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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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Adaptive cyclic gradient methods with interpolation

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Computational Optimization and Applications 2025年 1-25页

作者： Xie, Yixin Sun, Cong Yuan, Ya-Xiang Beijing100876 China Ministry of Education Beijing100876 China State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China

Gradient method is an important method for solving large scale problems. In this paper, a new gradient method framework for unconstrained optimization problem is proposed, where the stepsize is updated in a cyclic way. The Cauchy step is approximated by the quadratic interpolation. And the cycle for stepsize update is adjusted adaptively. Combining with the adaptive nonmonotone line search technique, we prove the global convergence of the proposed method. Furthermore, its sublinear convergence rate for convex problems and R-linear convergence rate for problems with quadratic functional growth property are analyzed. Numerical results show that our proposed algorithm enjoys good performances in terms of both computational cost and obtained function values. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

关键词： Interpolation

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On greedy randomized coordinate updating iteration methods for solving symmetric eigenvalue problems

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Applied Numerical Mathematics 2025年 216卷 76-97页

作者： Bai, Zhong-Zhi State Key Laboratory of Mathematical Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences P.O. Box 2719 Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In order to compute the smallest eigenvalue and its corresponding eigenvector of a large-scale, real, and symmetric matrix, we propose a class of greedy randomized coordinate updating iteration methods based on the principle that the indices of larger entries in absolute value of the current residual are selected with a higher probability and, with respect to this index set, the next iterate is updated from the current iterate along with the selected coordinate such that the corresponding entry of the residual is annihilated, resulting in fast convergence rates of the proposed iteration methods. Under appropriate conditions, we prove the convergence of both sequences of the Rayleigh-quotients and the acute angles between the iterates and the eigenvector in terms of the expectation. By numerical experiments, we show that this class of greedy randomized coordinate updating iteration methods are advantageous over the parameterized power method and the coordinate descent method in both iteration counts and computing times. Moreover, with theoretical analysis and computational performance, we confirm that the convergence property of this class of iteration methods can be improved significantly by suitably choosing the arbitrary nonnegative parameter involved in the greedy probability criterion. © 2025 IMACS

关键词： Eigenvalues and eigenfunctions

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Pre-trained Semantic Interaction based Inductive Graph Neural Networks for Text Classification 31

Pre-trained Semantic Interaction based Inductive Graph Neura...

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31st International Conference on Computational Linguistics, COLING 2025

作者： Wang, Shiyu Zhou, Gang Lu, Jicang Chen, Jing Huang, Ningbo State Key Laboratory of Mathematical Engineering and Advanced Computing China

ISBN: (纸本)9798891761964

Nowadays, research of Text Classification (TC) based on graph neural networks (GNNs) is on the rise. Both inductive methods and transductive methods have made significant progress. For transductive methods, the semantic interaction between texts plays a crucial role in the learning of effective text representations. However, it is difficult to perform inductive learning while modeling interactions between texts on the graph. To give a universal solution, we propose the graph neural network based on pre-trained semantic interaction called PaSIG. Firstly, we construct a text-word heterogeneity graph and design an asymmetric structure to ensure one-way message passing from words to the test texts. Meanwhile, we use the context representation capability of the pre-trained language model to construct node features that contain classification semantic information. Afterward, we explore the adaptative aggregation methods with a gated fusion mechanism. Extensive experiments on five datasets have shown the effectiveness of PaSIG, with the accuracy exceeding the baseline by 2.7% on average. While achieving state-of-the-art performance, we have also taken measures of subgraph sampling and intermediate state preservation to achieve fast inference. © 2025 Association for Computational Linguistics.

关键词： Graph neural networks

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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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High-temperature optoelectronic synaptic devices based on 4H-SiC

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Science China(Information Sciences) 2025年第4期68卷 151-159页

作者： Mingxuan BU Yue WANG Zhenyi NI Dongke LI Deren YANG Xiaodong PI State Key Laboratory of Silicon and Advanced Semiconductor Materials & School of Materials Science and Engineering Zhejiang University Institute of Advanced Semiconductors & Zhejiang Provincial Key Laboratory of Power Semiconductor Materials and Devices ZJU-Hangzhou Global Scientific and Technological Innovation Center Zhejiang University

Optoelectronic synaptic devices operating at high temperatures have application potential across many important fields, including the aerospace and defense industries. However, limited research exists on such devices. Herein, we fabricate4H-SiC-based high-temperature optoelectronic synaptic devices that are capable of achieving diverse synaptic functionalities at temperatures as high as 600 K. The synaptic functionalities are realized for these devices through carrier capture and release of the deep-level defects introduced via electronic irradiation. A 3 × 3 array of high-temperature optoelectronic synaptic devices enables the image memory functions. A neural network model constructed using this array addresses the issue of color quantization. The optoelectronic synaptic devices thus developed are capable of high-temperature applications.

关键词： optoelectronic synaptic devices 4H-SiC synaptic plasticity neuromorphic computing high-temperature devices

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A Short Review on Polyethylene-based Ionomers: Synthesis, Structure, and Applications

Chem and Bio Engineering

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Chem and Bio engineering 2025年第3期2卷 156-170页

作者： Jia, Tinghao Wang, Ruijia Zhang, Mengen Ren, Congjing Yang, Yao Wang, Jingdai Yang, Yongrong College of Chemical and Biological Engineering State Key Laboratory of Chemical Engineering Zhejiang University Hangzhou310027 China ZJU-Hangzhou Global Scientific and Technological Innovation Center Zhejiang University Hangzhou311200 China State Key Laboratory of Chemical Engineering College of Chemical and Biological Zhejiang University Hangzhou310027 China

Polyethylene-based ionomers (PE ionomers) are polymers featuring polyethylene as the main chain structure with a small fraction of ionic functional groups pendant to the polyethylene backbone. Due to this combination of nonpolar covalent skeletons and polar ionic groups, PE ionomers can exhibit various properties, depending on their specific composition and structure, such as clarity, adhesivity, abrasiveness, enhanced mechanical strength, shape memory, and healable capabilities. These extraordinary properties have led to the broad applications of PE ionomers in the past decades for cosmetics packaging, coatings, blends, ion-exchange membranes, high voltage insulation materials, and adhesives and even hold great potential in the emerging fields of shape memory and healable smart materials. This review provides an in-depth overview of the latest progress in the field of PE ionomers, with a particular focus on diverse synthetic methods and structural models, as well as important related applications. The structure-property relationship is also discussed interstitially, providing ideas for the subsequent development of PE ionomers with novel structures and fresh applications. © 2024 The Authors. Co-published by Zhejiang University and American Chemical Society.

关键词： Adhesives

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A model LayerDFN for characterizing the inherent anisotropic rocks with large-scale and dense joints

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Journal of Rock Mechanics and Geotechnical engineering 2025年第3期17卷 1569-1584页

作者： Gang Han Shuling Huang Chuanqing Zhang Xiuli Ding Yuting Zhang Yang Gao Jun He Key Laboratory of Geotechnical Mechanics and Engineering of the Ministry of Water Resources Changjiang River Scientific Research InstituteWuhan430010China State Key Laboratory of Geomechanics and Geotechnical Engineering Institute of Rock and Soil MechanicsChinese Academy of SciencesWuhan430071China University of Chinese Academy of Sciences Beijing101408China

Large-scale and heavily jointed rocks have inherent planes of anisotropy and secondary structural planes,such as dominant joint sets and random fractures,which result in significant differences in their failure mechanism and deformation behavior compared to other rock *** address this issue,inherent anisotropic rocks with large-scale and dense joints are considered to be composed of the rock matrix,inherent planes of anisotropy,and secondary structural *** a new implicit continuum model called LayerDFN is developed based on the crack tensor and damage tensor theories to characterize the mechanical properties of inherent anisotropic ***,the LayerDFN model is implemented in the FLAC3D software,and a series of numerical results for typical example problems is compared with those obtained from the 3DEC,the analytical solutions,similar classical models,laboratory uniaxial compression tests,and field rigid bearing plate *** results demonstrate that the LayerDFN model can effectively capture the anisotropic mechanical properties of inherent anisotropic rocks,and can quantitatively characterize the damaging effect of the secondary structural ***,the numerical method based on the LayerDFN model provides a comprehensive and reliable approach for describing and analyzing the behavior of inherent anisotropic rocks,which will provide valuable insights for engineering design and decision-making processes.

关键词： Inherent anisotropic rocks Secondary structural planes Constitutive model Crack tensor Damage tensor

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Research on Intrusion Tolerance System Based on Behavioral Baseline and Defense-in-Depth Architecture

Research on Intrusion Tolerance System Based on Behavioral B...

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2024 International Conference on Mechatronics and Intelligent Control, ICMIC 2024

作者： Meng, Qi Wang, Xuemeng Yang, Kai Meng, Long Wang, Jiancheng Fei, Jinlong State Key Laboratory of Mathematical Engineering and Advanced Computing PLA Strategic Support Force Information Engineering University Zhengzhou China

ISBN: (数字)9781510686847

ISBN: (纸本)9781510686830

Tolerance technology is the third-generation network security technology commonly used in the world. It is derived from the category of information survival and endogenous security technology. A scholar from Carnegie Mellon University gave this survival technology a definition: the so-called "invasion survival technology".It is the ability of the system to perform its own tasks within a limited time when external attacks, failures and accidents have occurred. It assumes that we cannot detect intrusions to the system completely and correctly. When external intrusions or failures occur suddenly, we can use tolerance technology to solve the problem of survival of the system to ensure the confidentiality, integrity, and integrity of the information system. reliability and non-repudiation. In the current Internet security incidents, countless experiences and lessons tell us that it is not enough to rely on blocking and defensing for network *** on the existing network defense-in-depth architecture and the common behavior and parameter baselines of current emergency response systems, this paper designs an intrusion-tolerant system based on the behavioral baseline and network-in-depth architecture, which realizes intrusion tolerance and malicious behavior blocking under high confrontation intensity. To adapt to the maximum recovery and necessary tolerance under the attack technology of international APT organizations, and to protect the integrity and availability of the system to the greatest extent. © 2025 SPIE.

关键词： Network intrusion

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Social Media User Geolocation Based on Large Language Models 2nd

Social Media User Geolocation Based on Large Language Model...

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2nd International Conference on Data Security and Privacy Protection, DSPP 2024

作者： Zhang, Meng Luo, Xiangyang Huang, Ningbo Key Laboratory of Cyberspace Situation Awareness of Henan Province Henan Zhengzhou China State Key Laboratory of Mathematical Engineering and Advanced Computing Henan Zhengzhou China

ISBN: (纸本)9789819785391

In the digital age, social media platforms have amassed a wealth of user-generated content, which contains valuable geographic information. However, the irregularities and noise in user-generated text, have led to suboptimal performance in traditional text-based user geolocation methods. We propose a unsupervised framework for user geolocation based on Large Language Models (LLMs), which utilizes the LLMs’ powerful text processing abilities to geolocate users based on user-generated text unsupervisedly. Firstly, preprocess the text using regularization rules and LLM to denoise and normalize user-generated text, thus enhancing data quality. Subsequently, appropriate prompts are designed to guide the knowledgeable LLM in understanding the user text’s geolocating mechanism, thereby profiling users. To refine user geolocation accuracy, five independent positioning iterations are conducted, with the most frequent occurrence identified as the final user location. Through a series of experiments, we have demonstrated the potential of utilizing large language models for processing noisy text and the effectiveness of geolocating users in an unsupervised setting. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： Large language model Social media Unsupervised user geolocation User-generated text

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