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Joint Design of Radar Receive Filter and Unimodular ISAC Waveform with Sidelobe Level Control

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arXiv 2025年

作者： Zhang, Kecheng Liu, Ya-Feng Wang, Zhongbin Yuan, Weijie Keskin, Musa Furkan Wymeersch, Henk Xia, Shuqiang School of System Design and Intelligent Manufacturing The Shenzhen Key Laboratory of Robotics and Computer Vision Southern University of Science and Technology Shenzhen518055 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 Beijing100190 China Department of Electrical Engineering Chalmers University of Technology Gothenburg41296 Sweden ZTE Corporation The State Key Laboratory of Mobile Network and Mobile Multimedia Technology Shenzhen518055 China

Integrated sensing and communication (ISAC) has been considered a key feature of next-generation wireless networks. This paper investigates the joint design of the radar receive filter and dual-functional transmit waveform for the multiple-input multiple-output (MIMO) ISAC system. While optimizing the mean square error (MSE) of the radar receive spatial response and maximizing the achievable rate at the communication receiver, besides the constraints of full-power radar receiving filter and unimodular transmit sequence, we control the maximum range sidelobe level, which is often overlooked in existing ISAC waveform design literature, for better radar imaging performance. To solve the formulated optimization problem with convex and nonconvex constraints, we propose an inexact augmented Lagrangian method (ALM) algorithm. For each subproblem in the proposed inexact ALM algorithm, we custom-design a block successive upper-bound minimization (BSUM) scheme with closed-form solutions for all blocks of variable to enhance the computational efficiency. Convergence analysis shows that the proposed algorithm is guaranteed to provide a stationary and feasible solution. Extensive simulations are performed to investigate the impact of different system parameters on communication and radar imaging performance. Comparison with the existing works shows the superiority of the proposed algorithm. © 2025, CC BY-NC-SA.

关键词： Mean square error

ORDER REDUCED METHODS FOR QUAD-CURL EQUATIONS WITH NAVIER TYPE BOUNDARY CONDITIONS

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Journal of computational mathematics 2020年第4期38卷 565-579页

作者： Weifeng Zhang Shuo Zhang Department of Engineering Mechanics and Department of Applied Mathematics Kunming University of Science and TechnologyKunming 650500China Shuo Zhang LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and System SciencesChinese Academy of SciencesBeijing 100190China

Quad-curl equations with Navier type boundary conditions are studied in this *** order reduced formulations equivalent to the model problems are presented,and finite element discretizations are *** convergence rates a... 详细信息

关键词： Quad-curl equation Order reduced scheme Regularity analysis Finite element method

A Dynamic Pyramidal Relaxation Method of AC OPF

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A Dynamic Pyramidal Relaxation Method of AC OPF

Power and Electrical engineering (ACPEE), 5th Asia Conference on

作者： Yu-Yang Tang Liang Chen Hongbo Du Sheng-Jie Chen Caixia Kou Xiaomeng Ai Bo Zhou Academy of Mathematics and Systems Science Chinese Academy of Sciences Institute of Computational Mathematics and Scientific/Engineering Computing Beijing China College of Sciences Beijing University of Posts and Telecommunications Beijing China Academy of Mathematics and Systems Science Chinese Academy of Sciences Institute of Applied Mathematics Beijing China School of Electrical and Electronic Engineering Huazhong University of Science and Technology Wuhan China Department of Industrial and Operations Engineering University of Michigan Ann Arbor United States

ISBN: (数字)9798350309638

ISBN: (纸本)9798350309645

The Alternating Current Optimal Power Flow (AC OPF) is crucial for power system analysis, yet existing algorithms face challenges in meeting the diverse requirements of practical applications. This paper presents a Pyramidal Relaxation (PR) formulation of the Branch Flow Model (BFM) for AC OPF, where surface conical constraints are approximated through a union of tetrahedrons in a Mixed Integer Linear Programming (MILP) relaxation. To reduce problem size and to enhance computational efficiency, we proposed a Dynamic Pyramidal Relaxation (DPR) method, where the cuts (inner approximation and outer approximation) are adaptively added. In practice, the DPR method is embedded into a MILP commercial solver based on the branch-and-cut framework. Case studies in different test systems validate the effectiveness in terms of feasibility, accuracy, and efficiency of our proposed method.

关键词： Electrical engineering computational modeling Power system dynamics Asia Linear approximation Relaxation methods Mixed integer linear programming

Energy based diffusion generator for efficient sampling of Boltzmann distributions

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arXiv 2024年

作者： Wang, Yan L., Guo H., Wu T., Zhou School of Mathematical Sciences Tongji University Shanghai China Department of Mathematics Shanghai Normal University Shanghai China School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Shanghai Jiao Tong University Shanghai China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing China

Sampling from Boltzmann distributions, particularly those tied to high-dimensional and complex energy functions, poses a significant challenge in many fields. In this work, we present the Energy-Based Diffusion Generator (EDG), a novel approach that integrates ideas from variational autoencoders and diffusion models. EDG leverages a decoder to transform latent variables from a simple distribution into samples approximating the target Boltzmann distribution, while the diffusion-based encoder provides an accurate estimate of the Kullback-Leibler divergence during training. Notably, EDG is simulationfree, eliminating the need to solve ordinary or stochastic differential equations during training. Furthermore, by removing constraints such as bijectivity in the decoder, EDG allows for flexible network design. Through empirical evaluation, we demonstrate the superior performance of EDG across a variety of complex distribution tasks, outperforming existing methods. Copyright © 2024, The Authors. All rights reserved.

关键词： Decoding

A BROKEN HARDY INEQUALITY ON FINITE ELEMENT SPACE AND APPLICATION TO STRAIN GRADIENT ELASTICITY

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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 illustrate a broken Hardy inequality on discontinuous finite element spaces, blowing up with a logarithmic factor with respect to the meshes size. This is motivated by numerical analysis for the strain gradient elasticity with natural boundary conditions. A mixed finite element pair is employed to solve this model with nearly incompressible materials. This pair is quasi-stable with a logarithmic factor, which is not significant in the approximation error, and converges robustly in the incompressible limit and uniformly in the microscopic material parameter. Numerical results back up that the theoretical predictions are nearly optimal. Moreover, the regularity estimates for the model over a smooth domain have been proved with the aid of the Agmon-Douglis-Nirenberg theory. Copyright © 2025, The Authors. All rights reserved.

关键词： Set theory

A predictor-corrector deep learning algorithm for high dimensional stochastic partial differential equations

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arXiv 2022年

作者： Zhang, He Zhang, Ran Zhou, Tao School of Mathematics Jilin University Jilin Changchun130012 China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

In this paper, we present a deep learning-based numerical method for approximating high dimensional stochastic partial differential equations (SPDEs). At each time step, our method relies on a predictor-corrector procedure. More precisely, we decompose the original SPDE into a degenerate SPDE and a deterministic PDE. Then in the prediction step, we solve the degenerate SPDE with the Euler scheme, while in the correction step we solve the second-order deterministic PDE by deep neural networks via its equivalent backward stochastic differential equation (BSDE). Under standard assumptions, error estimates and the rate of convergence of the proposed algorithm are presented. The efficiency and accuracy of the proposed algorithm are illustrated by numerical examples. Copyright © 2022, The Authors. All rights reserved.

关键词： Numerical methods

An extended plane wave framework for the electronic structure calculations of twisted bilayer material systems

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arXiv 2023年

作者： Dai, Xiaoying Zhou, Aihui Zhou, Yuzhi LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China CAEP Software Center for High Performance Numerical Simulation Beijing100088 China Institute of Applied Physics and Computational Mathematics Beijing100088 China

In this paper, we propose an extended plane wave framework to make the electronic structure calculations of the twisted bilayer 2D material systems practically feasible. Based on the foundation in [Y. Zhou, H. Chen, A. Zhou, J. Comput. Phys. 384, 99 (2019)], following extensions take place: (1) an tensor-producted basis set, which adopts PWs in the incommensurate dimensions, and localized basis in the interlayer dimension, (2) a practical application of a novel cutoff techniques we have recently developed, and (3) a quasi-band structure picture under the small twisted angles and weak interlayer coupling limits. With (1) and (2) now the dimensions of Hamiltonian matrix are reduced by about 2 orders of magnitude compared with the original framework. And (3) enables us to better organize the calculations and understand the results. For numerical examples, we study the electronic structures of the linear bilayer graphene lattice system with the magic twisted angle (∼ 1.05◦). The famous flat bands have been reproduced with their features in quantitative agreement with those from experiments and other theoretical calculations. Moreover, the extended framework has much less computational cost compared to the commensurate cell approximations, and is more extendable compared to the traditional model hamiltonians and tight binding models. Finally this framework can readily accommodate nonlinear models thus will laid the foundations for more effective yet accurate Density Functional Theory (DFT) calculations. © 2023, CC BY.

关键词： Electronic structure

Localization in the Incommensurate Systems: A Plane Wave Study via Effective Potentials

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arXiv 2023年

作者： Wang, Ting Zhou, Yuzhi Zhou, Aihui LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China CAEP Software Center for High Performance Numerical Simulation Beijing100088 China Institute of Applied Physics and Computational Mathematics Beijing100094 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In this paper, we apply the effective potentials in the localization landscape theory (Filoche et al., 2012, Arnold et al., 2016) to study the spectral properties of the incommensurate systems. We uniquely develop a plane wave method for the effective potentials of the incommensurate systems and utilize that, the localization of the electron density can be inferred from the effective potentials. Moreover, we show that the spectrum distribution can also be obtained from the effective potential version of Weyl’s law. We perform some numerical experiments on some typical incommensurate systems, showing that the effective potential provides an alternative tool for investigating the localization and spectrum distribution of the systems. Copyright © 2023, The Authors. All rights reserved.

关键词： Elastic waves

Evidence for validity and reliability of a research-based assessment instrument on measurement uncertainty

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Physical Review Physics Education Research 2024年第2期20卷 020125页

作者： Gayle Geschwind Michael Vignal Marcos D. Caballero H. J. Lewandowski National Institute of Standards and Technology and the University of Colorado Boulder Colorado 80309 USA Department of Physics Department of Physics and Astronomy and CREATE for STEM Institute Department of Computational Mathematics Science and Engineering Department of Physics and Center for Computing in Science Education

The Survey of Physics Reasoning on Uncertainty Concepts in Experiments (SPRUCE) was designed to measure students’ proficiency with measurement uncertainty concepts and practices across ten different assessment objectives to help facilitate the improvement of laboratory instruction focused on this important topic. To ensure the reliability and validity of this assessment, we conducted a comprehensive statistical analysis using classical test theory. This analysis includes an evaluation of the test as a whole, as well as an in-depth examination of individual items and assessment objectives. We make use of a previously reported on scoring scheme involving pairing items with assessment objectives, creating a new unit for statistical analysis referred to as a “couplet.” The findings from our analysis provide evidence for the reliability and validity of SPRUCE as an assessment tool for undergraduate physics labs. This increases both instructors’ and researchers’ confidence in using SPRUCE for measuring students’ proficiency with measurement uncertainty concepts and practices to ultimately improve laboratory instruction. Additionally, our results using couplets and assessment objectives demonstrate how these can be used with traditional classic test theory analysis.

关键词： Assessment Research methodology