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Stochastic SIRS models on networks: mean and variance of infection

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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Knowledge As Not Only Justified True Beliefs in Vision

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IEEE/CAA Journal of Automatica Sinica 2025年第2期12卷 297-299页

作者： Wenbo Zheng Fei-Yue Wang IEEE School of Computer Science and Artificial Intelligence Wuhan University of Technology Sanya Science and Education Innovation Park of Wuhan University of Technology the State Key Laboratory for Management and Control of Complex Systems Institute of Automation Chinese Academy of Sciences

COMPUTATIONAL knowledge vision [1] is emphasized as a novel perspective or field in this paper. It first proposes the visual hierarchy and its connection to knowledge, stating that knowledge is a justified true belief. To further the previous research, we concisely summarize our recent works and suggest a new direction that knowledge is also a thought framework in vision.

关键词： Computational modeling Visualization Artificial intelligence data models Visual perception Visual databases Training data

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From Plant Modeling to Narrative science:Growing and Enjoying Scientific Fruits Naturally and Humanistically

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IEEE/CAA Journal of Automatica Sinica 2024年第12期11卷 2522-2524页

作者： Fei-Yue Wang IEEE Macao University of Science and Technology Macao 999078China the State Key Laboratory for Management and Control of Complex Systems Chinese Academy of SciencesBeijing 100190China

Dear Editor,Modeling is the first and essential step for control and automation,and large models,from current Chat GPT or large language models(LLMs)to future large knowledge models of knowledge automation,would be th... 详细信息

关键词： smart knowledge automation

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Dynamic properties of mode Ⅰ and mode Ⅱ fractures of shale under impact loading

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Journal of Rock Mechanics and Geotechnical Engineering 2025年第2期17卷 1053-1067页

作者： Zelin Yan Linjuan Wang Jidong Jin Jianxiang Wang State Key Laboratory for Turbulence and Complex Systems Department of Mechanics and Engineering ScienceCollege of EngineeringPeking UniversityBeijing100871China School of Astronautics Beihang UniversityBeijing100191China

Controllable shock wave fracturing is an innovative engineering technique used for shale reservoir fracturing and *** the anisotropic fracture mechanism of shale under impact loading is vital for optimizing shock wave fracturing equipment and enhancing shale oil *** this study,using the well-known notched semi-circular bend(NSCB)sample and the novel double-edge notched flattened Brazilian disc(DNFBD)sample combined with a split Hopkinson pressure bar(SHPB),various dynamic anisotropic fracture properties of Lushan shale,including failure characteristics,fracture toughness,energy dissipation and crack propagation velocity,are comprehensively compared and discussed under mode Ⅰ and mode Ⅱ fracture ***,using a newly modified fracture criterion considering the strength anisotropy of shale,the DNFBD specimen is predicted to be a robust method for true mode Ⅱ fracture of anisotropic shale *** experimental results show that the dynamic mode Ⅱ fracture of shale induces a rougher and more complex fracture morphology and performs a higher fracture toughness or fracture energy compared to dynamic mode Ⅰ *** minimal fracture toughness or fracture energy occurs in the Short-transverse orientation,while the maximal ones occur in the Divider *** addition,it is interesting to find that the mode Ⅱ fracture toughness anisotropy index decreases more slowly than that in the mode Ⅰ fracture *** results provide significant insights for understanding the different dynamic fracture mechanisms of anisotropic shale rocks under impact loading and have some beneficial implications for the controllable shock wave fracturing technique.

关键词： Shale Controllable shock wave fracturing Dynamic fracture property Fracture toughness anisotropy Loading rate effect

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A zeroth-order algorithm for distributed optimization with stochastic stripe observations

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science China(Information sciences) 2023年第9期66卷 297-298页

作者： Yinghui WANG Xianlin ZENG Wenxiao ZHAO Yiguang HONG School of Automation and Electrical Engineering University of Science and Technology Beijing Key Laboratory of Intelligent Control and Decision of Complex Systems School of Automation Beijing Institute of Technology Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Department of Control Science and Engineering Tongji University

Recent years have seen a rising interest in distributed optimization problems because of their widespread applications in power grids, multi-robot control, and regression *** the last few decades, many distributed algorithms have been developed for tackling distributed optimization problems. In these algorithms, agents over the network only have access to their own local functions and exchange information with their neighbors.

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Analysis of the SEIR mean-field model in dynamic networks under intervention

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Infectious Disease Modelling 2025年第3期10卷 850-874页

作者： Li, Jiangmin Jin, Zhen Tang, Ming Complex System 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 Shanxi Key Laboratory for Mathematical Technology in Complex Systems Shanxi University Shanxi Taiyuan 030006 China School of Physics and Electronic Science East China Normal University Shanghai 200241 China Shanghai Key Laboratory of Multidimensional Information Processing East China Normal University Shanghai 200241 China

For emerging respiratory infectious diseases like COVID-19, non-pharmaceutical interventions such as isolation are crucial for controlling the spread. From the perspective of network transmission, non-pharmaceutical interventions like isolation alter the degree distribution and other topological structures of the network, thereby controlling the spread of the infectious disease. In this paper, we establish a SEIR mean-field propagation dynamics model for the synchronous evolution of dynamic networks caused by propagation and tracing isolation. We employ the reducing-dimension method to convert the mean-field model in networks into an equivalent and simpler low-dimension model, and then calculate the exact expression of the final size. In addition, we get the differential equations of the degree distribution over time in dynamic networks under tracing isolation and the relationships between the first and second moment of the dynamic network. While the degree of a node remains constant regardless of its state in many previous studies, this paper takes into account that the degree of each node changes over time whatever its state under the disease spread and intervention measures. © 2025 The Authors

关键词： Degree distribution Dynamic network The final size Tracing isolation

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A brief review of preparation and applications of monolithic aerogels in atmospheric environmental purification

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Journal of Environmental sciences 2025年第3期149卷 209-220页

作者： Linfeng Nie Shuangde Li Mengjie Cao Ning Han Yunfa Chen State Key Laboratory of Multiphase Complex Systems Institute of Process EngineeringChinese Academy of SciencesBeijing 100190China Center of Materials Science and Optoelectronics Engineering University of Chinese Academy of SciencesBeijing 100049China Key Laboratory of Science&Technology on Particle Materials Institute of Process EngineeringChinese Academy of SciencesBeijing 100190China

Monolithic aerogels are promising candidates for use in atmospheric environmental purification due to their structural advantages,such as fine building block size together with high specific surface area,abundant pore structure,***,monolithic aerogels possess a unique monolithic macrostructure that sets them apart from aerogel powders and nanoparticles in practical environmental clean-up *** review delves into the available synthesis strategies and atmospheric environmental applications of monolithic aerogels,covering types of monolithic aerogels including SiO_(2),graphene,metal oxides and their combinations,along with their preparation *** particular,recent developments for VOC adsorption,CO_(2)capture,catalytic oxidation of VOCs and catalytic reduction of CO_(2)are ***,challenges and future opportunities for monolithic aerogels in the atmospheric environmental purification field are *** reviewprovides valuable insights for designing and utilizing monolithic aerogel-based functional materials.

关键词： Monolithic aerogel Environmental purification Catalysis Adsorption

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Time-varying formation tracking control of high-order multi-agent systems with multiple leaders and multiplicative noise

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science China(Information sciences) 2024年第12期67卷 191-207页

作者： Ruru JIA Xiaofeng ZONG Qing WANG College of Artificial Intelligence Nankai University School of Automation China University of Geosciences Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems School of Automation Science and Electrical Engineering Beihang University

This work discusses the time-varying formation(TVF) tracking control problem of high-order multi-agent systems(MASs) with multiple leaders and multiplicative measurement noise. With the help of Lyapunov function tools and stochastic analysis methods, the TVF tracking protocol with multiple leaders and multiplicative noise is developed based on the relative state measurements, where followers are driven to realize the target TVF while tracking the convex combination formed by multiple leaders. Then, the TVF tracking problem is converted into the mean square asymptotic stability problem of a stochastic differential equation(SDE); sufficient conditions related to the control gains are given by stabilizing the corresponding stochastic system. Moreover, a TVF tracking algorithm is presented to outline the steps of protocol ***, the theoretical results are illustrated in terms of simulation examples.

关键词： multi-agent systems multiple leaders multiplicative measurement noise stochastic differential equation formation tracking control

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Phase entanglement negativity for bipartite fermionic systems

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Physical Review A 2024年第3期110卷 032417页

作者： Bing Xu Xiaofei Qi Jinchuan Hou School of Mathematics and Statistics Key Laboratory of Complex Systems and Data Science of Ministry of Education College of Mathematics

We discuss the behavior of positive linear maps in fermionic systems and then propose the phase partial transpose and the phase entanglement negativity. We show that every fermionic state which mixes local fermion-number parity must have nonvanishing nontrivial phase entanglement negativity, which gives an affirmative answer to a conjecture proposed by Shapourian and Ryu [Phys. Rev. A 99, 022310 (2019)]. In addition, we prove that the phase entanglement negativity is an entanglement monotone and establish some equalities and inequalities related to the phase entanglement negativity which, particularly, provide some upper bounds and lower bounds of the fermionic entanglement negativity. A more detailed discussion of the (1+M)-mode case is also presented, and our results generalize some known findings.

关键词： Quantum entanglement

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Multi-layer analytic solution for k-ωmodel equations via a symmetry approach

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Applied Mathematics and Mechanics(English Edition) 2023年第2期44卷 289-306页

作者： Fan TANG Weitao BI Zhensu SHE Department of Mechanics and Engineering Science College of EngineeringPeking UniversityBeijing 100871China State Key Laboratory for Turbulence and Complex Systems Peking UniversityBeijing 100871China

Despite being one of the oldest and most widely-used turbulence models in engineering computational fluid dynamics(CFD),the k-ωmodel has not been fully understood theoretically because of its high nonlinearity and complex model parameter ***,a multi-layer analytic expression is postulated for two lengths(stress and kinetic energy lengths),yielding an analytic solution for the k-ωmodel equations in pipe *** local balance equations are analyzed to determine the key parameters in the solution,which are shown to be rather close to the empirically-measured values from the numerical solution of the Wilcox k-ωmodel,and hence the analytic construction is fully *** results provide clear evidence that the k-ωmodel sets in it a multilayer structure,which is similar to but different,in some insignificant details,from the Navier-Stokes(N-S)*** finding explains why the k-ωmodel is so popular,especially in computing the near-wall ***,the analysis is extended to a newlyrefined k-ωmodel called the structural ensemble dynamics(SED)k-ωmodel,showing that the SED k-ωmodel has improved the multi-layer structure in the outer flow but preserved the setting of the k-ωmodel in the inner region.

关键词： turbulence model k-ωmodel structural ensemble dynamics(SED) multilayer structure symmetry

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