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Asymptotic Estimates for Spectral Estimators of Rotationally Invariant Matrices

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Asymptotic Estimates for Spectral Estimators of Rotationally...

IEEE International Symposium on Information Theory

作者： Zhuohang He Xiaojun Yuan Junjie Ma National Key Laboratory of Wireless Communications University of Electronic Science and Technology of China Chengdu China Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing China

ISBN: (数字)9798350382846

ISBN: (纸本)9798350382853

In this paper, we consider the recovery of low-rank matrices from noisy observations using spectral denoisers, where the singular values are denoised through an identical scalar smoothing function. We explore the asymptotic mean squared error (AMSE) of these denoisers within a framework where the rank of the matrix to be recovered grows linearly with the matrix size. We demonstrate that, under arbitrary i.i.d. noise and some mild regularity assumptions, the AMSE converges in probability to a deterministic function of the noise power. Our results are applicable to commonly used denoisers, including the best-rank-r denoiser, the singular-value soft-threshold denoiser, and the singular-value hard-threshold denoiser. To the best of our knowledge, this is the first study to establish an analytical expression for the asymptotic MSE under arbitrary i.i.d. noise. The derived analytical expression depends solely on the empirical distribution of the singular values of the low-rank matrix and the specific form of the spectral denoiser employed.

关键词： Smoothing methods Limiting Noise Noise reduction Noise measurement Information theory

GRADIENT-ENHANCED DEEP NEURAL NETWORK APPROXIMATIONS

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arXiv 2022年

作者： Feng, Xiaodong Zeng, Li LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing China

We propose in this work the gradient-enhanced deep neural networks (DNNs) approach for function approximations and uncertainty quantification. More precisely, the proposed approach adopts both the function evaluations and the associated gradient information to yield enhanced approximation accuracy. In particular, the gradient information is included as a regularization term in the gradient-enhanced DNNs approach, for which we present similar posterior estimates (by the two-layer neural networks) as those in the path-norm regularized DNNs approximations. We also discuss the application of this approach to gradient-enhanced uncertainty quantification, and present several numerical experiments to show that the proposed approach can outperform the traditional DNNs approach in many cases of interests. Copyright © 2022, The Authors. All rights reserved.

关键词： Deep neural networks

Using Data Mining Techniques to Analyze Facial Expression Motion Vectors 6th

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Using Data Mining Techniques to Analyze Facial Expression Mo...

6th International Conference on Dynamics of Information Systems, DIS 2023

作者： Roshanzamir, Mohamad Alizadehsani, Roohallah Roshanzamir, Mahdi Shoeibi, Afshin Gorriz, Juan M. Khosravi, Abbas Nahavandi, Saeid Acharya, U. Rajendra Department of Computer Engineering Faculty of Engineering Fasa University Fasa74617-81189 Iran Deakin University GeelongVIC Australia Department of Electrical and Computer Engineering University of Tabriz Tabriz Iran Data Science and Computational Intelligence Institute University of Granada Granada Spain Department of Signal Theory Networking and Communications Universidad de Granada Granada Spain Swinburne University of Technology HawthornVIC3122 Australia School of Mathematics Physics and Computing University of Southern Queensland Springfield Australia

ISBN: (纸本)9783031503191

Automatic recognition of facial expressions is a common problem in human-computer interaction. While humans can recognize facial expressions very easily, machines cannot do it as easily as humans. Analyzing facial changes during facial expressions is one of the methods used for this purpose by the machines. In this research, facial deformation caused by facial expressions is considered for automatic facial expression recognition by machines. To achieve this goal, the motion vectors of facial deformations are captured during facial expression using an optical flow algorithm. These motion vectors are then used to analyze facial expressions using some data mining algorithms. This analysis not only determined how changes in the face occur during facial expressions but can also be used for facial expression recognition. The facial expressions investigated in this research are happiness, sadness, surprise, fear, anger, and disgust. According to our research, these facial expressions were classified into 12 classes of facial motion vectors. We applied our proposed analysis mechanism to the extended Cohen-Kanade facial expression dataset. Our developed automatic facial expression system achieved 95.3%, 92.8%, and 90.2% accuracy using Deep Learning (DL), Support Vector Machine (SVM), and C5.0 classifiers, respectively. In addition, based on this research, it was determined which parts of the face have a greater impact on facial expression recognition. © 2024, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Data mining

Optimal-rate error estimates and a twice decoupled solver for a backward Euler finite element scheme of the Doyle-Fuller-Newman model of lithium-ion batteries

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arXiv 2024年

作者： Xu, Shu Cao, Liqun School of Mathematical Sciences Peking University Beijing100871 China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China State Key Laboratory of Scientific and Engineering Computing Beijing100190 China National Center for Mathematics and Interdisciplinary Sciences Chinese Academy of Sciences Beijing100190 China

We investigate the convergence of a backward Euler finite element discretization applied to a multi-domain and multi-scale elliptic-parabolic system, derived from the Doyle-Fuller-Newman model for lithium-ion batteries. We establish optimal-order error estimates for the solution in the norms l2(H1) and l2(L2(Hrq)), q = 0,1. To improve computational efficiency, we propose a novel solver that accelerates the solution process and controls memory usage. Numerical experiments with realistic battery parameters validate the theoretical error rates and demonstrate the significantly superior performance of the proposed solver over existing solvers. Copyright © 2024, The Authors. All rights reserved.

关键词： computational efficiency

Improved Turbo Message Passing for Compressive Robust Principal Component Analysis: Algorithm Design and Asymptotic Analysis

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arXiv 2024年

作者： He, Zhuohang Ma, Junjie Yuan, Xiaojun The National Key Laboratory of Wireless Communications University of Electronic Science and Technology of China Chengdu611731 China The Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100864 China

Compressive Robust Principal Component Analysis (CRPCA) naturally arises in various applications as a means to recover a low-rank matrix low-rank matrix L and a sparse matrix S from compressive measurements. In this paper, we approach the problem from a Bayesian inference perspective. We establish a probabilistic model for the problem and develop an improved turbo message passing (ITMP) algorithm based on the sum-product rule and the appropriate approximations. Additionally, we establish a state evolution framework to characterize the asymptotic behavior of the ITMP algorithm in the large-system limit. By analyzing the established state evolution, we further propose sufficient conditions for the global convergence of our algorithm. Our numerical results validate the theoretical results, demonstrating that the proposed asymptotic framework accurately characterize the dynamical behavior of the ITMP algorithm, and the phase transition curve specified by the sufficient condition agrees well with numerical simulations. © 2024, CC BY.

关键词： Asymptotic analysis

Statistical Multiplexing Gain Analysis of Centralized Open Radio Access Networks with Limited Cells and Heterogeneous Traffics

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IEEE Transactions on Vehicular Technology 2025年

作者： Wang, Lu Zhou, Yiqing Liu, Ya-Feng Liu, Ling Shi, Ningzhe Tian, Lin Shi, Jinglin National Key Laboratory of Transient Impact Beijing102202 China 208 Research Institute of China Ordnance Industries Beijing102202 China Chinese Academy of Sciences State Key Lab of Processors Institute of Computing Technology Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China Beijing Key Laboratory of Mobile Computing and Pervasive Device Beijing100190 China Chinese Academy of Sciences State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China Chinese Academy of Sciences Institute of Computing Technology Beijing100190 China Nanjing Institute of InforSuperBahn Nanjing211100 China

Centralized open radio access networks (O-RANs) aggregate computing resources of multiple cells to improve resource utilization and achieve statistical multiplexing gain (SMG), i.e., the ratio of the number of deployed resources (DepR) for distributed radio access network (D-RAN) to that for O-RAN. SMG of O-RAN has been investigated with infinite number of cells with homogeneous bursty-temporal traffic features. However, in practice, the number of cells is limited, and in the era of Internet of Things (IoT), cells with heterogeneous bursty-temporal traffics (het-traffics), should be considered. This paper analyzes the SMG of O-RAN with limited het-traffic cells. First of all, given traffic models of het-traffic cells following different bursty lognormal distribution and periodic time-varying features, required resources (ReqR) for D-RAN can be derived. Then, to obtain the distribution of ReqR for O-RAN with limited het-traffic cells, a Gaussian mixture model (GMM) based resource distribution approximation (GMM-RDA) is proposed. Thus SMG can be obtained for any given service rate. In simulations, the effectiveness of GMM-RDA is verified by Kolmogorov-Smirnov (K-S) test, and the accuracy of achieved SMG can be up to 99.7%, which is about 33% higher than that obtained by the law of large numbers (LLN) for infinite cells. Moreover, het-traffic cells resulting from service diversification can enhance SMG in O-RAN by 34.7%. © 1967-2012 IEEE.

关键词： Radio access networks

Helmholtz decomposition based windowed Green function methods for elastic scattering problems on a half-space

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arXiv 2023年

作者： Yin, Tao Zhang, Lu Zheng, Weiying Zhu, Xiaopeng 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 Zhejiang University Hangzhou310027 China LSEC NCMIS 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 Beijing100049 China

This paper proposes a new Helmholtz decomposition based windowed Green function (HD-WGF) method for solving the time-harmonic elastic scattering problems on a half-space with Dirichlet boundary conditions in both 2D and 3D. The Helmholtz decomposition is applied to separate the pressure and shear waves, which satisfy the Helmholtz and Helmholtz/Maxwell equations, respectively, and the corresponding boundary integral equations of type (I + T) = f, that couple these two waves on the unbounded surface, are derived based on the free-space fundamental solution of Helmholtz equation. This approach avoids the treatment of the complex elastic displacement tensor and traction operator that involved in the classical integral equation method for elastic problems. Then a smooth "slow-rise" windowing function is introduced to truncate the boundary integral equations and a "correction" strategy is proposed to ensure the uniformly fast convergence for all incident angles of plane incidence. Numerical experiments for both two and three dimensional problems are presented to demonstrate the accuracy and efficiency of the proposed method. Copyright © 2023, The Authors. All rights reserved.

关键词： Boundary integral equations

NEW C0 INTERIOR PENALTY METHOD FOR MONGE-AMPÈRE EQUATIONS

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arXiv 2024年

作者： Chu, Tianyang Guo, Hailong Zhang, Zhimin LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematics and Statistics The University of Melbourne ParkvilleVIC3010 Australia Department of Mathematics Wayne State University DetroitMI48202 United States

Monge-Ampère equation is a prototype second-order fully nonlinear partial differential equation. In this paper, we propose a new idea to design and analyze the C0 interior penalty method to approximation the viscosity solution of the Monge-Ampère equation. The new methods is inspired from the discrete Miranda-Talenti estimate. Based on the vanishing moment representation, we approximate the Monge-Ampère equation by the fourth order semi-linear equation with some additional boundary conditions. We will use the discrete Miranda-Talenti estimates to ensure the well-posedness of the numerical scheme and derive the error estimates. © 2024, CC BY.

关键词： Partial differential equations

Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection

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Science China mathematics 2021年第5期64卷 887-902页

作者： Hong-Lin Liao Xuehua Song Tao Tang Tao Zhou Department of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211101China Department of Mathematics and International Center for Mathematics Southern University of Science and TechnologyShenzhen 518055China Division of Science and Technology BNU-HKBU United International CollegeZhuhai 519087China NCMIS&LSEC Institute of Computational Mathematics and Scientific Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

In this work,we are concerned with the stability and convergence analysis of the second-order backward difference formula(BDF2)with variable steps for the molecular beam epitaxial model without slope *** first show that the variable-step BDF2 scheme is convex and uniquely solvable under a weak time-step *** we show that it preserves an energy dissipation law if the adjacent time-step ratios satisfy r_(k):=τ_(k)/τ_(k-1)<***,with a novel discrete orthogonal convolution kernels argument and some new estimates on the corresponding positive definite quadratic forms,the L^(2)norm stability and rigorous error estimates are established,under the same step-ratio constraint that ensures the energy stability,i.e.,0

关键词： molecular beam epitaxial growth variable-step BDF2 scheme discrete orthogonal convolution kernels energy stability convergence analysis