dataesr/scientific-paragraphs-categorization huggingface dataset:
, 1990; Benton et al. , 2000; Britt et al. , 2000; Carrano et al. , 2002; Piechowski et al. , 2014). More recently,  Griffin & Nesbitt (2016)  demonstrated that this feature no longer appeared dimorphic when accounting for ontogenetic series in the silesaurid Asilisaurus. At a larger scale,  Mallon (2017)  performed a statistical investigation on a large set of studies that hypothesized sexual dimorphism based on a wide diversity of anatomical proxies across the major clades of non-avian dinosaurs. However, among the 48 described occurrences, only nine datasets were suitable for statistical test, among which only one was considered to rigorously demonstrate dimorphism. Indeed, the combination of a principal component analysis and a mixture modelling analysis highlighted that the shift in posterior inclination between the 8 th and 9 th dermal plates of Stegosaurus mjosi was best explained by a bimodal distribution.
Yet, there is not robust evidence to postulate that the dimorphism shown in dermal plates would be sexspecific  (Saitta, 2015). As a consequence, it appears that no dataset enabled to rigorously demonstrate the presence of sexual dimorphism in non-avian dinosaurs  (Hone et al. , 2020). According to  Mallon (2017) , one should review three issues when demonstrating sexual dimorphism on extinct organisms: 1) sample size in order to ensure population representativeness; 2) methodology in order to use only suitable analyses to study sexual dimorphism, such as mixture modelling; (3) any other intraspecific morphological variation such as ontogeny and pathology, as well as taphonomy. Here, we studied the intraspecific femoral variability among a remarkable population of ornithomimosaurs  (Allain et al.
Moreover, the exceptionally high minimal number of individuals among the herd offers a singular opportunity to test for the presence of dimorphism and characterize its variation. We used a 3D Geometric Morphometric (3D GMM) approach that combines anatomical landmarks and sliding semilandmarks along curves and surfaces on both complete and fragmented femora and tibiae (Fig. S1A-B )  (Gunz et al. , 2005; Gunz and Mitteroecker, 2013). This method is well suited to study biological objects, including limb bones, and to detect subtle intraspecific shape variations  (Zelditch et al. , 2012; Botton-Divet et al. , 2016)  such as dimorphism  (Fabre et al. , 2014). We then investigated the resulting dataset using Principal Component Analyses (PCA) and Gaussian Mixture (GM) modelling as clustering analyses.
This clustering analysis calculates the number of Gaussian distributions present in a dataset by maximum likelihood estimations and has been demonstrated as a well-suited method for the identification of dimorphism  (Godfrey et al. , 1993; Dong, 1997; Fabre et al. , 2014; Manin et al. , 2016; Mallon, 2017; Saitta et al. , 2020)  Institutional abbreviation: ANG: Angeac-Charente Collection, Musée d'Angoulême, Angoulême, FR.
, 2015)  demonstrated that young male domestic ducks (Anas platyrhynchos) had more laterally curved femora than females, and that this sexually dimorphic feature disappeared along ontogeny. However, to our knowledge and aside  Duggan et al. (2015) , data about femoral obliquity is generally unavailable in most studies including sex determination in birds and other sauropsids. Therefore, because the femoral dimorphic features we highlighted in the Angeac-Charente ornithomimosaur herd were also demonstrated to vary between sexes in more or less closely related extant vertebrate clades, we infer it to be sexual. We found no allometry along the first PC axis (Table  S1 ), which indicates that the dimorphism we highlighted is not related to size. Ontogenetic allometry was often misinterpreted as sexual dimorphism in archosaurs, as demonstrated in the early dinosauriform Asilisaurus kongwe, the crocodylian Alligator mississippiensis and the bird Rhea americana  (Griffin and Nesbitt, 2016; Hone and Mallon, 2017; Hedrick et al.
3. 0. 0. 6  (Wiley et al. , 2005). We digitized anatomical landmarks and sliding semilandmarks along curves on each specimen and sliding semilandmarks along surfaces on one specimen (ANG 10 90), referred to as "the template" hereafter  (Cornette et al. , 2013). We then automatically projected the sliding semilandmarks along surfaces of the template onto every other specimen following the spline relaxation of semilandmarks along curves using the function "placePatch" of the Morpho package v. 2. 8  (Schlager, 2017). Then, we performed five iterations of another spline relaxation between landmark configurations of the template and the ones from every other specimen using the function "relaxLM" of Morpho. Finally, we performed a partial Procrustes fitting in order to compute a Procrustes consensus of every configuration and used it as a target for the two last iterations of spline relaxation using the function "slideLM" of Morpho.
These three steps of spline relaxations ensured that every semilandmark position was geometrically homogeneous in all specimens  (Gunz et al. , 2005). Finally, we performed a Generalized Procrustes Analysis (GPA) using the function "gpagen" of the R package geomorph v. 3. 3. 1  (Adams and Otárola-Castillo, 2013)  in order to align each femur in the Cartesian coordinate system by superimposing them based on their landmark configuration and to rule out the effect of size, location and orientation of the different landmark configurations  (Gower, 1975; Rohlf and Slice, 1990; Zelditch et al. , 2012).
As recommended by Mallon  (Mallon, 2017) , we performed mixture modelling analyses without a-priori knowledge about the number of groups in order to estimate how many morphological clusters would stand out in our dataset, if any, along each PC axis. Gaussians are well-suited functions to describe a biological population, especially when applied to a morphometric dataset  (Baylac et al. , 2003). We used the R package Mclust v. 5. 4. 7, which calculates the most-probable number of clusters in a dataset based on the detection of Gaussian distributions by maximum likelihood estimations  (Scrucca et al. , 2016). Bayesian Information Criteria (BIC; e. g. , an approximation of Bayes factors for comparing likelihood) were used to choose which model, among the several ones available, fitted best with our dataset (i.
e. , the model with the highest BIC), while simultaneously estimating the number of Gaussian distributions  (Fraley and Raftery, 2007). We computed 3D visualizations that highlighted which feature varied the most along each axis, and between clusters when dimorphism was identified. To do so, we first computed a 3D consensual mesh of all specimens of the sample by using the function "tps3d" from the R package Morpho v. 2. 8  (Schlager, 2017)  which performed a spline relaxation that minimized the bending energy of a Thin Plate Spline (TPS) between the template landmark configuration and a mean landmark configuration (obtained during the GPA). Then, the function used the resulting TPS deformation to warp the 3D mesh of the template onto the mean shape in order to compute a 3D consensual mesh  (Bardua et al.
Acknowledgments We warmly thank  D. Augier ,  J. -F. Tournepiche  ( The museum of Angoulême ) for access to specimens,  A. Aumont ,  G. Baron  ( La Rochelle Museum ) for access to specimens in temporary exhibit,  F. Goussard  ( MNHN ) for 3D digitizations with NextEngine and  L. Rozada  and  J. Goedert  ( MNHN ) for help with.
Objectives In evidence synthesis practice, dealing with studies with no cases in both arms has been a tough problem, for which there is no consensus in the research community. In this study, we propose a method to measure the potential impact of studies with no cases for meta-analysis results which we define as harms index (Hi) and benefits index (Bi) as an alternative solution for deciding how to deal with such studies. Methods Hi and Bi are defined by the minimal number of cases added to the treatment arm (Hi) or control arm (Bi) of studies with no cases in a meta-analysis that lead to a change of the direction of the estimates or its statistical significance. Both exact and approximating methods are available to calculate Hi and Bi. We developed the "hibi" module in Stata so that researchers can easily implement the method.
Real-world investigation We collected data from the Cochrane Database of Systematic Reviews from 2003 to 2018 for those binary metaanalyses that contained at least 1 study with no cases. A detailed description of the data collection process has been published previously  [20] [21] [22]. In brief, a program based on R software was developed to download the rm5 files for each Cochrane review automatically, containing the metadata for each review. The rm5 files were further transferred into csv files that formed the current dataset (a flow diagram is presented in Figure  S2 ). From the 6781 Cochrane reviews, we collected a total of 61,090 metaanalyses with binary outcomes, of which 658 contained at least 1 study with no cases. We further excluded 108 MA-CDZ and 108 MA-CSZ, leaving 442 meta-analyses eligible for the analysis in this article  [11].
Discussion In this study, we proposed the harms index and benefits index to measure the potential impact of studies with no cases on the results of meta-analyses. To the best of our knowledge, this is the first attempt to measure the robustness of meta-analysis in terms of studies with no cases. Considering the difficulties in dealing with studies with no cases in meta-analyses, this method provides a reasonable solution for researchers trying to decide whether studies with no cases can be discarded from their evidence synthesis. In addition, we provided an approximating method for Hi and Bi when the number of studies with no cases is large. Based on the real-world dataset, our method suggested that the approximating method worked well, especially for Hi. In addition, for meta-analysis with at most 6 studies with no cases, about 21.
, 2021) , which was developed for handling highly anisotropic elements. In this work, we demonstrate mesh adaptation on a hybrid type of flow: a nacelle under crosswind conditions, leading to inlet distortion. The focus is on "feature-based" adaptation but on two types of meshes: pure tetrahedral meshes with anisotropic adaptation and multi-element meshes with isotropic adaptation. As with our previous work, the former is resolved by the vertexcentered, compressible solver Wolf. The latter approach is combined with the cell-centered, compressible solver elsA, a more standard solver, typical of CFD software used in the aero-engine community today. The objective of this paper is twofold: (1) demonstrate the abilities of unstructured body-fitted mesh adaptation in this complex flow, characterised by flow separation, hysteresis and low overall Mach number, with both standard and more advanced numerical approaches and solvers and (2) compare between the typical multielement meshes with isotropic tetrahedra, commonly used in the industry today, with highly anisotropic tetrahedral meshes provided by the mesh adaptation algorithms.
Acknowledgement The work presented in this paper started when F. H. was a guest Professor at Trento University in October 2020 within the Quantum@Trento program. F. H. would like to warmly thank  Alessandra Bernardi  and  Iacopo Carusotto  for making this invitation possible. This work was partially supported by the  French Investissements d'Avenir programme , project  ISITE-BFC  (contract  ANR-15-IDEX-03 ). V. G. is partially supported by  Italian GNSAGA-INDAM.
Acknowledgments. We are grateful to  Laurin Köhler-Schindler ,  Stephen Muirhead ,  Gábor Pete  and  Alejandro Rivera  for inspiring discussions. Moreover, we are grateful to  Christophe Garban  for helpful comments on a previous version of this paper. This project has received funding from the  European Research Council (ERC)  under the  European Union 's  Horizon 2020 research and innovation program  (grant agreement No  851565 ). Both authors are supported by the  NCCR SwissMAP  funded by the  Swiss NSF ; HV is supported by the  SNF  Grant No  175505.
Concerning medical imaging, we shall focus on computer-aided cytology. Cytopathologists usually have to study the morphology and texture of cytoplasm and nuclei as imaged in microscopy to make a diagnosis decision. This task can be tedious since every slide supporting sample contains millions of cells and the presence of infected cells is rare. The use of PDEs on graphs for computer-aider cytology has been shown to be efficient for segmentation and semi-supervised classification of cells  24. All the results concerning cytology are produced using the database of the Cherbourg University Hospital. A software called PdESigraph is available upon request and will be accessible online soon. It contains all the necessary material for non-mathematicians to construct the appropriate graphs and apply the presented algorithms for the different inverse problems.
As for data clustering, it consists in splitting data into different families of objects sharing similar properties, such as infected cells in a medical database, etc. All these tasks can be achieved using the eikonal Eq. (  16 ), with h ≡ 1 and labels propagation as described before. One of the advantages of this formulation is that it allows segmentation on any graph representing images. In the examples below, we use a 4-adjacency grid graph to build an image partition. The obtained region map is then turned into a RAG. To allow labels growing beyond local neighbors, each vertex neighbor is extended by a k-NN based on mean color value. In the following examples, we perform segmentation using superpixels decomposition which allows reducing image complexity by regrouping pixels in a region map while preserving contours.
Thanks to this approach, only few seeds are needed to perform efficient segmentation of images containing multiple and non-adjacent objects to detect. Another application we can consider is indexation. In fact, after segmenting cells using the eikonal equation, we get a database of cells which can be represented in the form of a graph. The top of Fig. 4b  illustrates some abnormal cells that will be used as seeds. Then, using the eikonal equation one can compute the distance map and thus, find the closest cells to the abnormal cells, as illustrated in the bottom of Fig. 4b  where we can see 16 cells amongst the database that are the closest to the seeds. We conclude this section by applying our approach to semi-supervised classification of cells in a cytological slide into normal and abnormal classes.
We first perform segmentation using the eikonal equation as discussed above to extract nuclei. We used 10% seeds on a dataset of 3956 cells extracted from a cytological slide divided by the cytologists into 4 classes where nuclei are described by characteristics concerning the form, surface, color, and the texture of cells, etc. Then we perform label propagation using the eikonal equation (with p = 1, 2 ) on a nearest neighbour graph as described in the previous section. This gives the result illustrated in Fig. 5  which are promising since we get 98. 47% classification accuracy for p = 1 and 98. 27% for p = 2. These algorithms are present in the Antarctic software, which was developed during the phd thesis of X. Desquenes  35  to provide an accessible support to pathologists for the classification and the segmentation of cytological slides.
Numerical experiments In the last section, we present some numerical experiments to illustrate the linear convergence behaviour of PDHG and RAPDHG 1. We will first look at a two linear program to show that the linear rate of RAPDHG can be much faster than PDHG's. Then, we will exemplify the limits of the methods with a ridge regression problem where restarted averaging does not help and a non-polyhedral problem where we do not observe a linear rate of convergence.
Small linear program The first experiment is on a small LP where the dual optimal set is known: min x∈R 4 ,x≥0 -7x 1 -9x 2 -18x 3 -17x 4 2x 1 + 4x 2 + 6x 3 + 7x 4 ≤ 41 x 1 + x 2 + 2x 3 + 2x 4 ≤ 17 x 1 + 2x 2 + 3x 3 + 3x 4 ≤ 24 To give an estimate the quadratic error bound constant, we compute for several values of β the quantity η 2. We can do it because Z * is known for this small problem. Using a similar idea we can also get an estimate of the metric subregularity constant of the Lagrangian's gradient, here η ≈ 0. 0187. On Figure  3 , we can see that the actual rate of convergence is rather close to what is predicted by theory. Moreover, RAPDHG is much faster than PDHG. Yet, note that thousands of iterations for a LP with 4 variables and 3 constraints is not competitive with the state of the art.
Larger polyhedral problem We then run an experiment on a more realistic problem. We run PDHG and RAPDHG with adaptive restart on the following sparse SVM problem: min w∈R d n i=1 max(0, 1 -y i x i,: w) + w 1 where (y i , x i,: ) 1≤i≤n are the data points from the a1a dataset  [7]  (d = 119 and n = 1, 605). We normalized the data matrix so that x :,j 2 = 1. The convergence profile is given in Figure  4. The behaviour of the algorithms is similar to what was seen in the small size problem. Here however, we can see clearly two phases. In the beginning, we observe a sublinear convergence, where restart and averaging does not help. Then the linear rate kicks in after a nonnegligible time. We believe that it comes from something related to the condition G β (z; z * ) ≤ R in Proposition 13. Note that this cold start phase is quite long.
Ridge regression In this experiment, we test on a problem where restarting does not help. We consider least squares with 2 regularization min  where A and b are given by the real-sim dataset  [7]. Since we know the strong convexity-concavity parameter of the Lagrangian, we choose the step sizes σ and τ as in Section 5. 1. As a consequence, PDHG has a convergence rate that matches the theoretical lower bound for this class problem and cannot be improved. We can see on Figure  5  that, as expected, restart and averaging does not help: zk is consistently better than zk so that RAPDHG with adaptive restart selects the same sequence as PDHG and the the two curves match. We added a comparison with restarted-FISTA  [15]  to show that the choice of step sizes indeed suffices to get an algorithm with accelerated rate.
This work was supported by the  Agence National de la Recherche  grant  ANR-20-CE40-0027 ,  Optimal Primal-Dual Algorithms (APDO ) We denote C(z) = ∂f (x) × ∂g * (y) (where × denotes the Cartesian product), B(z) = [∇f 2 (x), ∇g *.
For each sample, the Poisson mixture is fitted with the same four distributions and the best model is kept using a Bayesian framework. This is done using the language R (R Core Team, 2021) and the rstan (Stan Development Team, 2020) package to estimate the hyperparameters by MCMC. The best model is then kept using the highest posterior model probability. Those probabilities are approximated using the bridge sampling computational technique  (Meng & Wong, 1996)  and the dedicated R package Bridgesampling  (Gronau et al. , 2020). All results are based on the following priors: a Gammað1,1Þ distribution for positive parameters and a Normalð0,1Þ for real parameters. Moreover, we simulated for each sample four MCMCs with 10,000 iterations each in order to ensure reasonable convergence for parameter estimation and for the posterior model probabilities.
In order to study how useful the discrete excesses can be, various Poisson mixtures have been simulated. Here, we fixed the sample size to n ¼ 1000, the threshold u to be the 95th or 97. 5th empirical quantiles, and simulated 1000 samples for each mixing distribution. For each sample, the discrete excesses are extracted, and the evd R package  (Stephenson, 2002)  is used to estimate the GPD parameters by maximum likelihood. Based on these estimations, the modified Anderson Darling test for the goodnessof-fit is applied. Finally, for the samples such that the GPD appears to be adequate, we test H 0 : γ ¼ 0 versus H 1 : γ ≠ 0. To do so, we fit these two models, evaluate the corresponding log likelihoods L 1 and L 0 , and conclude with the deviance statistic D ¼ 2 L 1 À L 0 ð Þwhich follows approximately a χ 2 1 distribution under suitable conditions  (Coles, 2001).
ACKNOWLEDGEMENTS This research was supported by the  GAMBAS  project funded by the  French National Research Agency  ( ANR-18-CE02-0025 ) and the  French national programme LEFE/INSU. Eric Marchand 's research is supported in part by the  Natural Sciences and Engineering Research Council of Canada. Finally, we thank two reviewers and Associate Editor for useful comments that led to an improved manuscript. ORCID Samuel Valiquette  https://orcid. org/0000-0001-5463-1586.
A compactness by concentration type argument is used to prove the convergence of minimizing sequences towards the heteroclinic solution. We point out that a complete existence proof for orthogonal domain walls for the Rayleigh-Bénard convection problem requires an additional analysis consisting in showing that the heteroclinic orbit in Theorem 1 persists as a perturbed heteroclinic of the full 12-dimensional reduced system, hence without restricting to the leading order system (1. 1)-(1. 2). Such a proof was given for symmetric domain walls in  [7, 8]. Acknowledgments: M. H. was partially supported by the project Optimal (ANR-20-CE30-0004) and the EUR EIPHI program (ANR-17-EURE-0002).
The majority of respondents were adults (60% between 30 and 60 years old) and the number of women was equal to the number of men (52%). However, the sample was not drawn with reference to a prede ned distribution; it is smaller and less representative than the Dakar sample. The two samples can therefore only be compared with caution. However, this comparison is made possible by the fact that the questionnaires used in France and Senegal were exactly the same with a few exceptions: age was assessed with two questions in Dakar in order to obtain the o cial and, above all, the real age of the individuals; ethnicity was asked in Dakar but not in Seine-Saint-Denis. In both territories, data were collected through directed, individual interviews carried out face-to-face using a questionnaire. In-person interviews ranged from 15 minutes to more than 30 minutes, depending on respondent availability and desire to talk.
Introductory remarks on viral disease dynamics The articles in this Research Topic show, many advances have been made in public health research, especially in the field of data collection, modeling (deterministic and random), and prediction: (i) public databases on COVID-19 have multiplied [see COVID-19 Open Data Repository (1) for example 301 public sites around the world allowing access to COVID-19 data], (ii) review articles on COVID-19 outbreak including statistics and models are numerous (in Frontiers in Public health alone, the site in WHO COVID-19 Research Database (2) counts 173 articles under heading Systematic review/Meta-Analysis) and (iii) the number of articles using a formal approach predicting COVID-19 waves is constantly growing (Google Scholar lists for example 144,000 articles with the query "modeling and forecasting COVID-19 pandemic").
The various facets of the recent mathematical and statistical models of viral disease data in this Research Topic In the Research Topic entitled "Mathematical and statistical modeling of infection and transmission dynamics of viral diseases, " the twelve papers are representative of different mathematical and statistical approaches to the recent COVID-19 pandemic, Hepatitis A/B virus, and Mpox disease data: We first present articles that deals with the recent COVID-19 pandemic. In Tormos et al. analyzed the role of in-person school reopening in Spain on the evolution of COVID-19 infections using an interrupted time-series perspective by exploring the dataset and modeling the dynamics of the disease in different Spanish regions and autonomous communities that reopened schools at varying moments in time during September 2020.