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arXiv 2025年

作者： Cao, Daomin Dai, Wei Li, Yafei Institute of Applied Mathematics Chinese Academy of Sciences Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China Beijing100191 China Key Laboratory of Mathematics Informatics and Behavioral Semantics Ministry of Education Beijing100191 China

In this paper, we mainly consider nonnegative weak solutions u ∈ D1,p(RN ) to the doubly D1,p(RN )-critical nonlocal quasi-linear Schrödinger-Hartree equation: (formula Presented), where N ≥ 3, 0 ≤ µ p and 1 N2 . When µ > 0, due to appearance of the Hardy potential, the equation has singularity at 0 ∈ RN and hence is not translation invariant, so sharp asymptotic estimates near the origin must be involved. First, we establish regularity and the sharp estimates on asymptotic behaviors near the origin and the infinity for any positive solution u ∈ D1,p(RN ) (and |∇u|) to more general equation −∆pu − µ |1/x|p up−1 = V (x) |1/x|s up−1 with N ≥ 2, 0 ≤ µ N ). Then, as a consequence, we can apply the method of moving planes to prove that all the nontrivial nonnegative solutions in D1,p(RN ) are radially symmetric and strictly radially decreasing about the origin 0 ∈ RN . The sharp asymptotic estimates and radial symmetry for more general weighted doubly D1,p-critical nonlocal quasi-linear equations were also derived. Our results extend the results in [26] from the special case µ = 0 to general cases 0 ≤ µ MSC Codes Primary: 35J92, Secondary: 35B06, 35B40 Copyright © 2025, The Authors. All rights reserved.

关键词： Schrodinger equation

ON THE SHARP QUANTITATIVE STABILITY OF CRITICAL POINTS OF THE HARDY-LITTLEWOOD-SOBOLEV INEQUALITY IN Rn WITH n ≥ 3

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arXiv 2025年

作者： Dai, Wei Hu, Yichen Peng, Shaolong Beijing100083 China Key Laboratory of Mathematics Informatics and Behavioral Semantics Ministry of Education Beijing100191 China School of Mathematical Sciences Dalian University of Technology Liaoning Dalian116024 China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

Assume n ≥ 3 and u ∈ Ḣ 1(Rn). Recently, Piccione, Yang and Zhao [41] established a nonlocal version of Struwe’s decomposition in [45], i.e., if u ≥ 0 and (formula presented), then dist(u, T) → 0, where dist(u, T) denotes the Ḣ 1(Rn)-distance of u from the manifold of sums of Talenti bubbles. In this paper, we establish the nonlocal version of the quantitative estimates of Struwe’s decomposition in Ciraolo, Figalli and Maggi [14] for one bubble and n ≥ 3, Figalli and Glaudo [28] for 3 ≤ n ≤ 5 and Deng, Sun and Wei [25] for n ≥ 6 and two or more bubbles. We prove that for n ≥ 3, α Copyright © 2025, The Authors. All rights reserved.

关键词： Choquet integral

Continuous adjoint-based error estimation and its application to adaptive discontinuous Galerkin method

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Applied mathematics and Mechanics(English Edition) 2016年第11期37卷 1419-1430页

作者： Huiqiang YUE Tiegang LIU V.SHAYDUROV Key Laboratory of Mathematics Informatics and Behavioral Semantics Ministry of EducationSchool of Mathematics and Systems Science Beihang University

An adaptive mesh refinement algorithm based on a continuous adjoint ap- proach is developed. Both the primal equation and the adjoint equation are approximated with the discontinuous Galerkin （DG） method. The proposed adaptive algorithm is used in compressible Euler equations. Numerical tests are made to show the superiority of the proposed adaptive algorithm.

关键词： adaptivity discontinuous Galerkin （DG） adjoint

GPMFS: Global Foundation and Personalized Optimization for Multi-Label Feature Selection

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arXiv 2025年

作者： Cao, Yifan Mi, Zhilong Yin, Ziqiao Guo, Binghui Dong, Jin School of Artificial Intelligence Beihang University Beijing100191 China Zhongguancun Laboratory Beijing100094 China Key Laboratory of Mathematics Informatics and Behavioral Semantics Beihang University Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing Beijing100191 China Hangzhou International Innovation Institute Beihang University Hangzhou311115 China Beijing Academy of Blockchain and Edge Computing Beijing100080 China

As artificial intelligence methods are increasingly applied to complex task scenarios, high dimensional multi-label learning has emerged as a prominent research focus. At present, the curse of dimensionality remains one of the major bottlenecks in high-dimensional multi-label learning, which can be effectively addressed through multi-label feature selection methods. However, existing multi-label feature selection methods mostly focus on identifying global features shared across all labels, which overlooks personalized characteristics and specific requirements of individual labels. This global-only perspective may limit the ability to capture label-specific discriminative information, thereby affecting overall performance. In this paper, we propose a novel method called GPMFS (Global Foundation and Personalized Optimization for Multi-Label Feature Selection). GPMFS firstly identifies global features by exploiting label correlations, then adaptively supplements each label with a personalized subset of discriminative features using a threshold-controlled strategy. Experiments on multiple real-world datasets demonstrate that GPMFS achieves superior performance while maintaining strong interpretability and robustness. Furthermore, GPMFS provides insights into the label-specific strength across different multi-label datasets, thereby demonstrating the necessity and potential applicability of personalized feature selection approaches. Copyright © 2025, The Authors. All rights reserved.

关键词： Feature extraction

The Recovery Guarantee for Orthogonal Matching Pursuit Method to Reconstruct Sparse Polynomials

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Numerical mathematics(Theory,Methods and Applications) 2022年第3期15卷 793-818页

作者： Aitong Huang Renzhong Feng Sanpeng Zheng School of Mathematics Science&Key Laboratory of Mathematics Informatics and Behavioral SemanticsMinistry of EducationBeihang UniversityBeijingChina

Orthogonal matching pursuit(OMP for short)algorithm is a popular method of sparse signal recovery in compressed *** paper applies OMP to the sparse polynomial reconstruction *** from classical research methods using mutual coherence or restricted isometry property of the measurement matrix,the recovery guarantee and the success probability of OMP are obtained directly by the greedy selection ratio and the probability *** results show that the failure probability of OMP given in this paper is exponential small with respect to the number of sampling *** addition,the recovery guarantee of OMP obtained through classical methods is lager than that of ℓ_(1)-minimization whatever the sparsity of sparse polynomials is,while the recovery guarantee given in this paper is roughly the same as that of ℓ_(1)-minimization when the sparsity is less than ***,the numerical experiments verify the availability of the theoretical results.

关键词： Reconstruction of sparse polynomial uniformly bounded orthogonal system orthogonal matching pursuit method probability of successful reconstruction sub-Gaussian random variable

Initial Error Tolerant Distributed Mean Field Control under Partial and Discrete Information

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arXiv 2025年

作者： Jin, Yuxin Wang, Haotian Yao, Wang Zhang, Xiao ShenYuan Honors College School of Mathematical Sciences Beihang University Beijing100191 China Key Laboratory of Mathematics Informatics and Behavioral Semantics Ministry of Education Beihang University Beijing100191 China School of Mathematical Sciences Beihang University Beijing100191 China School of Artificial Intelligence LMIB Beihang University Beijing100191 China Hangzhou International Innovation Institute of Beihang University Hangzhou311115 China

In this paper, an initial error tolerant distributed mean field control method under partial and discrete information is introduced, where each agent only has discrete observations on its own state. First, we study agents’ behavior in linear quadratic mean field games (LQMFGs) under heterogeneous erroneous information of the initial mean field state (MF-S), and formulate the relationships between initial errors and systemic deviations. Next, by capturing the initial error affection on the private trajectory of an agent, we give a distributed error estimation method based on maximum likelihood estimation (MLE), where each agent estimates information errors only based on discrete observations on its private trajectory. Furthermore, we establish an error-based segmented state estimation method, design the initial error tolerant distributed mean field control method (IET-DMFC), and demonstrate the consistent property of state estimation as observation frequency increases. Finally, simulations are performed to verify the efficiency of the algorithm and the consistent properties. Copyright © 2025, The Authors. All rights reserved.

关键词： Maximum likelihood

Rational Quasi-Interpolation Approximation of Scattered Data in R^(3)

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Numerical mathematics(Theory,Methods and Applications) 2018年第1期11卷 169-186页

作者： Renzhong Feng Lifang Song School of Mathematics and Systematic Science&Key Laboratory of Mathematics Informatics and Behavioral SemanticsMinistry of EducationBeijing University of Aeronautics and AstronauticsBeijing 100191China

This paper is concerned with a piecewise smooth rational quasi-interpolation with algebraic accuracy of degree(n+1)to approximate the scattered data in R *** firstly use the modified Taylor expansion to expand the mean value coordinates interpolation with algebraic accuracy of degree one to one with algebraic accuracy of degree(n+1).Then,based on the triangulation of the scattered nodes in R^(2),on each triangle a rational quasi-interpolation function is *** constructed rational quasi-interpolation is a linear combination of three different expanded mean value coordinates interpolations and it has algebraic accuracy of degree(n+1).By comparing accuracy,stability,and efficiency with the C^(1)-Tri-interpolation method of Goodman[16]and the MQ Shepard method,it is observed that our method has some computational advantages.

关键词： Scattered data mean value coordinates interpolation modified Taylor expansion rational quasi-interpolation algebraic accuracy

A MULTIVARIATE MULTIQUADRIC QUASI-INTERPOLATION WITH QUADRIC REPRODUCTION

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Journal of Computational mathematics 2012年第3期30卷 311-323页

作者： Renzhong Feng Xun Zhou School of Mathematics and Systematic Science Beijing University of Aeronautics and AstronauticsBeijing 100191China Key Laboratory of Mathematics Informatics and Behavioral SemanticsMinistry of EducationChina

In this paper, by using multivariate divided differences to approximate the partial derivative and superposition, we extend the multivariate quasi-interpolation scheme based on dimension-splitting technique which can reproduce linear polynomials to the scheme quadric polynomials. Furthermore, we give the approximation error of the modified scheme. Our multivariate multiquadric quasi-interpolation scheme only requires information of lo- cation points but not that of the derivatives of approximated function. Finally, numerical experiments demonstrate that the approximation rate of our scheme is significantly im- proved which is consistent with the theoretical results.

关键词： Quasi-interpolation Multiquadric functions Polynomial reproduction ：Pn-exact A-discretization of ：Da Approximation error.

A Survey of Hidden Convex Optimization

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Journal of the Operations Research Society of China 2020年第1期8卷 1-28页

作者： Yong Xia Key Laboratory of Mathematics Informatics and Behavioral Semantics of the Ministry of EducationSchool of Mathematics and System SciencesBeihang UniversityBeijing 100191China

Motivated by the fact that not all nonconvex optimization problems are difficult to solve,we survey in this paper three widely used ways to reveal the hidden convex structure for different classes of nonconvex optimiz... 详细信息

关键词： Convex programming Quadratic programming Quadratic matrix programming Fractional programming Lagrangian dual Semidefinite programming

Potential Indicator for Continuous Emotion Arousal by Dynamic Neural Synchrony 4th

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Potential Indicator for Continuous Emotion Arousal by Dyna...

4th International Workshop on Human Brain and Artificial Intelligence, HBAI 2024

作者： Pan, Guandong Wu, Zhaobang Yang, Yaqian Wang, Xin Liu, Longzhao Zheng, Zhiming Tang, Shaoting School of Computer Science and Engineering Beihang University Beijing100191 China Institute of Artificial Intelligence Beihang University Beijing100191 China Key Laboratory of Mathematics Informatics and Behavioral Semantics Beihang University Beijing100191 China Institute of Medical Artificial Intelligence Binzhou Medical University Yantai264003 China Zhongguancun Laboratory Beijing100094 China Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing Beihang University Beijing100191 China PengCheng Laboratory Shenzhen518055 China State Key Lab of Software Development Environment Beihang University Beijing100191 China

ISBN: (纸本)9789819640003

The need for automatic and high-quality emotion annotation is paramount in applications such as continuous emotion recognition and video highlight detection, yet achieving this through manual human annotations is challenging. Inspired by inter-subject correlation (ISC) utilized in neuroscience, this study introduces a novel Electroencephalography (EEG) based ISC methodology that leverages a single-electrode and feature-based dynamic approach. Our contributions are three folds: Firstly, we reidentify two potent emotion features suitable for classifying emotions-first-order difference (FD) an differential entropy (DE). Secondly, through the use of overall correlation analysis, we demonstrate the heterogeneous synchronized performance of electrodes. This performance aligns with neural emotion patterns established in prior studies, thus validating the effectiveness of our approach. Thirdly, by employing a sliding window correlation technique, we showcase the significant consistency of dynamic ISCs across various features or key electrodes in each analyzed film clip. Our findings indicate the method’s reliability in capturing consistent, dynamic shared neural synchrony among individuals, triggered by evocative film stimuli. This underscores the potential of our approach to serve as an indicator of continuous human emotion arousal. The implications of this research are significant for advancements in affective computing and the broader neuroscience field, suggesting a streamlined and effective tool for emotion analysis in real-world applications. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： Electroencephalography (EEG) Emotion Annotation Inter-subject Correlation