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Radial kinks in a Schwarzschild-like geometry

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Physical Review D 2024年第12期110卷 125025-125025页

作者： Jean-Guy Caputo Tomasz Dobrowolski Jacek Gatlik Panayotis G. Kevrekidis Laboratoire de Mathématiques INSA de Rouen Avenue de l’Université 76801 Saint-Etienne du Rouvray France Department of Computer Physics and Quantum Computing University of the National Education Commission in Krakow Podchora¸żych 2 30-084 Cracow Poland AGH University of Krakow Faculty of Physics and Applied Computer Science 30-059 Krakow Poland Department of Mathematics and Statistics University of Massachusetts Amherst Massachusetts 01003-4515 USA

We study the propagation of a domain wall (kink) of the ϕ4 model in a radially symmetric environment defined by a gravity source. This source introduces a Schwarzschild-like geometry. We introduce an effective model that accurately describes the dynamics of the kink center. This description works well even outside the perturbation region, i.e., even for large masses of the gravitating object. We observed that such a spherical domain wall surrounding a star-type object inevitably “collapses,” i.e., shrinks in radius toward the origin and offer an understanding of the latter phenomenology. The relevant analysis is presented for a circular domain wall and a spherical one.

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Semi-implicit Lagrangian Voronoi Approximation for the incompressible Navier-Stokes equations

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arXiv 2024年

作者： Kincl, Ondřej Peshkov, Ilya Boscheri, Walter Laboratory of Applied Mathematics DICAM University of Trento via Mesiano 77 Trento38123 Italy Laboratoire de Mathématiques UMR 5127 CNRS Université Savoie Mont Blanc Le Bourget du Lac73376 France Department of Mathematics and Computer Science University of Ferrara Ferrara Italy

We introduce Semi-Implicit Lagrangian Voronoi Approximation (SILVA), a novel numerical method for the solution of the incompressible Euler and Navier-Stokes equations, which combines the efficiency of semi-implicit time marching schemes with the robustness of time-dependent Voronoi tessellations. In SILVA, the numerical solution is stored at particles, which move with the fluid velocity and also play the role of the generators of the computational mesh. The Voronoi mesh is rapidly regenerated at each time step, allowing large deformations with topology changes. As opposed to the reconnection-based Arbitrary-Lagrangian-Eulerian schemes, we need no remapping stage. A semi-implicit scheme is devised in the context of moving Voronoi meshes to project the velocity field onto a divergence-free manifold. We validate SILVA by illustrative benchmarks, including viscous, inviscid, and multi-phase flows. Compared to its closest competitor, the Incompressible Smoothed Particle Hydrodynamics (ISPH) method, SILVA offers a sparser stiffness matrix and facilitates the implementation of no-slip and free-slip boundary conditions. Copyright © 2024, The Authors. All rights reserved.

关键词： Stiffness matrix

Classification of two-dimensional left(right) unital algebras over algebraically closed fields and

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Journal of Physics: Conference Series 2020年第1期1489卷

作者： H Ahmed U Bekbaev I Rakhimov Department of Math. Faculty of Science UPM Selangor Malaysia & Depart. of Math. Faculty of Science Taiz University Taiz Yemen Department of Science in Engineering Faculty of Engineering IIUM Malaysia Department of Mathematics Faculty of Computer and Mathematical Sciences UiTM Malaysia & Institute for Mathematical Research (INSPEM) UPM Serdang Selangor Malaysia

In this paper we describe all left, right unital and unital algebra structures on two-dimensional vector space over any algebraically closed field and . We tabulate the algebras and provide their unit elements.

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INVERSE PROBLEMS FOR QUANTUM GRAPH ASSOCIATED WITH SQUARE AND HEXAGONAL LATTICES

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arXiv 2024年

作者： Ando, K. Blåsten, E. Exner, P. Isozaki, H. Korotyaev, E. Lassas, M. Lu, J. Morioka, H. Department of Electrical and Electronic Engineering and Computer Science Ehime University Matsuyama790-8577 Japan School of Engineering Science LUT University Lahti Campus Lahti15210 Finland Department of Math. Analysis Saint-Petersburg State University Universitetskaya Nab. 7/9 St. Petersburg199034 Russia National Research University Higher School of Economics St. Petersburg Russia Doppler Institute for Mathematical Physics and Applied Mathematics Czech Technical University in Prague Břehová 7 Prague115 19 Czech Republic Nuclear Physics Institute Czech Academy of Science Rež 250 68 Czech Republic Graduate School of Pure and Applied Sciences University of Tsukuba Tsukuba305-8571 Japan Department of Mathematics and Statistics University of Helsinki HelsinkiFI-00014 Finland

We solve inverse problems from the D-N map for the quantum graph on a finite domain in a square lattice and that on a hexagonal lattice, as well as inverse scattering problems from the S-matrix for a locally perturbed... 详细信息

关键词： Inverse problems

New Convergence Aspects of Stochastic Gradient Algorithms

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arXiv 2018年

作者： Nguyen, Lam M. Nguyen, Phuong Ha Richtárik, Peter Scheinberg, Katya Takáč, Martin van Dijk, Marten IBM Research Thomas J. Watson Research Center Yorktown HeightsNY10598 United States Department of Electrical and Computer Engineering University of Connecticut StorrsCT06268 United States Computer Electrical and Math. Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal Kazakhstan School of Operations Research and Information Engineering Cornell University IthacaNY14850 United States Department of Industrial and Systems Engineering Lehigh University BethlehemPA18015 United States

The classical convergence analysis of SGD is carried out under the assumption that the norm of the stochastic gradient is uniformly bounded. While this might hold for some loss functions, it is violated for cases where the objective function is strongly convex. In Bottou et al. (2018), a new analysis of convergence of SGD is performed under the assumption that stochastic gradients are bounded with respect to the true gradient norm. We show that for stochastic problems arising in machine learning such bound always holds;and we also propose an alternative convergence analysis of SGD with diminishing learning rate regime. We then move on to the asynchronous parallel setting, and prove convergence of Hogwild! algorithm in the same regime in the case of diminished learning rate. It is well-known that SGD converges if a sequence of learning rates {ηt} satisfies P∞t=0 ηt → ∞ and P∞t=0 ηt2 t} is a diminishing sequence and P∞t=0 ηt → ∞. In other words, we extend the current state-of-the-art class of learning rates satisfying the convergence of SGD. Copyright © 2018, The Authors. All rights reserved.

关键词： Learning algorithms

Research on rough set theory and applications in China

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Lecture Notes in computer science

作者： Wang, Guoyin Zhang, Qinghua Huang, Houkuan Ye, Dongyi Hu, Qinghua Hu, Xuegang Shi, Zhongzhi Li, Yongli Shang, Lin An, Liping Sai, Ying Chen, Shanben Liang, Jiye Qin, Keyun Zeng, Huanglin Xie, Keming Miao, Duoqian Min, Fan Wu, Zhaocong Wu, Weizhi Dai, Jianhua Institute of Computer Science and Technology Chongqing University of Posts and Telecommunications Chongqing 400065 China School of Information Science and Technology Southwest Jiaotong University Chengdu 610031 China School of Computer and Information Technology Beijing Jiaotong University Beijing 100044 China College of Math. and Computer Fuzhou University Fuzhou 350002 China Harbin Institute of Technology PO Box 458 Harbin 150006 China School of Computer and Information Hefei University of Technology Hefei 230009 China Institute of Computing Technology Chinese Academy of Sciences Beijing 100080 China Lanzhou University No.222 Tianshui South Rd. Lanzhou 730000 China State Key Laboratory for Novel Software Technology Nanjing University Nanjing 210093 China Management Science and Engineering Department Business School Nankai University Tianjin 300071 China Shandong University of Finance No.40 Shun-geng Road Jinan 250014 China Welding Engineering Institute Shanghai Jiaotong University Shanghai 200030 China School of Computer and Information Technology Shanxi University Taiyuan 030006 China Intelligent Control Development Center Southwest Jiaotong University Chengdu 610031 China Artificial Intelligence of Key Laboratory Sichuan University of Science and Engineering Zigong 643000 China Department of Automation College of Information Engineering Taiyuan University of Technology Taiyuan 030024 China 4800 CaoAn Highway Shanghai 201804 China School of Computer Science and Technology University of Electronic Science and Technology of China Chengdu 610054 China School of Remote Sensing Information Engineering Wuhan University Wuhan 430079 China Institute for Information and System Sciences Faculty of Science Xi'an Jiaotong University Xi'an 710049 China Information College Zhejiang Ocean University Zhejiang 316004 China Institute of Artificial Intelligence Zhejiang University Hangzhou 310027 China

ISBN: (纸本)3540850635

This article gives a capsule view of research on rough set theory and applications ongoing at universities and laboratories in China. Included in this capsule view of rough set research is a brief description of the following things: Chinese research groups on rough set with their URLs for web pages, names of principal researchers (supervisors), numbers of graduate students, and topics being investigated. Statistical summaries showing the growth in the research on rough set theory and application in China are included. In addition, an introduction summarizing the research interests of Chinese researchers is included in this article. The contribution of this article is a complete overview of the principal research directions in rough set theory and its applications in China. © 2008 Springer-Verlag Berlin Heidelberg.

关键词： Rough set theory

The Manifold Scattering Transform for High-Dimensional Point Cloud Data

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arXiv 2022年

作者： Chew, Joyce Steach, Holly R. Viswanath, Siddharth Wu, Hau-Tieng Hirn, Matthew Needell, Deanna Krishnaswamy, Smita Perlmutter, Michael UCLA Department of Mathematics Los AngelesCA United States Yale University Department of Genetics New HavenCT United States UC Irvine Department of Computer Science IrvineCA United States Duke University Department of Mathematics DurhamNC United States Duke University Department of Statistical Science DurhamNC United States Michigan State University Department of Mathematics East Lansing United States Michigan State University Department of CMSE East Lansing United States Yale University Department of Computer Science New HavenCT United States Yale University Applied Math Program New HavenCT United States

The manifold scattering transform is a deep feature extractor for data defined on a Riemannian manifold. It is one of the first examples of extending convolutional neural network-like operators to general manifolds. The initial work on this model focused primarily on its theoretical stability and invariance properties but did not provide methods for its numerical implementation except in the case of two-dimensional surfaces with predefined meshes. In this work, we present practical schemes, based on the theory of diffusion maps, for implementing the manifold scattering transform to datasets arising in naturalistic systems, such as single cell genetics, where the data is a high-dimensional point cloud modeled as lying on a low-dimensional manifold. We show that our methods are effective for signal classification and manifold classification *** Codes 68T07 Copyright © 2022, The Authors. All rights reserved.

关键词： Numerical methods

Cooperative service model innovation and pilot application in the prevention and control on diabetic retinopathy with web-movable hand-hold fundus camera in regional health and medicine of digitization

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Cooperative service model innovation and pilot application i...

IEEE International Conference on Bioinformatics and Biomedicine, BIBM 2015

作者： Liang, ZhiWei Jiang, DongXu Lai, XiaoPing Mo, XueLian Liang, QianRong Luo, XiaoYan Zhou, LiWen Yuan, ZhongXun Xu, JianBiao Zhang, XiaoYang Xu, Ning Yuan, Ye An, Jing Zeng, JuanHong Zheng, ShouZeng Li, CanDong Zhou, Yi Dongguan and Guangzhou Univ. of Chinese Med. Coop. Acad. of Math. and Eng. for Chinese Medicine Dongguan Guangdong China Guangzhou University of Chinese Medicine Guangzhou Guangdong China Community Health Service Centers of Machong Town of Dongguan Dongguan Guangdong China Health Information and Statistics Center of Dongguan Dongguan Guangdong China Department of Ophthalmology Guangzhou 8th People's Hospital Guangdong China Company Ltd. of Health Science and Technology Beijing China Fujian University of Chinese Medicine Fuzhou China Computer Center Zhongshan School of Medicine Sun Yat-Sen University Guangzhou Guangdong China

ISBN: (纸本)9781467367981

Objective: Systems engineering theory, hand-hold fundus camera(FC) and internet cooperative platform were applied to help community staff, long distance specialists' organizations and teams to cooperate on the screening for diabetic fundus pathological change(or diabetic retinopathy, DR) in regional residents. It aims at promoting the ability to prevent and control (PC) the important non-infectious chronic diseases (NCD) to design a proper value-chain for mutually beneficial mode of interactions among regional health services, and the other corresponding social roles via technological and organizational innovation. Methods: 1. Organizational innovation mode: Based on the Concept of social-huge-system and systems engineering theory, a cross-functional flowchart was applied to hatch a valuable road map of PC of certain single important NCD, i.e. DR, as well as the evaluation on the systematic target efficacy. 2. Technological innovation and its social practice: twenty patients suffered from diabetes with no less than eight years diabetic history were prepared to be recruited from the resident health record in Machong Community Service Center, Dongguan, Guangdong, P.R. China. The health culture for DR was expressed to the residents by specialists' lecture. Besides, their fundus photos were collected via web-movable hand-hold FC assembled with Smartphone for data remote transmission or hand-hold digital FC with self-storage device, and sent to specialists' teams in different places to study. 3. Evaluation on the practice activity: Concerning .the experience of the screening for DR, the satisfaction with the service and quality, the willing to accept the health service & management, and the awareness for DR before and after the health culture for DR, survey forms were collected and analyzed from the spot inquires to the residents at the end of the activity and from the followup visit after one week later than the screening. Results: 1. The essential factors of sustainabl

关键词： Diagnosis

Optimal Polynomial Approximation to Rational Matrix Functions Using the Arnoldi Algorithm

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arXiv 2023年

作者： Chen, Tyler Greenbaum, Anne Wellen, Natalie NYU Courant Department of Mathematics 251 Mercer St. New YorkNY10003 United States NYU Tandon Department of Computer Science and Engineering 370 Jay St. New YorkNY11201 United States University of Washington Applied Math Dept. Box 353925 SeattleWA98195 United States

Given an n by n matrix A and an n-vector b, along with a rational function R(z):= D(z)−1N (z), we show how to find the optimal approximation to R(A)b from the Krylov space, span(b, Ab, . . ., Ak−1b), using the basis vectors produced by the Arnoldi algorithm. To find this optimal approximation requires running max{deg(D), deg(N)} − 1 extra Arnoldi steps and solving a k + max{deg(D), deg(N)} by k least squares problem. Here optimal is taken to mean optimal in the D(A)∗D(A)-norm. Similar to the case for linear systems, we show that eigenvalues alone cannot provide information about the convergence behavior of this algorithm and we discuss other possible error bounds for highly nonnormal *** Codes 65F10 (Primary), 65F60, 47A12, 47A25 (Secondary) © 2023, CC BY.

关键词： Rational functions