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An efficient quadratic programming relaxation based algorithm for large-scale MIMO detection

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arXiv 2020年

作者： Zhao, Ping-Fan Li, Qing-Na Chen, Wei-Kun Liu, Ya-Feng School of Mathematics and Statistics Beijing Institute of Technology Beijing China School of Mathematics and Statistics Beijing Key Laboratory on MCAACI Beijing Institute of Technology Beijing China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

Multiple-input multiple-output (MIMO) detection is a fundamental problem in wireless communications and it is strongly NP-hard in general. Massive MIMO has been recognized as a key technology in the fifth generation (5G) and beyond communication networks, which on one hand can significantly improve the communication performance, and on the other hand poses new challenges of solving the corresponding optimization problems due to the large problem size. While various efficient algorithms such as semidefinite relaxation (SDR) based approaches have been proposed for solving the small-scale MIMO detection problem, they are not suitable to solve the large-scale MIMO detection problem due to their high computational complexities. In this paper, we propose an efficient sparse quadratic programming (SQP) relaxation based algorithm for solving the large-scale MIMO detection problem. In particular, we first reformulate the MIMO detection problem as an SQP problem. By dropping the sparse constraint, the resulting relaxation problem shares the same global minimizer with the SQP problem. In sharp contrast to the SDRs for the MIMO detection problem, our relaxation does not contain any (positive semidefinite) matrix variable and the numbers of variables and constraints in our relaxation are significantly less than those in the SDRs, which makes it particularly suitable for the large-scale problem. Then we propose a projected Newton based quadratic penalty method to solve the relaxation problem, which is guaranteed to converge to the vector of transmitted signals under reasonable conditions. By extensive numerical experiments, when applied to solve small-scale problems, the proposed algorithm is demonstrated to be competitive with the state-of-the-art approaches in terms of detection accuracy and solution efficiency;when applied to solve large-scale problems, the proposed algorithm achieves better detection performance than a recently proposed generalized power *** Codes 90C2

关键词： Quadratic programming

Physics-informed neural networks to learn cardiac fiber orientation from multiple electroanatomical maps

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arXiv 2022年

作者： Herrera, Carlos Ruiz Grandits, Thomas Plank, Gernot Perdikaris, Paris Costabal, Francisco Sahli Pezzuto, Simone Department of Mechanical and Metallurgical Engineering School of Engineering Pontificia Universidad Católica de Chile Santiago Chile Institute of Mathematics and Scientific Computing University of Graz Graz Austria Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania Philadelphia United States Institute for Biological and Medical Engineering Schools of Engineering Medicine and Biological Sciences Pontificia Universidad Católica de Chile Santiago Chile Center for Computational Medicine in Cardiology Euler Institute Università della Svizzera italiana via Buffi 13 Lugano6900 Switzerland Gottfried Schatz Research Center Division of Biophysics Medical University of Graz Graz Austria

We propose FiberNet, a method to estimate in-vivo the cardiac fiber architecture of the human atria from multiple catheter recordings of the electrical activation. Cardiac fibers play a central role in the electromechanical function of the heart, yet they are difficult to determine in-vivo, and hence rarely truly patient-specific in existing cardiac models. FiberNet learns the fiber arrangement by solving an inverse problem with physics-informed neural networks. The inverse problem amounts to identifying the conduction velocity tensor of a cardiac propagation model from a set of sparse activation maps. The use of multiple maps enables the simultaneous identification of all the components of the conduction velocity tensor, including the local fiber angle. We extensively test FiberNet on synthetic 2-D and 3-D examples, diffusion tensor fibers, and a patient-specific case. We show that 3 maps are sufficient to accurately capture the fibers, also in the presence of noise. With fewer maps, the role of regularization becomes prominent. Moreover, we show that the fitted model can robustly reproduce unseen activation maps. We envision that FiberNet will help the creation of patient-specific models for personalized medicine. The full code is available at http://***/fsahli/FiberNet. © 2022, CC BY-NC-ND.

关键词： Inverse problems

HETEROGENEOUS MULTISCALE METHODS FOR FOURTH-ORDER SINGULAR PERTURBATIONS

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arXiv 2025年

作者： Liao, Yulei Ming, Pingbing Department of Mathematics Faculty of Science National University of Singapore 10 Lower Kent Ridge Road Singapore119076 Singapore LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We develop a numerical homogenization method for fourth-order singular perturbation problems within the framework of heterogeneous multiscale method. These problems arise from heterogeneous strain gradient elasticity and elasticity models for architectured materials. We establish an error estimate for the homogenized solution applicable to general media and derive an explicit convergence for the locally periodic media with the fine-scale Ε. For cell problems of size δ = NΕ, the classical resonance error O(Ε/δ) can be eliminated due to the dominance of the higher-order operator. Despite the occurrence of boundary layer effects, discretization errors do not necessarily deteriorate for general boundary conditions. Numerical simulations corroborate these theoretical findings. Copyright © 2025, The Authors. All rights reserved.

关键词： Convergence of numerical methods

Time-Division Energy Beamforming for Multiuser Wireless Power Transfer with Non-Linear Energy Harvesting

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arXiv 2020年

作者： Ma, Ganggang Xu, Jie Liu, Ya-Feng Vedady Moghadam, Mohammad R. Shenzhen China Shenzhen China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China TransferFi Pte Ltd Singapore

Energy beamforming has emerged as a promising technique for enhancing the energy transfer efficiency of wireless power transfer (WPT). However, the performance of conventional energy beamforming may seriously degrade due to the nonlinear radio frequency (RF) to direct current (DC) conversion at energy receivers (ERs). To tackle this issue, this letter proposes a new time-division energy beamforming, in which different energy beamforming matrices (of high ranks in general) are time shared to exploit the "convex-concave" shape of the RF-DC power relation at ERs. By considering a particular time duration for WPT, we maximize the minimum harvested DC energy among all ERs, by jointly optimizing the energy beamforming matrices and the corresponding time allocation. In order to solve the non-convex min-DC-energy maximization problem, we propose an efficient solution by using the techniques of alternating optimization and successive convex approximation (SCA). Numerical results show that the proposed time-division energy beamforming design indeed outperforms the conventional multi-beam and time-division-multiple-access (TDMA)-based energy transmissions. Copyright © 2020, The Authors. All rights reserved.

关键词： Energy harvesting

Numerical Investigations of a Class of Biological Models on Unbounded Domain

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Numerical mathematics(Theory,Methods and Applications) 2019年第1期12卷 169-186页

作者： Qiumei Huang Dongfang Li Jiwei Zhang Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing 100124China School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratoryof Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China Beijing Computational Science Research Center Beijing1000193China

This paper is concerned with numerical computations of a class of biologi-cal models on unbounded spatial *** overcome the unboundedness of spatial domain,we first construct efficient local absorbing boundary conditions(LABCs)to re-formulate the Cauchy problem into an initial-boundary value(IBV)*** that,we construct a linearized finite difference scheme for the reduced IVB problem,and provide the corresponding error estimates and stability *** delay-dependent dynamical properties on the Nicholson’s blowflies equation and the Mackey-Glass equa-tion are numerically ***,numerical examples are given to demonstrate the efficiency of our LABCs and theoretical results of the numerical scheme.

关键词： Biological models artificial boundary method absorbing boundary conditions finite difference method stability,convergence

Randomizing hypergraphs preserving degree correlation and local clustering

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arXiv 2021年

作者： Nakajima, Kazuki Shudo, Kazuyuki Masuda, Naoki Department of Mathematical and Computing Science Tokyo Institute of Technology Japan Department of Mathematics State University of New York Buffalo United States Computational and Data-Enabled Science and Engineering Program State University of New York Buffalo United States Faculty of Science and Engineering Waseda University Japan

Many complex systems involve direct interactions among more than two entities and can be represented by hypergraphs, in which hyperedges encode higher-order interactions among an arbitrary number of nodes. To analyze structures and dynamics of given hypergraphs, a solid practice is to compare them with those for randomized hypergraphs that preserve some specific properties of the original hypergraphs. In the present study, we propose a family of such reference models for hypergraphs, called the hyper dk-series, by extending the so-called dk-series for dyadic networks to the case of hypergraphs. The hyper dk-series preserves up to the individual node’s degree, node’s degree correlation, node’s redundancy coefficient, and/or the hyperedge’s size depending on the parameter values. Furthermore, we numerically find that higher-order hyper dk-series more accurately preserves the shortest path length and degree distribution of the one-mode projection of the original hypergraph, which the method does not intend to preserve. We also apply the hyper dk-series to numerical simulations of epidemic spreading and evolutionary game dynamics on empirical social hypergraphs. We find that the hyperedge’s size affects these dynamics more than any of the node’s properties and that the node’s degree correlation and redundancy in the empirical hypergraphs promote cooperation. Copyright © 2021, The Authors. All rights reserved.

关键词： Redundancy

A Robust Remote Client Password Authentication Technique for Smart Cities E-Governance Applications

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A Robust Remote Client Password Authentication Technique for...

Communications, computing, Cybersecurity, and Informatics (CCCI), International Conference on

作者： Mohammad S. Obaidat Chandrashekhar Meshram Deepak Kartikey Kuei-Fang Hsiao Agbotiname Lucky Imoize Sharad Kumar Barve King Abdullah II School of Information Technology The University of Jordan Amman Jordan School of Computer and Communication Engineering University of Science and Technology Beijing Beijing China Department of Computational Intelligence School of Computing SRM University Kattankulathur TN India School of Engineering The Amity University Noida UP India Department of Post Graduation Studies and Research in Mathematics Jayawanti Haksar Government Post Graduation College College of Barkatullah University Betul M.P. India Department of Mathematics S.S.P. Govt. College Waraseoni Balaghat M.P. India Computer Science Department University of Texas-Permian Basin Odessa TX USA Department of Electrical and Electronics Engineering Faculty of Engineering University of Lagos Lagos Nigeria Department of Electrical Engineering and Information Technology Institute of Digital Communication Ruhr University Bochum Germany Department of Mathematics Pandit S. N. Shukla University Shahdol Shahdol Madhya Pradesh India

Smart cities are fast proliferating the global space in recent times. In order to achieve the envisioned next-generation cities, the smart city paradigm aspires to develop a completely integrated network-based infrastructure. With the development of innovative smart cities, ICT-based e-governance has made it possible for services to be delivered intelligently and interactively via online platforms. However, the communication between government agencies and other stakeholders in the smart city ecosystem is through open channels, which poses serious security concerns. In order to address this problem, this work proposes a robust remote client password authentication technique for e-governance applications in smart cities. The proposed authentication technique is lightweight, resistant to several attacks, and achieves low computational overhead.

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On the generalized Calderón formulas for closed- And open-surface elastic scattering problems

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arXiv 2021年

作者： Xu, Liwei Yin, Tao School of Mathematical Sciences University of Electronic Science and Technology of China Sichuan Chengdu611731 China LSEC Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Science University of Chinese Academy of Sciences Beijing100049 China

The Calderón formulas (i.e., the combination of single-layer and hyper-singular boundary integral operators) have been widely utilized in the process of constructing valid boundary integral equation systems which could possess highly favorable spectral properties. This work is devoted to studying the theoretical properties of elastodynamic Calderón formulas which provide us with a solid basis for the design of fast boundary integral equation methods solving elastic wave problems defined on a close-surface or an open-surface in two dimensions. For the closed-surface case, it is proved that the Calderón formula is a Fredholm operator of second-kind except for certain circumstances. Regarding to the open-surface case, we investigate weighted integral operators instead of the original integral operators which are resulted from dealing with edge singularities of potentials corresponding to the elastic scattering problems by open-surfaces, and show that the Calderón formula is a compact perturbation of a bounded and invertible operator. To complete the proof, we need to use the wellposedness result of the elastic scattering problem, the analysis of the zero-frequency integral operators defined on the straight arc, the singularity decompositions of the kernels of integral operators, and a new representation formula of the hyper-singular operator. Moreover, it can be demonstrated that the accumulation point of the spectrum of the invertible operator is the same as that of the eigenvalues of the Calderón formula in the closed-surface case. Copyright © 2021, The Authors. All rights reserved.

关键词： Mathematical operators

POLYLLA: Polygonal meshing algorithm based on terminal-edge regions

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arXiv 2022年

作者： Salinas, Sergio Hitschfeld-Kahler, Nancy Ortiz-Bernardin, Alejandro Si, Hang Department of Computer Sciences Universidad de Chile Av. Beauchef 851 RM Santiago8370456 Chile Computational and Applied Mechanics Laboratory Department of Mechanical Engineering Universidad de Chile Av. Beauchef 851 RM Santiago8370456 Chile Numerical Mathematics and Scientific Computing Weierstrass Institute for Applied Analysis and Stochastics Mohrenstr. 39 Berlin Berlin10117 Germany

This paper presents an algorithm to generate a new kind of polygonal mesh obtained from triangulations. Each polygon is built from a terminal-edge region surrounded by edges that are not the longest-edge of any of the two triangles that share them. The algorithm is termed Polylla and is divided into three phases. The first phase consists of labeling each edge of the input triangulation according to its size;the second phase builds polygons (simple or not) from terminal-edges regions using the label system;and the third phase transforms each non simple polygon into simple ones. The final mesh contains polygons with convex and non convex shape. Since Voronoi based meshes are currently the most used polygonal meshes, we compare some geometric properties of our meshes against constrained Voronoi meshes. Several experiments were run to compare the shape and size of polygons, the number of final mesh points and polygons. For the same input, Polylla meshes contain less polygons than Voronoi meshes, and the algorithm is simpler and faster than the algorithm to generate constrained Voronoi meshes. Finally, we have validated Polylla meshes by solving the Laplace equation on an L-shaped domain using the Virtual Element Method (VEM). We show that the numerical performance of the VEM using Polylla meshes and Voronoi meshes is similar. Copyright © 2022, The Authors. All rights reserved.

关键词： Mesh generation