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Gelfand–Kirillov Dimension and Reducibility of Scalar Generalized Verma Modules

Acta Mathematica Sinica,English Series 2019年第11期35卷 1854-1860页

作者： Zhan Qiang BAI Wei XIAO School of Mathematical Sciences Soochow UniversitySuzhou 215006P.R.China College of Mathematics and statistics Shenzhen Key Laboratory of Advanced Machine Learning Applications Shenzhen UniversityShenzhen 518060P.R.China

The Gelfand–Kirillov dimension is an invariant which can measure the size of infinitedimensional algebraic structures. In this article, we show that it can also measure the reducibility of scalar generalized Verma modules. In particular, we use it to determine the reducibility of scalar generalized Verma modules associated with maximal parabolic subalgebras in the Hermitian symmetric case.

关键词： Gelfand–Kirillov dimension generalized Verma module reducibility

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Unified Variable Selection for Varying Coefficient Models with Longitudinal Data

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Journal of Systems Science & Complexity 2023年第2期36卷 822-842页

作者： XU Xiaoli ZHOU Yan ZHANG Kongsheng ZHAO Mingtao School of Management Science and Engineering Anhui University of Finance and Economics College of Mathematics and Statistics Institute of Statistical SciencesShenzhen Key Laboratory of Advanced Machine Learning and ApplicationsShenzhen University Institute of Statistics and Applied Mathematics Anhui University of Finance and Economics

Variable selection for varying coefficient models includes the separation of varying and constant effects,and the selection of variables with nonzero varying effects and those with nonzero constant *** paper proposes a unified variable selection approach called the double-penalized quadratic inference functions method for varying coefficient models of longitudinal *** proposed method can not only separate varying coefficients and constant coefficients,but also estimate and select the nonzero varying coefficients and nonzero constant *** is suitable for variable selection of linear models,varying coefficient models,and partial linear varying coefficient *** regularity conditions,the proposed method is consistent in both separation and selection of varying coefficients and constant *** obtained estimators of varying coefficients possess the optimal convergence rate of non-parametric function estimation,and the estimators of nonzero constant coefficients are consistent and asymptotically ***,the authors investigate the finite sample performance of the proposed method through simulation studies and a real data *** results show that the proposed method performs better than the existing competitor.

关键词： Double-penalized quadratic inference functions longitudinal data variable selection varying coefficient models

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The effect of deterministic noise on a quasi-subgradient method for quasi-convex feasibility problems

Journal of Applied and Numerical Optimization

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Journal of Applied and Numerical Optimization 2020年第2期2卷 235-247页

作者： Hu, Yaohua Liu, Yuping Li, Minghua Shenzhen Key Laboratory of Advanced Machine Learning and Applications College of Mathematics and Statistics Shenzhen University Shenzhen518060 China School of Mathematics and Big Data Chongqing University of Arts and Sciences Yongchuan Chongqing402160 China

The quasi-convex feasibility problem (QFP), in which the involved functions are quasi-convex, is at the core of the modeling of many problems in various areas such as economics, finance and management science. In this paper, we consider an inexact incremental quasi-subgradient method to solve the QFP, in which an incremental control of component functions in the QFP is employed and the inexactness stems from computation error and noise arising from practical considerations and physical circumstances. Under the assumptions that the computation error and noise are deterministic and bounded and a Hölder condition on component functions in the QFP, we study the convergence property of the proposed inexact incremental quasi-subgradient method, and particularly, investigate the effect of the inexact terms on the incremental quasi-subgradient method when using the constant, diminishing and dynamic stepsize rules. © 2020 Journal of Applied and Numerical Optimization.

关键词： Numerical methods

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A survey of clustering methods via optimization methodology

Journal of Applied and Numerical Optimization

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Journal of Applied and Numerical Optimization 2021年第1期3卷 151-174页

作者： Li, Xiaotian Cai, Linju Li, Jingchao Yu, Carisa Kwok Wai Hu, Yaohua Shenzhen Key Laboratory of Advanced Machine Learning and Applications College of Mathematics and Statistics Shenzhen University Shenzhen518060 China Department of Mathematics Statistics and Insurance Hang Seng University of Hong Kong Hong Kong Hong Kong

Clustering is one of fundamental tasks in unsupervised learning and plays a very important role in various application areas. This paper aims to present a survey of five types of clustering methods in the perspective of optimization methodology, including center-based methods, convex clustering, spectral clustering, subspace clustering, and optimal transport based clustering. The connection between optimization methodology and clustering algorithms is not only helpful to advance the understanding of the principle and theory of existing clustering algorithms, but also useful to inspire new ideas of efficient clustering algorithms. Preliminary numerical experiments of various clustering algorithms for datasets of various shapes are provided to show the preference and specificity of each algorithm. © 2021 Journal of Applied and Numerical Optimization.

关键词： Clustering algorithms

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IMPULSE NOISE REMOVAL BY L1 WEIGHTED NUCLEAR NORM MINIMIZATION

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Journal of Computational Mathematics 2023年第6期41卷 1171-1191页

作者： Jian Lu Yuting Ye Yiqiu Dong Xiaoxia Liu Yuru Zou Shenzhen Key Laboratory of Advanced Machine Learning and Applications College of Mathematics and StatisticsShenzhen UniversityShenzhen 518060China Guangdong Key Laboratory of Intelligent Information Processing Pazhou LabGuangzhou 510335China Department of Applied Mathematics and Computer Science Technical University of Denmark2800 Kgs.LyngbyDenmark

In recent years,the nuclear norm minimization(NNM)as a convex relaxation of the rank minimization has attracted great research *** assigning different weights to singular values,the weighted nuclear norm minimization(WNNM)has been utilized in many ***,most of the work on WNNM is combined with the l 2-data-fidelity term,which is under additive Gaussian noise *** this paper,we introduce the L1-WNNM model,which incorporates the l 1-data-fidelity term and the regularization from *** apply the alternating direction method of multipliers(ADMM)to solve the non-convex minimization problem in this *** exploit the low rank prior on the patch matrices extracted based on the image non-local self-similarity and apply the L1-WNNM model on patch matrices to restore the image corrupted by impulse *** results show that our method can effectively remove impulse noise.

关键词： Image denoising Weighted nuclear norm minimization l 1-data-fidelity term Low rank analysis Impulse noise

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BP Neural Network-Based Deep Non-negative Matrix Factorization for Image Clustering 16th

BP Neural Network-Based Deep Non-negative Matrix Factorizati...

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16th International Conference on Intelligent Computing, ICIC 2020

作者： Zeng, Qianwen Chen, Wen-Sheng Pan, Binbin College of Mathematics and Statistics Shenzhen University Shenzhen China Guangdong Key Laboratory of Media Security Shenzhen University Shenzhen China Shenzhen Key Laboratory of Advanced Machine Learning and Applications Shenzhen518060 China

ISBN: (纸本)9783030607951

Deep non-negative matrix factorization (DNMF) is a promising method for non-negativity multi-layer feature extraction. Most of DNMF algorithms are repeatedly to run single-layer NMF to build the hierarchical structure. They have to eliminate the accumulated error via fine-tuning strategy, which is, however, too time-consuming. To deal with the drawbacks of existing DNMF algorithms, this paper proposes a novel deep auto-encoder using back-propagation neural network (BPNN). It can automatically yield a deep non-negative matrix factorization, called BPNN based DNMF (BP-DNMF). The proposed BP-DNMF algorithm is empirically shown to be convergent. Compared with some state of the art DNMF algorithms, experimental results demonstrate that our approach achieves superior clustering performance and has high computing efficiency as well. © 2020, Springer Nature Switzerland AG.

关键词： Non-negative matrix factorization

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Underwater Image Enhancement via Multi-color Space Correction and Fusion 3

Underwater Image Enhancement via Multi-color Space Correctio...

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3rd International Conference on Electronic Information Engineering and Computer, EIECT 2023

作者： Zhou, Chenyu Chen, Bo Zhang, Ying Chen, Wensheng Pan, Binbin Ji, Jing Shenzhen University Shenzhen Key Laboratory of Advanced Machine Learning and Applications College of Mathematics and Statistics Shenzhen518060 China Shenzhen University Guangdong Key Laboratory of Intelligent Information Processing Shenzhen518060 China

ISBN: (纸本)9798350357707

Underwater image enhancement, as an important branch of image processing, has attracted the attention of many scholars in recent years. Due to selective scattering and degradation of light in water, images captured underwater are generally of low quality. To improve the accuracy of underwater image details and color, we propose a novel underwater image enhancement model, which is based on a Multi-color space fusion (MSF) strategy and assigns corresponding weights to each color channel for fusion. Qualitative and quantitative comparisons show that the proposed method can effectively remove image blur, achieve color correction, and significantly improve image sharpness. © 2023 IEEE.

关键词： Color

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Deep learning for Spectrum Sensing of Sub-Nyquist Sampled Signals 20

Deep Learning for Spectrum Sensing of Sub-Nyquist Sampled Si...

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20th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery, ICNC-FSKD 2024

作者： Li, Shiyao Ji, Hongbing Li, Lin Lu, Jian School of Electronic Engineering Xidian University Xi'an China College of Mathematics and Statistics Shenzhen University Shenzhen Key Laboratory of Advanced Machine Learning and Applications Shenzhen China

ISBN: (纸本)9798350356328

Traditional Nyquist rate sampling faces significant challenges as communication technology progresses towards 6G. Multi-coset sampling emerges as a viable solution by reducing the sampling rate. However, this method necessitates signal restoration before processing. In response, an intelligent spectrum management system has been developed that utilizes deep learning to directly extract semantic information from multi-coset sampled signals, eliminating the need for complex data preprocessing. The system integrates multi-band spectrum sensing and modulation recognition, achieving an impressive 99% accuracy in both modulation recognition of single signals and sub-band positioning of multiple signals. © 2024 IEEE.

关键词： Signal modulation

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A Zeroing Neurodynamic Approach for Solving Time-Varying Optimization Problem with Interval-Valued Cost Function 13

A Zeroing Neurodynamic Approach for Solving Time-Varying Opt...

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13th International Conference on Information Science and Technology, ICIST 2023

作者： Li, Haojin Qin, Sitian Jia, Hongyu Feng, Jiqiang Department of Mathematics Harbin Institute of Technology Weihai264209 China Department of Mathematics and Statistics Shenzhen Key Laboratory of Advanced Machine Learning and Applications Shenzhen University Shenzhen518060 China

ISBN: (纸本)9798350313925

Most of the research on uncertainty and imprecision that is widespread in the real world can be abstracted into interval-valued optimization problems whose cost function or constraint function is a closed interval. In this paper, a zeroing neurodynamic (ZND) approach is designed for solving a class of constrained time-varying optimization problems with closed interval-valued cost functions. By virtue of the projection operator and the optimality conditions of the interval-valued optimization problem, the time-varying interval-valued optimization problem is transformed into a nonlinear equation system to be solved. For the reformulated nonlinear equation system, the proposed ZND solver has the ability to track its theoretical solution within pre-defined time. This significantly improves the convergence rate of the ZND solver, making the ZND solver more promising for complex engineering tasks. To the best of our knowledge, it is the first time applying the ZND solver to solve the time-varying interval value optimization problem. Furthermore, the introduction of the projection operator greatly reduces the computational complexity of this ZND solver, saving costs for its hardware implementation. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach. © 2023 IEEE.

关键词： Cost functions

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On the first negative Hecke eigenvalue of an automorphic representation of GL_(2)(A_(Q))

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Science China Mathematics 2021年第11期64卷 2381-2394页

作者： Yuk-Kam Lau Ming Ho Ng Hengcai Tang Yingnan Wang Department of Mathematics The University of Hong KongHong KongChina Department of Mathematics The Chinese University of Hong KongHong KongChina Institute of Modern Mathematics School of Mathematics and StatisticsHenan UniversityKaifeng 475004China Shenzhen Key Laboratory of Advanced Machine Learning and Applications College of Mathematics and StatisticsShenzhen UniversityShenzhen 518060China

Letπbe a self-dual irreducible cuspidal automorphic representation of GL_(2)(A_(Q))with trivial central *** Hecke eigenvalue λπ(n)is a real multiplicative function in *** show that λπ(n)<0 for some n<<Q^... 详细信息

关键词： automorphic representation Hecke eigenvalue Maass cusp form sign change

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