dataesr/scientific-paragraphs-categorization huggingface dataset:
It is defined by CES p (X i ) = 1 J J ∑ i=1 Y i 1 I Y i > CVaR p (X i ) , J is optimised over the subset {10, 15, 20, 30}. Next, we keep the same metric and the same schema of the data generating of the first illustration; we change only the conditional distribution which is related to the distribution of the white noise. Specifically, instead of the normal and laplace distributions of the first part, we consider the student distribution, which is more popular in financial time series data. The impact of the technical parameters is checked using the ASE-error Equation (  13 ) for n = 100 and three values of p = 0. 01, 0. 05, andp = 0. 1. An average of 100 replications of this error is given in the following table. The results of Table  1  proves that the technical parameters also have an important effect on the estimation quality.
Real Data Example The object of this section is to evaluate the performance of the kernel estimator of the expected shortfall regression using a real financial time series data. In the previous section, we proved that the easy implantation of the constructed estimator for different kernels, different bandwidths as well as different conditional models. We have observed, without surprising, that its efficiency is strongly influenced by these parameters. Recall that the main motivation of this kernel smoothing is to overcome the problem of the non-elicitability of the expected shortfall model. However, in the multivariate statistics there exists some alternative solutions based on jointly estimation the CVaR p (• • • ) and CES p (•) using some adapted parametric scoring functions. Such solution has been studied by  [35] [36] [37].
Thus the main purpose of this section is to conduct a comparative empirical analysis between our nonparametric functional approach based on the kernel smoothing and the cited studies based on the semi-parametric multivariate techniques. It's worth remembering that the nonparametric functional tools is more appropriate that the parametric models to fit the high-frequency data (see  Ferraty and View [34] ). So, we want in this paragraph to highlight this feature of nonparametric functional data analysis. For this aim, we consider as financial time series the interday return of the stock index Nikkei during the period 11 October 1983 to 11 October 2022. The studied data was obtained from the website https://fred. stlouisfed. org/series/NIKKEI225 (accessed on 14 September 2022). Undoubtedly, this kind of financial times series data exhibits the principal characteristics of financial data: volatility, non-normality, heavy tailed distribution, excess kurtosis,.
In Figure  3 , we plot the process of the return index r(t). Often in financial times series analysis we aim to forecast a future values of the process Z(t) = -100 log r(t) r(t-1) index knowing its historical trajectory. In our functional context, we formulate this forecasting problem by putting Y i = Y = Z(d i ) (the value of Z(. ) at day d i ) and the functional covariate X i (t) = Z(t) t∈[d i -R,d i -1] that the historical values of the index of the last R-days before d i. In this empirical study, we conduct comparative study using different values of R = 3, 6, 10, 30, 90. We point out that for the Multivariate Semi-Parametric Model (MSPM), we use the code routine esreg from the R-package esrreg using two types of specification functions that defined the scoring functions (see Dimitriadis and Bayer  [37]  for more details in this approach).
This is the case when G 1 (t) = t and G 2 (t) = e t 1+e t seems more appropriate than the first case. It is he same thing for the functional case: the smoothing case is better than the non-smoothing case when R is large. An additional check is performed using another backtest based on the cover test developed by  Bayer and Dimitriadis [38]. We apply the version, the so-called one-side intercept expected shortfall regression backtest. Precisely, we compare our functional approach to the GARCH specifications with Student-t using this cover-test. The latter is available by the routine code esr-backtest from the R-package esrback. Here, we choose α = 0. 05. For our aim we split, randomly, many times (exactly 100 times), the data into subsets (70% learning sample and 30% testing sample), and for each time we compute the empirical p-values of both approaches when R = 90.
Acknowledgements M. W. is supported by  SFB-TRR 195  and  DFG Heisenbergprogramm. I. B. and U. F. are supported by an  ANR  project (No. ANR-19-CE40-0002 ). G. C. is supported by the Project  MESA  ( ANR-18-CE40-006 ) and by the Project  STARS  ( ANR-20-CE40-0008 ) of the  French National Research Agency (ANR). We acknowledge the  DAAD Procope program  held by  Roland Vergnioux  and the fifth author from  2019-2020.
Thoroughly grasping the mathematical method of R 0 calculation is still difficult for most practitioners and researchers in public health. Estimate R 0 directly through definition has been described in basic dynamic models without an explicit step-by-step derivation process  (Batabyal, 2021; Dearlove & Wilson, 2013; Getz et al. , 2018; Hethcote, 2000). Moreover, few of these methods agree with each other, even when based on the same dataset  (Li & Blakeley, 2011). Therefore, this study formularizes and generalizes an intelligible and straightforward definition-based method (DBM) for computing R 0 of dynamic models of single host species for the first time, from which one can work out the expression of R 0 with just pen and paper. The result that this method produces is mutually coherent with the next-generation method (NGM) and is typically equivalent to the Van den Driessche and Watmough approach.
Analysis and validation The symbolic toolbox of MATLAB (R2021a) was used to perform the inverse and eigenvalue operations for symbolic matrices. Numerical experiments of DBM and NGM were performed using fitted transmission parameters and other parameters in a published age-specific multi-group SEIAR model  (Zhao et al. , 2020). All codes of computation are available for download on GitHub and provided in supplementary materials (S1 Text: Supplementary Methods and Results).
Numerical simulations In this section, we investigate numerically the behaviour of the system (5. 10) with the parameters and functions described in Section 5. 2. We use a standard Cranck-Nicolson scheme for the Laplacians and the reaction terms are treated explicitly. The scheme uses an artificial Neumann boundary condition in the right end of the domain which has no impact over the results whatsoever as long as the numerical spatial domain is large enough and the scaling parameter ε is small enough. This rather simple scheme appears to be very robust even for small ε values, as long as the time step dt is of the same order of magnitude of ε. The Python code we used to produce the numerical simulations is available at https://github. com/ pierreabelroux/Leculier_Roux_2021. The figures can be obtained by uncommenting and running the different pieces of code in the part "Numerical experiments".
Acknowledgements:  Alexis Leculier  and  Pierre Roux  were supported by the  ERC ADORA. Pierre Roux  was supported by the  Advanced Grant Non local-CPD (Nonlocal PDEs for Complex Particle Dynamics: Phase Transitions, Patterns and Synchronization ) of the  European Research Council Executive Agency (ERC)  under the European Union's  Horizon 2020 research and innovation programme  (grant agreement No. 883363 ). Both autors want to warmly thank  Benoît Perthame  for his help and precious advice. Both authors want also to thank  Zhou Xu  for the time dedicated to fruitful discussions about the biological motivation of this project.
In particular, Perf(A) is a stable ∞-category which is furthermore idempotent complete. we say that an A-module M ∈ A-Mod is almost perfect 15 if π i (M) = 0 for i ≪ 0 and for every n ∈ Z the object τ ≤n (M) is compact in A-Mod ≤n. We denote by APerf(A) the full subcategory of A-Mod spanned by sheaves of almost perfect modules. Given a morphism f : A → B in CAlg we obtain an ∞-functor f * : A-Mod -→ B-Mod, which preserves perfect and sheaves of almost perfect modules. We can assemble these data into an ∞-functor QCoh : dAff op -→ Pr L, ⊗ st. Since the functors f * preserve perfect and sheaves of almost perfect modules, we obtain well defined subfunctors Perf , APerf : dAff op -→ Cat st, ⊗ ∞. Given a derived stack X ∈ dSt, we denote by QCoh(X), APerf(X) and Perf(X) the stable ∞categories of quasi coherent, almost perfect, and perfect complexes respectively.
Clinical Data and Sample Collection and Transportation Once patients are identified, their demographic and clinical details are recorded on a standardized-case-reporting form (CRF). Nasopharyngeal or nasal samples and throat swab samples are collected from each participant using an appropriate dacron swab and transported in viral transport medium to the laboratory in triple-layer packaging to maintaining the cold chain. Different modes of transportation are used to transport the samples. While hospitals from Kerala and Goa use the public train service to transport the samples, hospitals in Karnataka mostly use courier services barring those situated near MIV, which sends samples through patient attendees. A sample pick-up mechanism is developed by MIV to collect the samples coming by train.
Testing at the Laboratory Upon receipt of samples in the laboratory, they are checked if they fit the sample acceptance criteria, followed by sample registration and aliquoting of samples. The epidemiological and clinical information is entered into the laboratory information system. Samples are processed within 24 h of receipt at the laboratory. Viral RNA is extracted using commercially available QIAamp Viral RNA Mini Kit (Qiagen GmbH, Hilden, Germany) as per manufacturer's instructions. Amplification and detection for each RNA isolate is performed on Applied Biosystem's Real Time PCR 7500/Quant Studio 5 instruments by using primers and probe sets for Influenza A and B as per the WHO real-time RT-PCR protocol. Upon completion of tests, each result is verified by the virologist and approved by the laboratory manager before the data is entered into the laboratory information system and reported.
Analysis and Statistics Data was downloaded from the electronic database and was analysed using Stata software version 16 (College Station, TX, USA: StataCorp LLC). The frequency and percentages were used to describe the socio-demographic and clinical characteristics of the samples tested for influenza during the pre-COVID-19 and COVID-19 periods. The influenza positivity rate (the percentage of samples positive for influenza out of the tested samples) was calculated for the pre-COVID-19 and COVID-19 periods. Time-trend graphs were used to depict the number of samples tested, the influenza cases detected, and the influenza positivity rates each month during the pre-COVID-19 and COVID-19 periods. The number of samples tested (stratified by ILI and SARI) and the influenza cases detected per month during the study reference period (2015 to 2021) were deduced.
Influenza positivity is an important indicator of influenza transmission. Since there was no change in this indicator in our study, we are of the opinion that the reduction in influenza cases detected was less likely due to a reduction in transmission. There were several strengths to this study. First, we used the surveillance data from an influenza surveillance laboratory which catered to three states of southern India. Thus, the data generated can be considered representative of the epidemiological picture of influenza in these three states. Second, we performed a robust ITS analysis with data points spanning seven years (five years for the pre-COVID-19 period and two years for the COVID-19 period), thus accounting and adjusting for seasonal changes that might have affected influenza case detection.
Acknowledgments: This research was conducted through the  Structured Operational Research and Training Initiative (SORT IT ), a global partnership coordinated by  TDR , the  Special Programme for Research and Training in Tropical Diseases at the World Health Organization. The specific SORT IT program that led to this publication included a partnership of TDR with the WHO regional office for South East Asia (SEARO) and the  Global Outbreak Alert  and  Response Network  (GOARN) and was implemented along with the  International Union Against Tuberculosis and Lung Diseases , Paris and South East Asia offices; the  Tuberculosis Research and Prevention Center, Armenia ; the  INCLEN Trust International, India ;  Jawaharlal Institute of Postgraduate Medical Education and Research (JIPMER) ,  India , and the  Kirby Institute in Australia.
Simulated data in the plane We consider two synthetic datasets in the plane as depicted in Figure  1. The densities considered are uniform on chosen sets with smooth boundary. According to (3. 3), the degree bound should be proportional to n 1/4. For each value of n, we implement the following procedure: We consider two such supports: one with a hole and on with four connected components. The red line displays the boundary of the support estimated from the sample. As we can see, for n large enough, the method is able to identify the support set as well as its boundary and topological features correctly. • Choose d n = 2n 1/4. • Evaluate the empirical Christoffel function at each input point. • Choose the smallest value as a threshold and draw the corresponding level set. The results are presented in Figure  1.
Outlier detection We consider a thyroid disease dataset obtained from UCI repository  (Dua and Graff, 2017). This has 6 numerical descriptors so the effective dimension is 6. This dataset was used in  Aggarwal and Sathe (2015) ;  Keller et al. (2012)  to benchmark outlier detection methods. We adopt the following procedure, for each concurent method. • Split the dataset randomly into a training set of normal examples and a test set with half malfunctioning cases and half normal examples. • Estimate the support of the training set. This is done by computing a function for which a sublevel set represents the support, for example the Christoffel function or a kernel density estimate, and thresholding to a chosen value to obtain a set. • On the test set predict outlyingness for half of the data for which the estimated function is most below the chosen threshold value on the support.
Acknowledgements This work was mostly carried out during the first author's MS final project which was funded by the  CIMI labex  ( Centre International de Mathématiques et d'Informatique de Toulouse ). The third author acknowledges support of  ANR - 3IA Artificial and Natural Intelligence Toulouse Institute, ANR MASDOL  and  Air Force Office of Scientific Research, Air Force Material Command, USAF , under grant number  FA9550-19-1-7026/19IOE033  and  FA9550-18-1-0226. The authors would like to thank  Jonas Kahn  and  Sébastien Gerchinovitz  for motivating preliminary discussions on the topic. The authors are also grateful to  Vincent Guedj , for his advices on Lemma 3. 4 and its proof.
Background Brazil has been severely impacted by COVID-19 pandemics that is aggravated by the absence of a scientifically-driven coordinated informative campaign and the interference in public health management, which ultimately affected health measures to avoid SARS-CoV2 spread. The decentralization and resultant conflicts in disease control activities produced different protection behaviours and local government measures. In the present study, we investigated how political partisanship and socio-economic factors determined the outcome of COVID-19 at the local level in Brazil. Methods A retrospective study of COVID-19 deaths was carried out using mortality databases between Feb 2020, and Jun 2021 for the 5570 Brazilian municipalities. Socio-economic parameters including city categories, income and inequality indexes, health service quality and partisanship, assessed by the result of the second round of the 2018 Brazilian presidential elections, were included.
There are currently 5570 municipalities in Brazil, while the city is the most urbanised part of the municipality. The databases and details of this method are described below. Data sources COVID-19 mortality data. A retrospective study was carried out on COVID-19 deaths registered in the Influenza Epidemiological Surveillance Information System (SIVEP-Gripe), a system used by local, state, and federal governments to monitor severe acute respiratory infections in Brazil, which indicated the epidemic process of COVID-19 as early as epidemiological week 12 of 2020. 24 As requested by the Ministry of Health, SARS deaths should be reported in SIVEP-Gripe regardless of hospitalisation. This data source contains information about hospitalisation and deaths and consequently deals with the most severe cases.
Because COVID-19 is a disease that requires mandatory notification, the database includes information from public and private health systems. 25 e separated the two main waves of the pandemic in Brazil using the cut-off date of November 1st, 2020, when there was a large reduction in the number of deaths. We, therefore, analysed the data according to the two periods, from February to October 2020 and from November 2020 to June 2021. We analysed 472,634 COVID-19 deaths confirmed by laboratory tests with positive results from the quantitative RT-PCR test for SARS-CoV-2, from February 16th 2020 to June 17th 2021. The unit of analysis for this study was the municipality and the age-standardised mortality rate (SMR) was used to control for differences in demographic age structures. The SMR was calculated by the direct method using death data from COVID-19 from SIVEP Influenza.
Data on the human development index (HDI) and Gini index. The municipal-level HDI was calculated from municipal data on education, income, and longevity in the same way as the HDI. The data on the HDI, provided by Atlas Brasil,  28  was collected from the 2010 Demographic Census, which is the most recent source that includes the indices from all Brazilian municipalities. We used the HDI proportion of income component (HDI-Income) in our estimations. This choice met two conditions: The first was related to the characteristics of the country, which is heterogeneous and has an unequal distribution of wealth, and the second was related to the use of the Gini index, which captures part of this inequality, helping to explain how this context is shaped and if this amplified the effect of COVID-19 in Brazil, especially on deaths.
In general, municipalities with higher income have lower inequality, as measured by the high Gini index, with important exceptions in some rural areas where economic development has been more equitable. Healthcare service quality data. The infant mortality rate from preventable causes in children under 5 years was used to demonstrate the quality of local health before the COVID-19 pandemic. The rate was composed of data on infant deaths from preventable causes in 2019 obtained from the Mortality Information System and data on live births in 2019 from the Live Births Information System, both organised by the Ministry of Health and made available through the Department of Health Information. 26 ta on the 2018 presidential election. The electronic ballot box data of the second round of the presidential election on October 7th 2018 were obtained from the Electoral Data Repository of the Superior Electoral Court (TSE).
Statistical analyses In contrast to traditional statistical analysis, we employed Knowledge Discovery in Databases (KDD) and data mining which allows discovery using large datasets with no previous hypothesis. In this sense, regression trees were employed in this study to ensure an unbiased classification of municipalities that better explain the distribution of the COVID-19 impact, here expressed by the SMR. These classifications were based on independent variables without any previous categorisation because cut-off points are established throughout the model. 30 This approach can identify complex interactions between contextual variables without the a priori specification of interaction terms. In addition, it supports a large number of contextual variables relative to the number of observations.
In this study, the Monte Carlo test was used to evaluate independence as well as compare the p-values and select the nodes. A significance level of 0. 05 was adopted as a reference for the p-value to include the partitioning of the contextual variables. Based on these results, the groups were created and the predicted values of the terminal nodes were determined. Finally, the ctree function from the R package (or library), called partykit, version 3. 4. 0, was used. 33  regression tree with conditional inference was built to classify the outcome variable according to the different levels of response of the contextual variables to verify their effect on the occurrence of COVID-19 in Brazilian municipalities. This regression with conditional inference allowed us to estimate the occurrence of deaths from the disease by groups of municipalities considering the partisan issue that influenced the behaviour of the disease in the country.
Single Case RM was a left-handed, 19-year-old, female, second-year undergraduate Psychology student at the University of York who self-reported long-lasting difficulties with arithmetic since childhood. RM's behavioral and neuroimaging data were collected over a period of six months in 2009/2010. As reported elsewhere in detail (see  [48] ), RM had severe difficulties in arithmetic despite having average general cognitive skills, average reading and spelling skills and average working memory (WM) resources (see Table  1 ). Her performance on a standardized test of arithmetic (WRAT-3 arithmetic  [104] ) was below average (SS of 80). Her performance of oral arithmetic with single-digit operands (for a detailed report see  [48] ) was highly accurate, very slow and atypical for an adult. Apart from rule-based facts (i.
Data Analyses 2. 4. 1. Behavioral Analyses RM's performance on the background measures and her accuracy and responses times in the fMRI tasks were compared to the performance of the control group using a modified t-test. The test was developed by Crawford and Howell  [105]  to compare a single subject to a sample of control participants. In this method, the individual is treated as a sample of N = 1, and a modified version of an independent samples t-test is used to compare the individual to a normative sample. The t-tests were implemented using the Singlims_ES. exe program  [106, 114]. The Benjamini-Hochberg [107] method of controlling the false discovery rate (FDR) was used to correct for multiple comparisons, which increase the risk of type I errors. We chose to apply the Benjamini-Hochberg correction because it is better able to reduce false positives while minimizing false negatives than more conservative measures  [108].
fMRI Analysis Data pre-processing. All fMRI data were analyzed using FEAT (FMRI Expert Analysis Tool, Version 6. 00) part of FSL (FMRIB's Software Library  [115] ). The Brain Extraction Tool (BET  [116] ) was used to extract the brain from EPI data, and a temporal high pass filter of 0. 02 Hz was applied. The images were motion-corrected using MCFLIRT  [117] , slice timing corrected, and a Gaussian smoothing kernel of FWHM 5 mm was applied. The functional images were registered to the individual's structural T1 scans using FLIRT  [117, 118]  and were co-registered to a standard 2 mm MNI152 brain using FNIRT nonlinear registration  [119]. Single-subject analysis. Individual participants' whole-brain responses were modeled using a general linear model with each experimental condition (e. g. , multiplication trials, multiplication controls trials) used as a regressor.