dataesr/scientific-paragraphs-categorization huggingface dataset:
SEM/FEM coupling method In this section, the SEM partition is integrated using Newmark explicit time integration with a fine time step whereas the FEM partition uses Newmark time integration with a large time step, m defining the time step ratio between the two time scales. The purpose is to set up a co-simulation strategy coupling mature seismology SE software with FE code, both adopting energy conservative time integration schemes. More modern time integrators such as α-generalized method  [31, 32, 33 ], Krenk's schemes  [34, 35] , Tamma and co-author's methods  [36]  and composite Bathe methods  [37, 38] , provide desirable numerical damping to filter out the spurious frequencies coming from the space discretization for wave propagation problems. It has to be noted that engineering seismology software based on the SEM, devoted to wave propagation prediction, does not employ such type of numerical damping.
Discussion about GC method for SEM/FEM coupling with nonlinear mechanics It is important to note that, over one time step in the FEM partition, several Newton-Raphson iterations are needed to reach equilibrium. For each Newton-Raphson iteration, the FE code has to communicate to the coupling software before solving the interface problem at the beginning of the Newton-Raphson iteration (see Eq. (  23 )). As a consequence, if convergence is difficult to reach, such as for instance when damage constitutive laws are employed, a lot of data exchange are needed, which can be detrimental for the efficiency to the proposed SEM/FEM coupling strategy. Another drawback of the proposed coupling method in the case of nonlinear dynamics, is that we adopt the same time step in both partitions. As detailed in  [27] , the multi time step GC method can be applied for co-simulation, even if nonlinear constitutive laws are considered in the implicit FEM partition.
Full-SEM simulation The reference simulation is carried out using EFISPEC3D. The mesh, built using the meshing software CUBIT  [49] , is displayed in Figure  9. As can be seen, relatively small SE hexaedral elements have been generated for modeling the dam, with the finest mesh size at the top of the dam equal to H/8, that is 3. 125m. It leads to a reduction of the critical time step of the explicit time integration in comparison to the SE partition previously presented: the time step adopted in the full-SEM partition is equal to 0. 15ms, to be compared to 0. 25ms in SEM/FEM co-simulation. The relevance of the proposed multi time step SEM/FEM co-simulation, against full-SEM results, is assessed in the following.
Acknowledgments The first author would like to express his gratitude to  Jean-François Molinari , Director of the  Computational Solid Mechanics Laboratory (EPFL/LSMS) , who greatly facilitated his one-year experience at EPFL. The first author also thanks  Guillaume Anciaux  for the fruitful discussions about the use and development of Akantu FE code. This study has been conducted thanks to a grant provided by the  Swiss National Science Foundation  (" Scientific Exchanges " grant for three months) and direct founding from LSMS and  BRGM.
Statistical analysis An analysis was done (by D. C. ) based on randomised allocation (intention to treat), used data collected in the 12-mo follow-up questionnaire and the 12-mo clinic appointment. We used a generalised linear model with previous prostate radiotherapy and pad test weight at baseline and a random effect (intercept) for centre to analyse the primary outcome. We used the lower limit of the two-sided 95% confidence around the difference between groups to infer noninferiority between male slings and AUS, which is equivalent to a 2. 5% one-sided type 1 error rate. We calculated a p value for observing the difference under the null hypothesis of inferiority. EQ-5D  [12]  and ICIQ-UI SF  [8]  scores were analysed using a mixedeffect repeated-measure model on all available 6-and 12-mo data, adjusting for baseline outcome measure and design covariates (as for the primary outcome).
Although men who had developed UI after TURP for benign prostatic obstruction, prior to their PPI surgery, were included, there were only eight of 190 in the male sling group and nine of 190 in the AUS group, and these numbers were too small to offer a useful analysis. A limitation of this study is that we were unable to compare the severity of the MASTER men's incontinence with that of men in the case series reports, because the data from previous non-RCT studies do not contain adequate information for comparison. However, men in MASTER were more incontinent than the men included in the only other reported RCT  [3] , which contained a significant number of men described as "minimally incontinent". The wide range of PROMs allowed us to look at the trial results from a number of other perspectives.
Acknowledgements: The authors wish to thank the men who participated in MASTER. We also thank  Fiona Cherry ,  Lana Mitchell ,  Georgia Mannion-Krase ,  Maria Ntessalen ,  Andrea Fraser , and  Dianne Dejean  for their secretarial support and data management;  Kirsty Shearer ,  Caroline Peet ,  Karen Campbell , and  Elerita Flammini  (previous trial managers/assistant trial managers); the programming team in.
establishments depends on direct contact with consumers to carry on their activities. For example, mobility restrictions have been shown to be strongly correlated with consumption reduction  35, 36  and loss of Gross Domestic Production (GDP)  37  during the pandemic. Official measurements on the economic response of individuals and firms are typically available only several months after the events take place, and often with insufficient geographic detail. Digital traces of individuals, including mobility data, are instead widely diffused, readily available and contain information on the geographic position of users  [38] [39] [40]. In this work, we take advantage of a large-scale social network dataset comprising near realtime observations for over 4 million individuals, provided by Facebook through its "Data For Good" program, to measure Italian mobility patterns and assess how restrictions disrupted the corresponding mobility network.
Results Evolution of the Italian mobility network. We collect near real-time observations of individuals moving in the Italian peninsula in a period of 32 weeks, from February 24th to October 4th, 2020, based on data of the "Disease Prevention Movement Maps" provided by Facebook through their "Data for Good" program  56. Measurements are recorded with an 8-h frequency by aggregating individual trips of Facebook users moving between Bing map tiles  57. Mobility flows are constructed with proprietary mechanisms to ensure privacy and anonymization, e. g. , adding random noise and discarding flows with less than 10 individuals  58. Specifically, we collect observations of traffic flows within about 5,000 distinct tiles produced by an average daily number of almost 4 million individuals, representing Italian users who enabled Facebook geolocation on their mobile phones during the period of observation.
Discussion In this paper, we investigate the interplay between human mobility and the socioeconomic composition of Italian territories, with a specific focus on persistent effects which characterized mobility during and after the national lockdown put in place by Italian authorities in March 2020 to prevent the spread of the COVID-19. To this aim, we leverage a massive dataset of near real-time observations of movements for approximately 4 million daily individuals in a period of 32 weeks, from March to October 2020, and we rely on detailed information on the composition of the Italian productive system by sector, using official census statistics on the number of employees and revenues, and on the socioeconomic characteristics of Italian administrations. We show that pre-existing economic disparities among Italian territories can explain their reaction to lockdown restrictions and that two specific classes of territories emerge: the most affected and the least affected territories by interventions.
In addition, we define the nodal efficiency as the contribution of each node i to E glob (G): and, accordingly, the normalized nodal efficiency of node i as e norm i = e i • w min. ASIA database. The Italian National Registry of Active Firms (ASIA) is managed by Istat and reports information on all economic units on the national territory exercising industrial, commercial and services activities. It collects and updates annually identification information (name and address) and structure (economic activity, dependent and independent employees, legal form, date start and end activities, turnover) of firms within the register. Even though the data is collected at a granular level, for privacy reasons it has been provided to us by Istat at the province level and for each NACE Rev. 2 business sector which we aggregate in 21 macrocategories (see Table  S6  in the Supporting Information for details).
E glob (G) = 1 n(n -1) i� =j∈G 1 d ij E norm (G) = E glob (G) E ideal (G) = E glob (G) • w min e i = 1 n -1 i� =j∈G 1 d ij , Matching procedure for economic variables. Our analyses integrate data measured at the municipal level with information regarding the productive structure of the Italian economy at the level of provinces, i. e. at a more aggregate level. In order to ensure a reliable number of observations we bridge the two datasets towards the intermediate level of analysis of Local Labour Market (LLMs) which are comparable sub-regional geographical areas defined by the Italian National Institute of Statistics (Istat). As a result, our economic data cover different dimensions of the local socioeconomic context of each Italian LLM, in total 495 areas. Our three main variables of interest are Income per Capita, Inequality in the distributions of incomes and Population Density.
These variables have been collected at the municipal level and then aggregated at the level of LLMs mapping each Italian municipality to a unique LLM. We then integrate these variables with sector related ones (employees and revenues per employee) obtained from the ASIA database at the province level. Using publicly available data from Istat on the number of employee at municipal level, we were able to redistribute province level data to the LLM level of aggregation using the share of province employees for each municipality as partition coefficient and the municipality-to-LLM mapping to aggregate the municipality data. Description of economic variables. Declared income. This variable is the tax base of the personal income tax declared by tax payers in the 2018 tax return to the Revenue Agency for the 2017 financial year.
We use macroarea controls to make the estimation of interaction effects in our regression easier and avoid inflating the regression with too many covariates. Clustering, classification, multiple test analysis and quantile regression. We rely on several open-source packages to perform our analysis of the most and the least affected territories. We encode each LLM with a vector of socioeconomic covariates (see previous section) and we assign them a binary label, based on the lockdown and recovery indicators defined in the main text. We employ scipy  76  to carry out a hierarchical clustering of LLMs based on their standardized socioeconomic variables, using a cosine distance and average linkage to obtain clusters. We report similar results when using euclidean distance or other linkage approaches, e.
g. , complete or Ward linkage. We use scikit-learn  77  to train several binary classifiers, namely Logistic Regression, Support Vector Machine, Random Forest and K-Nearest Neighbors, in the task of classifying most vs least affected LLMs based on their socioeconomic variables. We apply standardization of features and use default hyperparameters as specified in the package, and we use stratified shuffle-split cross-validation to evaluate their performance. We employ scikit-posthocs  78  to perform multiple test comparisons and assess statistical differences in the distribution of features of the most and the least affected LLMs (and remaining ones). In particular, we apply Kruskal-Wallis test with Conover procedure and Bonferroni correction for p-values. Finally, all quantile regression results have been performed with the quantreg R package  73  on standardized variables with default options.
Simulation Study I The performance of maximum likelihood and Bayes estimations are evaluated using simulation results. We generate 1000 samples of size n = (50, 60, 70,. , 300) from the ESW distribution for some selected parameter values using Equation  (17). The bias, mean square error (MSE), the average length of CI (ALCI), and coverage probability (CP) of the estimates are computed using R3. 5. 3 developed by  [38]. For the MLEs, we use the package called maxLik developed by  [39]  in R-software by maxBFGS. This package allows us to obtain the MLEs and information matrix, and the package matlib elaborated by  [40]  can be used to get the inverse of the information matrix to compute the confidence interval. The resulting simulations are given in Figures  4 5 6 7. For the Bayes estimation, we used N = 3000 number of iterations and the first 30% as a burn-in sample.
Now, by considering the changes of variables u = (π/2) 1e -λx β 1 and r u = (π/2) 1 -e -λ[-(1/λ) log(1-2u/π)] β 2 /β 1 , we get R = α 1 π/2 0 cos u(sin u) α 1 -1 [sin(r u )] α 2 du. (23) The parameter R above has no closed form expression, but it can be easily calculated using mathematical software such as R and Matlab, among others. Moreover, when β 1 = β 2 , the expression of R can be deduced from Equation (10).
Acknowledgements The work of N. K. was partially supported by the  EIPHI Graduate School  (contract  ANR-17-EURE-0002 ). N. K. would like to thank  LPTMS laboratory (Université Paris-Saclay ) and  LPTHE laboratory (Sorbonne Université ) for hospitality. The work of G. K. was supported by  Carnot Pasteur doctoral school of the UBFC. We would like to thank the referees for several useful comments and suggestions.
We collected data from 10 EU/EEA countries on 240 COVID-19 outbreaks occurring from July-October 2021 in long-term care facilities with high vaccination coverage. Among 17,268 residents, 3,832 (22. 2%) COVID-19 cases were reported. Median attack rate was 18. 9% (country range: 2. 8-52. 4%), 17. 4% of cases were hospitalised, 10. 2% died. In fully vaccinated residents, adjusted relative risk for COVID-19 increased with outbreak attack rate. Findings highlight the importance of early outbreak detection and rapid containment through effective infection prevention and control measures. In 2021, morbidity and mortality among residents in long-term care facilities (LTCFs) dramatically declined with the progressive increase of coronavirus disease (COVID-19) vaccine uptake, still, several outbreaks, including severe cases and deaths, continued to occur during the second part of 2021  [1].
Data collection and analysis The data collection followed a protocol developed by the European Centre for Disease Prevention and Control (ECDC) to (i) obtain data on COVID-19 outbreaks in LTCFs, (ii) assess the severity of breakthrough infections by vaccination status in LTCF residents and staff, and (iii) assess determinants of infection, hospitalisation and death  [2]. Aggregate data were collected through the European surveillance portal for infectious diseases (EpiPulse). Data on COVID-19 outbreaks were reported on a voluntary basis, and included type of LTCF, starting date of the outbreak, ending date of the local vaccination campaign, vaccine product, testing strategy, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) sequencing results, and denominator data by vaccination status for residents and staff.
(3. 35) In the next subsection §3. 4. 1 we shall demonstrate this agreement in the case of a 3-node cyclic quiver, postponing the case of a general cyclic quiver with K nodes to §4. 5. In §3. 4. 2 we analyze the deep scaling contribution for general Abelian quivers with multiple oriented cycles We have also implemented a Mathematica code (included in the package CoulombHiggs. m [33]  which numerically solves the deformed Denef equations (3. 32) and then computes the integral (3. 34) (with the sum extended to all collinear solutions) by residue calculus. We have checked this algorithm correctly reproduces the index computed by the Jeffrey-Kirwan residue formula in a variety of 4-node and 5 node quivers with more than one cycle (see the Mathematica notebook available from  [33] ). Unfortunately, the numerical search of solutions to (3.
Acknowledgments We are grateful to  Pierre Descombes ,  Philippe Di Francesco ,  Mourad Ismaïl ,  Jan Manschot ,  Sergey Mozgovoy ,  Ashoke Sen ,  Piljin Yi  and  Jean-Bernard Zuber  for useful discussions related to parts of this project. The research of SM is supported by  Laureate  Award  15175  " Modularity in Quantum Field Theory and Gravity " of the  Irish Research Council.
In the case of perturbations of the Minkowski space, one considers initial data such that Σ = R 3 and the data are asymptotically flat i. e. g 0 tends to the Euclidean metric and k tends to 0 as |x| = r → ∞. The positive mass theorem  [SY79; Wit81]  then implies that g 0 = δ E (1 + 2m/r) + o(r -1-ρ ), where δ E is the Euclidean metric, ρ > 0 and where m > 0 unless the initial data correspond to an initial data set induced by the Minkowski space, in which case the solution of the evolution problem must naturally coincide with Minkowski space. The positive mass theorem limits the possible radial decay of the initial data. In particular, one cannot consider compact initial data, for which the metric perturbations would be all contained in some ball of finite radius. The closest one can get from those are initial data corresponding to the Schwarzschild metric outside from some compact set.
Moreover, we obtain sharp pointwise decay estimates on the components of the energy-momentum tensor T [f ] as well as its derivatives. Remark 1. 6. The geodesic completeness is a direct consequence of the asymptotics of the metric and its derivatives. See for instance  [LR05] , Section 16. Remark 1. 7. For simplicity, we have considered initial data which coincides with the Schwarzschild data outside of a compact set. Since we use a hyperboloidal foliation, our results do not extend immediately to more general data that would allow the Vlasov field to have non-compact support in the x variable. We note however that the method of this paper are readily applicable (with slightly different asymptotics) for initial data such that f is initially supported in B x × R 3 v , for some compact set B x , and the data for the metric is such that the analysis of  [CK93]  or  [LR10]  is applicable.
Eichmair as well as through the project Geometric transport equations and the non-vacuum Einstein flow (P 29900-N27). J. J. and J. S. are supported in part by the ANR grant AARG, "Asymptotic Analysis in General Relativity" (ANR-12-BS01-012-01). J. S. acknowledges funding from the European Research Council under the European Union's Horizon 2020 research and innovation program (project GE-OWAKI, grant agreement 714408). D. F. , J. J. and J. S. acknowledge the partial support of the Erwin Schrödinger International Institute for Mathematics and Physics during the workshop Geometric Transport equations in General Relativity, where part of this work has been written.
• The following estimates hold ||g t=0 -δ|| H N , ||∂ t g t=0 || H N -1 ≤ C(R) , ||(1 + |v| 2 ) q/2 f t=0 || W N +3,1 + ||(1 + |v| 2 ) (q+2)/2 f 0 || W N -2,1 ≤ C(R). • ∂ t g t=0 and f t=0 vanish for |x| > R. • g coincides with the metric of a Schwarzschild metric in wave coordinates for |x| > R. Moreover, we can shift the initial slice t = 0 to any other initial time, and we assume here that the pde data is given at time t = 2. By rescaling, we may as well assume that R = 1 and we shall do so in the remainder of the paper. To summarize, we assume that the initial data is given on {t = 2} and coincide with Schwarzschild data outside of the ball {|x| < 1}. We recall that the Schwarzschild metric g m in standard wave coordinates (t = x 0 , x 1 , x 2 , x 3 ) takes the form (see for instance  [Asa89] ) g m 00 = - r -m r + m , g m ab = r + m r -m ω a ω b + (r + m) 2 r 2 (δ ab -ω a ω b ), with ω a := x a /|x| and r = |x|.
(2. 26) 2. 11. Analysis of the support. Since our data is exactly Schwarzschild outside from a compact ball, it follows by a standard domain of dependence argument that the solution will be exactly Schwarzschild outside from some cone. More precisely, Proposition 2. 3. Let (g, f ) be a solution to the system (1. 1)-(1. 2) with initial data given on t = 2 coinciding with the data induced by the Schwarzschild metric for |x| ≥ 1. Then (g -g m ) is supported in the region K and vanishes in a neighborhood of the boundary {r = t -1, t ≥ 2}. Proof. We follow here the standard argument, as explained in [LM15, Section 4. 2] (see also  [LR05, Lemma 4. 1]). Essentially, we rewrite the equations in terms of q = g -g m and f , where g m is the Schwarzschild metric. We then prove that the equations are homogeneous (i.
08% of the population of Hubei; however, as of September 2, 2020, there were 6. 05 million cases, which represents about 2% of population. Logistic models are a simplified analysis of infection propagation without respect to rate of conversion between susceptible, infected, exposed and recovered. Zhou et al. (2020)  compared SEIR and logistic models and argued that logistic models are not effective for forecasting future pandemic dynamics if the known dynamics are exponential. Mathematically, logistic model assumes that prediction power and curve fitting of the model depends on the historical dataset so logistic model can predict the infection ratio accurately if it is controlled by population and growth rate. Carcione et al. (2020)  analysed how the value of R 0 impacts COVID-19 dynamics assuming that the rate of infection depends on measures taken and predicted a death toll of approximately 2.
Dataset description We used daily data about COVID-19 dynamics in each U. S. state  (COVID Tracking Project, 2020)  and European countries (Open Data, 2020) used. These datasets only contain the number of infected and recovered people; we assume that whole population is susceptible. Data for each state was divided by population. Data obtained from (www. covid track ing. com Copyright©2020 by The Atlantic Monthly Group, 2020) has errors that could distort the results, including reducing the number of dead people on some days, empty fields, NaN (not a number) values and zero new positive individuals on some days. In order to resolve these issues, we replaced empty rows NaNs values (missing values in data set) with previous known values, and if there is no value, then we replaced it with zero.
Thus, all newly infected and recovered statistics will be represented in next day. The EU's Open Data website contains the cumulative number of cases and deaths as well as the total population in each country in the world, which enables the calculation of the number of infected individuals as a fraction of the country's population. We used data from December 31, 2019 (Day 1) to September 13, 2020 for the U. S. and the seven most populated European countries. A graphical representation of the data used for analysis is shown in Fig. 1.