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CENTRAL LIMIT THEOREM FOR TEMPORAL AVERAGE OF BACKWARD EULER-MARUYAMA METHOD

Journal of Computational Mathematics 2025年第3期43卷 588-614页

作者： Diancong Jin School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific ComputingHuazhong University of Science and TechnologyWuhan 430074China

This work focuses on the temporal average of the backward Euler-Maruyama(BEM)method,which is used to approximate the ergodic limit of stochastic ordinary differential equations(SODEs).We give the central limit theorem(CLT)of the temporal average of the BEM method,which characterizes its asymptotics in *** the deviation order is smaller than the optimal strong order,we directly derive the CLT of the temporal average through that of original equations and the uniform strong order of the BEM *** the case that the deviation order equals to the optimal strong order,the CLT is established via the Poisson equation associated with the generator of original *** experiments are performed to illustrate the theoretical *** main contribution of this work is to generalize the existing CLT of the temporal average of numerical methods to that for SODEs with super-linearly growing drift coefficients.

关键词： Central limit theorem Temporal average Ergodicity Backward Euler-Maruyama method

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Adapted Runge-Kutta Methods for Nonlinear First-Order Delay BVPs with Time-variable Delay

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Acta Mathematicae Applicatae Sinica 2025年第2期41卷 400-413页

作者： Cheng-jian ZHANG Yang WANG Hao HAN 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 numerical solutions for nonlinear first-order boundary value problems(BVPs) with time-variable delay. For solving this kind of delay BVPs, by combining Runge-Kutta methods with Lagrange interpolation, a class of adapted Runge-Kutta(ARK) methods are developed. Under the suitable conditions, it is proved that ARK methods are convergent of order min{p, μ+ν +1}, where p is the consistency order of ARK methods and μ, ν are two given parameters in Lagrange interpolation. Moreover, a global stability criterion is derived for ARK methods. With some numerical experiments, the computational accuracy and global stability of ARK methods are further testified.

关键词： delay boundary value problems adapted Runge-Kutta method Lagrange interpolation error analysis global stability

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A DECOUPLED,LINEARLY IMPLICIT AND UNCONDITIONALLY ENERGY STABLE SCHEME FOR THE COUPLED CAHN-HILLIARD SYSTEMS

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Journal of Computational Mathematics 2025年第3期43卷 708-730页

作者： Dan Zhao Dongfang Li Yanbin Tang Jinming Wen 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 College of Information Science and Technology Jinan UniversityGuangzhou 510632China

We present a decoupled,linearly implicit numerical scheme with energy stability and mass conservation for solving the coupled Cahn-Hilliard *** time-discretization is done by leap-frog method with the scalar auxiliary variable(SAV)*** only needs to solve three linear equations at each time step,where each unknown variable can be solved *** is shown that the semi-discrete scheme has second-order accuracy in the temporal *** convergence results are proved by a rigorous analysis of the boundedness of the numerical solution and the error estimates at different *** examples are presented to further confirm the validity of the methods.

关键词： Coupled Cahn-Hilliard system Leap-frog method Scalar auxiliary variable Error estimate

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Attribute-Based Access Control Encryption

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IEEE Transactions on Dependable and Secure computing 2025年第3期22卷 2227-2242页

作者： Wang, Xiuhua Yu, Mengyang Wang, Yaohui Pi, Yinjia Xu, Peng Wang, Shuai Jin, Hai Han, Min Huazhong University of Science and Technology Hubei Key Laboratory of Distributed System Security School of Cyber Science and Engineering Wuhan430074 China State Key Laboratory of Cryptology Beijing100878 China Huazhong University of Science and Technology National Engineering Research Center for Big Data Technology and System Services Computing Technology and System Lab Hubei Key Laboratory of Distributed System Security Hubei Engineering Research Center on Big Data Security School of Cyber Science and Engineering Wuhan430074 China University of Electronic Science and Technology of China National Key Laboratory of Wireless Communications Chengdu611731 China Huazhong University of Science and Technology National Engineering Research Center for Big Data Technology and System Services Computing Technology and System Lab Cluster and Grid Computing Lab School of Computer Science and Technology Wuhan430074 China

The burgeoning complexity of communication necessitates a high demand for security. Access control encryption is a promising primitive to meet the security demand but the bulk of its constructions rely on formulating the access control policy with identities. Attribute-based access control policy in attribute-based encryption (ABE) is known to be more expressive without relying on enumerating identities. We propose a generic framework to build attribute-based access control encryption from ciphertext-policy ABE. Our instantiations prioritize different emphases on expressiveness and efficiency. The first instantiation supports multi-valued AND-gate access control structures, while the second supports the linear-secret-sharing access structure. Both are prototyped with efficiency validated empirically. © 2024 IEEE.

关键词： Ciphertext

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ERROR ANALYSIS OF FRACTIONAL COLLOCATION METHODS FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH NONCOMPACT OPERATORS

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Journal of Computational Mathematics 2025年第3期43卷 690-707页

作者： Zheng Ma Chengming Huang Anatoly A.Alikhanov 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 North-Caucasus Center for Mathematical Research North-Caucasus Federal UniversityStavropol 355017Russia North-Eastern Federal University Yakutsk 677000Russia

This paper is concerned with the numerical solution of Volterra integro-differential equations with noncompact *** focus is on the problems with weakly singular *** handle the initial weak singularity of the solution,a fractional collocation method is applied.A rigorous hp-version error analysis of the numerical method under a weighted H1-norm is carried *** result shows that the method can achieve high order convergence for such *** experiments are also presented to confirm the effectiveness of the proposed method.

关键词： Volterra integro-differential equation Noncompact operator Nonsmooth solution Collocation method Fractional polynomial hp-version error analysis

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A HIGH ORDER SCHEME FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH THE CAPUTO-HADAMARD DERIVATIVE

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Journal of Computational Mathematics 2025年第3期43卷 615-640页

作者： Xingyang Ye Junying Cao Chuanju Xu School of Science Jimei UniversityXiamen 361021China School of Data Science and Information Engineering Guizhou Minzu UniversityGuiyang 550025China School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing Xiamen UniversityXiamen 361005China

In this paper,we consider numerical solutions of the fractional diffusion equation with theαorder time fractional derivative defined in the Caputo-Hadamard sense.A high order time-stepping scheme is constructed,analyzed,and numerically *** contribution of the paper is twofold:1)regularity of the solution to the underlying equation is investigated,2)a rigorous stability and convergence analysis for the proposed scheme is performed,which shows that the proposed scheme is 3+αorder *** numerical examples are provided to verify the theoretical statement.

关键词： Caputo-Hadamard derivative Fractional differential equations High order scheme Stability and convergence analysis

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Network Intrusion Detection for Modern Smart Grids Based on Adaptive Online Incremental Learning

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IEEE Transactions on Smart Grid 2025年第3期16卷 2541-2553页

作者： Lu, Qiuyu An, Kexin Li, Jun'e Wang, Jin Wuhan University Key Laboratory of Aerospace Information Security and Trusted Computing Ministry of Education School of Cyber Science and Engineering Wuhan430072 China State Grid Hubei Electric Power Research Institute Energy Internet Research Center Wuhan430072 China

New and evolving cyber attacks against smart grids are emerging. This necessitates that the network intrusion detection systems (IDSs) have online learning ability. However, most existing methods struggle to handle new and evolving attacks while retaining old attack knowledge, and many of them employ deep models requiring long update periods. Therefore, we propose an IDS based on adaptive online incremental learning (AdaOIL-IDS). 1) A class-correlated broad learning system (CC-BLS) is proposed for intrusion detection. A weighted CC-factor derived from intra- and inter-class correlations is introduced in CC-BLS to improve classification accuracy. CC incremental learnings are designed to quickly add new inputs and additional nodes without retraining. The CC-factor for new inputs is adjusted based on correlations of new and old classes, which enables simultaneous adaptation to new attacks and new observations of old attacks while retaining more old knowledge. 2) An adaptive learning framework is proposed for online offline combined learning of models. Online learning and offline retraining are adaptive switched based on the real-time loss to achieve efficient lifelong learning. Experiment results show that CC-BLS has better performance than selected state-of-the-art incremental broad and deep models, and the proposed adaptive learning framework behaviors better effectiveness and efficiency than selected existing frameworks. © 2010-2012 IEEE.

关键词： Network intrusion

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Adaptive Early Warning Method of Cascading Failures Caused by Coordinated Cyber-Attacks

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CSEE Journal of Power and Energy Systems 2025年第1期11卷 406-423页

作者： Yufei Wang June Li Jian Qiu Yangrong Chen Key Laboratory of Aerospace Information Security and Trusted Computing Ministry of EducationSchool of Cyber Science and EngineeringWuhan UniversityWuhan Hubei430072China China Electric Power Research Institute Beijing102209China Electric Power Planning&Engineering Institute Beijing 100120China

In order to accurately receive early warning of the cascading failures caused by coordinated cyber-attacks(CFCC)in grid cyber-physical systems(GCPS),an adaptive early warning method of CFCC is ***,the evolutionary mechanism of CFCC is analyzed from the attackers'view,the CFCC mathematical model is established,and the transition processes of GCPS running states under the influence of CFCC staged failures are ***,the mathematical model of the adaptive early warning method is ***,the mathematical model of the adaptive early warning method is mapped as an adaptive control process with tolerating staged failures damage,and the solving process is presented to infer the CFCC and its next evolution trend.A decision-making idea for the optimal active defense scheme is proposed considering the costs and gains of various defense ***,to verify the effectiveness of the adaptive early warning method,the warning and defense processes of a typical CFCC are simulated in a GCPS experimental system based on CEPRI-36 BUS.

关键词： Adaptive control theory cascading failures coordinated cyber-attacks early warning grid cyber-physical systems

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A multi-strategy enhanced moth-flame optimization algorithm for complex inverse kinematics problems in series robots

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Cluster computing 2025年第5期28卷 1-37页

作者： Liu, Jianlin Huang, Haisong Fan, Qingsong Ma, Chi Key Laboratory of Advanced Manufacturing Technology Ministry of Education Guizhou University Guizhou Guiyang550025 China Guizhou Equipment Manufacturing Digital Workshop Modeling and Simulation Engineering Research Center Guizhou Guiyang550025 China State Key Laboratory of Intelligent Manufacturing Equipment and Technology Huazhong University of Science and Technology Wuhan430074 China School of Institute of Automotive Engineers Hubei University of Automotive Technology Shiyan442002 China

In this study of optimizing the dynamic characteristics of the manipulator, with the increase of motion redundancy, the complexity of solving the inverse motion problem increases significantly, making it extremely challenging to develop a general analytical solution algorithm. To address this challenge, this paper introduces a multi-strategy enhanced moth-flame optimization algorithm, DMFO. Firstly, the uneven initialization of MFO limits its comprehensive initial search capability and leads to slow convergence speed. Consequently, it lacks competitiveness in specific engineering problems. The mutation chaos strategy, quantum evolution strategy and precise elimination strategy are used to improve the formation of DMFO. Secondly, DMFO and eight meta-heuristic algorithms (GA, PSO, ABC, MFO, DE, WO, BKA, COA) are tested on CEC2017, demonstrating its superior local and global exploitation and exploration capabilities. Then these kinematics models of 4,6,7-DOF manipulators is established based on DH method, and the objective function is derived from the forward motion equation. The effectiveness of DMFO in solving the inverse kinematics of robot arms is validated through its application. Finally, the engineering verification is carried out on the manipulator UR16e, which highlights the success of DMFO in addressing the inverse motion problem of multi-DOF serial robots. © The Author(s), under exclusive licence to Springer science+Business Media, LLC, part of Springer Nature 2024.

关键词： Inverse kinematics

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On the deterioration of convergence rate of spectral differentiations for functions with singularities

arXiv

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arXiv 2025年

作者： Wang, Haiyong School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

Spectral differentiations are basic ingredients of spectral methods. In this work, we analyze the pointwise rate of convergence of spectral differentiations for functions containing singularities and show that the deteriorations of the convergence rate at the endpoints, singularities and other points in the smooth region exhibit different patterns. As the order of differentiation increases by one, we show for functions with an algebraic singularity that the convergence rate of spectral differentiation by Jacobi projection deteriorates two orders at both endpoints and only one order at each point in the smooth region. The situation at the singularity is more complicated and the convergence rate either deteriorates two orders or does not deteriorate, depending on the parity of the order of differentiation, when the singularity locates in the interior of the interval and deteriorates two orders when the singularity locates at the endpoint. Extensions to some related problems, such as the spectral differentiation using Chebyshev interpolation, are also discussed. Our findings justify the error localization property of Jacobi approximation and differentiation and provide some new insight into the convergence behavior of Jacobi spectral *** Codes 65D25, 41A10, 41A25 Copyright © 2025, The Authors. All rights reserved.

关键词： Chebyshev approximation

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