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Chung’s functional law of the iterated logarithm for the Brownian sheet

Frontiers of Mathematics in China 2022年第6期17卷 1015-1024页

作者： Yonghong LIU Ting ZHANG Yiheng TANG Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation School of Mathematics and Computing ScienceGuilin University of Electronic TechnologyGuilin541004China

In this paper,we investigate functional limit problem for path of a Brownian sheet,Chung’s functional law of the iterated logarithm for a Brownian sheet is *** main tool in the proof is large deviation and small devi... 详细信息

关键词： Brownian sheet Chung’s functional law of the iterated logarithm

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Improved image segmentation method based on Otsu thresholding and level set techniques 7

Improved image segmentation method based on Otsu thresholdin...

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2024 7th International Symposium on Big data and Applied Statistics, ISBDAS 2024

作者： Jing, Zhipeng Tang, Bo School of Mathematics and Computing Sciences Guangxi Colleges Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology Guilin541001 China

Image segmentation is a complex task in the field of image processing and computer vision, as it faces challenges such as noise, low contrast, and intensity variations. Due to the simplicity, efficiency, and ease of implementation of the Otsu algorithm, as well as its ability to improve accuracy in complex scenarios and enhance robustness against noise and lighting variations, a new grayscale pixel probability selection method has been proposed based on the classic Otsu method and Chan-Vese level set. By applying the Bayesian probability formula, the probability of a grayscale pixel is determined by the global prior and non-local prior. This improved Otsu method is combined with the Chan-Vese level set curve evolution method, resulting in a better image segmentation approach. Comparative experiments have demonstrated the advantages of this method. © Published under licence by IOP Publishing Ltd.

关键词： Image segmentation

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A TRUST-REGION METHOD FOR SOLVING TRUNCATED COMPLEX SINGULAR VALUE DECOMPOSITION

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Journal of computational Mathematics 2024年第4期42卷 999-1031页

作者： Jiaofen Li Lingchang Kong Xuefeng Duan Xuelin Zhou Qilun Luo School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationGuangxi Key Laboratory of Automatic Detecting Technology and InstrumentsGuilin University of Electronic TechnologyCenter for Applied Mathematics of Guangxi(GUET)Guilin 541004China School of Mathematical Sciences South China Normal UniversityGuangzhou 510000China School of Mathematics and Computing Science Guilin University of Electronic TechnologyGuilin 541004China School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationGuilin University of Electronic TechnologyCenter for Applied Mathematics of Guangxi(GUET)Guilin 541004China School of Mathematics and Statistics Yunan UniversityKunming 650000China

The truncated singular value decomposition has been widely used in many areas of science including engineering,and statistics,*** this paper,the original truncated complex singular value decomposition problem is formulated as a Riemannian optimiza-tion problem on a product of two complex Stiefel manifolds,a practical algorithm based on the generic Riemannian trust-region method of Absil et *** presented to solve the underlying problem,which enjoys the global convergence and local superlinear conver-gence *** experiments are provided to illustrate the efficiency of the proposed *** with some classical Riemannian gradient-type methods,the existing Riemannian version of limited-memory BFGS algorithms in the MATLAB toolbox Manopt and the Riemannian manifold optimization library ROPTLIB,and some latest infeasible methods for solving manifold optimization problems,are also provided to show the merits of the proposed approach.

关键词： Truncated singular value decomposition Riemannian optimization Trust-region method

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Conformal prediction based on principal component analysis for high-dimensional outlier detection

Conformal prediction based on principal component analysis f...

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2024 International Conference on Cloud Computing, Performance Computing, and Deep Learning, CCPCDL 2024

作者： Qian, Xiaoyu Wu, Jinru Lin, Youwu School of Mathematics and Computing Science Guangxi Colleges Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology Guilin541002 China Guilin541002 China

ISBN: (纸本)9781510683044

Current outlier detection methods exhibit many limitations in high-dimensional settings. Traditional statistical approaches rely on strong assumptions and lack practicality and generality. Meanwhile, despite the better performance, machine learning methods suffer from low interpretability and reliability due to their complex mechanisms and the absence of confidence estimation. Although outlier detection methods based on principal component analysis (PCA) have shown some advantages by extracting important features from high-dimensional data, they have not entirely solved these problems. Conformal prediction, a finite-sample distribution-free uncertainty quantification method recently applied to outlier detection, produces a set-valued prediction with a Type-I error guarantee and false discovery rate control. This paper proposes a new distribution-free method for high-dimensional outlier detection, PCA-CP, combining principal component analysis and conformal prediction. PCA-CP overcomes the shortcomings of previous methods, demonstrating high generality and reliability while achieving high performance. Experiments on simulation and real data show that PCA-CP outperforms previous methods, achieving higher power and lower False Discovery Rate, thus proving its significant advantages. © 2024 SPIE.

关键词： Prediction models

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Confidential Spatio-Temporal Graph Convolutional Networks with Differential Privacy for Traffic Forecasting 5

Confidential Spatio-Temporal Graph Convolutional Networks wi...

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5th International Conference on Electronic Communication and Artificial Intelligence, ICECAI 2024

作者： Chen, Xiangyang Xiao, Aiwen Pang, Weiling Jiang, Xinyi Ren, Zehua Tang, Min School of Mathematics and Computing Science Guangxi Colleges and Universities Guilin University of Electronic Technology Key Laboratory of Data Analysis and Computation Guilin541004 China Guilin541002 China

ISBN: (纸本)9798350386943

Traffic forecasting is essential for urban traffic management in intelligent transportation systems (ITS). However, it involves personal sensitive information, such as user location data. In this paper, we propose an innovative secure protocol for addressing the privacy challenges of traffic prediction in ITS. Our model integrates Spatio-Temporal Graph Convolutional Network (STGCN) and differential privacy (DP) to effectively protect user privacy on the premise of predictive performance. Our experimental results demonstrate that the model maintains a high level of prediction accuracy while offering privacy protection for the user data. On the PeMSD7 dataset, compared to the STGCN benchmark model, our model shows a slight increase of 0.5% in performance metrics (e.g., mean absolute error) while safeguarding the user data. Additionally, the model's average training time increases by roughly 8.4% in the ciphertext domain. © 2024 IEEE.

关键词： Differential privacy

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SINGULAR DOUBLE PHASE EQUATIONS

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Acta Mathematica Scientia 2023年第3期43卷 1031-1044页

作者：刘振海 Nikolaos S.PAPAGEORGIOU Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal UniversityYulin537000China Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis Guangxi Minzu UniversityNanning530006China Department of Mathematics National Technical UniversityZografou Campus15780AthensGreece

We study a double phase Dirichlet problem with a reaction that has a parametric singular term. Using the Nehari manifold method, we show that for all small values of the parameter, the problem has at least two positiv... 详细信息

关键词： double phase singular term unbalanced growth Musielak-Orlice spaces Nehari manifold positive solutions

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Characterizations of Weighted Besov Spaces with Variable Exponents

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Acta Mathematica Sinica,English Series 2024年第11期40卷 2855-2878页

作者： Sheng Rong WANG Peng Fei GUO Jing Shi XU School of Mathematics and Statistics Hainan Normal UniversityHaikou571158P.R.China Center for Applied Mathematics of Guangxi Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationSchool of Mathematics and Computing ScienceGuilin University of Electronic TechnologyGuilin541004P.R.China

In this paper,we first give characterizations of weighted Besov spaces with variable exponents via Peetre’s maximal *** we obtain decomposition characterizations of these spaces by atom,molecule and *** an applicatio... 详细信息

关键词： Besov space Muckenhoupt weight variable exponent Peetre’s maximal function atom molecule wavelet pseudo-differential operator

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The Study of Power Planning for Cyclists based on Genetic Algorithm 3

The Study of Power Planning for Cyclists based on Genetic Al...

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3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing, CAMMIC 2023

作者： Wu, Sixuan Tan, Qiancheng Xu, Dewei Mao, Rui School of Mathematics and Computing Science Guangxi Colleges Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology Guangxi Guilin541004 China

ISBN: (数字)9781510667617

ISBN: (纸本)9781510667600

This paper studies the power curve of two types riders (the Time Trial Specialist and the Sprinter) and set up a multi-objective optimization model by taking the total energy consumed and the total time used by a rider during the race as objective functions. By using the genetic algorithm to solve the multi-objective optimization model, the total energy and total time as far as possible to get the optimal solution under the condition of small number. The number of the optimal solutions corresponding to the rider in the process of competition has the opportunity to go beyond the opponent's corner number. The number of the optimal solutions can determine the relationship between the rider’s position on the course and the power the rider applies. Combining 2021 Tokyo Olympic Games, the model is applied to the individual time trials of two types of riders. © 2023 SPIE.

关键词： Genetic algorithms

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ERROR analysis OF VIRTUAL ELEMENT METHODS FOR THE TIME-DEPENDENT POISSON-NERNST-PLANCK EQUATIONS

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Journal of computational Mathematics 2025年第3期43卷 731-770页

作者： Ying Yang Ya Liu Yang Liu Shi Shu School of Mathematics and Computational Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationCenter for Applied Mathematics of Guangxi(GUET)Guilin University of Electronic TechnologyGuilin 541004China School of Mathematics and Computational Science Guilin University of Electronic TechnologyGuilin 541004China School of Mathematics and Computational Science Xiangtan UniversityXiangtan 411105China

We discuss and analyze the virtual element method on general polygonal meshes for the time-dependent Poisson-Nernst-Planck(PNP)equations,which are a nonlinear coupled system widely used in semiconductors and ion *** presenting the semi-discrete scheme,the optimal H1 norm error estimates are presented for the time-dependent PNP equations,which are based on some error estimates of a virtual element energy *** Gummel iteration is used to decouple and linearize the PNP equations and the error analysis is also given for the iteration of fully discrete virtual element *** numerical experiment on different polygonal meshes verifies the theoretical convergence results and shows the efficiency of the virtual element method.

关键词： Virtual element method Error estimate Poisson-Nernst-Planck equations Polygonal meshes Energy projection Gummel iteration

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Contact Extension and Symplectification

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Acta Mathematicae Applicatae Sinica 2023年第4期39卷 962-971页

作者： Qi-huai LIU An XIE Chao WANG School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationGuilin University of Electronic TechnologyGuilin 514001China School of Mathematical Sciences Yancheng Teachers UniversityYancheng 224002China Center for Applied Mathematics of Guangxi(GUET) Guilin 514001China

This paper mainly studies the contact extension of conservative or dissipative systems, including some old and new results for wholeness. Then extension of contact system is corresponding to the symplectification of contact Hamiltonian system. This is a reciprocal process and the relation between symplectic system and contact system has been discussed. We have an interesting discovery that by adding a pure variable p,the slope of the tangent of the orbit, every differential system can be regarded as an independent subsystem of contact Hamiltonian system defined on the projection space of contact phase space.

关键词： contact extension contact Hamiltonian system contact transformation

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