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Using markov chains to predict the natural progression of diabetic retinopathy

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International Journal of Ophthalmology(English edition) 2015年第1期8卷 132-137页

作者： Priyanka Srikanth Jaslok Hospital & Research Centre

AIM: To study the natural progression of diabetic retinopathy in patients with type 2 diabetes.METHODS: This was an observational study of 153 cases with type 2 diabetes from 2010 to 2013. The state of patient was noted at end of each year and transition matrices were developed to model movement between years. Patients who progressed to severe non-proliferative diabetic retinopathy(NPDR) were treated.markov chains and Chi-square test were used for statistical analysis.RESULTS: We modelled the transition of 153 patients from NPDR to blindness on an annual basis. At the end of year 3, we compared results from the markov model versus actual data. The results from Chi-square test confirmed that there was statistically no significant difference(P =0.70) which provided assurance that the model was robust to estimate mean sojourn times. The key finding was that a patient entering the system in mild NPDR state is expected to stay in that state for 5y followed by 1.07 y in moderate NPDR, be in the severe NPDR state for 1.33 y before moving into PDR for roughly8 y. It is therefore expected that such a patient entering the model in a state of mild NPDR will enter blindness after 15.29 y.CONCLUSION: Patients stay for long time periods in mild NPDR before transitioning into moderate NPDR.However, they move rapidly from moderate NPDR to proliferative diabetic retinopathy(PDR) and stay in that state for long periods before transitioning into blindness.

关键词： diabetes mellitus diabetic retinopathy markov chains Chi-square test transition probability matrix

POISSON LIMIT THEOREM FOR COUNTABLE markov chains IN markovIAN ENVIRONMENTS

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Applied Mathematics and Mechanics(English Edition) 2003年第3期24卷 298-306页

作者：方大凡王汉兴唐矛宁 Department of Mathematics Yueyang Normal University Department of Mathematics Shanghai UniversityShanghai 200436P.R.China Department of Mathematics Shanghai University

A countable markov chain in a markovian environment is considered.A Poisson limit theorem for the chain recurring to small cylindrical sets is mainly achieved.In order to prove this theorem,the entropy function h is introduced and the Shannon-McMillan-Breiman theorem for the markov chain in a markovian environment is shown. It's well-known that a markov process in a markovian environment is generally not a standard markov chain,so an example of Poisson approximation for a process which is not a markov process is given.On the other hand,when the environmental process degenerates to a constant sequence,a Poisson limit theorem for countable markov chains,which is the generalization of Pitskel's result for finite markov chains is obtained.

关键词： Poisson distributions markov chains random environments

Exponential Convergence Rates of markov chains under a Weaken Minorization Condition

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Acta Mathematica Sinica,English Series 2018年第12期34卷 1829-1836页

作者： Shu Lan HU Xin Yu WANG School of Statistics and Mathematics Zhongnan University of Economics and Law Wuhan 430073 P. R. China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 P. R. China

In this paper, we obtain the quantitative bound of the exponential convergence rates of markov chains under a weaken minorization condition, using the coupling method and the analytic approach. And also, we obtain the... 详细信息

关键词： Convergence rates markov chains coupling method analytic approach

A Maintenance Service Improvement Approach Based on Queue Networks: Application

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Open Journal of Applied Sciences 2024年第2期14卷 425-440页

作者： Aslain Brisco Ngnassi Djami Wolfgang Nzié Boukar Ousman Joseph Nkongho Anyi Ulrich Ngnassi Nguelcheu Department of Fundamental Sciences and Techniques of Engineer Chemical Engineering and Mineral Industries School University of Ngaoundere Ngaoundere Cameroon Laboratory of Mechanics Materials and Photonics National School of Agro-Industrial Sciences University of Ngaoundere Ngaoundere Cameroon Department of Electrical Engineering Energy and Automation National School of Agro-Industrial Sciences University of Ngaoundere Ngaoundere Cameroon Laboratory E3M Faculty of Industrial Engineering University of Douala Douala Cameroon Department of Physics Faculty of Science University of Ngaoundere Ngaoundere Cameroon

The quest to increase the performance of production systems that have become complex leads to the transfer to the maintenance function of the responsibility of guaranteeing the availability of such systems. Also, we will never stop saying that maintenance must integrate into all of the company’s initiatives, to affirm its role, which is to ensure greater availability and sustainability of the means of production. The objective of this paper is to evaluate the reliability and availability of a system without knowing the distribution law of the operating times. Among the methods for evaluating dependability criteria (Fault Trees, Petri Nets, etc.), we are interested in queues that have the advantage of taking into account functional dependencies, thus allowing a quantified optimization of maintenance. Indeed, queues make it possible to model parallel or sequential processes, implementing operations taking place at the same time or one after the other, meeting the needs of modeling production systems. The main result of this paper is the study of the influence of availability on the reliability of a multi-state production system.

关键词： markov chains Queues Availability Reliability Maintenance

Estimation of Spectral Gap for markov chains

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Acta Mathematica Sinica,English Series 1996年第4期12卷 337-360页

作者： Chen Mufa Department of Mathematics Beijing Normal University Beijing, 100875 China Department of Mathematics Beijing Normal University Beijing China

The study of the convergent rate (spectra gap) in the L^2-sense is motivated from several different fields: probability statistics, mathematical physics, computer science and so on and it is now an artive research topic. Based on a new approach (the coupling technique) introduced in [7] for the estimate of the convergent rate and as a continuation of [4],[5],[7-9],[23] and [24], this paper studies the estimate of the rate for time-continuous markov chains. Two variational formulas for the rate are presented here for the first time for birth-death processes. For diffusions, similar results are presented in an accompany paper [10]. The new formulas enable us to recover or improve the main known results. The connection between the sharp estimate and the corresponding eigenfunction is explored and illustrated by various examples. A previous result on optimal markovian couplings is also extended in the paper.

关键词： markov chains Spectral gap Couplings

Fully Polarimetric Land Cover Classification Based on markov chains

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Advances in Remote Sensing 2021年第3期10卷 47-65页

作者： Georgia Koukiou Vassilis Anastassopoulos Electronics Laboratory (ELLAB) Physics Department University of Patras Patras Greece

A novel land cover classification procedure is presented utilizing the information content of fully polarimetric SAR images. The Cameron coherent target decomposition (CTD) is employed to characterize land cover pixel by pixel. Cameron’s CTD is employed since it provides a complete set of elementary scattering mechanisms to describe the physical properties of the scatterer. The novelty of the proposed land classification approach lies on the fact that the features used for classification are not the types of the elementary scatterers themselves, but the way these types of scatterers alternate from pixel to pixel on the SAR image. Thus, transition matrices that represent local markov models are used as classification features for land cover classification. The classification rule employs only the most important transitions for decision making. The Frobenius inner product is employed as similarity measure. Ten different types of land cover are used for testing the proposed method. In this aspect, the classification performance is significantly high.

关键词： Fully Polarimetric SAR Coherent Decomposition Elementary Scatterers markov chains Land Cover Classification

A Note on markov chains in Stationary Random Environments

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Advances in Manufacturing 1999年第2期3卷 16-20页

作者： Wang Hanxing(College of Sciences, Shanghai University) Fang Dafan(Yueyang Normal College) College of Sciences Shanghai University Yueyang Normal College

We consider markov chains in stationary random environments. The conservative set C of the corresponding skew markov chain of this process can be thought of as a recurrent set of a standard markov chain. In some simpler cases, we give some sufficient conditions under which the conservative set C can be decomposed into at most countable minimal closed sets.

关键词： markov chains environmental processes conservative sets

利用markov chains研究企业资本运营状况及相关的财务管理决策

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利用Markov Chains研究企业资本运营状况及相关的财务管理决策

作者：孟德新中国农业大学

学位级别：硕士

经济预测方法有多种,常用的预测法需要大量样本资料来获取事物发展规律、保证预测效果,马尔科夫预测法正是通过对事物不同状态的初始概率与状态之间转移概率的研究,确定状态变化趋势,预测事物的未来。相比较而言,马尔科夫预测法不需要... 详细信息

经济预测方法有多种,常用的预测法需要大量样本资料来获取事物发展规律、保证预测效果,马尔科夫预测法正是通过对事物不同状态的初始概率与状态之间转移概率的研究,确定状态变化趋势,预测事物的未来。相比较而言,马尔科夫预测法不需要连续不断的历史资料和数据,只需要最近和当前的动态资料。运用马尔科夫预测法进行预测,主要原理就是建立马尔科夫预测模型,利用初始状态向量和状态转移概率矩阵来推知预测未来某一时期所处的状态。本文选取了一个企业的连续两年的经济业务来研究作为实证分析。本文共分为六个部分: 第一部分,主要介绍国内外关于马尔科夫链理论的研究现状,以及目前对所选取的研究对象——财务报表进行研究所应用的方法。第二部分,简单介绍了马尔科夫过程的定义和马尔科夫过程模型的基本应用种类,以及利用马尔科夫过程预测方法建立模型的具体步骤。第三部分,对企业的财务报表应用马氏过程进行预测的基本假设,包括状态的划分,转移矩阵的确定。第四部分,对选取的同一企业的两年的财务报表及所发生的具体经济业务运用马尔科夫模型进行研究,得出转移矩阵,加权平均后得出基本转移矩阵,进而对企业的后期经营提供报表预测。第五部分,对预测出的财务报表进行质量评估,进而评价企业的业务经营过程的合理性。第六部分,结论与建议,通过前几部分的阐述,企业的财务状况可以用马尔科夫过程进行预测,并且可以取得相对比较可靠的结果。

关键词： markov chains 转移矩阵六要素 “源”

markov chains Evaluation of Teaching Quality

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Markov Chains Evaluation of Teaching Quality