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REGULARITY THEORY AND NUMERICAL ALGORITHM FOR THE TIME-FRACTIONAL KLEIN-KRAMERS EQUATION

Journal of Computational mathematics 2025年第2期43卷 257-279页

作者： Jing Sun Daxin Nie Weihua Deng School of Mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex SystemsLanzhou UniversityLanzhou 730000China

Fractional Klein-Kramers equation can well describe subdiffusion in phase *** this paper,we develop the fully discrete scheme for time-fractional Klein-Kramers equation based on the backward Euler convolution quadrature and local discontinuous Galerkin *** to the obtained sharp regularity estimates in temporal and spatial directions after overcoming the hypocoercivity of the operator,the complete error analyses of the fully discrete scheme are *** is worth mentioning that the convergence of the provided scheme is independent of the temporal regularity of the exact ***,numerical results are proposed to verify the correctness of the theoretical results.

关键词： Time-fractional Klein-Kramers equation Regularity estimate Convolution quadrature Local discontinuous Galerkin method Error analysis

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Practical approach for detecting k-nonseparability of multipartite quantum states

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Science China(Physics,Mechanics & Astronomy) 2025年第1期68卷 28-44页

作者： Jie Guo Jinchuan Hou Xiaofei Qi Kan He College of Mathematics Taiyuan University of TechnologyTaiyuan 030006China School of Mathematics and Statistics Shanxi UniversityTaiyuan 030006China Key Laboratory of Complex Systems and Data Science of Ministry of Education Shanxi UniversityTaiyuan 030006China

The instantaneous detection of entanglement in quantum states poses a significant challenge in the fields of quantum computation and quantum information,and there are no practical methods or tools to complete this task satisfactorily so *** propose a sufficient and necessary criterion of k-nonseparability for any n-partite finite or infinite dimensional systems,2≤k≤*** criterion serves as the foundation for a practical scheme designed to detect entanglement and k-nonseparability across multipar-tite finite-dimensional *** exemplify the application of our scheme,we have developed a software tool that facilitates swift and precise identification of entanglement,k-nonseparability,and genuine entanglement within n-qubit systems,specifically tailored for systems with 2≤n≤4.

关键词： multipartite systems entanglement states entanglement witnesses k-nonseparability

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Aggregated Bisimulation and Identification of Finite-Valued Networks

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IEEE Transactions on Automatic Control 2025年第5期70卷 3346-3353页

作者： Ji, Zhengping Zhang, Xiao Cheng, Daizhan University of Chinese Academy of Sciences Key Laboratory of Systems and Control Academy of Mathematics and Systems Science School of Mathematical Sciences Beijing100190 China Hong Kong Polytechnic University Department of Applied Mathematics SAR 999077 Hong Kong Academy of Mathematics and Systems Science Chinese Academy of Sciences Key Laboratory of Systems and Control Beijing100190 China

We propose a method that combines aggregation and bisimulation to approximate large finite-valued networks by smaller models. With the algebraic state-space representation of a quotient system under observational equivalence, the aggregated bisimulation is performed by partitioning a network into blocks and replacing the dynamics of each block by that of its quotient system. If the aggregation is not a bisimulation, these quotient systems can be further replaced by probabilistic networks based on the relative frequency of transitions, which contain full information about the input–output dynamics. As an inverse problem of aggregation, simulated identification of finite-valued networks is studied. We give an upper bound on the minimal number of nodes required to identify a system, and design an online algorithm to reproduce the internal state dynamics from given input–output sequences. The results are illustrated with numerical examples. © 1963-2012 IEEE.

关键词： Inverse problems

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Toward Analytical Homogenized Relaxation Modulus for Fibrous Composite Material with Reduced Order Homogenization Method

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Computers, Materials & Continua 2025年第1期82卷 193-222页

作者： Huilin Jia Shanqiao Huang Zifeng Yuan HEDPS Center for Applied Physics and Technology(CAPT)Department of Mechanics and Engineering SciencePeking UniversityBeijing100871China State Key Laboratory for Turbulence and Complex Systems Peking UniversityBeijing100871China

In this manuscript,we propose an analytical equivalent linear viscoelastic constitutive model for fiber-reinforced composites,bypassing general computational *** method is based on the reduced-order homogenization(ROH)*** ROH method typically involves solving multiple finite element problems under periodic conditions to evaluate elastic strain and eigenstrain influence functions in an‘off-line’stage,which offers substantial cost savings compared to direct computational homogenization *** to the unique structure of the fibrous unit cell,“off-line”stage calculation can be eliminated by influence functions obtained *** the standard solid model to the ROH method enables the creation of a comprehensive analytical homogeneous viscoelastic constitutive *** method treats fibrous composite materials as homogeneous,anisotropic viscoelastic materials,significantly reducing computational time due to its analytical *** approach also enables precise determination of a homogenized anisotropic relaxation modulus and accurate capture of various viscoelastic responses under different loading *** sets of numerical examples,including unit cell tests,three-point beam bending tests,and torsion tests,are given to demonstrate the predictive performance of the homogenized viscoelastic ***,the model is validated against experimental measurements,confirming its accuracy and reliability.

关键词： Homogenized relaxation modulus viscoelastic standard solid model reduced order homogenization fibrous composite material

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Combine deep learning and Bayesian analysis to separate overlapping gravitational wave signals

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Science China(Physics,Mechanics & Astronomy) 2025年第5期68卷 205-219页

作者： Cunliang Ma Weiguang Zhou Zhoujian Cao Mingzhen Jia Jiangxi Provincial Key Laboratory of Multidimensional Intelligent Perception and Control Jiangxi University of Science and TechnologyGanzhou 341000China Institute of Applied Mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Fundamental Physics and Mathematical Sciences Hangzhou Institute for Advanced StudyUCASHangzhou 310024China

Future gravitational wave(GW)observatories,such as the Einstein Telescope,are anticipated to encounter overlapping GW signals,presenting considerable obstacles to GW data processing techniques,including signal identification and parameter *** this letter,we propose a scheme of combining deep learning and Bayesian analysis to disentangle overlapping GW *** deep learning part takes a data-driven approach that employs an encoder-separation-decoder framework which is powerful enough to extract the shape of the signal even when the GW signals completely *** Bayesian analysis part takes the matched filtering technique to extract the amplitude of the GW *** scheme can facilitate the utilization of existing GW detection and parameter estimation methods for future instances of overlapping *** methodology effectively reduces biases in parameter estimation when handling multiple intertwined ***,this marks the first known instance where deep learning has been successfully utilized to disentangle overlapping GW signals.

关键词： gravitational wave separation machine learning Einstein Telescope parameter estimation

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Stochastic SIRS models on networks: mean and variance of infection

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Infectious Disease Modelling 2025年第3期10卷 875-896页

作者： Chen, Tingting Liu, Guirong Jin, Zhen School of Mathematics and Statistics Shanxi University Shanxi Taiyuan 030006 China Complex Systems Research Center Shanxi University Shanxi Taiyuan 030006 China Key Laboratory of Complex Systems and Data Science of Ministry of Education Shanxi University Shanxi Taiyuan 030006 China

Due to the heterogeneity of contact structure, it is more reasonable to model on networks for epidemics. Because of the stochastic nature of events and the discrete number of individuals, the spread of epidemics is more appropriately viewed as a Markov chain. Therefore, we establish stochastic SIRS models with vaccination on networks to study the mean and variance of the number of susceptible and infected individuals for large-scale populations. Using van Kampen's system-size expansion, we derive a high-dimensional deterministic system which describes the mean behaviour and a Fokker-Planck equation which characterizes the variance around deterministic trajectories. Utilizing the qualitative analysis technique and Lyapunov function, we demonstrate that the disease-free equilibrium of the deterministic system is globally asymptotically stable if the basic reproduction number R₀ < 1;and the endemic equilibrium is globally asymptotically stable if R₀ > 1. Through the analysis of the Fokker-Planck equation, we obtain the asymptotic expression for the variance of the number of susceptible and infected individuals around the endemic equilibrium, which can be approximated by the elements of principal diagonal of the solution of the corresponding Lyapunov equation. Here, the solution of Lyapunov equation is expressed by vectorization operator of matrices and Kronecker product. Finally, numerical simulations illustrate that vaccination can reduce infections and increase fluctuations of the number of infected individuals and show that individuals with greater degree are more easily infected. © 2025 The Authors

关键词： Fokker-Planck equation Networks Stochastic SIRS models Van Kampen's system-size expansion Variance

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Modeling telomere shortening process

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Quantitative Biology 2025年第1期13卷 77-87页

作者： Panpan Han Yang Zhou Weihua Deng School of Mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex SystemsLanzhou UniversityLanzhouChina

Cell senescence has attracted much attention in the long history of human beings,and telomere shortening(TS)is one of the main concerns in the study of cell *** reveal the microscopic mechanism of TS process,we model it based on molecular stochastic process from the perspective of nonequilibrium statistical *** associate the TS process with the continuous time random walk and derive the Fokker–Planck equation to describe the length distribution of the *** further modify the model describing the TS process,similar to the anomalous tempered diffusion,and derive the Feynman–Kac equation characterizing the functional distribution of the TS ***,we study the statistics related to the critical telomere length l_(c),including the occupation time and first passage *** two kinds of statistics help us understand the time scale of cell senescence.

关键词： aging anomalous diffusion CTRW telomere shortening process

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Prediction and optimization for a threaded reusable spacecraft separation device

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Acta Astronautica 2025年 234卷 337-351页

作者： Shi, Tengfei Li, Xiangyu Liu, Caishan Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province School of Mechanics and Aerospace Engineering Southwest Jiaotong University Chengdu610031 China State Key Laboratory for Turbulence and Complex Systems College of Engineering Peking University Beijing100871 China

Accurately predicting and optimizing the performance of spacecraft separation is crucial for enhancing their reliability and applicability in space missions. However, the complex factors involved in separation processes, such as nonlinear contact and nonsmooth impact, present significant challenges to prediction and optimization. Therefore, this paper aims to develop a comprehensive prediction and optimization framework for a threaded separation device using learning techniques based on simulation dataset from an efficient dynamics model. The prediction work includes a classification model with over 99% accuracy for separation status using support vector machines, as well as a regression model with root mean square errors of less than 2% for separation responses using deep neural networks. The optimization of separation design is achieved through differential evolution, wherein the fast-learning prediction model is used as an iterative model to significantly enhance optimization speed. Based on these comprehensive models, systematic studies on separation status classification and response evaluation under various physical parameters demonstrate strong consistency with the dynamics model, but with significantly reduced computational time. Comprehensive optimization investigations for separation performance under different weight combinations were also conducted to provide guidelines for device design. These works not only offer valuable insights for the design of separation devices but also introduce new approaches for the prediction and optimization of other complex mechanical systems. © 2025

关键词： Deep neural networks

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Learning Causal Representations Based on a GAE Embedded Autoencoder

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IEEE Transactions on Knowledge and Data Engineering 2025年第6期37卷 3472-3484页

作者： Zhou, Kuang Jiang, Ming Gabrys, Bogdan Xu, Yong Northwestern Polytechnical University School of Mathematics and Statistics Xi'an710060 China Northwestern Polytechnical University Moe Key Laboratory for Complexity Science in Aerospace Xi'an710060 China University of Technology Sydney Complex Adaptive Systems Lab UltimoNSW2007 Australia

Traditional machine-learning approaches face limitations when confronted with insufficient data. Transfer learning addresses this by leveraging knowledge from closely related domains. The key in transfer learning is to find a transferable feature representation to enhance cross-domain classification models. However, in some scenarios, some features correlated with samples in the source domain may not be relevant to those in the target. Causal inference enables us to uncover the underlying patterns and mechanisms within the data, mitigating the impact of confounding factors. Nevertheless, most existing causal inference algorithms have limitations when applied to high-dimensional datasets with nonlinear causal relationships. In this work, a new causal representation method based on a Graph autoencoder embedded AutoEncoder, named GeAE, is introduced to learn invariant representations across domains. The proposed approach employs a causal structure learning module, similar to a graph autoencoder, to account for nonlinear causal relationships present in the data. Moreover, the cross-entropy loss as well as the causal structure learning loss and the reconstruction loss are incorporated in the objective function designed in a united autoencoder. This method allows for the handling of high-dimensional data and can provide effective representations for cross-domain classification tasks. Experimental results on generated and real-world datasets demonstrate the effectiveness of GeAE compared with the state-of-the-art methods. © 1989-2012 IEEE.

关键词： Contrastive Learning

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Invariant and Dual-Invariant Subspaces of k-Valued Networks

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Journal of systems Science & complexity 2025年第2期38卷 547-572页

作者： CHENG Daizhan QI Hongsheng ZHANG Xiao JI Zhengping Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Research Center of Semi-Tensor Product of Matrices:Theory and Applications Department of Applied Mathematics Hong Kong Polytechnic University School of Mathematical Sciences University of Chinese Academy of Sciences

For k-valued(control) networks, two types of(control) invariant subspaces are proposed,namely, the state-invariant and dual-invariant subspaces, which are subspaces of the state space and dual space, respectively. Algorithms are presented to check whether a dual subspace is dual-(control)invariant, and to construct state feedback controls. The bearing space of k-valued(control) networks is introduced. Using the structure of the bearing space, the universal invariant subspace is presented,which is independent of the dynamics of particular networks. Finally, the relation between the stateinvariant subspaces and the dual-invariant subspaces of a network is investigated. A duality property shows that if a dual subspace is invariant, then its perpendicular state subspace is also invariant, and vice versa.

关键词： Bearing spaces finite lattices finite rings invariant subspace k-valued (control) networks

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