dataesr/scientific-paragraphs-categorization huggingface dataset:
It will be of crucial importance to reduce the error bars on experimental data on v 3 {4} in central Pb+Pb collisions, in order to check whether the ratio v 3 {4}/v 3 {2} is independent of centrality, as suggested by ALICE data. Indeed, this observation does not seem compatible with existing models of initial conditions. The parametrizations of the initial state that are suitable for describing central Pb+Pb collisions, can not be employed in central p+Pb collisions, and vice versa. Indeed, the Glauber model, which is excluded by Pb+Pb data, provides the only reasonable description of p+Pb collisions. We do not consider this as a contradiction, because we are merely trying to identify the parametrization which captures the initial geometry in a given system, and we do not aim at a unified description of all systems.
ACKNOWLEDGEMENTS J. N. H. acknowledges the use of the Maxwell Cluster and the advanced support from the  Center of Advanced Computing  and  Data Systems  at the  University of Houston  and was supported by the  National Science Foundation  under Grant No. PHY-1513864. We thank  Matt Luzum  for useful discussions. G. G. wishes to thank  Scott Moreland  for kind assistance with the use of  T R ENTo.
In the sections to follow, we first review the corresponding estimation methods so far published in the statistical literature. Simulations were conducted to assess the performance of the proposed AR estimators. The methods were then applied to data on menopausal hormone therapy (MHT) and breast cancer from the E3N women cohort (Étude Épidémiologique auprès de Femmes de la Mutuelle Générale de l'Éducation Nationale)  [11]. For the purpose of our illustration, we considered 38,359 participants who were postmenopausal and free of cancer when they completed a self-administered questionnaire on their past use of any MHT in January 1992. In total, 17,185 (44. 8%) women had ever used MHT at baseline and were considered exposed thereafter. By June 2008 (for a maximal 16. 4 years and mean 14. 0 years of followup), 2,228 invasive breast cancers had been diagnosed (1,106 in unexposed women).
) of the AR as a function of time and their associated variances using the four approaches: two non-parametric approaches corresponding to the case where S 0 (. ) and S(. ) are both estimated by the Kaplan-Meier method (KM) and to the case where S 0 (. ) and S(. ) are estimated by the Kaplan-Meier and the weighted Kaplan-Meier methods, respectively (WKM)  [7] , one semiparametric approach using Cox's proportional hazards model (COX)  [7] , and one parametric approach corresponding to the case where survival functions are estimated assuming piecewise constant hazards (PCH)  [8]  considering four intervals of 5-year width. In the case where no event was generated in any five-year interval, the simulated dataset was discarded and replaced by a new one. We also considered the simpler approach based on Eq.
(  3 ) to estimate a global AR. Results of the time-dependent approaches are presented at times t = τ/4, τ/2, 3τ/4 and τ (respectively, 5, 10, 15 and 20 years). For the nonparametric and semiparametric approaches, estimates were obtained at times actually observed in the dataset so we considered values taken at the closest preceding time point. While nonparametric estimations are based on data available until the time of interest, semiparametric and parametric methods use data available over the whole follow-up period. To allow for a fairer comparison under the proportional hazards assumption, we also computed semiparametric and parametric estimators after censoring observation times at either τ/4 or τ/2. The parametric approach was then based on one or two interval(s) of 5-year width respectively.
Acknowledgements The authors wish to thank  Pascale Tubert-Bitter  for her constructive comments,  Mohammed Sedki  for statistical advice and  Agnès Fournier  for kindly sharing the E3N data. The authors are also grateful to all participants, practitioners and study staff of the E3N study. The E3N cohort is conducted with the financial support of  'Mutuelle Générale de l'Éducation Nationale' (MGEN) ; the  European Community ; ' Ligue nationale contre le Cancer '; ' Institut Gustave-Roussy '; ' Institut National de la Santé et de la Recherche Médicale' (Inserm) ; and ' Fondation de France '.
Funding This research was supported by the  French Medicines Agency ('Agence Nationale de Sécurité du Médicament et des produits de santé', ANSM)  and  French Government 's  Investissement d'Avenir program ,  Laboratoire d'Excellence "Integrative Biology of Emerging Infectious Diseases " (grant number  ANR-10-LABX-62-IBEID ). MG was a recipient of PhD grant from the  French Ministry of Research.
To patch together the estimates, we use implicitly a metric which should satisfy some admissibility properties. Although we have avoided in the main part of the text to resort to very general tools of pseudodifferential calculus, we hope that Section 7 could bring a more conceptual vision of the technicalities included in the previous sections. The paper ends with three appendices recalling some facts of geometry and pseudodifferential calculus. Acknowledgements. The first author is partially supported by the Agence Nationale de la Recherche under grant GERASIC ANR-13-BS01-0007-01. 2 A sharp estimate for a non-selfadjoint operator on R d.
Materials and Methods Epidemiological Data. Our epidemiological data includes the number of new suspected Chikungunya cases within each locality for each week during the first nine months of the outbreak (from December 2013 to August 2014). Here, we use the number of suspected cases rather than the number of confirmed cases because biological confirmation has not been made routinely after the first 5 months owing to logistic complexity, and thus does not reflect the disease activity over the whole period. Time series of suspected cases is frequently used to estimate epidemiological parameters, especially for infectious diseases with low symptom specificity like influenza viruses  25. These incidence time series have been estimated based on a network of sentinel practitioners that covers all the localities on the island with at least one medical doctor, resulting in 28 localities considered (6 localities do not have a MD).
The parameter τ represented the lag between the impact quantified on Twitter and its consequences for transmission. We have assumed that the behavior measured on Twitter could be a real-time indicator (τ = 0), a delayed indicator (τ = 1) when individuals talk on Twitter after having applied the protection, or an anticipated indicator (τ = -1) when the Twitter activity reflects the behavior change one month before its impact on mosquito population. The β(t) function is constrained positive. We then looked for the best estimation of x 1 , x 2 and x 3 that allowed the mathematical model to reproduce the epidemiological dynamics observed. Technically, we maximized the likelihood of the model predictions knowing the data by assuming a Gaussian distribution of the model errors through the Nelder-Mead algorithm implemented within the optim package in R  28  (Supplementary Materials S3).
Instead of excitation function it is better to use the EAAM (effective angular momentum) function c, whose axial component differs only in sign, j 3 ¼ Àc 3. Good agreement between LOD variability and global EAAM, as seen from Fig. 1 , allows us to assume in this work that DLOD/LOD ¼ c 3 holds, and all the components of c 3 obtained below influence Earth's rotation, resulting in LOD variations. To have a suitable unit to estimate this effect throughout this article we will multiply c 3 by the conventional value of LOD ¼ 86,400,000 ms, converting EAAM units to milliseconds. In contrast to global EAAM, we call the regional inputs as AAM (without E). We used NCEP/NCAR reanalysis data which were obtained through meteorological data processing with use of NWP (numerical weather prediction). The interpolated fields of wind and pressure all over the globe are available since 1948 with 6-hour steps.
Acknowledgements This work is supported by  Russian Foundation for Basic Research  grants No. 17-05-00989 , No. 16-05-00753 ,  NRU HSE  and visiting grants positions at Paris observatory and Wuhan university for the first author. The  Ohio State University (OSU)  component of the research was partially supported by grants by  NSF/IGFA Belmont Forum Project  (Grant No. ICER-1342644 ), and by the  Chinese Academy of Sciences/SAFEA   International Partnership Program for Creative Research Teams  (Grant No. KZZD-EW-TZ-05 ). We are especially thankful to  Y. H. Zhou  from  Shanghai Observatory  for providing AAM data grids. We thank the anonymous reviewers and the editor for their constructive comments which have led to an improved manuscript.
Acknowledgements We are grateful to  J. Caetano ,  M. Heinze ,  Y. Jiang ,  V. Kazakov ,  S. Komatsu ,  I. Kostov ,  A. Liashyk ,  D. Medina ,  D. Serban ,  N. Slavnov ,  F. Smirnov ,  E. Sobko ,  S. Valatka ,  B. Vicedo ,  J. -B. Wu ,  K. Zarembo  and  Y. Zenkevich  for discussions and helpful comments, and to  S. Valatka  for collaboration at an early stage of this project. We are especially grateful to  I. Kostov  and  D. Serban  for many discussions. We also thank  J. Caetano  and  Y. Jiang  for sharing some of their Mathematica code. We would like to thank  Ecole de Physique des Houches and Humboldt University Berlin , where a part of this work was done, for hospitality. The research leading to these results has received funding from the  People Programme  ( Marie Curie Actions ) of the European Union's  Seventh Framework Programme   FP7/2007-2013/ under REA Grant Agreement No 317089  (GATIS), from  European Research Council  ( Programme Ideas ERC-2012-AdG 320769 AdS-CFT-solvable ) and from the  ANR  grant  StrongInt  ( BLANC-SIMI-4-2011 ).
Acknowledgments: We are grateful to  Igor Kortchemski  for comments on a preliminary version of this work and for providing us with reference [1]. We also thank an anonymous referee for many useful suggestions and corrections. We thank the project "  Émergence: Combinatoire à Paris " funded by the city of Paris for supporting the visit of the first author during fall 2015. The first author is supported by the  ERC-Advance  grant  291092 , "Exploring the  Quantum Universe" (EQU) , while the second author is supported by  ANR-14-CE25-0014  ( ANR GRAAL ) and  ANR-15-CE40-0013  ( ANR Liouville ).
Acknowledgments:  J. -C. Wallet  warmly thanks  F. Latrémolière  for various exchanges and discussions on algebraic and group cohomological aspects connected to the present work. T. Poulain  thanks  COST Action   MP1405  QSPACE for partial financial support. General discussions with  M. Dubois-Violette  are gratefully acknowledged. This work is partially supported by  H2020   Twinning  project No. 692194 ,  RBI-T-WINNING  and we also acknowledge the support by  Croatian Science Foundation  under the project  IP-2014-09-9582.
and  D. Pardo  were partially funded by the  Projects of the Spanish Ministry of Economy and Competitiveness  with reference MTM2013-40824-P,  MTM2016-76329-R ,  MTM2016-81697-ERC  and the  Basque Government  Consolidated Research Group Grant  IT649-13  on " Mathematical Modeling, Simulation , and  Industrial Applications  ( M2SI )". Á. Rodríguez-Rozas  and  D. Pardo  were also partially funded by the  BCAM "Severo Ochoa " accreditation of excellence SEV-2013-0323 and the  Basque Government  through the  BERC 2014-2017 program. Á. Rodríguez-Rozas  acknowledges support from  Spanish Ministry  under Grant No. FPDI-2013-17098. D. Pardo  was also partially funded by the  ICERMAR  Project  KK-2015/0000097. I. Muga  was partially funded by the  CYTED   2011  project  712RT0449  and the  FONDECYT  project  1160774.
Our model can accommodate a meta-analysis in the presence of rare events, without excluding single-or double-zero studies from the dataset and can handle the case of incomplete reporting in the original studies, i. e. when cross-classified information is not provided. The paper is structured as follows. In section 2, we describe the datasets from orthopaedics and ophthalmology we use to exemplify our methods. We chose these particular examples because they include studies of different designs and they cover both the case of rare and common outcomes. In section 3, we present our model and discuss how it can be applied for the case of studies of different designs. In section 4, we present results from simulations that we conducted in order to assess the performance of our model and to compare it with the previously recommended beta-binomial model.
Example datasets 2. 1 Two surgical treatments for carpal tunnel syndrome Our first example comes from a Cochrane review  22  that compared the endoscopic release vs. any other open surgical intervention for carpal tunnel syndrome (CTS). CTS is a painful compression of a nerve at the root of the hand. One of the safety outcomes was the occurrence of minor complications (such as numbness around the incision or superficial infection) reported in 24 studies. Minor complications were rare: five out of 24 studies were single-zero and four were double-zero. In section 1. 1. of the online Appendix, we provide a detailed description of the data. We categorize the 24 studies in four different types, depending on their design and reporting:. Unilateral design (studies 1-12): patients received one intervention in one of their arms.
Simulations 4. 1 Data generation procedure and description of the scenarios We performed a small-scale simulation study to assess the performance of the model we proposed in this paper. We limited the simulations to the case of studies with bilateral design where only the marginal numbers of events are reported, and among which there is variability (heterogeneity). We explored a range of different scenarios. For each scenario, we simulated 100 datasets, with each dataset corresponding to an independent meta-analysis. Scenarios 1-20 aimed to compare our model with the bivariate beta-binomial model. This model has been previously recommended for meta-analysing rare events. 8 For these scenarios, we simulated 20 studies for each meta-analysis. Two additional scenarios (21 and 22) aimed to explore the importance of specifying informative priors for the parameters of our bivariate binomial model.
Analyses of the simulated datasets The simulated datasets were analysed using the bivariate binomial model discussed in section 3. 2. The model is also presented in more detail in section 2 of the online Appendix. We performed our analyses in OpenBUGS,  38, 39  the code is available in section 9 of the online Appendix. For each analysis, we simulated a single chain of 20,000 samples, and we discarded the first 5,000 samples. This was deemed to be sufficient based on some initial runs and also after visually inspecting the posterior distributions. 40 or the analysis of scenarios 1-20, we chose between using weakly informative prior distributions centred near the true value of the parameters, vague priors and misspecified priors for the correlation. These choices are described in detail in Table  4  of the online Appendix (section 10.
1). In addition, these scenarios were analysed using the bivariate (Sarmanov) beta-binomial model, which accounts for correlations in the 2 Â 2 tables. 21 For this, we used a routine in R  37  provided by Chen et al. 21 We also checked results by comparing with results obtained from the mmeta package in R, which also implements the beta-binomial model. 41 We compared our model with beta-binomial in terms of (a) mean bias; (b) mean squared error (MSE) (the mean of the squared bias); (c) empirical coverage (the percent of meta-analyses that included the true effect in their 95% credible interval (CrI)); (d) empirical power (percent of meta-analyses that rejected the null hypothesis of no treatment effect, when the true treatment effect was non-zero); and (e) the gain in precision (bivariate binomial model over beta-binomial model).
This was calculated as the percentage reduction of the mean width of the 95% CrI obtained from our model as compared to the 95% confidence interval from the beta-binomial model. The datasets generated under scenarios 21 and 22 were analysed multiple times, using only the model presented in this paper. Each dataset was analysed using first vague priors for all parameters, and then using vague priors for all model parameters except for one at a time. Details can be found in Table  5 , section 10. 2 of the online Appendix.
Surgical techniques for correcting myopia Two studies in this dataset had unclear design. We analysed these studies as if they were of unilateral design. We used the following prior distributions for the model parameters: u $ UðÀ5, 5Þ; u $ Uð0, 5Þ and $ UðÀ2, 2Þ. For heterogeneity, we use an informative prior distribution log  2  À Á $ NðÀ1:69, 1:68 2 Þ based on the empirical evidence. 33 We explore two options for correlation, $ Nð0:2, 0:1 2 Þ (low correlation), and $ Nð0:5, 0:1 2 Þ (moderate-high correlation). Results are presented in Figure  4. For our primary model, the posterior median estimate for u was 1. 35 (-0. 16, 2. 99) and for u was 2. 20 (1. 34, 3. 90). Accounting for correlations using our approach led to an increase in precision of the pooled estimates. For the case of random effects model, some of the increase in precision was again counterbalanced by an increase in the estimates for 2 , as in the CTS example.
36 Due to this fact, the use of frequentist approaches instead of Bayesian approaches is sometimes advocated. We understand the reasoning behind this view; in this paper, however, we argue in favour of a Bayesian approach. We think that the scarcity of information due to the rarity of events should not be seen as an argument against the use of Bayesian methods. On the contrary, we think that meta-analysts should opt for using Bayesian methods when they have the opportunity to include high quality, trustworthy external evidence in the analysis. The major limitation of our model lies on its complexity. The software code we provide might be computationally heavy when studies have very large sample sizes. This may be especially true if there are large, mixed-design studies in the dataset. Moreover, embarking into this complicated modelling will only make a difference in the estimates if the corresponding correlation is large.
Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: OE was supported by the  Swiss National Science Foundation  (grant title: ' Enhancing methods for evaluating the comparative safety of medical interventions '). GR was funded by the  German Research Foundation (DFG)  (grant  RU 1747/1-2 ). GS is a  Marie Sklodowska-Curie Fellow  ( MSCA-IF-703254 ).
Introduction Dose-finding studies are carried out in the very early stages of clinical evaluation, along with the first assessment of safety and pharmacokinetics (PK) in humans. The phase I dose-finding study is usually the first trial in human subjects and has the goals of evaluating the safety of the tested drug, finding the maximum tolerated dose (MTD), and identifying a recommended dose (RD) for subsequent trials. The PK data collected during such a study provides a first step in describing the dose-concentration and dose-toxicity response relationships. Phase II studies then evaluate efficacy in patients, and may involve pharmacodynamic (PD) markers. Phase I trials usually include a small number of healthy volunteers  (Chevret, 2006 ). An exception is in oncology, where, due to the potential high toxicity of drugs, even phase I trials are performed directly on patients  (Chevret, 2006).
The design and data collection will be more complex, as getting PK measures in real time during the trial can be challenging and expensive. PK data are generally collected and analyzed before going to Phase II, but usually not at the time of dose allocation in the ongoing Phase I study. On the other hand, in certain areas such as rare diseases, pediatrics, and biomarker-specific subgroups, the size and nature of the population will impose logistic and ethical constraints on clinical trials, limiting the number of patients to be recruited as well as the amount of information that can be obtained for each subject. In such cases, during the early phase, instead of conducting the PK and the dose allocation separately, the possibility to combine both types of information to allow a better estimation of the dose should therefore be considered.
Trial settings In order to compare the dose-finding methods, we simulated subject responses to all doses for each trial. We started by drawing individual PK parameters from the population distributions for each subject, as described in the previous subsection. Then, for each dose level and for all patients we computed concentration measurements to which we added a proportional error drawn from a normal distribution with zero mean and standard deviation of 20%. Finally, we simulated toxicity values at each dose level using Eq. (  13 ). Each simulated dataset was stored and, for each dose-finding method, subject responses were read from this complete dataset. In this way, when two methods coincide in dose allocation, the results of the simulated runs are the same. For each scenario, 1000 trials were simulated.
Partially supported by the  Slovenian Research Agency  ( I0-0035 , research program  P1-0285  and research projects  N1-0032 ,  J1-5433 ,  J1-6720 ,  J1-6743 , and  J1-7051 ). Partially supported by the  ANR  project  Stint  under Contract  ANR-13-BS02-0007 , by the  LABEX MILYON  ( ANR-10-LABX-0070 ) of  Université de Lyon , within the  program Investissements d'Avenir  ( ANR-11-IDEX-0007 ) operated by the  French National Research Agency (ANR) , and by the  ERC  Advanced Grant GRACOL, project number  320812. ‡  Unviersité de Lyon, CNRS, LIP, ENS de Lyon. Partially  supported by  ANR  project  Stint  under reference  ANR-13-BS02-0007  and by the  LABEX MILYON  ( ANR-10-LABX-0070 ) of  Université de Lyon , within the  program Investissements d'Avenir  ( ANR-11-IDEX-0007 ) operated by the  French National Research Agency (ANR).
Stimuli. The experiment was coded using Matlab 8. 4 with Psychtoolbox (v 3. 0. 12) and built on a published experimental design (see ref. 13). Visual stimuli were clouds of grey dots which appeared dynamically on a black computer screen (1024 × 768 pixels, 85 Hz refresh rate). Dots appeared within a virtual disk of diameter 12. 3 to 15. 2 degrees of visual angle; no dots could appear around the central fixation protected by an invisible inner disk of 3. 3 degrees. Two dots could not overlap. The duration of each dot varied between 35 ms and 294 ms, and their diameter between 0. 35 and 1. 14 degrees. A cloud of dots was characterized by its duration (D: total duration of the trial during which dots were presented), its numerosity (N: cumulative number of dots presented on the screen in the entire trial) and its surface (S: cumulative surface covered by the dots during the entire trial).
Statistical Analyses. To analyze the point-of-subjective equality (PSE) and the Weber Ratio (WR), participants' continuous estimates were first transformed into categorical values: a click between the center of the axis and the extreme demarcating '+' ('-') was considered as a '+' ('-') response. Proportions of '+' were computed on a per individual basis and separately for each target dimension and each experimental condition. Proportions of '+' responses were fitted using the logit function (Matlab 8. 4) on a per individual basis. Goodness-of-fits were individually assessed and participants for whom the associated p-values in the control conditions were >0. 05 were excluded from the analysis. On a per condition basis, PSE and WR that were 2 standard deviations away from the mean were disregarded and replaced by the mean of the group.