dataesr/scientific-paragraphs-categorization huggingface dataset:
Acknowledgments. We thank D. Abramovich, A. Beauville, M. Bousquet-Mélou, J. Bryan, C. Faber, T. Graber, F. Janda, Y. -P. Lee, D. Maulik, A. Okounkov, A. Pixton, D. Ranganathan, and Y. Ruan for conversations over the years related to monodromy and degeneration in Gromov-Witten theory. The last steps of the argument were completed at the Helvetic Algebraic Geometry Seminar hosted by A. Szenes at the University of Geneva in August 2021. H. A. was supported by Fondation Mathématique Jacques Hadamard. R. P. was supported by SNF-200020-182181, ERC-2017-AdG-786580-MACI, and SwissMAP. D. Z. was supported by ANR-18-CE40-0009 ENUMGEOM. This project has received funding from the European Research Council (ERC) under the European Union Horizon 2020 research and innovation program (grant agreement No 786580).
0. 8. 8 Acknowledgments. We thank D. Abramovich, A. Beauville, M. Bousquet-Mélou, J. Bryan, C. Faber, T. Graber, F. Janda, Y. -P. Lee, D. Maulik, A. Okounkov, A. Pixton, D. Ranganathan, and Y. Ruan for conversations over the years related to monodromy and degeneration in Gromov-Witten theory. The last steps of the argument were completed at the Helvetic Algebraic Geometry Seminar hosted by A. Szenes at the University of Geneva in August 2021. H. A. was supported by Fondation Mathématique Jacques Hadamard. R. P. was supported by SNF-200020-182181, ERC-2017-AdG-786580-MACI, and SwissMAP. D. Z. was supported by ANR-18-CE40-0009 ENUMGEOM. This project has received funding from the European Research Council (ERC) under the European Union Horizon 2020 research and innovation program (grant agreement No 786580).
Numerical results Obtaining a stable implementation of the fixed point equations can be challenging. We provide simulation details in appendix F along with a link to the script we used to produce the figures. Theoretical predictions (full lines) are compared with numerical experiments (points) conducted using standard convex optimization solvers from [PVG + 11]. The comparison with finite size (N ≡ a few hundreds) numerical experiments shows that, despite being asymptotic in nature, the predictions are accurate even at moderate system sizes. All experimental points were done with N = 200 and averaged one hundred times. with the data matrix F being Left : a Gaussian i. i. d. matrix and Right : a random orthogonal invariant matrix with a squared uniform density of singular values. We plot the angle between the estimator and the ground-truth vector θ = arccos(m * x /( √ ρ x q * x )) as a function of the aspect ratio α = M/N with three different losses: ridge regression, a Support Vector Machine with linear kernel and a logistic regression.
F Numerical implementation details The plots were generated using the toolbox available at https://github. com/cgerbelo/Replica_GLM_ orth. inv. git Here we give a few derivation details for implementation of the equations presented in Theorem 1. We provide the Python script used to produce the figures in the main body of the paper as an example. The experimental points were obtained using the convex optimization tools of [PVG + 11], with a data matrix of dimension N = 200, M = αN , for α ∈ [0. 1, 3]. Each point is averaged 100 times to get smoother curves. The theoretical prediction was simply obtained by iterating the equations from Theorem 1. This can lead to unstable numerical schemes, and we include a few comments about stability in the code provided with this version of the paper. For Gaussian data, the design matrices were simply obtained by sampling a normal distribution N (0, 1/M ), effectively yielding the Marchenko-Pastur distribution  [TVV04]  for averaging on the eigenvalues of F T F in the state evolution equations : λ F T F ∼ max(0, 1 -α)δ(λ -0) + α (0, λ -a) + (0, b -λ) + 2πλ (122) where a = 1 -1 α 2 , b = 1 + 1 α 2 , and (0, x) + = max(0, x).
Acknowledgments The authors would like to thank  Andrea Montanari ,  Benjamin Aubin ,  Yoshiyuki Kabashima  and  Lenka Zdeborová  for discussions. This work is supported by the  French Agence Nationale de la Recherche  under grant  ANR-17-CE23-0023-01 PAIL  and  ANR-19-P3IA-0001   PRAIRIE. Additional funding is acknowledged from "Chaire de recherche sur les modèles et sciences des données ",  Fondation CFM pour la Recherche-ENS.
An alternative option consists of computing the gradient analytically. Both these solutions are faced with limitations: the first approach gets computationally intractable in high dimensions, while the analytic gradients are sometimes impossible to estimate. All of these new techniques for cosmological analyses make the development of fast and differentiable simulations necessary. Böhm et al. (2021)  developed MADLens, a CPU-based Python package for producing non-Gaussian lensing convergence maps. These maps are differentiable with respect to the initial conditions of the underlying numerical simulations and to the cosmological parameters Ω m and σ 8. In this paper, we aim to efficiently compute gradients that benefit the development of new inference algorithms for weak-lensing surveys. To do so, we extended the framework of the FlowPM package  Modi et al.
The choice to extend the FlowPM code with the ODE implementation is motivated by the fact that to compute the gradient of the forward model, the original algorithm needs to store all the intermediate steps of the simulations. This induces a memory overhead that scales with the number of time steps in the simulation. In the adjoint ODE approach, this is instead replaced by solving another ODE backward in time when evaluating the gradient. We illustrate the potential of differentiating through ODE solvers, highlighting the fact that the simulations and the gradients presented in this paper are computed using one single GPU for 128 3 particles. The computational cost of the various steps of the simulations is listed in Table  1. It should be noted that when computing the gradient, some instability may arise from the ODE solver due to numerical errors in discretizing the continuous dynamics.
Validating simulations for LSST In this section, we compare the results from our simulation to other works, including the analytic models for the matter power spectrum Halofit  (Smith et al. 2003; Takahashi et al. 2012 ) and the cosmological N-body simulations, κTNG-Dark  (Osato et al. 2021). The κTNG simulations is a suite of publicly available weaklensing mock maps based on the cosmological hydrodynamical simulations IllustrisTNG, generated with the moving mesh code AREPO  (Springel 2010). In particular, we used the κTNG-Dark suit of maps based on the corresponding dark matter-only TNG simulations. The simulations have a side length of the box equal to 205 Mpc h -1 and 2500 3 CDM particles. To model the propagation of light rays and simulate the weak-lensing maps, a multiple-lens plane approximation is employed.
For lower source redshifts, the deficit of power in our simulations becomes worse. This can be explained considering that a given value of at lower redshift corresponds to smaller scales, some of those below the resolution of our simulations. We conclude that, if for z = 0. 91 and z = 1. 30, we have a general agreement with κTNG-Dark; with this specific setting of the model, we cannot model cases correctly with sources redshift lower than z = 0. 91. We want to highlight that the results shown are produced keeping the resolution of the simulations extremely low, and we do not expect to get the same precision as κTNG-Dark. The purpose of these tests and the overall goal of the paper is to present a proof of concept of the DLL package and its potential. In practice, we do not work at this resolution.
Indeed, while the peak counts reach the convergence with ∼1500 simulations, the C proves to be more sensitive to noise and thus, requires more realizations to convergence. In Fig. B. 1, we tested the stability of the Fisher contours by changing the number of simulated maps used to compute the Jacobian. The priors used in the forecast process, are listed in Table  2  following  Zhang et al. (2022). To take into account the partial coverage of the sky, we scaled the Fisher matrix by the ratio f map / f survey , where f map is the angular extend of our κmap 2 Code publicly available at: https://github. com/LSSTDESC/DifferentiableHOS/ statistics A61, page 9 of 18  Lanzieri, D. , et al. : A&A 679, A61 (2023)   f map = 25 deg 2 and f survey corresponds to the size of the convergence maps for a Stage IV-like survey f survey = 15 000 deg 2.
Conclusions In this paper, we present the Differentiable Lensing Lightcone (DLL) model, a fast lensing lightcone simulator providing access to the gradient. We extended the public FlowPM Nbody code, implementing the Born approximation in the Tensorflow framework to create non-Gaussian convergence maps of weak gravitational lensing. To allow DLL to run at low resolution without affecting significantly the accuracy, we complemented the FlowPM N-body code with the HPN scheme, a new correction scheme for quasi N-body solver, based on neural networks implemented as a Fourier-space filter. We validate our tool by comparing the C and peak counts statistics against predictions from κTNG-Dark simulations. To do this, we ran simulations following the evolution of 128 3 particles and we produced weak-lensing convergence maps for several redshift sources.
Acknowledgements. DESC acknowledges ongoing support from the  IN2P3 (France) , the  STFC (United Kingdom) , and the  DOE ,  NSF , and  LSST Corporation (United States). DESC uses resources of the  IN2P3 Computing Center  ( CC-IN2P3-Lyon/Villeurbanne -France ) funded by the  Centre National de la Recherche Scientifique ; the  National Energy Research Scientific Computing Center , a  DOE Office of Science User Facility  supported under Contract No. DE-AC02-05CH11231 ;  STFC   DiRAC HPC  Facilities, funded by  UK BEIS National E-infrastructure  capital grants; and the UK particle physics grid, supported by the  GridPP  Collaboration. This work was performed in part under  DOE  Contract  DE-AC02-76SF00515. This work was granted access to the HPC/AI resources of IDRIS under the allocation  2022-AD011013922  made by GENCI.
Introduction The era of "Big Data", which deals with massive datasets, has brought new analysis techniques for discovering new valuable information hidden in the data  [1]. Among these techniques is multilinear low-rank approximation (LRA) of matrices and tensors, which has recently attracted considerable attention from engineers and researchers in the signal processing and machine learning communities  [2]. A tensor is a multidimensional array and provides a natural representation of high-dimensional data. Low-rank approximation of tensors (t-LRA) can be considered as a multiway extension of LRA of matrices (which are two-way) to higher dimensions  [3]. Generally, t-LRA is referred to as tensor decomposition which factorizes a tensor into a sequence of basic components  [3]. As a result, t-LRA provides a useful tool for dealing with several large-scale multidimensional problems in modern data analysis that would otherwise be intractable by classical methods.
Thanks to the recursive least-squares technique in adaptive filtering and the alternating direction method of multipliers (ADMM) method, RACP is capable of online detecting sparse outliers and tracking successfully the underlying CP model of data streams over time. In parallel, some adaptive CP decomposition algorithms, such as  [17] [18] [19] [20] [21] , are capable of handling higher-order tensors. However, they do not handle incomplete datasets. Under the Tucker format, there are many adaptive methods capable of factorizing streaming tensors in online settings  [7]. Particularly, several Tucker trackers were proposed to decompose streaming tensors having one mode/dimension evolving with time. Some of them work under the assumption that temporal slices of the streaming tensor interact with the same core tensor of fixed size, such as RPTucker  [22] , BASS-Tucker  [23] , RT-NTD  [24] , BK-NTD  [24] , and D-TuckerO  [25].
Accordingly, when λ < 1, this can facilitate the tracking ability of estimators, especially in time-varying and non-stationary environments. The effective window length for λ < 1 is (1 -λ) -1 when t is large. When λ = 1, (9) boils down to its counterpart of (5) in batch setting. In the next two sections, we describe the two proposed algorithms for solving  (9)  under CP and Tucker decompositions. We make the following four assumptions for the convenience of deploying our algorithms as well as analyzing their performance. (A1) Observed tensor slices {X t } t≥1 are independent and identically distributed from a data-generating distribution, which is the underlying distribution of the dataset, having a compact set V. This assumption is very common for convergence analysis in online settings in general and adaptive tensor decomposition in particular, e.
Resource Availability Lead Contact: Further information and requests for resources should be directed to and will be fulfilled by the lead contact, Dr. Nguyen Linh Trung (linhtrung@vnu. edu. vn). Materials Availability: No new materials were generated in this study. Data and Code Availability: All original code has been deposited at https://github. com/thanhtbt/tensor tracking and archived in Figshare under the https://doi. org/10. 6084/m9. figshare. 22276105. Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.
Real Data To demonstrate the effectiveness of our algorithms on real datasets, we consider two related applications: video completion and multichannel EEG analysis. video, we use a set of binary masks of the same size as the video frames and their entries are derived from a Bernoulli model with probability ρ (i. e. , ρ indicates the missing density). Then, we apply the Hadamard product to multiply these masks with all video frames (each mask corresponds to each frame) in order to create zero entries, as in the previous tasks on synthetic data. We compare the proposed algorithms with OLSTEC  [9] , TeCPSGD  [8]  and CP-PETRELS  [10]. We set the value of λ at 0. 7 and 0. 999, respectively, for OLSTEC and CP-PETRELS. Besides, OLSTEC and TeCPSGD also depend on the regularization parameter µ whose value is fixed at 0.
1. The performance of these algorithms is shown statistically in Tab. 3 and graphically in Fig. 11. We can see that ATD outperforms adaptive CP algorithms in almost all tests. ACP also provides reasonable estimation accuracy on these data as compared to others. CP-PETRELS seems to fail to track the video background and thus fails to recover missing data. With respect to the running time, experimental results indicate that ACP is the fastest adaptive CP decomposition. We refer readers to to the supplemental information document for more experimental results (see Figs. S7-S10 ). Multichannel EEG Analysis: We follow the experimental framework in  [74, 75]  to illustrate the use of ACP for analyzing multichannel EEG signals. In this task, we use a public EEG dataset collected on 14 subjects during the stimulation of hands (EEG data: http://www.
erpwavelab. org/index. htm). The EEG signals are recorded using a system of 64 channels (electrodes) and we have 28 measurements per subject in total. We construct a 3rd-order EEG tensor of measurement × channel × time-frequency by taking a continuous wavelet transform of each EEG channel, as in our past works  [16, 76]. Note that, the resulting time-frequency representations are reshaped into vectors of length 4392 and are hence streamed. In a nutshell, we have the EEG tensor whose size is 28 × 64 × 4392 and its rank is set at 3 as provided in  [74, 75]. At each time, data of 20 (and 40) channels are assumed to be discarded randomly for our missing observation purpose. We evaluate the performance of ACP by comparing it with the adaptive NL-PETRELS algorithm in  [75]  and the batch CP-WOPT algorithm in  [74].
Housing conditions and household data collection The head of household was asked to answer a specific questionnaire documenting their individual characteristics (age, gender, education, profession), household structure (number and age of members) and housing conditions including housing equipment, goods and incomes of family (car, television, motorbike, cell phone, external funding…). Assessing social characteristics and housing conditions, three specific profiles have been determined. To determine household profile as social proxy the location and family structure, goods and incomes and housing conditions were used.
Serology analyses were performed at the Charles Mérieux Infectiology Centre in Bamako, Mali. Participants were defined as SARS-CoV-2 seropositive if they presented either a positive IgG or IgM result. Individuals were defined as SARS-CoV-2 seronegative if they presented a negative IgG and IgM result, or a negative IgG and a missing IgM result. Individuals with missing IgG results were excluded from the seroprevalence analysis. The seroprevalence was estimated as the number of SARS-CoV-2 seropositive by the number of participants. The number of infections for the district of Bamako was estimated using the population of Bamako by sex and age categories. The number of deaths was estimated by using the age-specific and sex-specific mortality data reported early in the pandemic (February-March in China, prior to the optimisation of clinical management).
Data analysis First, descriptive analyses estimated mean, prevalence and frequencies, associated with 95% CI. Household profiles were determined by using a twostep descriptive approach:  12  first a multiple component analysis, second a Hierarchical Ascendant Classification. Based on household level variables, this approach led to determine classes according to the different household profiles. Each individual was assigned to its household profile. Second, in order to estimate factors associated with SARS-CoV-2 seropositivity, we used logistic generalised additive multilevel models (GAMM). 13 We analysed the effects of age and sex at individual level, as well as household profile. 14 Intrahousehold contamination was assessed as a binary variable (more than one positive case or not). The GAMM approach allowed also verifying the non-linear effect of continuous covariates by using spline smoothing.
15 The model included random effects for household, compound and district sector to reflect sampling structure and potential correlations between participants sharing the same living space (household nested in compound sampled in the same sector). Main statistical tests were performed using an α-probability threshold of 5%, but with Bonferroni correction for subgroup analyses. Data analyses were performed using the SPSS software (IBM, Released 2020. IBM SPSS Statistics for Windows, V. 27. 0, IBM) for the questionnaire data management and descriptive analyses, and the R software (V. 4. 0. 0, R Core Team 2020. R Foundation for Statistical Computing, Vienna, Austria. ) with the following specific packages: (FactoMineR), (lme4), (gamm4).
Inclusions A sample of 174 housing units (separate living quarter) was investigated including 2015 inhabitants grouped in 306 identified household units. Of 2015 inhabitants, 1526 (75. 7%) participants aged ≥1 year provided a blood sample for the seroprevalence survey and 962 participants aged ≥12 years answered the Knowledge, Attitudes, Behaviours, Practices (KABP) survey (online supplemental appendix table A1). Data on housing conditions were collected for 220 of the 306 household units included, that is, 78. 9% of the household members tested (n=1204) (figure  2 ).
Acknowledgements We acknowledge the populations of the  Commune VI, Bamako , the community health association and all the community leaders. Contributors JG and HB conceived and designed the study protocol, helped by JL, IS, MC, BK, IB, AG, OD, AAD, MA, EB, LS-T, LV and M-KB. All the authors validated the study protocol. M-KB wrote the household and KABP questionnaires, with the help of JL, MC, JG and IS. MC, AKS and IS organised and supervised the samples and data collections, performed by AK, SS, ZD, CD, IT, ST, MH. ST and IT were in charge of the information system under the supervision of IS. JL, M-KB, MC and JG conceived and designed the data analysis. JL, M-KB and MC performed the data management and analysis, under the supervision of JG. BK and AKS designed and supervised the serological analysis, performed by MH, ES, KC.
This publication is based on work supported by the  NSF  through grant no. DMS-1348092. RC acknowledges support from  Rennes Métropole , through its  AIS program. CK is partially supported by the  ANR-FWF  project  ANuI  - ANR-17-CE40-0035 , the isite  BFC  project  NAANoD , the  EIPHI Graduate School  (contract  ANR-17-EURE-0002 ), by the  European Union   Horizon 2020 research and innovation program  under the  Marie Sklodowska-Curie RISE 2017  grant agreement no. 778010 IPaDEGAN and the  EITAG  project funded by the  FEDER de Bourgogne , the  region Bourgogne-Franche-Comté  and the  EUR EIPHI.
B. 1 Implementation Details In this subsection, we present some practical points concerning implementation details, for the language Python. Source code is in the GitHub link  [14]. Indeed, Python has already enough commands to implement New Q-Newton's method. There is a package, named numdifftools, which allows one to compute approximately the gradient and Hessian of a function. This package is also very convenient when working with a family f (x, t) of functions, where t is a parameter. Another package, named scipy. linalg, allows one to find (approximately) eigenvalues and the corresponding eigenvectors of a square matrix. More precisely, given a square matrix A, the command eig(A) will give pairs (λ, v λ ) where λ is an approximate eigenvalue of A and v λ a corresponding eigenvector. One point to notice is that even if A is a symmetric matrix with real coefficients, the eigenvalues computed by the command eig could be complex numbers, and not real numbers, due to the fact that these are approximately computed.
Acknowledgements The first author is supported by  Young Research Talents Grant  Number  300814  from the  Research Council of Norway. The research of this paper was also facilitated by a travel Grant from the  Trond Mohn Foundation  for the first author to visit Torus Actions SAS. We thank  Claire McLaughlin  for checking the manuscript, and thank anonymous referees for constructive feedbacks. Funding Open access funding provided by  University of Oslo (incl Oslo University Hospital).
Numerical Examples In this section, we illustrate the above results with several numerical examples of linear FIDE using MATLAB R2020a. The error estimation is given to show the accuracy and efficiency of our method (OM). The absolute error used is defined as follows: 1 ∫ 0 ⎛ ⎜ ⎜ ⎝ N-m � j=0 j C Φ j (x) -f (x) - 1 ∫ 0 K(x, ) N-m � j=0 j Φ j ( )d ⎞ ⎟ ⎟ ⎠ × ⎛ ⎜ ⎜ ⎝ C Φ i (x) - 1 ∫ 0 K(x, )Φ i ( )d ⎞ ⎟ ⎟ ⎠ dx = 0, (5. 5 ) 1 ∫ 0 ⎛ ⎜ ⎜ ⎝ N-m � j=0 j C Φ j (x) - 1 ∫ 0 K(x, ) N-m � j=0 j Φ j ( )d ⎞ ⎟ ⎟ ⎠ × ⎛ ⎜ ⎜ ⎝ C Φ i (x) - 1 ∫ 0 K(x, )Φ i ( )d ⎞ ⎟ ⎟ ⎠ dx 1 ∫ 0 f (x) ⎛ ⎜ ⎜ ⎝ C Φ i (x) - 1 ∫ 0 K(x, )Φ i ( )d ⎞ ⎟ ⎟ ⎠ dx, ∀i = 0, … , N -m. A = B, ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ A ji = ∫ 1 0 � C Φ j (x) -∫ 1 0 K(x, )Φ j ( )d �� C Φ i (x) -∫ 1 0 K(x, )Φ i ( )d � dx, = ( 0 , 1 , … , N-m ) T , B i = ∫ 1 0 f (x) � C Φ i (x) -∫ 1 0 K(x, )Φ i ( )d � dx.
Conclusion In this paper, we have presented a numerical method for solving linear Fredholm fractional integro-differential equations (FIDEs) with the aim of obtaining a more accurate solution. The novelty of our approach lies in the utilization of the least squares method in conjunction with spectral approximation using a compact combination of shifted Chebyshev polynomials of the first kind, instead of solely relying on shifted Chebyshev polynomials (SCP). By employing this method, we were able to transform the FIDEs into a system of linear algebraic equations, resulting in an excellent approximation with zero absolute error and achieving the best possible outcome. To validate our theoretical results, we provided appropriate examples and varied the order of the fractional derivative to observe the behavior of the solution using MATLAB R2020a.