dataesr/scientific-paragraphs-categorization huggingface dataset:
Acknowledgements We are pleased to thank  D. Leites  and  A. Veselov  for enlightening discussions. This project originated at the  Institut Mathématique de Jussieu (IMJ) ,  Université Paris 6. S. T. is grateful to IMJ for its hospitality. S. M. -G. and V. O. were partially supported by the  PICS05974  'PENTAFRIZ' of CNRS. R. E. S. was supported by  NSF  grant  DMS-1204471. S. T. was supported by  NSF  grant  DMS-1105442.
Only women were recruited in France, Norway, Utrecht (The Netherlands) and Naples  [18]. Information on usual dietary intake, lifestyle, environmental factors and anthropometry was collected from each individual at baseline. The dietary intake information was assessed with different dietary history questionnaires, food frequency questionnaires or a modified dietary history developed and validated separately in each participating country  [17]. The questions asked in the questionnaires included the frequency of consumption over the past 12 months preceding the administration, categorized into the number of times per day, per week, per month or per year. A calibration sub-study was carried out within the entire EPIC cohort by taking a stratified random sample of 36,900 subjects. In the calibration sub-study, a 24-HDR was administered once per subject using a specifically developed software program (EPIC-SOFT) designed to harmonize the dietary measurements across study populations  [19].
We used EPIC dietary intake data for leafy vegetables, fruiting vegetables and root vegetable sub-groups as a working example. We further assumed measurements on the 24-HDR (in g/day) as the unbiased reference measurements and those on the DQ as the biased main-study measurements. We excluded subjects with missing questionnaire data, missing dates of diagnosis or follow up, in the top and bottom 1% of the distribution of the ratio of reported total energy intake to energy requirement. We further excluded subjects with a history of cancer, myocardial infarction, stroke, angina, diabetes or a combination of these diseases at baseline. As a result, data for 430,215 subjects were eligible for the analyses. In the analysis, the data from the following centers were excluded: Umea ˚and Norway for leafy vegetables and Norway for fruiting vegetables.
We fitted the GAM model for consumption probability, assuming a binomial response and a logit link function using the mcgv package in R  [26]. In the GAM model, we included confounding variables in the disease model (Z). We used the partial prediction plot from the smoothed DQ component to identify plausible forms of parametric transformations for the DQ  [27]. From the selected set of parametric transformations, Akaike Information Criterion (AIC) was used to identify the optimal transformation. Similar to the consumption probability part, we explored optimal form of DQ for the consumed amount part of the calibration model with the GAM approach.
Acknowledgements  J. Buczyński  supported by  Marie Curie Outgoing Fellowship "Contact Manifolds ," Landsberg supported by  NSF  Grant  DMS-1006353. We thank  M. Mohlenkamp  for pointing out an error in an earlier version of this article, related to the rank of y + y + y in Theorem 1. 8. This paper grew out of questions raised at the 2008 AIM workshop Geometry and  Representation Theory of Tensors for Computer Science, Statistics  and  Other Areas , and the authors thank  AIM  and the conference participants for inspiration. The mathematics in this paper was finally completed while the authors were guests at the Mittag-Leffler Institute in Spring 2011 and we gratefully thank the institute for providing a wonderful environment for doing mathematics. We truly appreciate the help of the referee, his careful proofreading of the article, and his many thoughtful comments.
Analysis of the distance effect The distance effect was obtained by analyzing the data from the comparison task. As with the parity task, only correct trials with reaction times between 150 and 1200 ms were included. In order to calculate the amplitude of the distance effect, we grouped the trials based on the absolute value of the distance to the reference digit 5, and computed the average reaction time for the four distances (1, 2, 3 or 4), in each participant. The amplitude of the distance effect is given by the slope of the regression line when performing a regression analysis on the four average reaction times for each participant. A negative slope shows a decrease in reaction times as the distance between the target and the reference digit increases, which is characteristic of the distance effect.
Acknowledgments The first author is very grateful to  László Lovász  and  Miklós Simonovits  for suggesting to study the papers of Alexander Sidorenko. He also thanks  Benjamin Rossman  for the comments on the paper [19]. This research was partly done while the second author was visiting the  Alfréd Rényi Institute of Mathematics. He is very grateful to  Miklós Abért  and the  Institute  for their hospitality and support. He also would like to thank  Yanfeng Luo  for introducing the graph homomorphisms and  Jiang Zeng  for all his encouragement during this work. Special thanks goes to  Masao Ishikawa  for suggesting the name tree-walk algorithm.
The rationale for developing PDX models is based on the expectation that these models will represent enhanced preclinical tools and will be more predictive of human cancer biology and patient response to treatments. In addition, PDX models offer the potential for personalizing patient cancer treatment. Proving the value of PDX models may be approached from different perspectives: one such approach is to compare the histopathological, biological and genetic features of a PDX model with its donor tumor (also called 'validation'). The underlying hypothesis is that PDX models will retain key characteristics of the donor tumor and that these characteristics will be maintained through successive mouse-to-mouse passages in vivo. Table  2  summarizes the data from different studies in which PDX models have been compared to donor tumors using a variety of methods.
In general, these studies show that PDX models retain the principal characteristics of donor tumors, including fine tissue structure and subtle microscopic details such as gland architecture, mucin production or cyst development. At the biological level, most studies also show good concordance between tumors and the models derived from them. Analysis of gene expression profiles shows that there are no substantial changes between donor tumor and their corresponding PDX, with only genes involved in the stromal compartment and immune function being less represented in models, due to the replacement of the human stroma by murine elements. Indeed, using unsupervised clustering analysis, paired donor tumor and PDX model cluster together in most of the studies. Analyses of copy number alterations (CNAs) and exome sequencing data also show extraordinary concordance between paired samples, with a trend towards higher frequency of genomic alterations in the PDX model likely as a result of increased human tumor DNA purity in the PDX model.
This was also suggested in another study describing that many of the mutations detected in the breast PDX were also observed in brain metastases derived from the same patient  (24). Furthermore, mouse-to-mouse propagation does not substantially change the functional characteristics of the grafted tumor. Studies that have compared the response to drug treatments of PDX models from different passages (up to ten) show stable response rates across generations, further supporting the phenotypic stability of these models  (25, 26). In contrast, an interesting study compared the gene expression profiles of a donor tumor with those of PDX models and cell lines developed from that tumor, both in vitro and in vivo in conventional xenograft models. The data show that while the gene expression profile of PDX models is similar to the original tumor, cell lines developed from the same specimen display a different expression profile that is not restored by in vivo subcutaneous propagation in mice  (27).
Nevertheless ER+ subtypes are under-represented, in particular the recently described ER+ subtypes with good prognosis. Furthermore, when examining metabolism, the metabolic profiles as detected by high resolution magic angel spinning MR spectroscopy are remarkably similar when comparing patient material and tissue from orthotopically growing basal-like and luminal-like breast cancer  (32). A complementary approach to determine the value of PDX models in cancer research (discussed and illustrated below) is by analyzing the predictive value of the data obtained from PDX studies with regards to drug efficacy, biomarker analysis, and patient outcome. In this sense, a similar level of activity as observed in the clinic has consistently been shown in studies in which clinically applied drugs or regimens have been tested in PDX models.
One critical aspect of large preclinical studies in PDX models is that they not only help to prioritize potential clinical indications, but they may also facilitate the identification of potential drug efficacy biomarkers. The concordance between PDX models and human trials with regard to biomarkers of drug susceptibility and drug resistance is indeed notable. In CRC for example, it has been clearly shown in a number of studies that KRAS mutant PDX models do not respond to cetuximab. KRAS wild-type status is now a well-documented clinical biomarker for this targeted therapy  (28, 29). Similar data were observed in NSCLC  (21). In fact, it could be argued that if these preclinical studies had been conducted prior or in parallel to the clinical development of cetuximab, the discovery, validation and approval of KRAS mutation as a marker of resistance would have been expedited.
While these advances attest to the feasibility of genetic modification of PDX tumor preparations for imaging purposes, their utility in the routine implementation of BLI to follow PDX tumors in vivo remains to be seen. Efforts to harmonize and standardize study design and data analysis are also needed. For PDX preclinical studies to be fully integrated in clinical development pipelines, there first needs to be a consensus in the design of preclinical studies. This includes areas such as the number of models representing the tumor heterogeneity of the majority of tumor types, and the number of mice per model required for robust statistical interrogation, as per a clinical trial. Another important question is the homogeneity of the batch of mice in which a drug will be assayed, important when a large number of mice are needed.
With proper confidentiality and data protection systems, this information can be shared to permit rapid assessment of model availability, which will be particularly important for rare molecularly-defined tumor types. Furthermore, these networks will allow the conduction of multicenter preclinical trials as done for patients under a single protocol with rapid accrual and data generation. In that sense, within Europe a consortium of centers having interest and significant expertise in PDX models, has now emerged: EurOPDX is an initiative of translational and clinical researchers across Europe having the common goal to create a network of clinically relevant and annotated models of human cancer, and in particular PDX models. The primary goal of our initiative is to share PDX models in diverse cancer pathologies, in order to constitute a unique collection reproducing the heterogeneity of human cancer.
Supplementary Table  2  provides a summary of the models and the level of characterization of those models currently available across the EurOPDX Consortium. A shared database with harmonized annotation of models will be established and integrative systems-based analyses developed to elucidate novel therapeutic strategies and uncover predictive biomarkers for personalized cancer treatment. Annotation of the models will include anatomo-pathological data, clinico-pathological data from the patients the PDX were derived from, deep molecular profiling in particular with gene expression, copy number alterations and proteomics platforms, as well as pharmacogenomic data corresponding to current anticancer therapies. Additional technologies such as imaging are increasingly being used and the ideal database will also include such data as well as scanned images of pathology slides  (75).
In this way the Consortium will be able to quickly include any newly developed multimodal prognostic and predictive tool in the analysis pipeline. Making the data available for the analysis is not a trivial task as it implies standardization of platforms used for molecular characterization, data acquisition, data curation, normalization and quality control. Moreover, and as discussed above, harmonization and standardization of working practices for the implementation and use of PDX models, and in particular for the performance of more reproducible and predictive multicenter preclinical trials, will be a key objective of the network. Hypotheses will then be validated in proof-of-concept collaborative multicenter xenopatient trials within molecularly defined tumor subsets and on a population scale, as a prelude for prospective clinical trials in humans.
Acknowledgments We thank  N. Boulanger ,  A. Campoleoni ,  R. Manvelyan ,  E. Skvortsov ,  M. Taronna  and  S. Theisen  for useful discussions. We also acknowledge the GGI, Florence workshop on "Higher spins, Strings and Duality" where the present work was developed. The work of K. M. was supported in part by  Scuola Normale Superiore ,  INFN  ( I. S. TV12 ), the  MIUR-PRIN  contract  2009-KHZKRX , and the  ERC Advanced Investigator Grants no. 226455 "Supersymmetry, Quantum Gravity and Gauge Fields" (SUPERFIELDS).
Approximate Bayesian Computation (ABC) has become a popular technique in evolutionary genetics for elucidating population structure and history due to its flexibility. The statistical inference framework has benefited from significant progress in recent years. In population genetics, however, its outcome depends heavily on the amount of information in the dataset, whether that be the level of genetic variation or the number of samples and loci. Here we look at the power to reject a simple constant population size coalescent model in favor of a bottleneck model in datasets of varying quality. Not only is this power dependent on the number of samples and loci, but it also depends strongly on the level of nucleotide diversity in the observed dataset. Whilst overall model choice in an ABC setting is fairly powerful and quite conservative with regard to false positives, detecting weaker bottlenecks is problematic in smaller or less genetically diverse datasets and limits the inferences possible in non-model organism where the amount of information regarding the two models is often limited.
Understanding the evolutionary history of a population is an important aspect of studies on natural populations. Aside from giving information about the evolutionary past of organisms, inferring the demographic history and structure of a population is also necessary to understanding the effect of other population genetic processes. For instance, studies aiming to infer signatures of selection at candidate loci or across the genome depend on first knowing the background patterns of genetic variation produced by historical demographic events  [3, 4]. Methods for estimating demographic histories have therefore become increasingly impor-tant, and have fuelled the proliferation of studies using ABC to infer a suitable demographic model. A typical ABC workflow would consist of a number of steps: i) choose a set of summary statistics describing a given dataset; ii) perform a large number of simulations sampling a pre-supposed distribution of models and model parameters; iii) compute the summary statistics for the simulations; iv) apply a rejection threshold to focus on a region of the parameter space where the relationship between the summary statistics and parameters is assumed to be linear; v) perform either a regression to evaluate model parameters or perform a logistic regression to compare models.
This process has been relatively overlooked in the literature compared with advances in statistical methods that all somehow assume that data are properly summarized. Furthermore, even if a certain set of summary statistics is informative in accurately estimating parameters from two different demographic models separately, the same set of summary statistics may be uninformative when it comes to comparing these two models with each other  [8]. Besides estimating demographic parameters such as population divergence times or migration parameters, model choice is central to many questions in population genetics. The problem of appropriately summarizing the data could be more important for datasets containing low levels of information, either because of an insufficient sampling effort or low levels of variation.
Using population genetic simulations, we try to identify what happens when limitations are placed on the amount of information in the data, such as sample size, number of loci and level of genetic diversity. Firstly, this mimics many studies of natural populations where constraints are placed on the amount of data that can be collected. As the use of ABC has increased, so too has it been embraced in non-model organisms where the number of loci and samples are often limited. It is therefore of great interest to understand how a limited dataset impacts the use of ABC model choice. Secondly, it highlights which aspects of an ABC analysis, including the choice of summary statistics, are important in determining the power to reject a null demographic model in favor of a more complex alternative.
The model also contains a parameter controlling the severity of the bottleneck, and varying this parameter allows us to investigate the performance of model choice in ABC in more detail. We begin by exploring the relationship between the parameters of the models and a number of summary statistics commonly used in population genetics. Using a subset of these summary statistics, we assess the power to reject the SNM in favor of the BNM whilst varying: 1) the quality of the dataset; 2) the severity of the bottleneck; and 3) the tolerance of the rejection step.
Choice of summary statistics Figure  1  shows correlation coefficients between different summary statistics and the parameters of the SNM and BNM for the largest dataset with high genetic variance (n~20, l~30, h~0:005). The parameter h is strongly positively correlated with the means of many statistics, such as h W , p, h H , H e and S, as well as their quantiles and standard deviations. One exception is the standard deviation of H e which is strongly negatively correlated with h. This is in sharp contrast with p which responds positively to an increase in segregating sites. The standard deviation of Tajima's D is negatively correlated with h, showing that its precision increases with increasing variation. The average value of Fay and Wu's H is independent of h in the SNM and is slightly positively correlated with h in the BNM.
We performed a Principal Component Analysis (PCA) in order to quantify the main features that can be extracted from summary statistics. PCA reduces the dimensions of a set of potentially correlated variables into a smaller set of uncorrelated variables that best explain the variance in the data. Figure  S1  shows a PCA of the SNM (N B ~N0 , n~20, l~30, h~0:005) and the BNM (N B ~0:1N 0 , n~20, l~30, h~0:005) contrasted against the complete parameter space of the BNM (n~20, l~30). The two models are clearly separated on the first principal component (PC) Figure  1. Correlation between parameters and summary statistics. Correlation coefficients between parameters and summary statistics for a SNM (top) and a BNM (bottom) for the larger dataset (n~20, l~30). The parameters are given by theta and rho in the SNM and by theta, botEnd, botNe and rho in the BNM.
Comparison amongst sets of summary statistics We looked at the effect that a 90% reduction in the effective population size (N B ~0:1N) has on the power to reject the SNM for different sets of summary statistics (Table  1 ). All sets of summary statistics give good power for large datasets with high nucleotide diversity (n~20, l~30, h~0:005), with the proportion of Bayes factors exceeding 3 all being greater than 0. 99 (Y TPH ~0:985; Y SFS3 ~0:991; Y TzSFS3 ~0:999; Y SFS5 ~0:997; Y TPHzDH ~1). For a large dataset with low genetic diversity (n~20, l~30, h~0:0015), three sets of summary statistics are able to reject the SNM with a power greater than 0. 9 (Y SFS3 ~0:901; Y TzSFS3 ~0:907; Y TPHzDH ~0:95), with TPH, in contrast, having very low power (Y TPH ~0:019). Smaller datasets afford less power to reject the SNM, except when using the TPH+DH set of summary statistics with high nucleotide diversity (n~10, l~15, h~0:005), which still allows for a high degree of power in rejecting the SNM (Y TPHzDH ~0:95).
For large datasets with low genetic variation and the TPH+DH set of summary statistics the false positive rate is 0. 166 and 0. 397 for Bayes factor cutoffs of 1. 5 and 1 respectively. Similarily, for small datasets with high genetic variation the rate is 0. 110 and 0. 411 for cutoffs of 1. 5 and 1 respectively. In general, the inclusion of statistics that summarize elements of the site frequency spectrum give greater power, which is most clearly reflected in smaller, low diversity datasets (n~10, l~15, h~0:0015) by the power difference between TPH and the other three sets of summary statistics (Y TPH ~0; Y SFS3 ~0:306; Y TzSFS3 ~0:214; Y SFS5 ~0:339; Y TPHzDH ~0:373). The distri- butions of model probabilities (Figure  S2 ) under the SNM and BNM overlap for TPH, even for larger datasets where an increase in samples and loci leads only to a shift in the mean of the distribution so that the models are difficult to separate.
However, for sets of summary statistics that incorporate the site frequency spectrum (TPH, SFS5 and TPH+DH) a larger dataset increases the power to distinguish between the two models, and the distribution of model probabilities is skewed. Somewhat surprisingly, including h W with SFS3 decreases the power for datasets with low genetic diversity (n~10, l~15: Y SFS3 ~0:306, Y TzSFS3 ~0:214; n~20, l~30: Y SFS3 ~0:901, Y TzSFS3 ~0:738). To investigate the performance of T+SFS3 in datasets with low and high levels of nucleotide diversity, we extended our analysis to include scenarios with more severe (N B ~0:01N) and less severe (N B ~0:2N) bottlenecks. In genetically diverse datasets there is a clear difference between the value of h W in BNMs and SNMs (Figure  3 ), suggesting that the statistic is informative in choosing between the models.
In contrast, the distributions of h W for datasets of low nucleotide diversity overlap to some extent, implying that in this case the statistic is not as informative for distinguishing between the two models. In all scenarios considered, an increase in the severity of the bottleneck increases the power to correctly reject the SNM (Table  2 ). For all sets of summary statistics, there is excellent power to detect a 90% (0:1N) or 99% (0:01N) reduction in the effective population size with a large, genetically diverse sample (n~20, l~30, h~0:005). The choice of summary statistic becomes increasingly important for a smaller reduction in the population size of 80% as, even for large, genetically diverse samples (n~20, l~30, h~0:005), only the TPH+DH set of statistics performs well (0. 968). The TPH set of statistics performs poorly with smaller or genetically less diverse datasets, even for strong bottlenecks (0:01N), and seems to perform particularly badly in samples with low diversity.