Mathematical Modeling of Possibility Markov Chains by Possibility Theory

Statistical regression models are input-oriented estimation models that account for observation errors. On the other hand, an output-oriented possibility regression model that accounts for system fluctuations is proposed. Furthermore, the possibility Markov chain is proposed, which has a disidentifiable state (posterior) and a nondiscriminable state (prior). In this paper, we first take up the entity efficiency evaluation problem as a case study of the posterior non-discriminable production possibility region and mention Fuzzy DEA with fuzzy constraints. Next, the case study of the ex-ante non-discriminable event setting is discussed. Finally, we introduce the measure of the fuzzy number and the equality relation and attempt to model the possibility Markov chain mathematically. Furthermore, we show that under ergodic conditions, the direct sum state can be decomposed and reintegrated using fuzzy OR logic. We had already constructed the Possibility Markov process based on the indifferent state of this world. In this paper, we try to extend it to the indifferent event in another world. It should be noted that we can obtain the possibility transfer matrix by full use of possibility theory.

D-S理论和Markov链组合的桥梁性能退化预测研究

为准确预测桥梁性能退化,考虑到数据随机性和微小扰动发生状态跳跃,提出了一种D-S(Dempster-Shafer)证据理论和Markov链组合的桥梁性能退化组合预测模型和性能退化率的概念.该模型基于指数平滑(exponential smoothing,ES)方法获得新的预测数据序列,并利用Markov链和D-S理论不断进行优化,从而实现桥梁性能退化的组合预测.实际工程的应用结果表明:性能退化率可以直观地表征在梁性能退化的速度.其次,该模型的平均相对误差为1.54%,较于回归、灰色和模糊加权Markov链模型,精度分别提高了1.11%,0.88%和2.8%,而后验差比值为0.242,小于0.35;模型的标准差为9.021,相比其他模型分别减小了3.978,3.405和7.500,而变异系数为0.109,均小于其他模型,验证了组合预测模型在精度和稳定性方面的优越性,可为在役桥梁结构性能退化预测与维护提供理论基础.

东北地区土地覆被格局变化模拟:基于CLUE-S和Markov-CA模型的对比分析

研究以遥感解译的东北地区2000年、2010年、2015年的土地覆被变化为基础,充分考虑自然和社会因素对土地覆被变化的影响,分别通过CLUE-S模型和Markov-CA模型对东北地区2015年和2030年土地覆被格局进行模拟,研究结果表明:通过与遥感解译的2015年实际土地覆被类型数据对比验证,CLUE-S模型和Markov-CA模型模拟结果的总体Kappa指数分别为0.9700和0.9649,结果表明2种模型的模拟结果较为理想,CLUE-S模型的模拟精度较Markov-CA模型更高。2015—2030年东北地区草地、耕地、湿地、其他用地和水体面积呈现下降趋势,林地、人工表面面积呈现增加趋势,人地关系越发紧张。东北地区作为生态环境相对脆弱的区域需警惕不可持续的土地覆被变化,需权衡生态保护、粮食增加与基础设施建设的用地需求和协调发展。

Service Function Chain Deployment Algorithm Based on Multi-Agent Deep Reinforcement Learning

Aiming at the rapid growth of network services,which leads to the problems of long service request processing time and high deployment cost in the deployment of network function virtualization service function chain(SFC)under 5G networks,this paper proposes a multi-agent deep deterministic policy gradient optimization algorithm for SFC deployment(MADDPG-SD).Initially,an optimization model is devised to enhance the request acceptance rate,minimizing the latency and deploying the cost SFC is constructed for the network resource-constrained case.Subsequently,we model the dynamic problem as a Markov decision process(MDP),facilitating adaptation to the evolving states of network resources.Finally,by allocating SFCs to different agents and adopting a collaborative deployment strategy,each agent aims to maximize the request acceptance rate or minimize latency and costs.These agents learn strategies from historical data of virtual network functions in SFCs to guide server node selection,and achieve approximately optimal SFC deployment strategies through a cooperative framework of centralized training and distributed execution.Experimental simulation results indicate that the proposed method,while simultaneously meeting performance requirements and resource capacity constraints,has effectively increased the acceptance rate of requests compared to the comparative algorithms,reducing the end-to-end latency by 4.942%and the deployment cost by 8.045%.

基于CLUE-S和Markov模型的土地利用变化模拟预测

土地利用变化过程是极其复杂的,主要是因为其在变化的过程中不仅仅是单一因素作用的结果,而是多种因素掺杂在一起形成的复杂过程。在经济快速发展的今天,一旦区域土地利用存在不合理的情况,极容易影响区域资源可持续利用以及和谐稳定的状态,土地利用变化模拟预测可以改善土地利用结构、提高土地利用效率,帮助相关部门规划国土空间布局,缓解人地矛盾,实现自然资源可持续发展。本文是基于高分辨率遥感影像解译得到靖远县2期土地利用数据,并利用CLUE-S与Markov模型相结合的方法对靖远县未来土地利用变化从自然发展、耕地保护和生态安全三种情景进行预测。结果表明,(1)CLUE-S模型相对于小尺度的土地利用变化模拟预测的效果较好,精度较高。(2)建设用地在自然发展情景下的增加是最为显著的,在其他两种情景下受到限制因素后在减少,草地和耕地只有在自然发展情景下是减少,林地只在耕地保护情景下是减少,水域用地和未利用地都在自然发展情景下是增加的。(3)生态安全情景与耕地保护情景对未来土地利用变化的调控效果较好,林地、草地和耕地受到了更好的保护。研究表明,区域土地利用模拟预测可以更好地为土地利用规划编制提供参考。

Modeling urban land use dynamics using Markov-chain and cellular automata in Gondar City,Northwest Ethiopia

Modeling urban land-use dynamics is critical for urban experts’and infrastructure managers’planning.This study attempts to explore the land-use/land-cover(LULC)dynamics of Gondar using satellite images from 1984 to 2020.Markov-Chain and Cellular Automata(MC-CA)models have been recognized as performing well in predicting urban land-use change.However,only a few models work in Ethiopia in general,and no study in Gondar has applied this approach to study urban land-use patterns.Therefore,Gondar land-use/land cover changes of Gondar were predicted using the MC-CA model in IDRISI.The built-up area in Gondar city covered 1413 ha(3%of the total area)in 1984 and increased to 2380 ha(5%)in 1994;21153 ha(45.5%)in 2004;22622 ha(48.7%)in 2014;and 23427 ha(50.5%)in 2020.The area has been predicted to reach 57.5%in the 2050s,showing a faster increase that will cause a very vast loss of farmland.This will increase urban sprawl challenges as well as overall environmental disequilibrium in the preceding decade.Thus,innovative and careful structures and systems in urban planning are required to secure a sustainable urban future and to make our cities livable and competitive in the paradigm of sustainable cities.

Markov Chains Based on Random Generalized 1-Flipper Operations for Connected Regular Multi-digraphs

The properties of generalized flip Markov chains on connected regular digraphs are discussed.The 1-Flipper operation on Markov chains for undirected graphs is generalized to that for multi-digraphs.The generalized 1-Flipper operation preserves the regularity and weak connectivity of multi-digraphs.The generalized 1-Flipper operation is proved to be symmetric.Moreover,it is presented that a series of random generalized 1-Flipper operations eventually lead to a uniform probability distribution over all connected d-regular multi-digraphs without loops.

Air Quality Estimation Using Nonhomogeneous Markov Chains: A Case Study Comparing Two Rules Applied to Mexico City Data

A nonhomogeneous Markov chain is applied to the study of the air quality classification in Mexico City when the so-called criterion pollutants are used. We consider the indices associated with air quality using two regulations where different ways of classification are taken into account. Parameters of the model are the initial and transition probabilities of the chain. They are estimated under the Bayesian point of view through samples generated directly from the corresponding posterior distributions. Using the estimated parameters, the probability of having an air quality index in a given hour of the day is obtained.

Ecological Classroom Model for Vocabulary Teaching Based on Markov Chain

This paper explores the current English vocabulary teaching classroom based on an eco-linguistic perspective and the Markov chain,points out the ecological imbalance in the English vocabulary classroom,and proposes measures to solve the problem and strategies to build an ecological English vocabulary learning classroom,in order to provide some reference for future English vocabulary curriculum reform and curriculum design.In this paper,a random sample of 20 students from each class was taken from an advanced arts class and an advanced science class.The results show that after a semester of teaching process,the overall English scores of the arts and science classes improved,and since,the arts classes improved more and the teachers’teaching quality was better.

基于相似日的Grey-Markov与BP_Adaboost的短期光伏功率预测

针对相似日对光伏功率预测精度的影响,提出基于相似日的Grey-Markov与BP_Adaboost的光伏功率预测方法。为获取不同相似日,分别以辐照度和温度为相似变量,通过二维欧氏距离选取两组相似日;基于两组相似日数据,用灰色GM(1,1)模型预测光伏功率的总体趋势,用马尔科夫链对灰色模型的预测结果进行修正,得到两组预测结果;用BP_Adaboost对两组预测结果进行集成,以获得更高的预测精度。仿真结果表明,该方法提高了结果的预测精度与鲁棒性,可为光伏电站并网提供重要参考信息。

融合Mar-GLSTM的流程生产工艺质量预测算法

针对流程生产连续性强、时序耦合复杂等特点,传统神经网络不具备长期记忆能力,且在深层次网络训练时易出现训练参数灾难、梯度爆炸等问题,提出基于马尔可夫优化的融合门控循环单元(GRU)与长短期记忆网络(LSTM)的组合预测模型(Mar-G LSTM)。首先在循环神经网络结构中融入门控机制构建深度LSTM神经网络模型,对流程生产时序数据信息进行选择性记忆,学习时序数据序列的信息依赖,进而解决训练过程中的梯度爆炸问题;同时结合马尔可夫链对GRU-LSTM模型的预测结果进行修正优化,在降低模型的复杂度的情况下进一步提高了模型的预测精度。最后,结合某流程生产线的工艺数据进行分析验证,结果表明,Mar-G LSTM算法在预测精度上较随机森林模型、门控循环单元神经网络模型(GRU)、长短期记忆神经网络模型(LSTM)和卷积神经网络与门控循环单元网络组合模型(CNN-GRU)分别提高了37.42%、21.32%、17.91%和12.56%,所提Mar-G LSTM算法可实现流程生产质量的准确预测,为降低工艺参数调控任务的完成时间提供了思路和实现途径。

基于RS-SPA-Markov chain的生物质气化站安全评价与预测模型研究

本文在资料收集、实地考察、专家评估的基础上,建立了相对通用的生物质气化站安全评价指标体系,引入了RS-SPA-Markov chain安全评价与预测模型。通过实例应用,证明了该模型应用于生物质气化站安全评价与预测的可行性和科学性,为生物质气化站安全评价与预测提供了一种新的途径。

Auto-selection order of Markov chain for background sequences with chi-square test

Modeling non coding background sequences appropriately is important for the detection of regulatory elements from DNA sequences. Based on the chi square statistic test, some explanations about why to choose higher order Markov chain model and how to automatically select the proper order are given in this paper. The chi square test is first run on synthetic data sets to show that it can efficiently find the proper order of Markov chain. Using chi square test, distinct higher order context dependences inherent in ten sets of sequences of yeast S.cerevisiae from other literature have been found. So the Markov chain with higher order would be more suitable for modeling the non coding background sequences than an independent model.

Applicability of Markov chain-based stochastic model for bubbling fluidized beds

A Markov chain-based stochastic model （MCM） is developed to simulate the movement of particles in a 2D bubbling fluidized bed （BFB）. The state spaces are determined by the discretized physical cells of the bed, and the transition probability matrix is directly calculated by the results of a discrete element method （DEM） simulation. The Markov property of the BFB is discussed by the comparison results calculated from both static and dynamic transition probability matrices. The static matrix is calculated based on the Markov chain while the dynamic matrix is calculated based on the memory property of the particle movement. Results show that the difference in the trends of particle movement between the static and dynamic matrix calculation is very small. Besides, the particle mixing curves of the MCM and DEM have the same trend and similar numerical values, and the details show the time averaged characteristic of the MCM and also expose its shortcoming in describing the instantaneous particle dynamics in the BFB.

Ultralong nitrogen/sulfur Co-doped carbon nano-hollowsphere chains with encapsulated cobalt nanoparticles for highly efficient oxygen electrocatalysis

The development of simple and effective strategies to prepare electrocatalysts,which possess unique and stable structures comprised of metal/nonmetallic atoms for oxygen reduction reaction(ORR)and oxygen evolution reaction(OER),is currently an urgent issue.Herein,an efficient bifunctional electrocatalyst featured by ultralong N,S-doped carbon nano-hollow-sphere chains about 1300 nm with encapsulated Co nanoparticles(Co-CNHSCs)is developed.The multifunctional catalytic properties of Co together with the heteroatom-induced charge redistribution(i.e.,modulating the electronic structure of the active site)result in superior catalytic activities toward OER and ORR in alkaline media.The optimized catalyst Co-CNHSC-3 displays an outstanding electrocatalytic ability for ORR and OER,a high specific capacity of 1023.6 mAh gZn^(-1),and excellent reversibility after 80 h at 10mA cm^(-2)in a Zn-air battery system.This work presents a new strategy for the design and synthesis of efficient multifunctional carbon-based catalysts for energy storage and conversion devices.

Basic Lithofacies-Succession Model for the Wumishan Cyclothems: Their Markov Chain Analysis and Regularly Vertical Stacking Patterns in the Third-Order Sequences

The Mesoproterozoic Wumishan Formation in the Jixian section of Tianjin is a succession of 3300-m-thick carbonate strata formed in a period of about 100 Ma (1310±20 Ma-1207±10 Ma). In this succession of strata, the carbonate metre-scale cyclic sequences belonging to peritidal type with an approximately symmetrical lithofacies-succession are best developed. The wide development of 1:4 stacking patterns shows that these metre-scale cyclic sequences are genetically related to the short-eccentricity cycles, which are called the Wumishan cyclothems that could truly represent sedimentary cycles. Generally, massive and thick-bedded calcareous dolomites and dolomitic limestones of stromatolite biostromes and thrombolite bioherms constitute the central part of the Wumishan cyclothems. The lower and upper parts consist of tidal flat dolostones, sandy-muddy dolostone and the top part is composed of lagoonal facies dolomitic shales with a paleosol cap. Therefore, an approximately symmetrical lithofacies-succession is formed. Many features such as the clear deepening and shoaling vectors of cyclothems, and all kinds of marks of fresh-water diagenesis indicate that the Wumishan cyclothems are the product of autocyclic sedimentation governed by allocyclic high-frequency sea-level changes. The results of a Markov chain analysis reaffirm the existence of the lithofacies-succession model of the Wumishan cyclothems. The boundaries of the Wumishan cyclothems are marked by the instantaneous exposed punctuated surface, which leads to the discrepancy between the cyclothems and the parasequences of the sequence stratigraphy terminology system. It is difficult to form a judgment that the time span of the Milankovitch cycles in the Precambrian is certainly equal to that of the Phanerozoic, but the regularly vertical stacking patterns of the seventh-order rhythms, sixth-order cyclothems and fifth-order parasequence sets still indicate their consistency with the duration of the Milankovitch cycles in the Phanerozoic.

The Relations Among Various Markov Chains

Some basic equations and the relations among various Markov chains are established. These works are the bases in the investigation of the theory of Markov chain in random environment.

Weighted Markov chains for forecasting and analysis in Incidence of infectious diseases in jiangsu Province,China

This paper first applies the sequential cluster method to set up the classification standard of infectious disease incidence state based on the fact that there are many uncertainty characteristics in the incidence course.Then the paper presents a weighted Markov chain,a method which is used to predict the future incidence state.This method assumes the standardized self-coefficients as weights based on the special characteristics of infectious disease incidence being a dependent stochastic variable.It also analyzes the characteristics of infectious diseases incidence via the Markov chain Monte Carlo method to make the long-term benefit of decision optimal.Our method is successfully validated using existing incidents data of infectious diseases in Jiangsu Province.In summation,this paper proposes ways to improve the accuracy of the weighted Markov chain,specifically in the field of infection epidemiology.

THE CLASSIFICATION AND PERIOD OF STATES FOR MARKOV CHAIN IN RANDOM ENVIRONMENT

This paper is a continuation of [8]. In Section 1, three kinds of communication are introdnced for two states and the relations among them are investigated. In Section 2, two kinds of period of a state are introdnced and it is obtained that the period is a 'class property',i.e. two states x and y belong to same class implies the period of x is equal to the period of y.

Intrusion detection based on system calls and homogeneous Markov chains

A novel method for detecting anomalous program behavior is presented, which is applicable to hostbased intrusion detection systems that monitor system call activities. The method constructs a homogeneous Markov chain model to characterize the normal behavior of a privileged program, and associates the states of the Markov chain with the unique system calls in the training data. At the detection stage, the probabilities that the Markov chain model supports the system call sequences generated by the program are computed. A low probability indicates an anomalous sequence that may result from intrusive activities. Then a decision rule based on the number of anomalous sequences in a locality frame is adopted to classify the program＇s behavior. The method gives attention to both computational efficiency and detection accuracy, and is especially suitable for on-line detection. It has been applied to practical host-based intrusion detection systems.