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A folding preprocess for the max k-cut problem

Optimization Letters 2025年第5期19卷 899-917页

作者： Fakhimi, Ramin Validi, Hamidreza Hicks, Illya V. Terlaky, Tamás Zuluaga, Luis F. Department of Industrial and Systems Engineering Lehigh University Bethlehem United States Department of Industrial Manufacturing & Systems Engineering Texas Tech University Lubbock United States Department of Computational Applied Mathematics & Operations Research Rice University Houston United States

Given graph G=(V,E) with vertex set V and edge set E, the max k-cut problem seeks to partition the vertex set V into at most k subsets that maximize the weight (number) of edges with endpoints in different parts. This paper proposes a graph folding procedure (i.e., a procedure that reduces the number of the vertices and edges of graph G) for the weighted max k-cut problem that may help reduce the problem’s dimensionality. While our theoretical results hold for any k≥2, our computational results show the effectiveness of the proposed preprocess only for k=2 and on two sets of instances. Furthermore, we observe that the preprocess improves the performance of a MIP solver on a set of large-scale instances of the max cut problem. © The Author(s) 2025.

关键词： Network theory (graphs)

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Essentially Commuting with a Unitary

arXiv

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arXiv 2025年

作者： Chung, Jui-Hui Shapiro, Jacob Program in Applied and Computational Mathematics Princeton University United States Department of Mathematics Princeton University United States

Let R be a unitary operator whose spectrum is the circle. We show that the set of unitaries U which essentially commute with R (i.e., [U, R] ≡ UR − RU is compact) is path-connected. Moreover, we also calculate the set of path-connected components of the orthogonal projections which essentially commute with R and obey a non-triviality condition, and prove it is bijective with Z. Copyright © 2025, The Authors. All rights reserved.

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Asymptotic and Analytic Properties of Mixture Probability Models and Their Application to the Analysis of Complex Systems

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Moscow University computational mathematics and Cybernetics 2025年第4期48卷 317-360页

作者： Korolev, V. Yu. Shevtsova, I. G. Shestakov, O. V. Department of Computational Mathematics and Cybernetics Moscow State University Moscow Center for Basic and Applied Mathematics Moscow Russia

The paper presents a survey of the results obtained by the members of the department of Mathematical Statistics in the field of analytic and asymptotic properties of mixture probability models. Much attention is paid to the representation of some widely applied absolutely continuous probability distributions (gamma, Weibull, Student, Snedecor–Fisher, Mittag-Leffler, Burr, etc.) as mixtures of distributions possessing maximum differential entropy (normal and exponential). Some useful discrete distributions that are representable as mixed Poisson distributions are discussed as well. Examples are presented of limit theorems for statistics constructed from samples with random sizes in which the distributions mentioned above are limit laws. Also, the estimates of convergence rate in these theorems are presented. Some problems related to the application of methods of intellectual analysis of big arrays of dynamically accumulated data based on mixture probability models are discussed.

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Discontinuous Galerkin Finite Element Methods for Linear Port-Hamiltonian Dynamical Systems

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Journal of Scientific Computing 2025年第1期104卷 1-47页

作者： Cheng, Xiaoyu van der Vegt, J.J.W. Xu, Yan Zwart, H.J. School of Mathematics University of Science and Technology of China Anhui Hefei 230026 China Department of Applied Mathematics Mathematics of Computational Science Group University of Twente P.O. Box 217 Enschede 7500 AE Netherlands Department of Applied Mathematics Mathematics of Systems Theory Group University of Twente P.O. Box 217 Enschede 7500 AE Netherlands Department of Mechanical Engineering Dynamics and Control Group Eindhoven University of Technology P.O. Box 513 Eindhoven 5600 MB Netherlands

In this paper, we present discontinuous Galerkin (DG) finite element discretizations for a class of linear hyperbolic port-Hamiltonian dynamical systems. The key point in constructing a port-Hamiltonian system is a Stokes-Dirac structure. Instead of following the traditional approach of defining the strong form of the Dirac structure, we define a Dirac structure in weak form, specifically in the input-state-output form. This is implemented within broken Sobolev spaces on a tessellation with polyhedral elements. After that, we state the weak port-Hamiltonian formulation and prove that it relates to a Poisson bracket. In our work, a crucial aspect of constructing the above-mentioned Dirac structure is that we provide a conservative relation between the boundary ports. Next, we state DG discretizations of the port-Hamiltonian system by using the weak form of the Dirac structure and broken polynomial spaces of differential forms, and we provide a priori error estimates for the structure-preserving port-Hamiltonian discontinuous Galerkin (PHDG) discretizations. The accuracy and capability of the methods developed in this paper are demonstrated by presenting several numerical experiments. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

关键词： Dirac structure Discontinuous Galerkin methods Exterior calculus Port-Hamiltonian systems

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Numerical modeling of the ion-acoustic solitary waves arising in nonlinear dispersive system

Numerical modeling of the ion-acoustic solitary waves arisin...

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作者： Nikan, Omid Yang, Yin Avazzadeh, Zakieh School of Mathematics and Computational Science Xiangtan University National Center for Applied Mathematics in Hunan Hunan International Scientific and Technological Innovation Cooperation Base of Computational Science Hunan Xiangtan411105 China Department of Mathematical Sciences University of South Africa Florida South Africa

This paper proposes a numerical scheme for the (2 + 1)-dimensional nonlinear Zakharov–Kuznetsov–Benjamin–Bona–Mahony equation (ZK-BBME). The ZK-BBME represents a long-wave model with large wavelength that explains the water wave phenomena in nonlinear dispersive system. The solution of the ZK-BBME is discretized by using hybridization of the finite difference and localized radial basis function based on partition of unity method. The association of this hybridization leads to a meshless method and it does not requires any linearization. In the initial step, the PDE is converted into a nonlinear ODE system by making use of radial kernels. In the next step, the obtained nonlinear ODE system is solved based on an ODE solver of high order. The global collocation technique imposes a large computational cost because a dense algebraic system must be calculated. This proposed strategy is based on decomposing the initial domain into a number of sub-domains using kernel approximation on each sub-domain. Three numerical examples are illustrated to clarify the efficiency and accuracy of the proposed strategy. © 2023 John Wiley & Sons, Ltd.

关键词： Water waves

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Twin Bounded Least Squares Support Vector Regression 6th

Twin Bounded Least Squares Support Vector Regression

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6th IFIP TC 12 International Conference on Intelligence Science, ICIS 2024

作者： Chen, Ran Liu, Muhan Ma, Jinwen Department of Information and Computational Sciences School of Mathematical Sciences Peking University Beijing100871 China Department of Applied Mathematics China Agricultural University Beijing100083 China

ISBN: (纸本)9783031712524

Support Vector Machine (SVM) has received much attention in machine learning due to its profound theoretical research and practical application results. Support Vector Regression (SVR) has become a powerful tool for solving regression problems. Least Squares Support Vector Regression (LSSVR) has advantages in computing speed but can be prone to overfitting due to its sensitivity to noise and outliers. Additionally, Twin Support Vector Regression (TSVR) shows insufficient flexibility when dealing with large-scale data, and its robustness to noise could be improved. In response to these problems, this paper proposes an innovative solution: Twin Bounded Least Squares Support Vector Regression (TBLSSVR). This model combines the advantages of LSSVR and TSVR and introduces regularization terms to mitigate their limitations effectively. The regularization term helps minimize structural risk, reflecting the advantages of statistical learning theory and ensuring the stability of the solution. Experimental results demonstrate that TBLSSVR improves regression accuracy and significantly accelerates the solution speed, providing new directions and methods for future technology development. © IFIP International Federation for Information Processing 2025.

关键词： Vectors

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Learning the Exact Time Integration Algorithm for Initial Value Problems by Randomized Neural Networks

arXiv

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arXiv 2025年

作者： Dong, Suchuan Ni, Naxian Center for Computational and Applied Mathematics Department of Mathematics Purdue University United States

We present a method leveraging extreme learning machine (ELM) type randomized neural networks (NNs) for learning the exact time integration algorithm for initial value problems. The exact time integration algorithm for non-autonomous (including autonomous) systems can be represented by an algorithmic function in higher dimensions, which satisfies an associated system of partial differential equations with corresponding boundary conditions. Our method learns the algorithmic function by solving this associated system using ELM with a physics informed approach. The trained ELM network serves as the learned algorithm and can be used to solve the initial value problem with arbitrary initial data or arbitrary step sizes from some domain. When the right hand side of the non-autonomous system exhibits a periodicity with respect to any of its arguments, while the solution itself to the problem is not periodic, we show that in this case the algorithmic function is either periodic, or when it is not, satisfies a well-defined relation for different periods. This property can greatly simplify the network training for algorithm learning in many problems. We consider explicit and implicit NN formulations, leading to explicit and implicit time integration algorithms, and discuss how to train the ELM network by the nonlinear least squares method. Extensive numerical experiments with benchmark problems, including non-stiff, stiff and chaotic systems, show that the learned NN algorithm produces highly accurate solutions in long-time simulations, with its time-marching errors decreasing nearly exponentially with increasing degrees of freedom in the neural network. We compare extensively the computational performance (time-marching accuracy vs. time-marching cost) between the current NN algorithm and the leading traditional time integration algorithms. The learned NN algorithm is computationally competitive, markedly outperforming the traditional algorithms in many problems. Copyright ©

关键词： Least squares approximations

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Traveling antiferromagnetic domain walls in a magnetic field

arXiv

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arXiv 2025年

作者： Theodorou, George Komineas, Stavros Department of Mathematics and Applied Mathematics University of Crete Crete Heraklion70013 Greece Institute of Applied and Computational Mathematics FORTH Crete Heraklion Greece

We consider an antiferromagnet in one space dimension with easy-axis anisotropy in a perpendicular magnetic field. We study propagating domain wall solutions that can have a velocity up to a maximum vc. The width of the domain wall is a non-monotonic function of the velocity and it diverges to infinity at vc. Both features are in contrast to the case of the Lorentz invariant model in the absence of the field. We further study the modification of the wall profile when a Dzyaloshinskii-Moriya interaction is added. Finally, we present a propagating spiral expected to form when the system is forced at a velocity higher than the maximum velocity for domain walls and we give numerical results for the effect of the Dzyaloshinskii-Moriya interaction. © 2025, CC BY.

关键词： Magnetic fields

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TSI-GCN: Translation and scaling invariant GCN for 3D point cloud analysis

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Pattern Recognition Letters 2025年 195卷 30-36页

作者： Du, Zijin Liang, Jiye Yao, Kaixuan Cao, Feilong Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education School of Computer and Information Technology Shanxi University Taiyuan Shanxi030006 China Department of Applied Mathematics China Jiliang University Hangzhou Zhejiang310018 China

Point cloud is a crucial data format for 3D vision, but its irregularity makes it challenging to comprehend the associated geometric information. Although some previous research has attempted to improve deep learning on point cloud and achieved promising results, they often overlook the robust shape descriptors of 3D targets, making them susceptible to translation and scaling transformations. This paper proposes a novel framework for point cloud analysis, to achieve feature extraction with translation and scaling invariance. It mainly includes local adaptive kernel, translation and scaling invariant convolution (TSIConv), and graph attention pooling. The key component is the design of TSIConv, which extracts the shape information with translation and scaling invariance. Then it performs convolution with local adaptive kernels to capture the features in various shape structures. Following the convolution layer, we add the graph attention pooling to coarsen point cloud, thus achieving multi-scale analysis and computational overhead reduction. The proposed framework, consisting of two networks, completes point cloud classification and part segmentation tasks in an end-to-end manner. The property analysis and experiments demonstrate that our model strictly guarantees the translation and scaling invariance, meanwhile achieving comparable performance to previous methods. © 2025

关键词： Convolutional neural networks

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Stability and Lorentzian geometry for an inverse problem of a semilinear wave equation

引用

Analysis & PDE 2025年第5期18卷 1065-1118页

作者： Matti Lassas Tony Liimatainen Leyter Potenciano-Machado Teemu Tyni Department of Mathematics and Statistics University of Helsinki Helsinki Finland Department of Mathematics and Statistics University of Jyväskylä Jyväskylä Finland Research Unit of Applied and Computational Mathematics University of Oulu Oulu Finland

This paper concerns an inverse boundary value problem for a semilinear wave equation on a globally hyperbolic Lorentzian manifold. We prove a Hölder stability result for recovering an unknown potential ☆q☆ of the nonlinear wave equation ☆□☆g☆u☆+☆q☆u☆m☆=☆0☆, ☆m☆≥☆4☆, from the Dirichlet-to-Neumann map. Our proof is based on the recent higher-order linearization method and use of Gaussian beams. We also extend earlier uniqueness results by removing the assumptions of convex boundary and that pairs of light-like geodesics can intersect only once. For this, we construct special light-like geodesics and other general constructions in Lorentzian geometry. We expect these constructions to be applicable in studies of related problems as well.

关键词： Lorentzian geometry nonlinear wave equations inverse problems

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