Application of Cellular Automata and Markov Chain model for urban green infrastructure in Kuala Lumpur,Malaysia

Kuala Lumpur of Malaysia,as a tropical city,has experienced a notable decline in its critical urban green infrastructure(UGI)due to rapid urbanization and haphazard development.The decrease of UGI,especially natural forest and artificial forest,may reduce the diversity of ecosystem services and the ability of Kuala Lumpur to build resilience in the future.This study analyzed land use and land cover(LULC)and UGI changes in Kuala Lumpur based on Landsat satellite images in 1990,2005,and 2021and employed the overall accuracy and Kappa coefficient to assess classification accuracy.LULC was categorized into six main types:natural forest,artificial forest,grassland,water body,bare ground,and built-up area.Satellite images in 1990,2005,and 2021 showed the remarkable overall accuracy values of 91.06%,96.67%,and 98.28%,respectively,along with the significant Kappa coefficient values of 0.8997,0.9626,and 0.9512,respectively.Then,this study utilized Cellular Automata and Markov Chain model to analyze the transition of different LULC types during 1990-2005 and 1990-2021 and predict LULC types in 2050.The results showed that natural forest decreased from 15.22%to 8.20%and artificial forest reduced from 18.51%to 15.16%during 1990-2021.Reductions in natural forest and artificial forest led to alterations in urban surface water dynamics,increasing the risk of urban floods.However,grassland showed a significant increase from 7.80%to 24.30%during 1990-2021.Meanwhile,bare ground increased from 27.16%to 31.56%and built-up area increased from 30.45%to 39.90%during 1990-2005.In 2021,built-up area decreased to 35.10%and bare ground decreased to 13.08%,indicating a consistent dominance of built-up area in the central parts of Kuala Lumpur.This study highlights the importance of integrating past,current,and future LULC changes to improve urban ecosystem services in the city.

MULTI-DIMENSIONAL MARKOV CHAIN–BASED ANALYSIS OF CONFLICT PROBABILITY FOR SPECTRUM RESOURCE SHARING

In this paper, we consider the optimal problem of channels sharing with het-erogeneous traffic （real-time service and non-real-time service） to reduce the data conflict probability of users. Moreover, a multi-dimensional Markov chain model is developed to analyze the performance of the proposed scheme. Meanwhile, performance metrics are derived. Numerical results show that the proposed scheme can effectively reduce the forced termination probability, blocking probability and spectrum utilization.

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.

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.

Grey Markov chain and its application in drift prediction model of FOGs

A novel grey Markov chain predictive model is discussed to reduce drift influence on the output of fiber optical gyroscopes (FOGs) and to improve FOGs' measurement precision. The proposed method possesses advantages of grey model and Markov chain. It makes good use of dynamic modeling idea of the grey model to predict general trend of original data. Then according to the trend, states are divided so that it can overcome the disadvantage of high computational cost of state transition probability matrix in Markov chain. Moreover, the presented approach expands the applied scope of the grey model and makes it be fit for prediction of random data with bigger fluctuation. The numerical results of real drift data from a certain type FOG verify the effectiveness of the proposed grey Markov chain model powerfully. The Markov chain is also investigated to provide a comparison with the grey Markov chain model. It is shown that the hybrid grey Markov chain prediction model has higher modeling precision than Markov chain itself, which prove this proposed method is very applicable and effective.

A new grey forecasting model based on BP neural network and Markov chain

A new grey forecasting model based on BP neural network and Markov chain was proposed. In order to combine the grey forecasting model with neural network, an important theorem that the grey differential equation is equivalent to the time response model, was proved by analyzing the features of grey forecasting model（GM（1,1））. Based on this, the differential equation parameters were included in the network when the BP neural network was constructed, and the neural network was trained by extracting samples from grey system＇s known data. When BP network was converged, the whitened grey differential equation parameters were extracted and then the grey neural network forecasting model （GNNM（1,1）） was built. In order to reduce stochastic phenomenon in GNNM（1,1）, the state transition probability between two states was defined and the Markov transition matrix was established by building the residual sequences between grey forecasting and actual value. Thus, the new grey forecasting model（MNNGM（1,1）） was proposed by combining Markov chain with GNNM（1,1）. Based on the above discussion, three different approaches were put forward for forecasting China electricity demands. By comparing GM（1, 1） and GNNM（1,1） with the proposed model, the results indicate that the absolute mean error of MNNGM（1,1） is about 0.4 times of GNNM（1,1） and 0.2 times of GM（I, 1）, and the mean square error of MNNGM（1,1） is about 0.25 times of GNNM（1,1） and 0.1 times of GM（1,1）.

Testing and Evaluation for Web Usability Based on Extended Markov Chain Model

As the increasing popularity and complexity of Web applications and the emergence of their new characteristics, the testing and maintenance of large, complex Web applications are becoming more complex and difficult. Web applications generally contain lots of pages and are used by enormous users. Statistical testing is an effective way of ensuring their quality. Web usage can be accurately described by Markov chain which has been proved to be an ideal model for software statistical testing. The results of unit testing can be utilized in the latter stages, which is an important strategy for bottom-to-top integration testing, and the other improvement of extended Markov chain model (EMM) is to present the error type vector which is treated as a part of page node. this paper also proposes the algorithm for generating test cases of usage paths. Finally, optional usage reliability evaluation methods and an incremental usability regression testing model for testing and evaluation are presented. Key words statistical testing - evaluation for Web usability - extended Markov chain model (EMM) - Web log mining - reliability evaluation CLC number TP311. 5 Foundation item: Supported by the National Defence Research Project (No. 41315. 9. 2) and National Science and Technology Plan (2001BA102A04-02-03)Biography: MAO Cheng-ying (1978-), male, Ph.D. candidate, research direction: software testing. Research direction: advanced database system, software testing, component technology and data mining.

An Improved Markov Chain Model Based on Autocorrelation and Entropy Techniques and Its Application to State Prediction of Water Resources

According to the relationships among state transition probability matrixes with different step lengths, an improved Markov chain model based on autocorrelation and entropy techniques was introduced. In the improved Markov chain model, the state transition probability matrixes can be adjusted. The steps of the historical state of the event, which was significantly related to the future state of the event, were determined by the autocorrelation technique, and the impact weights of the event historical state on the event future state were determined by the entropy technique. The presented model was applied to predicting annual precipitation and annual runoff states, showing that the improved model is of higher precision than those existing Markov chain models, and the determination of the state transition probability matrixes and the weights is more reasonable. The physical concepts of the improved model are distinct, and its computation process is simple and direct, thus, the presented model is sufficiently general to be applicable to the prediction problems in hydrology and water resources.

Application of Exponential Distribution in Modeling of State Holding Time in HIV/AIDS Transition Dynamics

Markov modeling of HIV/AIDS progression was done under the assumption that the state holding time (waiting time) had a constant hazard. This paper discusses the properties of the hazard function of the Exponential distributions and its modifications namely;Parameter proportion hazard (PH) and Accelerated failure time models (AFT) and their effectiveness in modeling the state holding time in Markov modeling of HIV/AIDS progression with and without risk factors. Patients were categorized by gender and age with female gender being the baseline. Data simulated using R software was fitted to each model, and the model parameters were estimated. The estimated P and Z values were then used to test the null hypothesis that the state waiting time data followed an Exponential distribution. Model identification criteria;Akaike information criteria (AIC), Bayesian information criteria (BIC), log-likelihood (LL), and R2 were used to evaluate the performance of the models. For the Survival Regression model, P and Z values supported the non-rejection of the null hypothesis for mixed gender without interaction and supported the rejection of the same for mixed gender with interaction term and males aged 50 - 60 years. Both Parameters supported the non-rejection of the null hypothesis in the rest of the age groups. For Gender male with interaction both P and Z values supported rejection in all the age groups except the age group 20 - 30 years. For Cox Proportional hazard and AFT models, both P and Z values supported the non-rejection of the null hypothesis across all age groups. The P-values for the three models supported different decisions for and against the Null hypothesis with AFT and Cox values supporting similar decisions in most of the age groups. Among the models considered, the regression assumption provided a superior fit based on (AIC), (BIC), (LL), and R2 Model identification criteria. This was particularly evident in age and gender subgroups where the data exhibited non-proportional hazards and violated the assumptions required for the Cox Proportional Hazard model. Moreover, the simplicity of the regression model, along with its ability to capture essential state transitions without over fitting, made it a more appropriate choice.

A Fuzzy Probability-based Markov Chain Model for Electric Power Demand Forecasting of Beijing, China

In this study, a fuzzy probability-based Markov chain model is developed for forecasting regional long-term electric power demand. The model can deal with the uncertainties in electric power system and reflect the vague and ambiguous during the process of power load forecasting through allowing uncertainties expressed as fuzzy parameters and discrete intervals. The developed model is applied to predict the electric power demand of Beijing from 2011 to 2019. Different satisfaction degrees of fuzzy parameters are considered as different levels of detail of the statistic data. The results indicate that the model can reflect the high uncertainty of long term power demand, which could support the programming and management of power system. The fuzzy probability Markov chain model is helpful for regional electricity power system managers in not only predicting a long term power load under uncertainty but also providing a basis for making multi-scenarios power generation/development plans.

On the Markov Chain Binomial Model

Rudolfer [1] studied properties and estimation of a state Markov chain binomial (MCB) model of extra-binomial variation. The variance expression in Lemma 4 is stated without proof but is incorrect, resulting in both Lemma 5 and Theorem 2 also being incorrect. These errors were corrected in Rudolfer [2]. In Sections 2 and 3 of this paper, a new derivation of the variance expression in a setting involving the natural parameters ?is presented and the relation of the MCB model to Edwards’ [3] probability generating function (pgf) approach is discussed. Section 4 deals with estimation of the model parameters. Estimation by the maximum likelihood method is difficult for a larger number n of Markov trials due to the complexity of the calculation of probabilities using Equation (3.2) of Rudolfer [1]. In this section, the exact maximum likelihood estimation of model parameters is obtained utilizing a sequence of Markov trials each involving n observations from a {0,1}-?state MCB model and may be used for any value of n. Two examples in Section 5 illustrate the usefulness of the MCB model. The first example gives corrected results for Skellam’s Brassica data while the second applies the “sequence approach” to data from Crouchley and Pickles [4].

The Stationary Distributions of a Class of Markov Chains

The objective of this paper is to find the stationary distribution of a certain class of Markov chains arising in a biological population involved in a specific type of evolutionary conflict, known as Parker’s model. In a population of such players, the result of repeated, infrequent, attempted invasions using strategies from{0,1,2,…,m-1}, is a Markov chain. The stationary distributions of this class of chains, for m ε {3,4,…,∞} are derived in terms of previously known integer sequences. The asymptotic distribution (for m →∞) is derived.

Identifying the dependency pattern of daily rainfall of Dhaka station in Bangladesh using Markov chain and logistic regression model

Bangladesh is a subtropical monsoon climate characterized by wide seasonal variations in rainfall, moderately warm temperatures, and high humidity. Rainfall is the main source of irrigation water everywhere in the Bangladesh where the inhabitants derive their income primarily from farming. Stochastic rainfall models were concerned with the occurrence of wet day and depth of rainfall for different regions to model the daily occurrence of rainfall and achieved satisfactory results around the world. In connection to the Markov chain of different order, logistic regression is conducted to visualize the dependence of current rainfall upon the rainfall of previous two-time period. It had been shown that wet day of the previous two time period compared to the dry day of previous two time period influences positively the wet day of current time period, that is the dependency of dry-wet spell for the occurrence of rain in the rainy season from April to September in the study area. Daily data are collected from meteorological department of about 26 years on rainfall of Dhaka station during the period January 1985-August 2011 to conduct the study. The test result shows that the occurrence of rainfall follows a second order Markov chain and logistic regression also tells that dry followed by dry and wet followed by wet is more likely for the rainfall of Dhaka station and also the model could perform adequately for many applications of rainfall data satisfactorily.

On Numerical Approach to Non-Markovian Stochastic Systems Modeling

The paper considers the problem of representing non-Markovian systems that evolve stochastically over time. It is often necessary to use approximations in the case the system is non-Markovian. Phase type distribution is by now indispensable tool in creation of stochastic system models. The paper suggests a method and software for evaluating stochastic systems approximations by Markov chains with continuous time and countable state space. The performance of a system is described in the event language used for generating the set of states and transition matrix between them. The example of a numerical model is presented.

Arriving at estimates of a rate and state fault friction model parameter using Bayesian inference and Markov chain Monte Carlo

The critical slip distance in rate and state model for fault friction in the study of potential earthquakes can vary wildly from micrometers to few me-ters depending on the length scale of the critically stressed fault.This makes it incredibly important to construct an inversion framework that provides good estimates of the critical slip distance purely based on the observed ac-celeration at the seismogram.To eventually construct a framework that takes noisy seismogram acceleration data as input and spits out robust estimates of critical slip distance as the output,we first present the performance of the framework for synthetic data.The framework is based on Bayesian inference and Markov chain Monte Carlo methods.The synthetic data is generated by adding noise to the acceleration output of spring-slider-damper idealization of the rate and state model as the forward model.

高等院校教师人才流动的Markov-chain预测模型

介绍并解析随机过程理论中的马尔科夫过程与马尔科夫链;针对高等院校教师人才流动变化过程,利用马尔科夫过程分析方法建立描述人员流动变化趋势的Markov-chain预测模型,详细阐述了模型的算法步骤.以某所高等院校教师人才流动的状态转移数据作为算例,运用新建立的预测模型,对该院校教师人才的流动趋势做出了预测分析.最后,将教师进修状态纳入分析范围,进行了教师职业生涯和职务发展趋势预测的深入分析.应用模型对实际算例的求解结果表明:Markov-chain预测模型及算法,叙述简洁、运算方便,为高等院校教师人才流动,乃至其他行业人才流动的预测提供了一种新的、有效的思路和方法.

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.

Coverage Modeling and Reliability Analysis Using Multi-state Function

Fault tree analysis is an effective method for predicting the reliability of a system. It gives a pictorial representation and logical framework for analyzing the reliability. Also, it has been used for a long time as an effective method for the quantitative and qualitative analysis of the failure modes of critical systems. In this paper, we propose a new general coverage model （GCM） based on hardware independent faults. Using this model, an effective software tool can be constructed to detect, locate and recover fault from the faulty system. This model can be applied to identify the key component that can cause the failure of the system using failure mode effect analysis （FMEA）.

Bayesian zero-failure reliability modeling and assessment method for multiple numerical control(NC) machine tools

A new problem that classical statistical methods are incapable of solving is reliability modeling and assessment when multiple numerical control machine tools(NCMTs) reveal zero failures after a reliability test. Thus, the zero-failure data form and corresponding Bayesian model are developed to solve the zero-failure problem of NCMTs, for which no previous suitable statistical model has been developed. An expert-judgment process that incorporates prior information is presented to solve the difficulty in obtaining reliable prior distributions of Weibull parameters. The equations for the posterior distribution of the parameter vector and the Markov chain Monte Carlo(MCMC) algorithm are derived to solve the difficulty of calculating high-dimensional integration and to obtain parameter estimators. The proposed method is applied to a real case; a corresponding programming code and trick are developed to implement an MCMC simulation in Win BUGS, and a mean time between failures(MTBF) of 1057.9 h is obtained. Given its ability to combine expert judgment, prior information, and data, the proposed reliability modeling and assessment method under the zero failure of NCMTs is validated.