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arXiv 2024年

作者： Kincl, Ondřej Peshkov, Ilya Boscheri, Walter Laboratory of Applied Mathematics DICAM University of Trento 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 Ferrara44121 Italy

This paper contributes to the recent investigations of Lagrangian methods based on Voronoi meshes. The aim is to design a new conservative numerical scheme that can simulate complex flows and multi-phase problems with more accuracy than SPH (Smoothed Particle Hydrodynamics) methods but, unlike diffuse interface models on fixed grid topology, does not suffer from the deteriorating quality of the computational grid. 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, that is efficiently re-constructed at each time step. The main novelty stems from combining a Lagrangian Voronoi scheme with a semi-implicit integrator for compressible flows. This allows to model low-Mach number flows without the extremely stringent stability constraint on the time step and with the correct scaling of numerical viscosity. The implicit linear system for the unknown pressure is obtained by splitting the reversible from the irreversible (viscous) part of the dynamics, and then using entropy conservation of the reversible sub-system to derive an auxiliary elliptic equation. The method, called SILVA (Semi-Implicit Lagrangian Voronoi Approximation), is validated in a variety of test cases that feature diverse Mach numbers, shocks and multi-phase flows. Copyright © 2024, The Authors. All rights reserved.

关键词： Topology

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On embedding triconnected cubic graphs on point sets

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Electronic Notes in Discrete math.matics 2007年第SPEC. ISS.期29卷 531-538页

作者： García, Alfredo Hurtado, Ferran Huemer, Clemens Tejel, Javier Valtr, Pavel Departamento de Métodos Estadísticos Facultad de Ciencias Universidad de Zaragoza 50009-Zaragoza Pedro Cerbuna 12 Spain Dept. Matematica Aplicada II. Universitat Politecnica de Catalunya. Jordi Girona 1-3. 08034 Barcelon Spain Dept. Matematica Aplicada II. Universitat Politecnica de Catalunya. Jordi Girona 1-3. 08034 Barcelon Spain Departamento de Métodos Estadísticos Facultad de Ciencias Universidad de Zaragoza 50009-Zaragoza Pedro Cerbuna 12 Spain Dept. of Applied Math. Institute for Theoretical Computer Science (ITI) Charles University 118 00 Praha 1 Malostranské nám. 25 Czech Republic

We show that for a given set S of 2n points in general position in the plane, there is a cubic 3-connected crossing-free geometric graph on the vertex set S if and only if the interior of the convex hull of S contains at least n - 1 points of S. We also give similar results for sets of odd cardinality. Analogous partial results are given if the 3-connected crossing-free geometric graph is not required to be cubic. © 2007.

关键词： 3-connected graphs cubic graphs embeddings in the plane geometric graphs

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Two topics in hyperelliptic cryptography

HP Laboratories Technical Report

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HP Laboratories Technical Report 2000年第118期

作者： Hess, Florian Seroussi, Gadiel Smart, Nigel Information Theory Research Group HP Laboratories Palo Alto Sch. of Math. and Statistics F07 University of Sydney NSW 2006 Australia Hewlett-Packard Laboratories 1501 Page Mill Road Palo Alto CA 650-857-1501 United States Department of Computer Science Bristol University Woodland Road Bristol BS8 1UB United Kingdom

In this paper we address two important topics in hyperelliptic cryptography. The first is how to construct in a verifiably random manner hyperelliptic curves for use in cryptography in generas two and three. The second topic is how to perform divisor compression in the hyperelliptic case. Hence in both cases we generalize concepts used in the more familiar elliptic curve case to the hyperelliptic context.

关键词： Public key cryptography

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Fuzzy reference gain-scheduling approach as intelligent agents: FRGS agent

Fuzzy reference gain-scheduling approach as intelligent agen...

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IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

作者： J.E. Araujo K.H. Kienitz A. Sandri J.D.S. da Silva Integration and Testing Laboratory - LIT São José dos Campos SP BRAZIL Department of Electronics Engineering Instituto Tecnológico de Aeronáutica - ITA São José dos Campos SP BRAZIL Computer Sci. and Applied Math. Associated Lab - LAC Instituto Nacional de Pesquisas Espaciais - INPE São José dos Campos SP BRAZIL

Goal driven intelligent agents and fuzzy reference gain-scheduling (FRGS) approach are described As interchangeable concepts that are able to deal with dynamic complex problems. It is advocated that the FRGS approach may be viewed as an autonomous goal-based agent, that is, a fuzzy logic based agent able to autonomously adapt itself to environmental changes introduced by external inputs. The concept of fuzzy systems and intelligent agent are employed in decision-making problems to lead to a certain degree of autonomy in decision support system. Although the FRGS method was originally proposed for control application, this approach was extended to decision-making tasks due to its ability of emulating human reasoning. This new agent approach uses the external input information also denominated reference (goal) as the driven mechanism to determine the behavior of the system in order to achieve the desired objectives (goal). Thus, the FRGS approach can be modeled in the framework of an adaptive and goal (also context or environment) driven agent.

关键词： Intelligent agent Decision making Humans Control systems Fuzzy logic Fuzzy systems Decision support systems Intelligent systems Knowledge based systems Testing

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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

arXiv

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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

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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

arXiv

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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

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New Convergence Aspects of Stochastic Gradient Algorithms

arXiv

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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

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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

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