dataesr/scientific-paragraphs-categorization huggingface dataset:
Numerical simulations In this section, and via MATLAB software, we give some numerical simulations to illustrate our analytical results. The used parameters and related values are summarized in Table  1. Here, we assume that W is of the same scale as the infectious population and decreases over time if no further input occurs (Figure  1 ). Remark 7. 1. As the study of the characteristic equation with two different delays becomes is more complicated, numerical simulations show that the asymptotic behavior of equilibria remains the same for ≠ τ ν, as illu- strated in Figures  2  and 3.
EPSRC  Grant Number  EP/K032208/1 , where the third author joined the project, and where preliminary versions of this work were presented. B. D. also gratefully acknowledges the support of a  Simons Foundation  fellowship on the  INI Random Geometry program , and thanks the  Max Planck Institute for Mathematics, Bonn , for its hospitality. G. B. acknowledges financial support from the  Simons Foundation  and the  Max-Planck Gesellschaft. J. B. acknowledges financial support from the  Agence Nationale de la Recherche  via the grants  ANR-12-JS02-001-01  " Cartaplus " and  ANR-14-CE25-0014  " GRAAL ", and the  City of Paris  through the project " Combinatoire à Paris ". B. D. acknowledges financial support from the  Agence Nationale de la Recherche  via the grant  ANR-14-CE25-0014  " GRAAL "; he is also partially funded by the  CNRS Projet international de coopération scientifique (PICS)  " Conformal Liouville Quantum Gravity " n o  PICS06769.
Acknowledgements SMG is very grateful to  Patrick Popescu-Pampu  for bringing to her knowledge interesting references, in particular [13, Prop. 5. 21]. The authors would like to thank  Valentin Ovsienko  and  Christophe Reutenauer  for stimulating discussions on the subject,  Perrine Jouteur  for pointing out major typos in the previous version of the article, and the anonymous referees whose valuable comments helped to greatly improve the presentation of the paper.
We acknowledge the complexity of pathogen responses to land use modification  56  and the important limitations of our findings. The datasets used here are all static yet global and accessible. The static nature of the datasets is one limitation in our assessment, as risk might vary temporally due to changes not apparent in static data. Hotspots may change in response to changes in economic and agricultural policies at national and subnational levels, international agreements such as Agenda 2030, and climate change adaptation  57. There are also several empirical data limitations. For instance, although the data sources for the health facilities are generally accurate  35  , omission errors can occur. Hospitals and clinics may close over time and while new ones are built, so it is important to take these limitations into consideration in local contexts, especially when access to healthcare is not possible using motorized vehicles.
We also included wild mammals as potential secondary (aka intermediate) hosts, minus the known bat hosts (Scenario 3, Scenario 4), because EID risk is elevated in forested tropical regions experiencing land-use changes and where wildlife biodiversity (mammal species richness) is high. SARS-CoV-2 has also been detected in wildlife (spillback events)  63, 75. To avoid collinearity, we only selected variables with productmoment correlation coefficient (r) values < ±0. 7 (Supplementary Fig. 11 ). The study region was divided into a spatial grid composed of 0. 25 decimal degrees-sized tiles (~27 km). All variables were resampled to match this resolution. For data layers that were counted from shapefiles (other mammal species numbers), we applied median values for resampling. We ran a univariate hotspot analysis based on Getis-ord G*i values  82  considering each factor individually at 95% and 99% cut-off for critical values using rgeoda 0.
We compared travel time in high-risk areas among scenarios using Wilcoxon's test. China has the largest number of pixels with healthcare facilities in the world, followed by other countries considered in our analysis, such as India, Indonesia, Thailand, and Malaysia. We assume that the travel time to healthcare dataset is adequately accurate for our study region since source data from Google Maps and Open Street Map data sources have robust quality controls  35. More details on healthcare facility data coverage and accuracy in our study region are provided in Supplementary Tables  2  and 3. All analyses were done in QGIS 3. 10. 7 85 , R 4. 1. 3  86  , and bash  87.
Acknowledgements We thank  Dr. Jinhong Luo  and  Marco A. R. Mello  for their comments on earlier versions of the draft. Massey University's subscription to New Zealand eScience Infrastructure (NeSi) enabled us to use highperformance computing facilities. Te Pūnaha Matatini  gave us support during the 2022 Mahia Te Mahi workshop. R. L. M. , D. T. S. H. , and R. S. J. are supported by  Bryce Carmine  and  Anne Carmine  ( née Percival ) through the  Massey University Foundation ; D. T. S. H. is supported by the  Royal Society Te Apārangi , grant No. MAU1701.
On the other hand many real-world datasets for instance in finance refer to discrete observation times  [8]. Therefore, it appears natural to consider discrete-time variants of (generalized) telegraph type processes calling still for thorough analytical investigation. In a recent work  [25] , we introduced a discrete-time semi-Markovian version of the telegraph process, the 'squirrel random walk' (SRW), which is also subject of the present paper. We chose that name since the SRW walker (the 'squirrel') in a sense has a 'weaker' memory as in walks with a full memory of their history such as the 'elephant' walker in the so called elephant random walk (ERW)  [30]. Our paper is organized as follows. In Section 2 we give a brief account for discrete-time renewal processes and introduce pertinent generating functions for the present study.
Acknowledgements. It is a pleasure to thank Dustin Clausen, Emanuele Dotto, Yonatan Harpaz, Gijsbert Scheltus Karel Sebastiaan Heuts, Corina Keller, Achim Krause, Markus Land, Denis Nardin, Thomas Nikolaus, Stefan Schwede, Wolfgang Steimle and Lior Yanovski for several very useful discussions. We further thank Shaul Barkan and Jan Steinebrunner for pointing out an omission in the verification of orthogonality for the factorisation system on span categories in the original version of this paper. The authors have no competing interest to declare. Funding statement. During the preparation of this text, FH and SL were members of the Hausdorff Center for Mathematics at the University of Bonn funded by the German Research Foundation (DFG), and FH was furthermore a member of the cluster 'Mathematics Münster: Dynamics-Geometry-Structure' at the University of Münster under grant nos.
EXC 2047 and EXC 2044, respectively. FH would also like to thank the Mittag-Leffler Institute for its hospitality during the research program 'Higher Algebraic Structures in Algebra, Topology and Geometry', supported by the Swedish Research Council (VR) under grant no. 2016-06596. FH and JN were further supported by the European Research Council (ERC) through the grants 'Moduli Spaces, Manifolds Competing interest. and Arithmetic', grant no. 682922, and 'Derived Symplectic Geometry and Applications', grant no. 768679, respectively. SL was supported by the DFG Schwerpunktprogramm 1786 'Homotopy Theory and Algebraic Geometry' (project ID SCHW 860/1-1). https://doi. org/10. 1017/fms. 2023. 107 Published online by Cambridge University Press.
Raw seismic waveforms were recorded in the Kiirunavaara mine (Sweden) by a seismic network (253 seismic sensors spanning the 3D volume around the ore body  (Dineva et al. , 2022) ). From the raw seismic waveforms, P-and S-wave arrival times were automatically retrieved and manually revised by the local seismic system provider (Institute of Mine Seismology, IMS). These arrival times are the data used to solve the geophysical inverse problem of locating the seismic source. In the first data set, the seismic source is a man-made blast used to calibrate the seismic system. The position of the seismic source is known with an accuracy less than 1 meter. This data set can be used as the input of a robust field test, as the source location is known with an accuracy higher than the half-width of the characteristic wavelength of the P-wave (given a blast corner frequency close to 1000 Hz, if we assume Vp = 6600 m/s, for example, the half-wavelength is 3.
3 m. ). Due to the limited amount of explosive used (5 kg), seismic waves have been clearly recorded at 57 seismic sensors only (with 57 P-and 9 S-wave arrival times), which translates in a minimum and maximum sensor distance from the source of 83 and 710 meters, respectively. The second data set is based on P-and S-waves generated during a M w 4. 2 event that occurred on May 18th, 2020. This large event partially destroyed the mine infrastructure in a section about 1300 meters wide  (Dineva et al. , 2022). The resulting P-and S-waves were recorded at 151 seismic sensors (151 P-wave and 81 S-wave arrival times) as far as about 2130 meters from the preliminary seismic source location. Our preliminary seismic source is the official location  (Dineva et al. , 2022) , even though the damaged area may be as large as 700×250 meters.
Acknowledgments We thanks  Mirjana Boskovic  for discussion on calibration blasts in Kiruna mine. N. P. A. research is conducted with the financial support of the  Ministero dell'Istruzione e del Merito  in the framework of the programme " Dipartimenti di eccellenza  ( 2018 -2022 )". The Generic Mapping Tools software has been used for plotting the figures of this manuscript (Wessel & Smith, 1998).
The empirical estimations underlying the impact analysis 12. This paper exploits a new measure of human capital, derived in  Égert et al (2022) , that makes use of mean years of schooling and OECD data from the Programme for International Student Assessment (PISA) and the Programme for the International Assessment of Adult Competencies (PIAAC). The new measure is a cohort-weighted average of past PISA scores (representing the quality of education) of the working age population and the corresponding mean years of schooling (representing the quantity of education). Weights for PISA and mean years of schooling are estimated from the data. The idea underlying the new measure can be summarised as follows: • PIAAC adult test scores could be used to calculate a cohort weighted stock measure of human capital.
Empirical evidences achieved on real data set and artificially noisy data sets confirm the effectiveness of the proposed method compared with the classical approach based on angular velocity transformation. The R functions developed for this paper will be provided in a Github repository. The representation and analysis of the motion of human body is a research subject which has been constantly expanding with the increasing use of sensors. In time series analysis, smoothing is a fundamental step in real world applications, especially when sensors are involved, because a certain amount of noise is captured. The presence of noise can lead to unstable results or even wrong conclusions when data are analyzed and classification or clustering algorithms are applied. In this paper, data registered by a motion sensor called MetaMotionR (MMR), from Mbientlab, are analysed.
The sensor measures the spatial orientation of the hips and stores it as a quaternion time series. The motion of the hip joint is registered under two different conditions: natural walking and a walking made difficult by a knee immobilizer orthosis to simulate a walking impairment due to Amyotrophic Lateral Sclerosis (ALS), Multiple Sclerosis (MS) and other neurodegenerative diseases. In this context, different smoothing techniques for quaternion time series are reviewed. The smoothing technique proposed in 1 has been selected for its simplicity of implementation and its power in making available all the techniques developed in Euclidean spaces. On the basis of this method, a new technique is proposed and compared with the previous one on real and artificially noisy data to understand how the influence of the level of the noise affects the performance of a smoothing methods.
The rest of this paper is organized as follows: "Quaternion time series smoothing methods" section reviews the literature related to smoothing 1D quaternion time series and introduces our proposal. In "Description of the differences between approaches" section a theoretical comparison of some of the methods is presented. "Experimental results" section shows the experimental settings and results of the quaternion wavelet smoothing of real and noisy data in terms of classification performance. In "A real application: data on a human behaviour study" section the application of the proposed method to a real dataset related to a human behaviour study is described. Conclusions and further ideas for research are summarized in "Conclusions" section. Most of the existing smoothing methods for this type of signal are generalizations of classical smoothing techniques originally introduced for Euclidean spaces: the Fourier transform, spline functions, and wavelets.
The MATLAB code to compute the wavelet filter coefficients was presented, but the code to perform a wavelet analysis on quaternion signals is not provided. In  10  an application of MVWs to a simulated quaternion time series is described. Fletcher extended this work 13 adding new wavelet filters of different lengths and explained how to arrange the filters in a matrix for analysing images, applying it to the analysis of a colour vector image. In 14 a different approach to analysing a quaternion signal is presented, with multi-resolution techniques, based on second generation wavelet transform. The quaternion lifting scheme is defined as follows: the input data set is split into two disjoint sets of even and odd indexed samples; samples with odd indices are predicted based on the sample with even indices, using the SLERP or SQUAD methods for quaternion time series (more details are in Section 2 of Supplementary materials).
Data description. The original data set consists of 54 unit quaternion time series of 101 observations each. The time goes from 0 to 100 (%) in steps of 1%. The data were recorded by a wearable motion sensor called Meta-MotionR (MMR) an Inertial Measurement Unit (IMU) from Mbientlab. It is a device that combines a three-axis accelerometer, a gyroscope, and magnetometer, to determine its orientation in the form of a unit quaternion. It is worn at the level of the hip to measure the angle of rotation of the hip during walking movements, at a frequency of 100 Hz. The signal captured by a motion sensor is periodic and composed of actual walking steps referred to as gait cycles. A gait cycle is defined as the sequence of movements performed by the body during the phase delimited by two successive contacts of a given foot with the ground.
We therefore compute an average gait cycle, referred to as the individual gait pattern, by jointly aligning in time and pointwise averaging the segmented gait cycles. Data related to 27 healthy subjects were collected under two different conditions. The first evaluation was made letting the subject perform a natural walking movement. Another record was made using a knee immobilizer orthosis to simulate a walking impairment. To represent 3D rotations we choose a unit quaternion representation for convenience, as suggested in the literature on 3D rotation analysis  21. A unit quaternion represents a 3D rotation between a given object's frame, or coordinate system (the IMU's coordinate system), and a fixed coordinate system defined as the reference. We choose the first orientation observed of the Individual Gait Pattern (IGP) as the reference, and each unit quaternion of the IGP represents the rotation between this first orientation and the one observed at a given time.
For this reason, in the original (  5 ) exp(q) = exp(w)(cos(|v|), x |v| sin(|v|), y |v| sin(|v|), z |v| sin(|v|)) dataset, the first element of each time series is the quaternion (1 0 0 0), representing the identity rotation. We also processed the data in order to 'straighten' the IGP, so that the first and the last element of the IGP are the identity rotation. In order to apply wavelet methods, the original time series is re-sampled to have 128 time points. Figure  1  depicts the component-wise representation of the individual gait pattern data; color represents the two conditions in which the data are collected and that will be used for the classification task: the natural walk and the hindered walk. Alternative representations are provided in Section 3 of Supplementary Materials. In order to understand the influence of noise on the performance of the different smoothing methods, we applied the methods described in "Methods and experimental settings" section to data to which different levels of noise had been added.
• α = 0. 01 , β = 0. 01. Moderate noise, moderately correlated. • α = 0. 01 , β = 0. 1. Moderate noise, weakly correlated. • α = 0. 1 , β = 0. 01. High noise, moderately correlated. The datasets obtained are visually represented in Section 1. 1 of Supplementary Materials. Methods and experimental settings. Wavelet smoothing method with Fourier and spline smoothing, each one embedded in one of the two transformations from H 1 to R 3 , are compared. In order to smooth signals using wavelets, the discrete wavelet transform was applied, with soft thresholding in its generalized sense for multidimensional signals  23  : where w are the p-dimensional vectors of the detail coefficients of the DWT. The chosen threshold was the uni- versal threshold as generalized in  23  : t p = σ 3 log(N) where σ is the standard deviation of the noise.
0001 and β = 0. 0001. The accuracy and the AUC were evaluated and considered as target variables, and smoothing method and type of transformation were considered as covariates. All the computations were performed using the R software (R Core Team (2017)), the figures are generated with the ggplot2 package (v3. 3. 3; Wickham, 2016) and the plotly package (Plotly Technologies Inc. Collaborative data science. Montréal, QC, 2015. https:// plot. ly. ). The R functions developed for this work will be provided in a Github repository.
A real application: data on a human behaviour study In order to confirm the potential of our proposed method, this section reports the empirical evidence achieved on a highly noised dataset. The data considered are related to a behavioural study about small free-standing conversational groups. A sample of the dataset (called CongreG8) is available at the following link: https:// zenodo. org/ record/ 45378 11 and it is described in  27. The dataset contains full-body motion data collected from free-standing conversational groups of three human with a newcomer that approaches the group with the intention of joining it. For each method (Fourier, spline and wavelet) and transformation (logarithm and angular velocity) the best result is presented, where the best result is identified by using the sum of the accuracy and the AUC.
After the preliminary selection, a dataset containing quaternion time series related to 80 subjects, 27 of which labeled as "Ignore" and 53 as "Welcome", is obtained. The final dataset is shown in Fig. 6. Alternative representations are provided in Section 3 of Supplementary Materials. The time series are extremely noised at a visual inspection and the discriminatory power is not clear. Figure  7  depicts the results obtained adapting the pipeline described in "Experimental results" section. Performances of the different smoothing methods are evaluated in terms of classification performances measured as accuracy and AUC. In Fig. 7 , shape distinguishes between Fourier, spline or wavelet smoothing methods and colours distinguish between logarithm and angular velocity transformations. The classification of data without the application of any smoothing method obtain and accuracy of 0.
6 and an AUC of 0. 665. We observe that the accuracy is slightly improved by Fourier in logarithm method, Fourier in angular velocity and wavelets in angular velocity. This improvement does not correspond to an improvement of the AUC, that is lower than the original dataset classification one. The best methods are cubic and quintic splines with logarithm transformation, that obtain the best results in terms of AUC. The accuracy is 0. 6 as the original classification, but could be improved varying the threshold for classification (set as 0. 5 by default). We also observe that the application of different wavelets do not introduce any variability in the results. Wavelets applied with the logarithm method reach the same performances of the data without smoothing. Angular velocity methods show better results in terms of accuracy but much worse in terms of AUC.
Instead, we obtained no evidence about which one of the different smoothing techniques in R 3 should be used, it seems to depend on the particular data set to be analyzed and should be evaluated on a case by case basis. The application of the proposed method to a real noisy dataset confirms the conclusion of the simulated study. Further avenues of research include the application of different noise models to evaluate the influence of the particular nature of the data set, the application of other classification models, and a deeper analysis of the classical smoothing methods applied in this context. Furthermore, quaternion representation and visualization methods in R will be explored in depth. The approach described in this paper can be exploited in terms of the functional representation of quaternion time series, but this aspect needs further study.
• For ε < 0. 55, the equilibrium point E 0 is a locally asymptotically stable focus. • When ε ≈ 0. 55, the system of Chua in the fixed point E 0 becomes unstable, and a period-one limit cycle appears for 0. 55 < ε ≤ 0. 60, as shown in Fig. 15a. • When ε ≈ 0. 68, a new bifurcation occurs, and the period-one limit cycle becomes unstable and a period-two limit cycle appears (Fig. 15b ). • For ε ≈ 0. 706, a-period-4 limit cycle appears through a new bifurcation, as shown in Fig. 15c , followed by a bifurcation to a period-8 limit cycles at ε ≈ 0. 7109; (see Fig. 15d ). This bifurcation process continues up to a critical value of ε = 0. 72, where one chaotic attractor appears; (see Fig. 15e ). At ε = 0. 80 a 1-scroll chaotic attractor appears (see Fig. 15f ). 1/ These results (all figures) are obtained by integrating the differential equation, using the Matlab program over a sufficient period of time.
We introduce a new dataset of ten economic measures in percentage of gross domestic product implemented by governments worldwide between January 2020 and June 2021 to fight COVID-19. The measures coded include fiscal measures (wage support, cash transfers, in-kind transfers, tax cuts, sectorial support and credit schemes), tax deferrals, off-budget measures, and main policy rate cuts. The data can be used to study the impact of economic measures on different outcomes, and to understand the diffusion of economic policies during crises.
Objective Several research groups expressed the intention to inventory all the measures taken by governments during the COVID-19 pandemic  [ 1 , 2 , 3 ]. However, most of these effort s have primarily focused on NPIs and have rarely included the systematically quantified expenses related to a variety of economic measures. Some projects either focus on some specific measures or on some geographical areas. For example, Gentilini et al. [4]  created a database that lists social protection actions taken by governments during the COVID-19 pandemic in 151 countries but does not cover overall fiscal responses. Other projects have focused on geographical areas, such as the Asian Development Bank's COVID-19 Policy or the COVID-19 Observatory in Latin America and the Caribbean. 1 In this paper, we introduce a new dataset of government COVID-19 fiscal responses  [5].