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Machine Learning-Powered data Cleaning for LEGEND: A Semi-Supervised Approach Using Affinity Propagation and Support Vector Machines

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arXiv 2024年

作者： León, E. Li, A. Schott, M.A. Bahena Bos, B. Busch, M. Chapman, J.R. Duran, G.L. Gruszko, J. Henning, R. Martin, E.L. Wilkerson, J.F. Department of Physics and Astronomy University of North Carolina Chapel HillNC27599 United States Triangle Universities Nuclear Laboratory DurhamNC27708 United States Data Science & Statistical Modeling Analysis Group BostonMA02119 United States Department of Physics UC San Diego La Jolla CA92093 United States Halıcıoğlu Data Science Institute UC San Diego La Jolla CA92093 United States Department of Physics Duke University DurhamNC27708 United States

Neutrinoless double-beta decay (0νββ) is a rare nuclear process that, if observed, will provide insight into the nature of neutrinos and help explain the matter-antimatter asymmetry in the universe. The Large Enriched Germanium Experiment for Neutrinoless Double-Beta Decay (LEGEND) will operate in two phases to search for 0νββ. The first (second) stage will employ 200 (1000) kg of High-Purity Germanium (HPGe) enriched in 76Ge to achieve a half-life sensitivity of 1027 (1028) years. In this study, we present a semi-supervised data-driven approach to remove non-physical events captured by HPGe detectors powered by a novel artificial intelligence model. We utilize Affinity Propagation to cluster waveform signals based on their shape and a Support Vector Machine to classify them into different categories. We train, optimize, and test our model on data taken from a natural abundance HPGe detector installed in the Full Chain Test experimental stand at the University of North Carolina at Chapel Hill. We demonstrate that our model yields a maximum sacrifice of physics events of 0.024−+00004003% after data cleaning. Our model is being used to accelerate data cleaning development for LEGEND-200 and will serve to improve data cleaning procedures for LEGEND-1000. © 2024, CC BY.

关键词： Support vector machines

Cohomology and Deformation Theory of O-Operators on Hom-Lie Conformal Algebras

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SSRN

SSRN 2024年

作者： Asif, Sania Wang, Yao Mosbahi, Bouzid Basdouri, Imed School of Mathematics and Statistics Nanjing University of Information Science and Technology Jiangsu Nanjing210044 China Center for Applied Mathematics of Jiangsu Province Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing University of Information Science and Technology Jiangsu Nanjing210044 China University of Sfax Department of Mathematics Faculty of Sciences of Sfax BP 1171 Sfax3000 Tunisia University of Gafsa Faculty of Sciences of Gafsa Gafsa2112 Tunisia

关键词： Algebra

An Enhanced Finite Element Algorithm for Thermal Darcy Flows with Variable Viscosity 1

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21st International Conference on Computational Science, ICCS 2021

作者： Salhi, Loubna El-Amrani, Mofdi Seaid, Mohammed Laboratory Modeling Simulation and Data Analysis University Mohammed VI Polytechnic Benguerir Morocco Mathematics and Applications Laboratory FST Abdelmalek Essaadi University Tangier Morocco Department of Engineering University of Durham South Road DurhamDH1 3LE United Kingdom International Water Research Institute University Mohammed VI Polytechnic Benguerir Morocco

ISBN: (数字)9783030779801

ISBN: (纸本)9783030779795

This paper deals with the development of a stable and efficient unified finite element method for the numerical solution of thermal Darcy flows with variable viscosity. The governing equations consist of coupling the Darcy equations for the pressure and velocity fields to a convection-diffusion equation for the heat transfer. The viscosity in the Darcy flows is assumed to be nonlinear depending on the temperature of the medium. The proposed method is based on combining a semi-Lagrangian scheme with a Galerkin finite element discretization of the governing equations along with an robust iterative solver for the associate linear systems. The main features of the enhanced finite element algorithm are that the same finite element space is used for all solutions to the problem including the pressure, velocity and temperature. In addition, the convection terms are accurately dealt with using the semi-Lagrangian scheme and the standard Courant-Friedrichs-Lewy condition is relaxed and the time truncation errors are reduced in the diffusion terms. Numerical results are presented for two examples to demonstrate the performance of the proposed finite element algorithm. © 2021, Springer Nature Switzerland AG.

关键词： Linear systems

An elementary approach based on variational inequalities for modelling a friction-based locomotion problem

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arXiv 2024年

作者： Chen, Panyu González, Álvaro Mateos Mertz, Laurent Department of Computer Science Duke University United States University of Michigan-Shanghai Jiao Tong University Joint Institute Shanghai Jiao Tong University Shanghai200240 China Modeling Data Analysis & Computational Tools for Biology Research Group Biomathematics Unit Department of Biodiversity Ecology & Evolution Faculty of Biological Sciences Complutense University of Madrid Madrid28040 Spain Department of Mathematics City University of Hong Kong Kowloon Hong Kong

We propose an elementary proof based on a penalization technique to show the existence and uniqueness of the solution to a system of variational inequalities modelling the friction-based motion of a two-body crawling ... 详细信息

关键词： Friction

ROTA-BAXTER OPERATORS, DIFFERENTIAL OPERATORS, PRE- AND NOVIKOV STRUCTURES ON GROUPS AND LIE ALGEBRAS

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arXiv 2024年

作者： Gao, Xing Guo, Li Han, Zongjian Zhang, Yi School of Mathematics and Statistics Lanzhou University Lanzhou730000 China Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics Lanzhou730070 China Department of Mathematics and Computer Science Rutgers University NewarkNJ07102 United States School of Mathematical Sciences Tonji University Shanghai200092 China School of Mathematics and Statistics Center for Applied Mathematics of Jiangsu Province Jiangsu International Joint Laboratory on System Modeling and Data Analysis NUIST Jiangsu Nanjing210044 China

Rota-Baxter operators on various structures have found important applications in diverse areas, from renormalization of quantum field theory to Yang-Baxter equations. Relative Rota-Baxter operators on Lie algebras are closely related to pre-Lie algebras and post-Lie algebras. Some of their group counterparts have been introduced to study post-groups, skew left braces and set-theoretic solutions of Yang-Baxter equations, but searching suitable notions of relative Rota-Baxter operators on groups with weight zero and pre-groups has been challenging and has been the focus of recent studies, by provisionally imposing an abelian condition. Arising from the works of Balinsky-Novikov and Gelfand-Dorfman, Novikov algebras and their constructions from differential commutative algebras have led to broad applications. Finding their suitable counterparts for groups and Lie algebras has also attracted quite much recent attention. This paper uses one-sided-inverse pairs of maps to give a perturbative approach to a general notion of relative Rota-Baxter operators and differential operators on a group and a Lie algebra with limit-weight. With the extra condition of limit-abelianess on the group or Lie algebra, we give an interpretation of relative Rota-Baxter and differential operators with weight zero. These operators motivate us to define pre-groups and Novikov groups respectively as the induced structures. The tangent maps of these operators are shown to give Rota-Baxter and differential operators with weight zero on Lie algebras. The tangent spaces of the pre-Lie and Novikov Lie groups are pre-Lie algebras and Novikov Lie algebras, fulfilling the expected property. Furthermore, limit-weight relative Rota-Baxter operators on groups give rise to skew left braces and then set-theoretic solutions of the Yang-Baxter *** Codes 22E60, 17B38, 17B40, 16W99, 45N05 Copyright © 2024, The Authors. All rights reserved.

关键词： Lie groups

Multi-dimensional Graph Linear Canonical Transform

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arXiv 2024年

作者： Li, Na Zhang, Zhichao Han, Jie Chen, Yunjie Cao, Chunzheng School of Mathematics and Statistics Center for Applied Mathematics of Jiangsu Province Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing University of Information Science and Technology Nanjing210044 China Key Laboratory of System Control and Information Processing Ministry of Education Shanghai200240 China Key Laboratory of Computational Science and Application of Hainan Province Haikou571158 China School of Remote Sensing and Geomatics Engineering Nanjing University of Information Science and Technology Nanjing210044 China

Many multi-dimensional (M-D) graph signals appear in the real world, such as digital images, sensor network measurements and temperature records from weather observation stations. It is a key challenge to design a transform method for processing these graph M-D signals in the linear canonical transform domain. This paper proposes the two-dimensional graph linear canonical transform based on the central discrete dilated Hermite function (2-D CDDHFs-GLCT) and the two-dimensional graph linear canonical transform based on chirp multiplication-chirp convolution-chirp multiplication decomposition (2-D CM-CC-CM-GLCT). Then, extending 2-D CDDHFs-GLCT and 2-D CM-CC-CM-GLCT to M-D CDDHFs-GLCT and M-D CM-CC-CM-GLCT. In terms of the computational complexity, additivity and reversibility, M-D CDDHFs-GLCT and M-D CM-CC-CM-GLCT are compared. Theoretical analysis shows that the computational complexity of M-D CM-CC-CM-GLCT algorithm is obviously reduced. Simulation results indicate that M-D CM-CC-CM-GLCT achieves comparable additivity to M-D CDDHFs-GLCT, while M-D CM-CC-CM-GLCT exhibits better reversibility. Finally, M-D GLCT is applied to data compression to show its application advantages. The experimental results reflect the superiority of M-D GLCT in the algorithm design and implementation of data compression. Copyright © 2024, The Authors. All rights reserved.

关键词： Chirp modulation

Graph Chirp Signal and Graph Fractional Vertex-Frequency Energy Distribution

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arXiv 2025年

作者： Cui, Manjun Zhang, Zhichao School of Mathematics and Statistics The Center for Applied Mathematics of Jiangsu Province The Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing University of Information Science and Technology Nanjing210044 China School of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing210044 China Key Laboratory of System Control and Information Processing Ministry of Education Shanghai Jiao Tong University Shanghai200240 China Key Laboratory of Computational Science and Application of Hainan Province Hainan Normal University Haikou571158 China

Graph signal processing (GSP) has emerged as a powerful framework for analyzing data on irregular domains. In recent years, many classical techniques in signal processing (SP) have been successfully extended to GSP. Among them, chirp signals play a crucial role in various SP applications. However, graph chirp signals have not been formally defined despite their importance. Here, we define graph chirp signals and establish a comprehensive theoretical framework for their analysis. We propose the graph fractional vertex-frequency energy distribution (GFED), which provides a powerful tool for processing and analyzing graph chirp signals. We introduce the general fractional graph distribution (GFGD), a generalized vertex-frequency distribution, and the reduced interference GFED, which can suppress cross-term interference and enhance signal clarity. Furthermore, we propose a novel method for detecting graph signals through GFED domain filtering, facilitating robust detection and analysis of graph chirp signals in noisy environments. Moreover, this method can be applied to real-world data for denoising more effective than some state-of-the-arts, further demonstrating its practical significance. Copyright © 2025, The Authors. All rights reserved.

关键词： Wiener filtering

Online federated learning framework for classification

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arXiv 2025年

作者： Guo, Wenxing Xie, Jinhan Lu, Jianya Jiang, Bei Dai, Hongsheng Kong, Linglong School of Mathematics Statistics and Actuarial Science University of Essex ColchesterCO4 3SQ United Kingdom Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan University Kunming650091 China Department of Mathematical and Statistical Sciences University of Alberta EdmontonABT6G 2G1 Canada School of Mathematics Statistics and Physics Newcastle University Newcastle upon TyneNE1 7RU United Kingdom

In this paper, we develop a novel online federated learning framework for classification, designed to handle streaming data from multiple clients while ensuring data privacy and computational efficiency. Our method leverages the generalized distance-weighted discriminant technique, making it robust to both homogeneous and heterogeneous data distributions across clients. In particular, we develop a new optimization algorithm based on the Majorization-Minimization principle, integrated with a renewable estimation procedure, enabling efficient model updates without full retraining. We provide a theoretical guarantee for the convergence of our estimator, proving its consistency and asymptotic normality under standard regularity conditions. In addition, we establish that our method achieves Bayesian risk consistency, ensuring its reliability for classification tasks in federated environments. We further incorporate differential privacy mechanisms to enhance data security, protecting client information while maintaining model performance. Extensive numerical experiments on both simulated and real-world datasets demonstrate that our approach delivers high classification accuracy, significant computational efficiency gains, and substantial savings in data storage requirements compared to existing methods. © 2025, CC BY.

关键词： Federated learning

Corrigendum and addendum to “From risk sharing to pure premium for a large number of heterogeneous losses” [Insurance: Mathematics and Economics 96 (2021) 116–126]

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Insurance: Mathematics and Economics 2021年 101卷 640-644页

作者： Michel Denuit Christian Y. Robert Institute of Statistics Biostatistics and Actuarial Science - ISBA Louvain Institute of Data Analysis and Modeling - LIDAM UCLouvain Louvain-la-Neuve Belgium Laboratory in Finance and Insurance - LFA CREST - Center for Research in Economics and Statistics ENSAE Paris France

This paper supplements the previous contribution by Denuit and Robert (2021) . First, the compound Poisson case is revisited and the strong law of large number is rigorously established for the conditional expectations defining the conditional mean risk allocation. Then, a weak law of large numbers is proposed, providing the actuary with a criterion ensuring that the variance of individual contributions tends to 0. This is appealing for applications since this behavior is a key success factor for collaborative insurance pools.

关键词： G22 Conditional expectation Risk pooling Law of large number