^*$. By Lemma \\[lem:piYsigma\\], $\\pi(W^\\sigma) = \\pi^*(W)$. By these comments we get the equation on the right in .", "\n\n\\[note:gamma\\] . ", "The scalar $\\gamma$ does not change under the adjustments of Lemma \\[lem:balanced\\](iii).", "\n\n\\[lem:piWWs2\\] . ", "We have $$\\begin{aligned}\n\\pi(W W^*) &= f^2 \\gamma, & \\pi(W^* W) &= f^2 \\gamma, \\label{eq:piWWsfgamma}\n\\\\ \n\\pi^*(W W^*) &= f^2 \\gamma, & \\pi^*(W^* W) &= f^2 \\gamma. ", " \\label{eq:piWWsfgamma2}\\end{aligned}$$\n\nBy Lemma \\[lem:piYZ\\](i), $\\pi(W W^*) = \\pi(W^* W) = \\pi(W) \\pi(W^*)$. By this and , , we obtain . ", "The equations are similarly obtained.", "\n\nRecall the map $\\rho$ from Lemma \\[lem:rho\\].", "\n\n\\[lem:WrhoWsrhos\\] . ", "We have $$\\begin{aligned}\n W^\\rho &= f^2 \\gamma \\, (W^*)^{-1}, &\n (W^*)^{\\rho^*} &= f^2 \\gamma \\, W^{-1}. ", " \\label{eq:WrhoWsrhos}\\end{aligned}$$\n\nFirst we obtain the equation on the left in . ", "In the equation on the left in for $i=0$, multiply each side on the right by $E_0$ to get $$W^* W E^*_0 E_0 = E_0 W^* W E_0.$$ By Lemma \\[lem:E0YE0\\], $E_0 W^* W E_0 = \\pi(W^* W) E_0$. By these comments and , $$\\begin{aligned}\n W^* W E^*_0 E_0 &= f^2 \\gamma \\, E_0. ", "\\end{aligned}$$ In this line, multiply each side on the left by $(W^*)^{-1}$ to get $$\\begin{aligned}\n W E^*_0 E_0 &= f^2 \\gamma \\, (W^*)^{-1} E_0. ", "\\end{aligned}$$ By this and Lemmas \\[lem:AcalAEs0\\], \\[lem:rho\\] we get the equation on the left in . ", "The equation on the right in is similarly obtained.", "\n\n\\[lem:gammanonzero\\] . ", "We have $\\gamma \\neq 0$.\n\nWe have $W^\\rho \\neq 0$ since $W \\neq 0$ and $\\rho$ is bijective. ", "By this and we get $\\gamma \\neq 0$.\n\nWe now give our main result in this section. ", "Recall the elements $\\{A_i\\}_{i=0}^d$ from and the scalar $\\nu$ from .", "\n\n\\[thm:WtiinvAi\\] . ", "We have $$\\begin{aligned}\n W &= f \\gamma \\sum_{i=0}^d \\tau_i^{-1} A_i, &\n W^{-1} &= \\nu^{-1} f^{-1} \\gamma^{-1} \\sum_{i=0}^d \\tau_i A_i, \\label{eq:WWinv}\n\\\\\n W^* &= f \\gamma \\sum_{i=0}^d \\tau_i^{-1} A^*_i, &\n (W^*)^{-1} &= \\nu^{-1} f^{-1} \\gamma^{-1} \\sum_{i=0}^d \\tau_i A^*_i. ", " \\label{eq:WsWsinv}\\end{aligned}$$\n\nFirst we obtain the equation on the left in . ", "By and , $$W^\\rho = f \\gamma \\sum_{i=0}^d \\tau_i^{-1} E^*_i.$$ In this line, apply $\\rho^*$ to each side, and use Lemmas \\[lem:rhorhospre\\], \\[lem:rhorhos\\] to get the equation on the left in . ", "Next we obtain the equation on the right in . ", "By , $W^{-1} = f^{-2} \\gamma^{-1} (W^*)^{\\rho^*}$. In the equation on the right in , apply $\\rho^*$ to each side and use Lemma \\[lem:rhorhos\\] to get $(W^*)^{\\rho^*} = f \\nu^{-1} \\sum_{i=0}^d \\tau_i A_i$. By these comments we get the equation on the right in . ", "The equations are similarly obtained.", "\n\nWe mention a lemma for later use. ", "Recall the scalars $\\{k_i\\}_{i=0}^d$ from .", "\n\n\\[lem:piW\\] . ", "We have $$\\gamma = \\nu^{-1} \\sum_{i=0}^d k_i \\tau_i. ", " \\label{eq:gamma}$$\n\nIn the equation on the right in , apply $\\pi$ to each side, and use , .", "\n\nIn [@C:spinLP Theorem 1.13], the spin Leonard pairs are classified. ", "By that classification, there are five families of spin Leonard pairs, called type I–V; see [@C:spinLP Lemmas 1.7–1.11]. ", "For each family, the eigenvalue sequence and the intersection numbers are explicitly given. ", "In terms of [@T:survey Section 35], type I is of $q$-Racah type, type II is of Racah type, type III is of Krawtchouk type, type IV is of Bannai-Ito type with odd diameter, and type V is of Bannai-Ito type with even diameter. ", "In [@C:spinLP Theorem 1.18], for each spin Leonard pair $A,A^*$ the corresponding Boltzmann pairs are given. ", "We say that two Boltzmann pairs for $A,A^*$ are [*equivalent*]{} whenever one is obtained from the other by the adjustments in Lemma \\[lem:WinvWsinv\\]. ", "The Leonard pair $A, A^*$ has precisely one equivalence class of Boltzmann pairs, unless $A, A^*$ has type V and the intersection number $a_i$ is independent of $i$ for $0 \\leq i \\leq d$. In this case $A, A^*$ has precisely two equivalence classes of Boltzmann pairs. ", "For one of the equivalence classes we have $\\tau_i = (-1)^{\\lceil i/2 \\rceil}$ for $0 \\leq i \\leq d$, and for the other equivalence class, we have $\\tau_i = (-1)^{\\lfloor i/2 \\rfloor}$ for $0 \\leq i \\leq d$.\n\nLeonard pairs of $q$-Racah type {#sec:qRacah}\n===============================\n\nIn this section we consider a special case of Leonard pair, said to have $q$-Racah type [@Huang]. ", "This is the “most general” type of Leonard pair. ", "Throughout this section the following notation is in effect. ", "Fix a nonzero $q \\in {\\mathbb{F}}$ such that $q^4 \\neq 1$. Let $\\Phi = (A; \\{E_i\\}_{i=0}^d; A^*; \\{E^*_i\\}_{i=0}^d)$ denote a Leonard system on $V$ with parameter array $(\\{{\\theta}_i\\}_{i=0}^d; \\{{\\theta}^*_i\\}_{i=0}^d; \\{{\\varphi}_i\\}_{i=1}^d; \\{\\phi_i\\}_{i=1}^d)$. To avoid trivialities we assume $d \\geq 1$.\n\n[[@Huang Definition 5.1] ]{} \\[def:qRacah\\] . ", "We say that $\\Phi$ has [*$q$-Racah type*]{} whenever there exist nonzero $a$, $b \\in {\\mathbb{F}}$ such that $$\\begin{aligned}\n {\\theta}_i &= a q^{2i-d} + a^{-1} q^{d-2i} && (0 \\leq i \\leq d), \\label{eq:qRacahthi}\n\\\\\n {\\theta}^*_i &= b q^{2i-d} + b^{-1}q^{d-2i} && (0 \\leq i \\leq d). ", " \\label{eq:qRacahthsi}\\end{aligned}$$ In this case the scalars $a$, $b$ are unique.", "\n\n[[@Huang Corollary 6.4] ]{} \\[lem:c\\] . ", "Assume that $\\Phi$ has $q$-Racah type. ", "Let $a$, $b \\in {\\mathbb{F}}$ denote nonzero scalars that satisfy , . ", "Then there exists a nonzero $c \\in {\\mathbb{F}}$ such that for $1 \\leq i \\leq d$, $$\\begin{aligned}\n {\\varphi}_i &= \n a^{-1}b^{-1} q^{d+1}(q^i - q^{-i})(q^{i-d-1} - q^{d-i+1})(q^{-i}-a b c q^{i-d-1})(q^{-i}-a b c^{-1}q^{i-d-1}), \\label{eq:vphii}\n\\\\\n \\phi_i &=\n a b^{-1} q^{d+1}(q^i - q^{-i})(q^{i-d-1} - q^{d-i+1})(q^{-i}-a^{-1} b c q^{i-d-1})(q^{-i}-a^{-1} b c^{-1}q^{i-d-1}). ", "\\label{eq:phii}\\end{aligned}$$ Moreover, $c$ is unique up to inverse.", "\n\n\\[def:Huangdata\\] . ", "Assume that $\\Phi$ has $q$-Racah type. ", "Let $a$, $b \\in {\\mathbb{F}}$ denote nonzero scalars that satisfy , , and let $c \\in {\\mathbb{F}}$ denote a nonzero scalar that satisfies , . ", "We call the sequence $(a,b,c,d)$ a [*Huang data*]{} of $\\Phi$.\n\n\\[note:Huang\\] . ", "Assume that $\\Phi$ has $q$-Racah type with Huang data $(a,b,c,d)$. Then $(a,b,c^{-1},d)$ is a Huang data for $\\Phi$, and $\\Phi$ has no further Huang data.", "\n\nFor the rest of this section, assume that $\\Phi$ has $q$-Racah type with Huang data $(a,b,c,d)$.\n\n[[@Huang Definition 7.1] ]{} \\[lem:condabc\\] . ", "The following [(i)–(iii)]{} hold:\n\n- $q^{2i} \\neq 1$ for $1 \\leq i \\leq d$;\n\n- Neither of $a^2$, $b^2$ is among $q^{2d-2}, q^{2d-4}, \\ldots, q^{2-2d}$;\n\n- None of $a b c$, $a^{-1} b c$, $a b^{-1} c$, $a b c^{-1}$ is among $q^{d-1}, q^{d-3}, \\ldots, q^{1-d}$.\n\n\\[lem:Huang2\\] . ", "The Leonard system $$(-A; \\{E_i\\}_{i=0}^d; - A^*; \\{E^*_i\\}_{i=0}^d) \\label{eq:LS-A}$$ has $q$-Racah type with Huang data $(-a, -b, c, d)$.\n\nUse Definitions \\[def:qRacah\\], \\[def:Huangdata\\].", "\n\nRecall the intersection numbers $\\{b_i\\}_{i=0}^{d-1}$, $\\{c_i\\}_{i=1}^d$ of $\\Phi$ from .", "\n\n\\[lem:bici\\] . ", "We have $$\\begin{aligned}\nb_i &=\n \\frac{ (q^{i-d}-q^{d-i}) (b q^{i-d} - b^{-1} q^{d-i}) ( a b q^i - c q^{d-i-1})(a b q^i - c^{-1} q^{d-i-1}) }\n {a b q^{d-1} (b q^{2i-d} - b^{-1} q^{d-2i}) (b q^{2i-d+1} - b^{-1} q^{d-2i-1} ) }, \\\\\nc_i &= \n \\frac{ (q^i-q^{-i}) (b q^i - b^{-1} q^{-i}) (b q^i - a c q^{d-i+1}) (b q^i - a c^{-1} q^{d-i+1}) }\n {a b q^{d+1} (b q^{2i-d} - b^{-1} q^{d-2i}) (b q^{2i-d-1} - b^{-1} q^{d-2i+1}) } $$ for $1 \\leq i \\leq d-1$, and $$\\begin{aligned}\n b_0 &= \n \\frac{(q^{-d} - q^d) (a b - c q^{d-1}) (a b - c^{-1} q^{d-1} ) }\n {a b q^{d-1} (b q^{1-d} - b^{-1} q^{d-1}) }, \\\\\n c_d &= \n \\frac{(q^d - q^{-d}) (a c - b q^{d-1}) (a c^{-1} - b q^{d-1}) }\n {a b q^{d-1} (b q^{d-1} - b^{-1} q^{1-d}) }. ", " $$\n\nEvaluate , using –.", "\n\nWe recall some notation. ", "For $\\alpha \\in {\\mathbb{F}}$, $$\\begin{aligned}\n (\\alpha; q)_n &= (1-\\alpha) (1-\\alpha q) \\cdots (1- \\alpha q^{n-1}) & n &= 0, 1, 2, \\ldots\\end{aligned}$$ We interpret $(\\alpha;q)_0 = 1$. Recall the scalar $\\nu$ be from .", "\n\n\\[lem:qRacahnu1\\] . ", "We have $$\\nu = \\frac{a^d b^d c^d q^{d(1-d)} (a^{-2};q^2)_d (b^{-2}; q^2)_d }\n { (a b^{-1} c q^{1-d}; q^2)_d (a^{-1} b c q^{1-d}; q^2)_d}.$$\n\nEvaluate using –.", "\n\nRecall the scalars $\\{k_i\\}_{i=0}^d$ from .", "\n\n\\[lem:kiqRacah\\] . ", "We have $k_0 = 1$, and $$k_i =\n \\frac{q^{2 i d} (1-b^2 q^{4i-2d}) \\, (b^2 q^{2-2d};q^2)_i \\, (q^{-2d}; q^2)_i \\, (a b c q^{1-d};q^2)_i \\, (a b c^{-1} q^{1-d}; q^2)_i }\n {a^{2i} (1-b^2 q^{2i-2d}) \\, (b^2 q^2; q^2)_i \\, (q^2; q^2)_i \\, (a^{-1} b c q^{1-d}; q^2)_i \\, (a^{-1} b c^{-1} q^{1-d}; q^2)_i}$$ for $1 \\leq i \\leq d-1$, and $$k_d = \n \\frac{q^{2 d^2} (b^2 q^{2-2d};q^2)_d \\, (q^{-2d}; q^2)_d \\, (a b c q^{1-d};q^2)_d \\, (a b c^{-1} q^{1-d}; q^2)_d }\n {a^{2d} (b^2; q^2)_d \\, (q^2; q^2)_d \\, (a^{-1} b c q^{1-d}; q^2)_d \\, (a^{-1} b c^{-1} q^{1-d}; q^2)_d}.$$\n\nEvaluate using –.", "\n\nWe now turn our attention to the self-dual case.", "\n\n\\[lem:selfdualab\\] . ", "The Leonard system $\\Phi$ is self-dual if and only if $a=b$.\n\nBy Lemma \\[lem:selfdualparam\\] and Definition \\[def:qRacah\\].", "\n\nWe now turn our attention to the spin case.", "\n\n[[@C:spinLP Theorem 1.13] ]{} \\[lem:spinLP0\\] . ", "The following hold.", "\n\n- Assume $d \\geq 3$, and $A,A^*$ is a spin Leonard pair. ", "Then $b=a$ and $c \\in \\{a, a^{-1}, -a, -a^{-1} \\}$.\n\n- Assume that $b=a$ and $c \\in \\{a, a^{-1}, -a, -a^{-1} \\}$. Then $A,A^*$ is a spin Leonard pair.", "\n\n\\[note:Huang2\\] . ", "We have a comment about Lemma \\[lem:spinLP0\\]. ", "Assume that $b=a$ and $c \\in \\{-a, -a^{-1} \\}$. By Note \\[note:Huang\\] we may assume that $c=-a$. Replacing $\\Phi$ by we may assume that $c=a$.\n\nIn view of Note \\[note:Huang2\\] we focus on the case $a=b=c$.\n\n\\[lem:qRacahbi\\] . ", "Assume that $a=b=c$. Then $$\\begin{aligned}\nb_0 &= \\frac{(q^{-d}-q^d)(a^3 - q^{d-1}) } { a (a+ q^{d-1}) }, \\\\\nb_i &= \n \\frac{(q^{i-d} - q^{d-i} ) (a q^{i-d} - a^{-1} q^{d-i} ) (a^3 - q^{d-2i-1} ) }\n {a (a q^{2i-d} - a^{-1} q^{d-2i}) (a + q^{d-2i-1}) }\n && (1 \\leq i \\leq d-1), \\\\\nc_i &=\n \\frac{a (q^i - q^{-i})(a q^i - a^{-1}q^{-i})(a^{-1} - q^{d-2i+1} ) }\n {(a q^{2i-d} - a^{-1} q^{d-2i} ) (a + q^{d-2i+1} ) }\n && (1 \\leq i \\leq d-1), \\\\\nc_d &= \\frac{(q^{-d}-q^d)(a-q^{d-1}) }{ q^{d-1} (a + q^{1-d}) }. ", " $$\n\nSet $a=b=c$ in Lemma \\[lem:bici\\].", "\n\n\\[lem:qRacahnu\\] . ", "Assume that $a=b=c$. Then $$\\nu = \\frac{a^{3d} (a^{-2};q^2)_d^2 } {q^{d(d-1)} (a q^{1-d};q^2)_d^2}. ", " \\label{eq:nu3}$$\n\nSet $a=b=c$ in Lemma \\[lem:qRacahnu1\\].", "\n\n\\[lem:ki3\\] . ", "Assume that $a=b=c$. Then $k_0 = 1$, and $$k_i =\n \\frac{q^{2 i d} (1-a^2 q^{4i-2d}) \\, (a^2 q^{2-2d};q^2)_i \\, (q^{-2d}; q^2)_i \\, (a^3 q^{1-d};q^2)_i }\n {a^{2i} (1-a^2 q^{2i-2d}) \\, (a^2 q^2; q^2)_i \\, (q^2; q^2)_i \\, (a^{-1} q^{1-d}; q^2)_i}$$ for $1 \\leq i \\leq d-1$, and $$k_d = \n \\frac{q^{2 d^2} (a^2 q^{2-2d};q^2)_d \\, (q^{-2d}; q^2)_d \\, (a^3 q^{1-d};q^2)_d }\n {a^{2d} (a^2; q^2)_d \\, (q^2; q^2)_d \\, (a^{-1} q^{1-d}; q^2)_d}.$$\n\nSet $a=b=c$ in Lemma \\[lem:kiqRacah\\].", "\n\n[[@C:spinLP Theorem 1.18] ]{} \\[lem:W\\] . ", "Assume that $a=b=c$. Let $f$, $\\{\\tau_i\\}_{i=0}^d$ denote nonzero scalars in ${\\mathbb{F}}$ such that $\\tau_0 = 1$. Define $$\\begin{aligned}\n W &= f \\sum_{i=0}^d \\tau_i E_i, &\n W^* &= f \\sum_{i=0}^d \\tau_i E^*_i. ", " \\label{eq:defWpre}\\end{aligned}$$\n\n- Assume that $W, W^*$ is a Boltzmann pair for $A,A^*$. Then one of the following holds provided that $d \\geq 3$: $$\\begin{aligned}\n \\tau_i &= (-1)^i a^{-i} q^{i(d-i)} && (0 \\leq i \\leq d), \\label{eq:defti}\n \\\\\n \\tau_i ^{-1} &= (-1)^i a^{-i} q^{i(d-i)} && (0 \\leq i \\leq d). ", " \\label{eq:deftiinv}\\end{aligned}$$\n\n- Assume that one of , holds. ", "Then $W, W^*$ is a balanced Boltzmann pair for $A,A^*$.\n\n\\[note:ti\\] . ", "Referring to Lemma \\[lem:W\\], if holds then holds for the Boltzmann pair $W^{-1}, (W^*)^{-1}$. For this reason we will focus on .", "\n\n\\[lem:new\\] . ", "Assume that $b=a$ and define $\\{\\tau_i\\}_{i=0}^d$ by . ", "Let $0 \\neq f \\in {\\mathbb{F}}$ and define $W$, $W^*$ as in . ", "Assume that $W,W^*$ is a Boltzmann pair for $A,A^*$. Then $c \\in \\{a, a^{-1} \\}$.\n\nFirst assume that $d \\geq 3$. By way of contradiction assume that $c \\not\\in \\{a, a^{-1} \\}$. By Lemma \\[lem:spinLP0\\](i) we have $c \\in \\{-a, - a^{-1} \\}$ and $\\text{\\rm Char}({\\mathbb{F}}) \\neq 2$. By Note \\[note:Huang\\] we may assume that $c = -a$. Thus $\\Phi$ has Huang data $(a,a,-a,d)$. By Lemma \\[lem:Huang2\\] the Leonard system has Huang data $(-a,-a,-a,d)$. By Definition \\[def:balanced\\] and Lemma \\[lem:affine\\] the pair $W, W^*$ is a Boltzmann pair for $-A, -A^*$. Applying Lemma \\[lem:W\\](i) to the Leonard system , one of the following holds: $$\\begin{aligned}\n \\tau_i &= (-1)^i (-a)^{-i} q^{i (d-i)} && (0 \\leq i \\leq d), \n\\\\\n \\tau_i ^{-1} &= (-1)^i (-a)^{-i} q^{i (d-i)} && (0 \\leq i \\leq d). ", " \\end{aligned}$$ In either case, comparing the values of $\\tau_1$, $\\tau_3$ with we get a contradiction by $\\text{\\rm Char}({\\mathbb{F}}) \\neq 2$ and Lemma \\[lem:condabc\\]. ", "We have shown the assertion for the case $d \\geq 3$. Next assume that $d \\leq 2$. Consider the matrices that represent the elements $A$, $A^*$, $\\{E_i\\}_{i=0}^d$, $\\{E^*_i\\}_{i=0}^d$, $W$, $W^*$ with respect to the $\\Phi$-split basis for $V$. We represent these matrices in terms of $a$, $c$, $q$ using –. ", "The matrices representing $A,A^*$ are as in Lemma \\[lem:split\\]. ", "The matrices representing $\\{E_i\\}_{i=0}^d$, $\\{E^*_i\\}_{i=0}^d$ can be obtained using . ", "The matrices representing $W, W^*$ are obtained by . ", "Now compute each side of in matrix form, and compare the $(d,0)$-entries to get $(a-c) (a c -1)=0$. Thus $c \\in \\{a, a^{-1} \\}$.\n\nThe following lemma is a reformulation of a special case of [@GR 2.22].", "\n\n\\[lem:GR\\] . ", "Let $\\alpha$, $\\beta$ denote commuting indeterminates. ", "Then $$\\begin{aligned}\n\\sum_{i=0}^{d}\n \\frac{(1-\\alpha q^{-4i}) \\, (\\alpha^{-1} q^2; q^2)_i \\, (\\beta^{-1}; q^2)_i \\, (q^{-2d}; q^2)_i \\, q^{i(2d-i+3)} (-\\beta)^i }\n {(1-\\alpha q^{-2i})\\, (q^2,q^2)_i \\, (\\beta q^2/\\alpha; q^2)_i \\, (q^{2d+2}/\\alpha; q^2)_i }\n = \\frac{(\\alpha q^{-2d}, q^2)_d }\n {(\\alpha q^{-2d}/\\beta, q^2)_d }. ", " \\label{eq:GR}\\end{aligned}$$\n\nUsing $$(x; q^2)_i = (x^{-1};q^{-2})_i (- x)^i q^{i(i-1)}.$$ one routinely checks that the left-hand side of is equal to $$\\sum_{i=0}^d\n \\frac{ (\\alpha q^{-2}; q^{-2})_i \\, (1- \\alpha q^{-4i}) \\, (\\beta; q^{-2})_i \\, (q^{2d}; q^{-2})_i }\n {(q^{-2}; q^{-2})_i \\, (1-\\alpha q^{-2i}) \\, (\\alpha q^{-2}/\\beta; q^{-2})_i \\, (\\alpha q^{-2d-2}; q^{-2})_i }\n \\left( - \\frac{ \\alpha q^{-2d-2} } { \\beta } \\right)^i q^{i(1-i)}.$$ By this and [@GR 2.22], the left-hand side of is equal to $$\\frac{ (\\alpha q^{-2}; q^{-2} )_d }\n { (\\alpha q^{-2}/\\beta; q^{-2})_d}.$$ One checks that $$(\\alpha q^{-2}; q^{-2})_d = (\\alpha q^{-2d}; q^2)_d, \\qquad\\qquad\n (\\alpha q^{-2}/\\beta; q^{-2})_d = (\\alpha q^{-2d}/\\beta; q^2)_d.$$ The result follows.", "\n\n\\[lem:sumkiti\\] . ", "Referring to Lemma \\[lem:W\\], assume that the $\\{\\tau_i\\}_{i=0}^d$ satisfy . ", "Then $$\\begin{aligned}\n \\sum_{i=0}^d k_i \\tau_i &= \n \\frac{ (a^{-2}; q^2)_d } { (a q^{1-d}; q^2)_d }. ", " \\label{eq:sumkiti3}\\end{aligned}$$ Moreover the scalar $\\gamma$ from Lemma \\[lem:defgamma\\] satisfies $$\\begin{aligned}\n\\gamma &= \\frac{q^{d(d-1)} (a q^{1-d};q^2)_d} {a^{3d} (a^{-2};q^2)_d }. ", " \\label{eq:gamma3}\\end{aligned}$$\n\nWe first show . ", "Using the data in Lemma \\[lem:ki3\\] we find that the left-hand side of is equal to the sum $$\\begin{array}{l}\n\\displaystyle\n1 +\n \\sum_{i=1}^{d-1}\n \\frac{(1-\\alpha^{-1} q^{4i}) \\, (\\alpha^{-1} q^2; q^2)_i \\, (\\beta^{-1}; q^2)_i \\, (q^{-2d}; q^2)_i \\, (-\\beta)^i \\, q^{i(2d-i+1)}}\n {(1-\\alpha^{-1} q^{2i})\\, (q^2,q^2)_i \\, (\\beta q^2/\\alpha; q^2)_i \\, (q^{2d+2}/\\alpha; q^2)_i }\n\\\\\n\\displaystyle\n\\quad +\n \\frac{(\\alpha^{-1} q^2; q^2)_d \\, (\\beta^{-1}; q^2)_d \\, (q^{-2d}; q^2)_d \\, (- \\beta)^d \\, q^{d(d+1)} }\n {(q^2; q^2)_d \\, (\\beta q^2/\\alpha; q^2)_d \\, (q^{2d}/\\alpha; q^2)_d }, \n\\end{array} \n \\label{eq:sum}$$ where $\\alpha = a^{-2} q^{2d}$, $\\beta = a^{-3} q^{d-1}$. One routinely checks that the sum is equal to the the left-hand side of . ", "Thus holds by Lemma \\[lem:GR\\]. ", "To get , evaluate using , .", "\n\nType II matrices and spin models {#sec:spin}\n================================\n\nWe now turn our attention to type II matrices and spin models. ", "For the rest of this paper, fix a finite nonempty set $X$. Let ${\\text{\\rm Mat}_X({\\mathbb{C}})}$ denote the ${\\mathbb{C}}$-algebra consisting of the matrices that have all entries in ${\\mathbb{C}}$ and whose rows and columns are indexed by $X$. For ${{\\sf R}}\\in {\\text{\\rm Mat}_X({\\mathbb{C}})}$ and $x$, $y \\in X$ the $(x,y)$-entry of ${{\\sf R}}$ is denoted by ${{\\sf R}}(x,y)$. Let ${{\\sf I}}$ (resp.", " ${{\\sf J}}$) denote the identity matrix (resp.", " all $1$’s matrix) in ${\\text{\\rm Mat}_X({\\mathbb{C}})}$. For ${{\\sf R}}, {{\\sf S}}\\in {\\text{\\rm Mat}_X({\\mathbb{C}})}$ let ${{\\sf R}}\\circ {{\\sf S}}$ denote their Hadamard (entry-wise) product. ", "Let ${{\\sf V}}$ denote the vector space over ${\\mathbb{C}}$ consisting of the column vectors whose entries are indexed by $X$. Note that $\\dim {{\\sf V}}= |X|$. The algebra ${\\text{\\rm Mat}_X({\\mathbb{C}})}$ acts on ${{\\sf V}}$ by left multiplication. ", "For $y \\in X$ define $\\widehat{y} \\in {{\\sf V}}$ that has $y$-entry $1$ and all other entries $0$. Note that $\\{\\widehat{y}\\}_{y \\in X}$ form a basis for ${{\\sf V}}$. For a real number $\\alpha > 0$ let $\\alpha^{1/2}$ denote the positive square root of $\\alpha$.\n\n[[@Jones Definition 2.1] ]{} \\[def:type2\\] . ", "A matrix ${{\\sf W}}\\in {\\text{\\rm Mat}_X({\\mathbb{C}})}$ is said to be [*type II*]{} whenever ${{\\sf W}}$ is symmetric with all entries nonzero and $$\\begin{aligned}\n \\sum_{y \\in X} \\frac{{{\\sf W}}(a,y)} {{{\\sf W}}(b,y)}\n &= |X| \\delta_{a,b} && (a,b \\in X). ", " \\label{eq:type2}\\end{aligned}$$\n\nFor a symmetric ${{\\sf W}}\\in {\\text{\\rm Mat}_X({\\mathbb{C}})}$ with all entries nonzero, define ${{\\sf W}}^- \\in {\\text{\\rm Mat}_X({\\mathbb{C}})}$ by $$\\begin{aligned}\n {{\\sf W}}^- (y,z) &= ({{\\sf W}}(y,z) )^{-1} && (y,z \\in X). ", " \\label{eq:defW-}\\end{aligned}$$ Referring to the equation , for $a,b \\in X$ the left-hand side is equal to the $(a,b)$-entry of ${{\\sf W}}{{\\sf W}}^-$.\n\n\\[lem:type2W-\\] . ", "Assume ${{\\sf W}}\\in {\\text{\\rm Mat}_X({\\mathbb{C}})}$ is symmetric with all entries nonzero. ", "Then the following [(i)–(iii)]{} are equivalent:\n\n- ${{\\sf W}}$ is type II;\n\n- ${{\\sf W}}{{\\sf W}}^- = |X| \\,{{\\sf I}}$;\n\n- ${{\\sf W}}{{\\sf W}}^- = \\alpha {{\\sf I}}$ for some $\\alpha \\in {\\mathbb{C}}$.\n\n\\(i) $\\Rightarrow$ (ii) By and .", "\n\n\\(ii) $\\Rightarrow$ (iii) Clear.", "\n\n\\(iii) $\\Rightarrow$ (i) By the comment below .", "\n\n\\[note:type2\\] . ", "Assume ${{\\sf W}}\\in {\\text{\\rm Mat}_X({\\mathbb{C}})}$ is type II. ", "Then $\\alpha {{\\sf W}}$ is type II for $0 \\neq \\alpha \\in {\\mathbb{C}}$. Moreover, ${{\\sf W}}^{-1}$ and ${{\\sf W}}^-$ are type II.", "\n\n[[@N:analgebra Section 1] ]{} \\[def:NW\\] . ", "Assume ${{\\sf W}}\\in {\\text{\\rm Mat}_X({\\mathbb{C}})}$ is type II. ", "For $b,c \\in X$ define $\\text{\\bf u}_{b,c} \\in {{\\sf V}}$ by $$\\begin{aligned}\n \\text{\\bf u}_{b,c} = \\sum_{y \\in X} \\frac{{{\\sf W}}(b,y)}{{{\\sf W}}(c,y)} \\, \\widehat{y}. ", " \\label{eq:defubc}\\end{aligned}$$ Define $$N({{\\sf W}}) = \\{ B \\in {\\text{\\rm Mat}_X({\\mathbb{C}})}\\,|\\, \n \\text{$B$ is symmetric}, \\; B \\mathbf{u}_{b,c} \\in {\\mathbb{C}}\\mathbf{u}_{b,c} \\text{ for all $b,c \\in X$} \\}.$$\n\n[[@N:analgebra Theorem 6] ]{} \\[lem:Nomuraalg\\] . ", "Assume ${{\\sf W}}\\in {\\text{\\rm Mat}_X({\\mathbb{C}})}$ is type II. ", "Then $N({{\\sf W}})$ is a commutative subalgebra of ${\\text{\\rm Mat}_X({\\mathbb{C}})}$ that contains ${{\\sf J}}$ and is closed under the Hadamard product.", "\n\nWe have a comment.", "\n\n\\[lem:NW-\\] . ", "Assume ${{\\sf W}}\\in {\\text{\\rm Mat}_X({\\mathbb{C}})}$ is type II. ", "Then $N(\\alpha {{\\sf W}})= N({{\\sf W}})$ for $0 \\neq \\alpha \\in {\\mathbb{C}}$. Moreover each of $N({{\\sf W}}^-)$, $N({{\\sf W}}^{-1})$ is equal to $N({{\\sf W}})$.\n\nClearly $N(\\alpha {{\\sf W}})=N({{\\sf W}})$. For $b,c \\in X$ define $\\text{\\bf u}^-_{b,c} \\in {{\\sf V}}$ by $$\\begin{aligned}\n \\text{\\bf u}^-_{b,c} = \\sum_{y \\in X} \\frac{{{\\sf W}}^-(b,y)}{{{\\sf W}}^-(c,y)} \\, \\widehat{y}. ", "\\end{aligned}$$ Using , we obtain $$\\text{\\bf u}^-_{b,c} = \\sum_{y \\in X} \\frac{{{\\sf W}}(c,y)} {{{\\sf W}}(b,y)} \\widehat{y} = \\text{\\bf u}_{c,b}.$$ By this and Definition \\[def:NW\\] we find $N({{\\sf W}}^-) = N({{\\sf W}})$. We have ${{\\sf W}}^- = |X| {{\\sf W}}^{-1}$ by Lemma \\[lem:type2W-\\], so $N({{\\sf W}}^{-1}) = N({{\\sf W}}^-)$. The result follows.", "\n\n[[@Jones Definition 2.1] ]{} \\[def:spin\\] . ", "A matrix ${{\\sf W}}\\in {\\text{\\rm Mat}_X({\\mathbb{C}})}$ is called a [*spin model*]{} whenever ${{\\sf W}}$ is type II and $$\\begin{aligned}\n \\sum_{y \\in X} \\frac{{{\\sf W}}(a,y) {{\\sf W}}(b,y)} {{{\\sf W}}(c,y)}\n &= |X|^{1/2} \\; \\frac{{{\\sf W}}(a,b)} {{{\\sf W}}(a,c) {{\\sf W}}(b,c)} && (a,b,c \\in X). ", " \\label{eq:type3}\\end{aligned}$$\n\nThe equation is often called the type III condition.", "\n\n[[@Jones Section 2] (see also [@KMW Proposition 2.1]). ]{} ", "\\[note:spin\\] . ", "Assume ${{\\sf W}}\\in {\\text{\\rm Mat}_X({\\mathbb{C}})}$ is a spin model. ", "Then $-{{\\sf W}}$ is a spin model. ", "Moreover ${{\\sf W}}^-$ is a spin model.", "\n\n[[@N:analgebra Lemma 8] ]{} \\[lem:Nomuraalg2\\] . ", "Assume ${{\\sf W}}\\in {\\text{\\rm Mat}_X({\\mathbb{C}})}$ is a spin model. ", "Then ${{\\sf W}}\\in N({{\\sf W}})$.\n\nHadamard matrices and spin models\n=================================\n\nIn this section we consider a certain class of type II matrices and spin models.", "\n\n\\[def:Hmatrix\\] . ", "A matrix ${{\\sf H}}\\in {\\text{\\rm Mat}_X({\\mathbb{C}})}$ is called [*Hadamard*]{} whenever every entry is $\\pm 1$ and ${{\\sf H}}{{\\sf H}}^{\\sf t} = |X| \\,{{\\sf I}}$.\n\n\\[exam1\\] . ", "The matrix $${{\\sf H}}= \n \\begin{pmatrix}\n 1 & -1 & -1 & -1 \\\\\n -1 & 1 & -1 & -1 \\\\\n -1 & -1 & 1 & -1 \\\\\n -1 & -1 & -1 & 1\n \\end{pmatrix}$$ is Hadamard.", "\n\n\\[lem:Htype2\\] . ", "A symmetric Hadamard matrix is type II.", "\n\nBy Definitions \\[def:type2\\] and \\[def:Hmatrix\\].", "\n\n\\[lem:Htype\\] . ", "For ${{\\sf W}}\\in {\\text{\\rm Mat}_X({\\mathbb{C}})}$ and $0 \\neq \\alpha \\in {\\mathbb{C}}$ the following are equivalent:\n\n- ${{\\sf W}}$ is type II with all entries $\\pm \\alpha$;\n\n- there exists a symmetric Hadamard matrix ${{\\sf H}}$ such that ${{\\sf W}}= \\alpha {{\\sf H}}$.\n\n\\(i) $\\Rightarrow$ (ii) Assume that ${{\\sf W}}$ is type II with all entries $\\pm \\alpha$. Define ${{\\sf H}}= \\alpha^{-1} {{\\sf W}}$. Then the entries of ${{\\sf H}}$ are $\\pm 1$. Moreover, by Note \\[note:type2\\], ${{\\sf H}}$ is type II. ", "Applying Lemma \\[lem:type2W-\\] to ${{\\sf H}}$ and using ${{\\sf H}}^- ={{\\sf H}}$, we obtain ${{\\sf H}}^2 = |X| {{\\sf I}}$. The matrix ${{\\sf H}}$ is symmetric since it is type II. ", "By these comments ${{\\sf H}}$ is a symmetric Hadamard matrix.", "\n\n\\(ii) $\\Rightarrow$ (i) Assume that there exists a symmetric Hadamard matrix ${{\\sf H}}$ such that ${{\\sf W}}= \\alpha {{\\sf H}}$. Then ${{\\sf W}}$ is symmetric and satisfies . ", "So ${{\\sf W}}$ is type II. ", "Clearly the entries of ${{\\sf W}}$ are $\\pm \\alpha$.\n\n\\[def:Htype\\] . ", "A type II matrix ${{\\sf W}}\\in {\\text{\\rm Mat}_X({\\mathbb{C}})}$ is said to have [*Hadamard type*]{} whenever there exists a symmetric Hadamard matrix ${{\\sf H}}$ and $0 \\neq \\alpha \\in {\\mathbb{C}}$ such that ${{\\sf W}}= \\alpha {{\\sf H}}$.\n\nWe have an example of a spin model having Hadamard type.", "\n\n\\[example2\\] . ", "Let the matrix ${{\\sf H}}$ be from Example \\[exam1\\]. ", "Then the matrix ${{\\sf W}}= \\sqrt{-1} \\, {{\\sf H}}$ is a spin model of Hadamard type.", "\n\n\\[noteH\\] . ", "Spin models of Hadamard type sometimes cause technical problems, so occasionally we will assume that a spin model under discussion does not have Hadamard type.", "\n\nDistance-regular graphs {#sec:DRG}\n=======================\n\nWe now turn our attention to distance-regular graphs [@BI; @BCN; @DKT]. ", "Let $\\Gamma$ denote an undirected, connected graph, without loops or multiple edges, with vertex set $X$. For $x,y \\in X$ let $\\partial(x,y)$ denote the path-length distance between $x$ and $y$. By the [*diameter*]{} of $\\Gamma$ we mean $D = \\max \\{\\partial(x,y) \\,|\\, x,y \\in X\\}$. To avoid trivialities, we always assume $D \\geq 1$. For $x \\in X$ define $$\\begin{aligned}\n \\Gamma_i (x) &= \\{y \\in X \\,|\\, \\partial (x,y) = i\\} && (0 \\leq i \\leq D).\\end{aligned}$$ The graph $\\Gamma$ is said to be [*regular*]{} whenever ${{\\sf k}}= |\\Gamma_1 (x)|$ is independent of $x \\in X$. In this case, ${{\\sf k}}$ is called the [*valency*]{} of $\\Gamma$. The graph $\\Gamma$ is said to be [*distance-regular*]{} whenever for $0 \\leq h, i, j \\leq D$ and vertices $x,y \\in X$ at distance $\\partial(x,y)=h$, the number $$\\begin{aligned}\n {{\\sf p}}^h_{i j} &= |\\Gamma_i(x) \\cap \\Gamma_j(y)|\\end{aligned}$$ is independent of $x$, $y$. The integers ${{\\sf p}}^h_{i j}$ are called the [*intersection numbers*]{} of $\\Gamma$.\n\nFor the rest of this section, assume that $\\Gamma$ is distance-regular. ", "Define $$\\begin{aligned}\n {{\\sf k}}_i &= {{\\sf p}}^0_{i i} && (0 \\leq i \\leq D). ", " \\label{eq:defki2}\\end{aligned}$$ We have $|\\Gamma_i (x)| = {{\\sf k}}_i$ for $x \\in X$ and $0 \\leq i \\leq D$. Observe that ${{\\sf k}}_0=1$, and that $\\Gamma$ is regular with valency ${{\\sf k}}={{\\sf k}}_1$. Moreover $$\\sum_{i=0}^D {{\\sf k}}_i = |X|. ", " $$ For $0 \\leq h,i,j \\leq D$ the scalar ${{\\sf p}}^h_{i j}$ is zero (resp.", " nonzero) if one of $h,i,j$ is greater than (resp.", " equal to) the sum of the other two. ", "Define $$\\begin{aligned}\n {{\\sf c}}_i &= {{\\sf p}}^i_{1, i-1} && (1 \\leq i \\leq D), \\label{eq:defci}\n\\\\\n {{\\sf a}}_i &= {{\\sf p}}^i_{1 i} && (0 \\leq i \\leq D), \\label{eq:defai}\n\\\\\n {{\\sf b}}_i &= {{\\sf p}}^i_{1, i+1} && (0 \\leq i \\leq D-1). ", " \\label{eq:defbi}\\end{aligned}$$ For notational convenience define ${{\\sf c}}_0 = 0$ and ${{\\sf b}}_D = 0$. We have ${{\\sf c}}_i {{\\sf b}}_{i-1} \\neq 0$ for $1 \\leq i \\leq D$. Moreover $$\\begin{aligned}\n{{\\sf a}}_0 &= 0, &\n{{\\sf b}}_0 &= {{\\sf k}}, &\n{{\\sf c}}_1 &= 1, &\n{{\\sf c}}_i + {{\\sf a}}_i + {{\\sf b}}_i &= {{\\sf k}}\\quad (0 \\leq i \\leq D). ", " \\label{eq:a0b0c1}\\end{aligned}$$ By [@BCN Chapter 4, (1c)], $$\\begin{aligned}\n {{\\sf k}}_i &= \\frac{{{\\sf b}}_0 {{\\sf b}}_1 \\cdots {{\\sf b}}_{i-1} }\n {{{\\sf c}}_1 {{\\sf c}}_2 \\cdots {{\\sf c}}_i } && (0 \\leq i \\leq D). ", " $$\n\nFor $0 \\leq i \\leq D$ define ${{\\sf A}}_i \\in {\\text{\\rm Mat}_X({\\mathbb{C}})}$ that has $(x,y)$-entry $1$ if $\\partial(x,y)=i$ and $0$ if $\\partial(x,y) \\neq i$ $(x,y \\in X)$. Note that ${{\\sf A}}_i$ is symmetric. ", "The matrix ${{\\sf A}}_i$ is called the [*$i^\\text{\\rm th}$ distance-matrix*]{} of $\\Gamma$. Note that ${{\\sf A}}_0 = {{\\sf I}}$, and ${{\\sf A}}_1$ is the adjacency matrix of $\\Gamma$. Observe that $$\\begin{aligned}\n {{\\sf A}}_i \\circ {{\\sf A}}_j &= \\delta_{i,j} {{\\sf A}}_i \\qquad (0 \\leq i,j \\leq D),\n \\qquad\\qquad\n \\sum_{i=0}^D {{\\sf A}}_i = {{\\sf J}}, \\label{eq:Ai2}\n\\\\\n {{\\sf A}}_i {{\\sf A}}_j &= \\sum_{h=0}^D {{\\sf p}}^h_{ij} {{\\sf A}}_h \\qquad\\qquad\n (0 \\leq i,j \\leq D). ", " \\label{eq:AiAj2}\\end{aligned}$$ By the equation on the left in the matrices $\\{{{\\sf A}}_i\\}_{i=0}^D$ are linearly independent. ", "Let ${{\\sf M}}$ denote the subspace of ${\\text{\\rm Mat}_X({\\mathbb{C}})}$ with basis $\\{{{\\sf A}}_i\\}_{i=0}^D$. We have ${{\\sf p}}^h_{i j} = {{\\sf p}}^h_{j i}$ for $0 \\leq h,i,j \\leq D$. By this and , ${{\\sf M}}$ is a commutative subalgebra of ${\\text{\\rm Mat}_X({\\mathbb{C}})}$. By , ${{\\sf M}}$ is closed under $\\circ$ and contains ${{\\sf J}}$. We call ${{\\sf M}}$ the [*Bose-Mesner algebra of $\\Gamma$*]{}.", "\n\nBy [@BCN Theorem 2.6.1(ii)] there exists a basis $\\{{{\\sf E}}_i\\}_{i=0}^D$ for the ${\\mathbb{C}}$-vector space ${{\\sf M}}$ such that $$\\begin{aligned}\n{{\\sf E}}_0 &= |X|^{-1} {{\\sf J}}, &\n{{\\sf E}}_i {{\\sf E}}_j &= \\delta_{i,j} {{\\sf E}}_i \\quad (0 \\leq i, j \\leq D), &\n\\sum_{i=0}^D {{\\sf E}}_i &= {{\\sf I}}. ", " \\label{eq:Ei}\\end{aligned}$$ We have $${{\\sf V}}= \\sum_{i=0}^D {{\\sf E}}_i {{\\sf V}}\\qquad\\qquad \\text{(direct sum)}. ", " \\label{eq:VsumEi}$$ In the above sum, the summands are the common eigenspaces for ${{\\sf M}}$. For $0 \\leq i \\leq D$ the matrix ${{\\sf E}}_i$ is the projection onto the eigenspace ${{\\sf E}}_i {{\\sf V}}$. We call $\\{{{\\sf E}}_i\\}_{i=0}^D$ the [*primitive idempotents*]{} of $\\Gamma$. We call ${{\\sf E}}_0$ the [*trivial primitive idempotent*]{}. ", "The primitive idempotents are unique up to ordering of the nontrivial primitive idempotents.", "\n\nSince ${{\\sf M}}$ is closed under $\\circ$, there exist ${{\\sf q}}^h_{i j} \\in {\\mathbb{C}}$ $(0 \\leq h,i,j \\leq D)$ such that $$\\begin{aligned}\n {{\\sf E}}_i \\circ {{\\sf E}}_j &= |X|^{-1} \\sum_{h=0}^D {{\\sf q}}^h_{i j} {{\\sf E}}_h && (0 \\leq i,j \\leq D). ", " \\label{eq:EicircEj}\\end{aligned}$$ The scalars ${{\\sf q}}^h_{i j}$ are called the [*Krein parameters*]{} of $\\Gamma$ [@BI]. ", "By [@BI Theorem 3.8] each Krein parameter is real and nonnegative. ", "Define $$\\begin{aligned}\n {{\\sf m}}_i &= q^0_{i i} && (0 \\leq i \\leq D). ", " \\label{eq:defmi}\\end{aligned}$$ We have ${{\\sf m}}_0 = 1$. By [@BI Proposition 3.7], ${{\\sf m}}_i = \\text{\\rm rank} ({{\\sf E}}_i)$ $(0 \\leq i \\leq D)$. So by , $$\\sum_{i=0}^D {{\\sf m}}_i = |X|.$$\n\nSince each of $\\{{{\\sf A}}_i\\}_{i=0}^D$ and $\\{{{\\sf E}}_i\\}_{i=0}^D$ is a basis for ${{\\sf M}}$, there exist matrices $P$, $Q \\in \\text{\\rm Mat}_{D+1}({\\mathbb{C}})$ such that $$\\begin{aligned}\n {{\\sf A}}_j &= \\sum_{i=0}^D P_{i j} {{\\sf E}}_i, &\n {{\\sf E}}_j &= |X|^{-1} \\sum_{i=0}^D Q_{i j} {{\\sf A}}_i && (0 \\leq j \\leq D). ", " \\label{eq:defPQ}\\end{aligned}$$ Using we find $P Q = |X| I$. Using ${{\\sf A}}_0 = {{\\sf I}}$ and ${{\\sf E}}_0 =|X|^{-1} {{\\sf J}}$ we obtain $$\\begin{aligned}\n P_{i 0} &= 1, & Q_{i 0} &= 1 && (0 \\leq i \\leq D). ", " $$ By [@BCN Lemma 2.2.1(ii)], $$\\begin{aligned}\n {{\\sf k}}_j &= P_{0j}, & {{\\sf m}}_j &= Q_{0j} && (0 \\leq j \\leq D). ", " \\label{eq:kjP0j}\\end{aligned}$$ Define $$\\begin{aligned}\n {\\theta}_i &= P_{i 1}, & {\\theta}^*_i &= Q_{i 1} && (0 \\leq i \\leq D). ", " \\label{eq:defthithsi}\\end{aligned}$$ By the equation on the left in with $j=1$, $$\\begin{aligned}\n {{\\sf A}}_1 &= \\sum_{i=0}^D {\\theta}_i {{\\sf E}}_i. ", " $$ So ${\\theta}_i$ is the eigenvalue of ${{\\sf A}}_1$ corresponding to ${{\\sf E}}_i$ $(0 \\leq i \\leq D)$. We call $\\{{\\theta}_i\\}_{i=0}^D$ (resp.", " $\\{{\\theta}^*_i\\}_{i=0}^D$) the [*eigenvalue sequence*]{} (resp. [*", "dual eigenvalue sequence*]{}) [*of $\\Gamma$ with respect to the ordering $\\{{{\\sf E}}_i\\}_{i=0}^D$*]{}.", "\n\n\\[def:vi2\\] . ", "Define polynomials $\\{v_i\\}_{i=0}^D$ in ${\\mathbb{C}}[\\lambda]$ such that $v_0=1$ and $$\\begin{aligned}\n \\lambda v_i &= {{\\sf c}}_{i+1} v_{i+1} + {{\\sf a}}_i v_i + {{\\sf b}}_{i-1} v_{i-1} && (1 \\leq i \\leq D-1).\\end{aligned}$$\n\n[[@T:subconst1 Lemma 3.8] ]{} \\[lem:vi\\] . ", "The following [(i)–(iv)]{} hold.", "\n\n- For $0 \\leq i \\leq D$ the polynomial $v_i$ has degree $i$ and leading coefficient $(c_1 c_2 \\cdots c_i)^{-1}$.\n\n- For $0 \\leq i \\leq D$, ${{\\sf A}}_i = v_i ({{\\sf A}}_1)$.\n\n- The algebra ${{\\sf M}}$ is generated by ${{\\sf A}}_1$.\n\n- The scalars $\\{{\\theta}_i\\}_{i=0}^D$ are mutually distinct.", "\n\n\\[lem:Pij\\] . ", "For the polynomials $\\{v_i\\}_{i=0}^D$ from Definition \\[def:vi2\\], $$\\begin{aligned}\n P_{i j} &= v_j ({\\theta}_i) && (0 \\leq i,j \\leq D). ", " $$\n\nIn the equation on the left in , multiply each side on the right ${{\\sf E}}_i$ to get ${{\\sf A}}_j {{\\sf E}}_i = P_{i j} {{\\sf E}}_i$. By Lemma \\[lem:vi\\](ii), ${{\\sf A}}_j {{\\sf E}}_i = v_j ({{\\sf A}}_1) {{\\sf E}}_i$. Using ${{\\sf A}}_1 {{\\sf E}}_i = {\\theta}_i {{\\sf E}}_i$ one finds that $v_j ({{\\sf A}}_1) {{\\sf E}}_i = v_j ({\\theta}_i) {{\\sf E}}_i$. By these comments we obtain $P_{i j} = v_j ({\\theta}_i)$.\n\nWe recall the dual Bose-Mesner algebra. ", "For the rest of this section, fix $x \\in X$. For $0 \\leq i \\leq D$ let ${{\\sf E}}^*_i = {{\\sf E}}^*_i (x)$ denote the diagonal matrix in ${\\text{\\rm Mat}_X({\\mathbb{C}})}$ that has $(y,y)$-entry $1$ if $\\partial(x,y)=i$ and $0$ if $\\partial (x,y) \\neq i$ $(y \\in X)$. By construction, $$\\begin{aligned}\n {{\\sf E}}^*_i {{\\sf E}}^*_j &= \\delta_{i,j} {{\\sf E}}^*_i \\qquad (0 \\leq i,j \\leq D),\n&\n \\sum_{i=0}^D {{\\sf E}}^*_i &= {{\\sf I}}.\\end{aligned}$$ Consequently $\\{{{\\sf E}}^*_i\\}_{i=0}^D$ form a basis for a commutative subalgebra ${{\\sf M}}^* = {{\\sf M}}^*(x)$ of ${\\text{\\rm Mat}_X({\\mathbb{C}})}$. We call ${{\\sf M}}^*$ the [*dual Bose-Mesner algebra of $\\Gamma$ with respect to $x$*]{}. ", "We call $\\{{{\\sf E}}^*_i\\}_{i=0}^D$ the [*dual primitive idempotents of $\\Gamma$ with respect to $x$*]{}. ", "For $0 \\leq i \\leq D$ we have $${{\\sf E}}^*_i {{\\sf V}}= \\text{Span} \\{ \\widehat{y} \\,|\\, y \\in \\Gamma_i (x) \\}$$ and ${{\\sf k}}_i = \\text{rank} ({{\\sf E}}^*_i) $. ", "Moreover $${{\\sf V}}= \\sum_{i=0}^D {{\\sf E}}^*_i {{\\sf V}}\\qquad\\qquad \\text{(direct sum)}. ", " $$ In the above sum, the summands are the common eigenspaces for ${{\\sf M}}^*$. For $0 \\leq i \\leq D$ the matrix ${{\\sf E}}^*_i$ is the projection onto the eigenspace ${{\\sf E}}^*_i {{\\sf V}}$. For $0 \\leq i \\leq D$ let ${{\\sf A}}^*_i = {{\\sf A}}^*_i (x)$ denote the diagonal matrix in ${\\text{\\rm Mat}_X({\\mathbb{C}})}$ whose $(y,y)$-entry is the $(x,y)$-entry of $|X| {{\\sf E}}_i$ $(y \\in X)$. By and , $$\\begin{aligned}\n {{\\sf A}}^*_i {{\\sf A}}^*_j = \\sum_{h=0}^D {{\\sf q}}^h_{i j} {{\\sf A}}^*_h \\qquad\\qquad (0 \\leq i,j \\leq D), \\label{eq:AsiAsj}\n\\\\\n {{\\sf A}}^*_0 = {{\\sf I}}, \\qquad\\qquad\\qquad\n \\sum_{i=0}^D {{\\sf A}}^*_i = |X| {{\\sf E}}^*_0. ", " \\notag $$ By we find that for $0 \\leq j \\leq D$, $$\\begin{aligned}\n {{\\sf E}}^*_j &= |X|^{-1} \\sum_{i=0}^D P_{i j} {{\\sf A}}^*_i,\n&\n {{\\sf A}}^*_j &= \\sum_{i=0}^D Q_{i j} {{\\sf E}}^*_i. ", " \\label{eq:Esi}\\end{aligned}$$ By the matrices $\\{{{\\sf A}}^*_i\\}_{i=0}^D$ form a basis for the ${\\mathbb{C}}$-vector space ${{\\sf M}}^*$. We call $\\{{{\\sf A}}^*_i\\}_{i=0}^D$ the [*dual distance-matrices of $\\Gamma$ with respect to $x$*]{}. ", "We call ${{\\sf A}}^*_1$ the [*dual adjacency matrix*]{} of $\\Gamma$ with respect to $x$. By the equation on the right in with $j=1$, $${{\\sf A}}^*_1 = \\sum_{i=0}^D {\\theta}^*_i {{\\sf E}}^*_i.$$ So ${\\theta}^*_i$ is the eigenvalue of ${{\\sf A}}^*_1$ corresponding to ${{\\sf E}}^*_i$ $(0 \\leq i \\leq D)$.\n\nThe algebras ${{\\sf M}}$ and ${{\\sf M}}^*$ are related as follows. ", "By [@T:subconst1 Lemma 3.2], $$\\begin{aligned}\n {{\\sf E}}^*_i {{\\sf A}}_h {{\\sf E}}^*_j = 0 \\qquad \\text{if and only if} \\qquad {{\\sf p}}^h_{i j} =0 \\qquad (0 \\leq h,i,j \\leq D),\n\\\\\n {{\\sf E}}_i {{\\sf A}}^*_h {{\\sf E}}_j = 0 \\qquad \\text{if and only if} \\qquad {{\\sf q}}^h_{i j} =0 \\qquad (0 \\leq h,i,j \\leq D).\\end{aligned}$$\n\n\\[lem:AiEs0E02\\] . ", "For $0 \\leq i \\leq D$, $$\\begin{aligned}\n {{\\sf A}}_i {{\\sf E}}^*_0 {{\\sf E}}_0 &= {{\\sf E}}^*_i {{\\sf E}}_0,\n&\n {{\\sf E}}_i {{\\sf E}}^*_0 {{\\sf E}}_0 &= |X|^{-1} {{\\sf A}}^*_i {{\\sf E}}_0, \\label{eq:AiEs0E02}\n\\\\\n {{\\sf A}}^*_i {{\\sf E}}_0 {{\\sf E}}^*_0 &= {{\\sf E}}_i {{\\sf E}}^*_0,\n&\n {{\\sf E}}^*_i {{\\sf E}}_0 {{\\sf E}}^*_0 &= |X|^{-1} {{\\sf A}}_i {{\\sf E}}^*_0. ", " \\label{eq:AsiE0Es02}\\end{aligned}$$\n\nFor $y,z \\in X$, compare the $(y,z)$-entry of each side using the definition of ${{\\sf A}}^*_i$ and ${{\\sf E}}^*_i$.\n\n\\[lem:E0Es0E0\\] . ", "We have $$\\begin{aligned}\n |X| \\, {{\\sf E}}_0 {{\\sf E}}^*_0 {{\\sf E}}_0 &= {{\\sf E}}_0, &\n |X| \\, {{\\sf E}}^*_0 {{\\sf E}}_0 {{\\sf E}}^*_0 &= {{\\sf E}}^*_0.\\end{aligned}$$\n\nFor the equation on the right in , set $i=0$ and use ${{\\sf A}}_0 = {{\\sf I}}$, ${{\\sf A}}^*_0 = {{\\sf I}}$.\n\nLet ${{\\sf T}}= {{\\sf T}}(x)$ denote the subalgebra of ${\\text{\\rm Mat}_X({\\mathbb{C}})}$ generated by ${{\\sf M}}$ and ${{\\sf M}}^*$. We call ${{\\sf T}}$ the [*Terwilliger algebra of $\\Gamma$ with respect to $x$*]{} [@T:subconst1].", "\n\nBy a [*${{\\sf T}}$-module*]{} we mean a subspace of ${{\\sf V}}$ that is invariant under the action of ${{\\sf T}}$. The ${{\\sf T}}$-module ${{\\sf V}}$ is said to be [*standard*]{}. ", "A ${{\\sf T}}$-module $U$ is said to be [*irreducible*]{} whenever $U \\neq 0$ and there is no ${{\\sf T}}$-submodule of $U$ other than $0$, $U$.\n\n[[@T:subconst1 Lemma 3.4] ]{} \\[lem:decomp\\] . ", "The following hold.", "\n\n- The standard ${{\\sf T}}$-module ${{\\sf V}}$ is a direct sum of irreducible ${{\\sf T}}$-modules.", "\n\n- Each irreducible ${{\\sf T}}$-module $U$ is a direct sum of the nonzero subspaces among ${{\\sf E}}_0 U, {{\\sf E}}_1 U$, $\\ldots, {{\\sf E}}_D U$, and a direct sum of the nonzero subspaces among ${{\\sf E}}^*_0 U, {{\\sf E}}^*_1 U, \\ldots, {{\\sf E}}^*_D U$.\n\nLet $U$ denote an irreducible ${{\\sf T}}$-module. ", "We say that $U$ is [*thin*]{} (resp.", " [*dual thin*]{}) whenever $\\dim {{\\sf E}}^*_i U \\leq 1$ (resp. ", "$\\dim {{\\sf E}}_i U \\leq 1$) for $0 \\leq i \\leq D$. Define the [*diameter*]{} $d=d(U)$ and [*dual diameter*]{} $d^* = d^* (U)$ by $$\\begin{aligned}\n d &= |\\{ i \\,|\\, 0 \\leq i \\leq D, \\; {{\\sf E}}^*_i U \\neq 0\\}| - 1,\n&\n d^* &= |\\{ i \\,|\\, 0 \\leq i \\leq D, \\; {{\\sf E}}_i U \\neq 0\\}| - 1.\\end{aligned}$$ If $U$ is thin (resp.", " dual thin) then the dimension of $U$ is $d+1$ (resp.", " $d^* + 1$). ", "If $U$ is both thin and dual thin, then $d=d^*$.\n\nWe recall the primary ${{\\sf T}}$-module [@T:subconst1 Lemma 3.6]. ", "Define $$\\text{\\bf 1} = \\sum_{y \\in X} \\widehat{y}.$$ Observe that the entries of $\\text{\\bf 1}$ are all $1$.\n\n[[@T:subconst1 Lemma 3.6] ]{} \\[lem:primary\\] . ", "For $0 \\leq i \\leq D$, $$\\begin{aligned}\n {{\\sf A}}_i \\widehat{x} &= {{\\sf E}}^*_i \\text{\\bf 1}, &\n {{\\sf A}}^*_i \\text{\\bf 1} &= |X| {{\\sf E}}_i \\widehat{x}.\\end{aligned}$$ Moreover, ${{\\sf M}}\\widehat{x} = {{\\sf M}}^* \\text{\\bf 1}$ is a thin, dual-thin, irreducible ${{\\sf T}}$-module of diameter $D$.\n\n\\[def:primary\\] . ", "The ${{\\sf T}}$-module in Lemma \\[lem:primary\\] is called [*primary*]{}. ", "Let ${{\\sf U}}$ denote the primary ${{\\sf T}}$-module.", "\n\n\\[lem:faithful0\\] . ", "The following hold:\n\n- the map ${{\\sf M}}\\to {{\\sf U}}$, ${{\\sf B}}\\mapsto {{\\sf B}}\\widehat{x}$ is a ${\\mathbb{C}}$-linear bijection;\n\n- the map ${{\\sf M}}^* \\to {{\\sf U}}$, ${{\\sf B}}\\mapsto {{\\sf B}}\\text{\\bf 1}$ is a ${\\mathbb{C}}$-linear bijection.", "\n\n\\(i) The map is ${\\mathbb{C}}$-linear by construction, and surjective by Lemma \\[lem:primary\\]. ", "It is a bijection since ${{\\sf M}}$, ${{\\sf U}}$ have the same dimension.", "\n\n\\(ii) The map is ${\\mathbb{C}}$-linear by construction, and surjective by Lemma \\[lem:primary\\]. ", "It is a bijection since ${{\\sf M}}^*$, ${{\\sf U}}$ have the same dimension.", "\n\n\\[cor:faithful\\] . ", "The following hold.", "\n\n- Let ${{\\sf B}}\\in {{\\sf M}}$ such that ${{\\sf B}}{{\\sf U}}= 0$. Then ${{\\sf B}}=0$.\n\n- Let ${{\\sf B}}\\in {{\\sf M}}^*$ such that ${{\\sf B}}{{\\sf U}}=0$. Then ${{\\sf B}}=0$.\n\n\\(i) We have ${{\\sf B}}\\widehat{x}=0$ since $\\widehat{x} \\in {{\\sf U}}$, so ${{\\sf B}}=0$ in view of Lemma \\[lem:faithful0\\](i).", "\n\n\\(ii) We have ${{\\sf B}}\\text{\\bf 1} = 0$ since $\\text{\\bf 1} \\in {{\\sf U}}$, so ${{\\sf B}}=0$ in view of Lemma \\[lem:faithful0\\](ii).", "\n\nNext we discuss general irreducible ${{\\sf T}}$-modules. ", "For an irreducible ${{\\sf T}}$-module $U$, define the [*endpoint*]{} $r=r(U)$ by $$\\begin{aligned}\n r &= \\text{\\rm min} \\{i \\,|\\, 0 \\leq i \\leq D, \\; {{\\sf E}}^*_i U \\neq 0 \\}.\\end{aligned}$$\n\n[[@T:subconst1 Lemma 3.9] ]{} \\[lem:Tmodule1\\] . ", "Let $U$ denote an irreducible ${{\\sf T}}$-module with endpoint $r$ and diameter $d$. Then the following hold.", "\n\n- We have ${{\\sf E}}^*_i U \\neq 0$ if and only if $r \\leq i \\leq r+d$ $(0 \\leq i \\leq D)$.\n\n- If $U$ is thin then $U$ is dual thin.", "\n\nNext we recall the $Q$-polynomial property. ", "The ordering $\\{E_i\\}_{i=0}^D$ is said to be [*$Q$-polynomial*]{} whenever ${{\\sf q}}^h_{ij}$ is zero (resp.", " nonzero) if one of $h,i,j$ is greater than (resp.", " equal to) the sum of the other two $(0 \\leq h,i,j \\leq D)$. The graph $\\Gamma$ is said to be [*$Q$-polynomial with respect to $\\{{{\\sf E}}_i\\}_{i=0}^D$*]{} whenever the ordering $\\{{{\\sf E}}_i\\}_{i=0}^D$ is $Q$-polynomial. ", "For the rest of this section, assume that $\\Gamma$ is $Q$-polynomial with respect to $\\{{{\\sf E}}_i\\}_{i=0}^D$. Define $$\\begin{aligned}\n {{\\sf c}}^*_i &= {{\\sf q}}^i_{1, i-1} && (1 \\leq i \\leq D), \\label{eq:defcsi}\n\\\\\n {{\\sf a}}^*_i &= {{\\sf q}}^i_{1 i} && (0 \\leq i \\leq D), \\label{eq:defasi}\n\\\\\n {{\\sf b}}^*_i &= {{\\sf q}}^i_{1, i+1} && (0 \\leq i \\leq D-1). ", " \\label{eq:defbsi}\\end{aligned}$$ For notational convenience define ${{\\sf c}}^*_0 = 0$ and ${{\\sf b}}^*_D = 0$. We have ${{\\sf c}}^*_i {{\\sf b}}^*_{i-1} \\neq 0$ for $1 \\leq i \\leq D$. Abbreviate ${{\\sf m}}= {{\\sf m}}_1$. By [@BI Proposition 3.7], $$\\begin{aligned}\n{{\\sf a}}^*_0 &= 0, &\n{{\\sf b}}^*_0 &= {{\\sf m}}, &\n{{\\sf c}}^*_1 &= 1, &\n{{\\sf c}}^*_i + {{\\sf a}}^*_i + {{\\sf b}}^*_i &= {{\\sf m}}\\quad (0 \\leq i \\leq D).\\end{aligned}$$ By [@BCN Lemma 2.3.1(iv)], $$\\begin{aligned}\n {{\\sf m}}_i &= \n \\frac{{{\\sf b}}^*_0 {{\\sf b}}^*_1 \\cdots {{\\sf b}}^*_{i-1} }\n {{{\\sf c}}^*_1 {{\\sf c}}^*_2 \\cdots {{\\sf c}}^*_i} && (0 \\leq i \\leq D). ", " $$\n\n\\[def:vsi\\] . ", "Define polynomials $\\{v^*_i\\}_{i=0}^D$ in ${\\mathbb{C}}[\\lambda]$ such that $v^*_0=1$ and $$\\begin{aligned}\n \\lambda v^*_i &= {{\\sf c}}^*_{i+1} v^*_{i+1} + {{\\sf a}}^*_i v^*_i + {{\\sf b}}^*_{i-1} v^*_{i-1} && (1 \\leq i \\leq D-1).\\end{aligned}$$\n\n[[@T:subconst1 Lemma 3.11] ]{} \\[lem:vsi\\] . ", "The following [(i)–(iv)]{} hold.", "\n\n- For $0 \\leq i \\leq D$ the polynomial $v^*_i$ has degree $i$ and leading coefficient $({{\\sf c}}^*_1 {{\\sf c}}^*_2 \\cdots {{\\sf c}}^*_i)^{-1}$.\n\n- For $0 \\leq i \\leq D$, ${{\\sf A}}^*_i = v^*_i ({{\\sf A}}^*_1)$.\n\n- The algebra ${{\\sf M}}^*$ is generated by ${{\\sf A}}^*_1$.\n\n- The scalars $\\{{\\theta}^*_i\\}_{i=0}^D$ are mutually distinct.", "\n\n\\[lem:Qij\\] . ", "For the polynomials $\\{v^*_i\\}_{i=0}^D$ from Definition \\[def:vsi\\], $$\\begin{aligned}\n Q_{i j} &= v^*_j ({\\theta}^*_i) && (0 \\leq i,j \\leq D). ", " $$\n\nSimilar to the proof of Lemma \\[lem:Pij\\].", "\n\nLet $U$ denote an irreducible ${{\\sf T}}$-module. ", "Define the [*dual endpoint*]{} $s=s(U)$ by $$\\begin{aligned}\n s &= \\text{\\rm min} \\{i \\,|\\, 0 \\leq i \\leq D, \\; {{\\sf E}}_i U \\neq 0 \\}.\\end{aligned}$$\n\n[[@T:subconst1 Lemma 3.9] ]{} \\[lem:Tmodule2\\] . ", "Let $U$ denote an irreducible $T$-module with dual endpoint $s$ and dual diameter $d^*$. Then the following hold.", "\n\n- We have ${{\\sf E}}_i U \\neq 0$ if and only if $s \\leq i \\leq s+d^*$ $(0 \\leq i \\leq D)$.\n\n- If $U$ is dual thin then $U$ is thin.", "\n\n[[@T:subconst1 Lemmas 3.9, 3.12] ]{} \\[lem:U\\] . ", "Let $U$ denote a thin irreducible ${{\\sf T}}$-module with endpoint $r$, dual endpoint $s$, and diameter $d$. Then the sequence $$({{\\sf A}}_1; \\{{{\\sf E}}_{s+i}\\}_{i=0}^d; {{\\sf A}}^*_1; \\{{{\\sf E}}^*_{r+i}\\}_{i=0}^d) \\label{eq:UPhi}$$ acts on $U$ as a Leonard system, with eigenvalue sequence $\\{{\\theta}_{s+i} \\}_{i=0}^d$ and dual eigenvalue sequence $\\{ {\\theta}^*_{r+i} \\}_{i=0}^d$.\n\nConsider the Leonard system on $U$. Any object $\\omega$ associated with this Leonard system will be denoted by $\\omega(U)$.\n\nRecall the primary ${{\\sf T}}$-module ${{\\sf U}}$. By Lemma \\[lem:U\\] the sequence $$({{\\sf A}}_1; \\{{{\\sf E}}_i\\}_{i=0}^D; {{\\sf A}}^*_1; \\{{{\\sf E}}^*_i\\}_{i=0}^D) \\label{eq:U0Phi}$$ acts on ${{\\sf U}}$ as a Leonard system, with eigenvalue sequence $\\{{\\theta}_i\\}_{i=0}^D$ and dual eigenvalue sequence $\\{{\\theta}^*_i\\}_{i=0}^D$.\n\n\\[lem:nu3\\] . ", "We have $$\\nu ({{\\sf U}}) = |X|. ", " $$\n\nBy Lemma \\[lem:nuE0Es0E0\\], $\\nu({{\\sf U}}) {{\\sf E}}_0 {{\\sf E}}^*_0 {{\\sf E}}_0 = {{\\sf E}}_0$ holds on ${{\\sf U}}$. Now by Lemma \\[lem:E0Es0E0\\] and Corollary \\[cor:faithful\\] we obtain the result.", "\n\n\\[lem:AiEs0E03\\] . ", "For the Leonard system in on ${{\\sf U}}$, consider the elements $\\{A_i\\}_{i=0}^D$ and $\\{A^*_i\\}_{i=0}^D$ from Definition \\[def:Ai\\]. ", "Then for $0 \\leq i \\leq D$, ${{\\sf A}}_i$ acts on ${{\\sf U}}$ as $A_i$, and ${{\\sf A}}^*_i$ acts on ${{\\sf U}}$ as $A^*_i$.\n\nBy Lemma \\[lem:rhorhos2\\] the following holds on ${{\\sf U}}$: $${{\\sf E}}^*_i {{\\sf E}}_0 {{\\sf E}}^*_0 = \\nu({{\\sf U}})^{-1} A_i {{\\sf E}}^*_0. ", " $$ Comparing this with the equation on the right in , and using Lemma \\[lem:nu3\\], we find that $A_i = {{\\sf A}}_i$ on ${{\\sf E}}^*_0 {{\\sf U}}$. The subspace ${{\\sf E}}^*_0 {{\\sf U}}$ is spanned by $\\widehat{x}$, so $A_i ={{\\sf A}}_i$ on ${{\\sf U}}$ in view of Lemma \\[lem:faithful0\\](i). ", "The result for ${{\\sf A}}^*_i$ is similarly obtained.", "\n\n\\[lem:phijqhij\\] . ", "For $0 \\leq h, i, j \\leq D$, $$\\begin{aligned}\n p^h_{i j} ({{\\sf U}}) &= {{\\sf p}}^h_{i j}, &\n q^h_{i j} ({{\\sf U}}) &= {{\\sf q}}^h_{i j}.\\end{aligned}$$\n\nCompare the equations , with , and use Lemma \\[lem:AiEs0E03\\].", "\n\n\\[lem:ciaibi\\] . ", "We have $$\\begin{aligned}\nc_i ({{\\sf U}}) &={{\\sf c}}_i & c^*_i ({{\\sf U}}) &={{\\sf c}}^*_i && (1 \\leq i \\leq D), \\label{eq:cipU} \\\\\na_i ({{\\sf U}}) &= {{\\sf a}}_i & a^*_i ({{\\sf U}}) &= {{\\sf a}}^*_i && (0 \\leq i \\leq D), \\label{eq:aipU} \\\\\nb_i ({{\\sf U}}) &= {{\\sf b}}_i & b^*_i ({{\\sf U}}) &= {{\\sf b}}^*_i && (0 \\leq i \\leq D-1). ", " \\label{eq:bipU}\\end{aligned}$$\n\nWe first obtain the equations on the left in –. ", "Apply Lemma \\[lem:AA1\\] to the Leonard system on ${{\\sf U}}$, and use Lemma \\[lem:AiEs0E03\\] to find that ${{\\sf A}}_1 = c_1({{\\sf U}}) {{\\sf A}}_1 + a_0 ({{\\sf U}}) {{\\sf I}}$ holds on ${{\\sf U}}$. By this and Corollary \\[cor:faithful\\](i) we obtain $c_1 ({{\\sf U}}) = 1$ and $a_0 ({{\\sf U}})=0$. Now compare the equations in Lemma \\[lem:phij\\] with –, and use Lemma \\[lem:phijqhij\\]. ", "This gives the equations on the left in –. ", "Next we obtain the equations on the right in –. ", "Apply Lemma \\[lem:AA1\\] to the dual of the Leonard system on ${{\\sf U}}$, and use Lemma \\[lem:AiEs0E03\\] to find that ${{\\sf A}}^*_1 = c^*_1 ({{\\sf U}}) {{\\sf A}}^*_1 + a^*_0 ({{\\sf U}}) {{\\sf I}}$ holds on ${{\\sf U}}$. By this and Corollary \\[cor:faithful\\](ii) we obtain $c^*_1 ({{\\sf U}}) = 1$ and $a^*_0 ({{\\sf U}})=0$. Now apply Lemma \\[lem:phij\\] to the dual of the Leonard system on ${{\\sf U}}$ to get $$\\begin{aligned}\nc^*_i ({{\\sf U}}) &= q^i_{1,i-1} ({{\\sf U}}) && (1 \\leq i \\leq D), \\\\\na^*_i ({{\\sf U}}) &= q^i_{1,i} ({{\\sf U}}) && (0 \\leq i \\leq D), \\\\\nb^*_i ({{\\sf U}}) &= q^i_{1,i+1} ({{\\sf U}}) && (0 \\leq i \\leq D-1).\\end{aligned}$$ Now compare these equations with –, and use Lemma \\[lem:phijqhij\\]. ", "This gives the equations on the right in –.", "\n\n\\[lem:nuki\\] . ", "For $0 \\leq i \\leq D$, $$\\begin{aligned}\nk_i ({{\\sf U}}) &= {{\\sf k}}_i, & k^*_i ({{\\sf U}}) &= {{\\sf m}}_i. ", " \\label{eq:kipU}\\end{aligned}$$\n\nTo get the equation on the left in , apply Lemma \\[lem:kip0ii\\] to the Leonard system on ${{\\sf U}}$, and compare the result with using Lemma \\[lem:phijqhij\\]. ", "To get the equation on the right in , apply Lemma \\[lem:kip0ii\\] to the dual of the Leonard system on ${{\\sf U}}$, and compare the result with using Lemma \\[lem:phijqhij\\].", "\n\n\\[def:qRacahDRG\\] . ", "Let $0 \\neq q \\in {\\mathbb{C}}$. The $Q$-polynomial ordering $\\{{{\\sf E}}_i\\}_{i=0}^D$ is said to have [*$q$-Racah type*]{} whenever there exists an affine transformation of the Leonard system on ${{\\sf U}}$, that has $q$-Racah type.", "\n\nFormally self-dual distance-regular graphs {#sec:DRGsd}\n==========================================\n\nIn this section we discuss a type of distance-regular graph, said to be formally self-dual. ", "Let $\\Gamma$ denote a distance-regular graph with diameter $D \\geq 1$. Recall the distance-matrices $\\{{{\\sf A}}_i\\}_{i=0}^D$ and primitive idempotents $\\{{{\\sf E}}_i\\}_{i=0}^D$ in the Bose-Mesner algebra ${{\\sf M}}$ of $\\Gamma$. Recall the matrices $P$, $Q \\in \\text{\\rm Mat}_{D+1}({\\mathbb{C}})$ from . ", "Fix $x \\in X$ and abbreviate ${{\\sf T}}={{\\sf T}}(x)$, ${{\\sf M}}^* = {{\\sf M}}^*(x)$, and ${{\\sf E}}^*_i = {{\\sf E}}^*_i (x)$, ${{\\sf A}}^*_i = {{\\sf A}}^*_i (x)$ for $0 \\leq i \\leq D$.\n\n\\[def:FSD\\] . ", "The graph $\\Gamma$ is said to be [*formally self-dual with respect to $\\{{{\\sf E}}_i\\}_{i=0}^D$*]{} whenever $P=Q$.\n\nThe following fact is well-known; see [@BCN Section 2.3]. ", "We give a short proof for completeness.", "\n\n\\[lem:duality\\] . ", "Assume that $\\Gamma$ is formally self-dual with respect to $\\{{{\\sf E}}_i\\}_{i=0}^D$. Then ${{\\sf p}}^h_{i j} = {{\\sf q}}^h_{i j}$ for $0 \\leq h,i,j \\leq D$.\n\nConsider the ${\\mathbb{C}}$-linear map $\\sigma : {{\\sf M}}\\to {{\\sf M}}^*$ that sends ${{\\sf E}}_i \\mapsto {{\\sf E}}^*_i$ for $0 \\leq i \\leq D$. Clearly $\\sigma$ is bijective. ", "We have ${{\\sf E}}_i {{\\sf E}}_j = \\delta_{i,j} {{\\sf E}}_i$ and ${{\\sf E}}^*_i {{\\sf E}}^*_j = \\delta_{i,j} {{\\sf E}}^*_i$ for $0 \\leq i,j \\leq D$. Thus $\\sigma$ is an isomorphism of ${\\mathbb{C}}$-algebras. ", "By the equation on the left in and the equation on the right in with $P=Q$, we find that $\\sigma$ sends ${{\\sf A}}_j \\mapsto {{\\sf A}}^*_j$ for $0 \\leq j \\leq D$. Now we get the result by and .", "\n\nBy Lemma \\[lem:duality\\], if $\\Gamma$ is formally self-dual with respect to $\\{{{\\sf E}}_i\\}_{i=0}^D$, then $\\Gamma$ is $Q$-polynomial with respect to $\\{{{\\sf E}}_i\\}_{i=0}^D$.\n\n\\[lem:Asivi\\] . ", "Assume that $\\Gamma$ is formally self-dual with respect to $\\{{{\\sf E}}_i\\}_{i=0}^D$. Let the polynomials $\\{v_i\\}_{i=0}^D$ (resp.", " $\\{v^*_i\\}_{i=0}^D$) be from Definition \\[def:vi2\\] (resp.", " Definition \\[def:vsi\\]). ", "Then $v_i = v^*_i$ for $0 \\leq i \\leq D$.\n\nRecall the intersection numbers $\\{ {{\\sf c}}_i \\}_{i=1}^D$, $\\{ {{\\sf a}}_i\\}_{i=0}^D$, $\\{{{\\sf b}}_i \\}_{i=0}^{D-1}$ and the Krein parameters $\\{ {{\\sf c}}^*_i \\}_{i=1}^D$, $\\{ {{\\sf a}}^*_i\\}_{i=0}^D$, $\\{{{\\sf b}}^*_i \\}_{i=0}^{D-1}$ of $\\Gamma$. By Lemma \\[lem:duality\\], ${{\\sf p}}^h_{i j} = {{\\sf q}}^h_{i j}$ for $0 \\leq h,i,j \\leq D$. By – and – we see that ${{\\sf c}}_i = {{\\sf c}}^*_i$ $(1 \\leq i \\leq D)$, ${{\\sf a}}_i = {{\\sf a}}^*_i$ $(0 \\leq i \\leq D)$, ${{\\sf b}}_i = {{\\sf b}}^*_i$ $(0 \\leq i \\leq D-1)$. Now $v_i = v^*_i$ $(0 \\leq i \\leq D)$ by Definitions \\[def:vi2\\], \\[def:vsi\\].", "\n\nThe formally self-dual condition is characterized as follows. ", "Recall the eigenvalue sequence $\\{{\\theta}_i\\}_{i=0}^D$ and dual eigenvalue sequence $\\{{\\theta}^*_i\\}_{i=0}^D$ of $\\Gamma$ with respect to $\\{{{\\sf E}}_i\\}_{i=0}^D$.\n\n\\[prop:DRGsd\\] . ", "The following [(i)–(iii)]{} are equivalent:\n\n- $\\Gamma$ is formally self-dual with respect to $\\{{{\\sf E}}_i\\}_{i=0}^D$;\n\n- $\\Gamma$ is $Q$-polynomial with respect to $\\{{{\\sf E}}_i\\}_{i=0}^D$ and ${\\theta}_i = {\\theta}^*_i$ for $0 \\leq i \\leq D$;\n\n- the sequence acts on the primary ${{\\sf T}}$-module ${{\\sf U}}$ as a self-dual Leonard system.", "\n\n\\(i) $\\Rightarrow$ (ii) As we saw above Lemma \\[lem:Asivi\\], $\\Gamma$ is $Q$-polynomial with respect to $\\{{{\\sf E}}_i\\}_{i=0}^D$. By Definition \\[def:FSD\\] we have $P=Q$. By this and we obtain ${\\theta}_i ={\\theta}^*_i$ $(0 \\leq i \\leq D)$.\n\n\\(ii) $\\Rightarrow$ (iii) Let $\\Phi$ denote the Leonard system in on ${{\\sf U}}$. Then $\\Phi$ has eigenvalue sequence $\\{{\\theta}_i\\}_{i=0}^D$ and dual eigenvalue sequence $\\{{\\theta}^*_i\\}_{i=0}^D$. We assume ${\\theta}_i = {\\theta}^*_i$ for $0 \\leq i \\leq D$, so $\\Phi$ is self-dual by Lemma \\[lem:selfdualparam\\].", "\n\n\\(iii) $\\Rightarrow$ (i) We show that $P=Q$. Let $\\sigma$ denote the duality of the Leonard system in . ", "Then, on ${{\\sf U}}$, $\\sigma$ swaps ${{\\sf E}}_i$ and ${{\\sf E}}^*_i$ for $0 \\leq i \\leq D$. By Lemmas \\[lem:selfdualAi\\] and \\[lem:AiEs0E03\\], on ${{\\sf U}}$, $\\sigma$ swaps ${{\\sf A}}_i$ and ${{\\sf A}}^*_i$ for $0 \\leq i \\leq D$. Now comparing and , we obtain $P=Q$.\n\nFrom a spin model to spin Leonard pairs {#sec:spindrg}\n=======================================\n\nLet $\\Gamma$ denote a distance-regular graph with vertex set $X$ and diameter $D \\geq 1$. In this section we recall what it means for a spin model ${{\\sf W}}$ to be afforded by $\\Gamma$. For such ${{\\sf W}}$ and all $x \\in X$, we construct a spin Leonard pair on each irreducible ${{\\sf T}}(x)$-module.", "\n\nRecall the Bose-Mesner algebra ${{\\sf M}}$ of $\\Gamma$. Let ${{\\sf W}}$ denote a spin model in ${\\text{\\rm Mat}_X({\\mathbb{C}})}$. Recall the algebra $N({{\\sf W}})$ from Definition \\[def:NW\\] and Lemma \\[lem:Nomuraalg\\].", "\n\n\\[def:afford\\] . ", "We say that [*$\\Gamma$ affords ${{\\sf W}}$*]{} whenever ${{\\sf W}}\\in {{\\sf M}}\\subseteq N({{\\sf W}})$.\n\n\\[lem:afford\\] . ", "Assume that ${{\\sf W}}$ is afforded by $\\Gamma$. Then each of the spin models $-{{\\sf W}}$, ${{\\sf W}}^-$ is afforded by $\\Gamma$.\n\nBy Definition \\[def:afford\\], ${{\\sf W}}\\in {{\\sf M}}\\subseteq N({{\\sf W}})$. We have $-{{\\sf W}}\\in {{\\sf M}}$, and $N(-{{\\sf W}}) = N({{\\sf W}})$ by Lemma \\[lem:NW-\\]. ", "Thus $-{{\\sf W}}\\in {{\\sf M}}\\subseteq N(-{{\\sf W}})$, and so $-{{\\sf W}}$ is afforded by $\\Gamma$. We have ${{\\sf W}}^{-1} \\in {{\\sf M}}$, since for any invertible $B \\in {\\text{\\rm Mat}_X({\\mathbb{C}})}$ the element $B^{-1}$ is a polynomial in $B$. By this and Lemma \\[lem:type2W-\\](ii), ${{\\sf W}}^- \\in {{\\sf M}}$. By Lemma \\[lem:NW-\\], $N({{\\sf W}}^-) = N({{\\sf W}})$. Thus ${{\\sf W}}^- \\in {{\\sf M}}\\subseteq N({{\\sf W}}^-)$, and so ${{\\sf W}}^-$ is afforded by $\\Gamma$.\n\nFor the rest of this section, assume that ${{\\sf W}}$ is afforded by $\\Gamma$.\n\n[[@JMN Section 3.1] ]{} \\[def:Psi\\] . ", "We define a map $\\Psi : N({{\\sf W}}) \\to {\\text{\\rm Mat}_X({\\mathbb{C}})}$ as follows. ", "For ${{\\sf B}}\\in N({{\\sf W}})$ and $b,c \\in X$ the $(b,c)$-entry of $\\Psi({{\\sf B}})$ is the eigenvalue of ${{\\sf B}}$ for the eigenvector $\\text{\\bf u}_{b,c}$ from Definition \\[def:NW\\]. ", "So $$\\begin{aligned}\n {{\\sf B}}\\text{\\bf u}_{b,c} &= \\Psi({{\\sf B}})(b,c) \\text{\\bf u}_{b,c}.\\end{aligned}$$ Note that the map $\\Psi$ is ${\\mathbb{C}}$-linear.", "\n\nRecall the distance-matrices $\\{{{\\sf A}}_i\\}_{i=0}^D$ of $\\Gamma$.\n\n[[@CN:hyper Lemma 5.1] ]{} \\[lem:MPsi\\] . ", "There exists an ordering $\\{{{\\sf E}}_i\\}_{i=1}^D$ of the nontrivial primitive idempotents of $\\Gamma$ such that $$\\begin{aligned}\n \\Psi ({{\\sf A}}_i) &= |X| {{\\sf E}}_i && (0 \\leq i \\leq D). ", " $$ Moreover $\\Gamma$ is formally self-dual with respect to $\\{{{\\sf E}}_i\\}_{i=0}^D$.\n\nFor the rest of this section, fix the ordering of the primitive idempotents from Lemma \\[lem:MPsi\\]. ", "Since $\\{{{\\sf E}}_i\\}_{i=0}^D$ is a basis for ${{\\sf M}}$ and ${{\\sf W}}$ is an invertible element in ${{\\sf M}}$, there exist nonzero scalars $f$, $\\{\\tau_i\\}_{i=0}^D$ in ${\\mathbb{C}}$ such that $\\tau_0 = 1$ and $${{\\sf W}}= f \\sum_{i=0}^D \\tau_i {{\\sf E}}_i. ", " \\label{eq:defWfti}$$\n\n\\[lem:W-2\\] . ", "We have $$\\begin{aligned}\n {{\\sf W}}^{-1} &= f^{-1} \\sum_{i=0}^D \\tau_i^{-1} {{\\sf E}}_i, &\n {{\\sf W}}^- &= |X| f^{-1} \\sum_{i=0}^D \\tau_i^{-1} {{\\sf E}}_i.\\end{aligned}$$\n\nThe first equation follows from . ", "The second equation follows from the first equation and Lemma \\[lem:type2W-\\](ii).", "\n\nFor the rest of this section fix $x \\in X$. Abbreviate ${{\\sf T}}={{\\sf T}}(x)$ and ${{\\sf A}}^*_i = {{\\sf A}}^*_i (x)$, ${{\\sf E}}^*_i = {{\\sf E}}^*_i(x)$ for $0 \\leq i \\leq D$. Define $$\\label{def:Ws}\n {{\\sf W}}^* = f \\sum_{i=0}^D \\tau_i {{\\sf E}}^*_i.$$ Note that ${{\\sf W}}^*$ is invertible.", "\n\n[[@CW Theorem 5.3, Corollary 5.4] ]{} \\[lem:balenced2\\] . ", "We have $$\\begin{aligned}\n {{\\sf A}}_1 {{\\sf W}}^* {{\\sf W}}&= {{\\sf W}}^* {{\\sf W}}{{\\sf A}}^*_1, \\label{eq:A1WsW=WsWAs1}\n\\\\\n {{\\sf W}}{{\\sf W}}^* {{\\sf W}}&= {{\\sf W}}^* {{\\sf W}}{{\\sf W}}^*. ", " \\label{eq:balanced2}\\end{aligned}$$\n\n[[@C:thin Lemma 2.7] ]{} \\[lem:Cur\\] . ", "We have $$\\begin{aligned}\n{{\\sf W}}&= |X|^{1/2} f^{-1} \\sum_{i=0}^D \\tau_i^{-1} {{\\sf A}}_i, &\n{{\\sf W}}^{-1} &= |X|^{-3/2} f \\sum_{i=0}^D \\tau_i {{\\sf A}}_i, \\label{eq:WWs}\n\\\\\n{{\\sf W}}^* &= |X|^{1/2} f^{-1} \\sum_{i=0}^D \\tau_i^{-1} {{\\sf A}}^*_i, &\n({{\\sf W}}^*)^{-1} &= |X|^{-3/2} f \\sum_{i=0}^D \\tau_i {{\\sf A}}^*_i. ", " \\label{eq:WWs2}\\end{aligned}$$\n\n\\[lem:WsW-0\\] . ", "For $y \\in X$, $$\\begin{aligned}\n {{\\sf W}}^* (y,y) &= \\frac{ |X|^{1/2} } {{{\\sf W}}(x,y)} . ", " $$\n\nLet $i = \\partial (x,y)$. By we obtain ${{\\sf W}}^*(y,y) = f \\tau_i$. By the equation on the left in we obtain ${{\\sf W}}(x,y ) = |X|^{1/2} f^{-1} \\tau_i^{-1}$. The result follows.", "\n\n\\[lem:f\\] . ", "The scalar $f$ satisfies $$f^{-2} = |X|^{-3/2} \\sum_{i=0}^D {{\\sf k}}_i \\tau_i. ", " \\label{eq:f-2}$$\n\nRecall the primary ${{\\sf T}}$-module ${{\\sf U}}$. By Lemma \\[lem:U\\] the sequence $$({{\\sf A}}_1; \\{{{\\sf E}}_i\\}_{i=0}^D; {{\\sf A}}^*_1; \\{{{\\sf E}}^*_i\\}_{i=0}^D)$$ acts on ${{\\sf U}}$ as a Leonard system. ", "By Theorem \\[thm:WtiinvAi\\] and Lemmas \\[lem:piW\\], \\[lem:nu3\\], $$\\begin{aligned}\n {{\\sf W}}&= f \\gamma \\sum_{i=0}^D \\tau_i^{-1} {{\\sf A}}_i, &\n \\gamma &= |X|^{-1} \\sum_{i=0}^D {{\\sf k}}_i \\tau_i.\\end{aligned}$$ Comparing this with the equation on the left in , we get the result.", "\n\nWe now describe the irreducible ${{\\sf T}}$-modules. ", "The following result is essentially due to Curtin [@C:thin Theorem 8.3].", "\n\n\\[prop:C2\\] . ", "Every irreducible ${{\\sf T}}$-module is thin, provided that ${{\\sf W}}$ does not have Hadamard type.", "\n\nWe refer to the equation on the left in . ", "We claim that $$\\text{ $\\tau_{i-1}$, $\\tau_i$, $\\tau_{i+1}$ are mutually distinct for $1 \\leq i \\leq D-1$}. ", " \\label{eq:aux}$$ By way of contradiction, assume that there exists an integer $j$ $(1 \\leq j \\leq D-1)$ such that $\\tau_{j-1}$, $\\tau_j$, $\\tau_{j+1}$ are not mutually distinct. ", "Then either (i) $\\tau_j \\in \\{\\tau_{j-1}, \\tau_{j+1}\\}$; or (ii) $\\tau_{j-1} = \\tau_{j+1}$. For the moment assume (i). ", "Then by [@CN:someformula Corollary 4.6] we get $\\tau_i \\in \\{\\tau_0, -\\tau_0\\}$ for $0 \\leq i \\leq D$, contradicting Lemma \\[lem:Htype\\]. ", "Next assume (ii). ", "Then $\\tau_1 \\in \\{\\tau_0, - \\tau_0\\}$ by [@CN:someformula Corollary 4.7]. ", "By this and [@CN:someformula Corollary 4.6] we get $\\tau_i \\in \\{\\tau_0, - \\tau_0\\}$ for $0 \\leq i \\leq D$, contradicting Lemma \\[lem:Htype\\]. ", "The claim is proved. ", "In [@C:thin Theorem 3.8] Curtin showed that every irreducible ${{\\sf T}}$-module is thin under the condition that $$\\tau_i \\not\\in \\{\\tau_0, - \\tau_0\\} \\; \\text{ for } 1 \\leq i \\leq D. \\label{eq:aux2}$$ Analyzing the proof of this theorem, we find that this theorem is implied by Lemmas 3.4 and 3.7 in [@C:thin]. ", "Analyzing the proof of these lemmas, we find that these lemmas still hold if we replace the condition with . ", "Thus the conclusion of [@C:thin Theorem 3.8] holds under the assumption . ", "The result follows.", "\n\nLet $U$ denote a thin irreducible ${{\\sf T}}$-module with endpoint $r$, dual endpoint $s$, and diameter $d$. By Lemmas \\[lem:U\\] the sequence $$({{\\sf A}}_1; \\{{{\\sf E}}_{s+i}\\}_{i=0}^d; {{\\sf A}}^*_1; \\{{{\\sf E}}^*_{r+i}\\}_{i=0}^d) \\label{eq:LS5}$$ acts on $U$ as a Leonard system. ", "By [@CN:hyper Lemma 4.4, Theorems 4.1, 5.5] we have $r=s$, and the Leonard system on $U$ is self-dual.", "\n\n\\[lem:spinLP3\\] . ", "The pair ${{\\sf A}}_1, {{\\sf A}}^*_1$ acts on $U$ as a spin Leonard pair, and ${{\\sf W}}, {{\\sf W}}^*$ acts on $U$ as a balanced Boltzmann pair for this Leonard pair.", "\n\nBy Definition \\[def:spinLP\\] and we see that the pair ${{\\sf A}}_1, {{\\sf A}}^*_1$ acts on $U$ as a spin Leonard pair, and the pair ${{\\sf W}}, {{\\sf W}}^*$ acts on $U$ as a Boltzmann pair for this Leonard pair. ", "This Boltzmann pair is balanced by Definition \\[def:balanced\\] and .", "\n\nFrom a spin model to spin Leonard pairs; the $q$-Racah case {#sec:spinqRacah}\n===========================================================\n\nLet $\\Gamma$ denote a distance-regular graph with vertex set $X$, diameter $D \\geq 3$, and valency at least $3$. Recall the distance-matrices $\\{{{\\sf A}}_i\\}_{i=0}^D$ in the Bose-Mesner algebra ${{\\sf M}}$ of $\\Gamma$. Let ${{\\sf W}}$ denote a spin model afforded by $\\Gamma$. Fix an ordering $\\{{{\\sf E}}_i\\}_{i=0}^D$ of the primitive idempotents of $\\Gamma$ from Lemma \\[lem:MPsi\\]. ", "Note that $\\Gamma$ is formally self-dual with respect to $\\{{{\\sf E}}_i\\}_{i=0}^D$. Let $\\{{\\theta}_i\\}_{i=0}^D$ denote the eigenvalue sequence of $\\Gamma$ with respect to the ordering $\\{{{\\sf E}}_i\\}_{i=0}^D$. As we saw below Lemma \\[lem:MPsi\\], there exist nonzero scalars $f$, $\\{\\tau_i\\}_{i=0}^D$ in ${\\mathbb{C}}$ such that $\\tau_0=1$ and $${{\\sf W}}= f \\sum_{i=0}^D \\tau_i {{\\sf E}}_i.$$ Fix $x \\in X$. Abbreviate ${{\\sf T}}={{\\sf T}}(x)$ and ${{\\sf A}}^*_i = {{\\sf A}}^*_i(x)$, ${{\\sf E}}^*_i = {{\\sf E}}^*_i(x)$ for $0 \\leq i \\leq D$. Define $${{\\sf W}}^* = f \\sum_{i=0}^D \\tau_i {{\\sf E}}^*_i.$$ Recall the primary ${{\\sf T}}$-module ${{\\sf U}}$. By Proposition \\[prop:DRGsd\\] the sequence $$({{\\sf A}}_1; \\{{{\\sf E}}_i\\}_{i=0}^D; {{\\sf A}}^*_1; \\{E^*_i \\}_{i=0}^D) $$ acts on ${{\\sf U}}$ as a self-dual Leonard system. ", "This Leonard system has eigenvalue sequence $\\{{\\theta}_i\\}_{i=0}^D$. Fix $0 \\neq q \\in {\\mathbb{C}}$, and assume that the ordering $\\{{{\\sf E}}_i\\}_{i=0}^D$ has $q$-Racah type.", "\n\n\\[lem:alphabeta\\] . ", "There exist scalars $a$, $\\alpha$, $\\beta$ in ${\\mathbb{C}}$ with $a$, $\\alpha$ nonzero that satisfy the following [(i), (ii)]{}.", "\n\n- The sequence $$({{\\sf A}}; \\{{{\\sf E}}_i\\}_{i=0}^D; {{\\sf A}}^*; \\{{{\\sf E}}^*_i\\}_{i=0}^D) \\label{eq:LSonpU}$$ acts on ${{\\sf U}}$ as a Leonard system of $q$-Racah type, where $$\\begin{aligned}\n {{\\sf A}}_1 &= \\alpha {{\\sf A}}+ \\beta {{\\sf I}}, &\n {{\\sf A}}^*_1 &= \\alpha {{\\sf A}}^* + \\beta {{\\sf I}}. ", " \\label{eq:defAAs0}\\end{aligned}$$\n\n- The Leonard system on ${{\\sf U}}$ has Huang data $(a,a,a,D)$.\n\nBy Definition \\[def:qRacahDRG\\] there exists $\\alpha$, $\\beta \\in {\\mathbb{C}}$ with $\\alpha \\neq 0$ such that the sequence acts on ${{\\sf U}}$ as a Leonard system of $q$-Racah type, where ${{\\sf A}}$, ${{\\sf A}}^*$ are from . ", "This Leonard system is self-dual. ", "By Definition \\[def:qRacah\\] there exists $0 \\neq a \\in {\\mathbb{C}}$ such that $$\\begin{aligned}\n {\\theta}_i &= \\alpha (a q^{2i-D} + a^{-1} q^{D-2i}) + \\beta && (0 \\leq i \\leq D). ", " \\label{eq:thi2}\\end{aligned}$$ By and this Leonard system has eigenvalue sequence $\\{a q^{2i-D} + a^{-1} q^{D-2i}\\}_{i=0}^D$. By Lemmas \\[lem:affine\\], \\[lem:spinLP3\\] the pair ${{\\sf A}}, {{\\sf A}}^*$ acts on ${{\\sf U}}$ as a spin Leonard pair. ", "By these comments and Lemmas \\[lem:selfdualab\\], \\[lem:spinLP0\\](i) the Leonard system $\\eqref{eq:LSonpU}$ has Huang data $(a,a,c,D)$ with $c \\in \\{a, a^{-1}, -a, - a^{-1} \\}$. By Note \\[note:Huang\\] we may assume $c \\in \\{a, -a\\}$. Replacing ${{\\sf A}}, {{\\sf A}}^*$ with $-{{\\sf A}}, - {{\\sf A}}^*$ and replacing $\\alpha$ with $- \\alpha$, we may assume by Lemma \\[lem:Huang2\\] that $c = a$. The result follows.", "\n\nFor the rest of this section, let the scalars $a, \\alpha,\\beta$ be as in Lemma \\[lem:alphabeta\\].", "\n\n[[@CW Corollaries 6.5, 6.7] ]{} \\[lem:aq\\] . ", "We have $$\\begin{aligned}\n q^{2i} &\\neq 1 && (1 \\leq i \\leq D), \\label{eq:restq}\n\\\\\n a^2 q^{2i} &\\neq 1 && (1-D \\leq i \\leq D-1), \\label{eq:resta}\n\\\\\n a^3 q^{2i-D-1} &\\neq 1 && (1 \\leq i \\leq D). ", " \\label{eq:resta2}\\end{aligned}$$\n\nApply Lemma \\[lem:condabc\\] to the Leonard system on ${{\\sf U}}$.\n\n\\[lem:ti\\] . ", "One of the following holds: $$\\begin{aligned}\n \\tau_i &= (-1)^i a^{-i} q^{i (D-i)} && (0 \\leq i \\leq D), \\label{eq:ti}\n\\\\\n \\tau_i^{-1} &= (-1)^i a^{-i} q^{i (D-i)} && (0 \\leq i \\leq D). ", " \\label{eq:tiinv}\\end{aligned}$$\n\nApply Lemma \\[lem:W\\](i) to the Leonard system on ${{\\sf U}}$, and use Lemma \\[lem:alphabeta\\].", "\n\n\\[note:tiinv\\] . ", "Replacing ${{\\sf W}}$ by ${{\\sf W}}^-$ if necessary, and using Lemmas \\[lem:afford\\], \\[lem:W-2\\], we may assume that holds. ", "We adopt this assumption for the rest of the section.", "\n\nWe mention a lemma for later use. ", "For the moment, let $D$, $d$, $r$ denote arbitrary nonnegative integers such that $r+d \\leq D$, and let $a$, $q$ denote arbitrary nonzero scalars in ${\\mathbb{C}}$.\n\n\\[lem:tr+i\\] . ", "With the above notation, define $\\widetilde{a} = a q^{2r+d-D}$. Then the following hold.", "\n\n- Define $$\\begin{aligned}\n {\\theta}_i &= a q^{2i-D} + a^{-1} q^{D-2i} && (0 \\leq i \\leq D).\\end{aligned}$$ Then $$\\begin{aligned}\n {\\theta}_{r+i} &= \\widetilde{a} q^{2i-d} + (\\widetilde{a})^{-1} q^{d-2i} && (0 \\leq i \\leq d).\\end{aligned}$$\n\n- Define $$\\begin{aligned}\n \\tau_i &= (-1)^i a^{-i} q^{i (D-i)} && (0 \\leq i \\leq D).\\end{aligned}$$ Then $$\\begin{aligned}\n \\tau_{r+i} &= \\tau_r \\widetilde{\\tau}_i && (0 \\leq i \\leq d), \\label{eq:tr+i}\\end{aligned}$$ where $$\\begin{aligned}\n \\widetilde{\\tau}_i &= (-1)^i ( \\widetilde{a})^{-i} q^{i(d-i)} && (0 \\leq i \\leq d). ", " \\label{eq:deftti}\\end{aligned}$$\n\nRoutine verification.", "\n\nWe return our attention to $\\Gamma$. Let $U$ denote a thin irreducible ${{\\sf T}}$-module, with endpoint $r$ and diameter $d$. Note that $U$ has dual endpoint $r$ by the sentence below . ", "Consider the sequence $$\\Phi = ( {{\\sf A}}_1; \\{{{\\sf E}}_{r+i}\\}_{i=0}^d; {{\\sf A}}^*_1; \\{{{\\sf E}}^*_{r+i} \\}_{i=0}^d).$$\n\n\\[lem:Phi\\] . ", "The sequence $\\Phi$ acts on $U$ as a self-dual Leonard system, with eigenvalue sequence $\\{{\\theta}_{r+i} \\}_{i=0}^d$.\n\nApply Lemma \\[lem:U\\] to the Leonard system $\\Phi$ on $U$.\n\n\\[lem:WonU\\] . ", "On $U$ we have $$\\begin{aligned}\n {{\\sf W}}&= f \\tau_r \\sum_{i=0}^d \\widetilde{\\tau}_i {{\\sf E}}_{r+i}, &\n {{\\sf W}}^* &= f \\tau_r \\sum_{i=0}^d \\widetilde{\\tau}_i {{\\sf E}}^*_{r+i}, \\label{eq:WonU}\\end{aligned}$$ where $\\{ \\widetilde{\\tau}_i\\}_{i=0}^d$ are from .", "\n\nBy construction, on $U$ we have $$\\begin{aligned}\n {{\\sf W}}&= f \\sum_{i=0}^d \\tau_{r+i} {{\\sf E}}_{r+i}, &\n {{\\sf W}}^* &= f \\sum_{i=0}^d \\tau_{r+i} {{\\sf E}}^*_{r+i}.\\end{aligned}$$ By this and we get the result.", "\n\nOur next goal is to obtain the intersection numbers of the Leonard system $\\Phi$ on $U$.\n\n\\[lem:tildePhi\\] . ", "The sequence $$({{\\sf A}}; \\{{{\\sf E}}_{r+i} \\}_{i=0}^d; {{\\sf A}}^*; \\{{{\\sf E}}^*_{r+i}\\}_{i=0}^d) \\label{eq:tildePhi}$$ acts on $U$ as a Leonard system of $q$-Racah type with Huang data $$(a q^{2r+d-D}, a q^{2r+d-D}, a q^{2r+d-D}, d). ", " $$\n\nBy Lemma \\[lem:Phi\\] and the sequence acts on $U$ as a self-dual Leonard system. ", "For $0 \\leq i \\leq D$ define $$\\begin{aligned}\n \\widetilde{{\\theta}}_i &= a q^{2i-D} + a^{-1} q^{D-2i},\\end{aligned}$$ and observe by that ${\\theta}_i = \\alpha \\widetilde{{\\theta}}_i + \\beta$. Now by and Lemma \\[lem:Phi\\] the Leonard system on $U$ has eigenvalue sequence and dual eigenvalue sequence $\\{\\widetilde{{\\theta}}_{r+i}\\}_{i=0}^d$. By Lemma \\[lem:tr+i\\](i) the Leonard system on $U$ has $q$-Racah type with Huang data $(\\widetilde{a}, \\widetilde{a}, \\widetilde{c},d)$ for some nonzero $\\widetilde{c} \\in {\\mathbb{C}}$, where $\\widetilde{a}$ is from Lemma \\[lem:tr+i\\]. ", "By Lemmas \\[lem:affine\\], \\[lem:spinLP3\\] the pair ${{\\sf A}}, {{\\sf A}}^*$ acts on $U$ as a spin Leonard pair, and ${{\\sf W}}, {{\\sf W}}^*$ acts on $U$ as a Boltzmann pair for this Leonard pair. ", "By this and Lemmas \\[lem:new\\], \\[lem:WonU\\] we obtain $\\widetilde{c} \\in \\{ \\widetilde{a}, (\\widetilde{a})^{-1} \\}$. By this and Note \\[note:Huang\\] the sequence $(\\widetilde{a}, \\widetilde{a}, \\widetilde{a}, d)$ is a Huang data for $\\Phi$ on $U$. The result follows.", "\n\nRecall the intersection numbers $\\{c_i (U)\\}_{i=1}^d$, $\\{b_i(U)\\}_{i=0}^{d-1}$ for the Leonard system $\\Phi$ on $U$.\n\n[[@CW Theorem 8.5] ]{} \\[lem:ciUbiU\\] . ", "For the Leonard system $\\Phi$ on $U$ the intersection numbers satisfy $$\\begin{aligned}\nb_i(U) &=\n \\frac{ \\alpha (q^{i-d} - q^{d-i}) (a q^{2r+i -D} - a^{-1} q^{D-2r-i})(a^3-q^{3D-2d-6r-2i-1}) }\n {a q^{D-d-2r} (a q^{2r+2i-D} - a^{-1} q^{D-2r-2i} ) (a + q^{D-2r-2i-1} ) }, \\label{eq:biU}\n\\\\\nc_i(U) &=\n \\frac{ \\alpha a (q^{i}- q^{-i})(a q^{d+2r+i-D} - a^{-1} q^{D-d-2r-i})\n (a^{-1} - q^{2d-D+2r-2i+1}) }\n {q^{d-D+2r} (a q^{2r+2i-D} - a^{-1} q^{D-2r-2i}) (a + q^{D-2r-2i+1} ) } \\label{eq:ciU}\\end{aligned}$$ for $1 \\leq i \\leq d-1$ and $$\\begin{aligned}\nb_0(U) &=\n \\frac{ \\alpha (q^{-d} - q^d) ( a^3 - q^{3D-2d-6r-1} ) }\n {a q^{D-d-2r} (a + q^{D-2r-1}) }, \\label{eq:b0U}\n\\\\\nc_d(U) &=\n \\frac{ \\alpha (q^{-d} - q^d)(a - q^{D-2r-1}) }\n { q^{d-1} (a + q^{D-2d-2r+1}) }. ", " \\label{eq:cdU}\\end{aligned}$$\n\nFor the Leonard system on $U$, compute the intersection numbers using Lemmas \\[lem:qRacahbi\\] and \\[lem:tildePhi\\]. ", "Adjust these intersection numbers using to get the result.", "\n\nRecall the intersection numbers $\\{{{\\sf c}}_i\\}_{i=1}^D$, $\\{{{\\sf b}}_i\\}_{i=0}^{D-1}$ of $\\Gamma$.\n\n[[@CN:someformula Theorem 1.1] ]{} \\[lem:cibi\\] . ", "The intersection numbers of $\\Gamma$ satisfy $$\\begin{aligned}\n{{\\sf b}}_0 &=\n \\frac{ \\alpha (q^{-D} - q^D)(a^3 - q^{D-1}) }\n {a (a + q^{D-1}) }, \\label{eq:b0}\n\\\\\n{{\\sf b}}_i &=\n \\frac{ \\alpha (q^{i-D} - q^{D-i})(a q^{i-D} - a^{-1} q^{D-i}) (a^3 - q^{D-2i-1}) }\n {a (a q^{2i-D} - a^{-1} q^{D-2i}) (a + q^{D-2i-1}) } && (1 \\leq i \\leq D-1), \\label{eq:bi}\n\\\\\n{{\\sf c}}_i &=\n \\frac{\\alpha a (q^{i} - q^{-i})(a q^i - a^{-1} q^{-i}) (a^{-1} - q^{D-2i+1} ) }\n { (a q^{2i-D} - a^{-1} q^{D-2i}) (a + q^{D-2i+1} ) } && (1 \\leq i \\leq D-1), \\label{eq:ci}\n\\\\\n{{\\sf c}}_D &=\n \\frac{ \\alpha (q^{-D} - q^D) (a - q^{D-1}) }\n {q^{D-1} (a + q^{1-D}) }. ", " \\label{eq:cd}\\end{aligned}$$\n\nApply Lemma \\[lem:ciUbiU\\] with $U={{\\sf U}}$ and use Lemma \\[lem:ciaibi\\].", "\n\n[[@CW Theorem 6.4, 6.8] ]{} \\[lem:thi\\] . ", "We have $$\\begin{aligned}\n \\alpha &= \n \\frac{(a q^{2-D} - a^{-1} q^{D-2}) ( a + q^{D-1}) }\n {q^{D-1} (q^{-1} - q)(a q - a^{-1} q^{-1}) (a - q^{1-D}) }, \\label{eq:alpha}\n\\\\\n \\beta &=\n \\frac{q (a+a^{-1}) (a + q^{-D-1}) (a q^{2-D}- a^{-1} q^{D-2}) }\n { (q-q^{-1}) (a - q^{1-D}) (a q - a^{-1} q^{-1}) }. ", " \\label{eq:beta}\\end{aligned}$$\n\nBy , ${{\\sf c}}_1=1$. By this and we obtain . ", "By , , we have ${{\\sf b}}_0 = {\\theta}_0$. By this and , , we obtain .", "\n\n\\[lem:X\\] . ", "We have $$\\begin{aligned}\n |X| &= \\frac{a^{3D} (a^{-2}; q^2)_D^2 }\n {q^{D(D-1)} (a q^{1-D};q^2)_D^2}.\\end{aligned}$$\n\nBy Lemmas \\[lem:qRacahnu\\] and \\[lem:nu3\\].", "\n\nRecall the scalars $\\{{{\\sf k}}_i\\}_{i=0}^D$ from .", "\n\n\\[lem:ki4\\] . ", "We have ${{\\sf k}}_0 = 1$, and $${{\\sf k}}_i =\n \\frac{q^{2 i D} (1-a^2 q^{4i-2D}) \\, (a^2 q^{2-2D};q^2)_i \\, (q^{-2D}; q^2)_i \\, (a^3 q^{1-D};q^2)_i }\n {a^{2i} (1-a^2 q^{2i-2D}) \\, (a^2 q^2; q^2)_i \\, (q^2; q^2)_i \\, (a^{-1} q^{1-D}; q^2)_i}$$ for $1 \\leq i \\leq D-1$, and $${{\\sf k}}_D = \n \\frac{q^{2 D^2} (a^2 q^{2-2D};q^2)_D \\, (q^{-2D}; q^2)_D \\, (a^3 q^{1-D};q^2)_D }\n {a^{2D} (a^2; q^2)_D \\, (q^2; q^2)_D \\, (a^{-1} q^{1-D}; q^2)_D}.$$\n\nBy Lemmas \\[lem:ki3\\] and \\[lem:nuki\\].", "\n\n\\[lem:sumkiti4\\] . ", "We have $$\\begin{aligned}\n \\sum_{i=0}^D {{\\sf k}}_i \\tau_i &= \n \\frac{ (a^{-2}; q^2)_D } { (a q^{1-D}; q^2)_D }. ", " $$\n\nBy Lemmas \\[lem:sumkiti\\] and \\[lem:nuki\\].", "\n\nWe have been discussing the $q$-Racah case. ", "For a discussion of the non $q$-Racah cases, see [@CN:someformula].", "\n\nFrom spin Leonard pairs to a spin model {#sec:spinLPtospinmodel}\n=======================================\n\nIn Sections \\[sec:spindrg\\], \\[sec:spinqRacah\\] we considered a distance-regular graph $\\Gamma$ that affords a spin model ${{\\sf W}}$. We used ${{\\sf W}}$ to construct a family of spin Leonard pairs. ", "We now reverse the logical direction, and obtain a spin model afforded by $\\Gamma$ from some spin Leonard pairs. ", "In this section we work with general $\\Gamma$, and in the next section we consider the $q$-Racah case. ", "For this section our main results are Theorems \\[thm:main0\\] and \\[thm:main\\].", "\n\nLet $\\Gamma$ denote a distance-regular graph with vertex set $X$ and diameter $D \\geq 1$. Recall the distance-matrices $\\{{{\\sf A}}_i\\}_{i=0}^D$ and the primitive idempotents $\\{{{\\sf E}}_i\\}_{i=0}^D$ in the Bose-Mesner algebra ${{\\sf M}}$ of $\\Gamma$. Assume that $\\Gamma$ is formally self-dual with respect to $\\{{{\\sf E}}_i\\}_{i=0}^D$. For $x \\in X$, consider the dual Bose-Mesner algebra ${{\\sf M}}^*(x)$ and the Terwilliger algebra ${{\\sf T}}(x)$. For $0 \\leq i \\leq D$ we have the elements ${{\\sf E}}^*_i(x)$ and ${{\\sf A}}^*_i(x)$ from the paragraph below Lemma \\[lem:Pij\\]. ", "Let $f$, $\\{\\tau_i\\}_{i=0}^D$ denote nonzero scalars in ${\\mathbb{C}}$ such that $\\tau_0 = 1$. Define $${{\\sf W}}= f \\sum_{i=0}^D \\tau_i {{\\sf E}}_i. ", " $$ For $x \\in X$ define $${{\\sf W}}^*(x) = f \\sum_{i=0}^D \\tau_i {{\\sf E}}^*_i(x). ", " \\label{eq:defWs}$$ Note that ${{\\sf W}}$ and ${{\\sf W}}^*(x)$ are invertible. ", "For the rest of this section, we make the following assumption.", "\n\n\\[assump0\\] . ", "Assume that for all $x \\in X$ and all irreducible ${{\\sf T}}(x)$-modules $U$,\n\n- $U$ is thin;\n\n- $U$ has the same endpoint and dual-endpoint;\n\n- the pair ${{\\sf A}}_1, {{\\sf A}}^*_1(x)$ acts on $U$ as a spin Leonard pair, and ${{\\sf W}}, {{\\sf W}}^*(x)$ acts on $U$ as a balanced Boltzmann pair for this spin Leonard pair;\n\n- $f$ satisfies .", "\n\nUnder Assumption \\[assump0\\] we show that ${{\\sf W}}$ is a spin model afforded by $\\Gamma$. From now until the beginning of Theorem \\[thm:main\\], fix $x \\in X$ and abbreviate ${{\\sf W}}^* = {{\\sf W}}^*(x)$, ${{\\sf T}}= {{\\sf T}}(x)$ and ${{\\sf E}}^*_i = {{\\sf E}}^*_i (x)$, ${{\\sf A}}^*_i = {{\\sf A}}^*_i (x)$ for $0 \\leq i \\ \\leq D$.\n\n\\[lem:type2pre\\] . ", "We have $$\\begin{aligned}\n {{\\sf W}}&= |X|^{1/2} f^{-1} \\sum_{i=0}^D \\tau_i^{-1} {{\\sf A}}_i, &\n {{\\sf W}}^{-1} &= |X|^{-3/2} f \\sum_{i=0}^D \\tau_i {{\\sf A}}_i. ", " \\label{eq:WWinv2}\\end{aligned}$$\n\nWe first show that holds on the primary ${{\\sf T}}$-module ${{\\sf U}}$. By Proposition \\[prop:DRGsd\\](i), (iii) the sequence $$({{\\sf A}}_1; \\{{{\\sf E}}_i\\}_{i=0}^D; {{\\sf A}}^*_1; \\{{{\\sf E}}^*_i\\}_{i=0}^D) \\label{eq:LS6}$$ acts on ${{\\sf U}}$ as a self-dual Leonard system. ", "Let $\\sigma : \\text{\\rm End}({{\\sf U}}) \\to \\text{\\rm End}({{\\sf U}})$ denote the duality of this Leonard system. ", "So $\\sigma$ swaps the action of ${{\\sf A}}_1$, ${{\\sf A}}^*_1$ on ${{\\sf U}}$, and swaps the action of ${{\\sf E}}_i$, ${{\\sf E}}^*_i$ on ${{\\sf U}}$ for $0 \\leq i \\leq D$. By Assumption \\[assump0\\](iii), ${{\\sf A}}_1, {{\\sf A}}^*_1$ acts on ${{\\sf U}}$ as a spin Leonard pair, and ${{\\sf W}}, {{\\sf W}}^*$ acts on ${{\\sf U}}$ as a balanced Boltzmann pair for this Leonard pair. ", "In Lemmas \\[lem:PSL\\], \\[lem:PSL2\\] we used this Boltzmann pair to obtain a duality for this Leonard pair, which must coincide with the above duality $\\sigma$ by the uniqueness of the duality. ", "By this and , we find that the results below in Section \\[sec:spinLP\\] apply to the Leonard system on ${{\\sf U}}$. Apply Theorem \\[thm:WtiinvAi\\], Lemma \\[lem:piW\\] and to this Leonard system, and use Lemmas \\[lem:nu3\\], \\[lem:AiEs0E03\\], \\[lem:nuki\\] to show that holds on ${{\\sf U}}$. The result follows in view of Corollary \\[cor:faithful\\].", "\n\n\\[lem:type2\\] . ", "The matrix ${{\\sf W}}$ is type II.", "\n\nWe invoke Lemma \\[lem:type2W-\\]. ", "By construction ${{\\sf W}}$ is symmetric. ", "Each entry of ${{\\sf W}}$ is nonzero by the equation on the left in . ", "By that equation and we obtain $${{\\sf W}}^- = |X|^{-1/2} f \\sum_{i=0}^D \\tau_i {{\\sf A}}_i. ", " \\label{eq:W-}$$ Comparing with the equation on the right in , we obtain ${{\\sf W}}^{-} = |X| {{\\sf W}}^{-1}$. Therefore ${{\\sf W}}{{\\sf W}}^- = |X| I$. The result follows by Lemma \\[lem:type2W-\\].", "\n\n\\[lem:WWsW\\] . ", "We have $${{\\sf W}}{{\\sf W}}^* {{\\sf W}}= {{\\sf W}}^* {{\\sf W}}{{\\sf W}}^*. ", " \\label{eq:WWsW}$$\n\nBy Assumption \\[assump0\\](iii) the pair ${{\\sf W}}, {{\\sf W}}^*$ acts on each irreducible ${{\\sf T}}$-module as a balanced Boltzmann pair. ", "The result follows in view of Lemma \\[lem:decomp\\](i).", "\n\n\\[lem:WsW-\\] . ", "For $y \\in X$, $$\\begin{aligned}\n {{\\sf W}}^* (y,y) &= \\frac{ |X|^{1/2} } {{{\\sf W}}(x,y)} . ", " $$\n\nLet $i = \\partial (x,y)$. By we obtain ${{\\sf W}}^*(y,y) = f \\tau_i$. By the equation on the left in we obtain ${{\\sf W}}(x,y ) = |X|^{1/2} f^{-1} \\tau_i^{-1}$. The result follows.", "\n\n\\[lem:type3\\] . ", "For $a,b \\in X$, $$\\sum_{y \\in X} \\frac{{{\\sf W}}(a,y) {{\\sf W}}(b,y) } { {{\\sf W}}(x,y) }\n = |X|^{1/2} \\, \\frac{ {{\\sf W}}(a,b) } { {{\\sf W}}(a,x) {{\\sf W}}(b,x) } .$$\n\nFor each side of , compute the $(a,b)$-entry and evaluate the result using Lemma \\[lem:WsW-\\]. ", "Here are some details: $$\\begin{aligned}\n ({{\\sf W}}{{\\sf W}}^* {{\\sf W}})(a,b)\n &= \\sum_{y \\in X} {{\\sf W}}(a,y) {{\\sf W}}^*(y,y) {{\\sf W}}(y,b) \n\\\\\n &= |X|^{1/2} \\,\\sum_{y \\in X} \\frac{{{\\sf W}}(a,y) {{\\sf W}}(b,y)}{{{\\sf W}}(x,y)},\\end{aligned}$$ and $$\\begin{aligned}\n ({{\\sf W}}^* {{\\sf W}}{{\\sf W}}^*)(a,b)\n &= {{\\sf W}}^*(a,a) {{\\sf W}}(a,b) {{\\sf W}}^*(b,b)\n\\\\\n &= |X| \\, \\frac{{{\\sf W}}(a,b)}{{{\\sf W}}(a,x) {{\\sf W}}(b,x)}.\\end{aligned}$$\n\n\\[thm:main0\\] . ", "The matrix ${{\\sf W}}$ is a spin model.", "\n\nThe matrix ${{\\sf W}}$ satisfies the requirements of Definition \\[def:spin\\] by Lemmas \\[lem:type2\\] and \\[lem:type3\\].", "\n\nNext we show that the spin model ${{\\sf W}}$ is afforded by $\\Gamma$.\n\n\\[lem:WWsbEi\\] . ", "For $0 \\leq i \\leq D$, $${{\\sf W}}{{\\sf W}}^* {{\\sf E}}_i = {{\\sf E}}^*_i {{\\sf W}}{{\\sf W}}^*. ", " \\label{eq:WWsEiEsiWWs}$$\n\nLet $U$ denote an irreducible ${{\\sf T}}$-module with endpoint $r$ and diameter $d$. By Assumption \\[assump0\\](i), (ii) we see that $U$ is thin with dual endpoint $r$. By these comments and Lemma \\[lem:U\\] the sequence $$({{\\sf A}}_1; \\{{{\\sf E}}_{r+j}\\}_{j=0}^d; {{\\sf A}}^*_1; \\{{{\\sf E}}^*_{r+j} \\}_{j=0}^d)$$ acts on $U$ as a Leonard system. ", "By Assumption \\[assump0\\](iii) the pair ${{\\sf W}}, {{\\sf W}}^*$ acts $U$ as a balanced Boltzmann pair for the Leonard pair ${{\\sf A}}_1, {{\\sf A}}^*_1$ on $U$. By these comments and Lemma \\[lem:EiWsW\\], $$\\begin{aligned}\n {{\\sf W}}{{\\sf W}}^* {{\\sf E}}_{r+j} &= {{\\sf E}}^*_{r+j} {{\\sf W}}{{\\sf W}}^* \\end{aligned}$$ holds on $U$ for $0 \\leq j \\leq d$. Thus holds on each irreducible ${{\\sf T}}$-module. ", "Now holds by Lemma \\[lem:decomp\\](i).", "\n\n\\[thm:main\\] . ", "The spin model ${{\\sf W}}$ is afforded by $\\Gamma$.\n\nBy Definition \\[def:afford\\] we must show that ${{\\sf W}}\\in {{\\sf M}}\\subseteq N({{\\sf W}})$. By construction ${{\\sf W}}\\in {{\\sf M}}$. To obtain ${{\\sf M}}\\subseteq N({{\\sf W}})$, we show that for all $b,c \\in X$ the vector $\\text{\\bf u}_{b,c}$ is contained in ${{\\sf E}}_i {{\\sf V}}$, where $i = \\partial (b,c)$. Using Definition \\[def:NW\\] and Lemma \\[lem:WsW-\\], $$\\text{\\bf u}_{b,c} = ({{\\sf W}}^*(b))^{-1} {{\\sf W}}^* (c) \\text{\\bf 1}\n = ({{\\sf W}}{{\\sf W}}^*(b))^{-1} {{\\sf W}}{{\\sf W}}^*(c) \\text{\\bf 1}.$$ Using Lemma \\[lem:WWsbEi\\] with $i=0$, $${{\\sf W}}{{\\sf W}}^*(c) \\text{\\bf 1} \\in {{\\sf W}}{{\\sf W}}^*(c) {{\\sf E}}_0 {{\\sf V}}= {{\\sf E}}^*_0 (c) {{\\sf W}}{{\\sf W}}^*(c) {{\\sf V}}= {{\\sf E}}^*_0 (c) {{\\sf V}}= \\text{\\rm Span} \\{\\widehat{c} \\} \\subseteq {{\\sf E}}^*_i(b) {{\\sf V}}.$$ By the above comments and Lemma \\[lem:WWsbEi\\], $$\\text{\\bf u}_{b,c} \\in ({{\\sf W}}{{\\sf W}}^*(b))^{-1} {{\\sf E}}^*_i (b) {{\\sf V}}= {{\\sf E}}_i ({{\\sf W}}{{\\sf W}}^*(b))^{-1} {{\\sf V}}= {{\\sf E}}_i {{\\sf V}}.$$ We have shown that $\\text{\\bf u}_{b,c}$ is contained in ${{\\sf E}}_i {{\\sf V}}$ and is therefore a common eigenvector for ${{\\sf M}}$. So ${{\\sf M}}\\subseteq N({{\\sf W}})$ in view of Definition \\[def:NW\\]. ", "The result follows.", "\n\nFrom spin Leonard pairs to a spin model; the $q$-Racah case {#sec:construction}\n===========================================================\n\nIn this section we start with a suitable distance-regular graph $\\Gamma$ of $q$-Racah type, and obtain a spin model afforded by $\\Gamma$. The result is given in Theorem \\[thm:main3\\].", "\n\nLet $\\Gamma$ denote a distance-regular graph with vertex set $X$, diameter $D \\geq 1$, and intersection numbers $\\{{{\\sf c}}_i\\}_{i=1}^D$, $\\{{{\\sf a}}_i\\}_{i=0}^D$, $\\{{{\\sf b}}_i\\}_{i=0}^{D-1}$. Recall the distance-matrices $\\{{{\\sf A}}_i\\}_{i=0}^D$ and primitive idempotents $\\{{{\\sf E}}_i\\}_{i=0}^D$ in the Bose-Mesner algebra ${{\\sf M}}$ of $\\Gamma$. Throughout this section we make the following assumptions.", "\n\n\\[assump\\] . ", "Assume that $\\Gamma$ is formally self-dual with respect to $\\{{{\\sf E}}_i\\}_{i=0}^D$, with eigenvalue sequence $\\{{\\theta}_i\\}_{i=0}^D$. Assume that there exist nonzero scalars $a$, $q \\in {\\mathbb{C}}$ that satisfy – and – with $\\alpha$, $\\beta$ from , . ", "Assume that for all $x \\in X$ and all irreducible ${{\\sf T}}(x)$-modules $U$,\n\n- $U$ is thin;\n\n- $U$ has the same endpoint and dual-endpoint;\n\n- the intersection numbers $\\{c_i(U)\\}_{i=1}^d$, $\\{b_i(U)\\}_{i=0}^{d-1}$ satisfy –.", "\n\nUnder Assumption \\[assump\\] we construct a spin model ${{\\sf W}}$ that is afforded by $\\Gamma$.\n\n\\[def:main3\\] . ", "Define scalars $\\{\\tau_i\\}_{i=0}^D$ in ${\\mathbb{C}}$ by $$\\begin{aligned}\n \\tau_i &= (-1)^i a^{-i} q^{i(D-i)} && (0 \\leq i \\leq D). ", " \\label{eq:ti3}\\end{aligned}$$ Define $f \\in {\\mathbb{C}}$ such that $$f^2 = \\frac{ |X|^{3/2} (a q^{1-D}; q^2)_D } \n { (a^{-2}; q^2)_D }. ", " \\label{eq:f}$$ Note that $f$, $\\{\\tau_i\\}_{i=0}^D$ are nonzero. ", "Define $${{\\sf W}}= f \\sum_{i=0}^D \\tau_i E_i. ", " $$\n\nWe are going to show that ${{\\sf W}}$ is a spin model afforded by $\\Gamma$. Fix $x \\in X$ and abbreviate ${{\\sf T}}= {{\\sf T}}(x)$ and ${{\\sf E}}^*_i = {{\\sf E}}^*_i (x)$, ${{\\sf A}}^*_i = {{\\sf A}}^*_i (x)$ for $0 \\leq i \\leq D$. Recall the scalars $\\alpha$, $\\beta$ from , . ", "Define ${{\\sf A}}\\in {{\\sf M}}$ and ${{\\sf A}}^* \\in {{\\sf M}}^*$ such that $$\\begin{aligned}\n {{\\sf A}}_1 &= \\alpha {{\\sf A}}+ \\beta {{\\sf I}}, &\n {{\\sf A}}^*_1 &= \\alpha {{\\sf A}}^* + \\beta {{\\sf I}}. ", " \\label{eq:defAAs}\\end{aligned}$$ Let $U$ denote an irreducible ${{\\sf T}}$-module with endpoint $r$ and diameter $d$. By Lemma \\[lem:U\\] and since $U$ is thin, each of the sequences $$\\begin{aligned}\n \\Phi &= ({{\\sf A}}_1; \\{{{\\sf E}}_{r+i}\\}_{i=0}^d; {{\\sf A}}^*_1 ; \\{{{\\sf E}}^*_{r+i}\\}_{i=0}^d),\n\\\\\n \\widetilde{\\Phi} &= ({{\\sf A}}; \\{{{\\sf E}}_{r+i}\\}_{i=0}^d; {{\\sf A}}^* ; \\{{{\\sf E}}^*_{r+i}\\}_{i=0}^d)\\end{aligned}$$ acts on $U$ as a Leonard system. ", "By construction these Leonard systems are self-dual.", "\n\n\\[lem:tPhi\\] . ", "The Leonard system $\\widetilde{\\Phi}$ on $U$ has $q$-Racah type with Huang data $$( a q^{2r+d-D}, a q^{2r+d-D}, a q^{2r+d-D}, d). ", " \\label{eq:Huangdata}$$\n\nBy [@Huang Lemma 7.3] there exists a Leonard system $\\Psi$ of $q$-Racah type with Huang data . ", "By Lemma \\[lem:selfdualab\\] this Leonard system is self-dual. ", "The eigenvalue sequence and intersection numbers of $\\Psi$ are obtained using Definition \\[def:Huangdata\\] and Lemma \\[lem:qRacahbi\\]. ", "The eigenvalue sequence and intersection numbers of $\\Phi$ on $U$ are given in Assumption \\[assump\\]. ", "Adjusting these using we obtain the eigenvalue sequence and intersection numbers of $\\widetilde{\\Phi}$ on $U$. These match the eigenvalue sequence and intersection numbers of $\\Psi$. By Lemmas \\[lem:isomorphic\\], \\[lem:parray\\] the Leonard system $\\Psi$ is isomorphic to the Leonard system $\\widetilde{\\Phi}$ on $U$. The result follows.", "\n\nDefine $$\\begin{aligned}\n {{\\sf W}}^* &= f \\sum_{i=0}^D \\tau_i {{\\sf E}}^*_i.\\end{aligned}$$\n\n\\[lem:WWs3\\] . ", "On $U$ we have $$\\begin{aligned}\n {{\\sf W}}&= f \\tau_r \\sum_{i=0}^d \\widetilde{\\tau}_i {{\\sf E}}_{r+i}, &\n {{\\sf W}}^* &= f \\tau_r \\sum_{i=0}^d \\widetilde{\\tau}_i {{\\sf E}}^*_{r+i}, \\label{eq:WWsaux}\\end{aligned}$$ where $\\{\\widetilde{\\tau}_i\\}_{i=0}^d$ are from .", "\n\nSimilar to the proof of Lemma \\[lem:WonU\\].", "\n\n\\[lem:spinLP\\] . ", "The pair ${{\\sf A}}_1, {{\\sf A}}^*_1$ acts on $U$ as a spin Leonard pair, and the pair ${{\\sf W}}, {{\\sf W}}^*$ acts on $U$ as a balanced Boltzmann pair of this Leonard pair.", "\n\nBy Lemmas \\[lem:spinLP0\\](ii), \\[lem:tPhi\\] the pair ${{\\sf A}}, {{\\sf A}}^*$ acts on $U$ as a spin Leonard pair. ", "By and Lemmas \\[lem:W\\](ii), \\[lem:WWs3\\] the pair ${{\\sf W}},{{\\sf W}}^*$ acts on $U$ as a balanced Boltzmann pair for the Leonard pair ${{\\sf A}},{{\\sf A}}^*$ on $U$. The result follows in view of Lemma \\[lem:affine\\].", "\n\nRecall the integers $\\{{{\\sf k}}_i\\}_{i=0}^D$ from .", "\n\n\\[lem:f2\\] . ", "The scalar $f$ from Definition \\[def:main3\\] satisfies $$f^{-2} = |X|^{-3/2} \\sum_{i=0}^D {{\\sf k}}_i \\tau_i.$$\n\nBy Lemma \\[lem:tPhi\\] the sequence $$({{\\sf A}}; \\{{{\\sf E}}_i\\}_{i=0}^D; {{\\sf A}}^*; \\{{{\\sf E}}^*_i\\}_{i=0}^D)$$ acts on the primary ${{\\sf T}}$-module ${{\\sf U}}$ as a Leonard system of $q$-Racah type with Huang data $(a,a,a,D)$. Applying Lemma \\[lem:sumkiti\\] to this Leonard system we obtain $$\\sum_{i=0}^D {{\\sf k}}_i \\tau_i \n = \\frac{ (a^{-2}; q^2)_D }\n { (a q^{1-D}; q^2 )_D }. ", " \\label{eq:f2aux2}$$ The result follows from and .", "\n\n\\[thm:main3\\] . ", "The matrix ${{\\sf W}}$ in Definition \\[def:main3\\] is a spin model afforded by $\\Gamma$.\n\nFor $x \\in X$ let $U$ denote an irreducible ${{\\sf T}}(x)$-module. ", "By Lemmas \\[lem:affine\\] and \\[lem:spinLP\\] the pair ${{\\sf A}}_1, {{\\sf A}}^*_1(x)$ acts on $U$ as a spin Leonard pair, and ${{\\sf W}}, {{\\sf W}}^*(x)$ acts on $U$ as a balanced Boltzmann pair for this Leonard pair. ", "By Lemma \\[lem:f2\\] the scalar $f$ satisfies . ", "Thus Assumption \\[assump0\\] is satisfied. ", "Now ${{\\sf W}}$ is a spin model by Theorem \\[thm:main0\\]. ", "This spin model is afforded by $\\Gamma$ by Theorem \\[thm:main\\].", "\n\nThe spin model ${{\\sf W}}$ in Theorem \\[thm:main3\\] does not have Hadamard type, since $\\tau_1 \\neq \\pm \\tau_0$ by and .", "\n\nExamples {#sec:example}\n========\n\nThe article [@CN:someformula Section 9] includes a list of the known spin models that are contained in the Bose-Mesner algebra of a distance-regular graph $\\Gamma$. In this section we display the listed spin models for which $\\Gamma$ has $q$-Racah type. ", "Each displayed example satisfies the requirements of Assumption \\[assump\\]. ", "For each displayed example we describe $\\Gamma$, and give the parameters $q$, $a$ that satisfy –, –. ", "We now display the examples. ", "The presentation of the display is explained in Example 0.", "\n\n- Name of the graph $\\Gamma$ \\[Reference to definition\\].", "\n\n - diameter $D$, intersection numbers $\\{{{\\sf b}}_0, \\ldots, {{\\sf b}}_{D-1}; {{\\sf c}}_1, \\ldots, {{\\sf c}}_D\\}$, number of vertices $|X|$.\n\n - parameters $q$, $a$.\n\n- Complete graph $K_n$ $(n \\geq 2)$ [@BCN Appendix A1].", "\n\n - $D = 1$, $\\{n-1; 1\\}$, $|X|=n$.\n\n - $q$ is any nonzero complex number such that $q^4 \\neq 1$, and $a$ is any complex number such that $a \\neq 1$ and $a+a^{-1}=n-2$.\n\n- $4$-cycle $C_4$.\n\n - $D=2$, $\\{2,1; 1,2\\}$, $|X|=4$.\n\n - $q$ is any nonzero complex number such that $q^4 \\neq 1$, and $a$ is any complex number such that $a^2=-1$.\n\n- Higman-Sims graph [@HS].", "\n\n - $D=2$, $\\{22,21; 1, 6\\}$, $|X|=100$.\n\n - $q$ is any complex number such that $q^2+ q^{-2}=-3$, and $a = - q^{-3}$.\n\n- Hadamard graph $H_m$ $(m \\geq 2)$ [@Ito].", "\n\n - $D=4$, $\\{4m, 4m-1, 2m, 1; 1, 2m, 4m-1,4m\\}$, $|X|=16m$.\n\n - $q$ is any complex number such that $q^4+q^{-4}=4m-2$, and $a$ is any complex number such that $a^2=-1$.\n\n- Double cover of the Higman-Sims graph [@BCN Appendix A.5].", "\n\n - $D=5$, $\\{22,21,16,6,1;1,6,16,21,22\\}$, $|X|=200$.\n\n - $q$ is any complex number such that $q^2+q^{-2}=3$, and $a$ is any complex number such that $a^2= -1$.\n\n- Odd cycle $C_{2m+1}$ $(m \\geq 2)$.\n\n - $D=m$, $\\{2,1, \\ldots, 1; 1,1, \\ldots,1\\}$, $|X|=2m+1$.\n\n - $q \\in {\\mathbb{C}}$ is any primitive $2m+1$ root of unity, and $a= - q^m$.\n\n- Even cycle $C_{2m}$ $(m \\geq 3)$.\n\n - $D=m$, $\\{2,1,\\ldots,1; 1,\\ldots,1,2\\}$, $|X|=2m$.\n\n - $q \\in {\\mathbb{C}}$ is any primitive $4m$ root of unity, and $a$ is any complex number such that $a^2= -1$.\n\nBy Theorem \\[thm:main3\\], for each of the above Examples (1)–(7), the matrix ${{\\sf W}}$ from Definition \\[def:main3\\] is a spin model afforded by $\\Gamma$.\n\n[10]{}\n\nR.C. Alperin, $\\text{\\rm PSL}_2(\\mathbb{Z}) = \\mathbb{Z}_2 \\star \\mathbb{Z}_3$, Amer.", " Math.", " Monthly 100 (1993) 385–386.", "\n\nE. Bannai, Et.", " Bannai, Spin models on finite cyclic groups, J. Algebraic Combin.", " 3 (1994) 243–259.", "\n\nE. Bannai, T. Ito, Algebraic Combinatorics I, Association Schemes, Benjamin/Cummings Publishing Co. Inc., Menlo Park, CA, 1984.", "\n\nA.E. Brower, A.M. Cohen, A. Neumaier, Distance-Regular Graphs, Springer-Verlag, Berlin, 1989.", "\n\nJ.S. Caughman IV, N.Wolff, The Terwilliger algebra of a distance-regular graph that supports a spin model, J. Algebraic Combin.", " 21 (2005) 289–310.", "\n\nB. Curtin, Distance-regular graphs which support a spin model are thin, Discrete Math.", " 197/198 (1999) 205–216.", "\n\nB. Curtin, Spin Leonard pairs, Ramanujan J. 13 (2007) 319–332.", "\n\nB. Curtin, K. Nomura, Some formulas for spin models on distance-regular graphs, J. Combin.", " Theory B 75 (1999) 206–236.", "\n\nB. Curtin, K. Nomura, Spin models and strongly hyper-self-dual Bose-Mesner algebras, J. Alg.", " Combin.", " 13 (2001) 173–186.", "\n\nE.R. van Dam, J.H. Koolen, H. Tanaka, Distance-regular graphs, Electronic J. Combinatorics DS22 Apr 15, 2016.", "\n\nG. Gasper, M. Rahman, Basic Hypergeometric Series, Encyclopedia of Mathematics and Its Applications 96, Cambrigde University Press, 2004.", "\n\nD.G. Higman, C.C. Sims, A simple group of order 44,352,000, Math.", " Zeitschr.", " 105 (1968) 110–113.", "\n\nH. Huang, The classification of Leonard triples of QRacah type, Linear Algebra Appl. ", "436 (2012) 1442–1472.", "\n\nN. Ito, Hadamard graphs, I, Graphs and Combinatorics 1 (1985) 57–64.", "\n\nF. Jaeger, Strongly regular graphs and spin modles for the Kauffman polynomial, Geom. ", "Dedicata 44 (1992) 23–52.", "\n\nF. Jaeger, M. Matsumoto, K. Nomura, Bose-Mesner algebras related with type II matrices and spin models, J. Alg.", " Combin.", " 8 (1998) 39–72.", "\n\nV.F.R. Jones, On knot invariants related to some statistical mechanical models, Pacific J. Math.", " 137 (1989) 311–336.", "\n\nK. Kawagoe, A. Munemasa, Y. Watatani, Generalized spin models, J. Knot Theory and its Ramifications 3 (1994) 465–475.", "\n\nA. Munemasa, private communication.", "\n\nK. Nomura, Spin models constructed from Hadamard matrices, J. Combin.", " Theory (A) 68 (1994) 251–261.", "\n\nK. Nomura, An algebra associated with a spin model, J. Alg.", " Combin.", " 6 (1997) 53–58.", "\n\nK. Nomura, P. Terwilliger, Linear transformations that are tridiagonal with respect to both eigenbases of a Leonard pair, Linear Algebra Appl.", " 420 (2007) 198–207.", "\n\nK. Nomura, P. Terwilliger, Affine transformations of a Leonard pair, Electron. ", "J. Linear Algebra 16 (2007) 389-418.", "\n\nJ. Rotman, Advanced Modern Algebra, 2nd edition, AMS, Providence, RI, 2010.", "\n\nP. Terwilliger, The subconstituent algebra of an association scheme I, J. Algebraic Combin. ", "1 (1992) 363–388.", "\n\nP. Terwilliger, Two linear transformations each tridiagonal with respect to an eigenbasis of the other, [*Linear Algebra Appl.*]{} [**", "330**]{} (2001), 149–203.", "\n\nP. Terwilliger, Leonard pairs and the $q$-Racah polynomials, Linear Algebra Appl.", " 387 (2004) 235–276.", "\n\nP. Terwilliger, An algebraic approach to the Askey scheme of orthogonal polynomials, Orthogonal polynomials and special functions, Lecture Notes in Math., ", "1883, Springer, Berlin, 2006, pp. ", "255–330; [arXiv:math/0408390]{}.", "\n\nDistance-regular graphs of $q$-Racah type and the universal Askey-Wilson algebra, J. Combin.", " Theory (A) 125 (2014) 98–112.", "\n\nKazumasa Nomura\\\nTokyo Medical and Dental University\\\nKohnodai, Ichikawa, 272-0827, Japan\\\nEmail: knomura@pop11.odn.ne.jp\n\nPaul Terwilliger\\\nDepartment of Mathematics\\\nUniversity of Wisconsin\\\n480 Lincoln Drive\\\nMadison, WI 53706, USA\\\nEmail: terwilli@math.wisc.edu\n\n[**Keywords.**]{} ", "Leonard pair, spin model, distance-regular graph, Bose-Mesner algebra\\\n[**2010 Mathematics Subject Classification.**]{} ", "05E30, 15A21\n" ]

{ "pile_set_name": "ArXiv" }

[ 0.005988023952095809, 0, 0.011363636363636364, 0.007692307692307693, 0.014492753623188406, 0.011655011655011656, 0, 0, 0.0125, 0.016129032258064516, 0, 0, 0, 0.007662835249042145, 0.03669724770642202, 0, 0, 0.020224719101123594, 0.0136986301369863, 0.011254019292604502, 0, 0, 0.008583690987124463, 0.007751937984496124, 0.007462686567164179, 0.00199203187250996, 0.0072992700729927005, 0.013888888888888888, 0, 0, 0, 0.013054830287206266, 0.012195121951219513, 0.008547008547008548, 0.0032679738562091504, 0.009174311926605505, 0.009433962264150943, 0, 0.0030864197530864196, 0.02030456852791878, 0.014285714285714285, 0.018518518518518517, 0.007272727272727273, 0.028846153846153848, 0.008264462809917356, 0.015384615384615385, 0, 0.008695652173913044, 0.004830917874396135, 0, 0.023809523809523808, 0, 0, 0, 0.012048192771084338, 0.009900990099009901, 0, 0, 0.02127659574468085, 0, 0.034482758620689655, 0.018867924528301886, 0.021739130434782608, 0, 0, 0, 0, 0.01818181818181818, 0.013333333333333334, 0.01818181818181818, 0.013333333333333334, 0.013071895424836602, 0.017857142857142856, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0106951871657754, 0.0022271714922048997, 0.017142857142857144, 0.008, 0.01060070671378092, 0.004878048780487805, 0.009584664536741214, 0.024390243902439025, 0.02262443438914027, 0.008403361344537815, 0.0078125, 0, 0.0032858707557502738, 0, 0, 0, 0.0015220700152207, 0.007889546351084813, 0, 0.0043859649122807015, 0, 0, 0.008368200836820083, 0, 0.014925373134328358, 0.01694915254237288, 0.006024096385542169, 0.011844331641285956, 0, 0, 0, 0, 0, 0, 0.00510204081632653, 0, 0.0053475935828877, 0.013986013986013986, 0.007407407407407408, 0.003355704697986577, 0.00801068090787717, 0.010078387458006719, 0, 0.018867924528301886, 0.0136986301369863, 0, 0, 0, 0, 0.00558659217877095, 0.02127659574468085, 0.016587677725118485, 0.006172839506172839, 0, 0.014084507042253521, 0.005115089514066497, 0, 0.0017825311942959, 0.006756756756756757, 0, 0.00904977375565611, 0, 0, 0.002028397565922921, 0, 0, 0.014285714285714285, 0, 0, 0.004048582995951417, 0, 0.020905923344947737, 0, 0.01935483870967742, 0.015151515151515152, 0, 0, 0.008048289738430584, 0, 0, 0.005660377358490566, 0.02040816326530612, 0.014814814814814815, 0.007575757575757576, 0.013888888888888888, 0, 0, 0.04054054054054054, 0, 0.02702702702702703, 0.005434782608695652, 0, 0.011494252873563218, 0, 0.01694915254237288, 0.015625, 0.006688963210702341, 0, 0, 0.003745318352059925, 0, 0.010362694300518135, 0.0030303030303030303, 0, 0, 0.0196078431372549, 0, 0, 0.02127659574468085, 0, 0.013157894736842105, 0, 0.01694915254237288, 0, 0.0136986301369863, 0, 0.013333333333333334, 0, 0, 0, 0.007662835249042145, 0.010050251256281407, 0.0041841004184100415, 0.005714285714285714, 0.007518796992481203, 0, 0.03508771929824561, 0.010471204188481676, 0.009375, 0, 0.017543859649122806, 0.013333333333333334, 0.011673151750972763, 0.013333333333333334, 0, 0.04411764705882353, 0.017857142857142856, 0, 0.03125, 0.00684931506849315, 0, 0, 0.03225806451612903, 0, 0, 0.024154589371980676, 0, 0.010135135135135136, 0.008944543828264758, 0.002004008016032064, 0, 0, 0.024691358024691357, 0, 0.0058823529411764705, 0.01639344262295082, 0, 0.008064516129032258, 0, 0.008032128514056224, 0.020833333333333332, 0, 0, 0, 0.013157894736842105, 0.008888888888888889, 0, 0.014336917562724014, 0.014492753623188406, 0.023255813953488372, 0.014545454545454545, 0.003125, 0.01818181818181818, 0.025974025974025976, 0, 0.011363636363636364, 0.009345794392523364, 0, 0.019417475728155338, 0, 0.020134228187919462, 0, 0, 0.015384615384615385, 0, 0, 0, 0, 0.006968641114982578, 0, 0.011450381679389313, 0.021739130434782608, 0.00796812749003984, 0.008064516129032258, 0.017857142857142856, 0, 0, 0.007142857142857143, 0.011627906976744186, 0.014705882352941176, 0.04819277108433735, 0.014598540145985401, 0.027777777777777776, 0.011834319526627219, 0, 0, 0.015789473684210527, 0, 0, 0.008350730688935281, 0, 0.012307692307692308, 0.02702702702702703, 0.03125, 0.009615384615384616, 0.015873015873015872, 0, 0, 0, 0.013392857142857142, 0, 0, 0.02197802197802198, 0, 0.015444015444015444, 0, 0.00437636761487965, 0, 0.009950248756218905, 0, 0.0038314176245210726, 0.021052631578947368, 0.018867924528301886, 0.00819672131147541, 0.01818181818181818, 0, 0.03007518796992481, 0, 0.022727272727272728, 0, 0, 0.008928571428571428, 0.008620689655172414, 0.02564102564102564, 0.010752688172043012, 0.005988023952095809, 0, 0, 0, 0, 0.0051813471502590676, 0, 0.005208333333333333, 0.013888888888888888, 0, 0.019230769230769232, 0.011627906976744186, 0.01282051282051282, 0, 0, 0.005208333333333333, 0, 0.003663003663003663, 0, 0.0045662100456621, 0.006535947712418301, 0, 0.030303030303030304, 0, 0.018867924528301886, 0, 0, 0, 0, 0.017094017094017096, 0, 0.013157894736842105, 0, 0.011235955056179775, 0, 0.040697674418604654, 0.014084507042253521, 0, 0.02127659574468085, 0, 0.027777777777777776, 0, 0.007518796992481203, 0.006756756756756757, 0.00980392156862745, 0, 0, 0, 0, 0, 0, 0.026490066225165563, 0, 0.010309278350515464, 0, 0.007662835249042145, 0, 0, 0, 0, 0, 0, 0.014285714285714285, 0.008264462809917356, 0, 0.013333333333333334, 0.01834862385321101, 0.006578947368421052, 0.014925373134328358, 0.010362694300518135, 0.02040816326530612, 0, 0.013927576601671309, 0.0034482758620689655, 0, 0.023809523809523808, 0, 0, 0.018469656992084433, 0, 0, 0, 0, 0.012345679012345678, 0.01948051948051948, 0.013605442176870748, 0.01060070671378092, 0.014423076923076924, 0, 0, 0.0012484394506866417, 0, 0, 0.00881057268722467, 0, 0.017142857142857144, 0, 0, 0.035175879396984924, 0, 0, 0.024390243902439025, 0, 0, 0, 0.03278688524590164, 0.013157894736842105, 0, 0.02127659574468085, 0.00881057268722467, 0, 0, 0, 0.01, 0, 0, 0.020242914979757085, 0, 0.009174311926605505, 0.0056657223796034, 0, 0.028169014084507043, 0.015503875968992248, 0, 0, 0, 0.01488833746898263, 0.005780346820809248, 0, 0, 0, 0, 0.004975124378109453, 0, 0, 0.014326647564469915, 0.007594936708860759, 0, 0.012987012987012988, 0, 0.014084507042253521, 0, 0.01675257731958763, 0.03125, 0, 0.006944444444444444, 0.0049504950495049506, 0, 0.015306122448979591, 0.00398406374501992, 0.006493506493506494, 0.007575757575757576, 0.01060070671378092, 0, 0.010638297872340425, 0.012448132780082987, 0, 0, 0, 0.029850746268656716, 0.015384615384615385, 0, 0.029850746268656716, 0.017341040462427744, 0.0036101083032490976, 0.029850746268656716, 0.0196078431372549, 0, 0, 0.029850746268656716, 0.01288659793814433, 0.0084985835694051, 0.021739130434782608, 0.006622516556291391, 0, 0.03278688524590164, 0, 0.013888888888888888, 0, 0.02564102564102564, 0.0196078431372549, 0.013888888888888888, 0.005434782608695652, 0, 0.01675977653631285, 0.012658227848101266, 0, 0.05128205128205128, 0, 0, 0.005836575875486381, 0.022222222222222223, 0.01639344262295082, 0.0056179775280898875, 0, 0, 0.006711409395973154, 0, 0, 0, 0, 0, 0.03731343283582089, 0.0027675276752767526, 0, 0.007220216606498195, 0, 0, 0, 0.007751937984496124, 0.011049723756906077, 0.011194029850746268, 0.0044444444444444444, 0.0075046904315197, 0, 0.004889975550122249, 0.003215434083601286, 0, 0, 0, 0, 0.007936507936507936, 0.029850746268656716, 0, 0.0055762081784386614, 0, 0.014705882352941176, 0.007042253521126761, 0, 0, 0, 0, 0, 0.014545454545454545, 0, 0.003289473684210526, 0, 0.013986013986013986, 0.00641025641025641, 0.001445086705202312, 0, 0.006097560975609756, 0, 0.0030165912518853697, 0, 0, 0.0026954177897574125, 0.002849002849002849, 0.002652519893899204, 0, 0.007736943907156673, 0, 0, 0, 0, 0, 0, 0, 0.012269938650306749, 0, 0, 0.008547008547008548, 0.006289308176100629, 0.003067484662576687, 0, 0, 0, 0, 0.01020408163265306, 0, 0.010101010101010102, 0, 0, 0, 0.012944983818770227, 0.007352941176470588, 0, 0.00823045267489712, 0, 0.0072992700729927005, 0, 0, 0, 0, 0.007936507936507936, 0.015128593040847202, 0, 0.010169491525423728, 0, 0, 0, 0, 0.01818181818181818, 0, 0.009852216748768473, 0, 0.0072992700729927005, 0.0196078431372549, 0.003444316877152698, 0.030303030303030304, 0.009302325581395349, 0, 0, 0.007407407407407408, 0.013071895424836602, 0, 0, 0, 0, 0, 0, 0.0025906735751295338, 0, 0, 0.004166666666666667, 0, 0, 0, 0.015384615384615385, 0.011627906976744186, 0, 0, 0.005154639175257732, 0, 0.0049504950495049506, 0.005714285714285714, 0, 0, 0.0029850746268656717, 0, 0, 0.005076142131979695, 0, 0, 0, 0.013975155279503106, 0, 0, 0.002849002849002849, 0.007142857142857143, 0, 0.005979073243647235, 0.009009009009009009, 0, 0.00819672131147541, 0.006622516556291391, 0.01340033500837521, 0.011494252873563218, 0.015873015873015872, 0, 0.017699115044247787, 0, 0.005050505050505051, 0, 0, 0.009345794392523364, 0.012195121951219513, 0, 0.016666666666666666, 0.009708737864077669, 0, 0, 0, 0, 0, 0, 0, 0.00411522633744856, 0.02097902097902098, 0, 0, 0, 0, 0, 0, 0, 0, 0.014492753623188406, 0, 0.013333333333333334, 0.02097902097902098, 0, 0.006289308176100629, 0, 0, 0, 0.006666666666666667, 0.029411764705882353, 0, 0.018072289156626505, 0.018691588785046728, 0, 0.0056925996204933585, 0.0047562425683709865, 0.005649717514124294, 0, 0, 0, 0.002890173410404624, 0.029411764705882353, 0, 0.012096774193548387, 0.012106537530266344, 0, 0.02127659574468085, 0.013043478260869565, 0.015625, 0.009569377990430622, 0.021897810218978103, 0, 0.016, 0, 0, 0.011049723756906077, 0, 0.008012820512820512, 0, 0, 0.007142857142857143, 0.015384615384615385, 0.014925373134328358, 0, 0.009009009009009009, 0.00398406374501992, 0.019417475728155338, 0.01549053356282272, 0.02040816326530612, 0.026119402985074626, 0.018633540372670808, 0.006002400960384154, 0.0058823529411764705, 0, 0.0064516129032258064, 0.0056657223796034, 0.007633587786259542, 0.022727272727272728, 0, 0.010752688172043012, 0, 0, 0.005555555555555556, 0, 0, 0.02594810379241517, 0, 0, 0, 0, 0.014925373134328358, 0.012987012987012988, 0.008849557522123894, 0, 0, 0.0017123287671232876, 0, 0, 0, 0, 0, 0.011461318051575931, 0.0028011204481792717, 0, 0.0056179775280898875, 0.017543859649122806, 0.007936507936507936, 0.0051813471502590676, 0.011627906976744186, 0, 0.029411764705882353, 0.02857142857142857, 0, 0, 0, 0.018433179723502304, 0, 0, 0.011764705882352941, 0.037037037037037035, 0, 0, 0, 0, 0.0037735849056603774, 0.014957264957264958, 0, 0.008264462809917356, 0, 0, 0.007832898172323759, 0.007317073170731708, 0.05405405405405406, 0, 0.00548159749412686, 0, 0.006134969325153374, 0, 0, 0, 0.004291845493562232, 0, 0.007194244604316547, 0, 0, 0, 0.003289473684210526, 0, 0.0021231422505307855, 0.019230769230769232, 0, 0.015267175572519083, 0.016129032258064516, 0.03225806451612903, 0.007407407407407408, 0, 0.011904761904761904, 0, 0.01048951048951049, 0.022222222222222223, 0, 0.017241379310344827, 0.02586206896551724, 0.022727272727272728, 0, 0, 0.005859375, 0, 0, 0, 0.018433179723502304, 0.02127659574468085, 0, 0, 0, 0.00819672131147541, 0.006896551724137931, 0, 0, 0, 0, 0, 0.012658227848101266, 0.002570694087403599, 0.005681818181818182, 0.004098360655737705, 0.003605769230769231, 0, 0, 0, 0.015151515151515152, 0, 0.015503875968992248, 0.031578947368421054, 0.023255813953488372, 0, 0.022727272727272728, 0, 0.03125, 0.03260869565217391, 0, 0.0425531914893617, 0, 0, 0.02702702702702703, 0.02158273381294964, 0.029850746268656716, 0, 0, 0.034482758620689655, 0, 0.014285714285714285, 0.03409090909090909, 0, 0.035398230088495575, 0, 0, 0, 0, 0.03361344537815126, 0, 0.028169014084507043, 0, 0.01639344262295082, 0, 0, 0.027777777777777776, 0, 0.04938271604938271, 0.027777777777777776, 0.03896103896103896, 0.010638297872340425, 0, 0, 0, 0.024096385542168676, 0, 0.012738853503184714, 0, 0, 0.010638297872340425, 0, 0.03484320557491289, 0.008333333333333333, 0 ]

[ "1982–83 FC Barcelona season\n\nThe 1982–83 season was the 84th season for FC Barcelona.", "\n\nSquad\n\nLa Liga\n\nLeague table\n\nResults\n\nExternal links\n\nwebdelcule.com\n\nCategory:FC Barcelona seasons" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.011764705882352941, 0 ]

[ "Here is a list of frequently asked questions about youth hockey. ", "If you have any additional questions, please contact\n.", "\n\nWhat are the age groups?", "\n\nMites are our youngest group of players. ", "Ages 4-8 and who are generally just beginning to play hockey and learn the basics of puck control, shooting, skating and participating on a team.", "\n\nSquirts are the 9 and 10 year-olds.", "\n\nPeewees are ages 11 and 12.", "\n\nBantams are ages 13 and 14.", "\n\nMidgets are ages 15 through 18.", "\n\nWhat are the goals of Mite Hockey?", "\n\nThe goal for Mite Hockey Players is to pickup basic skills and have fun playing hockey. ", "Mite hockey players will learn how to skate forward, backwards, stick handling, puck control, pass the puck and shoot. ", "They will learn teamwork and the basics of hockey. ", "They will have a blast.", "\n\nWhat equipment do I need?", "\n\nProtective equipment is a important and all youth hockey players need the following: a helmet with face mask, shoulder pads, elbow pads, gloves, hockey pants, shin guards, protective cup, stick and skates. ", "See a video on getting suited up from USA Hockey.", "\n\nThe rink has a limited supply of initial gear available for rent to get new mite players out on the ice. ", "While we do not have unlimited supplies, we will do our best to make sure every skater has the equipment they need. ", "Ask about current local resources for purchasing equipment and we will help you in any way we can.", "\n\nIs hockey safe for my child?", "\n\nYouth hockey is relatively safe. ", "This is especially true for our younger players such as Mites. ", "No checking (intentional collisions or hitting) is permitted until they are Bantams (13-14). ", "Incidental contact does occur. ", "Each skater does wear protective equipment. ", "Safety is a top priority and proper fitting equipment is required. ", "Injuries can and do occur but studies have shown that hockey is quite safe for children, especially in the youngest age group.", "\n\nIs youth hockey open to boys and girls?", "\n\nAbsolutely. ", "Girls and Boys are both encouraged to play.", "\n\nDoes my child have to know how to skate to participate?", "\n\nNo. ", "Many of our first year skaters have never even been on the ice. ", "Our coaches are trained and certified to work with the youth on their skating ability, stick handling, puck control, passing and shooting. ", "Most of all, we want the kids to have fun and they will quickly pick up the basics of skating.", "\n\nWhat is the commitment level required for my child to play youth hockey?", "\n\nWe will have two or three 1-hour on-ice sessions per week. ", "Generally each age group will have one or two evening practices during the work week and on Saturdays. ", "Do to scheduling requirements and competing interests for time on the ice the schedule does change and advanced notice is given. ", "Games are generally on Saturday and if there are games there will be no Saturday practice. ", "The amount of travel varies greatly on age group and commitment of the team. ", "Mites will only travel any further than Moscow a couple of times a year. ", "As kids get older they will travel more frequently depending on commitment level and how many tournaments they choose to take part in. ", "It is important that your child attend as many practices, scrimmages and games as possible though as their skills, especially at the younger ages quickly develop.", "\n\nWhat is the time commitment for parents/guardians?", "\n\nParents and guardians need to be able to get their child to the facility. ", "It is strongly recommended you get your child there at least 15 minutes early to ensure adequate time to get into their equipment, lace their skates and be ready to get on the ice. ", "If you need assistance getting your Mite age child ready we ask you to get their earlier so coaches can be ready on the ice with skaters. ", "We only have an hour of ice time so the team will not wait to start practice for late-comers. ", "Also, LCAHA is a volunteer organization and we do ask for participation from our parents and guardians. ", "Whether there's in interest in coaching, refereeing, or helping with fundraising and tournament efforts, this program just wouldn't exist without our many volunteers.", "\n\nIt is required of all volunteers who are in any way working with children to be screened through the Idaho Amateur Hockey Association. ", "The cost is free and only takes a few minutes. ", "See screening information from IAHA.", "\n\nWho coaches the teams?", "\n\nAll coaches are volunteers that have gone through a standard background check as required by the Idaho Amateur Hockey Association. ", "Coaches must also be certified by attending USA Hockey approved coaching clinics and complete required training modules.", "\n\nWhen are practices and scrimmages?", "\n\nPractices are currently scheduled for weekday evenings depending on your team and Saturday beginning in October or November. ", "Scrimmages and other games will be announced as the season progresses.", "\n\nI've heard about ADM (American Development Model) and what is it?", "\n\nADM is a new model that USA Hockey is pushing associations to adopt. ", "Much of the intent is to make hockey more affordable, retain hockey players (especially in the higher age groups), develop skill, and most important Make Hockey Fun! ", "There is a lot of good information on the ADM model on the ADM website www.admkids.com.", "\n\nHow long is the hockey season?", "\n\nThe season generally runs from the end of October or early November through early March.", "\n\nCan I come to practice and check things out?", "\n\nDefinitely. ", "Practices, scrimmages and games are open to anybody who wants to see what hockey is all about. ", "Feel free to talk to the coaches after the practice or even talk to parents at the rink.", "\n\nHow do I register my child?", "\n\nYou will need to register your child with USA Hockey before registering for Youth Hockey. ", "Please see our Registration Page for more information on registering your child. ", "There is a fee for registration through USA Hockey for most age groups.", "\n\nIs there travel involved?", "\n\nFor Mite hockey there will be very little travel. ", "In keeping with the ADM Model (see www.admkids.com) we are very much looking to keep youth hockey affordable and enjoyable for our younger players. ", "Our older (aged 7-8) and more experienced players may choose to travel for games to places such as Tri-Cities, Spokane, McCall or Moscow. ", "However, many of our younger players and even many of our older players will likely only travel as far as Moscow." ]

{ "pile_set_name": "Pile-CC" }

[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.027777777777777776, 0.011111111111111112, 0, 0, 0, 0, 0, 0.02040816326530612, 0, 0, 0, 0, 0, 0.015873015873015872, 0.010752688172043012, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.009615384615384616, 0, 0.0072992700729927005, 0, 0.027777777777777776, 0, 0.007518796992481203, 0.008333333333333333, 0, 0, 0, 0.029850746268656716, 0.028169014084507043, 0.006024096385542169, 0.034482758620689655, 0, 0, 0, 0, 0, 0, 0, 0.021739130434782608, 0, 0.014084507042253521, 0, 0, 0.013513513513513514, 0.014492753623188406, 0 ]

[ "DEC \n" ]

{ "pile_set_name": "Github" }

[ 0.045454545454545456 ]

[ "Services We Offer\n\nCCTV SECURITY in Kolkata\n\nDigi Man Solutions Pvt. ", "Ltd. is a company that is engaged in providing excellent security services to various companies as well as individuals. ", "We have a team of highly efficient security personnel that strives to protect the interior and exterior premises of a building appropriately. ", "Besides this, we provide an excellent quality CCTV security surveillance system for complete safety of your space.", "\n\nOur technicians install the CCTV security surveillance system at any location as per the clients̢۪ requirements. ", "So, contact us anytime." ]

{ "pile_set_name": "Pile-CC" }

[ 0.014492753623188406, 0, 0, 0.008771929824561403, 0.008547008547008548, 0 ]

[ "Q:\n\nPropability of same characters next to each other in words\n\nAt the start , I have word of length N(N characters in a word) And each character can only be A,B or C\nNow the words that i want is words that have 3 or more same character that is next to each other.", "\nExample N=4\nWant: AAAB,BBBB,ACCC........\nDon't want: AABC CACC...\nNow I want to know how many words do I want in the length N\nExample\nN=3, I will only want 3 words , AAA,BBB,CCC\nAs far as I can think of is to use ternary numeral system. ", "But haven't got any Ideas yet.", "\nCan you guys kindly help me to figure out the idea to solve this problem. ", "Thank you.", "\n---EDIT!!", "\nI found this set of number that I can use , but I have no idea how they are relate to each other , if you can, please provide me answer :)\n3, 15, 63, 237, 843, 2889, 9651.......\n\nA:\n\nIt will be much simpler to describe words with two or less repeated characters. ", "Those can be constructed inductively:\n\nLet $A_n$ denote the number of words of length $n$ ending with two different characters and let $B_n$ denote the number of words of length $n$ ending with two identical characters. ", "Then we must have\n$$\n\\begin{align}\nA_{n+1}&=2(A_n+B_n)\\\\\nB_{n+1}&=A_n\n\\end{align}\n$$\nSince $B_n=A_{n-1}$, these can be combined to the recurrence relation\n$$\nA_{n+1}=2(A_n+A_{n-1})\n$$\nThen note that $A_1=3$ and $A_2=6$. This recurrence can be solved to obtain\n$$\nA_n=\\frac{\\sqrt 3\\left((1+\\sqrt 3)^n-(1-\\sqrt 3)^n\\right)}2\n$$\nThis produces a list starting with 3, 6, 18, 48, 132, 360, 984, 2688, 7344, 20064, 54816, 149760, 409152, 1117824, 3053952, 8343552, 22795008, 62277120, 170144256, 464842752.", "\n\nNow we are able to give a closed form expression for the number $C_n$ of words of length $n$ having at most two consecutive repetitions of a letter, namely:\n$$\nC_n=A_n+B_n=A_n+A_{n-1}\n$$\nand from that we easily get the number $D_n$ of words of length $n$ having at least three consecutive repetition of some letter:\n$$\nD_n=3^n-C_n=3^n-(A_n+A_{n-1})\n$$\n\nBased on this we should have:\n$$\n\\begin{align}\nD_2&=3^2-(6+3)&&=0\\\\\nD_3&=3^3-(18+6)&&=3\\\\\nD_4&=3^4-(48+18)&&=15\\\\\nD_5&=3^5-(132+48)&&=63\\\\\n&\\vdots\\\\\nD_{20}&=3^{20}-(464842752+170144256)&&=2851797393\n\\end{align}\n$$\nand so on. ", "The values of $D_3,...,D_{20}$ form the list:\n\n3, 15, 63, 237, 843, 2889, 9651, 31641, 102267, 326865, 1035411, 3255993, 10177131, 31649217, 98001603, 302348361, 929840091, 2851797393\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0, 0.029411764705882353, 0, 0, 0, 0, 0, 0, 0.002, 0.008620689655172414, 0 ]

[ "Now, Barack Obama – who, as well as being the President of the United States, is also the 55-year-old father of Malia, 18, and Sasha, 15 – has revealed what he told his daughters on the morning Trump was elected.", "\n\nObama with Sasha (left) and Malia (right): \"At any given moment there’s going to be flare-ups of bigotry that you may have to confront.\"", "\n\n“What I say to them is that people are complicated,” Obama told theNew Yorker’s David Remnick.", "\n\n“Societies and cultures are really complicated. … ", "This is not mathematics; this is biology and chemistry. ", "These are living organisms, and it’s messy.”", "\n\nThe relationship between Obama and Trump has been hostile since at least 2011, when Trump became one of the most prominent and persistent peddlers of the racist ‘birther’ conspiracy theory. ", "He repeatedly alleged that Obama had been born in Kenya, questioned whether he was a legitimate U.S. citizen, and demanded that the president release his birth certificate (American presidents have to be born in a U.S. state).", "\n\nIn response, Obama took to openly mocking the reality star billionaire. ", "At the 2011 White House Correspondents’ Association Dinner, which Trump attended, Obama walked onstage to the Rick Derringer song Real American. ", "Later, he announced that he was about to show the audience his “long-form birth video” – before playing the opening scene from The Lion King.", "\n\nDuring Trump’s presidential campaign, Obama struck a more serious tone in his criticism of the Republican candidate.", "\n\n“One of the most disturbing things about this election is just the unbelievable rhetoric coming from the top of the Republican ticket,” he said. ", "He added that Trump’s language “tells you he's insecure enough that he pumps himself up by putting others down – not a character trait that I would advise in the Oval Office.”", "\n\nAfter Trump’s election victory last week, however, the two men met privately for the first time at the White House. ", "According to theNew Yorker profile, their conversation made clear that the President-elect’s “grasp of such matters” as the Iran nuclear deal, counter-terrorism policy and healthcare “was, as the debates had made plain, modest at best”.", "\n\nBut in a public statement, Obama said that the pair had had “an excellent conversation” and stressed that he would do his best to make sure that Trump’s presidency was “successful”.", "\n\nImages: Rex Features\n\nTopics\n\nShare this article\n\nAuthor\n\nMoya Crockett\n\nMoya is Women’s Editor at stylist.co.uk, where she is currently overseeing the Visible Women campaign. ", "As well as writing about inspiring women and feminism, she also covers subjects including careers, podcasts and politics. ", "Carrying a tiny bottle of hot sauce on her person at all times is one of the many traits she shares with both Beyoncé and Hillary Clinton." ]

{ "pile_set_name": "Pile-CC" }

[ 0.014150943396226415, 0.007246376811594203, 0.03125, 0, 0, 0, 0.010416666666666666, 0.004424778761061947, 0.013513513513513514, 0.020689655172413793, 0, 0.01694915254237288, 0, 0.005714285714285714, 0.00847457627118644, 0.00423728813559322, 0.01092896174863388, 0.02247191011235955, 0, 0.014492753623188406 ]

[ "Inhibitory effects of curcumin-free aqueous turmeric extract on benzo[a]pyrene-induced forestomach papillomas in mice.", "\nThe modulating effects of curcumin-free aqueous turmeric extract (CFATE), ethanolic turmeric extract (ETE) and turmeric (T) powder on the benzo(a)pyrene (B(a)P)-induced forestomach tumors were investigated in Swiss female albino mice receiving oral administration of B(a)P at a dose of 1 mg twice weekly for 4 weeks. ", "Administration of 0.2%/1.0%/5.0% turmeric-derived CFATE as sole source of drinking water or 0.01%/0.05%/0.25% ETE in diet or 0.2%/1.0%/5.0% T in diet, 2 weeks before, during and 2 weeks after the last dose of B(a)P (during initiation period) resulted in significant suppression of B(a)P-induced tumorigenesis when compared with the group receiving B(a)P and control diet/drinking water. ", "Among different fractions tested, CFATE appears to be more powerful as not only did it reduce the tumor multiplicity to the lowest levels but it also significantly reduced the tumor incidence. ", "Administration of 5.0% turmeric-derived CFATE as the sole source of drinking water or 0.25% ETE/5.0% T in diet starting from 48 h after the last dose of B(a)P (during the post-initiation period) until the termination of the experiment, also inhibited the formation of multiple gastric tumors by B(a)P, although the suppression of tumor multiplicity was appreciably more in the groups that received 5.0% turmeric-derived CFATE/0.25% ETE treatment during initiation with carcinogen, i.e. 2 weeks before, during and 2 weeks after the last dose of B(a)P. The present data clearly indicate the potential of turmeric-derived CFATE as a powerful chemopreventive fraction and also demonstrate the efficacy of lower, i.e. 1/25th and/or 1/5th of the reported, chemopreventive doses of T/ETE (essentially curcumins) in inhibiting B(a)P-induced forestomach tumors in mice." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0.0031446540880503146, 0.00516795865633075, 0.0051813471502590676, 0.0011627906976744186 ]

[ "Spider silk softening by water uptake: an AFM study.", "\nWe have investigated the mechanical properties of spider dragline fibers of three Nephila species under varied relative humidity. ", "Force maps have been collected by atomic force microscopy. ", "The Young's modulus E was derived from the indentation curves of each pixel by the modified Hertz model. ", "An average decrease in E by an order of magnitude was observed upon immersion of the fiber in water. ", "Single fiber stretching experiments were carried out for comparison, and also showed a strong dependence on relative humidity. ", "However, the absolute values of E are significantly higher than those obtained by indentation. ", "The results of this work thus show that the elastic properties of spider silk are highly anisotropic, and that the silk softens significantly for both tensile and compressional strain (indentation) upon water uptake. ", "In addition, the force maps indicate a surface structure on the sub-micron scale." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0.038461538461538464, 0.007633587786259542, 0, 0.01904761904761905, 0, 0, 0, 0, 0 ]

[ "ZOC (software)\n\nZOC is a popular computer-based terminal emulator and Telnet software client for the Microsoft Windows and Apple Macintosh macOS operating systems that supports telnet, modem, SSH 1 and 2, ISDN, serial, TAPI, Rlogin and other means of communication. ", "Its terminal emulator supports Xterm emulation with full colors, meta-keys and local printing, VT102, VT220 and several types of ANSI as well as Wyse, TVI, TN3270, and Sun's CDE. ", "It supports full keyboard remapping, scripting in REXX and other languages, and support for named pipes.", "\n\nZOC is commercial software developed by Markus Schmidt of EmTec Innovative Software in Germany, a firm which produces software for various aspects of communications via telephone, PC, ISDN and the like. ", " Price was about US$80, with a free evaluation period of 30 days; ZOC can be downloaded for evaluation from EmTec or several shareware distribution sites. ", "Emtec produce two other associated but independent telecommunications programmes for use over TCP/IP, modem, ISDN etc.: ", "PyroTrans, an FTP package including client and server, and PyroBatchFTP, a programmable FTP tool.", "\n\nHistory \nZOC was first released for OS/2 in October 1993 (v0.95) and for Windows in November 1996 (v3.02). ", "In 1997 it was selected as runner-up in the OS/2 e-Zine! ", "Readers' Choice Awards. ", "ZOC released version 3.11 in January 1999. ", "Support for OS/2 was discontinued with the release of version 5. ", "Mac OS X has been supported from version 6.", "\n\nFeatures\n\nProtocols \n Secure Shell (SSH V1/V2) based on OpenSSH 6.6 with public/private key authentication, port forwarding (tunneling) and Smart Card support.", "\n Telnet (RFC-Telnet, pure TCP sockets, SSL-Telnet)\n modem via serial port and TAPI (Windows modem)\n ISDN via CAPI V2.0 (including X.25 and X.31 support)\n Rlogin\n File transfer protocols: ASCII, X-Modem, Y-Modem, Z-Modem, Kermit, SCP\n\nTerminals emulated \n Linux (Xterm) console-like\n VT52, VT100, VT102, VT220\n ANSI-BBS, ANSI-SCO, Avatar\n IBM like TN3270 and TN5250\n Sun-CDE\n QNX V4\n Wyse 30, 50, 60\n TVI 9xx (TVI 920, TVI 925, TVI 950)\n TTY\n Xterm\n Full support for line graphics when using any font\n\nAutomation \nScripting\n REXX language for scripting (fully featured programming language with over 75 extensions to control the terminal emulator) — a REXX interpreter is supplied with ZOC, and another interpreter can be specified in configuring ZOC\n AppleScript support with access to all internal script commands on macOS\n recorded login scripts, macro commands, automatic replies on incoming text\n DDE supported in Windows version, allowing ZOC to act as a communication server\n\nUser interface \n Tabbed interface for multiple concurrent connections and overview display to show thumbnails of open sessions\n Keys for macros, remappable keyboard, user button bar\n Online chat support\n Configurable display.", "\n\nSee also \n Comparison of SSH clients\n\nReferences\n\nExternal links \n \n\nCategory:Internet Protocol based network software\nCategory:Terminal emulators\nCategory:Secure Shell\nCategory:Rexx (programming language)\nCategory:Telnet" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.018796992481203006, 0.0335195530726257, 0, 0.014634146341463415, 0.01282051282051282, 0.016666666666666666, 0.030927835051546393, 0.00909090909090909, 0, 0, 0.023255813953488372, 0, 0, 0.012422360248447204, 0.014900662251655629, 0.008968609865470852 ]

[ "Ученые Оклендского технологического университета в Новой Зеландии выяснили, что пень новозеландского каури (агатиса южного) является живой частью гигантского суперорганизма, который включает в себя десятки или даже сотни деревьев. ", "При этом пень сохраняет жизнедеятельность, являясь паразитом. ", "Об этом сообщает издание Live Science.", "\n\nПо словам исследователей, пень оставался бы мертвым, если бы не был соединен с корневой системой других деревьев, поскольку у него отсутствует собственная зеленая фотосинтезирующая ткань. ", "Ночью он получает воду и питательные вещества, которые остальные растения получали в течение дня.", "\n\nУченые проследили за движением питательного сока и определили, что деревья и пень потребляли воду в разное время суток. ", "Днем пень «бездействует», пока живые растения транспортируют влагу до своих корней и листьев. ", "Ночью пень перемещал воду через свои оставшиеся ткани. ", "Таким образом, деревья играют роль насосов, включающихся попеременно в единой гидравлической системе. ", "По мнению ученых, остатки дерева могут играть роль моста, обеспечивающего связь корневых систем друг с другом.", "\n\nВ то же время такая система является уязвимой для патогенов, которые могут распространяться от одного зараженного дерева на весь лес через корни." ]

{ "pile_set_name": "OpenWebText2" }

[ 0.012987012987012988, 0.03225806451612903, 0.02631578947368421, 0.005263157894736842, 0, 0.00819672131147541, 0, 0, 0.00980392156862745, 0.01818181818181818, 0 ]

[ "That data comes from the latest polling from Gallup, which confirms the widening gulf between red states and blue states when it comes to health coverage. ", "This divide existed before health reform went into effect; however, it’s only gotten worse under Obamacare, which has helped the national uninsurance rate plunge to record lows but which has been implemented unevenly across the country.", "\n\nStates that have worked to fully implement Obamacare — which involves agreeing to both accept the law’s optional Medicaid expansion and set up their own insurance marketplaces — have seen the largest drops in their uninsurance rates over the past six months. ", "According to Gallup, the biggest success stories in this area are Arkansas and Kentucky, which have both nearly cut their percentage of uninsured residents in half. ", "In some counties in Kentucky, the uninsurance rate fell from more than 20 percent before Obamacare to just five percent after the law’s provisions took effect.", "\n\nBut the GOP-led states that have resisted Obamacare at all costs aren’t experiencing the same gains. ", "Their uninsurance rates are falling at a much slower rate. “", "The already notable gap between the two groups of states widened through the first quarter to 4.3 points, as states that have implemented these core mechanisms of the Affordable Care Act reduced their uninsured rates three times more than states that did not implement these core mechanisms,” Gallup researchers explain.", "\n\nTo make matters worse, the states that have refused to embrace Obamacare are the same ones that could have benefited from it the most. ", "Those states had higher uninsurance rates to begin with, and they’re home to people who tend to be poorer and sicker than the residents in other states. ", "In that context, it’s not entirely surprising that the 10 states that currently have the highest percentages of uninsured residents — Texas, Mississippi, Georgia, Florida, Louisiana, Montana, Arizona, Oklahoma, Alaska, and New Mexico — are led by GOP politicians. ", "Although some lawmakers and grassroots activists in those states have pushed for Medicaid expansion, they’ve ultimately been blocked by Obamacare opponents, and none of those states are fully implementing health reform in 2014.", "\n\nThanks to the ongoing political resistance to Obamacare, about six million people have been locked out of health reform altogether, left unable to qualify for either public insurance or federal assistance to purchase private insurance. ", "States’ refusal to expand Medicaid is disproportionately harming low-income people of color, who stand to benefit most from the policy.", "\n\nLike ThinkProgress on Facebook\n\nBy clicking and submitting a comment I acknowledge the ThinkProgress Privacy Policy and agree to the ThinkProgress Terms of Use. ", "I understand that my comments are also being governed by Facebook, Yahoo, AOL, or Hotmail’s Terms of Use and Privacy Policies as applicable, which can be found here." ]

{ "pile_set_name": "Pile-CC" }

[ 0.0064516129032258064, 0.00423728813559322, 0.0038314176245210726, 0.006060606060606061, 0.006289308176100629, 0.009708737864077669, 0, 0.003125, 0, 0, 0.003787878787878788, 0.004405286343612335, 0.004201680672268907, 0.007407407407407408, 0.006134969325153374, 0.01818181818181818 ]

[ "Griffith Ridge\n\nGriffith Ridge () is a rock ridge long in the Bowers Mountains of Victoria Land, Antarctica, located just within the mouth of Champness Glacier, where the latter joins the larger Lillie Glacier. ", "This geographical feature was first mapped by the United States Geological Survey from surveys and U.S. Navy air photos, 1960–62, and was named by the Advisory Committee on Antarctic Names for Lieutenant Harry G. Griffith, U.S. Navy, public works officer at McMurdo Station, Hut Point Peninsula, Ross Island, 1967. ", "This ridge lies situated on the Pennell Coast, a portion of Antarctica lying between Cape Williams and Cape Adare.", "\n\nReferences\n\nCategory:Ridges of Victoria Land\nCategory:Pennell Coast" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.009433962264150943, 0.015873015873015872, 0.017543859649122806, 0 ]

[ "Obruk, Bor\n\nObruk is a village in Bor district of Niğde Province, Turkey. ", " At it is situated to the west of Turkish state highway . ", "Its distance to Bor is and to Niğde is . ", " The population of Obruk was 1522 as of 2011.", "\n\nReferences \n\nCategory:Villages in Turkey\nCategory:Populated places in Niğde Province\nCategory:Bor (Niğde) District\nCategory:Lycaonia" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.02702702702702703, 0, 0.023809523809523808, 0.022222222222222223, 0.007462686567164179 ]

[ "H-Y antigen in a fertile XY female horse.", "\nThe presence of significantly reduced levels of H-Y antigen in the blood of an XY mare is consistent with the view that H-Y genes comprise a system of testis determinants. ", "Loss or suppression of a critical portion of H-Y genes and subthreshold expression of H-Y antigen could account for a failure of testicular differentiation, thereby allowing a measure of ovarian development in an XY embryo." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0.024390243902439025, 0.005780346820809248, 0.004484304932735426 ]

[ "Dorema Roof Pole Plug 21.5mm\n\nDorema Roof Pole Plug 21.5mm\n\nFitting at the end of the awning pole, the Roof Pole Plug enables a metal pole clamp to be fitted to the pole. ", "The bolt of the metal clamp (not supplied) goes through the hole of the canopy pole end and is tightened by the wing nut.", "\n\nMaterial: Strong black plastic\n\nLength: 63mm\n\nWidth At Widest Point: 26mm approx\n\nBarcode Number: 4875435389336\n\nArt Nr: 38933V\n\nPenrose Touring - Delivery Charges At A Glance\n\nRegion\n\nOrders less than £25.00\n\nOrders £25 and over\n\nEXCEPTIONS: Orders with heavy or large items\n\nMainland UK\n\n£3.50\n\nFREE!", "\n\nFREE!", "\n\nNorthern Ireland\n\n£3.50\n\nFREE! ( ", "Note: with exceptions )\n\n£35.00\n\nHighlands & Islands of Scotland\n\n£7.45\n\nFREE! ( ", "Note: with exceptions )\n\n£35.00\n\nThe Isle of Man\n\n£12.95\n\nFREE! ( ", "Note: with exceptions )\n\n£35.00\n\nThe Isles of Scilly\n\n£12.95\n\nFREE! ( ", "Note: with exceptions )\n\n£35.00\n\nDispatching Your Order\n\nPenrose Touring will normally dispatch your order within 7 working days. ", "In the vast majority of cases, because products are generally available from stock, your order will be despatched earlier than this. ", "If for any reason we are unable to honour this commitment then we will endeavour to inform you as soon as possible. ", "We only send orders to addresses within\n\nMainland United Kingdom.", "\n\nThe Isle of Man\n\nThe Isles of Scilly\n\nNorthern Ireland\n\nThe Highlands and Islands of Scotland\n\nHowever, if you live outside these regions and wish to place an order with us we respectively request you contact us first and we will provide you with a price for shipping your order." ]

{ "pile_set_name": "Pile-CC" }

[ 0.005847953216374269, 0, 0.003289473684210526, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]

[ "\n882 So.2d 1050 (2004)\nAntonio SMITH, Appellant,\nv.\nSTATE of Florida, Appellee.", "\nNo. ", "4D02-5026.", "\nDistrict Court of Appeal of Florida, Fourth District.", "\nAugust 24, 2004.", "\n*1051 Carey Haughwout, Public Defender, and Louis G. Carres, Assistant Public Defender, West Palm Beach, for appellant.", "\nCharles J. Crist, Jr., Attorney General, Tallahassee, and Melynda L. Melear, Assistant Attorney General, West Palm Beach, for appellee.", "\nTAYLOR, J.\nWe withdraw our previously issued opinion of August 11, 2004, and substitute the following in its place.", "\nAntonio Smith appeals his conviction and sentence for battery on a law enforcement officer, resisting arrest without violence, and possession of cannabis. ", "He contends that the trial court erred in not finding a discovery violation for the state's failure to disclose a material witness. ", "The defendant also asserts that the court improperly imposed a habitual felony offender sentence without first considering a pre-sentence investigation report. ", "Because we reverse the judgment of conviction and remand for a new trial, the sentencing issue is moot.", "\nDeputy Edward Chavez-Velando of the Broward Sheriff's Office was patrolling an apartment complex in Lauderdale Lakes at about 2:30 a.m., when a Jeep passed him in the parking lot. ", "The driver was smoking a marijuana cigarette. ", "When the vehicle parked, the deputy approached it and asked the driver for identification. ", "The driver handed the deputy the driver's license of the defendant, Antonio Smith. ", "The deputy examined the photo on the license and concluded that the driver was the same as the person pictured on the license. ", "He also noted that the address listed on the license was for the apartment complex where the driver said he lived.", "\nWhen the deputy conducted a consensual pat down search of the driver, he located a small one-inch sized bag of marijuana in the driver's coin pocket. ", "At that point it began to pour rain, and the driver began to walk away toward the building. ", "When the deputy told the man he was under arrest, he lunged forward to flee. ", "The deputy grabbed his shirt, but the man hit him in the chest with his elbow, sending the deputy backwards. ", "The man fled into the apartment building before the officer could recover and disappeared.", "\nDeputy Chavez-Velando went to the apartment shown on the driver's license and spoke to a woman there. ", "The woman permitted the deputy to search the apartment. ", "The search revealed mail and other items belonging to Smith, indicating that he was in fact living there.", "\nAt trial, the driver's license was admitted into evidence. ", "The deputy testified *1052 that it was the same license that he obtained from the person he spoke with on the night of the incident and that he had no doubt that this person was the same as the person pictured on the license. ", "He positively identified the defendant in court. ", "The deputy also testified that he discovered that the vehicle the defendant was driving that night was leased to an individual whose name, address, and phone number appeared on lease papers found in the glove compartment. ", "The deputy stated that he contacted the owner (lessee) and questioned him regarding his knowledge of the vehicle's whereabouts and who was driving it.", "\nThen, the prosecutor questioned the deputy as follows:\nQ. What did you do as a result of speaking with that person, without going into what the person said?", "\nA. Well, we did ask ... did he know the whereabouts of his vehicle, who had his vehicle. ", "We also indicated to him that the vehicle was going to be held for certain procedures, that he wouldn't be able to get the vehicle at that time. ", "And he did indicate that he was going to make a phone call to the person —\nMR. ", "GELIN: Objection as to hearsay, Judge.", "\nTHE COURT: As to what he indicated, sustained.", "\nQ. Okay. ", "What did you do as a result of speaking with him and explaining to him that the vehicle was going to be towed?", "\nA. A phone call was made to the person he had lent the vehicle to, who he indicated was Antonio Smith.", "\nMR. ", "GELIN: Again, Judge, objection to hearsay.", "\nTHE COURT: Overruled.", "\nMS. ", "FEISTMAN: Okay.", "\nMR. ", "GELIN: Side bar, please.", "\nDefense counsel moved for a mistrial, asserting the state's failure to disclose during discovery the name and address of the vehicle's owner. ", "He requested a Richardson hearing.[1] The court denied the motion for mistrial, but instructed the jury not to consider the last question and answer about the officer having called the person who purportedly borrowed the car and this person identifying himself as Antonio Smith.", "\nThe court announced that, in an abundance of caution, it would hold a Richardson hearing. ", "The court asked the prosecutor why she had not disclosed the identity of the vehicle's owner to the defense. ", "The prosecutor responded that she had no information about the owner. ", "She further explained that she had moved for a continuance at the beginning of the trial to try to get that information but that the court had denied her motion. ", "Without further inquiry, the court concluded that there had not been a violation of discovery rules.", "\nThe defendant asserted an alibi defense at trial and called four witnesses to testify that he was in Orlando at a Halloween party on the night in question. ", "The defendant acknowledged that the driver's license in evidence was his, but claimed that he lost his license shortly before this incident, perhaps somewhere at the apartment complex. ", "The jury found the defendant guilty on all charges.", "\nThe defendant contends that the trial court reversibly erred in denying relief for a discovery violation by the state. ", "The violation became apparent during trial when the arresting officer testified that he had made contact with the person who had leased the vehicle allegedly driven by the person who accosted the deputy. ", "The identity of the vehicle's lessee was not *1053 disclosed to the defense before trial. ", "The trial court, however, found no discovery violation after hearing the state's explanation that it did not know the name of the lessee and did not intend to call him as a witness at trial.", "\nWhen, as here, a trial court finds no discovery violation, that conclusion is reviewed for an abuse of discretion. ", "See State v. Evans, 770 So.2d 1174, 1183 (Fla.2000); Pender v. State, 700 So.2d 664, 667 (Fla.1997). ", "As the defendant correctly argues, the state's duty to disclose witnesses is not limited to listing those witnesses it intends to call at trial. ", "Rather, the state is obligated to timely disclose, upon request, the names and addresses of all persons \"known to the prosecutor to have information that may be relevant to any offense charged or any defense thereto.\" ", "Fla. R.Crim. ", "P. 3.220(b)(1)(A).", "\nFurther, though the rule requires disclosure of persons \"known to the prosecutor,\" case law makes clear that the knowledge of law enforcement officers is imputed to the prosecutor for purposes of this rule. ", "See Griffin v. State, 598 So.2d 254, 256 (Fla. 1st DCA 1992); Hutchinson v. State, 397 So.2d 1001 (Fla. 1st DCA 1981). ", "Thus, we agree with the defendant that the trial court abused its discretion in finding no discovery violation based on the prosecutor's intention not to call the witness and her lack of knowledge of the witness's name. ", "Presumably, the officer knew the name and that was enough to trigger a full Richardson inquiry into the discovery violation.", "\nThe failure to conduct a Richardson hearing where a discovery violation occurred was per se reversible error until the Florida Supreme Court adopted the following harmless error standards in State v. Schopp, 653 So.2d 1016, 1020-21 (Fla.1995):\nIn determining whether a Richardson violation is harmless, the appellate court must consider whether there is a reasonable possibility that the discovery violation procedurally prejudiced the defense. ", "As used in this context, the defense is procedurally prejudiced if there is a reasonable possibility that the defendant's trial preparation or strategy would have been materially different had the violation not occurred. ", "Trial preparation or strategy should be considered materially different if it reasonably could have benefitted the defendant. ", "In making this determination every conceivable course of action must be considered. ", "If the reviewing court finds that there is a reasonable possibility that the discovery violation prejudiced the defense or if the record is insufficient to determine that the defense was not materially affected, the error must be considered harmful. ", "In other words, only if the appellate court can say beyond a reasonable doubt that the defense was not procedurally prejudiced by the discovery violation can the error be considered harmless.", "\nThe burden is on the State to establish that the error is harmless. ", "Id. at 1020.", "\nGiven appellant's defense that he was not driving the vehicle owned by the undisclosed witness at the time these charges arose, we cannot say beyond a reasonable doubt that the defense was not procedurally prejudiced by the discovery violation. ", "As appellant points out, there is a reasonable possibility that this person's evidence would have assisted defendant in the presentation of his defense. ", "We therefore cannot consider the discovery violation harmless.", "\nREVERSED and REMANDED.", "\nFARMER, C.J., and GUNTHER, J., concur.", "\nNOTES\n[1] Richardson v. State, 246 So.2d 771 (Fla.1971).", "\n" ]

{ "pile_set_name": "FreeLaw" }

[ 0.0379746835443038, 0, 0, 0, 0, 0.016666666666666666, 0.022058823529411766, 0.008620689655172414, 0.00641025641025641, 0, 0, 0, 0.022099447513812154, 0, 0, 0.012048192771084338, 0, 0, 0, 0, 0, 0, 0, 0.009708737864077669, 0, 0.009523809523809525, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.02631578947368421, 0, 0.1, 0, 0.009708737864077669, 0, 0.023809523809523808, 0, 0, 0, 0, 0.041666666666666664, 0, 0.0035971223021582736, 0.01098901098901099, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.005263157894736842, 0, 0.019801980198019802, 0.006896551724137931, 0, 0, 0, 0, 0.008403361344537815, 0, 0.008064516129032258, 0.013452914798206279, 0, 0, 0, 0, 0, 0.014492753623188406, 0, 0, 0, 0, 0.043478260869565216, 0.07692307692307693, 0, 0 ]

[ "It is known that the time taken to perform a hydrolysis process is reduced noticeably when the hydrolysis process is performed for a conventional object at high temperatures and high pressures.", "\nConsidering commercialization of hydrolysis objects, reducing the time taken to perform the hydrolysis for an object plays an important role in the unit cost of production. ", "Accordingly, apparatuses for providing a high temperature and high pressure condition in various methods to a hydrolysis object are supplied.", "\nIn this connection, Korean Patent No. ", "1992-0017580 discloses that a pressure is applied to a pressure container via a supply line for supplying liquid for pressing an object provided in a pressure container, to cool the pressure container, using refrigerant.", "\nHowever, in case of heating or cooling the pressure container itself to control the heat of the pressure container, the heat is transmitted to the object via the pressure container and the liquid. ", "Accordingly, it takes a relatively long time to change the temperature of the object. ", "Especially, when a mass of pressure containers and objects in consideration of productivity, the hydrolysis takes a longer time and more energy is consumed in case of applying heat to pressure containers outside.", "\nMoreover, there may be a difference between the quantities of the heat supplied in accordance with external environment and the equipment set in accordance with an external temperature of an installation space has to be re-set disadvantageously.", "\nIn a process for raising the applied temperature to destruct enzyme after the hydrolysis process of the object, dissolved gas degasified from the object unless the temperature is raised with maintaining a critical pressure might be dispersed to the object and the hydrolyzed object might be spoiled. ", "When using only an external heater of the pressure container in a process for raising the temperature of the pressure container, with maintaining the critical pressure to prevent the spoiled object, the time taken to raise the temperature and energy efficiency might deteriorate to deteriorate the productivity disadvantageously.", "\nAlso, when a process for removing the pressure and a process for cooling to secure the object in a state where the object a critical pressure or higher is applied to is completely hydrolyzed are performed simultaneously, the decay of the object caused by the dispersion of the dissolved gas might occur rapidly. ", "Accordingly, the temperature has to be cooled to the lowest value so as to make the density of solvent (e.g., water) primarily, in a state of maintaining the critical pressure to minimize the decay of the object caused by the dispersion of the dissolved gas.", "\nIn case of depending on only a heating/cooling source outside the pressure container in a process for cooling the object maintaining a high temperature as well as a critical pressure, much time might be spent on the cooling of the object disadvantageously." ]

{ "pile_set_name": "USPTO Backgrounds" }

[ 0, 0, 0, 0.02564102564102564, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]

[ "{\n \"jsonSchemaSemanticVersion\": \"1.0.0\",\n \"imports\": [\n {\n \"corpusPath\": \"cdm:/foundations.1.1.cdm.json\"\n },\n {\n \"corpusPath\": \"/core/operationsCommon/Common.1.0.cdm.json\",\n \"moniker\": \"base_Common\"\n },\n {\n \"corpusPath\": \"/core/operationsCommon/DataEntityView.1.0.cdm.json\",\n \"moniker\": \"base_DataEntityView\"\n },\n {\n \"corpusPath\": \"JmgTermReg.1.0.cdm.json\"\n },\n {\n \"corpusPath\": \"/core/operationsCommon/Tables/SupplyChain/ProductionControl/Reference/JmgIpcActivity.1.0.cdm.json\"\n },\n {\n \"corpusPath\": \"/core/operationsCommon/Tables/Finance/Ledger/Main/CompanyInfo.1.0.cdm.json\"\n }\n ],\n \"definitions\": [\n {\n \"entityName\": \"JmgEventCtrl\",\n \"extendsEntity\": \"base_Common/Common\",\n \"exhibitsTraits\": [\n {\n \"traitReference\": \"is.", "CDM.entityVersion\",\n \"arguments\": [\n {\n \"name\": \"versionNumber\",\n \"value\": \"1.0\"\n }\n ]\n }\n ],\n \"hasAttributes\": [\n {\n \"name\": \"Approved\",\n \"dataType\": \"JmgApproved\",\n \"isNullable\": true,\n \"description\": \"\"\n },\n {\n \"name\": \"EventCode\",\n \"dataType\": \"JmgEventCode\",\n \"description\": \"\"\n },\n {\n \"name\": \"ProfileDate\",\n \"dataType\": \"JmgProfileDate\",\n \"isNullable\": true,\n \"description\": \"\"\n },\n {\n \"name\": \"TerminalId\",\n \"dataType\": \"JmgTerminalId\",\n \"isReadOnly\": true,\n \"isNullable\": true,\n \"description\": \"\"\n },\n {\n \"name\": \"TermRegRecID\",\n \"dataType\": \"JmgTermRegStartRecID\",\n \"isNullable\": true,\n \"description\": \"\"\n },\n {\n \"name\": \"Worker\",\n \"dataType\": \"JmgWorkerRecId\",\n \"isNullable\": true,\n \"description\": \"\"\n },\n {\n \"name\": \"DataAreaId\",\n \"dataType\": \"string\",\n \"isReadOnly\": true\n },\n {\n \"entity\": {\n \"entityReference\": \"JmgTermReg\"\n },\n \"name\": \"Relationship_JmgTermRegRelationship\",\n \"resolutionGuidance\": {\n \"entityByReference\": {\n \"allowReference\": true\n }\n }\n },\n {\n \"entity\": {\n \"entityReference\": \"JmgIpcActivity\"\n },\n \"name\": \"Relationship_SwitchJmgIpcActivityRelationship\",\n \"resolutionGuidance\": {\n \"entityByReference\": {\n \"allowReference\": true\n }\n }\n },\n {\n \"entity\": {\n \"entityReference\": \"CompanyInfo\"\n },\n \"name\": \"Relationship_CompanyRelationship\",\n \"resolutionGuidance\": {\n \"entityByReference\": {\n \"allowReference\": true\n }\n }\n }\n ],\n \"displayName\": \"Switch code\"\n },\n {\n \"dataTypeName\": \"JmgApproved\",\n \"extendsDataType\": \"integer\"\n },\n {\n \"dataTypeName\": \"JmgEventCode\",\n \"extendsDataType\": \"string\"\n },\n {\n \"dataTypeName\": \"JmgProfileDate\",\n \"extendsDataType\": \"date\"\n },\n {\n \"dataTypeName\": \"JmgTerminalId\",\n \"extendsDataType\": \"string\"\n },\n {\n \"dataTypeName\": \"JmgTermRegStartRecID\",\n \"extendsDataType\": \"bigInteger\"\n },\n {\n \"dataTypeName\": \"JmgWorkerRecId\",\n \"extendsDataType\": \"bigInteger\"\n }\n ]\n}" ]

{ "pile_set_name": "Github" }

[ 0, 0.00411214953271028 ]

[ "Q:\n\nSecureData even for admins with external login\n\nGiven:\nA WebService which stores user Data and a server with a database. ", "\nA Administrator which can acces the sever wit hthe webservice and the server with the database.", "\nForeach user is a dedicated database.", "\nAim:\nStore the data in a way so that even not the administrator can access it with the secret of the user.", "\nThoughts:\nTo make sure that the Administrator can't access the data stored by many users the data can be encrypted with a user secret. ", "and / or the database can be created with a derivation of the user secret as password. ", "\nThe data can then be decrypted on the client side.", "\nQuestion:\nThis works with common user logins so I could use the user password or a hash of it as database password / Encryption.", "\nBut Is there a practice what to do if the user authenticates with a external oAuth Login (Google,Facebook,Github...)? ", "In this case i don't have any secrets / password of the user.", "\nFor me it would feel a little awkward to ask him for a \"MasterKey\". ", "Are there any experiences on this scenario or real world examples?", "\n\nA:\n\nThe rule is that if the data is in clear text at any moment on a machine it is accessible to the admin of the machine. ", "Because by definition, an admin can use administrative tools and can read memory of any process or install spys on any network route.", "\nDoing so without good reason is of course a professional fault and the admin can be fired for that, not speaking of legal actions, but technically it can be done.", "\nThe only thing that could be done here would be to have different administrative zones, and configure the system so that the database machine admins cannot access the data. ", "For that, the main server should be distinct from the database server and the database should only contain encrypted data. ", "It can make sense if you have an internal server but want to store the database externally for redundancy reasons. ", "But a much more common use case would be to have an internal database, and only store encrypted dumps in the cloud.", "\nTL/DR: if you cannot trust the admin, you cannot trust the machine, so the webservice should only process encrypted data, which means that you need something else and elsewhere to actually process, encrypt and decrypt the data.", "\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0.024, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]

[ "Traumatic brain injury results in mast cell increase and changes in regulation of central histamine receptors.", "\nExperimental fluid-percussion models produce brain injury by rapidly injecting saline into the closed cranium of rats. ", "In this study our purpose was to determine how the central histaminergic system, which controls excitability and neurotransmitter release through G-protein coupled receptors, is affected by the pathophysiology of traumatic brain injury. ", "We found that mast cell infiltration, as a result of the trauma, occurred primarily in the injured cortex and did not proceed beyond the fimbria of the hippocampus. ", "In comparing injured animals with controls we found that H3 receptor binding densities are significantly decreased bilaterally in the cortex but are significantly increased bilaterally in the thalamus. ", "H3 receptor binding densities may well be affected by mast cell secretion of mediators (i.e. histamine, heparin, leukotrienes), evidenced by detection of a cosecreted enzyme (mast cell tryptase) in the extracellular region. ", "Moreover, we detected significant decreases in H1 and H3 receptor mRNA as well as Cu/Zn-dependent superoxide dismutase (SOD) mRNA in the thalamic region closest to the trauma. ", "These significant decreases delineate the extent of cellular damage because of trauma and may underlie sustained cognitive and motor deficits displayed by these animals." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0, 0, 0, 0, 0, 0.005681818181818182, 0 ]

[ "Lupus disease - definition, causes and symptoms\n\nLupus is a disease that is deadly. ", "This disease equivalent to cancer diseases, many world died because of this disease. ", "Lupus disease attacks the human immune system excessively, thereby disrupting the body's health. ", "The term is in Latin lupus Lupus is a \"coyote\". ", "Lupus Disease characteristic feature is if the attack chest pain will arise, causing the sufferer to experience difficulties when breathing. ", "In patients with this disease initially as having skin disorders, such as redness around the nose and cheeks. ", "There are red blotches on the face and arms, experience hair loss, often experience swelling in the joints and ulcers as well as feel the heat and prolonged fatigue. ", "This disease not only affects the skin, but also can attack almost all organs in the human body.", "\n\nSymptoms of Lupus Disease\n\nThe most common symptoms are patient will often feel weak, excessive fatigue, aches and joints pain.", "\n\nThe emergence of the digestive disorders such as diarrhea, thrush continuous and prolonged high fever.", "\n\nPatients will have anemia, because red blood cells will be destroyed if this disease.", "\n\nIn patients skin will appear red rash that extends on both cheeks, like a butterfly. ", "And a red rash that almost resembles the disc may appear on the skin on the entire body. ", "There are also on the skin of the patient will easily scorched by sun.", "\n\nIf there are four symptoms of lupus above mandatory blood test to make sure you are positive or not affected by lupus." ]

{ "pile_set_name": "Pile-CC" }

[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]

[ "Nearly 2 000 people were arrested in Egypt this week. ", "Their crime? ", "Daring to protest against the country’s military government. ", "The act of protesting is outlawed, so many of those arrested had already weighed up the risk of arrest before taking to the streets.", "\n\nMost of those arrested are said to be teenagers and, as rights groups slam the continuing clampdown in Egypt, state media insist all footage of protests has been doctored.", "\n\nMilitary power is an important part of the state’s oppressive ability. ", "But embattled South African military technology and defence company Denel wants to supply missiles to the Egyptian navy, despite constant and serious human rights abuses by that country’s repressive military government.", "\n\nShould this deal, estimated to be worth R4.5-billion, go ahead it could go a long way towards ensuring Denel’s survival without calling on the state for bailouts.", "\n\nThe state-owned arms manufacturer — which very nearly did not meet its payroll obligations as recently as two months ago — is one of many critical state-owned entities operating hand to mouth, dependent on state cash and bond purchases.", "\n\nIn May this year, Denel wrote to the department of defence requesting approval to use three different components of a missile — intellectual property for the Marlin seeker and dual-pulse rocket motor, as well as warhead technology — so that it could develop the Umkhonto-Radar missile, known as Umkhonto-R.\n\nThe missile is mainly fired from warships and is built to shoot down planes and drones. ", "Denel wanted to supply the missile to the Egyptian navy.", "\n\nIn a letter responding to Denel’s request to use the department of defence’s intellectual property, its arms procurement agent — Armscor — said the intellectual property could be used as long as it remained in South Africa, and was not transferred to Egypt. ", "It also said that a 10% royalty of the proceeds from the contract had to be reinvested in the maintenance and further development of the missile.", "\n\nDenel’s letter noted that: “The 10% royalty shall be calculated on the total value of the 96 units of Umkhonto-R which will be supplied to Egypt.” ", "The state arms company also intends to sell 32 units of an infrared variant of the Umkhonto-R.\n\nEarlier this month, during its presentation to Parliament’s portfolio committee on public enterprises, Denel said that there is an imminent contract, which includes a R1.5-billion advance, focusing on Egypt’s navy and ThyssenKrupp Marine Systems vessels.", "\n\nDenel chief executive Danie du Toit said that they anticipated R30-billion in the next two years, which will change the entity’s financial misfortunes. ", "In August, the government had to pump R1.8-billion into Denel because it was struggling to pay salaries and suppliers. ", "This came after it posted a R1.76-billion loss in 2018.", "\n\nBut Denel’s intended supply of Umkhonto-R missiles to the Egyptian navy appears to be in conflict with the National Conventional Arms Control Act.", "\n\nThe Act stipulates that South Africa will not export armaments to countries that abuse human rights — which Egypt has been accused of doing — and countries that are in conflict, or subject to United Nations’ and other international embargoes.", "\n\nThis year, a Human Rights Watch report said that since President Abdel Fattah al-Sisi got his second term in what is described as an unfree and unfair presidential elections, his security forces have “escalated a campaign of intimidation, violence, and arrests against political opponents, civil society activists, and many others who have simply voiced mild criticism of the government”.", "\n\nThe report went on to say: “The government continued to silence critics through arrests and unfair prosecutions of journalists and bloggers, and the Parliament issued severely restrictive laws that further curtail freedom of speech.”", "\n\nLast year UN human rights experts condemned Egypt’s human rights abuses. ", "In a press statement, they said: “We are gravely concerned at the human rights defenders’ prolonged periods of detention, reportedly arising from their peaceful and legitimate defence of human rights.”", "\n\nThe UN last month postponed an anti-torture conference that was meant to be held in Cairo after an uproar from human rights activists.", "\n\nIn an apparent defence of its initial decision to host the conference, a UN spokesperson — as quoted by The Guardian — said there was value in hosting a conference “that aims to try and reduce torture” in a country and region where torture takes place.", "\n\nDenel, which makes ammunition, missiles and armoured vehicles for South Africa and customers in Africa, the Gulf and Europe, said that Umkhonto-R will be developed together with its Umkhonto-InfraRed (IR). ", "When that missile was fired from aboard the Valour-class frigate SAS Amatola in 2005, South Africa became one of only a handful of countries to have fielded a functional, operational anti-missile air defence system.", "\n\nBut to complete the sale, the arms manufacturer will also have to obtain permission from the National Conventional Arms Control Commission (NCACC), which controls the trade in arms, as well as the rendering of foreign military assistance.", "\n\nThe committee — which is chaired by Minister in the Presidency Jackson Mthembu and comprises several ministers and deputy ministers — assesses a host of issues before making a decision. ", "This includes the national security interest of the country and its allies, the potential to contribute to internal repression and the suppression of human rights and fundamental freedoms, and the potential to contribute to the escalation of regional military conflicts.", "\n\nWhen asked to confirm whether Denel had submitted an application, Mthembu referred all queries to the head of the NCACC’s secretariat, Makhosonke Jele.", "\n\nJele asked what interest the application was to the Mail & Guardian, adding that any information about arms sales is “strictly regulated”: “As a citizen, should this be of interest, and you deem it to be in the interest of the public to know, this will be considered under [the] Promotion of Access to Information Act.”", "\n\nA government source with know-ledge of the deal said it made sense because of the unlikelihood of surface-to-air missiles being used by Egypt against its own citizens. “", "You must remember Egypt is not under any arms embargo, so the financial benefits far outweigh the possibility of us finding ourselves on the wrong side of history,” the source said.", "\n\nDenel spokesperson Pamela Malinda said: “Denel markets and sells all its products and solutions within the framework of the South African Constitution, the National Conventional Arms Control Act and the relevant United Nations resolutions.”" ]

{ "pile_set_name": "OpenWebText2" }

[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0038461538461538464, 0, 0, 0.008571428571428572, 0.01948051948051948, 0.008403361344537815, 0, 0.013513513513513514, 0.004098360655737705, 0.002564102564102564, 0.00425531914893617, 0.013333333333333334, 0, 0.007352941176470588, 0.007874015748031496, 0, 0.004651162790697674, 0.008333333333333333, 0.005319148936170213, 0, 0.026143790849673203, 0.006230529595015576, 0, 0, 0.01652892561983471 ]

[ "<?", "xml version=\"1.0\" encoding=\"UTF-8\"?", ">\n<!--", "\n /**\n * Copyright © Magento, Inc. All rights reserved.", "\n * See COPYING.txt for license details.", "\n */\n-->\n\n<entities xmlns:xsi=\"http://www.w3.org/2001/XMLSchema-instance\"\n xsi:noNamespaceSchemaLocation=\"urn:magento:mftf:DataGenerator/etc/dataProfileSchema.xsd\">\n <entity name=\"CatalogRuleProductConditions\">\n <data key=\"categoryIds\">Magento\\CatalogRule\\Model\\Rule\\Condition\\Product|category_ids</data>\n </entity>\n</entities>\n" ]

{ "pile_set_name": "Github" }

[ 0, 0.02857142857142857, 0, 0, 0, 0.008547008547008548 ]

[ "Based on the award-winning book of the same name, Training Ain’t Performance is a highly interactive learning event that delivers the key concepts, principles, and tools to transform you into an effective performance consultant.", "\n\nEach community focuses on a key area of the talent development field and is led by a community manager whose in-depth knowledge will ensure that the content, offerings, and resources are consistent with your needs.", "\n\nFor many organizations, content management is considered a critical\nstrategy for keeping up with a fast-paced and resource-constrained\nbusiness environment. ", "According to Forrester, the demand for\nenterprise content management (ECM) software reached a staggering\n$3.9 bil...More »" ]

{ "pile_set_name": "Pile-CC" }

[ 0.0043859649122807015, 0, 0, 0.01639344262295082 ]

[ "Q:\n\nsegment BCD to 7 decoder in verilog\n\nI am writing a code for simulating a bcd to seven segment decoder. ", "When i am doing so , i am getting red and blue lines in the waveform window(in Modelsim), which means that the input is not driven and the output is in undefined state. ", "But when i running the code by forcing the values then it shows the correct results. ", "From this i am able to figure out that the problem is in my testbench . ", "I would rally appreciate if anybody can take a look at m code and point out what i am doing wrong.", "\nCODE\n//BCD to seven segment display\nmodule seven_segment;\nreg [3:0] BCD;\nwire [6:0] display;\nparameter stop_time = 200;\n\nbcd_seven n(display,BCD); //Instantiation of the bcd to seven segment display code\n\ninitial #stop_time $finish;\n\ninitial\nbegin\nBCD = 0;\n#10 BCD = 1;\n#10 BCD = 2;\n#10 BCD = 3;\n#10 BCD = 4;\n#10 BCD = 5;\n#10 BCD = 6;\n#10 BCD = 7;\n#10 BCD = 8;\n#10 BCD = 9;\nend\ninitial begin\n$monitor(\"display = %d BCD = %b\",display,BCD);\nend\nendmodule \n\n//Decsription of the BCD to seven segment display\nmodule bcd_seven(D,BCD);\noutput D; \nreg [6:0] D;\ninput [3:0] BCD;\n\nparameter BLANK = 7'b0000000;\nparameter ZERO = 7'b1111110;\nparameter ONE = 7'b0110000;\nparameter TWO = 7'b1101101;\nparameter THREE = 7'b1111001;\nparameter FOUR = 7'b0110011;\nparameter FIVE = 7'b1011011;\nparameter SIX = 7'b1011111;\nparameter SEVEN = 7'b1110000;\nparameter EIGHT = 7'b1111111;\nparameter NINE = 7'b1111011;\n\n//I have doubt especially in this section\nalways @(BCD)\ncase(BCD)\n0: D = ZERO;\n1: D = ONE;\n2: D = TWO;\n3: D = THREE;\n4: D = FOUR;\n5: D = FIVE;\n6: D = SIX;\n7: D = SEVEN;\n8: D = EIGHT;\ndefault: D = BLANK;\nendcase\nendmodule\n\nA:\n\nI did notice one bug in your code. ", "You are missing the case statement for BCD = 9. ", "But that wouldn't explain the other issues you are seeing. ", "\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0.009259259259259259, 0, 0, 0, 0, 0.01713796058269066, 0.020833333333333332, 0, 0 ]

[ "Last night, my wife and I finished our marathon of Master of None’s season 2 and I must admit: boy, what a delight – especially foodwise.", "\n\nSure, I could stay here praising great moments like the one where Dev (Aziz Ansari’s character) goes on several dates with very different women thanks to a popular dating app; the last scene on “The Dinner Party” episode where – literally – words could not describe; the lifetime struggle of Denise to be accepted as “Lebanese” by her family; or the amazing episode where the intersecting lives of different New Yorkers are shown.", "\n\nBut no. ", "Today, I’ll talk about one of the main characters that often steal the show: the food.", "\n\nFirst and foremost, I think is fair to say that I’m a fan of Aziz Ansari. ", "I don’t know whether this is because of his likeability or my nostalgic feelings towards Parks and Recreation – btw, Aziz, if you read this, I’m still waiting on a Amy Poehler cameo on MoN!", "\n\nThat being said, it’s worth mentioning that Aziz has a serious love for food IRL. ", "The show’s co-creator (along with Anzari), Alan Yang, has even mentioned that “one of the reasons Aziz and I became friends is that we liked food.“.", "\n\nMaybe that’s why food is so omnipresent in Master of None – and not just any old grub, but the good stuff too, like a three-star Michelin restaurant. ", "Not feeling fancy enough? ", "That’s ok, you can always go to a food truck festival and grab some juicy pork ribs – whether your religion allows it or not.", "\n\nOur beloved characters are constantly eating around New York City bars and restaurants, and this season we even get to go to Italy!", "\n\nJust a quick note: I’m sure this will wear off in a few weeks, since we just finished season 2, but I find funny how my wife and I are suddenly shouting “Allora!” ", "and “Buona Notte!” ", "around our house, just to immediately laugh after that. {", "lol emoji}\n\n“Master of None and the quest to find the best of everything”\n\nIn my opinion, Dev is a new kind of character for TV, one that you could call a “casual-urban optimizer”. ", "Let me explain: yes, he goes to fancy restaurants, has great taste in music, wears nice clothes and live in a loft that I wish it were mine. ", "But Dev is not elitist or pretentious about his lifestyle – he just likes to find the best stuff that’s out there, and has fun while at it.", "\n\nNow the thing is: I can relate to that. ", "I still check Foursquare, Tripadvisor, Facebook, Instagram and whatnot in search for tips before going or even choosing a bar or a restaurant. ", "Where should I go? ", "What should I order? ", "I want to make the most of it! ", "You probably know a Dev – or might even be a Dev too – but is not that common to see someone like this on TV.", "\n\nEither way, nearly every episode features some notable mouth-watering meal. ", "I’m sure some of it are product placement (it has to, right?!), ", "but since is so well incorporated to the show’s identity, it does not bother, at all. ", "Also, if this is what it takes to dream about a meal like that…\n\n… who cares?!", "\n\n“I’m getting hungry. ", "Why should I watch MoN?”, ", "you might ask.", "\n\nWell, Master of None also excels at mixing light and fun subjects that might end up forgotten or even sucked up in our daily rush to get things done with some red flags subjects like religion, parents, racism, feminism, being single, being married… the list, much like our life, goes on.", "\n\nIf you haven’t seen the show yet, go and do yourself a favor. ", "The music is great, the photography is beautiful and the dialogue is remarkable. ", "Dev’s conversations with his friends are the glue that holds Master of None together. ", "It reminds me of another great TV show – Seinfeld: some of the funniest and most insightful moments occur when they are arguing while sitting around a table or just walking down the street.", "\n\nThese scenes make you feel like you’re part of Dev’s crew, and are definitely part of the reason why Master of None is so easy and, much like the food depicted on the show, delightful to binge-watch.", "\n\nSo, who’s up for a bite?" ]

{ "pile_set_name": "OpenWebText2" }

[ 0, 0.006944444444444444, 0, 0, 0.013157894736842105, 0.021164021164021163, 0.023809523809523808, 0.02027027027027027, 0.006578947368421052, 0, 0, 0, 0, 0, 0, 0.0055248618784530384, 0, 0.014388489208633094, 0, 0.013986013986013986, 0, 0, 0, 0.01834862385321101, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.011627906976744186, 0, 0.004975124378109453, 0 ]

[ "Research centers and laboratories at the University of California, Berkeley\n\nThe University of California, Berkeley, contains many research centers and laboratories.", "\n\nSpace Sciences Lab\n\nSETI@Home\n\nHelen Wills Neuroscience Institute\n\nLawrence Berkeley National Laboratory\n\nMathematical Sciences Research Institute\n\nRenewable and Appropriate Energy Laboratory\nThe Renewable and Appropriate Energy Laboratory (RAEL) is a research laboratory based at the University of California, Berkeley led by Dan Kammen. ", "It focuses on designing, testing, and disseminating renewable and appropriate energy systems.", "\n\nCenter for New Music and Audio Technologies\n\nCenter for the Built Environment\n\nBerkeley APEC Study Center\n\nThe Berkeley APEC Study Center (BASC) is an APEC Study Center. ", "It was established in 1996 in response to the Asia-Pacific Economic Cooperation (APEC) Leaders Education Initiative introduced by President Bill Clinton and endorsed by the leaders of the other APEC member nations at their historic meetings on Blake Island, Seattle in November 1993. ", "BASC conducts multidisciplinary research activities that analyze political, economic and business trends in the Asia-Pacific with a special emphasis on the APEC forum. ", "The institute also provides academic supports for the dissemination of APEC's mission and conducts \"international conferences, colloquia, and outreach to the business and policy community\". ", "BASC is currently engaged in researching domestic determinants of East Asian regionalism and the effects of the rise of Russia, India and China on the U.S.-EU transatlantic alliance. ", "Previous areas of research include Northeast Asian and Asian institutional architecture, bilateral trade agreements in the Asia-Pacific, EU transregionalism strategies, and strategies for international trade and politics in Latin America.", "\n\nThe Berkeley Roundtable on the International Economy (BRIE)\nBRIE conducts a variety of research in the area of political economy, with a particular focus on high-tech trade. ", "BRIE projects have shown, for example, that national comparative advantage is created not revealed, that high-tech trade patterns are massively influenced by domestic policies, and that what a nation produces and trades—the composition of domestic production—matters for its growth and security. ", "BRIE is co-directed by Professors John Zysman and Steven S. Cohen, though a number of other faculty members, visiting scholars, and graduate students are also affiliated with the institute.", "\n\nInstitute of International Studies\nThe Institute of International Studies was established in 1955, and its current research focuses on peace and global security in the 21st century; environment, demography, and sustainability; globalization, development, and human rights; and technological change and the transformation of the global economy. ", "IIS hosts several major research programs, provides support to Berkeley faculty, awards fellowships to Berkeley graduate students, and offers research training to undergraduates.", "\n\nRegional and Area Studies Centers\nUC Berkeley hosts a number of research units that are focused on specific areas of the world. ", "These centers host visiting scholars, organize events, provide support to Berkeley faculty and students, and perform a wide array of other functions. ", "A number of the institutions focus on Asia; the Institute of East Asian Studies often collaborates with the Center for Japanese Studies, the Center for Chinese Studies, the Center for Korean Studies, Center for Southeast Asia Studies, and the Center for Buddhist Studies. ", "Other research centers include the Canadian Studies Program, the Center for African Studies, the Center for Latin American Studies, the Center for Middle Eastern Studies, the Center for South Asia Studies, the Institute of European Studies, and the Institute of Slavic, East European, and Eurasian Studies.", "\n\nInstitute of Transportation Studies\n\nInstitute of Transportation Studies has been recognized as one of the world's leading centers for transportation research. ", "They also conduct industry specific education programs.", "\n\nReferences\n\nExternal links\n UCB Research Units\n About Berkeley - Research\n\nCategory:University of California, Berkeley-related lists\nCategory:Laboratories in California\nCategory:Lists of universities and colleges in the United States\nCategory:Research institutes in the San Francisco Bay Area\nCategory:Science and technology in the San Francisco Bay Area\nCategory:University and college laboratories in the United States\nCategory:University of California, Berkeley" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.006060606060606061, 0.01466275659824047, 0, 0.011627906976744186, 0.01056338028169014, 0.005952380952380952, 0.005263157894736842, 0, 0.004201680672268907, 0.005681818181818182, 0.0033783783783783786, 0.015873015873015872, 0.002890173410404624, 0.011235955056179775, 0, 0.006666666666666667, 0.022058823529411766, 0.02287581699346405, 0, 0, 0.006437768240343348 ]

[ "\"By the way, that was slow and easy.\" \"", "I don't think you should do it.\" \"_\" \"", "Most jocks are a bunch of narcissistic jerks.\" \"", "I have been asked to be the interim head coach.\" \"", "Congratulations.\" \"", "So, if my job doesn't look like yours, then it's not legitimate?\" \"", "You can barely pay your rent.\" \"", "I'm 20 years old.\" \"", "I don't need to think about my future.\" \"", "This would make a good musical.\" \"", "Why don't we work on this, together?\" \"", "You could be the composer?\" \"", "I'm in.\" \"", "You invited me for a booty call, I want more than that.\" \"", "That's called a relationship.\" \"", "I guess we just want different things.\" \"", "Are you saying that you regret having sex with Tank, or that it was not consensual?\" \"_\" \"", "If we're gonna get past this,\" \"I need you to know the truth and be okay with it.\" \"_\" \"", "♪ Oh, oh, oh, oh, whoa ♪\" \"♪ oh, oh, oh, oh, whoa ♪\" \"♪ the world is yours to shape ♪\" \"♪ just possibilities ♪\" \"_\" \"_\" \"_\" \"_\" \"_\" \"_\" \"_\" \"_\" \"_\" \"_\" \"_\" \"_\" \"11 wins in a row!\" \"", "Suck it, artificial intelligence.\" \"", "I didn't know you were back on house arrest?\" \"", "Ha, that's funny.\" \"", "I will have you know I have an excellent excuse for wasting so much time.\" \"", "My \"Everyday Hero\" project is officially on hold.\" \"", "I thought you just got the go-ahead to paint all those benches?\" \"", "I did, but now they need to do background checks on everyone that I picked.\" \"", "Including the 79-year-old woman who volunteers as a crossing guard.\" \"", "Gotta make sure that she's not some drug kingpin.\" \"", "Any word from Emmett?\" \"", "No.\" \"", "Every day I wake up thinking today will be the day that he calls, and then total radio silence.\" \"", "It's like torture.\" \"", "Just give it time.\" \"", "He'll come around, honey.\" \"", "John:\" \"Yeah.\" \"", "I got it, thanks.\" \"", "That is ridiculous!\" \"", "Haven't had my first cup of coffee and already I'm putting out fires.\" \"", "What's wrong?\" \"", "Another one of my assistants quit.\" \"", "Everyone's jumping ship to follow Coach Walsh to his new team.\" \"", "I'm sorry, honey.\" \"", "Leaving me completely short-handed.\" \"", "We have this huge game against the Badgers this week.\" \"", "If we win, I'm going to ask the athletic director to call off the search for the new head coach and give me the job full time.\" \"", "Wow.\" \"", "Where am I going to find help with such short notice?\" \"", "Oh, you're kidding, right?\" \"", "You said Al you're doing is playing the waiting game?\" \"", "Honey, this would be great!\" \"", "I would love you to work with me.\" \"", "It'll keep your mind off Emmett.\" \"", "All right.\" \"", "Really?\" \"", "You're in?\" \"", "Let's play ball!\" \"", "So, uh, let me get your number?\" \"", "Um...\" \"Royce.\" \"", "Royce.\" \"", "I know that.\" \"", "You know what?\" \"", "It's cool.\" \"", "I'm just gonna see you around.\" \"", "Oh, hey.\" \"", "Have I mentioned what a bad idea it is to get involved with someone who lives right down the hall?\" \"", "Another Mingo sighting?\" \"", "He hooked up with some girl last night.\" \"", "I have a great idea to take your mind off him.\" \"", "We should join a sorority!\" \"", "I'm not the sorority type.\" \"", "Well, you know, party girls whose main talent is holding each other's hair back while they puke?\" \"", "I'll give you a pass on that stereotyping because you have had a bad morning.\" \"", "I hear it's a lot of fun.\" \"", "And don't you want to leave college with a few good stories to tell?\" \"", "I could stand to meet a few people.\" \"", "Yes!\" \"(", "Giggling)\" \"(Both giggling)\" \"You know how I've been looking all over for a place to do my ukulele circle?\" \"", "Well, I finally found one.\" \"", "The Cracked Mug, Regina's new coffee house.\" \"", "It's so nice of her.\" \"", "Yeah.\" \"", "Good game last week.\" \"_\" \"", "Who's that?\" \"_\" \"", "She signs.\" \"", "She must be in the deaf program?\" \"_\" \"", "Your stock is on the rise around here.\" \"", "Hey, what's up?\" \"", "So, T-money, we going out again, tonight?\" \"_\" \"(", "Laughing)\" \"_\" \" _ - _\" \"_\" \"Enjoy your night, \"T-money.\"\" \"(", "Accompanied by piano) ♪ I wanna find an up-and-comer ♪\" \"♪ and make a little whoopee ♪\" \"♪ it's fun without any strings ♪\" \"♪ it's love without any rings ♪\" \"♪ and that's why I wanna be ♪\" \"♪ a baseball groupie ♪\" \"I'll be waiting by the bus.\" \"", "Yes!\" \"(", "Applauding)\" \"Oh my god, I love it!\" \"", "Really?\" \"", "You're not just being polite?\" \"", "Well, you can count the number of Broadway shows I've seen on one hand, but if the rest of the songs are that good, you've got a massive hit on your hands.\" \"", "Well, how do you feel about this massive hit having its world premiere at the cracked mug?\" \"", "We need a place to put on a showcase.\" \"", "Maybe stage a few numbers?\" \"", "Invite some potential investors?\" \"", "Are you kidding?\" \"", "Eric and I could stand to get some butts in the door.\" \"", "How's next week?\" \"", "I'll call him right now.\" \"", "Well, that was easy.\" \"", "Okay, I'm gonna put up fliers at UMKC, and we have to rehearse every night this week.\" \"", "Yeah, uh, except Thursday.\" \"", "I'm taking Lily to Vesuvius.\" \"", "Whoa, fancy.\" \"", "Yeah.\" \"", "I'm going to ask her to move in with me.\" \"", "And I hope she reacts better than that.\" \"", "I love Lily, but don't you think it's a little soon after Nikki to get so involved with someone?\" \"", "One of the problems with me and Nikki was we never had the chance to live together before we got married.\" \"", "And honestly, I wasn't asking for your opinion.\" \"", "You're right.\" \"", "Forget I said anything.\" \"", "I will.\" \"", "Can we get back to work?\" \"", "Skye:\" \"So, how are you doing?\" \"", "I get it.\" \"", "Breakups are the worst.\" \"_\" \"", "Well, I'm here if you ever want to talk.\" \"_\" \"_\" \"", "To make your own student film?\" \"", "You realize they don't usually let freshman direct, right?\" \"", "In fact, I'm pretty sure the list begins and ends with George Lucas.\" \"_\" \"", "You'd knock it out of the park.\" \"_\" \"", "I'd love to.\" \"(", "Chuckling)\" \"♪ ♪\" \"♪ isn't it funny?\" \"", "♪\" \"♪ I like to dance when I'm on my own ♪\" \"♪ whenever it's sunny ♪\" \"Why does it feel like we've walked into a beauty contest?\" \"", "♪ I fly in my dreams almost every night ♪\" \"♪ ♪\" \"Okay, maybe you were right?\" \"", "Maybe this isn't for me?\" \"", "No, that's ridiculous.\" \"", "Any sorority here would be lucky to have you.\" \"", "♪ Mind the gap, mind the girl ♪\" \"♪ have another drink on me ♪\" \"♪ grab a seat in the world ♪\" \"I know that girl from my geology class.\" \"", "♪ ♪\" \"(Laughing) That's hilarious!\" \"", "Go for it!\" \"", "Come.\" \"", "I'll introduce you.\" \"", "Um, do your thing.\" \"", "I'll be here if you need me.\" \"", "♪ Not everything's peachy, no ♪\" \"♪ but let's keep a good attitude ♪\" \"♪ my friends know I always run late on a plan ♪\" \"♪ ♪\" \"Hi, I'm Erin.\" \"", "Theta.\" \"", "Theta Delta Pi.\" \"", "Daphne.\" \"", "I saw you signing.\" \"", "One of my study partners is in the deaf program.\" \"", "Are you rushing?\" \"", "I'm just here supporting a friend.\" \"", "I'm pre-med.\" \"", "I don't think I'll have time.\" \"", "Yeah.\" \"", "I said the same thing last year.\" \"", "What do you mean?\" \"", "I was drowning.\" \"", "But the senior Thetas helped me pick my schedule, they gave me advice on the best professors.\" \"", "Look, I'm telling you, it's worth joining just for the test banks alone.\" \"", "Tests from all the previous years?\" \"", "Yeah.\" \"", "And since Thetas tend to be over-achievers, the networking is pretty insane.\" \"", "Wow.\" \"", "I thought it was just a bunch of dumb parties.\" \"", "First of all, they aren't dumb, they're awesome.\" \"", "And, like anything, you can find the clichés if you're looking for them.\" \"", "You're right.\" \"", "And hopefully, it's like finding your tribe.\" \"", "When you know, you know.\" \"", "So, you want to meet a few people?\" \"", "Yeah, I do.\" \"", "♪ ♪\" \"♪ mind the gap, mind the girl ♪\" \"I need you to make a very straight line from third base here, all the way there to home plate.\" \"", "Okay?\" \"", "Very straight.\" \"", "Got that?\" \"", "Yep.\" \"", "You're talking to an artist here.\" \"", "Making lines is kind of my thing.\" \"", "Okay, thank you, sweetie.\" \"", "I'm checking in with Travis now.\" \"(", "Phone buzzing)\" \"Hey!\" \"", "Uh, hey?\" \"", "Hey, hi, Emmett?\" \"", "What... _\" \"Hey.\" \"", "Oh, I am so glad that you called.\" \"", "It's really good to see you.\" \"_\" \"_\" \"", "Oh.\" \"(", "Sighs)\" \"So, how have you been?\" \"_\" \"_\" \"", "That's great!\" \"", "That's really great.\" \"", "I got commissioned by the city to do an art project.\" \"_\" \"_\" \"", "Look at us.\" \"", "Still a power couple, right?\" \"_\" \"_\" \"", "Oh, uh, sure.\" \"", "Hey, I miss... you...\" \"(Sighs)\" \"That's your third bouncer, today.\" \"_\" \"", "Okay, no, no, no.\" \"", "Whatever is going on, leave it in the locker room, okay?\" \"", "When you're here, I need your head in the game.\" \"", "You understand me?\" \"", "Bay, where's Bay?\" \"", "Bay!\" \"", "Get over here!\" \"", "You got your phone?\" \"", "Yeah, why?\" \"", "Okay, I need you to video this young man so that I can show him everything that he's doing wrong today.\" \"", "Okay?\" \"", "I'm gonna go work with the infielders.\" \"", "Good luck.\" \"", "Someone needs a Xanax.\" \"_\" \"", "You okay?\" \"_\" \"", "All right, what did you do?\" \"_\" \"", "Because you're the guy and she is the nicest person on the planet.\" \"_\" \"", "Oh, apologize.\" \"", "Profusely and immediately.\" \"_\" \"", "No!\" \"", "No, no, no, no!\" \"", "This is not the end.\" \"_\" \"", "Do you still love her?\" \"_\" \"", "Then you have to keep talking to each other.\" \"", "You two are meant to be together.\" \"", "There is no way that I am letting you go down without a fight.\" \"", "Hey, Red, wait up!\" \"", "Whoa, hey, hey.\" \"", "Hey, where is the fire?\" \"", "I can't talk.\" \"", "I have way too much studying to do before pref day.\" \"", "Whoa.\" \"", "You're rushing?\" \"", "Yeah.\" \"", "Why?\" \"", "Just did not strike me as the type.\" \"", "What do you know about it?\" \"", "A lot, actually.\" \"", "You got the tri-ups.\" \"", "Those girls will drink you right under the table.\" \"(", "With Southern accent) Rho Kappa Eps are your good old Southern girls.\" \"", "Although they are a bit prissy for my tastes.\" \"", "And then... you've got the Thetas.\" \"", "My personal favorite.\" \"", "Sounds like you have a lot of experience.\" \"", "Um, you're mad at me about yesterday morning.\" \"", "Not sure what you're talking about.\" \"", "I just wanted to let you know that it wasn't like I was trying to rub your face in it or anything.\" \"", "It was just bad timing.\" \"", "It's fine.\" \"", "You were honest with me about who you are.\" \"", "Hook up with whoever you want.\" \"", "Ugh, I'm sorry Travis got you involved.\" \"", "I'm not.\" \"", "You two are my friends, and I'm just here to help.\" \"", "Talk to me.\" \"", "I don't know.\" \"", "It's that whole jock culture.\" \"", "It's the game.\" \"", "It changes them.\" \"", "Well, right now, it's the other way around.\" \"", "What do you mean?\" \"", "He's miserable.\" \"", "He can't hit the broad side of a barn.\" \"", "Maybe one of those Spirit Girls can help him out.\" \"", "What are Spirit Girls?\" \"", "Pocket-sized hotties that go to all the games.\" \"", "Is that was this is about?\" \"", "Mary Beth, Travis would never cheat on you.\" \"", "If he did, I'd kill him.\" \"", "It's not just that.\" \"", "He used to be so sweet and considerate.\" \"", "Now, it's like he barely knows I exist.\" \"", "You just hit a bump in the road.\" \"", "You two are good together.\" \"", "You have a history.\" \"", "You don't just throw all of that away.\" \"", "Talk to him tell him how you feel.\" \"", "No, I'm not gonna nag him.\" \"", "If he wants to talk, he can come to me.\" \"(", "Sighs) Fine.\" \"", "I'll talk to him.\" \"", "♪ ♪\" \"♪ girls playing tonight ♪\" \"♪ at terminal five ♪\" \"Welcome to pref day.\" \"", "I'm Stephanie.\" \"", "I'm your rush counselor.\" \"", "Over the next few hours, you'll be interviewed by the five sororities on campus.\" \"", "At the end, you'll rank your top three in order of preference.\" \"", "If you match, you'll get a bid.\" \"_\" \"_\" \"_\" \"_\" \"_\" \"", "Ok, ladies.\" \"", "Let's get started.\" \"(", "Giggling)\" \"_\" \"_\" \"(Both laughing)\" \"Kathryn, hi!\" \"", "What are you doing here?\" \"", "I was just putting up fliers for our musical showcase.\" \"", "Excellent!\" \"", "This is Julian Stanton.\" \"", "He's one of our professors in the deaf program.\" \"", "Pleasure to meet you.\" \"", "Hi, I'm Kathryn Kennish.\" \"", "Julian recently joined from Gallaudet.\" \"", "It was a tough call, but Lily is quite the persuasive recruiter.\" \"", "How do you two know each other?\" \"", "Oh, Kathryn's my b... um...\" \"You know Daphne Vasquez in our program?\" \"", "Kathryn's her mum.\" \"", "Oh, I see the resemblance.\" \"(", "Nervous laughter)\" \"Thank you.\" \"", "Well, I have to run.\" \"", "I'll see you at the staff meeting, later?\" \" ", "Yeah, I'll see you later.\" \" ", "All right.\" \"", "Bye.\" \"", "Oh, gosh!\" \"", "I'm late for a class visit.\" \"", "Shall I take some of those and put them across the other side of campus?\" \" ", "Yeah, sure.\" \"", "Thank you.\" \" ", "Cool.\" \"", "Okay.\" \"", "Bye.\" \"", "So, tell me why you want to be a Theta?\" \"", "Well, I want to be a part of the sisterhood.\" \"", "You don't have to give me the canned answer.\" \"", "Just relax.\" \"", "Right.\" \"", "Okay.\" \"", "Um...\" \"Well, Thetas put a big emphasis on academics.\" \"", "That's something that's really important to me.\" \"", "I got a 4.0 GPA all through high school.\" \"", "I'm doing my best to continue the trend.\" \"", "Well, we don't like to focus on ourselves all the time.\" \"", "I worked at a free clinic in East Riverside last year.\" \"", "That's really why I decided to go pre-med.\" \"", "To help those less fortunate.\" \"", "Oh.\" \"", "Uh, here's a fascinating thing about me,\" \"I was switched with another baby at the hospital.\" \"", "I was raised by the wrong set of parents.\" \"", "We didn't find out till I was 15.\" \"", "Wow.\" \"", "And, it turns out that my biological father is John Kennish.\" \"", "He played for the Royals.\" \"", "Kind of a celebrity.\" \"", "Crazy, right?\" \"", "I don't really follow sports.\" \"", "Oh, he's also a state senator.\" \"", "And my mom is Kathryn Kennish, the novelist.\" \"", "She wrote a book about us.\" \"", "It was a bestseller.\" \"", "Cool.\" \"", "I think you should meet some of the other Thetas.\" \"", "Oh, that'd be great!\" \"", "Here's our rush chair now.\" \"", "Daphne, this is Royce.\" \"", "Hi, nice to meet you.\" \"", "Hi.\" \"", "You look so familiar to me.\" \"", "Do we have a class together?\" \"", "I don't think so.\" \"", "Hmm.\" \"", "What's your major?\" \"", "Pre-med.\" \"", "Ah, I'm Russian lit.\" \"", "Hmm.\" \"", "What dorm do you live in?\" \"", "Hanes.\" \"", "I saw you yesterday morning.\" \"", "Oh, you have nothing to be embarrassed about.\" \"", "That guy Mingo hooks up with everyone.\" \"", "Oh...\" \"No, no!\" \"", "I mean, even me.\" \"", "Well, just that one time.\" \"", "We're not together or anything.\" \"", "He doesn't want a relationship, so...\" \"I'm gonna stop talking now.\" \"", "Oh, it's fine, really.\" \"", "So, you're pre-med?\" \"_\" \"", "Hi.\" \"", "I'm looking for lily Summers.\" \"_\" \"", "No.\" \"", "It's okay.\" \"", "Thank you.\" \"", "Oh, hi, Kathryn, you're still here?\" \"", "Yeah.\" \"", "I was just gonna put some more musical fliers up here, but, um, I...\" \"I gotta go home.\" \"", "Kathryn.\" \"", "You get close to people you work with, but I promise there's nothing going on between Julian and I.\" \"It's really... it's none of my business.\" \"", "No, I'm glad you came back so we could talk about it.\" \"", "But, I promise, you have nothing to worry about.\" \"", "Well, it's just that you introduced me as Daphne's mom, not Toby's.\" \"", "I did?\" \"", "I did.\" \"", "Look, does Julian know you have a boyfriend?\" \"", "Honey, I am not judging.\" \"", "It's just that I know how Toby feels about you, and I don't want to see him get his heart broken again.\" \"", "Yeah.\" \"", "Okay.\" \"", "I want all of you here two hours before the game, tomorrow.\" \"(", "Groaning)\" \"I was not asking for any opinions, okay?\" \"", "Everybody needs a really good warmup.\" \"", "3:00, no exceptions.\" \"", "That's it.\" \"", "Bay, it's all yours.\" \"", "All right.\" \"", "Well, now if you would all just stack your equipment right over here in some nice, neat piles.\" \"", "That... would be amazing.\" \"", "Or, you could do that.\" \"", "That works too.\" \"", "Thank you.\" \"", "Thank you.\" \"_\" \"", "Yeah.\" \"_\" \"", "No, of course not.\" \"", "But, think about it from her side.\" \"", "You're on this whole new journey without her.\" \"_\" \"", "You have to show her that she is still the most important thing in your life.\" \"", "Stephanie:\" \"Okay, it's time to write down your preferences.\" \"", "Remember, the more sororities you list, the better your chances of getting a bid.\" \"", "So, how did it go with Lambda?\" \"", "I think it went well.\" \"", "I liked all the girls, and they seemed to like me.\" \"", "So, you're gonna put them down first?\" \"", "Actually, I'm thinking about doing a suicide bid.\" \"", "Suicide?\" \"", "Just them.\" \"", "No one else.\" \"", "Are you sure?\" \"", "Lambda is where I feel like I belong.\" \"", "It's them or nobody for me.\" \"", "Hey, I got your text.\" \"", "What's up?\" \"_\" \"_\" \"", "Can't you reschedule?\" \"_\" \"", "First of all, I suck at pitching.\" \"", "It's one of the reasons I'm a DP and not a director.\" \"", "Second, my ASL is nowhere near good enough.\" \"_\" \"_\" \"", "Hey, Tim!\" \"", "Uh, have you seen Travis?\" \"", "Yeah, I saw him get into a car out front.\" \"", "Just a few minutes ago.\" \"", "Huh.\" \"_\" \"_\" \"", "Okay, it's 3:00, everyone checked in?\" \"", "I don't see Travis.\" \"", "He was heading to the locker room to go get an ice pack for his shoulder.\" \"", "I hope you mean a heat pack.\" \"", "Yeah, that one.\" \"", "Okay, when you see him, tell him I want him to do 12 pitches at 50 feet, and then 16 at 60.\" \"", "I will definitely tell him that.\" \"", "Here you go.\" \"", "Iris Watkins?\" \"", "I'm gonna wait for you.\" \"", "Stop torturing yourself!\" \"", "Go ahead.\" \"(", "Sighs)\" \"(Gasps and giggles)\" \"I'm in!\" \"", "I'm gonna be a Lambda!\" \"", "Yay!\" \"", "Oh!\" \" (", "Both laughing)\" \" Oh, congratulations!\" \"", "Yes, yes, yes.\" \"", "That's all of them.\" \"", "Oh, but Daphne didn't get an envelope?\" \"", "Oh, I'm sorry.\" \"", "If there's no envelope, it means you didn't get a bid.\" \"", "I don't understand.\" \"", "I made a single bid for Theta.\" \"", "I guess they didn't want me.\" \"", "Well, then they're idiots.\" \"", "It's fine.\" \"", "I wasn't really that into it anyway.\" \"", "Ok, here we go.\" \"", "One, two, a-one-two-three-four.\" \"(", "All playing ukulele)\" \"For you.\" \"", "And that's when our hero realizes... that he's broken the sound barrier...\" \"Forever.\" \"", "Really?\" \"", "So, it's the whole post-apocalyptic, dystopian Fritz Lang, thing?\" \"", "But it's silent.\" \"", "You got that, right?\" \"", "Epstein:\" \"Yeah, I got that.\" \"", "It's just that everyone wants to do silent since The Artist won the Oscar.\" \"", "So, it's a no?\" \"", "Emmett, you're pitching me what you think I want to hear.\" \"", "Next time, tell me a story that you want to watch.\" \"", "Something personal.\" \"", "Uh, Professor?\" \"", "A love story.\" \"", "About a deaf boy who falls in love for the very first time... with a hearing girl.\" \"", "Epstein:\" \"That's interesting.\" \"", "It certainly hasn't been done to death.\" \"", "Keep talking.\" \"", "Thank you.\" \"", "Yeah, I'll see you guys around.\" \"", "Okay.\" \"", "Thank you for coming.\" \"", "I wanna introduce you to everyone if you... _\" \"Oh, right.\" \"", "Well, let me drive you.\" \"", "I wanna be there to watch you pitch, anyway.\" \"_\" \"_\" \"", "Oh, well, you got a ride?\" \"_\" \"_\" \"", "Anna drove you all the way over here just to wait in the car?\" \"_\" \"", "Why would she do that?\" \"_\" \"", "A fan?\" \"", "Can't you see how ridiculous that is?\" \"_\" \"_\" \"_\" \"", "No, you're right.\" \"", "It shouldn't, but it does.\" \"", "I can't do this anymore.\" \"_\" \"", "I've worked really hard to be the kind of person who's not needy and insecure, but this relationship is turning me into someone I don't want to be.\" \"_\" \"", "You're a freshman in college.\" \"", "You should be able to hang out with whoever you want.\" \"", "Date whoever you want.\" \"_\" \"", "You're the first person I ever fell in love with.\" \"", "The first person I ever thought about a future with.\" \"", "I lost my virginity to you.\" \"", "I learned a new language for you.\" \"", "I will always love you.\" \"", "But this relationship isn't right for me anymore.\" \"", "Please, don't make it harder than it is for me to do this.\" \"", "All right, all right, let's go!\" \"", "Oh, hey.\" \"", "Athletic director just got here.\" \"", "Is my star pitcher all warmed up?\" \"", "Uh, not exactly.\" \"", "Where is he?\" \"", "Okay, don't freak out.\" \"", "Um, I was covering for him.\" \" ", "What?\" \" ", "I'm sorry, but he had something really important to do for Mary Beth.\" \"", "He's blowing off a ball game for his girlfriend?\" \"", "What the hell is he thinking?\" \"", "You can't blame it all on Travis.\" \"", "He was following my advice.\" \"", "I didn't know that he would miss the game.\" \"", "Bay, you're the one who is supposed to be on my side here.\" \"", "Do you have any idea how important this game is to me?\" \"", "Maybe too important?\" \"", "What did you just say?\" \"", "Travis is going through a really hard time, right now, but you don't care about that.\" \"", "If it's not about baseball, it doesn't matter to you.\" \"_\" \"", "You're not pitching.\" \"", "You are benched.\" \" ", "Dad, please!\" \" ", "Those are the rules.\" \"", "Please tell me that it went well with Mary Beth?\" \"", "Uh, can I talk to you?\" \"", "Sure.\" \"", "What's up?\" \"", "I didn't get a bid from Theta.\" \"", "I know.\" \"", "It was a competitive year, I'm sorry.\" \"", "I think we both know why I didn't get in.\" \"", "We do?\" \"", "We hooked up with the same guy and you blackballed me.\" \"", "Look, I'm not allowed to discuss the decision-making process.\" \"", "Ugh, okay, fine.\" \"", "I'm not even sure why I care, since it's catty, and shallow, and pretty much exactly what I expected from someone in a sorority before I started this whole stupid process.\" \"", "The reason you didn't get a bid had nothing to do with Mingo.\" \"", "In fact, I voted for you.\" \"", "Tara is the one who blackballed you.\" \"", "Tara?\" \"", "The girl you interviewed with.\" \"", "She said you were trying way too hard to impress her.\" \"", "I'm sorry you didn't get in.\" \"", "And, I'm even more sorry I hooked up with a guy that you are clearly obsessed with.\" \"", "But, if you're looking for a catty and superficial girl,\" \"I think you should try looking in the mirror.\" \" ", "Do you want anything else?\" \" ", "No, no, I'm good.\" \"", "Toby, this dinner was perfect, thank you.\" \"", "Okay then.\" \"", "Toby, if this is...\" \"No!\" \"", "No, it's not a ring.\" \"(", "Laughing nervously)\" \"With my history, that's totally fair.\" \"(", "Chuckles)\" \"No, uh, please, just open it.\" \"", "Okay.\" \"", "I want you to move in with me.\" \"", "I want to wake up next to you every morning.\" \"", "I want to go to sleep with you every night.\" \"", "I want you to be 10 feet away when I'm flossing.\" \"", "All of it.\" \"", "That's so lovely.\" \"", "Thank you.\" \"", "We can start moving your things in tonight.\" \"", "Toby...\" \"I have feelings for someone else.\" \"", "What?\" \"", "I didn't mean for it to happen, and nothing has happened.\" \"", "It's just feelings.\" \"", "And that doesn't mean that I don't still have them for you.\" \"", "Who is it?\" \"", "He's a colleague.\" \"", "We've spent a lot of time together.\" \"", "At work, I mean.\" \"", "I'm sorry.\" \"", "I really don't want us to break up.\" \"", "I'm just confused.\" \"", "Me too.\" \"", "Daphne:\" \"You should have seen me in that interview.\" \"", "I was overselling myself like I was in some bad infomercial.\" \"", "Aww, honey.\" \"", "And then, when I found out that I didn't get a bid,\" \"I got in this girl's face.\" \"", "I swear, two more minutes and I would have been pulling out her hair.\" \"", "I'm trying not to laugh.\" \"", "don't!\" \"", "It's mortifying!\" \"", "I didn't even know you were rushing.\" \"", "I don't know.\" \"", "I wasn't planning on it, but then you go through the process and you see everyone in their groups, and they all look so happy.\" \"", "And they have each other, and then you start to think,\" \"I need to do this.\" \"", "I need a group of overnight best friends.\" \"", "That's completely human.\" \"", "I never thought I'd be the kind of girl who got caught up in some outsider label of who's cool.\" \"", "And yet, I'm sitting here feeling like a total loser because the Thetas didn't want me.\" \"", "Sweetie, it doesn't make you pathetic that you want to find your people.\" \"", "I just don't think they're Thetas.\" \"", "Yeah, well, that's good because the Thetas don't think I'm their people, either.\" \"(", "Chuckling)\" \"You'll find them.\" \"", "Hmm?\" \"(", "Mugs clink)\" \"(Playing ukulele)\" \"(Knock at the door)\" \"Hey.\" \"", "Hey.\" \"", "Come on in.\" \"", "I can play almost anything, as long as it's in C.\" \"You got any requests?\" \"", "Yeah.\" \"", "I want you to give Travis another chance.\" \" ", "Bay, please.\" \" ", "Just listen.\" \"", "I know that you think that he is way too caught up in baseball, but he was late to the game, and my dad benched him.\" \"", "And our backup pitcher was a total disaster.\" \"", "And we ended up losing the biggest game of the year by seven runs.\" \"", "And Travis is persona non grata with the whole team.\" \"", "I didn't want that.\" \"", "I know.\" \"", "And...\" \"I'm not trying to make you feel guilty.\" \"", "I just want you to see what a priority you are to him.\" \"", "Sometimes, things just don't work out.\" \"", "I don't accept that.\" \"", "Well, I think you're gonna have to, 'cause it's really over.\" \"", "I'm sorry.\" \"", "Thanks.\" \"", "And just 'cause it's over for us, doesn't mean it's over for you and Emmett.\" \"", "What are you talking about?\" \"", "You're a good friend, and I know you care about me and Travis, but come on, that's the relationship you should be fighting for.\" \"(", "Sighs)\" \"(Playing the piano)\" \"Hey.\" \"", "What are you doing here?\" \"", "I thought you were out with Lily?\" \"", "Oh, we finished early.\" \"", "Huh.\" \"", "How was dinner?\" \"", "It was fine.\" \"", "Um, whole moving in thing is not gonna happen, though.\" \"", "Oh.\" \"", "You were right.\" \"", "I decided it's just too soon.\" \"", "Is there anything I can do to help?\" \"", "I was thinking maybe we could get some work done.\" \"", "Sure.\" \"", "You look beautiful.\" \"", "I'm on my way to bid night.\" \"", "I feel so bad.\" \"", "I wish you were going to your own.\" \"", "Go have a great time, then come back and tell me all their dirty little secrets.\" \"", "Wow.\" \"", "Wow.\" \"", "Wow.\" \"", "You are smoking.\" \"", "Do you go here?\" \"", "I'm Mingo, by the way.\" \"", "Very funny.\" \"", "So, uh, where's the fancy dress?\" \"", "I thought tonight was the big signing ceremony?\" \"", "Oh, um, I decided not to join a sorority.\" \"", "Um, you know, actually... the truth is I didn't get a bid.\" \"", "Oh.\" \"", "Well, that's their loss and my gain.\" \"", "Why is that?\" \"", "Sorority pledges have, like, no free time.\" \"", "I wouldn't see you for the next two months.\" \"", "Who says you're gonna see me?\" \"", "What are you doing, tonight?\" \"", "You wanna come up to my room, and like...\" \"Play darts?\" \"", "Uh...\" \"You know what, actually, not tonight.\" \"", "I'm busy.\" \"", "I'm hanging with my tribe.\" \"", "♪ ♪\" \"_\" \"_\" \"_\" \"_\" \"_\" \"_\" \"_\" \"♪ Been right here all ♪\" \"♪ along ♪\" \"♪ ♪\" \"_\" \"_\" \"Congratulations!\" \"", "You're making a movie!\" \"_\" \"", "Just let me be your DP.\" \"(", "Chuckling)\" \"(Woman vocalizing)\" \"What's all this?\" \"", "A new shipment of gloves came in.\" \"", "I'm breaking in the leather.\" \"", "Got an extra rag?\" \"", "Uh, so, how did it go with the athletic director?\" \"", "The search is still on.\" \"", "Guess I'm not getting that job.\" \"", "At least not yet.\" \"", "You were right, Dad.\" \"", "I should have been watching your back.\" \"", "There will be other games.\" \"", "You know, I'm tough on my guys because my coaches were tough on me, and that's what got me to the majors.\" \"", "I know this game better than I know anything else.\" \"", "This is what I'm supposed to be doing.\" \"", "♪\" \"I know what you mean.\" \"", "Hey, dad, do you think that you could find someone to fill in for me or a while?\" \"", "Sure, sweetie.\" \"", "Need to get back to that art project?\" \"", "No.\" \"", "Uh, not exactly.\" \"", "I'm going to L.A.\" \"(Woman vocalizing)\" \"♪ ♪\"" ]

{ "pile_set_name": "OpenSubtitles" }

[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.041666666666666664, 0, 0, 0, 0, 0, 0.0625, 0, 0, 0, 0, 0, 0.015384615384615385, 0, 0, 0.017857142857142856, 0, 0, 0, 0, 0, 0.03333333333333333, 0, 0.02857142857142857, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.038461538461538464, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.017857142857142856, 0, 0, 0, 0.011363636363636364, 0, 0, 0, 0, 0, 0, 0, 0.009259259259259259, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.013333333333333334, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.006993006993006993, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.010416666666666666, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.027777777777777776, 0, 0, 0.05263157894736842, 0, 0, 0, 0, 0, 0, 0, 0, 0.07142857142857142, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.034482758620689655, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.023809523809523808, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.043478260869565216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.058823529411764705, 0, 0, 0, 0, 0, 0, 0.018867924528301886, 0, 0, 0, 0.038461538461538464, 0, 0, 0.037037037037037035, 0, 0.014925373134328358, 0, 0.027777777777777776, 0.047619047619047616, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.017857142857142856, 0, 0.023255813953488372, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.015873015873015872, 0, 0, 0, 0, 0, 0.02127659574468085, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.02631578947368421, 0, 0, 0, 0, 0, 0, 0.02857142857142857, 0, 0, 0, 0.037037037037037035, 0.009433962264150943, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.027777777777777776, 0, 0.018518518518518517, 0.08333333333333333, 0.03571428571428571, 0, 0, 0, 0, 0.045454545454545456, 0, 0, 0, 0.010638297872340425, 0, 0, 0.0625, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.024390243902439025, 0, 0, 0, 0.030303030303030304, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.014705882352941176, 0, 0, 0, 0.012987012987012988, 0, 0.016666666666666666, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.014705882352941176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.02857142857142857, 0, 0, 0, 0, 0, 0, 0.013888888888888888, 0, 0, 0.027777777777777776, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0196078431372549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.015625, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.022727272727272728, 0, 0.03571428571428571, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.022222222222222223, 0, 0, 0, 0, 0, 0.01818181818181818, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.012658227848101266, 0, 0.007633587786259542, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.022222222222222223, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.043478260869565216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]

[ "The Lightning Network for Dummies: Part 1\n\nRouting and Capital Lock-Ups\n\nIn the past few months, we’ve seen a huge surge in interest around the Lightning Network with releases and community lead initiatives such as the Lightning Torch as well as a remarkable level of evangelism by a number of notable individuals — one favorite amongst the community is Square and Twitter CEO, Jack Dorsey.", "\n\nNaturally, this rise in popularity has coincided with a number of concerns regarding the network’s viability and the audience it is ultimately intended to serve. ", "In this article and subsequent, I will be addressing some of these concerns, so we can all more aptly understand Lightning’s current limitations and vectors for improvement.", "\n\nThe complexity of the Lightning Network is so vast, given all the BOLT specifications, as they’re planning to solve some of Lightning’s hardest economic/technical problems with very clever, advanced cryptography. ", "We think it’s important that everyone has a common understanding of the inter-workings so we can ensure the esoterica doesn’t lead to false or misleading media headlines.", "\n\nRouting Problems? ", "Not Quite\n\nThe Lightning Network uses onion-style routing whereby payment information is encrypted in a nested fashion so that intermediary nodes along the route only know who they received the payment from and who to send it to next. ", "This allows for the network to have a higher degree of privacy in the facilitation of its payments (provided that intermediaries don’t compare records).", "\n\nFor those not familiar with this sort of routing, take the instance, here, where A wishes to send a payment to E.\n\nBecause A has to define the route between it and E, it needs to keep an updated view of the entire network and there is no evidence this can be done at scale. ", "Now, you might be thinking to yourself — why does A need an entire view of the entire network, shouldn’t it just need to know one or more routes between it and E? ", "Well, you’re right, it doesn’t need to maintain a view of the entire network — although, this is one of the common concerns raised by critics of the Lightning Network. ", "So, we want to ensure we make this clear, right here. ", "Nodes do not need to maintain an updated view of the entire network, they only need to know how to route payments to counter-parties of interest to them. ", "The way in which this local view is created is up to participants (Ex: Alex Bosworth’s implementation), who are able to leverage all advertised channel information to do so.", "\n\nNote: For those who would like to know more about this system, please reference BOLT #7: P2P Node and Channel Discovery.", "\n\nMoving on… if A has identified a route between it an E (routing information in the Lightning Network for public channels is public domain and easily accessible), it must then determine if there is enough capital available in the route to make the payment. ", "Below, I have updated the previous diagram with the amount of capital available for lockup by each of the members of the channel.", "\n\nNote: It should be noted that this is an inaccurate representation of capital lockup in the Lightning Network (lockup is done between parties on channels, not by each party individually). ", "This explanation is merely used to get the point across of capital availability in the network for individual nodes and their capacity.", "\n\nSo, A wishes to send a 1 BTC payment to E and cannot find a route which can fully collateralize this payment. ", "Does anyone see what is wrong, here? ", "The Lightning Network is intended for small payments, 1 BTC is well beyond that and should really just be sent over the Bitcoin blockchain. ", "So, let’s try again with a few more decimal points.", "\n\nSo, let’s say that A wishes to send .0005 BTC (~$2) to E, but there is still not enough available capital in the known routes to send this transaction given that most of each intermediary’s capital is currently locked routing other payments. ", "Well, given that intermediaries in the Lightning Network take fees, it’s likely that someone would capitalize on this deficiency in the network and fill this gap.", "\n\nCapital Lock-ups\n\nAnother concern regarding Lightning is this idea that capital will be locked up for days in channels to facilitate payments — this is simply untrue. ", "Most time-locks in the Lightning Network can be greatly decreased to a matter of seconds given that most of the protocol can be automated through clever engineering of clients which can quickly facilitate the payment protocol and monitor all open channels.", "\n\nAnd what’s to stop A from making multiple payments to E? ", "A could very well send a payment of .0002 BTC along the H->I->J->E route while simultaneously sending a .0003 BTC payment along the K->L->E route or send multiple .0001 BTC payments along the B->C->D->E route. ", "I point this out because many critics ignore the ability to packetize payments with things like AMP to facilitate larger transactions on the Lightning Network.", "\n\nSo, if A does decide to do this, it would create a routable payment that was encrypted such that only K could decrypt it to see that they needed to send it to L who could then decrypt to see that they needed to send it to E who could then decrypt it and get the plaintext payment. ", "And in this way, we are able to send payments in a semi-private manner as intermediaries only know who they get the payment from and who it is going to. ", "This is only semi-private, though, given that intermediaries could compare information to gather the full route of the payment.", "\n\nI’d like to show you a picture of the Lightning Network from a few months ago to illustrate a few additional points, here.", "\n\nAs anyone can clearly see, Lightning (like any decentralized network) is developing its own set of supernodes / hubs — something that my example didn’t even account for. ", "This means that new participants of the network will be provided with the optionality of connecting to only those whom they care about or connecting to a supernode and having access to a much larger group with only a single hop. ", "This greatly diminishes the memory overhead that nodes will have to maintain for route in the network and also allows for much shorts routes in the network through more reliable channels.", "\n\nNow, sending payments through a single hop can completely undermine any privacy for payments, but it’s a tradeoff that users are free to make for themselves. ", "And that’s one of the great things about this project — users are free to take as much or as little risk that they please with the capital they put up as well as the payments that they elect to facilitate.", "\n\nGoing Forward\n\nI look forward to the continued expansion and development of the Lightning Network. ", "I’m quite sure there will be additional concerns raised as the network continues gaining popularity, but people should bear in mind that most of these are not innate to the network and can be resolved with clever engineering.", "\n\nWe hope these primers serve as a means overtime to debunking the technical misunderstandings of Lightning to ensure that myths don’t proliferate; don’t just trust, verify.", "\n\nTable of Contents" ]

{ "pile_set_name": "OpenWebText2" }

[ 0.010256410256410256, 0, 0, 0.013953488372093023, 0, 0, 0, 0, 0.0036231884057971015, 0, 0.005952380952380952, 0, 0, 0.005780346820809248, 0.02459016393442623, 0.003875968992248062, 0, 0.005263157894736842, 0, 0, 0, 0.014285714285714285, 0, 0, 0.006172839506172839, 0, 0.00390625, 0, 0, 0.012578616352201259, 0, 0, 0, 0.008064516129032258, 0, 0, 0, 0, 0, 0.009900990099009901, 0, 0, 0 ]

[ "Robert Amsel\n\nRobert Amsel (born August 16, 1946 in Albany, New York) is an LGBT activist mainly known for his work in the Mattachine Society, a gay civil rights organization that was prominent in New York City throughout the 1960s. ", "When the society disbanded in 1987, he was one of its most active members.", "\n\nBiography\nWhile attending Syracuse University between 1964 and 1968 (from which he obtained a Bachelor of Fine Arts degree), he came out into gay life. ", "During the summer of 1967, while staying with his sister in New York, he volunteered at the Mattachine Society. ", "As a result, he met Dick Leitsch, then president of the group.", "\n\nMadolin Cervantes, a heterosexual woman who devoted her life to homosexual equality and was an officer of the society, had a large, rent-controlled apartment on West End Avenue, where the couple lived for another year, upon Amsel's graduation from Syracuse University. (", "During Amsel's senior year, Leitsch had shared an apartment with Amsel in Syracuse but traveled back and forth between Syracuse and New York.)", "\n\nAccording to Amsel, \"Our phones in Madolin's pension, as we called it, were tapped, presumably by the F.B.I., who regarded folks seeking gay equality as a subversive group. ", "In those days, tapping was primitive and reel-to-reel tape recorders were used to record private conversations. ", "Frequently, the tape would run out and one could actually hear the spinning of the tape reels. ", "When you know you're being taped, you might as well have fun with it. ", "For this reason, I would have outrageous conversations in which I provided blow-by-blow descriptions of wild sexual escapades with prominent political foes of the era. ", "If possible, we never said anything over the phone lines that was true.\"", "\n\nAt the time of the Stonewall riots, Dick Leitsch had been upgraded to executive director of Mattachine and Amsel was its president. ", " Amsel would later write a cover article for the September 15, 1987, edition of The Advocate. ", "The article, cumbersomely titled by the magazine as \"Back to Our Future? ", "A Walk on the Wild Side of Stonewall\", was written by Amsel to \"set the record straight – or gaily forward.\" ", " (An edited version, titled \"Recalling the Stonewall Uprising\", appears in the college textbook, \"America Firsthand, Volume 2, Eighth Edition,\" Bedford/St. Martin's, 2011.) ", "Over the 18 years since the riots had occurred, they had evolved more into myth than fact and all the previous work of fighting for gay equality had been forgotten. ", " Additionally, Amsel strove to unite gay people in their then current fight against a callous Administration in Washington regarding the AIDS epidemic. ", " During this period, Amsel volunteered as a \"buddy\" to AIDS victims.", "\n\nAlthough Amsel played second-fiddle to his older lover, several of his own contributions to the gay movement included setting up a Mattachine Society branch in Syracuse, New York, which ultimately died out but was supplanted by newer organizations. ", " He also was one of a group of four Mattachine workers who started the now-common practice of surveying political candidates for office on gay rights issues.", "\n\nIn 1978, the faltering relationship of Amsel and Leitsch ended when Amsel moved to London for several years. ", " Amsel returned to New York in the summer of 1981 but ultimately moved to Harrisburg, Pennsylvania, where he purchased a house, which he renovated and eventually sold. ", "He moved to Steelton, PA. ", "Continuing his education, he also received his master's degree in American Studies from Penn State - Harrisburg.", "\n\nIn recent years, he has authored two supernatural novels, \"Manhattan Pharaoh\" (2004) and \"Devil Goddess\" (2006). ", " Although not gay novels per se, both books have prominent homosexual characters, as might be expected.", "\n\nSee also\nLGBT history\nLesbian American history\nMattachine Society\n\nReferences\n\nExternal links\nAmsel, Robert. \"", "Recalling the Stonewall Uprising\", \"America Firsthand, Volume 2, Eighth Edition, Bedford/St. Martin's, 2010 http://www.bedfordstmartins.com/Catalog/Product.aspx?isbn=9780312489076&tab=tableofcontents\nAmsel, Robert. \"", "Back to Our Future? ", "A Walk on the Wild Side of Stonewall\", The Advocate, 15 September 1987.", "\nhttps://www.cs.cmu.edu/afs/cs/user/scotts/bulgarians/stonewall.txt\n\nCategory:Living people\nCategory:1946 births\nCategory:American civil rights activists\nCategory:LGBT people from New York (state)\nCategory:LGBT rights activists from the United States\nCategory:People from Albany, New York\nCategory:Activists from New York (state)" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.012875536480686695, 0, 0.006493506493506494, 0.008928571428571428, 0.016129032258064516, 0.011029411764705883, 0.028169014084507043, 0.011428571428571429, 0, 0, 0, 0, 0, 0.029850746268656716, 0.02127659574468085, 0, 0.009174311926605505, 0.011560693641618497, 0, 0.013157894736842105, 0.014705882352941176, 0.00796812749003984, 0.006369426751592357, 0.02702702702702703, 0, 0, 0.017857142857142856, 0, 0, 0.017857142857142856, 0.018518518518518517, 0, 0.014084507042253521, 0.00303951367781155 ]

[ "Gaia tops one trillion observations\n\nOn 14 April 2018, about 10 days before the second Gaia Data Release, the spacecraft and daily data processing systems have reached yet another stunning milestone: the number of star transits has reached 100 billion!", "\n\nThe Gaia satellite has two telescopes pointing to two regions of the sky separated by 106.5 degrees. ", "The satellite spins at a rate of 6 hours per revolution with the two telescopes scanning a great circle and the stars continuously transiting the focal plane. ", "Every day, Gaia instruments record about 70 million transits. ", "A full transit includes an observation in the sky mapper (to detect the objects in the sky), 9 observations for astrometry, 2 for spectrophotometry and 3 for radial velocity measurements (see a video explaining the measuring process here: https://www.youtube.com/watch?v=bbfb8VhH7L0). ", "Roughly speaking, each transit yields 10 individual observations for astrometry (counting the sky mapper). ", "Therefore, the 100 billion individual transits mean 1 trillion (1000 billion) individual observations acquired.", "\n\nThere are obviously more transits than real, physical objects. ", "As already anticipated, Gaia DR2 will contain “only” 1.7 billion sources, but each of them has been observed a number of times – that is, the features of each source have been determined from the data of several transits. ", "We have estimated that each source will be observed, on average, in 70 transits during the nominal five-year mission, which means we should reach (and most probably exceed) 120 billion transits – that is, 1.7 billion sources times 70 transits. ", "So far, in 3.7 years of nominal operations and considering 1.7 billion sources, Gaia has already observed each source more than 50 times on average.", "\n\nAs a consequence of the non-uniform density of sources in the sky, the number of objects transiting the focal plane varies very significantly with time. ", "Figure 1 shows a time-time illustration of this fact. ", "In the top panel, the horizontal axis is the day since the start of nominal operations (labelled in months), the vertical axis is the minute of the day (labelled in hours), and the colours indicate the average number of transits per second acquired during that day and minute. ", "As said, the density of transits strongly varies with time, from just a few tens per second up to several thousands per second when Gaia observes from the emptiest areas of the sky to the densest areas of the Milky Way.", "\n\nThe top panel of Figure 1 shows some interesting features. ", "One can see black “gaps”, which correspond to the times when the Gaia instruments were not acquiring data. ", "Some are just calibration or on-board configuration activities, others are spacecraft manoeuvres, and others are “safe modes” – with the February 2018 event being the most remarkable one, easily seen towards the right end of the plot. ", "Overall, Gaia instruments have been off during less than 1.7% of the time (with almost half of this time corresponding to the mentioned safe mode).", "\n\nApart from the gaps, changes in the way of scanning and changes in the way of working of the instruments are seen as sudden changes in the picture. ", "The most remarkable feature of the plot is the observational pattern, which basically corresponds to the four revolutions per day and the two viewing directions. ", "Each telescope crosses the Milky Way disc twice in each revolution producing a total of 16 crossings each day. ", "These crossings are the narrow bright bands in the top panel of Figure 1. ", "Every few months Gaia scans almost exactly along the Galactic plane, which is seen as the bands of the top panel getting steeper and also as peaks in the bottom panel.", "\n\nIn between the bands we also see two bright dots. ", "These are the Magellanic Clouds, satellite galaxies to our own Galaxy. ", "Like the Milky Way they are conspicuous objects even to the naked eye.", "\n\nBecause of the precession of the spin axis around the Sun-Earth direction, the scanned great circle varies its inclination with respect to the galactic plane, and from time to time that great circle coincides with the plane. ", "In these periods the number of transits reaches the maximum capacity available on board and some objects are not observed or their observations are not downloaded to the ground.", "\n\nMaybe we can better understand the scale at which Gaia operates with the following equivalence: If we would like to observe each of the DR2 sources during just one second, we would need 54 years. ", "Gaia has already observed each star during more than four seconds 500 times in less than four years. ", "The accumulated exposure time exceeds 133 thousand years!", "\n\nGaia is now almost 45 months into its mission. ", "The second Gaia data release, due on 25th April 2018, covers the first 22 months, so we have in fact already twice as much data at hand.", "\n\nThe nature of DPAC data processing requires to iterate several times over the data in order to achieve high accuracy in both calibrations and the results delivered with a Gaia data release. ", "In order to facilitate intermediate data releases the amount of data processed is kept limited for the earlier releases with more and more data being added to the processing for each subsequent release. ", "For Gaia DR3 DPAC will process about 34 months of data, while for Gaia DR4 it is planned to process the full five year set of raw data from the nominal mission." ]

{ "pile_set_name": "Pile-CC" }

[ 0.003968253968253968, 0, 0, 0, 0.0035087719298245615, 0, 0, 0, 0.0045045045045045045, 0, 0.006756756756756757, 0, 0, 0, 0.0045662100456621, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.005050505050505051, 0.009900990099009901, 0, 0, 0.007352941176470588, 0, 0, 0.0125 ]

[ "/*\n * Copyright (C) 2005-2019 by Centre National d'Etudes Spatiales (CNES)\n *\n * This file is licensed under MIT license:\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to deal\n * in the Software without restriction, including without limitation the rights\n * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell\n * copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.", "\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. ", " IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\n * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN\n * THE SOFTWARE.", "\n */\n\n\n#ifndef SRGRConversionParameters_h\n#define SRGRConversionParameters_h\n\n#include <EnvisatAsar/EnvisatAsarRecord.h>\n\nnamespace ossimplugins\n{\n\n/**\n * @ingroup SRGRConversionParametersRecord\n * @brief This class is able to read the ASAR SRGRConversionParameters record\n */\nclass SRGRConversionParameters : public EnvisatAsarRecord\n{\npublic:\n /**\n * @brief Constructor\n */\n SRGRConversionParameters();\n\n /**\n * @brief Destructor\n */\n virtual ~SRGRConversionParameters();\n\n /**\n * @brief This function writes the SRGRConversionParameters in a stream\n */\n friend std::ostream& operator<<(std::ostream& os, const SRGRConversionParameters& data);\n\n /**\n * @brief This function reads a SRGRConversionParameters from a stream\n */\n friend std::istream& operator>>(std::istream& is, SRGRConversionParameters& data);\n\n /**\n * @brief Copy constructor\n */\n SRGRConversionParameters(const SRGRConversionParameters& rhs);\n\n /**\n * @brief Copy operator\n */\n SRGRConversionParameters& operator=(const SRGRConversionParameters& rhs);\n\n /**\n * @brief This function is able to create a new instance of the class\n */\n EnvisatAsarRecord* Instantiate()\n {\n return new SRGRConversionParameters();\n };\n\n /**\n * @brief This function is able to create a new instance of the class initialised with the data of the calling instance\n */\n EnvisatAsarRecord* Clone()\n {\n return new SRGRConversionParameters(*this);\n };\n\n /**\n * @brief Reads the class data from a stream\n */\n void Read(std::istream& is)\n {\n is>>*this;\n };\n\n /**\n * @brief Writes the class to a stream\n */\n void Write(std::ostream& os)\n {\n os<<*this;\n };\n\n\n /**\n * @brief first_zero_doppler_time day\n */\n int get_first_zero_doppler_time_day()\n {\n return _first_zero_doppler_time_day;\n };\n /**\n * @brief first_zero_doppler_time second\n */\n unsigned int get_first_zero_doppler_time_sec()\n {\n return _first_zero_doppler_time_sec;\n };\n /**\n * @brief first_zero_doppler_time micro sec\n */\n unsigned int get_first_zero_doppler_time_microsec()\n {\n return _first_zero_doppler_time_microsec;\n };\n /**\n * @brief attach_flag\n */\n bool get_attach_flag()\n {\n return _attach_flag;\n };\n /**\n * @brief input_mean_flag\n */\n float get_slant_range_time()\n {\n return _slant_range_time;\n };\n /**\n * @brief input_std_dev_flag\n */\n float get_ground_range_origin()\n {\n return _ground_range_origin;\n };\n /**\n * @brief input_gaps_flag\n */\n float* get_srgr_coef()\n {\n return _srgr_coef;\n };\n\n /**\n * @brief first_zero_doppler_time day\n */\n int _first_zero_doppler_time_day;\n /**\n * @brief first_zero_doppler_time sec\n */\n unsigned int _first_zero_doppler_time_sec;\n /**\n * @brief first_zero_doppler_time microsec\n */\n unsigned int _first_zero_doppler_time_microsec;\n /**\n * @brief attach_flag\n */\n bool _attach_flag;\n /**\n * @brief input_mean_flag\n */\n float _slant_range_time;\n /**\n * @brief input_std_dev_flag\n */\n float _ground_range_origin;\n /**\n * @brief input_gaps_flag\n */\n float _srgr_coef[5];\n\n\nprivate:\n\n};\n}\n#endif\n\n\n" ]

{ "pile_set_name": "Github" }

[ 0.008438818565400843, 0.004651162790697674, 0.0036900369003690036, 0.010187838268067495 ]

[ "Die britische Premierministerin will das Unterhaus bis Mitte März über einen ergänzten Brexit-Vertrag mit der EU abstimmen lassen. ", "In der EU überlegt man hingegen, den Brexit gleich ganz zu vertagen.", "\n\nGut einen Monat vor dem geplanten Austritt Großbritanniens aus der Europäischen Union droht der Brexit-Zeitplan durcheinander zu geraten. ", "Eine für nächste Woche erwartete wichtige Abstimmung im britischen Parlament sagte Premierministerin Theresa May ab. ", "In der EU scheint man unterdessen zu überlegen, den Brexit vollständig zu verschieben.", "\n\nWie der britische „Guardian“ unter Berufung auf EU-Diplomaten berichtet, prüft die Europäische Union derzeit, ob statt der geplanten 21 Monate dauernden Übergangsphase auch eine Verschiebung des Brexits bis 2021 möglich wäre. ", "Dem Bericht zufolge sollen unter anderem der Europäische Ratspräsident Donald Tusk und der Generalsekretär der EU-Kommission, Martin Selmayr, diesen Plan unterstützen.", "\n\nMit einem Verbleib Großbritanniens für weitere zwei Jahre würde auch der sogenannte Backstop vermieden. ", "Dieser sieht vor, dass Großbritannien – auch über die Übergangsphase hinaus – so lange in der der gemeinsamen Zollunion bleibt, bis sich die EU und die britische Regierung auf ein Handelsabkommen verständigen können. ", "Zusätzlich bliebe Nordirland im europäischen Binnenmarkt. ", "Auf diese Weise soll eine „harte Grenze“ zwischen Nordirland und der Republik Irland vermieden werden. ", "Dies lehnt eine Parlamentsmehrheit in London ab, da dann Großbritannien auf unabsehbare Zeit den EU-Regeln unterworfen bleiben könnte.", "\n\nAuch einige Mitglieder der britischen Regierung fordern eine Verschiebung des Brexit, sollte in den kommenden Tagen kein Durchbruch im Parlament erzielt werden. ", "In einem Gastbeitrag für die „Daily Mail“ schrieben Arbeitsministerin Amber Rudd, Wirtschaftsminister Greg Clark und Justizminister David Gauke, sie wollen einen „desaströsen“ ungeregelten EU-Austritt verhindern. ", "Damit steigen die Chancen, dass das Parlament am Mittwoch bei der Abstimmung May die Kontrolle über den Brexit-Kurs aus der Hand nimmt. ", "Ein „No Deal“ könne die nationale Sicherheit schwächen, die Ökonomie stark schädigen und zum Zerfall des Vereinigten Königreichs führen.", "\n\nMay: Brexit-Abstimmung im Parlament bis 21. ", "März\n\nDerweil kündigte May an, das Parlament bis spätestens zum 12. ", "März über ihren umstrittenen Brexit-Plan abstimmen zu lassen. „", "Wir werden diese Woche keine entscheidende Abstimmung im Parlament beantragen, aber wir werden sicherstellen, dass das bis zum 12. ", "März passieren wird“, sagte sie vor Reportern am Sonntag während des Flugs nach Ägypten zum Gipfeltreffen von Arabischer Liga und EU.", "\n\n„Es ist weiterhin unsere Auffassung, die Europäische Union mit einem Vertrag am 29. ", "März zu verlassen“, sagte May mitreisenden Journalisten. ", "Es habe gute Fortschritte und konstruktive Gespräche mit Vertretern der EU gegeben. ", "May hatte eine erste Abstimmung über den Brexit-Vertrag im Januar mit der schlimmsten Niederlage in der modernen britischen Geschichte verloren und Nachbesserungen durch weitere Verhandlungen mit der EU versprochen. ", "Allerdings lehnt die EU ein Aufschnüren des mit ihr ausgehandelten Brexit-Vertrages ab.", "\n\nBrexit-Gespräche in Ägypten\n\nAuch in Scharm el-Scheich will May am Rande des Gipfels mit EU-Regierungschefs über den Brexit verhandeln. ", "Geprüft wird ein Zusatz zum Brexit-Vertrag, in dem die vorläufige Natur der Auffanglösung für die irische Grenze betont würde. ", "In dem ägyptischen Badeort findet derzeit ein Treffen zwischen der Europäischen Union und der Arabischen Liga statt.", "\n\nEin Gespräch zwischen May und EU-Ratspräsident Donald Tusk am Rande des Spitzentreffens endete ohne konkretes Ergebnis. ", "Aus EU-Kreisen hieß es im Anschluss, Tusk habe May noch einmal darin erinnert, dass sich die Staats- und Regierungschefs bei einem Treffen am 21. ", "und 22. ", "März nur dann mit einem neuen Lösungsvorschlag beschäftigen würden, wenn dieser absehbar auch in Großbritannien mehrheitsfähig sei.", "\n\nLabour kritisierte die Parlamentsabstimmung bis spätestens am 12. ", "März als „absolut rücksichtslosen“ Versuch Mays, die Abgeordneten zu einer Entscheidung zwischen einem Brexit ohne und einem mit Vertrag zu entscheiden. ", "Ein Brexit ohne Vertrag wollen die meisten Politiker auf beiden Seiten des Ärmelkanals unbedingt vermeiden, denn in diesem Fall wird mit einem starkem konjunkturellen Dämpfer gerechnet.", "\n\nMehr zum Thema 1/\n\nEin neues Kräftemessen steht für May am Mittwoch im Unterhaus an. ", "Dann wollen Abgeordnete in einer Reihe von Abstimmungen versuchen, die Verantwortung für den Brexit dem Parlament zu übertragen.", "\n\nIn Scharm el-Scheich regte Österreichs Regierungschef Kurz an, den für den 29. ", "März terminierten Brexit zu verschieben, falls die britischen Abgeordneten nicht bis Anfang März den Ausstiegs-Vertrag billigen würden. ", "Auch drei britische Minister sprachen sich gegebenenfalls für eine Verschiebung aus. ", "Ein „No-Deal-Brexit“ stelle ein Risiko für die britischen Unternehmen, die Sicherheit und die territoriale Einheit Großbritanniens dar, schrieben Arbeitsministerin Amber Rudd, Wirtschaftsminister Greg Clark und Justizminister David Gauke in einem Beitrag der „Daily Mail“ am Samstag." ]

{ "pile_set_name": "OpenWebText2" }

[ 0.030534351145038167, 0.04411764705882353, 0.02142857142857143, 0.02564102564102564, 0.03488372093023256, 0.017543859649122806, 0.029940119760479042, 0.009433962264150943, 0.02304147465437788, 0.017241379310344827, 0.02912621359223301, 0.007462686567164179, 0.018404907975460124, 0.023474178403755867, 0.03676470588235294, 0.022058823529411766, 0.021739130434782608, 0, 0, 0.007633587786259542, 0.03007518796992481, 0.023255813953488372, 0, 0.047619047619047616, 0.023148148148148147, 0.022988505747126436, 0.014492753623188406, 0.03937007874015748, 0.02586206896551724, 0.03278688524590164, 0.03424657534246575, 0, 0.007633587786259542, 0, 0.006535947712418301, 0.010810810810810811, 0.011494252873563218, 0.0390625, 0.024691358024691357, 0.014705882352941176, 0.011764705882352941, 0.02120141342756184 ]

[ "[Flavonoid constituents of Melicope triphylla MERR.II].", "\nFrom the leaves of Melicope triphylla MERR., ", "three new flavonoids (1-3) were isolated, together with nine known flavonoids, 4',5-dihydroxy-3,3',7- trimethoxyflavone (4), 5-hydroxy-3,3',4',7-tetramethoxyflavone (5), 3,3',4',5,7-pentamethoxyflavone (6), 7-hydroxy-3,3',4',5,8-pentamethoxyflavone (7), 3,3',4',5,7,8-hexamethoxyflavone (8), 5-hydroxy-3,7,8-trimethoxy-3',4'-methylenedioxyflavone (9), 7-hydroxy-3,5,8- trimethoxy-3',4'-methylenedioxyflavone (10), 3,5,7,8-tetramethoxy-3',4'-methylenedioxyflavone (11), and 5-hydroxy- 3,6,7,8-tetramethoxy-3',4'-methylenedioxyflavone (12). ", "The structures of 1, 2, and 3 were established as 5-hydroxy-3,7-dimethoxy-3',4'-methylenedioxyflavone, 5-hydroxy-7-isopentenyloxy-3,8-dimethoxy-3',4'-methylenedioxyfl avone, and 4'-hydroxy-7-isopentenyloxy-3,3',5,8-tetramethoxyflavone by their respective chemical and spectral data. ", "The 20 flavonoids isolated from this plant were examined for the piscicidal activities." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0.01818181818181818, 0.021739130434782608, 0, 0, 0 ]

[ "Diet Affects Autoinflammatory Disease Via Gut Microbes\n\nAt a Glance A study in mice revealed how diet-induced changes to intestinal bacteria can influence susceptibility to autoinflammatory disease.", "\n\nThe results could help guide new approaches to treat autoinflammatory diseases in susceptible people.", "\n\nYamanaka et al., ", "courtesy of BMC Microbiol., ", "2009, 9:11\n\nIn autoinflammatory diseases, the innate immune system, for unknown reasons, becomes activated and triggers inflammation. ", "This part of the immune system is the body’s rapid first line of defense against infection. ", "The short-term heat, swelling, and redness of inflammation are a normal part of the body’s protective response to injury or infection. ", "But prolonged inflammation can seriously damage the body.", "\n\nRecent research suggests that diet can affect certain autoimmune diseases. ", "A team led by Dr. Thirumala-Devi Kanneganti of St. Jude Children’s Research Hospital studied mutant mice that develop a condition resembling chronic recurrent multifocal osteomyelitis in humans. ", "This rare inflammatory bone condition is marked by pain and joint swelling, and can cause slow growth and permanent bone deformity. ", "Their study was funded in part by NIH’s National Institute of Arthritis and Musculoskeletal and Skin Diseases (NIAMS), National Cancer Institute (NCI), and National Institute of Allergy and Infectious Diseases (NIAID). ", "It appeared online on September 28, 2014, in Nature.", "\n\nAs expected, mutant mice fed a regular diet developed hind paw inflammation, bone erosion, and enlarged lymph nodes by day 100. ", "Tissue analysis showed infiltrating immune cells, such as neutrophils, and significant bone destruction. ", "However, mutant mice fed a diet rich in saturated fats and cholesterol were largely protected.", "\n\nDiets high in fat and cholesterol are known to cause changes in gut microbe communities. ", "The team’s analysis showed that the intestinal microbiota in regular-fed mutant mice was markedly different from that of healthy wild-type mice. ", "Some of the differences, such as increased Prevotella bacteria in the mutant animals, have been linked to inflammation. ", "These changes were significantly reduced in mutant mice fed a high-fat diet.", "\n\nAntibiotics protected the regular-diet mutant mice from osteomyelitis. ", "To further explore the role of the intestinal microbiota in autoinflammatory disease, the team performed fecal transplantation studies. ", "Transplanting the microbiota of regular-fed mutant mice to young mice boosted Prevotella levels and sped osteomyelitis. ", "Conversely, transplanting the microbiota of high-fat-fed mice into young mice limited Prevotella and protected mice from osteomyelitis.", "\n\nTo better understand the mechanisms involved, the researchers analyzed levels of interleukin-1β (IL-1β), which has previously been linked to inflammatory bone disease, in the animals’ footpads. ", "IL-1β protein concentrations were significantly increased in the footpads of regular-fed mutant mice, whereas levels in those fed a high-fat diet were comparable to healthy controls. ", "This suggests that the high-fat diet suppressed osteomyelitis in the susceptible mice by affecting levels of IL-1β.", "\n\nTogether, these findings show that diet affects osteomyelitis in susceptible mice by altering the intestinal microbiota, which in turn influence IL-1β levels in distant neutrophils. ", "Exactly how the microbiota affect IL-1β levels remains to be determined.", "\n\n“Multiple lines of evidence suggest that dietary consumption can impact human disease; however, the scientific mechanisms involved have been lacking,” Kanneganti says. “", "Our results demonstrate that diet can influence immune-mediated disorders by shaping the composition of commensal bacteria.”", "\n\n—by Harrison Wein, Ph.D." ]

{ "pile_set_name": "OpenWebText2" }

[ 0.005050505050505051, 0, 0, 0.03571428571428571, 0, 0, 0, 0, 0, 0.010256410256410256, 0, 0.0273972602739726, 0.019230769230769232, 0, 0, 0, 0, 0, 0.008333333333333333, 0, 0, 0, 0.008333333333333333, 0.007407407407407408, 0.01020408163265306, 0.00546448087431694, 0.008695652173913044, 0.005434782608695652, 0.013888888888888888, 0.005847953216374269, 0, 0.038461538461538464 ]

[ "Metadata\n\nDAVIS ON THE COLORADO RIVER PROBLEM 387\nlands feasible of irrigation in the United States, including the Mohave Valley lands.", "\nNature has provided two feasible dam sites that will utilize all the head Available here, without submerging the Mohave Valley. ", "One of these sites is above, at Bulls Head, and one below, near the mouth of Williams River. ", "The latter is necessary for a high diversion dam for the Parker-Gila Valley Project, the construction of which the author assumes. ", "It would be built to the greatest height possible without damage to the City of Needles, or about 100 ft. ", "The proposed dam in Mohave Canyon would conflict with this, and would also submerge the dam site at Bulls Head, just above the Mohave Valley. ", "It would leave undeveloped 40 ft. ", "of power head below Boulder Canyon, which would thus be lost.", "\nThe dam site in the Mohave Canyon was examined twenty years ago and at intervals since by various engineers, including William Mulholland and J. B. Lippincott, Members, Am. ", "Soc. ", "C. E., and on account of the destruction of land, water, and other property, was unanimously regarded as infeasible, and for this reason, its foundations were not explored. ", "Any money spent thereon would be wasted for reasons already given. ", "It was never seriously advocated until it became necessary to kill the proposal to build a dam in Boulder Canyon and develop enough power to repay the cost. ", "This emphasizes the real point at issue, that is, whether the immense resources of the Lower Colorado are to be retained in the control of the Federal Government or turned over to private corporations. ", "This is a question on which engineers and others may honestly differ, and which the speaker will not discuss. ", "It should be considered on its merits, and not combatted indirectly to the great sacrifice of the natural resources of land and water.", "\nWanton Destruction of Valuable Storage.—Perhaps the most destructive feature of the author's plan is the proposed building of a high dam at Devils Slide, thus restricting the height of the Boulder Dam to 387 ft., ", "and its storage capacity to about 10,000,000 acre-ft. ", "Such a reservoir would rapidly fill with sediment, and thus be destroyed much earlier than necessary.", "\nIt has been shown that large storage capacity is necessary to convert the Colorado River from a destructive torrent into a source of vast wealth, and that this storage will steadily be destroyed by silting. ", "Yet, here is a proposal to build a high dam in the middle of the best reservoir site in the Basin, and thus wantonly destroy its value. ", "It is idle to reply that other reservoirs can be provided above, because these are of limited capacity, and, therefore, of limited life; moreover, they do not intercept all the water nor all the silt.", "\nProper Plan of Development.—The plan of development proposed herein is shown on Fig. ", "21 (a) as compared with that proposed by the author on Fig. ", "21(6).", "\nThe speaker's plan would be to build the Boulder Dam to a height sufficient to back up water to the dam site at Bridge Canyon. ", "This dam would impound about 28,500,000 acre-ft. ", "of water, control floods more perfectly than any smaller reservoir, and develop power more cheaply than any smaller dam, in sufficient quantity to repay its cost with interest." ]

{ "pile_set_name": "Pile-CC" }

[ 0, 0, 0.010752688172043012, 0, 0, 0.007042253521126761, 0, 0, 0.011494252873563218, 0, 0.005780346820809248, 0, 0, 0.0049504950495049506, 0, 0, 0, 0, 0, 0, 0, 0, 0.011627906976744186, 0.016666666666666666, 0, 0, 0, 0 ]

[ "Effects of antigastrin drugs on the interaction of 125I-human gastrin with rat gastric mucosa membranes.", "\nA method for studying the interaction of 125I-human gastrin with a rat gastric mucosal membrane fraction is described, and the saturability, high affinity and reversibility of the preparations, as well as the correlation of pharmacological responses to antigastrin-drugs with the observed binding are discussed. ", "Proglumide and other antigastrin drugs inhibit gastrin binding in a dose-dependent way, and their activities in such a system are well correlated with the \"in vivo\" antisecretory activities of these drugs." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0, 0 ]

[ "Severe immune thrombocytopenia possibly elicited by the anti-influenza viral agent peramivir.", "\nA 44-year-old man whose platelet count had been at the lower limit of the normal range for years visited the urgent care department of our hospital for treatment of a high fever and severe fatigue. ", "The influenza A virus was detected, and the patient therefore received the intravenous antiviral agent, peramivir. ", "One week later, he developed systemic petechial rashes. ", "A peripheral blood examination showed a markedly decreased platelet count (3.0×10(9) cells/L), and the bone marrow findings were compatible with a diagnosis of immune thrombocytopenia (ITP). ", "Furthermore, a drug-induced lymphocyte-stimulating test was positive for peramivir. ", "The thrombocytopenia slowly responded to treatment with oral prednisolone. ", "This case suggests that neuraminidase inhibitors, including peramivir, can elicit or worsen ITP." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0, 0, 0, 0.010471204188481676, 0, 0, 0.010416666666666666 ]

[ "538 U.S. 1061\nDeFRANKv.", "PALMATEER, SUPERINTENDENT, OREGON STATE PENITENTIARY.", "\nNo. ", "02-9746.", "\nSupreme Court of United States.", "\nMay 27, 2003.", "\n\n1\nCERTIORARI TO THE UNITED STATES COURT OF APPEALS FOR THE NINTH CIRCUIT.", "\n\n\n2\nC. A. 9th Cir. ", "Certiorari denied. ", "Reported below: 49 Fed. ", "Appx. ", "171.", "\n\n" ]

{ "pile_set_name": "FreeLaw" }

[ 0, 0, 0, 0, 0.03125, 0, 0.013333333333333334, 0.05, 0.05263157894736842, 0.041666666666666664, 0, 0, 0 ]

[ "Thursday, August 13, 2009\n\nIt is interesting how the subject of grief of losing a loved one is explored in recent local cinema. ", "Since Mark Meily's Crying Ladies (2003), grief has been tackled with much humor (there is Gil Portes' Mourning Girls (2006) and Soxie Topacio's Ded na si Lolo (Grandpa is Dead, 2009)), primarily concentrating on the absurdity of the customs and procedures related to grieving, with the ridiculousness of the ceremonies overtaking the subject of grief itself. ", "More maverick filmmakers would tackle grief, concentrating on its paralytic effects on the person suffering. ", "There is Lav Diaz who, in Melancholia (2008), explores the extent a wife would undergo (transforming into a prostitute in a faraway resort town) to cure herself of the consuming melancholy of losing her husband, not knowing whether he is dead or alive. ", "And I Love You So director Laurenti Dyogi, and his team of writers and producers, would not go as far as Diaz’s outrageous proposal. ", "First of all, Melancholia primarily uses grief to humanize its loftier ambitions, from the political, to the moral, to the philosophical. ", "And I Love You So, the attempt of Star Cinema, one of the Philippines' few active mainstream film studios, to tackle grief or its audience-friendly fantastical impression of it, takes such anguish as a mere conflict in its overly familiar plot to challenge two would-be lovers from realizing a romance already predestined by formula.", "\n\nAnd I Love You So centers on Lara (Bea Alonzo), a pre-school teacher whose perfect husband Oliver (Derek Ramsey) dies after only a few months of marital bliss. ", "Dyogi, schmaltz-conjurer par excellence, accompanies Oliver's tragic death (which conveniently happens on Lara's birthday, while the two are dancing under a perfectly starry night sky and in a beach that is ornamented by a birthday cake made out of sand and candles) with swelling dramatic music and frenetic cuts to slow-motioned footage of Oliver falling on his sand castle and Lara crying and screaming on the top of her lungs for help. ", "Thereafter, Lara spends her days and nights in concealed misery, that is until she meets Chris (Sam Milby), a club DJ who also has his own marital problems but nevertheless, falls in love with Lara. ", "Problems arise: a new relationship, after only a few months since Oliver's death, for Lara seems inappropriate; Chris, on the other hand, is sick and tired of falling for women who can't entirely fall in love with him (after having a wife who cheated on him with her ex-boyfriend), and it is quite obvious that Lara is still deeply in love with her dead husband, enough to conjure him from thin air for advices and comfort.", "\n\nOf course, the inevitable fate of Chris and Lara is to be together in perpetual bliss that we can assuredly conjure after their long-awaited kiss gives way to the film's end credits. ", "Knowing that, the middle part, which consists mostly of the two lovebirds flirting with, and fawning for, and later on, fighting with each other, is negligible, just a tool to enunciate the fantasy that Star Cinema has been perpetuating with their non-stop onslaught of hugely commercial romances: that love trumps everything, whether it be class difference (Cathy Garcia-Molina's A Very Special Love (2008) and You Changed My Life (2009)), environmental advocacy (Jose Javier Reyes' When Love Begins (2008)), the American Dream (Garcia-Molina's You Are the One (2006)), a highly careless and promiscuous past (Joyce Bernal's For the First Time (2008)), obesity (Jade Castro's My Big Love (2008)), racial stereotyping (Reyes' Can This Be Love (2005)), familial meddling (Lino Cayetano's I've Fallen For You (2007)), and with And I Love You So, devastating grief.", "\n\nThe previous litany of conflicts and the corresponding Star Cinema movie that makes use of the conflict does not only expose the studio's lack of ingenuity in determining titles for its romantic films (most of which adopt song titles or famous verses from famous songs as their title), but also the creative void, the inability to take risks, and the unforgivable laziness that undoubtedly infest the studio's filmmaking process. ", "The retort is predictable: filmmaking is a business and the movie going public pays to be elated and entertained, not to feel more depressed or reminded of the problems that hound their lives outside the theater. ", "I agree to a certain degree. ", "If anything, the fact that the films that these mainstream film studios produce earn profits, despite the fact that reliance to formula has overtaken any form of creative freedom from any of the artists involved in the production and has turned these movies into mere clones, is telling of the moribund state of this contemporary culture, where what is popular is entertainment that draws its audience farthest from reality.", "\n\nIt is therefore not surprising that the greatest accolade a Filipino artist would ever dream of is now being bestowed upon Carlo J. Caparas, a hack who made himself filthy rich from peddling the misfortunes of others in the most sensationalist yet artistically inept way possible. ", "During the time when Caparas' movies were drawing people to the theaters, Filipinos were clamoring for movies that depict misfortune worse than theirs (not even the poorest living Filipino would want to trade places with the numerous massacre victims that also became victims of Caparas' talentless movie-making). ", "That is exactly my problem with Caparas' reasoning that his ability to communicate with the masses makes him a worthy National Artist. ", "While his films may have communicated very well with most Filipinos, it only does so because it speaks to their misfortune of being too poor to be authentically happy of their lot. ", "Caparas' films, like the formulaic films that Star Cinema has been producing for the sake of profit, exploit the country's malaise, and it behooves me why anyone would even consider Caparas, or any maker of movies who thrive with such parasitic mentality whether consciously or not, an artist.", "\n\nForgive my digression. ", "Now, let me give this review of And I Love You So its proper conclusion.", "The film's cinematography, musical score, editing, acting, scripting, and direction are all wondrously orchestrated to momentarily transport you to an fantasy universe where good husbands die young, divorces are easy, renting out your condo can land you a platonic relationship, lack of parking skills can turn that platonic relationship into a romantic one, and running around Cubao barefooted will win you a second chance at a happily ever after, without even the threat of having your feet covered with soot. ", "For that and the plenty of times Star Cinema has made us forget our problems for the price of a movie ticket, let's give the studio its National Artist Award. ", "Oh wait, studios, being juridical persons, are not eligible to be awarded. ", "What the heck, I'm sure President Arroyo can do something about that too.", "\n\nSunday, August 09, 2009\n\nI've never heard and seen a gunshot as ferociously certain as that final gunshot in Michael Mann's Public Enemies. ", "That single gunshot, tame and quiet if compared to the numerous tommy gun battles that populate the film, killed John Dillinger (Johnny Depp), legendary bank robber. ", "Along with the death of Dillinger, is the death of an era championed by criminals of unquestionable renown and mythified reputations. ", "Mann maps the dying days of the era with the surehandedness of a watch-maker, unflinching to the temptation of showing off more than what is required for his purposes. ", "He creates not a film about Dillinger, although Mann's camera delights in capturing every gesture, swagger, and posturing of Depp as the celebrated felon, but an approximated document of the moods of a period characterized by fear, fascination, respect, and awe of these public personalities. ", "That gunshot could have come from anywhere (from the cowardly investigator whose hatred for Dillinger has become personal; or Melvin Purvis (Christian Bale), who was specifically tasked to kill Dillinger; or any anonymous cop who was stationed near the Biograph), and it did not really matter. ", "Dillinger had to die that specific death and his body had to be ripped by the public like a basket full of souvenirs. ", "The gunshot just had to happen.", "\n\nThat Public Enemies skirts from characterizing Dillinger only emphasizes Mann's insistence on differentiating myth from person. ", "What we know of and learn about him from the film is limited to the reputation established from the various literature and popular representations through the years, Depp's wonderfully iconic portrayal, and the unsurprising romanticism as can be absorbed from his unabashed love angle with gorgeous mestiza coat check girl Billie Frechette (Marion Cotillard). \"", "I like baseball, movies, good clothes, whiskey, fast cars... and you. ", "What else do you need to know?\" ", "tells Dillinger to Billie, before spiriting her away into a Depression-era fantasy. ", "Mann channels his uniquely flirtatious Dillinger, and proposes the same Dillinger quote to his audience, manufacturing Public Enemies' Dillinger, not out of autobiographical notes and accurate recounts, but from the American myth that he has become, with his seamless bank robberies, his perfectly planned jailbreaks, his impeccably classy lawlessness (Mann adds a sequence in the film, arguably fictitious, where Dillinger visits the police station, enters the unit specifically assigned for his capture, walks around the office as the cops are busy watching a game, communicates with one of the cops by asking the score, and nonchalantly leaves the compound), and his fairy tale romance with the heartbreakingly tragic end, all overtake his actual history.", "\n\nMann makes use of digital video instead of film. ", "The effect is even more apparent here, than in Collateral (2004) or Miami Vice (2006), where digital video complements the vastly modern and urban vistas that are dominated by steel, asphalt, and smog. ", "The period milieu (Depression-era architecture, tommy guns, monochrome suits and automobiles) of Public Enemies feels anachronistic to its digital video aesthetics. ", "In this case, the seeming anachronism is not a disadvantage, as it lends to the perceptual discord that resonates throughout the feature, giving the film a more palpable grit that bears more resemblance to the hyper-real actioners of this post-9/11 era to the stylized ones made during an era where an actual interaction between the public and such violence is more of a far-fetched nightmare than a distinct possibility. ", "Grabbed by the neck by the arresting immediacy of the film's digital video aesthetic, the audience is left with no choice but to get swept away by Dillinger's daring exploits and the period-forced fantasies he proposes to fulfill, enough to smell the melancholic air of that era's eventual demise.", "\n\nThe film is not so much about an era that belonged solely to Dillinger that his timely death signaled its end. ", "Public Enemies, much more than an auteurist recount of the death of an era (and this differentiates the film from such elegiac films like Sam Peckinpah's Pat Garrett and Billy the Kid (1973) and most recently, Andrew Dominik's The Assassination of Jesse James by the Coward Robert Ford (2008), films which primarily mourned the passing of the Old West by the deaths of the heroes that represented the era's virtues), sufficiently details the birth pains of a new era of evolving criminals and adapting law enforcers. ", "When Dillinger witnesses his own obsolescence during the moment he is introduced to the future by a room of desk crooks amassing wealth far greater than any of his elegantly executed bank heists, he knew that he is being replaced. ", "As his comrades' numbers dwindle, either by death, capture, or a logical decision to seek out surer ways of earning an illegal buck, the film retreats from edifying Dillinger into exposing his clever front. ", "That the film ended with Billie in jail, being told by the cop that the fantasy of escape that Dillinger promised her is now an impossibility, simply summarizes the gargantuan lie that birthed these infamous criminals. ", "Beyond their often told and retold exploits, the millions of dollars they robbed from the banks, their famous deaths, are the millions that will swallow anything, whether it be crooks turned into mystified idols, to momentarily escape their sorry lots in life. ", "Truth be told, criminals post-Dillinger can never have the same plebeian charm of also being a dreamer, a toiler, a hero.", "\n\nTuesday, August 04, 2009\n\nJerrold Tarog's Mangatyanan (The Blood Trail) tells the story of Laya (Che Ramos), the daughter of a legendary photographer. ", "While she has grown up to be a very able photographer herself, she is consistently hounded by her father's reputation and more pertinently, memories of her father taking advantage of her while she was growing up. ", "Thus, Laya seems emotionally impenetrable, adamantly refusing to visit her father on his deathbed, despite being indefatigably persuaded by Luzviminda (Irma Adlawan), her mother who left her when she was still very young, oblivious to the fact that her only daughter is being sexually abused by her husband at home. ", "Instead of personally taking care of her dying father, she accepts a job to travel to Isabela province to photograph a rare ritual called mangatyanan by the Labwanans, a tribe whose numbers have been dwindling because its youth have been losing interest in its old ways.", "\n\nMangatyanan is definitely easy to admire. ", "The cinematography is exquisite, with cinematographer Mackie Galvez giving both urban and rural landscapes sun-drenched yet melancholic hues. ", "The musical score, composed also by Tarog who utilizes gentle melodies and rhythms to accompany the impressively evocative visuals, enunciates the emotional deadlock that consumes the film. ", "The plot, while simple and straightforward, holds considerable depth, most especially in the way it portrays such sensitive matters like incest, rape, and forgiveness with both comfortable distance and ample sensitivity. ", "The acting is mostly superb, especially Ramos, whose Laya is externally an emotionally guarded character with enough acuteness to make her adequately personable, and Adlawan, whose Luzviminda is all at once pathetic, because of her persistence in reaching out to her unwilling daughter, and sympathetic, because of her quiet acknowledgment of the difficulties of her daughter. ", "Mangatyanan is undoubtedly masterfully made, with each minute of the film crafted with the meticulousness that one can normally expect from an experienced filmmaker.", "\n\nIt is important to note that Mangatyanan is only Tarog's sophomore feature. ", "Tarog declares Mangatyanan as the middle part of his Camera Trilogy, the first part of which is Confessional (2007), about a wedding videographer who travels to Cebu to document the famous Sinulog Festival but instead, gets involved in the attempt of a local politician (Publio Briones, III, who plays the Labwanan chief in Mangatyanan) at redemption through his video camera. ", "It is therefore inevitable and normal that Mangatyanan is assessed with heightened expectations from those whose interests were aroused by Confessional's endearing wit and social satire. ", "It is also very understandable why Mangatyanan was met mostly with admiration, because replacing the playfulness that lifts Confessionalfrom its social and political commentary is an unattractive seriousness that pervades the entirety of Mangatyanan, and instead of the organic feel of Confessionalwhich plays like an ordinary vacation video (the one that you'd usually catch during family reunions) that went absolutely wrong, Mangatyanan indulges in a deliberately concocted storyline, directed with hardly any humor. ", "In other words, Mangatyanan, probably because of its technical proficiency and Tarog's near-perfect direction, turns out to be an opaque film. ", "It suffices to digest it at surface level: a well-made melodrama about a woman who needs to forgive.", "\n\nHowever, Mangatyanan is a film that deserves more than just surface level viewing. ", "As middle part of Tarog's Camera Trilogy, the viewer is instructed to view the film with more astute perception. ", "Where Confessionalutilizes the camera as an instrument to reveal truth, Mangatyanan uses the camera as an instrument to hide truth. ", "The camera becomes Laya's device for pretended normalcy, as it induces other people to perceive her as her father's daughter, notwithstanding the abuses which are known only to her, because she has inherited his talent and profession, the same way a good lawyer would have children who would be lawyers, a doctor, children who would be doctors, and so on. ", "The camera produces pictures, like the ones taken by Laya's father that are hanging on the Labwanan chief's room, that are on surface level pertaining to the mangatyanan, but upon further investigation, actually pertains to a device created by the Labwanans to attract tourists and their money. ", "The photography project which Laya embarks on seeks to preserve the culture of a dying tribe, but beyond the seemingly lofty goal of these pictures are the unvisualized ills that infest the tribe itself, from the unwillingness of the chief's only son (Bor Ocampo) to continue the tribe's legacy to the familial troubles that result out of the tribe's impending natural death because of the allure of modernity.", "\n\nEven Tarog's camera becomes a tool of falsity, as he skillfully and deviously weaves his invented tribe and its rituals and fluently spoken dialect into momentary reality. ", "Fortunately, Tarog does not burden the film with a moral stance, portraying perpetrator and victim with as much humanity (although fractured) as possible. ", "To force a moral stance would only muddle the lofty intent and cheat the narrative of its emotional and thematic complexity. ", "Finally, Mangatyanan does not differentiate between truth and lies since in its cinematic language, the two are purposely indistinguishable. ", "The film ends reasonably, like the well-crafted melodrama that it was meant to be with Laya reunited with her mother, who is forgiven without her faults absolutely forgotten. ", "As both well-made melodrama and middle part of Tarog's self-imposed Camera Trilogy, what Mangatyanan does effectively is to modulate redemption through forgiveness (Confessional forwards redemption through confession), notwithstanding the extent of the sin, the gravity of the harm, and the length of the hurt.", "\n\nSaturday, August 01, 2009\n\nHumanity has an innate fascination for stories where characters triumph despite their incapacity; and childhood, with all its appurtenant limitations such as the supposed insufficiency in maturity, physical capability, and moral discernment, simply makes for good cinema. ", "More specifically, the forced resilience of children, much more than their inherent innocence, has been the ample subject of many well-regarded films. ", "In Francois Truffaut's 400 Blows (1959), Antoine Doinel's imperfect coming-of-age concludes in an austere note with the film's iconic final freeze frame of Antoine's face as he reaches the limits of living a life on the run. ", "Trapped between the wide sea and the constricted life, resulting from his derelict childhood, that he is about to live, Antoine is simply fearful and anguished, as can be gleaned from his face. ", "His bleak perception of the adult world and the harsh repercussions of such perception, define the palpable disconnection, universal and timely, between the child and adults, arising specifically from the failure of adults.", "\n\nLocally, the same failure of adults force the young protagonists of Maryo J. de los Reyes' Magnifico (2003), where a boy unknowingly bears the burden of trying to ease his little town's poverty, and Aureaus Solito's Ang Pagdadalaga ni Maximo Oliveros (The Blossoming of Maximo Oliveros, 2005), where a prepubescent homosexual boy serves as housekeeper to his family of crooks, to bear duties, responsibilities and consequences far greater than what their tender ages require of them. ", "These young protagonists' perception of the adult world is more tolerant, probably because the Filipino culture compels children to share the responsibility of their families. ", "Unlike Truffaut's Antoine, they accede to the oftentimes unfair demands of the cruel world that they will inevitably inherit instead of turning into careless and belligerent rebels. ", "Thus, it can be argued that the emotional resonance of these films is greater or at least, more, considering that the hardships experienced by the characters are borne out of innocence and selflessness, instead of mere immaturity and irresponsibility. ", "Vic Acedillo, Jr.'s Ang Nerseri (The Nursery) seems to spring from the same source as De los Reyes and Solito's films. ", "However, it begs for more than just admiration for its young protagonist, as it manages to deglamorize the child's feat to achieve something more intriguing.", "\n\nAng Nerseri, loosely based from writer-director Acedillo's own childhood experiences, imagines siblings, all of whom are either drug dependents or lunatics, that suddenly find themselves abandoned and motherless. ", "Cocoy (Timothy Mabalot), the youngest and seemingly the least crazy of the brood, becomes surrogate parent to his elder siblings; paying regular visits to his brother (Alwyn Uytingco) who is recovering from drug addiction, sends his other abusive brother (Lance Raymundo) to the rehab, and takes care of his catatonic sister (Claudia Enrique). ", "The film mostly centers on Cocoy's escapades, his burgeoning sexual appetite, his worsening psychological state, and his growing detachment from the rest of the world. ", "The film tirelessly meanders around its theme of domestic dysfunction as viewed from the perspective of its young protagonist who leaps from one responsibility to another with the crazed diligence of an obsessive-compulsive individual. ", "Before finally losing steam with its intended redundancy, it attempts to reach a climactic boiling point, only to come full circle and end in an emotionally poignant note.", "\n\nAcedillo spices the purposely tedious depictions of domestic dysfunction with dry humor. ", "Aside from the attractively acrid wit that pervades the film, it indulges in visual innovations: utilizing orchids as visual metaphors; inverting the screen to show Cocoy's sister's flipped point of view; and finally, filtering all hues from the film except for the blues and the greens. ", "The consequences of such aesthetic playfulness is inevitable. ", "The seeming irrationality of the polarizing visual exercise (Acedillo made use of the video function of the Canon 5-A digital still camera in the shoot, and modified the colors during post-production) might be regarded as artistic masturbation on the part of Acedillo, but it also imposes a vital task to the film's viewers to discern the probable implications (interpretations range from drug use, an incomplete perspective of the world, hopelessness, and a lot more) of the blues and the greens swimming in a frame of dull gray.", "\n\nThe viewers' empathy obviously belongs to Cocoy, who inherits the responsibilities abandoned by his mother (Jaclyn Jose), and becomes the supposed victim of his parent's irresponsibility. ", "Acedillo makes sure that his viewers are thoroughly immersed in his experiences, coursing through the horror of sudden parenthood, the excitement of his first sexual encounter, and the immense frustration resulting from knowing yet denying the painful truth. ", "We are provided with a glimpse of that painful truth only during the film's final sequence. ", "In full color, Cocoy sees his mother removing the orchid seedlings from an empty bottle that serves as nursery. ", "She is quietly distraught, as can be gleaned from the tears flowing from her eyes. ", "At that moment, Cocoy's portrayed suffering because of his mother's absence is given a vantage point outside Cocoy's, and that is of his mother's. ", "While the mother's palpable sadness is surely not be enough to absolve her from neglecting and abandoning her family, it provides ample understanding that her failure and subsequent surrender is not without a tremendous ache. ", "This is the same ache that Cocoy painfully witnesses, struggles to understand, forcefully denies and subsequently acts on, without benefit of a conclusive triumph or a hurtless defeat.", "\n\nI always liked it slow (Leonard Cohen)\n-\nI’m slowing down the tuneI never liked it fastYou want to get there soonI want to get there lastIt’s not because I’m oldIt’s not the life I ledI always liked..." ]

{ "pile_set_name": "Pile-CC" }

[ 0, 0.011142061281337047, 0, 0.003952569169960474, 0.015037593984962405, 0.007246376811594203, 0, 0.012345679012345678, 0.004545454545454545, 0.010050251256281407, 0.002364066193853428, 0.005405405405405406, 0.009280742459396751, 0, 0, 0, 0, 0.0035335689045936395, 0.006369426751592357, 0.014814814814814815, 0, 0.006825938566552901, 0, 0, 0.001953125, 0, 0, 0.0136986301369863, 0.007042253521126761, 0.012048192771084338, 0.007462686567164179, 0.005952380952380952, 0.010238907849829351, 0.017006802721088437, 0, 0, 0.007692307692307693, 0.00554016620498615, 0, 0, 0, 0.00395778364116095, 0.0196078431372549, 0, 0.012121212121212121, 0, 0.006734006734006734, 0, 0.01160541586073501, 0, 0, 0.0045662100456621, 0, 0, 0.0196078431372549, 0, 0.012658227848101266, 0, 0.022727272727272728, 0.007042253521126761, 0.005263157894736842, 0, 0.010610079575596816, 0, 0.01282051282051282, 0.007957559681697613, 0.0053475935828877, 0.0038461538461538464, 0.013986013986013986, 0, 0, 0.008849557522123894, 0.007575757575757576, 0.0028089887640449437, 0.003389830508474576, 0.004878048780487805, 0, 0.0064516129032258064, 0, 0.0070921985815602835, 0.005714285714285714, 0.00967741935483871, 0, 0, 0.013333333333333334, 0.005154639175257732, 0, 0.00823045267489712, 0, 0.005494505494505495, 0, 0.03361344537815126, 0, 0.009302325581395349, 0.011627906976744186, 0.005952380952380952, 0, 0, 0, 0.003472222222222222, 0, 0.0018867924528301887, 0.010526315789473684, 0, 0, 0.008928571428571428, 0, 0.013605442176870748, 0, 0.005434782608695652, 0.0049261083743842365 ]

[ "Raúl Fuster\n\nRaúl Fuster Arnao (born 23 July 1985) is a Spanish retired professional footballer who played as a left back.", "\n\nHe played 118 matches in Segunda División during six seasons, in representation of three clubs.", "\n\nClub career\nBorn in Elche, Province of Alicante, Fuster made his senior debut with hometown's Elche CF's reserves, in Tercera División. ", "After a loan to Valencian Community neighbours Villajoyosa CF he was promoted to the first team in 2007, quickly becoming a very important defensive unit.", "\n\nAfter contributing with 27 games to Elche's sixth place in 2009–10, Fuster signed with another side in Segunda División, Gimnàstic de Tarragona. ", "After two seasons with them, suffering relegation in his second and during which he scored his only goal as a professional in a 2–4 away loss against Córdoba CF, he was released.", "\n\nIn the summer of 2012, Fuster joined CD Lugo also of the second level. ", "In the following transfer window he switched to Segunda División B where he would spend the next six years, with UD Salamanca, Lleida Esportiu, SD Ponferradina, UE Llagostera and Ontinyent CF.", "\n\nOn 28 March 2019, after the club's dissolution, Fuster left Ontinyent. ", "The following month, he joined amateurs CF Intercity.", "\n\nFuster announced his retirement in August 2019, aged 34.", "\n\nReferences\n\nExternal links\n\nCategory:1985 births\nCategory:Living people\nCategory:People from Elche\nCategory:Spanish footballers\nCategory:Valencian footballers\nCategory:Association football defenders\nCategory:Segunda División players\nCategory:Segunda División B players\nCategory:Tercera División players\nCategory:Divisiones Regionales de Fútbol players\nCategory:Elche CF Ilicitano footballers\nCategory:Elche CF players\nCategory:Villajoyosa CF footballers\nCategory:Gimnàstic de Tarragona footballers\nCategory:CD Lugo players\nCategory:UD Salamanca players\nCategory:Lleida Esportiu footballers\nCategory:SD Ponferradina players\nCategory:UE Llagostera footballers" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.01639344262295082, 0.010309278350515464, 0.007246376811594203, 0.006493506493506494, 0.02040816326530612, 0, 0.0136986301369863, 0.03125, 0, 0.018867924528301886, 0, 0.007587253414264037 ]

[ "East Wave Radio\n\nEast Wave Radio is a community-based radio station based in Lenasia, South Africa. ", "It broadcasts on 92.2 FM .", "\n\nSee also\nLists of radio stations in Africa\n\nExternal links\nGauteng community radio stations\n\nCategory:Community radio stations in South Africa\nCategory:Media in Lenasia" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.01, 0, 0.011764705882352941 ]

[ "/******************************************************************************\n *\n * Copyright(c) 2007 - 2011 Realtek Corporation. ", "All rights reserved.", "\n * \n * This program is free software; you can redistribute it and/or modify it\n * under the terms of version 2 of the GNU General Public License as\n * published by the Free Software Foundation.", "\n *\n * This program is distributed in the hope that it will be useful, but WITHOUT\n * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or\n * FITNESS FOR A PARTICULAR PURPOSE. ", "See the GNU General Public License for\n * more details.", "\n *\n * You should have received a copy of the GNU General Public License along with\n * this program; if not, write to the Free Software Foundation, Inc.,\n * 51 Franklin Street, Fifth Floor, Boston, MA 02110, USA\n *\n *\n ******************************************************************************/\n#ifndef _RTW_VHT_H_\n#define _RTW_VHT_H_\n\n#define\tLDPC_VHT_ENABLE_RX\t\t\tBIT0\n#define\tLDPC_VHT_ENABLE_TX\t\t\tBIT1\n#define\tLDPC_VHT_TEST_TX_ENABLE\t\tBIT2\n#define\tLDPC_VHT_CAP_TX\t\t\t\tBIT3\n\n#define\tSTBC_VHT_ENABLE_RX\t\t\tBIT0\n#define\tSTBC_VHT_ENABLE_TX\t\t\tBIT1\n#define\tSTBC_VHT_TEST_TX_ENABLE\t\tBIT2\n#define\tSTBC_VHT_CAP_TX\t\t\t\tBIT3\n\n#define\tBEAMFORMING_VHT_BEAMFORMER_ENABLE\tBIT0\t// Declare our NIC supports beamformer\n#define\tBEAMFORMING_VHT_BEAMFORMEE_ENABLE\tBIT1\t// Declare our NIC supports beamformee\n#define\tBEAMFORMING_VHT_MU_MIMO_AP_ENABLE\t\tBIT2\t\t\t/*Declare our NIC support MU-MIMO AP mode*/\n#define\tBEAMFORMING_VHT_MU_MIMO_STA_ENABLE\tBIT3\t\t\t/*Declare our NIC support MU-MIMO STA mode*/\n#define\tBEAMFORMING_VHT_BEAMFORMER_TEST\t\tBIT4\t\t\t/*Transmiting Beamforming no matter the target supports it or not*/\n#define\tBEAMFORMING_VHT_BEAMFORMER_STS_CAP\t\t(BIT8|BIT9|BIT10)\t\t/*Asoc rsp cap*/\n#define\tBEAMFORMING_VHT_BEAMFORMEE_SOUND_DIM\t\t(BIT12|BIT13|BIT14)\t\t/*Asoc rsp cap*/\n\n\n//VHT capability info\n#define SET_VHT_CAPABILITY_ELE_MAX_MPDU_LENGTH(_pEleStart, _val)\t\t\tSET_BITS_TO_LE_1BYTE(_pEleStart, 0, 2, _val)\n#define SET_VHT_CAPABILITY_ELE_CHL_WIDTH(_pEleStart, _val)\t\t\tSET_BITS_TO_LE_1BYTE(_pEleStart, 2, 2, _val)\n#define SET_VHT_CAPABILITY_ELE_RX_LDPC(_pEleStart, _val)\t\t\tSET_BITS_TO_LE_1BYTE(_pEleStart, 4, 1, _val)\n#define SET_VHT_CAPABILITY_ELE_SHORT_GI80M(_pEleStart, _val)\t\t\t\tSET_BITS_TO_LE_1BYTE(_pEleStart, 5, 1, _val)\n#define SET_VHT_CAPABILITY_ELE_SHORT_GI160M(_pEleStart, _val)\t\t\t\tSET_BITS_TO_LE_1BYTE(_pEleStart, 6, 1, _val)\n#define SET_VHT_CAPABILITY_ELE_TX_STBC(_pEleStart, _val)\t\t\t\tSET_BITS_TO_LE_1BYTE(_pEleStart, 7, 1, _val)\n#define SET_VHT_CAPABILITY_ELE_RX_STBC(_pEleStart, _val)\t\t\t\tSET_BITS_TO_LE_1BYTE((_pEleStart)+1, 0, 3, _val)\n#define SET_VHT_CAPABILITY_ELE_SU_BFER(_pEleStart, _val)\t\t\t\tSET_BITS_TO_LE_1BYTE((_pEleStart)+1, 3, 1, _val)\n#define SET_VHT_CAPABILITY_ELE_SU_BFEE(_pEleStart, _val)\t\t\t\tSET_BITS_TO_LE_1BYTE((_pEleStart)+1, 4, 1, _val)\n#define SET_VHT_CAPABILITY_ELE_BFER_ANT_SUPP(_pEleStart, _val)\t\t\t\tSET_BITS_TO_LE_1BYTE((_pEleStart)+1, 5, 3, _val)\n#define SET_VHT_CAPABILITY_ELE_SOUNDING_DIMENSIONS(_pEleStart, _val)\t\t\t\tSET_BITS_TO_LE_1BYTE((_pEleStart)+2, 0, 3, _val)\n\n#define SET_VHT_CAPABILITY_ELE_MU_BFER(_pEleStart, _val)\t\t\t\tSET_BITS_TO_LE_1BYTE((_pEleStart)+2, 3, 1, _val)\n#define SET_VHT_CAPABILITY_ELE_MU_BFEE(_pEleStart, _val)\t\t\t\tSET_BITS_TO_LE_1BYTE((_pEleStart)+2, 4, 1, _val)\n#define SET_VHT_CAPABILITY_ELE_TXOP_PS(_pEleStart, _val)\t\t\t\tSET_BITS_TO_LE_1BYTE((_pEleStart)+2, 5, 1, _val)\n#define SET_VHT_CAPABILITY_ELE_HTC_VHT(_pEleStart, _val)\t\t\t\tSET_BITS_TO_LE_1BYTE((_pEleStart)+2, 6, 1, _val)\n#define SET_VHT_CAPABILITY_ELE_MAX_RXAMPDU_FACTOR(_pEleStart, _val)\t\tSET_BITS_TO_LE_2BYTE((_pEleStart)+2, 7, 3, _val) //B23~B25\n#define SET_VHT_CAPABILITY_ELE_LINK_ADAPTION(_pEleStart, _val)\t\t\t\tSET_BITS_TO_LE_1BYTE((_pEleStart)+2, 2, 2, _val)\n#define SET_VHT_CAPABILITY_ELE_MCS_RX_MAP(_pEleStart, _val)\t\t\t\tSET_BITS_TO_LE_2BYTE((_pEleStart)+4, 0, 16, _val) /* B0~B15 indicate Rx MCS MAP, we write 0 to indicate MCS0~7. ", "by page */\n#define SET_VHT_CAPABILITY_ELE_MCS_RX_HIGHEST_RATE(_pEleStart, _val)\t\t\t\tSET_BITS_TO_LE_2BYTE((_pEleStart)+6, 0, 13, _val) \n#define SET_VHT_CAPABILITY_ELE_MCS_TX_MAP(_pEleStart, _val)\t\t\t\tSET_BITS_TO_LE_2BYTE((_pEleStart)+8, 0, 16, _val) /* B0~B15 indicate Tx MCS MAP, we write 0 to indicate MCS0~7. ", "by page */\n#define SET_VHT_CAPABILITY_ELE_MCS_TX_HIGHEST_RATE(_pEleStart, _val)\t\t\t\tSET_BITS_TO_LE_2BYTE((_pEleStart)+10, 0, 13, _val) \n\n\n#define GET_VHT_CAPABILITY_ELE_MAX_MPDU_LENGTH(_pEleStart)\t\t\tLE_BITS_TO_1BYTE(_pEleStart, 0, 2)\n#define GET_VHT_CAPABILITY_ELE_CHL_WIDTH(_pEleStart)\t\t\t\tLE_BITS_TO_1BYTE(_pEleStart, 2, 2)\n#define GET_VHT_CAPABILITY_ELE_RX_LDPC(_pEleStart)\t\t\tLE_BITS_TO_1BYTE(_pEleStart, 4, 1)\n#define GET_VHT_CAPABILITY_ELE_SHORT_GI80M(_pEleStart)\t\t\t\tLE_BITS_TO_1BYTE(_pEleStart, 5, 1)\n#define GET_VHT_CAPABILITY_ELE_SHORT_GI160M(_pEleStart)\t\t\t\tLE_BITS_TO_1BYTE(_pEleStart, 6, 1)\n#define GET_VHT_CAPABILITY_ELE_TX_STBC(_pEleStart)\t\t\t\tLE_BITS_TO_1BYTE(_pEleStart, 7, 1)\n#define GET_VHT_CAPABILITY_ELE_RX_STBC(_pEleStart)\t\t\t\tLE_BITS_TO_1BYTE((_pEleStart)+1, 0, 3)\n#define GET_VHT_CAPABILITY_ELE_SU_BFER(_pEleStart)\t\t\t\t\tLE_BITS_TO_1BYTE((_pEleStart)+1, 3, 1)\n#define GET_VHT_CAPABILITY_ELE_SU_BFEE(_pEleStart)\t\t\t\t\tLE_BITS_TO_1BYTE((_pEleStart)+1, 4, 1)\n/*phydm-beamforming*/\n#define GET_VHT_CAPABILITY_ELE_SU_BFEE_STS_CAP(_pEleStart)\tLE_BITS_TO_2BYTE((_pEleStart)+1, 5, 3)\n#define GET_VHT_CAPABILITY_ELE_SU_BFER_SOUND_DIM_NUM(_pEleStart)\tLE_BITS_TO_2BYTE((_pEleStart)+2, 0, 3)\n#define GET_VHT_CAPABILITY_ELE_TXOP_PS(_pEleStart)\t\t\t\tLE_BITS_TO_1BYTE((_pEleStart)+2, 5, 1)\n#define GET_VHT_CAPABILITY_ELE_MAX_RXAMPDU_FACTOR(_pEleStart)\tLE_BITS_TO_2BYTE((_pEleStart)+2, 7, 3)\n#define GET_VHT_CAPABILITY_ELE_RX_MCS(_pEleStart)\t\t\t\t\t ((_pEleStart)+4)\n#define GET_VHT_CAPABILITY_ELE_MCS_RX_HIGHEST_RATE(_pEleStart)\t\t\tLE_BITS_TO_2BYTE((_pEleStart)+6, 0, 13) \n#define GET_VHT_CAPABILITY_ELE_TX_MCS(_pEleStart)\t\t\t\t\t ((_pEleStart)+8)\n#define GET_VHT_CAPABILITY_ELE_MCS_TX_HIGHEST_RATE(_pEleStart)\t\t\tLE_BITS_TO_2BYTE((_pEleStart)+10, 0, 13) \n\n\n//VHT Operation Information Element\n#define SET_VHT_OPERATION_ELE_CHL_WIDTH(_pEleStart, _val)\t\t\tSET_BITS_TO_LE_1BYTE(_pEleStart, 0, 8, _val)\n#define SET_VHT_OPERATION_ELE_CHL_CENTER_FREQ1(_pEleStart, _val)\t\t\tSET_BITS_TO_LE_1BYTE(_pEleStart+1, 0, 8, _val)\n#define SET_VHT_OPERATION_ELE_CHL_CENTER_FREQ2(_pEleStart, _val)\t\t\tSET_BITS_TO_LE_1BYTE(_pEleStart+2, 0, 8, _val)\n#define SET_VHT_OPERATION_ELE_BASIC_MCS_SET(_pEleStart, _val)\t\t\tSET_BITS_TO_LE_2BYTE((_pEleStart)+3, 0, 16, _val)\n\n#define GET_VHT_OPERATION_ELE_CHL_WIDTH(_pEleStart)\t\tLE_BITS_TO_1BYTE(_pEleStart,0,8)\n#define GET_VHT_OPERATION_ELE_CENTER_FREQ1(_pEleStart)\tLE_BITS_TO_1BYTE((_pEleStart)+1,0,8)\n#define GET_VHT_OPERATION_ELE_CENTER_FREQ2(_pEleStart) LE_BITS_TO_1BYTE((_pEleStart)+2,0,8)\n\n//VHT Operating Mode \n#define SET_VHT_OPERATING_MODE_FIELD_CHNL_WIDTH(_pEleStart, _val)\t\tSET_BITS_TO_LE_1BYTE(_pEleStart, 0, 2, _val)\n#define SET_VHT_OPERATING_MODE_FIELD_RX_NSS(_pEleStart, _val)\t\t\tSET_BITS_TO_LE_1BYTE(_pEleStart, 4, 3, _val)\n#define SET_VHT_OPERATING_MODE_FIELD_RX_NSS_TYPE(_pEleStart, _val)\tSET_BITS_TO_LE_1BYTE(_pEleStart, 7, 1, _val)\n#define GET_VHT_OPERATING_MODE_FIELD_CHNL_WIDTH(_pEleStart)\t\t\tLE_BITS_TO_1BYTE(_pEleStart, 0, 2)\n#define GET_VHT_OPERATING_MODE_FIELD_RX_NSS(_pEleStart)\t\t\t\tLE_BITS_TO_1BYTE(_pEleStart, 4, 3)\n#define GET_VHT_OPERATING_MODE_FIELD_RX_NSS_TYPE(_pEleStart)\t\tLE_BITS_TO_1BYTE(_pEleStart, 7, 1)\n\n#define SET_EXT_CAPABILITY_ELE_OP_MODE_NOTIF(_pEleStart, _val)\t\t\tSET_BITS_TO_LE_1BYTE((_pEleStart)+7, 6, 1, _val)\n#define GET_EXT_CAPABILITY_ELE_OP_MODE_NOTIF(_pEleStart)\t\t\t\tLE_BITS_TO_1BYTE((_pEleStart)+7, 6, 1)\n\nstruct vht_priv\n{\n\tu8\tvht_option;\n\n\tu8\tldpc_cap;\n\tu8\tstbc_cap;\n\tu16\tbeamform_cap;\n\n\tu8\tsgi_80m;//short GI\n\tu8\tampdu_len;\n\n\tu8\tvht_op_mode_notify;\n\tu8\tvht_highest_rate;\n\tu8\tvht_mcs_map[2];\n\n\tu8\tvht_cap[32];\n};\n\nu8\trtw_get_vht_highest_rate(u8 *pvht_mcs_map);\nu16\trtw_vht_mcs_to_data_rate(u8 bw, u8 short_GI, u8 vht_mcs_rate);\nu64\trtw_vht_rate_to_bitmap(u8 *pVHTRate);\nvoid\trtw_vht_use_default_setting(_adapter *padapter);\nu32\trtw_build_vht_operation_ie(_adapter *padapter, u8 *pbuf, u8 channel);\nu32\trtw_build_vht_op_mode_notify_ie(_adapter *padapter, u8 *pbuf, u8 bw);\nu32\trtw_build_vht_cap_ie(_adapter *padapter, u8 *pbuf);\nvoid\tupdate_sta_vht_info_apmode(_adapter *padapter, PVOID psta);\nvoid\tupdate_hw_vht_param(_adapter *padapter);\nvoid\tVHT_caps_handler(_adapter *padapter, PNDIS_802_11_VARIABLE_IEs pIE);\nvoid\tVHT_operation_handler(_adapter *padapter, PNDIS_802_11_VARIABLE_IEs pIE);\nvoid\trtw_process_vht_op_mode_notify(_adapter *padapter, u8 *pframe, PVOID sta);\nu32\trtw_restructure_vht_ie(_adapter *padapter, u8 *in_ie, u8 *out_ie, uint in_len, uint *pout_len);\nvoid\tVHTOnAssocRsp(_adapter *padapter);\nu8\trtw_vht_mcsmap_to_nss(u8 *pvht_mcs_map);\n\n#endif\t//_RTW_VHT_H_\n\n" ]

{ "pile_set_name": "Github" }

[ 0, 0, 0.008583690987124463, 0.010362694300518135, 0, 0.012541057031949836, 0.00641025641025641, 0.006149791346365034 ]

[ "Oral management of patients with bleeding disorders. ", "Part 1: Medical considerations.", "\nAn overview of hemostasis, the pathophysiology of bleeding disorders, with a description of clinical features, and recent advances in treatment are presented. ", "This paper is the first of a series of two discussing the management of patients with bleeding disorders in preparation for various dental procedures." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0, 0, 0 ]

[ "Q:\n\nHelp for $\\int_0^{\\pi^2}\\int_\\sqrt{x}^{\\pi} \\sin(y^3) \\,\\mathrm{d}y \\,\\mathrm{d}x$\n\nSOLUTION\n$$\\begin{aligned}\nI &=\\int_\\sqrt{x}^{\\pi}\\int_0^{\\pi^2} \\sin(y^3) \\,\\mathrm{d}y \\,\\mathrm{d}x \\\\\n&=\\int_\\sqrt{x}^{\\pi}\\int_0^{\\pi^2} \\sin(y^3) \\,\\mathrm{d}x \\,\\mathrm{d}y \\\\\n&=\\int_\\sqrt{x}^{\\pi} \\pi^2 \\sin(y^3) \\,\\mathrm{d}y\n\\end{aligned}$$\n\nA:\n\nSo you want to integrate the function $f(x,y)=\\sin (y^3)$ with bounds $\\int_{x=0}^{x=\\pi^2}\\int_{y=\\sqrt x}^{y=\\pi}$.\nThis can be represented as the set\n\\begin{align}\n\\ S & =\\{ (x,y) \\in \\Bbb R^2:0≤x≤\\pi^2 \\;,\\; \\sqrt x≤y≤\\pi \\} \\\\\n\\ & =\\{ (x,y) \\in \\Bbb R^2:0≤x≤\\pi^2 \\;,\\; x≤y^2≤\\pi^2 \\} \\\\\n\\ & =\\{ (x,y) \\in \\Bbb R^2:0≤x≤y^2≤\\pi^2 \\} \\\\\n\\ & = \\{ (x,y) \\in \\Bbb R^2:0≤y^2≤\\pi^2 \\;,\\; 0≤x≤y^2\\} \\\\\n\\ & = \\{ (x,y) \\in \\Bbb R^2:0≤y≤\\pi \\;,\\; 0≤x≤y^2\\}\n\\end{align}\nBasically this is our region:\n\nThus, another way to parameterize this region is to have $\\int_{y=0}^{y=\\pi}\\int_{x=0}^{x=y^2}$ instead. ", "Hence\n\\begin{align}\n\\ \\int_{x=0}^{x=\\pi^2}\\int_{y=\\sqrt x}^{y=\\pi}\\sin (y^3)dydx & = \\int_{y=0}^{y=\\pi}\\int_{x=0}^{x=y^2}\\sin (y^3)dxdy\\\\\n\\ & = \\int_{y=0}^{y=\\pi} y^2\\sin (y^3)dy \\\\\n\\ & = \\Bigl[ -\\frac 13 \\cos(y^3) \\Bigr]_{y=0}^{y=\\pi} \\\\\n\\ & = \\frac 13 \\Bigl (1-\\cos (\\pi ^3) \\Bigr )\n\\end{align}\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0.02014846235418876, 0.013422818791946308 ]

[ "The Tomb of Ts'in\n\nThe Tomb of Ts'in is a 1916 adventure novel by the British writer Edgar Wallace. ", "Some passages of the plot appear to copy word-for-word his earlier story Captain Tatham (1909). ", "It is suggested that Wallace's embarrassment about recycling his work led to buying up most of the copies later, although the shortage of available copies may have to do with the fact that very few were originally printed by the publishers Ward Lock due to wartime shortages.", "\n\nIt involves a search for hidden treasure in China where an adventurer seeks out the missing tomb of Emperor Qin Shi Huang. ", "It predates the actual discovery of the Emperor's tomb by more than half a century.", "\n\nReferences\n\nBibliography\n \n\nCategory:1916 British novels\nCategory:Novels by Edgar Wallace\nCategory:British adventure novels" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.01, 0.010416666666666666, 0.007272727272727273, 0.008, 0, 0.008 ]

[ "And this is the final big announcement for NDY2014. ", "There are still a few things up our sleeves, but with this, the schedule has been posted and TICKETS WILL GO ON SALE THIS FRIDAY. ", "There are multiple events almost every night & a wicked pre-show happening Wednesday at S.H.I.B.G.B’s. ", "See what you want to see, skip what you don’t. ", "See the full schedule here: http://notdeadyettoronto.tumblr.com/NDY2014\n\n\n\nThe following bands will be joining the lineup…\n\n\n\nIRON LUNG\n\nPOWER TRIP\n\nCAREER SUICIDE\n\nMINDSET\n\nANASAZI\n\nPLEASURE LEFTISTS\n\nBLAZING EYE\n\nPUCE MARY\n\nCOLUMN OF HEAVEN\n\nTENEMENT\n\nTEENANGER\n\nBURNING LOVE\n\nDEMOLITION\n\nNOT AFRAID\n\nCAUGHT IN A CROWD\n\nPROXY\n\nABSOLUT\n\nVCR\n\nFURY\n\nBLACK BARON\n\nBORN WRONG\n\nRAZORHEADS\n\nTHE SENTENCED\n\nLIFE LIKE\n\nANIMAL MOTHER\n\nFARANG\n\nANCIENT HEADS\n\nWILD SIDE\n\nMARVELOUS MARK\n\nHIRED GOONS\n\nCONUNDRUM\n\n\n\nTickets will be available for most shows. ", "They go on sale THIS FRIDAY at Rotate This in Toronto and online at http://notdeadyet.bigcartel.com/ - There are no weekend passes available. ", "Buy tickets for what you want to see and skip what you don’t!", "\n\n\n\nPlease note that all online tickets are Will Call only!", "\n\n\n\nSee you in November!" ]

{ "pile_set_name": "OpenWebText2" }

[ 0.019230769230769232, 0, 0.009708737864077669, 0, 0.005504587155963303, 0.007042253521126761, 0, 0, 0 ]

[ "Jeromesville, Ohio\n\nJeromesville is a village in Ashland County, Ohio, United States. ", "The population was 562 at the 2010 census.", "\n\nHistory\nJeromesville was platted in 1815 ( near the site of a former and abandoned Native-American village named \"Jerometown\"). ", "It is named for Jean/John Baptiste Jerome, (a French-Canadian fur trader and pioneer settler), from whom, Christian Deardorf and William Vaughn purchased land and 'founded' a new pioneer village, (which was originally spelled \"Jeromeville\"). ", "A post office has been in operation at Jeromesville since 1816. [", "Note: the Native-American village of Jerometown is often attributed to be the same as \"Mohican Johnstown\"; however, the mid-1700s village named \"Mohican Johnstown\" was not at this same location.(see Lenape settlements)]\n\nIn 2018, Mayor Randy Spade founded the Jeromesville Junior Council, a group of 5th through 8th graders attending Hillsdale Local School District. ", "They are tasked with making Jeromesville a better place for both kids of today and the future. ", "The group was previously led by former Junior Mayor Landon Allis, and is currently led by Junior Mayor Alexis Luna. ", "This is the first Junior Village Council codified into law in the State of Ohio.", "\n\nGeography\nJeromesville is located at (40.804034, -82.195698).", "\n\nAccording to the United States Census Bureau, the village has a total area of , all land.", "\n\nDemographics\n\n2010 census\nAs of the census of 2010, there were 562 people, 208 households, and 154 families living in the village. ", "The population density was . ", "There were 234 housing units at an average density of . ", "The racial makeup of the village was 99.1% White and 0.9% Native American. ", "Hispanic or Latino of any race were 1.1% of the population.", "\n\nThere were 208 households of which 41.3% had children under the age of 18 living with them, 51.9% were married couples living together, 17.3% had a female householder with no husband present, 4.8% had a male householder with no wife present, and 26.0% were non-families. ", "21.6% of all households were made up of individuals and 7.2% had someone living alone who was 65 years of age or older. ", "The average household size was 2.70 and the average family size was 3.14.", "\n\nThe median age in the village was 33.3 years. ", "32.4% of residents were under the age of 18; 5.9% were between the ages of 18 and 24; 26.7% were from 25 to 44; 24.3% were from 45 to 64; and 10.7% were 65 years of age or older. ", "The gender makeup of the village was 49.6% male and 50.4% female.", "\n\n2000 census\nAs of the census of 2000, there were 478 people, 202 households, and 128 families living in the village. ", "The population density was 1,309.6 people per square mile (512.7/km²). ", "There were 210 housing units at an average density of 575.4 per square mile (225.2/km²). ", "The racial makeup of the village was 96.86% White, 0.42% African American, 1.26% Native American, and 1.46% from two or more races. ", "Hispanic or Latino of any race were 2.30% of the population.", "\n\nThere were 202 households out of which 30.7% had children under the age of 18 living with them, 51.0% were married couples living together, 10.4% had a female householder with no husband present, and 36.6% were non-families. ", "30.2% of all households were made up of individuals and 12.9% had someone living alone who was 65 years of age or older. ", "The average household size was 2.37 and the average family size was 2.96.", "\n\nIn the village, the population was spread out with 26.4% under the age of 18, 6.1% from 18 to 24, 31.8% from 25 to 44, 22.4% from 45 to 64, and 13.4% who were 65 years of age or older. ", "The median age was 37 years. ", "For every 100 females there were 92.0 males. ", "For every 100 females age 18 and over, there were 88.2 males.", "\n\nThe median income for a household in the village was $41,000, and the median income for a family was $46,250. ", "Males had a median income of $31,576 versus $21,667 for females. ", "The per capita income for the village was $16,864. ", "About 2.3% of families and 6.1% of the population were below the poverty line, including 7.4% of those under age 18 and 3.8% of those age 65 or over.", "\n\nEducation\nJeromesville Public Schools belong to the Hillsdale Local School District. ", "The district has one elementary school, one middle school, and one high school. ", "Students attend Hillsdale High School.", "\n\nReferences\n\nCategory:Villages in Ashland County, Ohio\nCategory:Villages in Ohio\nCategory:1815 establishments in Ohio" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0, 0, 0, 0.008264462809917356, 0, 0.013623978201634877, 0, 0.017241379310344827, 0.0125, 0, 0.01098901098901099, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.011494252873563218, 0, 0.02631578947368421, 0 ]

[ "Unusual biology across a group comprising more than 15% of domain Bacteria.", "\nA prominent feature of the bacterial domain is a radiation of major lineages that are defined as candidate phyla because they lack isolated representatives. ", "Bacteria from these phyla occur in diverse environments and are thought to mediate carbon and hydrogen cycles. ", "Genomic analyses of a few representatives suggested that metabolic limitations have prevented their cultivation. ", "Here we reconstructed 8 complete and 789 draft genomes from bacteria representing >35 phyla and documented features that consistently distinguish these organisms from other bacteria. ", "We infer that this group, which may comprise >15% of the bacterial domain, has shared evolutionary history, and describe it as the candidate phyla radiation (CPR). ", "All CPR genomes are small and most lack numerous biosynthetic pathways. ", "Owing to divergent 16S ribosomal RNA (rRNA) gene sequences, 50-100% of organisms sampled from specific phyla would evade detection in typical cultivation-independent surveys. ", "CPR organisms often have self-splicing introns and proteins encoded within their rRNA genes, a feature rarely reported in bacteria. ", "Furthermore, they have unusual ribosome compositions. ", "All are missing a ribosomal protein often absent in symbionts, and specific lineages are missing ribosomal proteins and biogenesis factors considered universal in bacteria. ", "This implies different ribosome structures and biogenesis mechanisms, and underlines unusual biology across a large part of the bacterial domain." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0.013333333333333334, 0, 0.009009009009009009, 0.008849557522123894, 0, 0.006097560975609756, 0, 0.005714285714285714, 0.007575757575757576, 0, 0, 0 ]

[ "###############################################################################\n# Copyright (c) 2000, 2006 IBM Corporation and others.", "\n# All rights reserved. ", "This program and the accompanying materials\n# are made available under the terms of the Eclipse Public License v1.0\n# which accompanies this distribution, and is available at\n# http://www.eclipse.org/legal/epl-v10.html\n#\n# Contributors:\n# IBM Corporation - initial API and implementation\n###############################################################################\n\ngenerateFeatureVersionSuffix=true\nbaseLocation=/home/adb/farrah/baseLocation\nbuildDirectory=/home/adb/farrah/src\np4.home=/home/adb/farrah/P4\noutputUpdateJars=true\nindividualSourceBundles=true\n#runPackager=true\n\nmapVersionTag=HEAD\nbootclasspath=${java.home}/lib/rt.jar\n\nbuildType=I\nbuildId=Build\nbuildLabel=${buildType}.${buildId}\ntimestamp=0000\ncollPlace=eclipse\ncollBase=.\nconfigs=*,*,*\narchivesFormat = *,*,*-zip\nbootclasspath=${java.home}/lib/rt.jar\njavacFailOnError=false\njavacDebugInfo=on\njavacVerbose=true\ncompileArg=-enableJavadoc\n\nbaseos=win32\nbasews=win32\nbasearch=x86\n\ncollectingFolder=eclipse\narchivePrefix=eclipse\n\nzipargs=\ntarargs=\n" ]

{ "pile_set_name": "Github" }

[ 0.007462686567164179, 0, 0.007858546168958742 ]

[ "TitleEntrepreneur, IT consultantCompanyKarhatsu IT Consulting OyBioHenri Karhatsu has been working in software\ndevelopment business over\nten years now. ", "Initially being master of science in economics he\nrealized that programming is so fascinating thing to do that he wanted\nto learn much more ending up with another master's degree, this time in\ncomputer science. ", "The past 5 years he has been a private IT consultant\nand eagerly learning about agile and lean way of working. ", "Besides\nwriting the actual software for his clients he has been helping them to\nfind alternative and more modern ways to manage software development.", "\nYou can read more about his thoughts in [his\nbloghttp://blog.karhatsu.com or\nfollow him on\nTwitterhttp://www.twitter.com/karhatsu" ]

{ "pile_set_name": "Pile-CC" }

[ 0.013157894736842105, 0, 0, 0, 0.015384615384615385 ]

[ "Q:\n\nUploading Wagtail images from outside of wagtail\n\nIn a Django model that cannot subclass Page, I want to convert an existing ImageField to use Wagtail images. ", "I have redefined the field as:\navatar = models.", "ForeignKey(\n 'wagtailimages.", "Image', null=True, on_delete=models.", "SET_NULL, related_name='+'\n)\n\nThe user needs to be able to upload an image to their profile view. ", "In forms.py for the Django view, I have:\navatar = forms.", "ImageField(\n label='Your Photo', required=False,\n error_messages={'invalid': \"Image files only\"}, widget=forms.", "FileInput())\n\nWhen I upload an image to the view, it crashes on:\nCannot assign \"<InMemoryUploadedFile: filename.jpg (image/jpeg)>\":\n\"UserProfile.avatar\" must be a \"Image\" instance.", "\n\nI'm pretty sure the problem is the field definition in the form, but I can't figure out what the right definition should be. ", "\nI know that I'll need to manually attach the image to the UserProfile and the Collection, but need to get past this error first. ", "Or is it a bad idea to try and use individual WT fields in a non-WT model? ", "Thanks.", "\n\nA:\n\nThe problem here is that the avatar ForeignKey field on your model is expecting to receive an instance of the wagtailimages.", "Image model. ", "The ImageField on the form isn't capable of providing this - it only provides a file object. ", "To make this work, you'll need to set up your form (which I'm assuming is a ModelForm) to create the wagtailimages.", "Image object at the same time as your own model. ", "It should be possible to do this with a custom save method as follows:\n\nRename avatar = forms.", "ImageField to something that doesn't clash with the avatar model field, such as avatar_image\nEnsure that avatar_image is included in your ModelForm's fields definition, but avatar isn't. ", "At this point, avatar_image is just an extra field on the form, with no connection to the model.", "\nDefine the following save method on the ModelForm:\nfrom wagtail.images.models import Image\n\ndef save(self, commit=False):\n if not commit:\n raise Exception(\"This form doesn't support save(commit=False)\")\n\n # build the instance for this form, but don't save it to the db yet\n instance = super(MyForm, self).save(commit=False)\n\n # create the Image object\n avatar = Image.objects.create(\n file=self.cleaned_data['avatar_image'],\n title=\"Image title\"\n # you may need to add more fields such as collection to make it a valid image...\n )\n\n # attach the image to your final model, and save\n instance.avatar = avatar\n instance.save()\n return instance\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0.006134969325153374, 0, 0.03225806451612903, 0, 0, 0.017857142857142856, 0.017094017094017096, 0, 0, 0.015384615384615385, 0.013333333333333334, 0, 0.007692307692307693, 0, 0.010752688172043012, 0.008695652173913044, 0, 0, 0.0053475935828877, 0, 0.009971509971509971 ]

[ "\n> * 原文地址：[DEALING WITH IMBALANCED DATA: UNDERSAMPLING, OVERSAMPLING AND PROPER CROSS-VALIDATION](http://www.marcoaltini.com/blog/dealing-with-imbalanced-data-undersampling-oversampling-and-proper-cross-validation)\n> * 原文作者：[Marco Altini](https://twitter.com/marco_alt)\n> * 译文出自：[掘金翻译计划](https://github.com/xitu/gold-miner)\n> * 本文永久链接：[https://github.com/xitu/gold-miner/blob/master/TODO/dealing-with-imbalanced-data-undersampling-oversampling-and-proper-cross-validation.md](https://github.com/xitu/gold-miner/blob/master/TODO/dealing-with-imbalanced-data-undersampling-oversampling-and-proper-cross-validation.md)\n> * 译者：[edvardhua](https://github.com/edvardHua)\n> * 校对者：[lileizhenshuai](https://github.com/lileizhenshuai), [lsvih](https://github.com/lsvih)\n\n# 在使用过采样或欠采样处理类别不均衡的数据后，如何正确的做交叉验证？", "\n\n**[关于我在这篇文章中使用的术语可以在 [Physionet](http://www.physionet.org/pn6/tpehgdb/) 网站中找到。 ", "本篇博客中用到的代码可以在 [github](https://github.com/marcoalt/Physionet-EHG-imbalanced-data)中找到]**\n\n几个星期前我阅读了一篇[交叉验证的技术文档（Cross Validation Done Wrong）](http://www.alfredo.motta.name/cross-validation-done-wrong)， 在交叉验证的过程中，我们希望能够了解到我们的模型的泛化性能，以及它是如何预测我们感兴趣的未知样本的。基于这个出发点，作者提出了很多好的观点（尤其是关于特征选择的）。我们的确经常在进行交叉验证之前进行特征选择，但是需要注意的是我们在特征选择的时候，不能将验证集的数据加入到特征选择这个环节中去。", "\n\n但是，这篇文章并没有涉及到我们在实际应用经常出现的问题。例如，如何在不均衡的数据上合理的进行交叉验证。在医疗领域，我们所拥有的数据集一般只包含两种类别的数据， **正常** 样本和 **相关** 样本。譬如说在癌症检查的应用我们可能只有很小一部分病人患上了癌症（相关样本）而其余的大部分样本都是健康的个体。就算不在医疗领域，这种情况也存在（甚至更多），比如欺诈识别，它们的数据集中的相关样本和正常样本的比例都有可能会是 1:100000。", "\n\n## 手头的问题\n\n因为分类器对数据中类别占比较大的数据比较敏感，而对占比较小的数据则没那么敏感，所以我们需要在交叉验证之前对不均衡数据进行预处理。所以如果我们不处理类别不均衡的数据，分类器的输出结果就会存在偏差，也就是在预测过程中大多数情况下都会给出偏向于某个类别的结果，这个类别是训练的时候占比较大的那个类别。这个问题并不是我的研究领域，但是自从我在[做早产预测的工作的时候](https://medium.com/40-weeks/37-772d7f519f9)经常会遇到这种问题。早产是指短于 37 周的妊娠，大部分欧洲国家的早产率约占 6-7％，美国的早产率为 11％，因此我们可以看到数据是非常不均衡的。", "\n\n我最近无意中发现两篇关于早产预测的文章，他们是使用 Electrohysterography (EHG)数据来做预测的。作者只使用了一个单独的 EHG 横截面数据（通过捕获子宫电活动获得）训练出来的模型就声称在预测早产的时候具备很高的精度（ [2], 对比没有使用过采样时的 AUC = 0.52-0.60，他的模型的 **AUC 可以达到 0.99** ）.", "\n\n这个结果给我们的感觉像是 **过拟合和错误的交叉验证** 所造成的，在我解释原因之前，让我们先来观看下面的数据：\n\n\n\n这四张密度图表示的是他所用到的四个特征的在两个类别上的分布，这两个类别为正常分娩与早产（f = false，表示正常分娩，使用红色的线表示；t = true, 则表示为早产，用蓝色的线表示）。我们从图中可以看到这四个特征并没有很强的区分两个类别的能力。他所提取出来的特征在两个特征上的分布基本上就是重叠的。我们可以认为这是一个无用输入，无用输出的例子，而不是说这个模型缺少数据。", "\n\n只要稍微思考一下该问题所在的领域，我们就会对 auc=0.99 这个结果提出质疑。因为区分正常分娩和早产没有一个很明确的区分。假设我们设置 37 周就为正常的分娩时间。 **", "那么如果你在第 36 周后的第 6 天分娩，那么我们则标记为早产。反之，如果在 37 周后 1 天妊娠，我们则标记为在正常的妊娠期内。** ", "很明显，这两种情况下区分早产和正常分娩是没有意义的，37 周只是一个惯例，因此，预测结果会大受影响并且对于分娩时间在 37 周左右的样本，结果会非常不精确。", "\n\n在[这里](http://www.physionet.org/pn6/tpehgdb/)可以下载到所使用的数据集。在这篇文章中我会重复的展示数据集中的一部分特点，并且展示我们在过采样的情况下该如何进行合适的交叉验证。希望我在这个问题上所提出的一些矫正方案能够在未来让我们避免再犯这样的错误。", "\n\n## 数据集，特征，性能评估和交叉验证技术\n\n**数据集**\n\n我们使用的数据来自于卢布尔雅那医学中心大学妇产科，数据中涵盖了从1997 年到 2005 年斯洛维尼亚地区的妊娠记录。他包含了从正常怀孕的 EHG 截面数据。 **", "这个数据是非常不均衡的，因为 300 个记录中只有 38 条才是早孕。** ", "更加详细的信息可以在 [3] 中找到。简单来说，我们选择 EHG 截面的理由是因为 EHG 测量的是子宫的电活动图，而这个活动图在怀孕期间会不断的变化，直到导致子宫收缩分娩出孩子。因此，研究推断非侵入性情况下监测怀孕活动可以尽早的发现哪些孕妇会早产。", "\n\n**特征与分类器**\n\n在 Physionet 上，你可以找到所有关于该研究的原始数据，但是为了让下面的实验不那么复杂，我们用到的是作者提供的另外一份数据来进行分析，这份数据中包含的特征是从原始数据中筛选出来的，筛选的条件是根据特征与 EHG 活动之间的相关频率。我们有四个特征（EHG信号的均方根，中值频率，频率峰值和样本熵，[这里](http://physionet.mit.edu/pn6/tpehgdb/tpehgdb.pdf) 有关如何计算这些特征值的更多信息）。据收集数据集的研究人员所说，大部分有价值的信息都是来自于渠道 3，因此我将使用从渠道 3 预提取出来的特征。详细的数据集也在 [github](https://github.com/marcoalt/Physionet-EHG-imbalanced-data) 可以找到。因为我们是要训练分类器分类器，所以我使用了一些常见的训练分类器的算法：逻辑回归、分类树、SVM 和随机森林。在博客中我不会做任何特征选择，而是将所有的数据都用来训练模型。", "\n\n**评测指标**\n\n在这里我们使用 **召回率** ， **真假率** 和 **AUC** 作为评测指标，关于指标的含义可以查看 [wikipedia](https://en.wikipedia.org/wiki/Sensitivity_and_specificity)\n\n**交叉验证**\n\n我决定使用 **留一法** 来做交叉验证。这种技术在使用数据集时或者当欠采样时不会有任何错误的余地。但是，当过采样时，情况又会有点不一样，所以让我们看下面的分析。", "\n\n## 类别不均衡的数据\n\n当我们遇到数据不均衡的时候，我们该如何做：\n\n- 忽略这个问题\n- 对占比较大的类别进行欠采样\n- 对占比较小的类别进行过采样\n\n## 忽略这个问题\n\n如果我们使用不均衡的数据来训练分类器，那么训练出来的分类器在预测数据的时候总会返回数据集中占比最大的数据所对应的类别作为结果。这样的分类器具备太大的偏差，下面是训练这样的分类器所对应的代码：\n\n```R\n#leave one participant out cross-validation\nresults_lr <- rep(NA, nrow(data_to_use))\nresults_tree <- rep(NA, nrow(data_to_use))\nresults_svm <- rep(NA, nrow(data_to_use))\nresults_rf <- rep(NA, nrow(data_to_use))\n\nfor(index_subj in 1:nrow(data_to_use))\n{\n #remove subject to validate\n training_data <- data_to_use[-index_subj, ]\n training_data_formula <- training_data[, c(\"preterm\", features)]\n\n #select features in the validation set\n validation_data <- data_to_use[index_subj, features]\n\n #logistic regression\n glm.fit <- glm(preterm ~.,\n data = training_data_formula,\n family = binomial)\n glm.probs <- predict(glm.fit, validation_data, type = \"response\")\n predictions_lr <- ifelse(glm.probs < 0.5, \"t\", \"f\")\n results_lr[index_subj] <- predictions_lr\n\n #classification tree\n tree.fit <- tree(preterm ~.,\n data = training_data_formula)\n predictions_tree <- predict(tree.fit, validation_data, type = \"class\")\n results_tree[index_subj] <- predictions_tree\n\n #svm\n svm <- svm(preterm ~.,\n data = training_data_formula\n )\n predictions_svm <- predict(svm, validation_data)\n results_svm[index_subj] <- predictions_svm\n\n #random forest \n rf <- randomForest(preterm ~.,\n data = training_data_formula)\n predictions_rf <- predict(rf, validation_data)\n results_rf[index_subj] <- predictions_rf \n}\n```\n\n从上面的代码可以看出，在每次迭代中，我只需选择 index_subj 下标所对应的数据作为验证集，然后使用剩余的数据（即训练数据）构建模型。结果如下图所示\n\n\n\n\n如预期的那样，分类器的偏差太大，召回率为零或非常接近零，而真假率为1或非常接近于1，即所有或几乎所有记录被检测为会正常分娩，因此基本没有识别出早产的记录。下面的实验则使用了欠采样的方法。", "\n\n## 对大类样本进行欠采样\n\n处理类别不平衡数据的最常见和最简单的策略之一是对大类样本进行欠采样。 ", "尽管过去也有很多关于解决数据不均衡的办法（例如，对具体样本进行欠采样，例如“远离决策边界”的方法）[4]，但那些方法都不能改进在简单随机选择样本的情况下有任何性能上的提升。 ", "因此，我们的实验将从占比较大的类别下的样本中随机选择 *n* 个样本，其中 *n* 的值等于占比较小的类别下的样本的总数，并在训练阶段使用它们，然后在验证中排除掉这些样本。 ", "代码如下：\n\n```R\n#leave one participant out cross-validation\nresults_lr <- rep(NA, nrow(data_to_use))\nresults_tree <- rep(NA, nrow(data_to_use))\nresults_svm <- rep(NA, nrow(data_to_use))\nresults_rf <- rep(NA, nrow(data_to_use))\n\nrows_preterm <- sum(data_to_use$preterm == \" t \") #weird string, haven't changed it for now\nfor(index_subj in 1:nrow(data_to_use))\n{\n #remove subject to validate\n training_data <- data_to_use[-index_subj, ]\n training_data_preterm <- training_data[training_data$preterm == \" t \", ]\n training_data_term <- training_data[training_data$preterm == \" f \", ]\n\n #get subsample to balance dataset\n indices <- sample(nrow(training_data_term), rows_preterm)\n training_data_term <- training_data_term[indices, ]\n training_data <- rbind(training_data_preterm, training_data_term)\n\n #select features in the training set\n training_data_formula <- training_data[, c(\"preterm\", features)]\n\n #select features in the validation set\n validation_data <- data_to_use[index_subj, features]\n\n #logistic regression\n glm.fit <- glm(preterm ~.,\n data = training_data_formula,\n family = binomial)\n glm.probs <- predict(glm.fit, validation_data, type = \"response\")\n predictions_lr <- ifelse(glm.probs < 0.5, \"t\", \"f\")\n results_lr[index_subj] <- predictions_lr\n\n #classification tree\n tree.fit <- tree(preterm ~.,\n data = training_data_formula)\n predictions_tree <- predict(tree.fit, validation_data, type = \"class\")\n results_tree[index_subj] <- predictions_tree\n\n #svm\n svm <- svm(preterm ~.,\n data = training_data_formula\n )\n predictions_svm <- predict(svm, validation_data)\n results_svm[index_subj] <- predictions_svm\n\n #random forest \n rf <- randomForest(preterm ~.,\n data = training_data_formula,\n sampsize = c(nrow(training_data_preterm), nrow(training_data_preterm)))\n predictions_rf <- predict(rf, validation_data)\n results_rf[index_subj] <- predictions_rf \n}\n```\n\n如上所述，上面的代码与之前最大的不同的是在每次迭代的时候，我们从占比较大的类别下的样本中选取了 *n* ，然后使用这个 n 个样本和占比类别较小的样本组成了训练集来训练我们的分类器。结果如下图所示：\n\n\n\n通过欠采样，我们解决了数据类别不均衡的问题，并且提高了模型的召回率，但是，模型的表现并不是很好。其中一个原因可能是因为我们用来训练模型的数据过少。一般来说，如果我们的数据集中的类别越不均衡，那么我们在欠采样中抛弃的数据就会越多，那么就意味着我们可能抛弃了一些潜在的并且有用的信息。现在我们应该这样问我们自己，我们是否训练了一个弱的分类器，而原因是因为我们没有太多的数据？还是说我们依赖了不好的特征，所以就算数据再多对模型也没有帮助？", "\n\n## 对少数类样本过采样\n\n如果我们在 **交叉验证** 之前进行过采样会导致 **过拟合** 的问题。那么产生这个问题的原因是什么呢？让我们来看下面的一个关于过采样的简单实例。", "\n\n最简单的过采样方式就是对占比类别较小下的样本进行重新采样，譬如说创建这些样本的副本，或者手动制造一些相同的数据。现在，如果我们在交叉验证之前做了过采样，然后使用留一法做交叉验证，也就是说我们在每次迭代中使用 N-1 份样本做训练，而只使用 1 份样本验证。 **", "但是我们注意到在其实在 N-1 份的样本中是包含了那一份用来做验证的样本的。所以这样做交叉验证完全违背了初衷。** ", "让我们用图形化的方式来更好的审视这个问题。", "\n\n\n\n最左边那列表示的是原始的数据，里面包含了少数类下的两个样本。我们拷贝这两个样本作为副本，然后再进行交叉验证。在迭代的过程，我们的训练样本和验证样本会包含相同的数据，如最右那张图所示，这种情况下会导致过拟合或误导的结果，合适的做法应该如下图所示。", "\n\n\n\n也就是说我们每次迭代做交叉验证之前先将验证样本从训练样本中分离出来，然后再对训练样本中少数类样本进行过采样（橙色那块图所示）。在这个示例中少数类样本只有两个，所以我拷贝了三份副本。这种做法与之前最大的不同就是训练样本和验证样本是没有交集的。因为我们获得一个比之前好的结果。即使我们使用其他的交叉验证方法，譬如 k-flod ，做法也是一样的。", "\n\n这是一个简单的例子，当然我们也可以使用更加好的方法来做过采样。其中一种使用的过采样方法叫做 **SMOTE** 方法，SMOTE 方法并不是采取简单复制样本的策略来增加少数类样本， **而是通过分析少数类样本来创建新的样本** 的同时对多数类样本进行欠采样。正常来说当我们简单复制样本的时候，训练出来的分类器在预测这些复制样本时会很有信心的将他们识别出来，你为他知道这些复制样本的所有边界和特点，而不是以概括的角度来刻画这些少数类样本。但是，SMOTE 可以有效的强制让分类的边界更加的泛化，一定程度上解决了不够泛化而导致的过拟合问题。在 SMOTE 的[论文](https://www.jair.org/media/953/live-953-2037-jair.pdf)中用了很多图来进行解释这个问题的原理和解决方案，所以我建议大家可以去看看。", "\n\n但是，我们有一定必须要清楚的是 **使用 SMOTE 过采样的确会提升决策边界，但是却并没有解决前面所提到的交叉验证所面临的问题。** ", "如果我们使用相同的样本来训练和验证模型，模型的技术指标肯定会比采样了合理交叉验证方法所训练出来的模型效果好。也就是说我在上面所举的例子对应的问题是仍然存在的。 **", "下面让我们来看一下在交叉验证之前进行过采样会得出怎样的结果。** ", "\n\n**错误的使用交叉验证和过采样**\n\n下面的代码将会先进行过采样，然后再进入交叉验证的循环，我们使用 SMOTE 方法合成了我们的样本：\n\n```R\ndata_to_use <- tpehgdb_features\ndata_to_use_smote <- SMOTE(preterm ~ . , ", "cbind(data_to_use[, c(\"preterm\", features)]), k=5, perc.over = 600)\n\nmetrics_all <- data.frame()\n\n#leave one participant out cross-validation\nresults_lr <- rep(NA, nrow(data_to_use_smote))\nresults_tree <- rep(NA, nrow(data_to_use_smote))\nresults_svm <- rep(NA, nrow(data_to_use_smote))\nresults_rf <- rep(NA, nrow(data_to_use_smote))\n\nfor(index_subj in 1:nrow(data_to_use_smote))\n{\n #remova subject to validate\n training_data <- data_to_use[-index_subj, ]\n\n #no need to balance the dataset anymore \n #select features in the training set\n training_data_formula <- training_data[, c(\"preterm\", features)]\n\n #select features in the validation set\n validation_data <- data_to_use_smote[index_subj, features]\n\n #logistic regression\n glm.fit <- glm(preterm ~.,\n data = training_data_formula,\n family = binomial)\n glm.probs <- predict(glm.fit, validation_data, type = \"response\")\n predictions_lr <- ifelse(glm.probs < 0.5, \"t\", \"f\")\n results_lr[index_subj] <- predictions_lr\n\n #classification tree\n tree.fit <- tree(preterm ~.,\n data = training_data_formula)\n predictions_tree <- predict(tree.fit, validation_data, type = \"class\")\n results_tree[index_subj] <- predictions_tree\n\n #svm\n svm <- svm(preterm ~.,\n data = training_data_formula\n )\n predictions_svm <- predict(svm, validation_data)\n results_svm[index_subj] <- predictions_svm\n\n #random forest \n rf <- randomForest(preterm ~.,\n data = training_data_formula)\n predictions_rf <- predict(rf, validation_data)\n results_rf[index_subj] <- predictions_rf \n}\n\nmetrics_lr <- data.frame(binary_metrics(as.numeric(as.factor(results_lr)), as.numeric(data_to_use_smote$preterm), class_of_interest = 2))\nmetrics_lr[, c(\"classifier\")] <- c(\"logistic_regression\")\nmetrics_all <- rbind(metrics_all, metrics_lr)\n\nmetrics_tree <- data.frame(binary_metrics(results_tree, as.numeric(data_to_use_smote$preterm), class_of_interest = 2))\nmetrics_tree[, c(\"classifier\")] <- c(\"tree\")\nmetrics_all <- rbind(metrics_all, metrics_tree)\n\nmetrics_svm <- data.frame(binary_metrics(results_svm, as.numeric(data_to_use_smote$preterm), class_of_interest = 2))\nmetrics_svm[, c(\"classifier\")] <- c(\"svm\")\nmetrics_all <- rbind(metrics_all, metrics_svm)\n\nmetrics_rf <- data.frame(binary_metrics(results_rf, as.numeric(data_to_use_smote$preterm), class_of_interest = 2))\nmetrics_rf[, c(\"classifier\")] <- c(\"random_forests\")\nmetrics_all <- rbind(metrics_all, metrics_rf) \n```\n\nR 包中的 SMOTE 函数在这里可以查看 [DMwR](https://cran.r-project.org/web/packages/DMwR/DMwR.pdf)。训练的结果如下：\n\n\n\n结果相当不错。尤其是随机森林在没有做任何特征工程和调参的前提下 **auc 的值达到了 0.93** ，但是与前面不同的是我们使用了 SMOTE 方法进行欠采样，现在这个问题的核心在于我们应该在什么时候使用恰当的方法，而不是使用哪种方法。在交叉验证之前使用过采样的确获得很高的精度，但模型已经 **过拟合** 了。你看，就算是最简单的分类树都可以获得 0.84 的 AUC 值。", "\n\n**正确的使用过采样和交叉验证**\n\n正确的在交叉验证中配合使用过拟合的方法很简单。就和我们在交叉验证中的每次循环中做特征选择一样，我们也要在每次循环中做过采样。 **", "根据我们当前的少数类创建样本，然后选择一个样本作为验证样本，假装我们没有使用在训练集中的数据来作为验证样本，这是毫无意义的。** ", "这一次，我们在交叉验证循环中过采样，因为验证集已经从训练样本中移除了，因为我们只需要插入那些不用于验证的样本来合成数据，我们交叉验证的迭代次数将和样本数一样，如下代码所示：\n\n```R\ndata_to_use <- tpehgdb_features\n\nmetrics_all <- data.frame()\n\n#leave one participant out cross-validation\nresults_lr <- rep(NA, nrow(data_to_use))\nresults_tree <- rep(NA, nrow(data_to_use))\nresults_svm <- rep(NA, nrow(data_to_use))\nresults_rf <- rep(NA, nrow(data_to_use))\n\nfor(index_subj in 1:nrow(data_to_use))\n{\n #remove subject to validate\n training_data <- data_to_use[-index_subj, ]\n training_data_smote <- SMOTE(preterm ~ . , ", "cbind(training_data[, c(\"preterm\", features)]), k=5, perc.over = 600)\n\n #no need to balance the dataset anymore \n #select features in the training set\n training_data_formula <- training_data_smote[, c(\"preterm\", features)]\n\n #select features in the validation set\n validation_data <- data_to_use[index_subj, features]\n\n #logistic regression\n glm.fit <- glm(preterm ~.,\n data = training_data_formula,\n family = binomial)\n glm.probs <- predict(glm.fit, validation_data, type = \"response\")\n predictions_lr <- ifelse(glm.probs < 0.5, \"t\", \"f\")\n results_lr[index_subj] <- predictions_lr\n\n #classification tree\n tree.fit <- tree(preterm ~.,\n data = training_data_formula)\n predictions_tree <- predict(tree.fit, validation_data, type = \"class\")\n results_tree[index_subj] <- predictions_tree\n\n #svm\n svm <- svm(preterm ~.,\n data = training_data_formula\n )\n predictions_svm <- predict(svm, validation_data)\n results_svm[index_subj] <- predictions_svm\n\n #random forest \n rf <- randomForest(preterm ~.,\n data = training_data_formula)\n predictions_rf <- predict(rf, validation_data)\n results_rf[index_subj] <- predictions_rf \n}\n```\n\n最后，使用了 SMOTE 过采样技术和合适交叉验证下模型的结果如下所示：\n\n\n\n如之前所说，更多的数据并没有解决任何的问题，对于使用“智能”的过采样。它带来了非常高的精确度，但那是过拟合。下面是一些关于召回率和真假率指标的结果的分析和总结可以看看。", "\n\n**召回率**\n\n[](/uploads/1/3/2/3/13234002/8854367_orig.jpg?402)\n\n[](/uploads/1/3/2/3/13234002/4587025_orig.jpg?402)\n\n[](/uploads/1/3/2/3/13234002/3900757_orig.jpg?402)\n\n[](/uploads/1/3/2/3/13234002/6433809_orig.jpg?402)\n\n**真假率**\n\n[](/uploads/1/3/2/3/13234002/6424600_orig.jpg?402)\n\n[](/uploads/1/3/2/3/13234002/7570624_orig.jpg?402)\n\n[](/uploads/1/3/2/3/13234002/5755279_orig.jpg?402)\n\n[](/uploads/1/3/2/3/13234002/9325217_orig.jpg?402)\n\n正如我们所看到，分别使用合适的过采样（第四张图）和欠采样（第二张图）在这个数据集上训练出来的模型差距并不是很大。", "\n\n## 总结\n\n在这篇文章中，我使用了不平衡的 EHG 数据来预测是否早产，目的是讲解在使用过采样的情况下该如何恰当的进行交叉验证。关键是过采样必须是交叉验证的一部分，而不是在交叉验证之前来做过采样。", "\n\n总结一下，当在交叉验证中使用过采样时，请确保执行了以下步骤从而保证训练的结果具备泛化性：\n\n- 在每次交叉验证迭代过程中，验证集都不要做任何与特征选择，过采样和构建模型相关的事情\n\n- 过采样少数类的样本，但不要选择已经排除掉的那些样本。", "\n\n- 用对少数类过采样和大多数类的样本混合在一起的数据集来训练模型，然后用已经排除掉的样本做为验证集\n\n- 重复 *n* 次交叉验证的过程，*n* 的值是你训练样本的个数（如果你使用留一交叉验证法的话）\n\n## **关于 EHG 数据、妊娠、分娩和早产分类的一份声明**\n\n显然，分析结果并不意味着利用 EHG 数据检测是否早产是不可能的。只能说明一个横截面记录和这些基本特征并不够用来区分早产。这里最可能需要的是多重生理信号的纵向记录（如EHG、ECG、胎儿心电图、hr/hrv等）以及有关活动和行为的信息。多参数纵向数据可以帮助我们更好地理解这些信号在怀孕结果方面的变化，以及对个体差异的建模，类似于我们在其他复杂的应用中所看到的，从生理学的角度来看，这是很不容易理解的。在 [Bloom](http://www.bloom.life/)，我们正致力于更好地建模这些变量，以有效地预测早产风险。然而，这一问题的内在局限性，仅仅关乎参考值是如何定义的（例如，37周这个阈值是非常武断的），因此需要小心地分析近乎完美的分类，正如我们在这篇文章中所看到的那样。", "\n\n\n\n## 引用文献\n\n[1] Fergus, Paul, et al. \"", "Prediction of preterm deliveries from EHG signals using machine learning.\" (", "2013): e77154. ", "PloS one.", "\n\n[2] Ren, Peng, et al. \"", "Improved Prediction of Preterm Delivery Using Empirical Mode Decomposition Analysis of Uterine Electromyography Signals.\" ", "PloS one. ", "10.7 (2015): e0132116.", "\n\n[3] Fele-Žorž, Gašper, et al. \"", "A comparison of various linear and non-linear signal processing techniques to separate uterine EMG records of term and pre-term delivery groups.\" ", "Medical & biological engineering & computing 46.9 (2008): 911-922.", "\n\n[4] Japkowicz, N. (2000). ", "The Class Imbalance Problem: Significance and Strategies. ", "In Proceedings of the 200 International Conference on Artificial Intelligence (IC-AI’2000): Special Track on Inductive Learning Las Vegas, Nevada.", "\n\n[5] Chawla, Nitesh V., et al. \"", "SMOTE: synthetic minority over-sampling technique.", "\"Journal of artificial intelligence research (2002): 321-357.", "\n\n\n---\n\n> [掘金翻译计划](https://github.com/xitu/gold-miner) 是一个翻译优质互联网技术文章的社区，文章来源为 [掘金](https://juejin.im) 上的英文分享文章。内容覆盖 [Android](https://github.com/xitu/gold-miner#android)、[iOS](https://github.com/xitu/gold-miner#ios)、[React](https://github.com/xitu/gold-miner#react)、[前端](https://github.com/xitu/gold-miner#前端)、[后端](https://github.com/xitu/gold-miner#后端)、[产品](https://github.com/xitu/gold-miner#产品)、[设计](https://github.com/xitu/gold-miner#设计) 等领域，想要查看更多优质译文请持续关注 [掘金翻译计划](https://github.com/xitu/gold-miner)。", "\n" ]

{ "pile_set_name": "Github" }

[ 0.010050251256281407, 0.024691358024691357, 0.008645533141210375, 0, 0.0064516129032258064, 0.016483516483516484, 0, 0.007462686567164179, 0, 0, 0, 0.006802721088435374, 0.008620689655172414, 0, 0.024, 0.008695652173913044, 0.004347826086956522, 0, 0.005813953488372093, 0, 0.011494252873563218, 0, 0, 0.003389830508474576, 0, 0, 0.017241379310344827, 0, 0, 0.004975124378109453, 0, 0.008, 0.0026666666666666666, 0, 0, 0, 0, 0.002690238278247502, 0.007462686567164179, 0, 0, 0, 0.0007830853563038371, 0.006134969325153374, 0, 0.007633587786259542, 0.007633587786259542, 0.007633587786259542, 0.007142857142857143, 0.007633587786259542, 0.007633587786259542, 0.007633587786259542, 0.005434782608695652, 0.009900990099009901, 0, 0.00625, 0, 0.013157894736842105, 0, 0, 0.04, 0, 0, 0, 0.030303030303030304, 0.00684931506849315, 0.015151515151515152, 0, 0.017241379310344827, 0, 0.030303030303030304, 0, 0, 0.007874015748031496, 0 ]

[ "Introduction {#Sec1}\n============\n\nThree-dimensional (3D) natural extracellular matrix (ECM) feature has inspired people to construct physiological-mimicking artificial environments for cellular culture \\[[@CR1]\\]. ", "As compared to the two-dimensional system, cells cultured in 3D environments are able to growth and contact in three dimensions thus reveal striking differences in physiological processes such as adhesion, proliferation, migration and differentiation \\[[@CR2]\\]. ", "Therefore, a wide variety of materials such as collagen, gel/hydrogel, alginate etc. ", "have been used to engineer 3D matrices \\[[@CR3]--[@CR6]\\]. ", "However, the features of soft tissue-like stiffness and biodegradability restrict their applications as stable coatings of implant for osteogenesis. ", "Although the additive manufacturing technology has been extensively used to engineer various metal and ceramic 3D matrix composites \\[[@CR7]\\], it still remains a challenge to construct desired 3D or quasi-3D nanoscaled topography \\[[@CR8]\\].", "\n\nAdditionally, ECM shows a hierarchical organization ranging from nano to macron scales. ", "The biomimetic nano-to-microscaled hierarchical topography features have demonstrated distinct biological activities \\[[@CR9]\\]. ", "For example, the hierarchical hybrid micro/nano-textured surface topography with titania nanotubes has been demonstrated to enhance multiple osteoblast functions \\[[@CR10]\\]. ", "Micropit and nanonodule hybrid topography of TiO~2~ also showed to up-regulate the proliferation and differentiation of osteoblast \\[[@CR11]\\]. ", "However, it is still unclear of the mechanism underlying how cells response to the micro/nano hierarchical topography due to the cellular sensitivity to various material features (such as topography, hardness, hydrophilicity, etc.) ", "as well as the lake of effective topography control under the same processing \\[[@CR12], [@CR13]\\].", "\n\nIn this study, we demonstrated the enhanced osteogenesis of quasi-three-dimensional hierarchical topography composed of density-controlled titania nanodots and nanorods, which was prepared by using spin self-assembly coating process and subsequent hydrothermal treatment. ", "The in vitro osteogenic performance was evaluated by exploring the adhesion, proliferation and differentiation of osteoblast as well as the viability of fibroblast. ", "And the in vivo osteointegration performance was evaluated by using histological analysis and push-out mechanical strength test after 4 weeks or 8 weeks of implantation. ", "Furthermore, the possible mechanism underlying cells response to the quasi-3D hierarchical topography based on the initial adsorption behaviors of fibronectin was also proposed.", "\n\nMaterials and methods {#Sec2}\n=====================\n\nConstruction of quasi-three-dimensional hierarchical topography {#Sec3}\n---------------------------------------------------------------\n\nThe quasi-three-dimensional hierarchical topography composed of titania nanodots and nanorods were engineered by two steps, as we described previously \\[[@CR14]\\]. ", "Briefly, the nanodots coating was firstly prepared by using the phase-separation-induced self-assembly technology. ", "An ethanol solution with a molar ratio of AcAc/TBOT/H~2~O of 0.3:1:1 with 40 mg/L PVP was dropped onto Si or SiO~2~ substrate by spin-coating at 8000 rpm for 40 s. The spin-coated substrate was then heated at 500 °C for 2 h in a muffle furnace. ", "The diameter of obtained nanodots was ranged from 30 to 110 nm, and the density was about 5.6 × 10^10^/cm^2^.\n\nThen, the nanorods films were further grown on the obtained nanodots films by using the hydrothermal treatment. ", "Briefly, 30 mL of concentrated HCl (36.5--38% by weight) was mixed with 30 mL of deionized water and the designed amount of TBOT to obtain a total volume of 60 mL. During the preparing hydrothermal solutions, HCl with water for dilution was stirred under ambient condition for 5 min. ", "Then a designed amount of TBOT was added and stirred until becoming a clear solution. ", "The hydrothermal solution was transferred to a 50 μL Teflon-lined stainless steel autoclave. ", "The hydrothermal growth was conducted at 160 °C for 2 h in an electric oven. ", "The dimension and density of nanorods were controlled by the adjustment of the concentration of TBOT. ", "The clinical used titanium implant was also used as the control. ", "The surface morphology of these samples was examined by field-emission scanning electron microscopy (FESEM, SU-70, Hitachi). ", "The diameter and height of nanorods were qualitative analyzed of more than 100 nanorods based on the SEM observation results (n ≥ 10). ", "The density of nanorods and percentage of nanorods area were calculated as the number and occupied area of nanorods on every square micron, respectively (n ≥ 10), based on the SEM images.", "\n\nCell culture {#Sec4}\n------------\n\nMouse calvaria-derived, pre-osteoblastic MC3T3-E1 cells (CRL-2594, ATCC) were used as model cells. ", "Cells were cultured in alpha-modified Minimum Essential Medium (Gibco), supplemented with 10% fetal bovine serum (PAA), 1% sodium pyruvate (Gibco), 1% antibiotic solution containing 10,000 units/mL penicillin and 10,000 mg/mL streptomycin (Gibco), 1% MEM non-essential amino acids (Gibco) in a humidified atmosphere of 5% CO~2~ at 37 °C. ", "Subconfluent MC3T3-E1 on polystyrene dishes were trypsinized with 0.25% trypsin/1 mM EDTA (Gibco) and were subcultured on the substrates at a density of 4 × 10^4^ cells/cm^2^. The NIH3T3 fibroblasts, cultured in Dulbecco's modified Eagle medium (PAA) and supplemented with 10% fetal bovine serum and antibiotic solution, were also inoculated onto substrates above. ", "The culture medium was renewed every 2 days for both cell types.", "\n\nMorphology and morphometry of cells {#Sec5}\n-----------------------------------\n\nIn order to evaluate the initial attachment behaviors of cells on various substrates, MC3T3-E1 cell morphology was observed by SEM. ", "After 3 h, culture media were removed and the specimens were fixed with 2.5% glutaraldehyde in PBS (0.1 M, pH 7.0) for more than 4 h, and washed three times in PBS for 15 min respectively. ", "Then they were post-fixed with 1% OsO~4~ in PBS for 1 h and washed three times in PBS for 15 min, followed by dehydration by a graded series of ethanol (50%, 70%, 80%, 90% and 95%) for 15 min and by 100% ethanol twice for 20 min. ", "Afterwards, the specimens were transferred to the mixture of ethanol and isoamyl acetate (v:v = 1:1) for 30 min and pure isoamyl acetate for 1 h, followed by final dehydration in Hitachi Model Hcp-2 critical point dryer with liquid CO~2~. Confocal laser scanning microscopy (LSM510 META, Zeiss) was used to examine cytoskeletal arrangement in MC3T3-E1 cell seeded onto specimens with different surfaces. ", "After 3 h of culture, cells were fixed in 4% paraformaldehyde and immunochemically stained with goat anti-actin polyclonal antibody (SC-1615, Santa Cruz Biotechnology), followed by a DylightTM 594-conjugated anti-goat secondary antibody (Jackson), counter stained with Hoechst 33258 (Sigma Aldrich), respectively. ", "The area, perimeter, Feret's diameter and migration of cells were quantified using Image-Pro Plus.", "\n\nCell attachment and proliferation assays {#Sec6}\n----------------------------------------\n\nInitial attachment of MC3T3-E1 and fibroblasts to specimen substrates (1 × 1 cm^2^) was evaluated by measuring the amount of cells attached to samples after 6 and 24 h of incubation. ", "Further cell proliferation was quantified in terms of cell density for 2 and 5 culture days. ", "500 μL cell suspension with a density of 4 × 10^4^ cells/cm^2^ was inoculated to a 24-multiwell plate containing the samples with different surfaces. ", "After 6 and 24 h, samples were transferred to another 24-well after washed by PBS three times, while there was no need to wash the samples when taking proliferation assays, then 500 μL fresh culture media and 50 μL of MTS (G358B, Promega, USA) solution were added in each well for 4 h at 37 °C. ", "Finally at indicated time, 120 μL of the culture media was dispensed onto another 96-mutliwell plate, and colorimetric measurement of formazan dye was performed on a microplate reader at 490 nm.", "\n\nWestern blot analysis {#Sec7}\n---------------------\n\nMC3T3-E1 cells were cultured on the substrates a density of 4 × 10^4^ cells/cm^2^ for 5, 7 and 14 days. ", "Cells on each type of specimen were treated with cell lysis buffer (9803, Cell Signaling). ", "The proteins were collected and separated by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) on 5% Tris--HCl reducing gels, followed by transferring to the PVDF membrane (Millipore). ", "The membrane was blocked by incubating in a blocking solution containing 5% skim milk (BD) and 0.1% TWEEN 20 (Fluka Chemika) for 2 h. After that, the sheets were incubated with ALP (ab65834, Abcam) or COL-I (ab6308, Abcam) at 4 °C overnight. ", "Then HRP-anti-Rb antibody (050884, KPL) was used for the expression of ALP and COL-I. Band densities on the Western blots were assessed using the Quantity One software (Versa Doc 5000, BioRad) and normalized to GAPDH proteins.", "\n\nGene expression analysis {#Sec8}\n------------------------\n\nGene expression was analyzed by real-time reverse transcription-polymerase chain reaction (real-time RT-PCR). ", "Total RNA was extracted from cultured MC3T3-E1 cells on the substrates with a density of 4 × 10^4^ cells/cm^2^ using the TRIzol reagent (Invitrogen) according to the manufacturer's recommended protocol. ", "The concentration and purity of total RNA were calculated with the absorbance at 260 and 280 nm. ", "Real-time PCR was performed in the LightCycler using SYBR green detection. ", "Gene expression was normalized to the housekeeping gene GAPDH. ", "PCR products were subjected to a melting curve analysis and analyzed by the 2^−∆∆CT^ method.", "\n\nBone nodule visualization {#Sec9}\n-------------------------\n\nBone nodule formation of the cells that cultured on different coatings was observed by SEM. ", "The cells were cultured in the presence of 5 mM glycerol-2-phosphate disodium salt hydrate (β-glycerophosphate; Sigma) and 50 μg/mL [l]{.smallcaps}-ascorbic acid (Sigma) when became confluency with an initial density of 4 × 10^4^ cells/cm^2^. After 21 days, the specimen was dehydrated in an ethanol solution of varying concentrations (i.e., 30, 50, 70, 90, and 100% twice, respectively) for 2 min at each concentration after being fixed with 2.5% glutaraldehyde in PBS (0.1 M, pH 7.0) overnight at 4 °C. ", "It was then dried in 100% hexamethyldisilazane (HMDS, Sigma) for 5 min and later dried in air after the removal of HMDS. ", "After being completely dried, the specimen was coated with gold, and observed by SEM. ", "The Ca elemental analysis of calcium nodule was carried out on the FE-SEM (Hitachi SU-70) equipped with an energy dispersive X-ray spectrum (EDS, Inca Energy-200) at an accelerating voltage of 10 kV.\n\nCollagen production {#Sec10}\n-------------------\n\nSirius red staining-based colorimetric assay was employed to quantify collagen production in fibroblasts. ", "Fibroblasts cultured on the substrates with a density of 4 × 10^4^ cells/cm^2^ were washed twice with PBS and fixed with Bouin's fluid for 1 h at room temperature, which was prepared by mixing 15 mL saturated aqueous picric acid with 5 mL 35% formaldehyde and 1 mL glacial acetic acid. ", "The cultures were washed by running tap water for 15 min before staining with 1 mL saturated solution of picric acid containing 0.04% of Fast green and 0.1% of Sirius red F3B, and incubated in the dark for 1 h with mild shaking. ", "They were then rinsed several times with distilled water until the elution fluid was completely free of color. ", "After that, the samples were dissolved in 0.25 mL 0.1 N sodium hydroxide using a microplate shaker for 30 min at room temperature. ", "Then 120 μL of the liquids were transferred to Nunc microtiter plates and the optical densities were measured using a spectrophotometer at 630 nm and 450 nm, respectively. ", "Results are presented relative to protein.", "\n\nCell adhesion assay {#Sec11}\n-------------------\n\nThe adhesive strength of MC3T3-E1 cells and fibroblasts to on the substrates was evaluated by the percentage of remaining cells after enzymatic treatment. ", "Cells incubated on samples with a density of 4 × 10^4^ cells/cm^2^ for 24 h were rinsed once with PBS to remove non-adherent cells, and then detached from the substrates by treatment with 0.05% v/v trypsin--EDTA at 37 °C for 1 min. ", "The detached and remaining cells were detected by MTS assay.", "\n\nProtein adsorption assay {#Sec12}\n------------------------\n\nBovine serum albumin (Pierce Biotechnology) was used as a model protein. ", "250 μL of protein solution (1 μg/mL protein/saline) was pipetted into a 24-multiwell plate with substrates (1 × 1 cm^2^). ", "After incubation for 2 and 24 h at 37 °C, non-adherent proteins were removed and mixed with bicinchoninic acid (Pierce Biotechnology) at 37 °C for 30 min. ", "The amount of the removed albumin as well as the total amount of albumin inoculated was quantified using a microplate reader at 570 nm. ", "The rate of albumin adsorption was calculated as the percentage of albumin adsorbed to relative to the total amount.", "\n\nEnzyme-linked immunosorbent assay {#Sec13}\n---------------------------------\n\nThe substrates (1 × 1 cm^2^) were immersed in excess BSA solution for 24 h at 37 °C for BSA adsorption. ", "Next, all the samples were immersed in a solution of excess fibronectin (Fn) (10 μg/mL from human plasma, Sigma-Aldrich) for another 24 h at 37 °C for Fn adsorption. ", "After that, surfaces were rinsed with PBS and non-specific antibody binding was blocked using a blocking buffer (1% BSA/PBS) for 30 min at 37 °C. ", "The primary monoclonal antibody HFN7.1 (Developmental Studies Hybridoma Bank) directed against the flexible linker between the 9th and 10th type III repeat and mAb1937 (Millipore) directed against the 8th type III repeat were used. ", "Substrates were incubated with primary antibody (1:4000 for HFN7.1 and 1:1000 mAb1937 in blocking buffer) for 1 h at 37 °C. ", "After washing with 0.1% Tween 20, all samples were incubated with alkaline phosphatase-conjugated anti-mouse IgG (1:5000, Jackson ImmunoResearch Laboratories) for 1 h at 37 °C, then washed again, and incubated with 4-methylumbelliferyl phosphate (4-MUP) liquid substrate system (Sigma-Aldrich) for 45 min at 37 °C. ", "Reaction products were quantified using a fluorescence plate reader at 365 nm excitation/460 nm emission.", "\n\nHemolysis test {#Sec14}\n--------------\n\nRabbit blood (8 mL) anti-coagulated with potassium oxalate was diluted with saline (10 mL). ", "0.2 mL of the blood was added to 10 mL of saline containing Ti as well as M-NR in different test tubes. ", "A positive (100% hemolysis induced by replacing saline with distilled water) and negative (0% hemolysis, saline with no material added) were also set up. ", "Each set of experiments was done in duplicate. ", "All test tubes were incubated at 37 °C for 60 min. ", "After incubation, the tubes were centrifuged at 750*g* for 5 min. ", "The percentage of hemolysis was calculated by measuring the optical density of the supernatant solution at 540 nm in a UV--visible spectrophotometer as per the following formula:$$\\documentclass[12pt]{minimal}\n \\usepackage{amsmath}\n \\usepackage{wasysym} \n \\usepackage{amsfonts} \n \\usepackage{amssymb} \n \\usepackage{amsbsy}\n \\usepackage{mathrsfs}\n \\usepackage{upgreek}\n \\setlength{\\oddsidemargin}{-69pt}\n \\begin{document}$$ Hemolysis \\, \\left ( \\% \\right) = \\frac{{{\\text{OD}}\\;{\\text{of}}\\;{\\text{the}}\\;{\\text{test}}\\;{\\text{sample}} - {\\text{OD}}\\;{\\text{of}}\\;{\\text{the}}\\;{\\text{negetive}}\\;{\\text{control}}}}{{{\\text{OD}}\\;{\\text{of}}\\;{\\text{the}}\\;{\\text{postive}}\\;{\\text{control}} - {\\text{OD}}\\;{\\text{of }}\\;{\\text{the}}\\;{\\text{negetive}}\\;{\\text{control}}}} \\times 100{\\text{\\% }} $$\\end{document}$$\n\nImplant biomechanical push-out test {#Sec15}\n-----------------------------------\n\nThe implant biomechanical push-out test was used to assess the biomechanical strength of bone-implant integration. ", "Briefly, 12 male New Zealand white rabbits weighing 2.5--3.0 kg were used in this study. ", "The animals were anesthetized intramuscularly with SuMianXin II (0.1--0.2 mL/kg, Quartermaster University of PLA, Chang Chun, P. R. of China, The Military Veterinary Institute). ", "Lidocaine was injected locally into the surgical site before the operation. ", "The medial surfaces of proximal tibias were selected for implantation by drilling with a 0.8 mm round burr and then enlarged using reamers with a final drill diameter of 3.0 mm. ", "All drilling procedures were carried out under profuse sterile saline irrigation. ", "The titanium implants (diameter, 3 mm; length, 8 mm) and the substrates were inserted into each prepared hole per tibia with 2 mm left outside. ", "Tibias containing a cylindrical implant were harvested at week 4 and 8 of healing with the top surface of the implant being horizontal. ", "Spiral CT (Brilliance 64 ct, Philips) was used to confirm that implants were free from cortical bone support to the lateral and bottom sides of the implant. ", "A testing machine (SANS CTT2500) equipped with a 2000 N load cell was used to load the implant vertically upward at a crosshead speed of 1 mm/min. ", "The push-out value was determined by measuring the peak of the load--displacement curve. ", "The experiment was performed in accordance with the guidelines for animal care established by Zhejiang University, Hangzhou, China.", "\n\nHistomorphometric analysis {#Sec16}\n--------------------------\n\nEach substrate was inserted into anterior-distal surfaces of per femur with 2 mm left outside. ", "The femurs with the implants were isolated after 4 and 8 weeks, and fixed in 4% paraformaldehyde solution. ", "After decalcification, the implants were gently removed, and the femoral tissues were dehydrated, cleared and embedded in paraffin. ", "Tissue sections, 4 μm in thickness, were mounted on glass slides and subjected to H&E staining. ", "Images were taken under a Nikon Eclipse E600 microscope, and the newly formed bone area, which was restricted to the 0.5 mm area surrounding the implant, was measured with Spot Advanced Software (Diagnostic Instruments, Sterling Heights, MI, USA). ", "The percentage of new bone edges in direct contact with the implant surface was also determined.", "\n\nStatistical analyses {#Sec17}\n--------------------\n\nThe number of samples was 3 for all studies, except for cell morphometry (n = 9), and the experiments about implant in vivo (n = 6). ", "All values are expressed as mean ± standard deviation. ", "Statistical analyses were carried out by a one-way analysis of variance (one-way ANOVA) and Scheffe's post hoc test with the SPSS software for multiple comparison tests, or using Student's t-test. ", "Differences were considered statistically significant when P \\< 0.05.", "\n\nResults {#Sec18}\n=======\n\nQuasi-three-dimensional hierarchical topography {#Sec19}\n-----------------------------------------------\n\nAs shown in Fig.", " [1](#Fig1){ref-type=\"fig\"}a, the nanodots film was firstly prepared by using the phase-separation-induced self-assembly technology. ", "And the obtained nanodots film provided the crystal seeds for nanorods growth during the subsequent hydrothermal treatment. ", "By controlling the concentrations of TBOT (Ti source), we strategized a series of size- and density-controlled rutile TiO~2~ nanorods coatings using the same processing. ", "As demonstrated in the SEM images and the corresponding quantitatively analysis (Fig.", " [1](#Fig1){ref-type=\"fig\"}b, c), we successfully achieved three typical quasi-three-dimensional hierarchically topographies: low density nanorods film (L-NR film) with 20 nm of dimension, 180 nm of height and 1000 nm of spacing, middle density nanorods film (M-NR film) with 30 nm of dimension, 420 nm of height and 300 nm of spacing, as well as the high density nanorods film (H-NR film) with 50 nm of dimension, 650 nm of height and 30 nm of spacing.", "Fig.", " 1Quasi-three-dimensional hierarchical topography. **", "a** Schematic diagram of the fabrication process. **", "b** SEM images from top (right) and cross-sectional (left) view of the nanodots film and three typical quasi-three-dimensional hierarchically topographies with controlled density of nanorods. **", "c** Quantitative analysis of the density, diameter, height as well as the percent of nanorods area of the three topographies (n ≥ 10)\n\nCellular morphology on various substrates {#Sec20}\n-----------------------------------------\n\nTo observe the cellular spreading behavior on various substrates, we carried out immunostaining and SEM after 1 day of culture. ", "As shown in Fig.", " [2](#Fig2){ref-type=\"fig\"}, the cellular actin cytoskeleton on titanium substrate appeared to be relative round, while they revealed to be fully spreading and noticeable pseudopods extensions on various nanorods films (SEM images). ", "Moreover, it's worth noting that filopodia preferred to anchor on the nanorods, deeply across the distinct 3D topography. ", "The corresponding quantitative analysis of cellular Feret's dimeter, average cell area, further confirmed these results and suggested that cells on the M-NR films achieved the optimal spreading. ", "Additionally, the decreased circularity and increased aspect ratio suggested greater protrusions and longer cell morphology.", "Fig.", " 2Cellular adhesion behavior on various substrates. **", "a** Upper, immunofluorescence observation of cellular cytoskeletonal morphology by staining the actin (red), and nuclei (blue). ", "Middle, SEM observation of the typical cellular pseudopodia. ", "Lower, the corresponding local amplification of filopodia (white arrows). **", "b** The corresponding quantitative analysis of cellular Feret's dimeter, average cell area, circularity and aspect ratio. **", "c** Cellular viability analysis (CCK-8 assay) for cellular adhesion (6 and 24 h) and proliferation (2 and 5 days)\n\nCellular proliferation on various substrates {#Sec21}\n--------------------------------------------\n\nThe cellular adhesion and proliferation behaviors were also evaluated to further study the effects of surface topography on cell behavior. ", "As shown in Fig.", " [2](#Fig2){ref-type=\"fig\"}c, the number of adhered cells on nanorods films was significantly up-regulated compared to that of titanium and nanodots films. ", "Specifically, cells on the M-NR and L-NR groups exhibited the optimal adhesion and proliferation, respectively.", "\n\nIn vitro evaluation of osteogenic differentiation of osteoblast {#Sec22}\n---------------------------------------------------------------\n\nTo probe the osteogenic differentiation of osteoblast on various substrates, we carried out western blot (WB) analysis of relative protein expression of the early osteogenic differentiation markers ALP (day 5 and 7) and the middle-stage osteogenic differentiation markers COL-I (day 7 and 14), respectively. ", "As shown in Fig.", " [3](#Fig3){ref-type=\"fig\"}a, cellular expression level of ALP and COL-I on all nanorods films showed significantly up-regulated compared to that of titanium and nanodots groups. ", "Moreover, cells on the M-NR films exhibited both up-regulated expression of ALP and COL-I upon various naorods films. ", "The corresponding gene expression results of PCR the WB results also confirmed the WB results, as indicated in Fig.", " [3](#Fig3){ref-type=\"fig\"}b. ", "The relative protein expression of later osteogenic differentiation marker osteocalcin (OC) was also consistent with the above results (Fig.", " [3](#Fig3){ref-type=\"fig\"}c). ", "Moreover, cells on M-NR films still demonstrated significantly up-regulated number of calcium nodule and relative calcium content after 21 days of culture (Fig.", " [3](#Fig3){ref-type=\"fig\"}d, e). ", "Interestingly, the Ca:P ratio also showed a slight difference between the four groups: Ti (0.89 ± 0.18), ND (1.17 ± 0.14), L-NR (1.36 ± 0.22), M-ND (1.61 ± 0.24), H-ND (1.46 ± 0.16), respectively.", "Fig.", " 3*In vitro* evaluation of osteogenic differentiation of osteoblast on various substrates. **", "a** Western blot analysis of relative protein expression of early and middle-stage osteogenic differentiation markers ALP and COL-I, respectively, after 5, 7 and 14 days of culture. ", "And **b** the corresponding PCR results of relative mRNA expression. **", "c** ELISA assay analysis of relative protein expression of later osteogenic differentiation marker osteocalcin (OC) after 14 days of culture. **", "d** SEM observation (right) and the corresponding EDS Ca elemental analysis (left) of calcium nodule after 21 days of culture. **", "e** Analysis of the relative calcium content\n\nViability of fibroblast on various substrates {#Sec23}\n---------------------------------------------\n\nWe further evaluated the adhesion, proliferation and collagen production behaviors of fibroblast on various substrates. ", "As shown in Fig.", " [4](#Fig4){ref-type=\"fig\"}a, there was no significantly difference on the adhesion behaviors between various substrates. ", "In contrast, fibroblast exhibited up-regulated proliferation and collagen production on titanium substrate compared to other substrates. ", "And the M-NR film appeared to be most disadvantageous to cellular proliferation and collagen production (Fig.", " [4](#Fig4){ref-type=\"fig\"}b, c).Fig.", " 4Evaluation of fibroblast viability on various substrates. ", "Cellular viability analysis (CCK-8 assay) for **a** cellular adhesion and **b** proliferation. **", "c** Analysis of relative protein expression of COL-1 on various substrate after 7 and 14 days of culture\n\nInitial protein adsorption behaviors on various substrates {#Sec24}\n----------------------------------------------------------\n\nTo gain insight into the mechanism underlying how the 3D hierarchically topography regulates the adhesion, proliferation and differentiation of osteoblast and fibroblast, we focused our attention on the initial protein adsorption behaviors on various substrates. ", "As shown in Fig.", " [5](#Fig5){ref-type=\"fig\"}a, the amount of initial adsorption of bovine serum albumin (BSA) protein increased along with the density of nanorods. ", "However, these results were not consistent with the total exposure amount as well as the relative exposure per Fn unit of HFN7.1 and mAb1937 critical functional motifs. ", "Although there was significantly difference on the total amount of initial Fn adsorption, we observed that the M-NR film group appeared to be more beneficial to the exposure of HFN7.1 and mAb1937 critical functional motifs (Fig.", " [5](#Fig5){ref-type=\"fig\"}b). ", "These distinct initial protein adsorption behaviors subsequently regulated the adhesion of osteoblast but had no significantly impact on fibroblast.", "Fig.", " 5Initial protein adsorption behaviors and their effects on cellular adhesion on various substrates. **", "a** The amount of initial adsorption (2 and 24 h) of bovine serum albumin (BSA) protein. **", "b** Adsorption behavior of fibronectin (Fn): upper, the amount of exposure of HFN7.1 and mAb1937 critical functional motifs of Fn; middle, the amount of adsorbed Fn protein; lower, the relative exposure per Fn unit of HFN7.1 and mAb1937 critical functional motifs. **", "c** Analysis of cellular adhesion strength of osteoblast and fibroblast on various substrates after 24 h of culture\n\nIn vivo osteointegration performance {#Sec25}\n------------------------------------\n\nWe further evaluated the in vivo osteointegration performance of various substrates. ", "Before that, we evaluated the bio-compatibility by the blood cell safety assays (data not shown). ", "The results indicated that the Ti and M-NR film group had no negative effect on haemolysis, suggesting a good bio-compatibility. ", "As shown in Fig.", " [6](#Fig6){ref-type=\"fig\"}a, the histological observation of the bone-implant interface suggested that the distinct quasi-three-dimensional hierarchical topography enhanced the new bone formation after 4 and 8 weeks of implantation compared to that of the clinical titanium, further supported by the quantitative analysis of the relative bone-implant contact (Fig.", " [6](#Fig6){ref-type=\"fig\"}b). ", "In contrast, we even observed that there were some inflammation regions on the boundary between clinical titanium and host bone after 4 weeks of implantation (Fig.", " [6](#Fig6){ref-type=\"fig\"}a). ", "Moreover, the push-out strength evaluation further confirmed the tight and novel osseointegrated performance of quasi-three-dimensional hierarchical topography, indicating nearly 50% superiority in push-out strength compared to that of the clinical titanium (Fig.", " [6](#Fig6){ref-type=\"fig\"}c). ", "To further evaluate the mechanical stability of surface nanostructures upon implantation, we further observed the surface topography of the implant after push-out test followed by ultrasonic cleaning for 1 h (data not shown). ", "The results indicated that the prepared surface nanorods structures were maintained without obvious damage in this study. ", "We speculated that there results might be attributed to mechanical stability originated from the in situ growth process.", "Fig.", " 6In vivo evaluation of osteointegration of the quasi-three-dimensional hierarchical topography. **", "a** Histologic analysis at the bone-implant interface of clinical titanium (control) and M-NR group after implantation for 4 and 8 weeks. ", "The arrows indicate the inflammation regions. **", "b** The corresponding quantitative analysis of the relative bone-to-implant contact. **", "c** The evaluation of push-out strength (n ≥ 5)\n\nDiscussion {#Sec26}\n==========\n\nFabrication of material features mimicking natural cellular ECMs provides physiologically relevant cellular microenvironments and thus has achieved distinct biological activities \\[[@CR15]\\]. ", "Although materials with 3D hierarchical structure features have been extensively studied, most of them are still limited to soft tissue scaffolds \\[[@CR16], [@CR17]\\]. ", "In terms of the bioactive coating materials used in hard tissue engineering, good chemical stability and mechanical strength are required. ", "Therefore, the bioactive inorganic material TiO~2~ was selected here to construct the quasi-three-dimensional hierarchical topography \\[[@CR18], [@CR19]\\]. ", "And the in situ growth processing of TiO~2~ nanorods ensured the stability of the coating, which was confirmed in our previous work \\[[@CR14]\\]. ", "Moreover, the distinct nanorods feature might act as a \"nailing\" effect between the coating and host bone, which was beneficial to the osteointegration performance.", "\n\nThe density of nanorods was observed to be critical to the cellular responses on various substrates. ", "We here speculate that cells are able to sense the spatial scale of a comparable size to cells themselves. ", "While the density of nanorods was too low or high (L-NR and H-NR groups), cells were still inclined to perceive two-dimensional microenvironments. ", "In contrast, when the density is moderate (M-NR), osteoblasts will be able to fully sense the quasi-three-dimensional hierarchical topography and thus appear to be significantly up-regulation of adhesion, proliferation and differentiation. ", "Moreover, the enhanced cell spreading morphology with decreased circularity and increased aspect ratio has demonstrated to improve osteogenic differentiation (Fig.", " [2](#Fig2){ref-type=\"fig\"}b) \\[[@CR20]\\]. ", "These results are consistent with the published literatures regarding the little difference of osteogenic differentiation between normal clinical titanium and substrates fabricated by using 3D printing technology. ", "These might be because of cells are hard to perceive the macro-scaled features fabricated using the current 3D printing technology. ", "Therefore, further modifications of nanoscaled structures are always needed to engineer the micro/nano hierarchical topography \\[[@CR21]\\]. ", "However, the modification processes always simultaneously changed various material features (such as roughness, hardness, hydrophilicity, etc.), ", "which are cell-sensitive characteristics \\[[@CR22]--[@CR25]\\]. ", "In this study, the typical quasi-three-dimensional hierarchical topographies were controlled under the same processing, thus it was very helpful to undercover the mechanism underlying how cells response to the quasi-three-dimensional hierarchical topography.", "\n\nThe initial protein adsorption onto material surface has been considered as the key role on the subsequent cellular responses \\[[@CR26], [@CR27]\\]. ", "Therefore, we here focus on the adsorption behaviors of serum albumin and Fn, which are the major plasma protein and the critical functional glycoprotein of ECM proteins that binds to integrins, respectively \\[[@CR28], [@CR29]\\]. ", "Although the total amount of initial adsorption of serum albumin on H-NR group was significantly up-regulated compared to other groups (Fig.", " [5](#Fig5){ref-type=\"fig\"}a), cells seemed to more like to adhere on M-HR surface (Fig.", " [2](#Fig2){ref-type=\"fig\"}c). ", "These anti-intuitive results suggested that the amount of the preadsorbed serum albumin protein might be probably not the most important role to regulate the subsequent cellular adhesion. ", "Further evaluation of the adsorption amount of Fn also indicated that there was no difference among various substrates (Fig.", " [5](#Fig5){ref-type=\"fig\"}b). ", "However, the total exposure amount as well as the relative exposure per Fn unit of HFN7.1 and mAb1937 critical functional motifs on M-NR were significantly up-regulated compared to that of other substrates. ", "The HFN7.1 and mAb1937 motifs have been demonstrated to bind the 9th and 10th type III repeats of Fn involving cell adhesion domain (RGD) as well as the 8th type III domain closer to the synergy domain (PHSRN) of Fn, respectively \\[[@CR30]\\]. ", "Therefore, we here emphasized that the protein configuration but not the amount might be more critical to the cellular responses. ", "And the distinct protein adsorption behaviors on quasi-three-dimensional hierarchical topography with moderate nanorods density, as schematically illustrated in Fig.", " [7](#Fig7){ref-type=\"fig\"}, directly affected the strength of initial cell adhesion (Fig.", " [5](#Fig5){ref-type=\"fig\"}c) as well as the subsequent proliferation, differentiation and osteointegration (Figs.", " [2](#Fig2){ref-type=\"fig\"}, [3](#Fig3){ref-type=\"fig\"} and [6](#Fig6){ref-type=\"fig\"}). ", "And the up-regulated ratio of Ca:P on M-NR film group also suggested that CaP type might transferred from calcium-deficient apatite to hydroxyapatite (Fig.", " [3](#Fig3){ref-type=\"fig\"}d, e) \\[[@CR31]\\].Fig.", " 7Schematic illustration of the possible mechanism underlying the enhanced osteogenesis of quasi-three-dimensional hierarchical topography. ", "The distinct quasi-three-dimensional hierarchical topography is beneficial to the exposure of critical functional motifs of fibronectin, thus the cellular spreading into three-dimensional space, and eventually enhancing the osteogenesis\n\nIn addition to the bone tissue, epithelium and connective tissues are also able to form interfaces with the implant surface \\[[@CR32]\\]. ", "To further explore the fibrogenic response by fibroblast (the most common cell type in connective tissue) to produce the collagen nodular foci, we evaluated the adhesion, proliferation and collagen production behaviors of fibroblast on various substrates. ", "The little difference of adhesion and proliferation between various substrates suggested fibroblast was not sensitive to the current quasi-three-dimensional hierarchical topography (Fig.", " [4](#Fig4){ref-type=\"fig\"}a, b). ", "However, they showed up-regulated collagen production potential on the normal titanium group compared to that of other substrates (Fig.", " [4](#Fig4){ref-type=\"fig\"}c). ", "These behaviors in difference with osteoblasts might be attributed to the distinct responses of certain cell types to different surface features. ", "It is known that osteoblasts prefer rough surfaces, while fibroblasts favor smooth surfaces \\[[@CR33]\\]. ", "The underlying mechanism based on the initial protein adsorption configuration corresponding to the different integrin populations present to osteoblast and fibroblast still needs to be further investigated. ", "In all, our results indicated that the current quasi-three-dimensional hierarchical topography is more suitable to form interface with bone tissue.", "\n\nConclusion {#Sec27}\n==========\n\nIn summary, we demonstrated the enhanced osteogenesis of distinct quasi-three-dimensional hierarchical topography composed of density-controlled titania nanodots and nanorods. ", "We demonstrated that cellular viability of osteoblast but not fibroblast, such as adhesion, proliferation, differentiation was dependent on the density of nanorods. ", "The middle density nanorods film (M-NR film) with 30 nm of dimension, 420 nm of height and 300 nm of spacing was identified to be the optimal characteristics for cellular pseudopods perception the distinct quasi-three-dimensional hierarchical topography. ", "Histological analysis showed that the designed topography significantly enhanced new bone formation and the relative bone-to-implant contact after implantation. ", "Strikingly, the biomechanical test in a rabbit tibia model revealed that the strength of bone integration of the quasi-three-dimensional hierarchical topography was more than 80% greater than that of the clinical titanium. ", "This work, therefore, provides insights into the mechanism of cell-biomaterial interactions as well as a strategy for optimizing osteointegration of hard tissue coatings.", "\n\n**Publisher\\'s Note**\n\nSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.", "\n\nMengfei Yu and Yu Liu contributed equally to this work\n\nThis work was financially supported by the National Natural Science Foundation of China (81600838, 81873720, 81670972, 51772273, 81501607), Key Research and Development Program of Zhejiang, China (2017C01054, 2018C03062), the 111-Project under Grant No. ", "B16042, the Medical Technology and Education of Zhejiang Province of China (2016KYB178, 2018KY501), the Zhejiang Provincial Natural Science Foundation (LY15E020004), the Zhejiang Provincial Chinese Medical Science Research Foundation (2016ZB077), the National Key Research and Development Program of China (2016YFC0902702), the Hangzhou Science and Technology Development Plan (20171226Y50).", "\n\nMY and LD conceived and designed the experiments. ", "MY and YL carried out the experiments. ", "MY, YL, LD, XY, JL, WZ, JH, KC, WW, BZ and HW analyzed the data. ", "LD and MY wrote the manuscript. ", "All authors commented on the manuscript. ", "All authors read and approved the final manuscript.", "\n\nThe authors declare that they have no competing interests.", "\n" ]

{ "pile_set_name": "PubMed Central" }

[ 0.009302325581395349, 0.0038022813688212928, 0.011764705882352941, 0.03389830508474576, 0, 0.01652892561983471, 0.011111111111111112, 0.007751937984496124, 0.005714285714285714, 0.020833333333333332, 0, 0.020202020202020204, 0, 0, 0, 0, 0.0028089887640449437, 0, 0.004081632653061225, 0, 0, 0, 0, 0, 0.00980392156862745, 0, 0.016, 0.007407407407407408, 0.0053475935828877, 0, 0.014792899408284023, 0.00821917808219178, 0, 0, 0.010582010582010581, 0.008695652173913044, 0.007425742574257425, 0.009554140127388535, 0.02040816326530612, 0, 0, 0, 0.010169491525423728, 0, 0, 0.01098901098901099, 0.004901960784313725, 0.01652892561983471, 0.022123893805309734, 0.005847953216374269, 0.009852216748768473, 0.010309278350515464, 0.02666666666666667, 0, 0.010869565217391304, 0, 0.0019801980198019802, 0.01652892561983471, 0, 0.008403361344537815, 0.006993006993006993, 0.004366812227074236, 0, 0, 0, 0, 0, 0.004310344827586207, 0.016666666666666666, 0.014814814814814815, 0, 0.0064516129032258064, 0, 0, 0.010869565217391304, 0.006024096385542169, 0.0136986301369863, 0.008620689655172414, 0.008064516129032258, 0.006349206349206349, 0, 0, 0, 0, 0, 0, 0, 0.0017376194613379669, 0, 0.02247191011235955, 0, 0, 0, 0, 0, 0, 0, 0, 0.007633587786259542, 0, 0, 0, 0.010416666666666666, 0.008064516129032258, 0, 0, 0, 0.02030456852791878, 0, 0.006666666666666667, 0, 0, 0.0058823529411764705, 0.011764705882352941, 0.002207505518763797, 0.25, 0, 0, 0, 0, 0.0625, 0.004291845493562232, 0, 0.005128205128205128, 0, 0.25, 0, 0, 0, 0, 0.008064516129032258, 0.002824858757062147, 0.0625, 0, 0.018018018018018018, 0.004464285714285714, 0.0625, 0.00558659217877095, 0.00847457627118644, 0.034782608695652174, 0, 0.014285714285714285, 0, 0.00625, 0, 0.015306122448979591, 0.25, 0, 0.005494505494505495, 0.014084507042253521, 0.006944444444444444, 0.007751937984496124, 0, 0.0625, 0, 0, 0.009174311926605505, 0, 0, 0.010309278350515464, 0.002012072434607646, 0.0625, 0, 0, 0.0043859649122807015, 0, 0, 0.25, 0, 0, 0, 0, 0, 0.007751937984496124, 0.0625, 0.0027397260273972603, 0, 0.006134969325153374, 0, 0.0038022813688212928, 0, 0, 0, 0, 0.25, 0, 0, 0, 0, 0.003663003663003663, 0.011904761904761904, 0, 0.019230769230769232, 0.006896551724137931, 0, 0, 0, 0.013605442176870748, 0, 0.006134969325153374, 0.023255813953488372, 0, 0, 0.007142857142857143, 0, 0.031746031746031744, 0, 0.013333333333333334, 0.013043478260869565, 0.014285714285714285, 0.011363636363636364, 0, 0, 0.008064516129032258, 0, 0, 0.00823045267489712, 0, 0.006060606060606061, 0.011111111111111112, 0, 0, 0.012903225806451613, 0.02040816326530612, 0, 0.0026666666666666666, 0, 0.005376344086021506, 0, 0.007407407407407408, 0, 0, 0.009523809523809525, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01282051282051282, 0.015345268542199489, 0.019230769230769232, 0, 0.07692307692307693, 0.03125, 0, 0, 0, 0 ]

[ "1. ", "Field\nEmbodiments relate to an epoxy resin composition for encapsulating a semiconductor device and a semiconductor package encapsulated using the same.", "\n2. ", "Description of the Related Art\nRecently, with general use of thin, small scale portable digital devices, a semiconductor package may be light, thin, and miniaturized in order to enhance mounting efficiency per unit volume of the semiconductor package mounted in the devices." ]

{ "pile_set_name": "USPTO Backgrounds" }

[ 0, 0, 0, 0 ]

[ "1. ", "FIELD OF THE INVENTION\nThe present invention relates to self-locking nut fasteners.", "\n2. ", "DESCRIPTION OF RELATED ART\nWhen using nut and bolt fasteners it is generally desirable to have means to prevent the nut from loosening due to vibration, thermal expansion, etc. ", "Typically this is done by placing a lock washer between the nut and the working surface to maintain bolt tension in the joint. ", "Having to use a separate washer is cumbersome particularly when the nut is being used in places with limited accessibility. ", "There are also assemblies where there is not enough space between the nut and workpiece for a lock washer. ", "Prior attempts to incorporate a locking feature into the nut itself include U.S. Pat. ", "No. ", "4,269,248 issued to MacLean et al, which discloses a fastener that has a wavy flange at one end that deforms when the nut is tightened, keeping the bolt in tension. ", "U.S. Pat. ", "No. ", "2,286,895 issued to Carlson discloses a lock nut that has a locking portion that bends when the fastener engages a working surface. ", "The locking portion clamps against an adjacent thread of the bolt increasing the frictional forces between the nut and the bolt. ", "Although these fasteners provide a locking feature, there has not been to this point a nut that is self-locking at both ends of the nut." ]

{ "pile_set_name": "USPTO Backgrounds" }

[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.006060606060606061, 0, 0, 0.007575757575757576, 0, 0 ]

[ "#if defined(__GNUC__)\n#pragma GCC diagnostic push\n#pragma GCC diagnostic ignored \"-Wunused-parameter\"\n#pragma GCC diagnostic ignored \"-Winvalid-offsetof\"\n#pragma GCC diagnostic ignored \"-Wtype-limits\"\n#endif\n\n#include \"quiche/quic/test_tools/test_certificates.h\"\n\n#if defined(__GNUC__)\n#pragma GCC diagnostic pop\n#endif\n\n#include <memory>\n\n#include \"test/mocks/network/mocks.h\"\n#include \"extensions/quic_listeners/quiche/envoy_quic_proof_source_base.h\"\n\nnamespace Envoy {\nnamespace Quic {\n\n// A test ProofSource which always provide a hard-coded test certificate in\n// QUICHE and a fake signature.", "\nclass TestProofSource : public EnvoyQuicProofSourceBase {\npublic:\n quic::QuicReferenceCountedPointer<quic::ProofSource::Chain>\n GetCertChain(const quic::QuicSocketAddress& /*server_address*/,\n const quic::QuicSocketAddress& /*client_address*/,\n const std::string& /*hostname*/) override {\n return cert_chain_;\n }\n\n const Network::MockFilterChain& filterChain() const { return filter_chain_; }\n\nprotected:\n void signPayload(const quic::QuicSocketAddress& /*server_address*/,\n const quic::QuicSocketAddress& /*client_address*/,\n const std::string& /*hostname*/, uint16_t /*signature_algorithm*/,\n quiche::QuicheStringPiece in,\n std::unique_ptr<quic::ProofSource::SignatureCallback> callback) override {\n callback->Run(true, absl::StrCat(\"Fake signature for { \", in, \" }\"),\n std::make_unique<EnvoyQuicProofSourceDetails>(filter_chain_));\n }\n\nprivate:\n quic::QuicReferenceCountedPointer<quic::ProofSource::Chain> cert_chain_{\n new quic::ProofSource::Chain(\n std::vector<std::string>{std::string(quic::test::kTestCertificate)})};\n\n Network::MockFilterChain filter_chain_;\n};\n\n} // namespace Quic\n} // namespace Envoy\n" ]

{ "pile_set_name": "Github" }

[ 0.01507537688442211, 0.001589825119236884 ]

[ "Media playback is unsupported on your device Media caption One defence worker in Glasgow confronted Defence Secretary Philip Hammond over \"threatening\" jobs, as Allan Little reports\n\nDefence Secretary Philip Hammond has predicted that a vote for Scottish independence would put defence jobs at risk.", "\n\nSpeaking to defence workers in Glasgow, he claimed the UK's shared defence forces provide benefits of scale.", "\n\nSNP defence spokesman Angus Robertson said Mr Hammond was spreading \"myths and misinformation\" in Scotland.", "\n\nThe SNP has said that, in the event of a \"yes\" vote, all existing military bases in Scotland would be retained.", "\n\nIt has insisted, however, that nuclear submarines would be removed from their base on the Clyde.", "\n\nMr Hammond said: \"Successive UK governments have deliberately chosen to sustain our sovereign capability - albeit at a financial premium.", "\n\n\"As a result no complex warships for the Royal Navy have been procured from outside the UK since the start of the 20th Century - except during the two world wars.", "\n\n\"Today that policy and the Royal Navy's scale delivers billions of pounds of investment and sustains thousands of Scottish jobs directly and indirectly, and I believe it is neither in Scotland's interest nor the rest of the United Kingdom's to put that at risk.\"", "\n\nMr Hammond also claimed the government of an independent Scotland would have to pay part of the cost of removing the Trident base from the Clyde.", "\n\nHe said: \"If we did have to move the Trident nuclear deterrent from Faslane as a result of the negotiations that happen after any independence vote, it would take about 10 years at least to design and construct a suitable alternative site. ", "It would cost a very large amount of money.", "\n\n\"I can't say precisely how much, but it would be many billions of pounds. ", "And that timescale and that cost would have to be taken into account within the overall negotiations.\"", "\n\nAsked if an independent Scotland would pay part of these costs, he replied: \"Absolutely, it would pay part of that bill. ", "Those costs would have to be taken into account as part of the overall settlement.\"", "\n\nDefence co-operation\n\nCommenting after the defence secretary's speech, the SNP's leader in Westminster and defence spokesman Angus Robertson said: \"Another day, another scare story.", "\n\n\"Scotland is a maritime nation but we have no maritime patrol aircraft. ", "They used to be based here until they were all scrapped by the UK government.", "\n\nMedia playback is unsupported on your device Media caption Angus Robertson, leader of the SNP in Westminster, says the UK government does not take Yes plans for defence seriously\n\n\"We are a maritime nation but we have no maritime naval patrol vessels.", "\n\n\"Independence gives us the advantage of being able to make better decisions - so we have those maritime capabilities, so we have the things that we need as opposed to the things that we don't want, like Trident.\"", "\n\n'Threads of a rope'\n\nMr Hammond's speech followed comments by the first sea lord about the prospect of Scottish independence.", "\n\nAdmiral Sir George Zambellas told the BBC that it would be like \"pulling threads out of rope\".", "\n\nSir George said: \"I believe very strongly that, for a premier league navy, respected around the world, with a big responsibility, for us to be divided would be less efficient for both the UK and Scotland.", "\n\n\"The nature of our military construct, infrastructure, basing, people, equipment and the families who support a hard-pressed navy, all of those add up to a construct which doesn't bear dividing its efficiency, and my job is to provide the navy as efficiently as I can.", "\n\n\"The way we do business means that if you try to pull some threads out of the rope it's much less efficient, and that applies particularly to the navy because it's so hard-pressed.", "\n\nBut Col Stuart Crawford, who has advised the SNP on defence matters, said an independent Scotland would be \"more than capable\" of running its own armed forces.", "\n\nHe told the BBC Scottish forces would have a regional, not global, focus.", "\n\nHe said: \"Scotland would be more than capable of running its own armed forces should the country become independent.", "\n\n\"We shouldn't imagine that those armed forces would be a microcosm of the UK's armed forces - not just 10% of the UK inventory if you like.", "\n\n\"It would be something much more modest with a different focus.\"", "\n\nThe Scottish independence referendum is scheduled for September 18." ]

{ "pile_set_name": "OpenWebText2" }

[ 0.023411371237458192, 0, 0.027522935779816515, 0.008849557522123894, 0, 0, 0.006097560975609756, 0.007575757575757576, 0, 0.004132231404958678, 0, 0, 0, 0, 0, 0.01092896174863388, 0, 0, 0.007905138339920948, 0.004672897196261682, 0, 0.020833333333333332, 0.0048543689320388345, 0, 0, 0.012422360248447204, 0.013333333333333334, 0, 0, 0, 0 ]

[ "The effects of induced dental malocclusion on the fibrocartilage disc of the adult rabbit temporomandibular joint.", "\nUnilateral cast occlusal splints were fitted to the mandibular posterior teeth of adult rabbits, for periods of 1-28 days. ", "The reactivity of the mandibular disc was examined by the effect on cell proliferation across the anterior, intermediate and posterior discal bands, as measured by metaphase arrest using vincristine sulphate. ", "The effect on the disc was to activate cell proliferation on the splinted side. ", "Intensity of response varied according to the length of time after fitting the splint, and the site involved. ", "The findings suggested that the adult mandibular disc may participate in compensatory change at a cellular level and thus respond to changing functional loads placed upon the adult temporomandibular joints." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0, 0, 0, 0, 0 ]

[ "As with many other games recently, Anthony Bertolo also asking to fund his game “Heroes Of Forevia” on Kickstarter.", "\n\nHe asks $10,000 BUT if $20,000 will be raised then he will create a GNU/Linux client.", "\n\n\n\nHere what they have to say about the GNU/Linux version :\n\nWill there be a Linux port? ", "Well, if we can reach $20,000, there absolutely will be. ", "We’ve been developing the game on Windows and Mac, but we all have Linux installed on a personal device of some flavor (Ubuntu, Fedora, etc.). ", "We think a Linux port would be awesome, but it would also be a little more costly, because let’s face it, the game development tools on linux are lacking. ", "That doesn’t mean we can’t do it, just that it will be more costly in terms of time and resources.", "\n\nThat means, if you guys can help us reach double our target goal, we will support:\n\nWindows, Mac, Linux, iOS Tablets and Android Tablets.", "\n\nWhen we first thought up Heroes of Forevia, one of our primary goals was to make a game that would look good, yet something that could be ran on a wide range of hardward. ", "A delicate mix of beauty and performance, not unlike Pat.", "\n\nHeroes Of Forevia\n\nHeroes of Forevia is inspired by the fun, arcade action rpg Gauntlet Legends. ", "The entire idea of HoF is to be a game you can just jump in to and start having fun right away. ", "Not only will Heroes of Forevia provide a fun campaign, it will also have a fun and engaging online multiplayer mode where players share the same view reminiscent of the console and arcade game playing days.", "\n\nThe Story\n\nA group of heroes battle through the many lands of Forevia on a search to destroy the king of evil, Paticus. ", "Throughout their journey our heroes are faced with countless minions and multiple realms testing the very hero inside them.", "\n\nOur heroes will be armed not only with swords, axes, bows and staffs. ", "They will also be armed with unique special abilities and magic spells they can improve over the course of the game.", "\n\nIf at any point you realize the job is too great for one hero to handle, you can jump online and use the skill-based matchmaking system to match you with heroes just as good as you are.", "\n\nWith many puzzles to solve and enemies to fight, only one question remains: Who’s your hero?", "\n\nMultiplayer\n\nWe really want to dedicate a lot of time in making sure we can replicate the experience of playing a multiplayer game on the same T.V. To do this, we’ve developed a shared screen. ", "When you play Heroes of Forevia online, all players have the same view, and are constrained to the area the camera shows until all players are ready to move forward. ", "This is something many arcade and console games have, but something we feel was needed for a fast-paced action RPG.", "\n\nBoth in Campaign and Multiplayer, you will be able to level your hero up, learning a few new skills along the way. ", "Although we’ve only played our early alpha version of the multiplayer mode, it’s well on it’s way to being just as good as we planned it to be.", "\n\nThe last major component to our multiplayer system is matchmaking. ", "Although our target platform is Mac and PC, we wanted to have a solid matchmaking experience, where our matchmaking server will match you with players very similar to your own skill level. ", "Although we have many ideas for the matchmaking system, this is one of the components we stand to gain a lot of great ideas from those pledgers who will be taking part in the game development forum.", "\n\nThanks to c704710 for letting LGN know about this project\n\nLinks\n\n“Heroes Of Forevia” on Kickstarter\n\nThe GNU/Linux version of “Heroes Of Forevia”\n\nPopflame" ]

{ "pile_set_name": "OpenWebText2" }

[ 0.017391304347826087, 0, 0.011111111111111112, 0, 0.006993006993006993, 0, 0, 0.007194244604316547, 0.005780346820809248, 0.017543859649122806, 0, 0, 0, 0.01639344262295082, 0, 0, 0, 0, 0, 0.005128205128205128, 0, 0.008695652173913044, 0, 0, 0, 0.005291005291005291, 0, 0.0189873417721519 ]