dataesr/scientific-paragraphs-categorization huggingface dataset:
Thus, a difference in parameter estimates of β with or without conditioning on unmeasured confounders U 1 and U 2 would solely be due to the confounding bias of these unmeasured confounders. The simulation proceeded by generating a population of n P = 21,000 subjects. In scenarios 1 and 2, we focused on external validation samples, while in scenario 3, we generated an internal validation sample. For scenarios 1 and 2, a representative main sample (n M = 10,000) was randomly drawn from the population while the validation sample (n V = 1,000) was extracted from the remaining 11,000 subjects. In scenario 1 the validation sample was representative of the population, while in scenario 2 it was not. The variable U in the main data was considered as missing. For scenario 1, two series of simulations were run by varying the distribution of the confounders: Scenario 1.
Scenario 2: The population was generated as in scenario 1. a and non-representative validation samples were selected to investigate the sensitivity of each method to various selection biases. The probability of inclusion in the validation sample was a function of either X, Y, C or C � Y (in Scenario 2. a), where � represents an interaction effect between two variables, X + Y or X � Y (in Scenario 2. b), or U, U � X or U � Y (in Scenario 2. c). Scenarios 2. a and 2. b correspond to missing-at-random mechanisms, hence MICE is expected to be robust, while for scenario 2. c, data are missing not at random and MICE is expected to fail. TSC requires that the association between Y and X given C alone and given C and U be identical in the validation and the main sample. This assumption was violated in scenarios 2.
In the former case, which is untestable in practice, all methods are biased while in the latter, MICE provides an unbiased estimate in the pooled sample. Interestingly, the latter assumption can be evaluated in practice, as was illustrated in the BZD-fracture study. We focused mainly on external validation samples because this is the most frequent situation when existing cohorts are used as validation samples. Owing to differences in time periods, selection procedures and participation rates, such cohorts are not expected to be completely representative of the population targeted by the HAD. This motivated the investigation of the impact of departures from representativeness. However, some nationwide HAD are almost exhaustive, so existing cohorts in the country may be considered as internal validation samples if a linkage between the databases is possible.
A clear advantage of internal validation is that the measure of the exposure, outcome and observed confounders are common in both samples. In this context, the robustness of MICE is useful when the validation and main samples differ according to the distributions of both the outcome and exposure. The analysis of the relationship between BZD and fractures using EGB data illustrates how these methods may be applied and, to some extent, how their validity may be evaluated in real data analyses. While this is not the best design for this study because it may suffer from a survival bias, the analysis confirms that elderly users of BZD have an elevated risk of experiencing a fracture compared to unexposed subjects after controlling for confounders including BMI, education and CESD. The measures of exposure to drugs and outcome differed between the validation and main samples.
This publication represents the views of the authors and does not necessarily represent the opinion of the  French Medicines Agency. The Paquid study was funded by  Ipsen  and  Novartis  and the  Caisse Nationale de Solidariteet d'Autonomie. The  Three-City study  was supported by  Sanofi-Aventis , the  Fondation pour la Recherche Medicale , the  Caisse Nationale Maladie des Travailleurs Salaries ,  Direction Generale de la Sante, MGEN, Institut de la Longevite, and Conseils Regionaux d'Aquitaine and Bourgogne ,  Fondation de France ,  Ministry of Research-INSERM Programme "Cohortes et collections de donnees biologiques" ,  Agence Nationale de la Recherche   ANR PNRA 2006  and  LongVie 2007 , and the  "Fondation Plan Alzheimer " ( FCS 2009-2012 ). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Simulation scenarios In our simulations, we the following parameters: R 2 , the trial- level coefficient of determination between the effects of the treatment; N, the number of trials; n i , the number of patients per trial; and Kendall's τ, the dependence at the individual level between the two criteria. We generated databases, each containing a meta-analysis of = N 10, 20, or 40 randomized trials of average size = n 400, 200, or 100. The actual size of each trial n i was randomly generated from a uniform distribution between n 0. 5 and. These various choices allowed us to study the possible effect on the distance measures of the number of trials included in a meta-analysis and their size. Four scenarios were considered in terms of dependence at the Fig. ) at the trial level. Thus we took two extreme settings with a poor trial-level surrogate and a very good trial level-surrogate.
Acknowledgment. The author would like to thank his advisor  Adam Skalski  for bringing him the topic, helpful discussions and constant encouragement. A. Skalski also checked an earlier version of this paper carefully and gave many useful comments. This paper could not be finished without his help. The research was partially supported by the  NCN (National Centre of Science)  grant  2014/14/E/ST1/00525  and the  French "Investissements d'Avenir" program , project  ISITE-BFC  (contract  ANR-15-IDEX-03 ).
Pierre Alquier's work has been supported by  GENES  and by the  French National Research Agency (ANR)  under the grant  Labex Ecodec  ( ANR-11-LABEX-0047 ). † AGM  UMR8088 University Paris-Seine and CIMFAV, Universidad de Valparaiso, Chile. Paul Doukhan 's work has been developed within the  MME-DII center of excellence  ( ANR-11-LABEX-0023-01) & PAI-CONICYT MEC N o 80170072. ‡ CAM ,  Tianjin University, Tianjin ,  China. Fan Xiequan  has been partially supported by the  National Natural Science Foundation of China  (Grant N o 11601375.
The two latter data together with the known inclusion shape ω * are used to compute the following relative errors : err D = ||τ N -u |Γi || L 2 (Γi) ||u |Γi || L 2 (Γi) , err N = ||η N -σ(u, p)n |Γi || L 2 (Γi) ||σ(u, p)n |Γi || L 2 (Γi) , (22) err O = mes(ω * ∪ ω N ) -mes(ω * ∩ ω N ) mes(ω * ). where (η N , τ N , φ N ) is the approximate Nash equilibrium output from Algorithm 2, and ω N = 1 { φ N < 0}. These metrics are used to assess the efficiency of our approach. The stability w. r. t. noise was stressed by solving the joint inverse inclusion/completion problem with noisy perturbations of the Dirichlet data f σ = f + σN with N being a Gaussian white noise. Two different initial level-sets were used : φ 1 has as zero level-set the disk B(c 0 , r 0 ) where c 0 = (0, 0) and r 0 = 0. 30, and φ 2 is a periodic function with as zero level-set 30 fairly uniformly distributed small holes filling the whole domain Ω, see Figures  3(a ) and 4(a).
The solvers for Stokes, equation (  17 ) and adjoint systems, the sensitivity routines, and the minimization algorithms as well, were implemented using the Finite Element package FreeFem++  [34]. Test-case A. The exact inclusion is a disk ω * = B(c, r) centered at c and with a radius r where c = (0, 0) and r = 0. 10. The FreeFem++ implementation of Algorithm 2 was ran for two different initial contours, leading to very close results, both of them in good accordance with the exact solutions (inclusion and missing data). It can be however For the case of noisy Dirichlet data f σ given over Γ c , it can be seen from the profiles presented in Figure  5  that the boundary data recovery is remarkably stable with respect to the noise magnitude, and even more striking is the stability of the detected inclusion.
Morphometric analysis First, we entered the scale pictures into tps-Util 1. 60  [36]. For the analysis, we then used 20 landmarks  [24]  following the method of Rohlf and Slice [37] using tpsDIG2 2. 18 software  [35]. The intersections of wing veins with the wing margin, cross veins and major veins were used as locations for landmarks (Fig. 2 ). Morphometric analyses and graphical outputs were performed using various modules of the CLIC software  [15]. Centroid sizes are described as the square root of the sum of squared distances of a set of landmarks from their centroid, i. e. the square root of the sum of the variances of the landmarks around that centroid in xand ydirections  [10]. They were used as a size estimator and compared with R 3. 1. 2 [41]  using a Kruskal-Wallis test or nonparametric Wilcoxon-Mann-Whitney test followed by a post-hoc test (Mann-Whitney tests with Bonferroni correction).
25)  [20]. The thin-plate spline was computed using the software MorphoJ (version 1. 07)  [22]  in order to visualize the shape changes in the wings between the groups tested  [49]. The contribution of size to wing shape (residual allometry) was estimated by multivariate regression of partial warps on size. Finally, the presence of isolation by distance was researched using a Mantel test (correlation between Procruste values and geographical distances in meter) under PAST (version 3. 25). Analyses were performed by altitude groups. It was not possible to test the effect of month on wing morphometry because of the small number of specimens captured each month.
Second, differences in male and female wing phenotypes (shape and size) among groups were observed. Even though this study highlights wing differences between altitudinal groups, it was not possible to draw any conclusions regarding the effect of month on the mosquito phenotypes. In the case  of small populations or a low number of captured individuals, sampling size is limiting for discriminant analyses. Indeed, the variance of the dataset cannot be explained due to the low number of principal components. Climatic and environmental conditions (temperature, relative humidity, variation between night and day, etc. ) could exist depending on the month. Further studies should be considered with larger sample sizes according to month and altitude. For males and females, the size and shape analysis indicated significant differences among altitudinal populations.
Acknowledgements. This study was funded by the  EU  grant  FP7-261504  EDENext (http://www. edenext. eu). The contents of this publication are the sole responsibility of the authors and do not necessarily reflect the views of the  European Commission. The authors are grateful to  Eng. Migel Ali ,  GIS  expert at the  Geo Consulting & Invent Albania Company , who helped us prepare the map specifically for this manuscript. We also thank the families on mount Dajti who allowed us to carry out the field work on their properties,  Ada Shukullari ,  Erion Muhaxhiri ,  Elton Rogozi , and  Viola Jani  for their technical assistance, and  Heïdi Lançon  for the English revision of the manuscript.
Practical remarks and examples We conclude by noting that the results presented in this paper can be turned into an algorithm which allows to check the solvability of a given concrete system. The main steps can be summarized as follows. 1. Compute the formal exponents at each singular point. The practical calculation of the formal exponents presented in the previous section, is already implemented in Maple as a part of the general program ISOLDE  [4]  based on algorithms from  [1]. 2. Check the required smallness of the formal exponents of the system under consideration. 3. The simultaneous triangularizability of a set of matrices is equivalent to the solvability of the Lie algebra generated by them. This can be checked using the package LieAlgebras of Maple. 4 n order to illustrate the various steps of our algorithm we give two examples of computations performed by using our implementation in Maple.
Study site Our data was collected over three years of field monitoring (from 2013 to 2015). This monitoring was carried out on the Benfica Agriculture Installation Project (Projeto de Assentamento) site which is located in the Brazilian State of Pará (Fig. 2 ). This territory is located within the Amazonian rain forest on the territory of the Itupiranga municipality and covers 10,026 ha. The shape of Benfica is irregular and lies within a quadrilateral space formed by the straight line connection at the coordinates 05 • 12'20" south latitude, 05 • 20'40" south latitude and 49 • 48'00" west longitude, 49 • 56'40" west longitude. The particularity of this site is that it includes man-made spaces that, since 1989, have been progressively colonized by one thousand people, Sampaio (2008).
Field sampling The fieldwork protocol was developed in early 2012. Seven surface areas of pastureland were designated for this research project. Within each piece   (2017). We obtained the total number of seventeen transects from which we collected data regarding growth, sprouting and fruiting processes. In addition, we also used seven supplementary transects to obtain more data about the growth process, especially for stages 5 and 6 (Table  1 ). The counting and marking of all individuals at all six stages of development was performed within these transects. In 2013, 2,987 palm trees of all stages were identified. In 2014 and 2015, we surveyed the same palm trees, to which we respectively , added 471 and 482 newly recruited individuals of stage 1 (Table  2 ).
Hierarchy The ecological process was observed on transects belonging to the designated area of land. Only two levels were considered for the transition survival process: the transect and the whole studied area in Benfica. Moreover, our estimation concerning the probability of transition between stages (see Fig. 4 ) did not exhibit any structure at the level of the farmer's piece of land (each piece of land is separated by a red line). No spatial structure was observed, except for the transition from stage 2 to stage 3 where a link with spatial coordinates might be possible (see appendix and discussion) but it was difficult to estimate or ensure with our dataset. Therefore, we preferred to employ a multilevel model using the level of the transects and of the whole studied area in Benfica.
Computation with R and JAGS JAGS which uses the dialect of  BUGS Lunn et al. (2000) ,  Plummer (2003) ,  Lunn et al. (2013)  was used to fit the model to the data with the package rjags. The estimates of parameters were evaluated based on 200,000 samples after 50,000 burn-in samples, thinning to one draw for each sample, by MCMC simulation of the joint posterior distribution. The MCMC inference samples analysis was processed with the coda package  Plummer et al. (2006). Convergence diagnostics consisted of visuals (traces and autocorrelations) and statistical calculations using the test of  Gelman et al. (2003)  based on  Gelman and Rubin (1999). For all variables in the model, the Gelman criteria of between-chain variance over within-chain variance converged into one. More information on the convergence diagnosis and on the script of the model are available in the supplementary materials.
Overview of the phase III clinical trials In the CheckMate 141 clinical trial sponsored by Bristol-Myers Squibb (BMS) (NCT02105636), 361 recurrent and/or metastatic (R/M) head and neck squamous cell carcinoma (HNSCC) patients were randomized 2:1 to either nivolumab (N = 240) or standard of care (SOC) chemo monotherapy (N = 121)  [1]. The monotherapy treatment options included weekly applications of either methotrexate 40 mg/m 2 , docetaxel 30 mg/m 2 , or cetuximab 250 mg/m 2 (400 mg/m 2 loading dose first). The patients in the study were stratified based on prior cetuximab treatment only. In the KEYNOTE 040 clinical trial sponsored by Merck Sharp and Dohme (MSD) (NCT02252042), 495 R/M HNSCC patients were randomized 1:1 to either pembrolizumab (N = 247) or SOC chemo monotherapy (N = 248)  [2] [3] [4].
In CheckMate 141, the data cutoff point for the analyses of OS, progression free survival (PFS), and safety was December 18, 2015 with a median duration of follow-up for OS of 5. 1 months (range, 0 to 16. 8) and data on rate of response was based on a cutoff of May 5, 2016. Pembrolizumab had received FDA approval in August of 2016 and nivolumab in November of 2016. KEY-NOTE 040 had a data cutoff point of May 15, 2017. Correspondingly, in KEYNOTE 040, 12. 5% (31 of 248) of patients in the SOC arm received an ICI at the time of clinical progression. The impact of receiving subsequent ICI in the SOC arm had a significant impact on median OS, with patients in the SOC arm receiving subsequent ICI having a prolonged median OS of 20. 1 months (N = 15, 95% CI: 14. 0-NE months) as compared to a median OS of 9.
Let G be a countable group. For any probability measure µ on G, one can consider the random walk on G driven by µ: this is a sequence (S i ) i≥0 of random variables valued in G such that S 0 = X 0 and S n+1 = S n X n+1 , where (X i ) i≥0 are independent and identically distributed random variables with probability distribution µ. If the Date: July 21, 2017. The author was supported by ANR-14-CE25-0004 GAMME. 1 current state is x, the probability of being in y at the next step is µ(x -1 y). This implicitly defines a probability measure P µ on G N such that P µ (S n = y | X 0 = x) = µ (n) (x -1 y), where µ (n) denotes the n-fold convolution of µ. Recall that if f and h are two functions on G, the convolution of f and h is f * h(g) = k f (k)h(k -1 g). An interesting class of examples arises from a probability measure whose support generates the whole group G as a semigroup.
Acknowledgements. This paper contains some of the results of my doctoral dissertation. The question of links between the return probability of a metabelian group and the Krull dimension as a module of the derived subgroup of a metabelian group was suggested by Yves Cornulier and Romain Tessera. I am very grateful to them for many valuable discussions, helpful suggestions and careful reading. I would also like to warmly thank Peter Kropholler for stimulating discussions, comments and careful reading, as well as Anna Erschler for her interest and an interesting conversation.
Acknowledgments We like to thank  Ivan Corwin ,  Gregory Korchemsky ,  Vivien Lecomte ,  Kirone Mallick  and  Rodrigo A. Pimenta  for useful discussions. Further, we thank the anonymous referees for their useful comments. R. F. likes to thank  I. M. Szecsenyi  for interesting discussions and collaboration on a related topic. J. K. is supported by the  Simons Foundation  Grant No  454943. R. F. was supported by the visitor program of the IHÉS where a significant part of this work has been carried out. R. F. also likes to thank the  University of Modena and Reggio Emilia  for hospitality. Finally we thank the organizers of RAQIS'18 at LAPTh where this work originated.
This work has been partially supported by  FAPERJ   CNE E-26/201. 207/2014 ,by  CNPq Bolsa de Produtividade em Pesquisa   PQ 303538/2014-7 , by  ANR-15-CE40-0020-01  LSD of the  French National Research Agency  and by the  European Research Council (ERC)  under the European Unions  Horizon 2020 research and innovative programme  (grant agreement No  715734 ).
Acknowledgments M. L. is grateful to  Sanjay Ramassamy  for an inspiring remark, and the authors thank  Aran Raoufi  and  Gourab Ray  for many useful discussions. This article was finished during a stay of M. L. at IHES. M. L. thanks  IHES  for the hospitality. The research of M. L. was funded by  EPSRC  grants  EP/I03372X/1  and  EP/L018896/1  and was conducted when M. L. was at the  University of Cambridge. The research of H. D. -C. was funded by a  IDEX Chair from Paris Saclay , the  ERC CriBLaM , and by the  NCCR SwissMap  from the  Swiss NSF.
12 The authors posit this approach as a solution to the phenotype-genotype problem. They construct a so-called "voting" prior by assigning a count to each codon position based on the number of times that it is identified as important in the literature. 19 In such a study, the same amount of information is available for each biomarker. However, in other settings with many covariates, such as clinical variables, the variable selection literature is limited. We are motivated by clinical practice data in which dose modifications were made over multiple cycles for patients being treated with Irinotecan for colorectal cancer. We use elicited clinical relevance weights to reflect the medical experience of practicing physicians. 20 When a physician makes a decision regarding a patient's treatment or dose modification, certain patient characteristics and previous clinical outcomes are given more weight than others.
Each physician provided their clinical relevance weight associated with each grade of each toxicity type and each level of each covariate. (2) Next, we constructed a modification of the SSVS method, which we call weight-based SSVS (WBS), to identify covariates that influence dose adjustment. We used the elicited clinical relevance weights to compute the hyperparameters of the prior distributions of the variables' inclusion indicators to provide a basis for the WBS. (3) Third, we compared the influence of the physicians' clinical relevance weights using our proposed method with two other methods, the Lasso and conventional SSVS. We also studied the effect of sample size on our method. (4) Finally, we applied our WBS method to analyze the Irinotecan data set. The remainder of this paper is organized as follows.
Bayesian predictive model accuracy Unlike frequentist methods, the Bayesian approach provides a posterior distribution, which provides a basis for computing the log pointwise predictive density, proposed by Gelman et al. 25  We adapt this approach to the repeated measures structure of the Irinotecan data set. Denoting the prior distribution as p(, I, ,   2   ,  2  ) and the posterior distribution as p post (, I, ,   2   ,  2  | data), the posterior predictive distribution of d is p post ( d | data) = ∫ p ( d|𝜽, I, 𝛄, 𝜎 2 𝛾 , 𝜎 2 𝜖 ) p post ( 𝜽, I, 𝛄, 𝜎 2 𝛾 , 𝜎 2 𝜖 | data ) d𝜽dI d𝛄d𝜎 2 𝛾 d𝜎 2 𝜖. In practice, the distribution f i,k (d) depends on (, I, ,  2  ,  2  ), which are not known. We thus work with the log pointwise predictive density LPD = n ∑ i=1 K ∑ k=1 log p post ( di,k ) = n ∑ i=1 K ∑ k=1 log ∫ p ( di,k |𝜽, I, 𝛄, 𝜎 2 𝛾 , 𝜎 2 𝜖 ) p post (𝜽 | data)d𝜽dI d𝛄d𝜎 2 𝛾 d𝜎 2 𝜖.
CASE STUDY We extracted data for patients treated for metastatic colorectal cancer with a combination of drugs including Irinotecan from the Georges Pompidou University Hospital (HEGP) I2B2 warehouse with IRB approval. The protocol encompasses a theoretical dose of 180 mg/m 2 and a theoretical cycle of chemotherapy of 14 days. All patients who were treated with any other protocol including Irinotecan were excluded. One cycle was defined as doses being given over one to three successive days. When a patient received a dose more than 28 days later, we considered that to be the beginning of another protocol. The data included the covariates age, weight, total bilirubin, WHO score, treatment line, and the seven toxicity types registered on each cycle of chemotherapy, as described in Section 3, using the physicians' elicited clinical relevance weights.
In our database, we found 185 patients who had data for the first K = 5 cycles, among whom 70 patients had at least one cycle with complete toxicity data available. To test our method with a small sample, we randomly selected n = 10 patients having N = 33 complete forms. Among the 10 included patients, only 3 toxicities of grade 3 (asthenia) were observed (see Table  10  for description of covariates). For the case study, RMSEs were computed over these patients. Results are shown in Table  11. The best performance was obtained by WBS3, with the smallest RMSE and two variables selected: age > 80 years and asthenia of grade 3 respectively linked to dose reductions of -13. 4 mg/m 2 and -85. 3 mg/m 2. Asthenia 3 is selected by all methods, except the Lasso, and age is selected by these same methods, except WBS2.