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15 June 2023, Volume 40 Issue 3 Previous Issue    Next Issue

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Early Detection and Evolution Law Discovery of New Emerging Topic of Heterogeneous On-line Social Networks XU Xiaoyan, LV Wei, ZHANG Beibei, ZHOU Shuaipeng, WEI Wei 2023, 40 (3):  341-354.  doi: 10.3969/j.issn.1005-3085.2023.03.001 Abstract ( 95 )   PDF (1441KB) ( 55 )   Save The purpose of this study is to accurately identify the new emerging topic immediately and to identify its evolution law from all kinds of heterogeneous on-line social network data which are composed of short texts like news titles and micro-blogs, the results of which will provide valuable decision support for government officers and company administrators. Firstly, all kinds of heterogeneous on-line social network data are acquired and modeled as the time-varying network by using the co-occurrence of short texts' keywords, from which the topic early detection problem could be changed into the problem of dynamic community detection on the time-varying topic network; Secondly, we propose the dynamic community detection method with static Louvain algorithm embedded and with modularity gain and local network variation as quantification values. The proposed method  yields preferable results under both large amount of computer-generated data and real heterogeneous online social network data, community detection and propagation identification results under computer-generated and real heterogeneous online social network data validates the algorithms' efficiency and feasibility. Related Articles | Metrics

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Multigrid Algorithm for Solving the Steady State Distribution of Vacation Queueing Networks with Two Queues YANG Shuling, HAN Xiaozhuo 2023, 40 (3):  355-365.  doi: 10.3969/j.issn.1005-3085.2023.03.002 Abstract ( 110 )   PDF (256KB) ( 44 )   Save Vacation policy describes the interruption of service process in engineering systems and management systems. Vacation queueing networks can be used to simulate these complex systems and have a wide range of applications in practice. Since the analytic formulas of the steady state distribution of vacation queueing networks are difficult to obtain, it is of great importance to study the numerical solution method. An algebraic multigrid algorithm is proposed for solving the steady state distribution of vacation queueing networks including two M/M/2 queues. With the special quasi-tridiagonal structure in the steady state equation, the prolongation and restriction operators of the multigrid algorithm are constructed by the cyclic reduction strategy. They are dependent on the coefficient matrix of linear system and therefore can maintain its characteristics on the coarser grid level, thus improving the convergence speed of the numerical algorithm. Finally, numerical examples show the superiority of the proposed algorithm. Related Articles | Metrics

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Stochastic Approximation Backward-forward Algorithm for Solving Stochastic Variational Inequality Problems HE Yuehong, LONG Xianjun, TANG Ping 2023, 40 (3):  366-380.  doi: 10.3969/j.issn.1005-3085.2023.03.003 Abstract ( 128 )   PDF (485KB) ( 56 )   Save Due to its wide application in problems such as transportation, stochastic games and economic equilibrium, the numerical algorithm for stochastic variational inequality has attracted extensive attention. By means of the stochastic approximation method, a forward-backward algorithm with line search for solving stochastic variational inequalities is proposed. At each iteration, the algorithm only needs to calculate one projection onto the closed convex set, and does not require the information about the Lipschitz constant, thus avoiding a lot of unnecessary computation. Under mild assumptions, it is proved that the sequence generated by the algorithm converges almost surely to the solution of the stochastic variational inequality problem. With the help of natural residual function, the results of sublinear convergence rate and the iteration complexity of the algorithm are also obtained. Finally, the feasibility and effectiveness of the algorithm are verified by some numerical examples. Related Articles | Metrics

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Variable Selection in Mode Regression Models Using the Mixture Skew-normal Data ZENG Xin, WU Liucang, JU Yuanyuan 2023, 40 (3):  381-397.  doi: 10.3969/j.issn.1005-3085.2023.03.004 Abstract ( 71 )   PDF (289KB) ( 61 )   Save Variable selection in finite mixture of regression (FMR) models is frequently used in statistical modeling. The existing studies on FMR models mainly base on the normality ass-umption of regression error. However, this assumption is not suitable for studying asymmetric data. The performance of the mode is better than that of the mean for skewed data. This paper proposes a variable selection method for mixture of mode regression models basing on the skew-normal distribution. The consistency and the Oracle property are proved. A modified EM algorithm is developed to estimate the parameters in the model. Simulation studies are conducted to investigate the performance of the proposed methodologies. A real example is further provided to investigate the performance of the proposed methodologies. Related Articles | Metrics

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Effect of Multiple Instantaneous Chemical Controls within Each Generation on Pest Management LI Yanyun, LIANG Juhua 2023, 40 (3):  398-412.  doi: 10.3969/j.issn.1005-3085.2023.03.005 Abstract ( 52 )   PDF (509KB) ( 34 )   Save A discrete pest-natural enemy population model is built with multiple insecticide sprays within a generation. First, the Jury criterion is used to investigate the existence and stability of boundary equilibrium points and the existence of nontrivial equilibrium points. Then, this paper explores the effects of spraying time and instantaneous kill rate on pest control, and gives the conditions for the paradox of pest control strategy. Then it is examined about the role of continuous incorrect spraying of insecticides on pest outbreaks. The results show that incorrectly spraying insecticides multiple times within each generation of the pest can trigger more severe pest outbreaks. Finally, numerical simulations are conducted to verify the findings are conducted. Related Articles | Metrics

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Global Stability of an Epidemic Model with Age-structure WANG Fei, FU Liting 2023, 40 (3):  413-424.  doi: 10.3969/j.issn.1005-3085.2023.03.006 Abstract ( 166 )   PDF (535KB) ( 87 )   Save Based on reinfection, an epidemic model with vaccination, incubation and infection ages is presented to understand the impact of age of vaccination, age of latency and age of infection on global dynamics of the model. It is shown that the global dynamics of the model is determined by the basic regeneration number. First, the boundedness, existence, nonnegativity and asymptotic smoothness of the model are established by the theory of integrating partial differential equations along characteristic lines. Then, the steady states and basic reproduction number of the model are obtained by the theory of solutions to differential equations. By constructing a suitable Lyapunov functional and using the LaSalle invariance principle, it is verified that the disease-free steady state is globally asymptotically stable if the basic regeneration number is less than 1, and unstable if the basic regeneration number is larger than 1. Finally, by numerical simulation it is verified that the solution converges to the disease-free equilibrium point. Related Articles | Metrics

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Improved High Order Weighted Compact Nonlinear Difference Scheme LI Xiaogang, WANG Jianling, HU Weiyi, WANG Wenshuai 2023, 40 (3):  425-438.  doi: 10.3969/j.issn.1005-3085.2023.03.007 Abstract ( 90 )   PDF (1405KB) ( 27 )   Save Based on the fourth- and sixth-order central compact schemes with tridiagonal coefficient matrix, the fourth- and fifth-order weighted compact nonlinear difference schemes are obtained for solving hyperbolic conservation law equations, the function values of half-node are interpolated with the nonlinear combination of the fifth-order WENO difference scheme of large template and two small symmetrical templates. The computational accuracy and efficiency of the new scheme are verified by the results of linear convection equation. The resolution of the new scheme is verified by the results of one-dimensional inviscid Burgers equation. The ability of the new scheme to capture the shock discontinuity in nonlinear problems is verified by one - and two-dimensional Euler equations. The numerical experiments show that the proposed scheme is an efficient, high-order and high-resolution shock capturing scheme. Related Articles | Metrics

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A Positivity-preserving and Conservative Scheme Based on the Virtual Element Method for Radiation Diffusion Equations SHENG Meihua, YANG Di, GAO Zhiming 2023, 40 (3):  439-455.  doi: 10.3969/j.issn.1005-3085.2023.03.008 Abstract ( 68 )   PDF (891KB) ( 36 )   Save As a widely adopted numerical method in recent years, the virtual element method has many advantages. However, when solving some radiation diffusion equations derived from practical problems, the method may not guarantee the non-negativity of the numerical solution or maintain the local conservation property on general polygonal meshes. This paper uses the nonlinear two-point flux approximation as a post-processing procedure, and proposes a positivity-preserving and conservative scheme based on the virtual element method for radiation diffusion equations. The scheme obtains the cell-vertex values of the numerical solution by the lowest-order virtual element method. Then the positive cell-centered values are obtained by the nonlinear two-point flux approximation, where the local conservation property is maintained as well. The numerical results on arbitrary polygonal meshes demonstrate the second-order convergence rate for the solution scheme, and its high adaptability to deal with radiation diffusion problems with strong discontinuous or nonlinear diffusion coefficients. Related Articles | Metrics

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Centrosymmetric Solution to a Class of Quaternion Matrix Equations and Its Extremal Ranks WANG Yun, HUANG Jingpin 2023, 40 (3):  456-470.  doi: 10.3969/j.issn.1005-3085.2023.03.009 Abstract ( 70 )   PDF (165KB) ( 41 )   Save Investigated are the centrosymmetric matrix solution for a system of quaternion matrix equations and its extremal ranks. By using the properties of centrosymmetric matrix and M-P generalized inverse, a constrained problem is transformed into unconstrained equations. The necessary and sufficient conditions for the equations with centrosymmetric matrix solutions as well as their extremal rank are obtained. The obtained conclusions extend the results of related literature. Related Articles | Metrics

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Existence and Uniqueness of Periodic Solution to a Class of Volterra Differential System with Delays HUANG Minghui, JIN Chuhua 2023, 40 (3):  471-482.  doi: 10.3969/j.issn.1005-3085.2023.03.010 Abstract ( 344 )   PDF (170KB) ( 60 )   Save The periodic solutions for a class of Volterra differential systems with delays are discussed. By using techniques such as the fundamental solution matrix and Floquet theory, the Volterra system is integrally transformed to construct a new expression for the system solution; By using the Krasnoselskii fixed point method, the existence of periodic solutions for the studied system is obtained; the sufficient conditions for the uniqueness of the periodic solution of the system are obtained by using the contraction mapping principle. Finally, an example is given to verify the effectiveness of the conclusion. Related Articles | Metrics

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An Approximation Algorithm for the Squared Metric Facility Leasing Problem DUAN Yonghong, HAN Lu 2023, 40 (3):  483-492.  doi: 10.3969/j.issn.1005-3085.2023.03.011 Abstract ( 125 )   PDF (181KB) ( 45 )   Save The squared metric facility leasing problem is proposed for the first time. This problem is an extension of the facility leasing problem. Squared metric focuses on the impact of distance on the connection cost and has a wide range of practical applications. In the squared metric facility leasing problem, each client arrives at some time period, and needs to be connected to some facility that is being leased at its time of arrival. Leasing facilities incurs leasing costs. Connecting clients to facilities incurs connection costs. The connection cost equals to the square of the distance between the client and the facility. Assume that the distances are metric. The goal is to lease some facilities and connect each client so that the sum of the leasing and connection costs is minimized. A 9-approximation algorithm is proposed for the squared metric facility leasing problem, which is based on the primal-dual technique. Related Articles | Metrics

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Optimal Utility for an Insider YANG Jianqi 2023, 40 (3):  493-502.  doi: 10.3969/j.issn.1005-3085.2023.03.012 Abstract ( 49 )   PDF (191KB) ( 48 )   Save Based on the current jump-diffusion model and logarithmic utility function, the maximum expected utility problem and information utility comparison problem are considered within an insider information market. A measurable random variable with respect to maturity date is used to describe the insider information in the real financial market. On this basis, the insider information market model is constructed, and the general and the insider are defined. The multi-dimensional jump diffusion model is used to describe risky assets. Based on this model, the expected utility maximization problem of investors with two kinds of different information is put forward clearly. By the initial enlargement of filtration, the problems of expected utility maximization of general and insider, respectively, are solved through stochastic methods and explicit utility maximization strategies and corresponding maximization utilities are formulated respectively. Investment strategies are affected by market information. Investors often need to spend certain information costs to obtain information, and different information brings different effects to investors. Under the assumption of the same information cost, rational investors will always choose the information that can bring them more utility. For the purpose of comparing the utilities of different information, information utility ratio is defined as the ratio of two initials for gaining the equivalent maximized expected utility under different information conditions. Then, its five properties and the ratio of general information to insider information are given explicitly. Related Articles | Metrics

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Asymptotic Behavior of Solution to a Fully Parabolic Attraction-repulsion Chemotaxis System with Signal-dependent Sensitivities and Logistic Source ZHOU Xinlu, LI Zhongping 2023, 40 (3):  503-510.  doi: 10.3969/j.issn.1005-3085.2023.03.013 Abstract ( 61 )   PDF (163KB) ( 39 )   Save Chemotaxis is a phenomenon of the directed movement of cells in response to the concentration gradient of the chemical signal substance which is produced by cells. It can be divided into positive chemotaxis and negative chemotaxis according to the proximity or distance to the stimuli, which is meaningful to the survival and development of organisms. The study of chemotaxis is of great significance in the fields of biological oil recovery, ecological decontamination, biological population dynamics and the pathogenesis of infectious diseases. Therefore, a class of fully parabolic attraction-repulsion chemotaxis system with signal-dependent sensitivities and Logistic source is studied under homogeneous Neumann boundary conditions. The asymptotic behavior of the global bounded solution of the system is investigated by constructing an appropriate energy functional when it meets initial data and sensitivity functions satisfying some conditions. The result shows that the solution of the system will eventually converge to a constant steady state exponentially. Related Articles | Metrics