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BOUNDARY VALUE METHODS FOR CA PUTO FR ACTIONAL DIFFERENTIAL EQUATIONS

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Journal of Computational Mathematics 2021年第1期39卷 108-129页

作者： Yongtao Zhou Chengiian Zhang Huiru Wang School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China

This paper deals with the numerical computation and analysis for Caputo fractional differential equations(CFDEs).By combining the p-order boundary value methods(B-VMs)and the m-th Lagrange interpolation,a type of exte... 详细信息

关键词： Fractional differential equations Caputo derivatives Boundary value methods Local stability Unique solvability Convergence.

GLOBAL WELL-POSEDNESS FOR THE LANDAU-LIFSHITZ-BARYAKHTAR EQUATION IN 3

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arXiv 2024年

作者： Xu, Fan Liu, Bin School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China

This paper establishes the global well-posedness of the Landau-Lifshitz-Baryakhtar (LLBar) equation in the whole space 3. The study first demonstrates the existence and uniqueness of global strong solutions using the weak compactness approach. Furthermore, the existence and uniqueness of classical solutions, as well as arbitrary smooth solutions, are derived through a bootstrap argument. The proofs for the existence of these three types of global solutions are based on Friedrichs mollifier approximation and energy estimates, with the structure of the LLBar equation playing a crucial role in the derivation of the results. Copyright © 2024, The Authors. All rights reserved.

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A CHEMOTAXIS-FLUID MODEL DRIVEN BY LÉVY NOISE IN R2

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arXiv 2024年

作者： Xu, Fan Zhang, Lei Liu, Bin School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China

In this paper, we investigate the existence and uniqueness of global solutions to the Cauchy problem for a coupled stochastic chemotaxis-Navier-Stokes system with multiplicative Lévy noises in R2. The existence of global martingale solutions is proved under a framework that is based on the Faedo-Galerkin approximation scheme and stochastic compactness method, where the verification of tightness depends crucially on a novel stochastic version of Lyapunov functional inequality and proper compactness criteria in Fréchet spaces. A pathwise uniqueness result is also established with suitable assumption on the jump noises, which indicates that the considered system admits a unique global strong solution. Copyright © 2024, The Authors. All rights reserved.

关键词： Lyapunov functions

WELL-POSEDNESS AND INVARIANT MEASURES FOR THE STOCHASTICALLY PERTURBED LANDAU-LIFSHITZ-BARYAKHTAR EQUATION

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arXiv 2024年

In this paper, we study the initial-boundary value problem for the stochastic Landau-Lifshitz-Baryakhtar (SLLBar) equation with Stratonovich-type noise in bounded domains O ⊂ Rd, d = 1, 2, 3. Our main results can be briefly described as follows: (1) for d = 1, 2, 3 and any u0 ∈ H1, the SLLBar equation admits a unique local-in-time pathwise weak solution;(2) for d = 1 and small-data u0 ∈ H1, the SLLBar equation has a unique global-in-time pathwise weak solution and at least one invariant measure;(3) for d = 1, 2 and small-data u0 ∈ L2, the SLLBar equation possesses a unique global-in-time pathwise very weak solution and at least one invariant measure, while for d = 3 only the existence of martingale solution is obtained due to the loss of pathwise uniqueness. Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic systems

Inverse Lax-Wendroff boundary treatment for solving conservation laws with finite difference HWENO methods

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arXiv 2025年

作者： Zhu, Guanghao Jiang, Yan Zhao, Zhuang Zhang, Mengping School of Mathematical Sciences University of Science and Technology of China Anhui Hefei230026 China Laoshan Laboratory Qingdao266237 China School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University Fujian Xiamen361005 China

This paper presents a novel inverse Lax-Wendroff (ILW) boundary treatment for finite difference Hermite weighted essentially non-oscillatory (HWENO) schemes to solve hyperbolic conservation laws on arbitrary geometries. The complex geometric domain is divided by a uniform Cartesian grid, resulting in challenge in boundary treatment. The proposed ILW boundary treatment could provide high order approximations of both solution values and spatial derivatives at ghost points outside the computational domain. Distinct from existing ILW approaches, our boundary treatment constructs the extrapolation via optimized through a least squares formulation, coupled with the spatial derivatives at the boundary obtained via the ILW procedure. Theoretical analysis indicates that compared with other ILW methods, our proposed one would require fewer terms by using the relatively complicated ILW procedure and thus improve computational efficiency while preserving accuracy and stability. The effectiveness and robustness of the method are validated through numerical experiments. Copyright © 2025, The Authors. All rights reserved.

关键词： Numerical methods

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

A riemannian exponential augmented lagrangian method for computing the projection robust Wasserstein distance 23

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A riemannian exponential augmented lagrangian method for com...

Proceedings of the 37th International Conference on Neural Information Processing Systems

作者： Bo Jiang Ya-Feng Liu Ministry of Education Key Laboratory of NSLSCS School of Mathematical Sciences Nanjing Normal University Nanjing 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 Beijing China

Projection robust Wasserstein (PRW) distance is recently proposed to efficiently mitigate the curse of dimensionality in the classical Wasserstein distance. In this paper, by equivalently reformulating the computation of the PRW distance as an optimization problem over the Cartesian product of the Stiefel manifold and the Euclidean space with additional nonlinear inequality constraints, we propose a Riemannian exponential augmented Lagrangian method (REALM) for solving this problem. Compared with the existing Riemannian exponential penalty-based approaches, REALM can potentially avoid too small penalty parameters and exhibit more stable numerical performance. To solve the subproblems in REALM efficiently, we design an inexact Riemannian Barzilai-Borwein method with Sinkhorn iteration (iRBBS), which selects the stepsizes adaptively rather than tuning the step-sizes in efforts as done in the existing methods. We show that iRBBS can return an ε-stationary point of the original PRW distance problem within O(ε-3) iterations, which matches the best known iteration complexity result. Extensive numerical results demonstrate that our proposed methods outperform the state-of-the-art solvers for computing the PRW distance.

关键词：

TFGDA: Exploring Topology and Feature Alignment in Semi-supervised Graph Domain Adaptation through Robust Clustering 38

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TFGDA: Exploring Topology and Feature Alignment in Semi-supe...

38th Conference on Neural Information Processing Systems, NeurIPS 2024

作者： Dan, Jun Liu, Weiming Xie, Chunfeng Yu, Hua Dong, Shunjie Tan, Yanchao Zhejiang University China Queen Mary University of London United Kingdom Dalian University of Technology China Shanghai Jiao Tong University China Fuzhou University China Engineering Research Center of Big Data Intelligence Ministry of Education China Fujian Key Laboratory of Network Computing and Intelligent Information Processing China

Semi-supervised graph domain adaptation, as a branch of graph transfer learning, aims to annotate unlabeled target graph nodes by utilizing transferable knowledge learned from a label-scarce source graph. However, most existing studies primarily concentrate on aligning feature distributions directly to extract domain-invariant features, while ignoring the utilization of the intrinsic structure information in graphs. Inspired by the significance of data structure information in enhancing models' generalization performance, this paper aims to investigate how to leverage the structure information to assist graph transfer learning. To this end, we propose an innovative framework called TFGDA. Specially, TFGDA employs a structure alignment strategy named STSA to encode graphs' topological structure information into the latent space, greatly facilitating the learning of transferable features. To achieve a stable alignment of feature distributions, we also introduce a SDA strategy to mitigate domain discrepancy on the sphere. Moreover, to address the overfitting issue caused by label scarcity, a simple but effective RNC strategy is devised to guide the discriminative clustering of unlabeled nodes. Experiments on various benchmarks demonstrate the superiority of TFGDA over SOTA methods. © 2024 Neural information processing systems foundation. All rights reserved.

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A Multi-scale Framework for Out-of-Distribution Detection in Dermoscopic Images 1

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4th International Conference on Machine Learning for Cyber Security, ML4CS 2022

作者： Huang, Zhongzheng Wang, Tao Cai, Yuanzheng Liang, Lingyu College of Computer and Data Science Fuzhou University Fuzhou350108 China Fujian Provincial Key Laboratory of Information Processing and Intelligent Control College of Computer and Control Engineering and International Digital Economy College Minjiang University Fuzhou350108 China The Key Laboratory of Cognitive Computing and Intelligent Information Processing of Fujian Education Institutions Wuyi University Wuyishan354300 China Fujian Yilian-Health Nursing Information Technology Co. Ltd. Fuzhou350003 China School of Electronic and Information Engineering South China University of Technology Guangzhou510641 China

ISBN: (数字)9783031200960

ISBN: (纸本)9783031200953

The automatic detection of skin diseases via dermoscopic images can improve the efficiency in diagnosis and help doctors make more accurate judgments. However, conventional skin disease recognition systems may produce high confidence for out-of-distribution (OOD) data, which may become a major security vulnerability in practical applications. In this paper, we propose a multi-scale detection framework to detect out-of-distribution skin disease image data to ensure the robustness of the system. Our framework extracts features from different layers of the neural network. In the early layers, rectified activation is used to make the output features closer to the well-behaved distribution, and then an one-class SVM is trained to detect OOD data;in the penultimate layer, an adapted Gram matrix is used to calculate the features after rectified activation, and finally the layer with the best performance is chosen to compute a normality score. Experiments show that the proposed framework achieves superior performance when compared with other state-of-the-art methods in the task of skin disease recognition. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Chemical activation