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arXiv 2025年

作者： Liu, Fan Liu, Ya-Feng Cui, Yuanhao Masouros, Christos Xu, Jie Han, Tony Xiao Buzzi, Stefano Eldar, Yonina C. Jin, Shi National Mobile Communications Research Laboratory School of Information Science and Engineering Southeast University Nanjing210096 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematicsand Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Communication Engineering Beijing University of Posts and Telecommunications Beijing100876 China Department of Electronic and Electrical Engineering University College London LondonWC1E 7JE United Kingdom Guangdong518172 China Huawei Technologies Co. Ltd China Department of Electrical and Information Engineering University of Cassino and Southern Lazio CassinoI-03043 Italy Department of Electronics Information and Bioengineering Politecnico di Milano MilanoI-20133 Italy ParmaI-43124 Italy Faculty of Mathematics and Computer Science Weizmann Institute of Science Rehovot Israel

The Integrated Sensing and Communications (ISAC) paradigm is anticipated to be a cornerstone of the upcoming 6G networks. In order to optimize the use of wireless resources, 6G ISAC systems need to harness the communication data payload signals, which are inherently random, for both sensing and communication (S&C) purposes. This tutorial paper provides a comprehensive technical overview of the fundamental theory and signal processing methodologies for ISAC transmission with random communication signals. We begin by introducing the deterministic-random tradeoff (DRT) between S&C from an information-theoretic perspective, emphasizing the need for specialized signal processing techniques tailored to random ISAC signals. Building on this foundation, we review the core signal models and processing pipelines for communication-centric ISAC systems, and analyze the average squared auto-correlation function (ACF) of random ISAC signals, which serves as a fundamental performance metric for multi-target ranging tasks. Drawing insights from these theoretical results, we outline the design principles for the three key components of communication-centric ISAC systems: modulation schemes, constellation design, and pulse shaping filters. The goal is to either enhance sensing performance without compromising communication efficiency or to establish a scalable tradeoff between the two. We then extend our analysis from a single-antenna ISAC system to its multi-antenna counterpart, discussing recent advancements in multiinput multi-output (MIMO) precoding techniques specifically designed for random ISAC signals. We conclude by highlighting several open challenges and future research directions in the field of sensing with communication signals. Copyright © 2025, The Authors. All rights reserved.

关键词： Signal modulation

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Quantifying gender imbalance in East Asian academia: Research career and citation practice

arXiv

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arXiv 2023年

作者： Nakajima, Kazuki Liu, Ruodan Shudo, Kazuyuki Masuda, Naoki Department of Mathematical and Computing Science Tokyo Institute of Technology Meguro-ku Tokyo152-8552 Japan Department of Mathematics State University of New York at Buffalo Buffalo14260 United States Academic Center for Computing and Media Studies Kyoto University Sakyo-ku Kyoto606-8501 Japan Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo Buffalo14260 United States Center for Computational Social Science Kobe University Kobe657-8501 Japan

Gender imbalance in academia has been confirmed in terms of a variety of indicators, and its magnitude often varies from country to country. Europe and North America, which cover a large fraction of research workforce in the world, have been the main geographical regions for research on gender imbalance in academia. However, the academia in East Asia, which accounts for a substantial fraction of research, may be exposed to strong gender imbalance because Asia has been facing persistent and stronger gender imbalance in society at large than Europe and North America. Here we use publication data between 1950 and 2020 to analyze gender imbalance in academia in China, Japan, and South Korea in terms of the number of researchers, their career, and citation practice. We found that, compared to the average of the other countries, gender imbalance is larger in these three East Asian countries in terms of the number of researchers and their citation practice and additionally in Japan in terms of research career. Moreover, we found that Japan has been exposed to the larger gender imbalance than China and South Korea in terms of research career and citation practice. Copyright © 2023, The Authors. All rights reserved.

关键词： Geographical regions

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A high-order unfitted finite element method for moving interface problems

arXiv

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arXiv 2021年

作者： Ma, Chuwen Zheng, Weiying School of Mathematical Science University of Chinese Academy of Sciences Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China LSEC Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China School of Mathematical Science University of Chinese Academy of Sciences China

We propose a kth-order unfitted finite element method (2 ≤ k ≤ 4) to solve moving interface problem of the Oseen equations. Thorough error estimates for the discrete solutions are presented by considering errors from interface-tracking, time integration, and spatial discretization. In literatures on time-dependent Stokes interface problems, error estimates for the discrete pressure are usually sub-optimal, namely, (k−1)th-order, under the L2-norm. We have obtained a (k − 1)th-order error estimate for the discrete pressure under the H1-norm. Numerical experiments for a severely deforming interface show that optimal convergence orders are obtained for k = 3 and 4. Copyright © 2021, The Authors. All rights reserved.

关键词： Convolution

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Finite Element Method for a Nonlinear PML Helmholtz Equation with High Wave Number

arXiv

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arXiv 2022年

作者： Jiang, Run Li, Yonglin Wu, Haijun Zou, Jun Department of Mathematics Nanjing University Jiangsu210093 China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom Hong Kong Department of Mathematics The Chinese University of Hong Kong N.T. Shatin Hong Kong

A nonlinear Helmholtz equation (NLH) with high wave number and Sommerfeld radiation condition is approximated by the perfectly matched layer (PML) technique and then discretized by the linear finite element method (FEM). Wave-number-explicit stability and regularity estimates and the exponential convergence are proved for the nonlinear truncated PML problem. Preasymptotic error estimates are obtained for the FEM, where the logarithmic factors in h required by the previous results for the NLH with impedance boundary condition are removed in the case of two dimensions. Moreover, local quadratic convergences of the Newton's methods are derived for both the NLH with PML and its FEM. Numerical examples are presented to verify the accuracy of the FEM, which demonstrate that the pollution errors may be greatly reduced by applying the interior penalty technique with proper penalty parameters to the FEM. The nonlinear phenomenon of optical bistability can be successfully simulated. Copyright © 2022, The Authors. All rights reserved.

关键词： Finite element method

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Covariance-Based Activity Detection in Cooperative Multi-Cell Massive MIMO: Scaling Law and Efficient Algorithms

arXiv

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arXiv 2023年

作者： Wang, Ziyue Liu, Ya-Feng Wang, Zhaorui Yu, Wei The 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 Beijing100190 China The School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Guangdong Provincial Key Laboratory of Future Networks of Intelligence The Chinese University of Hong Kong Shenzhen518172 China The Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto TorontoONM5S 3G4 Canada

This paper focuses on the covariance-based activity detection problem in a multi-cell massive multiple-input multiple-output (MIMO) system. In this system, active devices transmit their signature sequences to multiple base stations (BSs), and the BSs cooperatively detect the active devices based on the received signals. While the scaling law for the covariance-based activity detection in the single-cell scenario has been extensively analyzed in the literature, this paper aims to analyze the scaling law for the covariance-based activity detection in the multi-cell massive MIMO system. Specifically, this paper demonstrates a quadratic scaling law in the multi-cell system, under the assumption that the path-loss exponent of the fading channel γ > 2. This finding shows that, in the multi-cell massive MIMO system, the maximum number of active devices that can be correctly detected in each cell increases quadratically with the length of the signature sequence and decreases logarithmically with the number of cells (as the number of antennas tends to infinity). Moreover, in addition to analyzing the scaling law for the signature sequences randomly and uniformly distributed on a sphere, the paper also establishes the scaling law for signature sequences based on a finite alphabet, which are easier to generate and store. Finally, this paper proposes two efficient accelerated coordinate descent (CD) algorithms with a convergence guarantee for solving the device activity detection problem. The first algorithm reduces the complexity of CD by using an inexact coordinate update strategy. The second algorithm avoids unnecessary computations of CD by using an active set selection strategy. Simulation results show that the proposed algorithms exhibit excellent performance in terms of computational efficiency and detection error probability. Copyright © 2023, The Authors. All rights reserved.

关键词： Fading channels

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A DECOUPLING TWO-GRID METHOD FOR THE STEADY-STATE POISSON-NERNST-PLANCK EQUATIONS

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Journal of computational mathematics 2019年第4期37卷 556-578页

作者： Ying Yang Benzhuo Lu Yan Xie School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology Guilin 541004 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing the National Center for Mathematics and Interdisciplinary Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

Poisson-Nernst-Planck equations are widely used to describe the electrodiffusion of ions in a solvated biomolecular system. Two kinds of two-grid finite element algorithms are proposed to decouple the steady-state Poisson-Nernst-Planck equations by coarse grid finite element approximations. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the two-grid algorithms for solving Poisson-Nernst-Planck equations.

关键词： Poisson-Nernst-Planck equations Two-grid finite element method Decoupling method Error analysis Gummel iteration

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A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type

arXiv

引用

arXiv 2023年

作者： Klar, Manuel Capodaglio, Giacomo D’Elia, Marta Glusa, Christian Gunzburger, Max Vollmann, Christian Department of Mathematics Universität Trier Trier54296 Germany Center for Computing Research Sandia National Laboratories AlbuquerqueNM87321 United States Computational Physics and Methods Group Los Alamos National Laboratory Los AlamosNM87545 United States Pasteur Labs BrooklynNY11205 United States Oden Institute for Computational Science and Engineering University of Texas Austin78712 United States

Nonlocal models allow for the description of phenomena which cannot be captured by classical partial differential equations. The availability of efficient solvers is one of the main concerns for the use of nonlocal models in real world engineering applications. We present a domain decomposition solver that is inspired by substructuring methods for classical local equations. In numerical experiments involving finite element discretizations of scalar and vectorial nonlocal equations of integrable and fractional type, we observe improvements in solution time of up to 14.6x compared to commonly used solver *** Codes 34B10, 65M60, 45P05, 45A99, 65R99 Copyright © 2023, The Authors. All rights reserved.

关键词： Domain decomposition methods

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A force-based gradient descent method for ab initio atomic structure relaxation

arXiv

引用

arXiv 2022年

作者： Hu, Yukuan Gao, Xingyu Zhao, Yafan Liu, Xin Song, Haifeng State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China CAEP Software Center for High Performance Numerical Simulation Beijing100088 China

Force-based algorithms for ab initio atomic structure relaxation, such as conjugate gradient methods, usually get stuck in the line minimization processes along search directions, where expensive ab initio calculations are triggered frequently to test trial positions before locating the next iterate. We present a force-based gradient descent method, WANBB, that circumvents the deficiency. At each iteration, WANBB enters the line minimization process with a trial stepsize capturing the local curvature of the energy surface. The exit is controlled by an unrestrictive criterion that tends to accept early trials. These two ingredients streamline the line minimization process in WANBB. The numerical simulations on nearly 80 systems with good universality demonstrate the considerable compression of WANBB on the cost for the unaccepted trials compared with conjugate gradient methods. We also observe across the board significant and universal speedups as well as the superior robustness of WANBB over several widely used methods. The latter point is theoretically established. The implementation of WANBB is pretty simple, in that no a priori physical knowledge is required and only two parameters are present without tuning. © 2022, CC BY.

关键词： Conjugate gradient method

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A mathematical aspect of Hohenberg-Kohn theorem

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Science China mathematics 2019年第1期62卷 63-68页

作者： Aihui Zhou LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences

The Hohenberg-Kohn theorem plays a fundamental role in density functional theory, which has become the most popular and powerful computational approach to study the electronic structure of *** this article, we study t... 详细信息

关键词： density functional theory electronic structure unique continuation principle Hohenberg-Kohn theorem

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Development of multifactor forecasting model based on fuzzy time series 35

Development of multifactor forecasting model based on fuzzy ...

引用

35th International Conference on Information Technologies, InfoTech 2021

作者： Demidova, Liliya Anatolievna Stepanov, Maksim Anatolievich Institute of Information Technologies Russian Technological University - MIREA Department of Corporate Information Systems Vernadsky Avenue78 Moscow119454 Russia Ryazan State Radio Engineering University Named after V.F. Utkin Faculty of Computing Engineering Department of Computational and Applied Mathematics Gagarin Str. 59/1 Ryazan390005 Russia

ISBN: (纸本)9781665403245

The problem of developing a multifactor forecasting model using the tools of fuzzy set theory has been considered. It is proposed to represent each of the analyzed factors, which have the same source of occurrence, but different trajectories of evolution, in the form of a fuzzy time series. The groups of fuzzy logical dependencies on the basis of fuzzy time series for each trajectory have been created. The multifactor forecasting model is developed with the use of these groups of fuzzy logical dependencies, taking into account the operations of union and intersection. Optimal parameter values of the forecasting model, providing a minimum value of the average forecasting error rate, have been determined using a genetic algorithm. An example which confirms the effectiveness of the proposed approach to the development of a multifactor forecasting model has been given. © 2021 IEEE.

关键词： Time series

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