dataesr/scientific-paragraphs-categorization huggingface dataset:
5. col instance than most competitors. For the wapXXa. col instances, the results obtained by TensCol are not so good as the other algorithms. On the contrary, TensCol excels on large graphs between 900 and 2000 vertices. Remarkably, it established 8 new best-known records (new upper bounds summarized in Table  3 ) by finding legal and equitable colorings with fewer colors compared to the current best-known k * values. As one can observe in Table  3 , TensCol significantly improves the best-known upper bound for three large graphs with 37 colors less for C2000. 9. col, 9 colors less for C2000. 5. col and 8 colors less for R1000. 5. col, while the improvement for the 6 other cases goes from -1 to -3 colors. These new solutions are available at https: //github. com/GoudetOlivier/TensCol.
col, the number of vertices is n = 2368 and the best coloring found in the literature only requires k = 42 colors). It was empirically noticed that the gradient descent used by TensCol is less informative in this case because the number of weights updated (n×k) at each iteration of the algorithm is reduced. In fact, TensCol benefits less from one of its main advantages which is to encode information on the possible colors for each vertex. In the extreme case of binary group assignment, with only two weights per vertex, our weight learning strategy is expected to be less effective compared to other approaches. This is consistent with the presented results that TensCol is more effective for large graphs with a high number of groups such as R1000. 5, C2000. 5 and C2000. 9 colored with 239, 172 and 431 colors (see Tables  6  and 8 ).
To learn more complex dependencies between the group assignments, it would be worth investigating advanced strategies to replace the weight tensor of candidate solutions by a product of tensors or even a deep generative neural network  [3]. Finally, the two coloring problems studied in this work are general models that can be used to formulate a number of real applications, such as scheduling and timetabling (see the book  [27]  for more application examples). The algorithm presented in this work could be adopted by researchers and practitioners to solve such real problems. The availability of the source code of our algorithm will further facilitate such applications.
The first aim of this paper is at filling this gap. Using a Taylor expansion of the double exponential introduced by  [7, 8] , we compute an expansion of the SL construction up to order three, with coefficients that depend on the curvature tensor and its covariant derivatives. Understanding this expansion then allows to give a proof of the convergence of the numerical scheme with iterated constructions, and to improve the scheme to a second-order method. We indeed prove that an arbitrary speed of convergence in 1  n α can be obtained where 1 ≤ α ≤ 2 and n is the number of parallelograms, or rungs of the ladder. This improves over the assumption made in  [18]  that only a first-order convergence speed can be reached with SL. These results are observed with a high accuracy in numerical experiments performed using the open-source Python package geomstats 2  [20].
The same implementation thus allows to observe both geometric structures. Furthermore, the curvature and its derivative may be computed explicitly  [19]  and confirm our predictions. We treat this example in detail to demonstrate the impact of curvature on the convergence, and the code for the computations, and all the experiments of the paper are available online at github. com/nguigs/ladder-methods. The first part of this paper is dedicated to Schild's ladder, while the second part applies the same methodology to the modified constructions. All the results are illustrated by numerical experiments along the way. The main proofs are in the text, and remaining details can be found in the appendices. Fig. 2  The double exponential and its inverse (left) and the neighboring logarithm (right) represented in a normal coordinate system centred at x.
F Implementation Our implementation of the ladder methods, and the fanning scheme are made available online at github. com/nguigs/ladder-methods. The repository also contains a notebook to reproduce all the experiments of this paper. It relies on the open-source Python package geomstats, with its default numpy back-end. The automatic differentiation of the autograd package is used to compute the logs of the infinitesimal schemes, with scipy's L-BFGS-B solver for the gradient descent.
Methods This was an international, blinded, prospective cohort study enrolling patients presenting to two adult large EDs at the Pitié-Salpêtrière APHP-Sorbonne Université hospital in Paris (LPS), France, and the Hospital Universitari Germans Trias i Pujol in Badalona, Spain (UHG). The study assessed MDW's ability to detect the development of sepsis in consecutive adult patients  (18-89 years)  presenting to the ED and who had a CBC-DIFF ordered. The study was registered in ClinicalTrials. gov (NCT03588325) and approved by the ethical committees of the respective participating countries.
Clinical data, follow-up, blinding and adjudication Clinical data at presentation, including past medical history, assessment of vital signs, symptoms, SIRS criteria  [12] , qSOFA  [13]  and SOFA scores  [14] , microbiological testing and treatments were recorded on an electronic case report form and patients followed up for at least 12 h. The clinical research team and physician adjudicators were blinded to MDW results at the time of clinical data entry and during assignment of the patients to Trial Registration ClinicalTrials. gov (NCT03588325). Keywords: Monocyte volume distribution width, MDW, Procalcitonin, C-reactive protein, Emergency department, Sepsis a clinical category. Adjudicators were also blinded to the results of PCT and CRP if not ordered by the treating ED physician. Study subjects were classified by at least two independent physician adjudicators at each site.
Statistical analysis General descriptive statistics and box plots were calculated for cell population variables. The sample size calculations were based on 95% two-sided confidence interval and 80% power. Proc power of SAS 9. 3 was used for calculating sample size based on the approach presented in Johnson et al. [17]  A target sensitivity of 75% with the lower limit of the 95% two-sided confidence interval of 65% and a target specificity of 70% with the lower limit of the 95% two-sided confidence interval of 65% were assumed. A minimum of 189 septic subjects and a minimum of 817 non-septic subjects were needed from both sites combined. Diagnostic ability was evaluated in terms of the area under the ROC curve (AUC), sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), positive and negative likelihood ratios, along with their 95% confidence intervals (CIs).
The score approach was used to calculate CI for sensitivity, specificity, PPV and NPV. Differences in AUC were used to demonstrate the added value of MDW in comparison with WBC alone, calculated using a one-predictor variable logistic model with WBC and a two-predictor variables logistic model with both WBC and MDW, as the predictor, and using sepsis status as the response. A similar approach was applied to analyze the diagnostic ability of PCT and CRP, and the combination with WBC and MDW for sepsis detection. AUC comparisons along with their CI were calculated as described by DeLong et al. [18]  SAS 9. 4 (SAS Institute, Cary, NC) statistical program was used for data analyses.
Acknowledgements The authors wish to acknowledge the support of the various clinical coordinators at  UHG  and  LPS  and the additional physician adjudicators at  UHG  that supported the study. LPS particularly thanks  Ilaria Cherubini  and  Enfel Houas  for excellent clinical research tasks, and  Juliana Fernandes  for dedicated MDW measurement. UHG also acknowledges  Tania Bruno Garcia  and  Maite Calzado Flores  for outstanding help with clinical data collection and monitoring. The authors are also grateful to the following  Beckman Coulter  employees  Mohamad Hasan  and  Gang Xu , for statistical support, to  Justin Rohrbach  for creation of the eCRF & data management and to  Ilya Grigorov  for critical review and edits to this manuscript.
Acknowledgments K. I. is supported by  JSPS Grants-in-Aid for Scientific Research (A)  (No. JP17H01091 ) and  Scientific Research (B)  (No. JP20H01902 ). N. T. is supported in part by  JSPS   Grant-in-Aid for Scientific Research  No. JP18K03623. M. Y. is supported in part by  JSPS   Grant-in-Aid for Scientific Research Numbers   JP18K18764 ,  JP21H01080 ,  JP21H00069. A. Non-invertibility of field-number changing transformations.
Acknowledgements 48 References 48 Acknowledgements. Informal discussions with colleagues at  CEREMADE  are gratefully acknowledged; we thank in particular,  Pierre Cardaliaguet ,  Djalil Chafaï  and  Stéphane Mischler. We also thank  Denis Belomestny  and  Nicolas Fournier  for insightful comments. This work partially answers a problem that was posed to us by  Sylvie Méléard  almost two decades ago (at a time we did not have the proper tools to address it!).
Acknowledgments We thank  F. Brochard-Wyart ,  D. Gonzalez-Rodriguez ,  K. Guevorkian ,  J. -F. Joanny , and  J. Prost  for insightful discussions and useful comments on the manuscript. This work received support from the  LabEx Cell(n)Scale (former CelTisPhyBio) , grants  ANR-11-LABX-0038  and  ANR-10-IDEX-0001-02.
Acknowledgment. N. R. is grateful to  T. Hmidi  for sharing the reference [15]. L. L. T. is grateful to  S. Monniaux ,  J. Olivier ,  S. Rigat  and  E. H. Youssfi  for useful discussions. The authors are grateful to  Bernard Helffer  for many useful comments. L. L. T. is supported by  ANR   DYRAQ ANR-17-CE40-0016-01. E. S has been partially funded by  Fondecyt (Chile)  project #  118-0355.
Compared to controls, dyslexics had higher and more variable detection thresholds. For the weakest proprioceptive stimuli, dyslexics were twice as long and twice as variable as controls. More, proprioceptive acuity strongly correlated with reading abilities, as measured by blind cognitive evaluations. These results unravel a new sensory impairment that cannot be attributed to a lack of reading practice, providing clear support to sensory theories of developmental dyslexia. Protocol registration: This protocol is part of the following registration, ClinicalTrials. gov Identifier: NCT03364010; December 6, 2017. Developmental dyslexia (DD) is a specific learning disorder causing persistent failure to acquire efficient reading. It is the most prevalent neurodevelopmental disorder, affecting about 9% of children 1 , and it has profound lifelong consequences on academic and professional success 2.
Data analysis. We computed all parameters using custom MATLAB programs (MathWorks). Reaction time. We computed visual and auditory reaction times as the time-interval between the presentation of the stimulus and the children's response on the keyboard/trigger. For each child and condition, we computed the mean and the variable reaction time (standard deviation of trials). Electromyography. We rectified, band-passed (30-300 Hz), and integrated (300 ms skipping window) EMG signals. Then, we computed the ratio of EMG before movement start (-300 ms) divided by maximum EMG during movement, and we used this ratio to compare muscle activation/relaxation between groups.
Stimuli All stimuli were prepared and presented using Matlab 2016b (mathworks. com) and the  Psychtoolbox-3 toolbox (psychtoolbox. org; Brainard 1997; Kleiner et al. 2007; Pelli 1997). Twenty different cue letters were used for active and passive conditions. The same cue letter was used once during the active and once during the passive condition in the counterbalanced order. Played back words during the passive condition were chosen from a list of 420 French words  (Ferrand and Alario, 1998). The audio stimuli presented during the task were recorded by male and female native French speakers in a neutral manner and registered in wav format with 11025Hz sampling frequency. The gender of the voice pronouncing words in the passive condition was matched to the participants' gender. During the experiment, participants were equipped with MRI compatible earphones and report buttons for the right hand.
Behavioral data analysis All continuous variables (numerosity performance, accuracy, accuracy ratio and performance monitoring) were analyzed using linear mixed-effects regressions with condition ("active", "passive" or "random", "repeat" for the control order experiment) as a fixed effect and a random intercept by participant and condition. The inclusion of additional random effects was guided by model comparison and selection based on Bayesian Information Criteria. Analyzes were performed using the lme4  (Bates et al. , 2015)  and lmerTest  (Kuznetsova et al. , 2017)  packages in R (R-project. org). The significance of fixed effects was estimated using Satterthwaite's approximation for degrees of freedom of F statistics  (Luke, 2017). Bayesian analysis was performed using the brms package  (Bürkner, 2017)  in R to examine the occurrence of possible repetition effects between random and repeated passive blocks in the control experiment.
Data simulation of absolute accuracy during numerosity estimations To examine weather absolute accuracy (correct numerosity estimations of words generated/heard) of numerosity estimations observed in the experimental data may be approximated by a noisy sampling process rather than counting, we performed data simulations. More specifically, we simulated 1000 numerosity estimations (as the main experiment contained 40 trials/subject * 25 subjects) from a normal distribution centred on 10 and standard deviation (SD) varying from 0. 5 to 6 with 0. 1 steps. We rounded each item to the nearest integer and counted how many times the number 10 was obtained. The simulation was iterated 10000 times.
fMRI data preprocessing Anatomical and functional images were processed and analyzed using SPM-12 (Welcome Centre for Human Neuroimaging, London, UK). Pre-processing steps included slice time correction, field-map distortion correction, realignment and unwarping to spatially correct for head motions and distortions, co-registration of structural and functional images, normalization of all images to common Montreal Neurological Institute (MNI) space, and spatial smoothing with a Gaussian kernel with a full-width at half maximum (FWHM) of 4 mm. Quality assurance of all EPI images was performed with the criteria of maximum 2 mm translation and 2° rotation between volumes. In addition, an excessive movement was estimated with the mean framewise displacement (FD)  (Power et al. , 2012)  with the exclusion threshold of 0.
Acknowledgments The authors are grateful for the technical support during data acquisition to the  Foundation Campus Biotech Geneva (FCBG) Human Neuroscience Platform of the Campus Biotech. This work was supported by the  Bertarelli Foundation  (grant number  532024 ), the  Swiss National Science Foundation  (grant number  3100A0-112493 ),  National Center of Competence in Research (NCCR)  " Synapsy -The Synaptic Bases of Mental Diseases " (grant number  51NF40 -185897 ), and two generous donors advised by  Carigest SA. Nathan Faivre  has received funding from the  European Research Council (ERC)  under the  European Union   Horizon 2020 research and innovation programme  (grant number  803122 ).
Toxicological bioassay A sublethal dose of deltamethrin (technical-grade 99% purity; Sigma-Aldrich, Buenos Aires, Argentina) was administrated to first-instar nymphs of T. infestans (5-7 days old, kept unfed after emergence)  [40]. The dorsal abdomen of each insect was treated with 0. 2 μl of a deltamethrin acetone solution (0. 005 mg/ml), i. e. 1 ng per insect (the median lethal dose [LD 50 ]), using a 10-μl Hamilton syringe equipped with a Hamilton PB-600-1 Repeating Dispenser (Hamilton Company, Reno, NV, USA). Insecticide doses lower than the LD 50 are considered to be sublethal  [37]. Two types of control groups were designated: insects treated topically with 0. 2 μl of pure acetone, and untreated insects (see subsection Experimental design and data collection). Insect mortality was evaluated 24 h after exposure.
Morphometric analysis and statistical treatment Data on the wing shape was extracted with a generalised full Procrustes fit and a projection to shape tangent space  [43]. A principal component analysis (PCA), based on the covariance matrix of landmark coordinates after the Procrustes fit  [43] , was used to examine the dimensionality of shape variation and to extract shape variables for subsequent analyses. We computed centroid size (CS; i. e. the square root of the sum of squared distances from each landmark to the centroid of the configuration) as a measure of wing size  [43]. These steps of morphometric analysis were performed using MorphoJ version 1. 07a software  [44]. To quantify the effects of study factors (i. e. full-sib family and treatment: control and deltamethrin exposure) and their interaction, we used analyses of variance (ANO-VAs) on wing CS and multivariate analyses of covariance (MANCOVAs) on wing shape variables.
ANOVAs for mean wing size included the fixed effect of treatment. MANCOVAs on shape variables included full-sib family and treatment as main effects and CS as a covariate. Size reaction norms can be represented as a line linking the mean wing size of each full-sib family within the control and deltamethrin-treated groups. We additionally performed a canonical variate analysis (CVA), including full-sib family and treatment as clustering variables, to visualise whether the dataset was structured by treatment. Shape reaction norms can be represented as lines linking the position of each full-sib family within control and deltamethrin-treated groups  [45]. The amount of individual and FA variation for wing size and shape was measured for each full-sib family and each group (control and treated) using regular ANOVAs for size and Procrustes ANOVAs for shape  [46] , considering individual, side, the interaction between individual and side as effects, the replicates being left in the residual term and accounting for ME.
To make our social networks resemble country-specific properties of the real world we rely on data from the Polymod survey  [19]  for three countries: Italy, Germany, and Great Britain. From these data we extract two sets of country-specific information: the age-dependent degree distribution, i. e. , how many contacts individuals of different ages have; and the age mix, i. e. , the distribution of ages of people with whom individuals of different ages come into contact. For each network we generate, we select one of the three degree distributions and one of the three age mixes, and create undirected links between the nodes, closely mimicking this empirical information. Importantly, our methodology allows us to generate networks with a degree distribution and an age mix calibrated on different countries.
Empirical data, artificial population networks, and the simulated diffusion process Description of empirical networks. Polymod data includes a representative sample of individuals living in the countries we considered. Among elements relevant to our analyses, respondents report their daily contacts, their age, and the age of their contacts  [19]. Contacts are either physical (defined as "skin-to-skin contact") or non-physical (defined as "a two-way conversation with three or more words in the physical presence of another person"). Participants for whom no information is missing (Italy N = 838; Germany N = 1,286; Great Britain N = 1,006) were selected to generate information on social networks' interage contacts (age mix) and degree distribution for the three countries considered. S1 Dataset helps visually representing the information contained in the data as ego-centered networks, with the survey's respondents are at the center of the "stars".
This statistic does not control for the effect of differences in the underlying population's age structure. Thus, the differences could be magnified or diminished if the population of nodes connected by these ties was the same. The network generation method that we adopted allows us to single out the effects of these elements. The second network property of interest is the degree distribution, i. e. , the number of daily contacts (edges). Table  1  reports the mean values, S2 Dataset plots the distributions. In line with the results reported by  [17]  for France, we find a wide variation within countries in the number of daily contacts between respondents. This skewed distribution is common to many empirical social networks, and is a key feature of complex networks  [21]. We preserve this aspect of empirical data in our method of reconstructing networks, to increase the realism of the model.
There are large differences in the average number of contacts reported across countries, with Italians reporting many more contacts (about 20 per day) than Germans (about 8 per day) with British in between (about 12). These differences are only partly compensated by Germans having on average longer contacts: see S3 Dataset. To sum up, the three countries differ empirically to a relevant extent in their network properties, though differences in degree distribution seem to be more pronounced than interage mix. S1 Appendix discusses the empirical data in more depth. Artificial population networks. To assess the extent to which these differences matter for the diffusion of the virus and which age groups are affected most, we built an artificial "national" population to use for the simulation and a counterfactual variation of its characteristics.
For each country, first we generated 1,500 nodes with age distribution calibrated on the age distribution of Italy from the UN data. In this data, ages are given in five-year age-bands. We assign each node a notional 'exact' age by allocating the 1,500 first to age-bands (in proportion to the UN data), then evenly within each age-band. Second, to each node in our artificial population we assigned a degree (number of contacts) corresponding to the empirical degree distribution of a Polymod respondent with the same age. Where several Polymod respondents had the same age as our artificial node, we selected one of these participants at random; if no respondents in the Polymod data had the same age as our artificial node, we searched for the respondent(s) with the age closest to the artificial node and if two respondents had an age equally distant from that of the artificial node, we selected one of the two at random.
Third, in each country, we grouped together all individuals in the Polymod data with a given age (both respondents and declared contacts), and created a unique list of the ages of all persons that came into contact with a person of that age. For instance, suppose a country contains two 20-year-old respondents. We list the ages of all the contacts they declared. Now suppose x other respondents whose ages 6 ¼ 20 declared having contacts with individuals aged 20. Then the ages of those other respondents are added to the list. In other words, for each tie including a node of age 20, we store the age of the individual at the other end of this tie. This gives us a distribution of the ages of all contacts of participants of a given age, in a given country. Then we equipped each artificial node with a personal list of contacts' ages, by randomly selecting values from this list n times (with n equal to that node's degree (assigned as explained above)).