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Explicit Convergence Rates of the Embedded M/G/1 Queue

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Acta Mathematica Sinica,English Series 2007年第7期23卷 1289-1296页

作者： Yuan Yuan LIU zhen ting hou School of Mathematics Central South University

This paper investigates the explicit convergence rates to the stationary distribution π of the embedded M/G/1 queue; specifically, for suitable rate functions r（n） which may be polynomial with r（n） = n^l, l 〉 0 or geometric with r（n） = α^n, a 〉 1 and ＂moments＂ f ≥ 1, we find the conditions under which Σ∞n=0 r（n）｜｜P^n（i,·） - π（·）｜｜f ≤ M（i） for all i ∈ E. For the polynomial case, the explicit bounds on M（i） are given in terms of both ＂drift functions＂ and behavior of the first hitting time on the state O; and for the geometric case, the largest geometric convergence rate α＊ is obtained.

关键词： convergence rate Markov chains queues polynomial ergodicity geometric ergodicity

Ergodicity of Quasi-birth and Death Processes(Ⅰ)

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Acta Mathematica Sinica,English Series 2007年第2期23卷 201-208页

作者： zhen ting hou Xiao Hua LI School of Mathematics Central South University School of science Beijing University of Posts and Telecommunications

Quasi-birth and death processes with block tridiagonal matrices find many applications in various areas. Neuts gave the necessary and sufficient conditions for the ordinary ergodicity and found an expression of the stationary distribution for a class of quasi-birth and death processes. In this paper we obtain the explicit necessary and sufficient conditions for/-ergodicity and geometric ergodicity for the class of quasi-birth and death processes, and prove that they are not strongly ergodic. Keywords ergodicity, quasi-birth and death process.

关键词： ergodicity quasi-birth and death process Markov chain matrix geometric solutions

Degree Distribution of a Scale-free Random Graph Model

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Acta Mathematica Sinica,English Series 2012年第3期28卷 587-598页

作者： Li TAN zhen ting hou Xin Ru LIU School of Mathematics Central South University School of Traffic and Transportation Engineering Central South University

In this paper, we consider the degree distribution of a general random graph with multiple edges and loops from the perspective of probability. Based on the first-passage probability of Markov chains, we give a new and rigorous proof to the existence of the network degree distribution and obtain the precise expression of the degree distribution. The analytical results are in good agreement with numerical simulations.

关键词： Degree distribution scale-free Markov chains

Markov Chain-based Degree Distributions of Evolving Networks

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Acta Mathematica Sinica,English Series 2012年第10期28卷 1981-1994页

作者： Xiang Xing KONG zhen ting hou Ding Hua SHI Quan Rong CHEN Qing Gui ZHAO School of Mathematics Central South University Department of Mathematics Shanghai University Department of Electronic Engineering City University of Hong KongP.R.China Department of Mathematics and Science Hunan First Normal University

In this paper, we study a class of stochastic processes, called evolving network Markov chains, in evolving networks. Our approach is to transform the degree distribution problem of an evolving network to a corresponding problem of evolving network Markov chains. We investigate the evolving network Markov chains, thereby obtaining some exact formulas as well as a precise criterion for determining whether the steady degree distribution of the evolving network is a power-law or not. With this new method, we finally obtain a rigorous, exact and unified solution of the steady degree distribution of the evolving network.

关键词： Evolving network Markov chain scale-free network degree distribution

Trends of alkaline phosphatase to prealbumin ratio in patients with hepatitis B linked to hepatocellular carcinoma development

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World Journal of Gastroenterology 2025年第2期31卷 42-51页

作者： Wen-Chong zhen Jing Sun Xue-ting Bai Qian Zhang Zi-Han Li Yi-Xin Zhang Rong-Xuan Xu Wei Wu Zhi-Han Yao Chun-Wen Pu Xiao-Feng Li School of Public Health Dalian Medical UniversityDalian 116044Liaoning ProvinceChina Graduate School Dalian Medical UniversityDalian 116044Liaoning ProvinceChina Dalian Public Health Clinical Center Dalian Municipal Research Institute for Public HealthDalian 116001Liaoning ProvinceChina Department of Epidemiology and Health Statistics Dalian Medical UniversityDalian 116044Liaoning ProvinceChina

BACKGROUND Chronic hepatitis B often progresses silently toward hepatocellular carcinoma(HCC),a leading cause of mortality *** detection of HCC is crucial,yet *** To investigate the role of dynamic changes in alkaline phosphatase to prealbumin ratio(APR)in hepatitis B progression to *** Data from 4843 patients with hepatitis B(January 2015 to January 2024)were *** incidence rates in males and females were compared using the log-rank *** were evaluated using Kaplan–Meier *** Linear Mixed-Effects Model was applied to track the fluctuation of APR levels over ***,Joint Modeling of Longitudinal and Survival data was employed to investigate the temporal relationship between APR and HCC *** The incidence of HCC was higher in *** ensure the model’s normality assumption,this study applied a logarithmic transformation to APR,yielding *** levels were higher in females(t=5.26,P<0.01).A 1-unit increase in ratio correlated with a 2.005-fold higher risk of HCC in males(95%CI:1.653-2.431)and a 2.273-fold higher risk in females(95%CI:1.620-3.190).CONCLUSION Males are more prone to HCC,while females have higher APR *** no baseline APR link,rising APR indicates a higher HCC risk.

关键词： Alkaline phosphatase to prealbumin ratio Chronic hepatitis B patients Hepatocellular carcinoma Retrospective cohort study Linear Mixed-Effect Mode Joint Modelling of Longitudinal and Survival data

Robust H2/H∞ Fuzzy Filtering for Nonlinear Stochastic Systems with Infinite Markov Jump

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Journal of Systems Science & Complexity 2020年第4期33卷 1023-1039页

作者： LIU Yueying hou ting College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China School of Mathematics and Statistics Shandong Normal UniversityJinan 250358China

Robust fuzzy filterings for a class of nonlinear stochastic systems with infinite Markov jump are explored based on T-S fuzzy model approach in this paper. First of all, the exponentially mean square stable filter with a prescribed H∞ performance is designed via linear matrix inequalities(LMIs). Secondly, H2/H∞ fuzzy filtering is solved in terms of LMIs by minimizing the estimation error energy under the worst case fuzzy disturbance. The corresponding fuzzy filter parameters can be received by convex optimization algorithms. And lastly, two illustrative examples are performed to manifest the validity of the proposed methods.

关键词： H2/H∞ filtering Markov

A multi-sequential number-theoretic optimization algorithm using clustering methods

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Journal of Central South University of Technology 2005年第z1期12卷 283-293页

作者： XU Qing-song LIANG Yi-zeng hou zhen-ting School of Mathematical Science and Computing Technology Central South University Changsha 410083 China School of Chemistry and Chemical Engineering Central South University Changsha 410083 China School of Mathematical Science and Computing Technology Central South University Changsha 410083 China

A multi-sequential number-theoretic optimization method based on clustering was developed and applied to the optimization of functions with many local extrema. Details of the procedure to generate the clusters and the sequential schedules were given. The algorithm was assessed by comparing its performance with generalized simulated annealing algorithm in a difficult instructive example and a D-optimum experimental design problem. It is shown the presented algorithm to be more effective and reliable based on the two examples.

关键词： retention ratio cluster contraction local search

Stability for discrete-time uncertain systems with infinite Markov jump and time-delay

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Science China(Information Sciences) 2021年第5期64卷 100-110页

作者： ting hou Yueying LIU Feiqi DENG School of Mathematics and Statistics Shandong Normal University College of Mathematics and Systems Science Shandong University of Science and Technology School of Automation Science and Engineering South China University of Technology

In this paper, we developed a stability analysis for discrete-time uncertain time-delay systems governed by an infinite-state Markov chain(DUTSs-IMC). Some sufficient conditions for the considered systems to be exponential stability in mean square with conditioning(ESMS-C) are derived via linear matrix inequalities(LMIs), which can be examined conveniently. Under novel sufficient conditions, the equivalence among asymptotical stability in mean square(ASMS), stochastic stability(SS), exponential stability in mean square(ESMS), and ESMS-C has been established. Besides, numerical simulations are employed in result validation.

关键词： infinite jump time-delay parametric uncertainties exponential stability in mean square with conditioning stochastic stability

Graph partitions and the controllability of directed signed networks

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Science China(Information Sciences) 2019年第4期62卷 100-110页

作者： Xianzhu LIU Zhijian JI ting hou Institute of Complexity Science College of Automation and Electrical Engineering Qingdao University School of Mathematics and Statistics Qingdao University College of Mathematics and Systems Science Shandong University of Science and Technology

This paper studies the controllability problem of signed networks which is presented by weighted and directed signed graphs. Graph partitions such as structural balance and almost equitable partitions(AEPs) are studied. We generalize the definition of AEPs to any graphs, directed or undirected, signed or unsigned, with or without edge weights. Based on AEP theory, a graph-theoretic necessary condition is proposed for the controllability of directed signed networks and an algorithm is given for the computation of the coarsest partition. Besides, the upper bound on the controllable subspace is derived when the system is uncontrollable.

关键词： controllability signed networks graph partition almost equitable partitions structural balance