Abstract:! The aim of this thesis is to find the optimal control of Markov chain with discounted evaluation of transitions in discrete and also in continuous time. We present Howard's iterative algorithm, the algorithm for finding the optimal control. Then the strategy is applied to the problem of optimal trading, where the goal is to maximize market price of the portfolio in infinite time horizont, given the existence of the proportional transaction costs. Market price is simulated with Brownian motion.

The global importance of and need for sustainable development demand an informed decision-making process from the built environment to ensure optimum service life, which depends on the ability to quantify changes in condition of building materials over time. The objective of this thesis is to develop a model, which translates expert knowledge and reasoning into probability values through the application of Fuzzy Logic Artificial Intelligence to supplement limited historical performance data on degradation of building materials for the development of Markov Chain transitional probability matrices to predict service life, condition changes over time, and consequences of maintenance levels on service life of buildings. The Markov Chain methodology, a stochastic approach used for simulating the transition from one condition to another over time, has been identified as the preferred method for service life prediction by a number of studies. Limited availability of historic performance data on degradation and durability of building materials, required to populate the Markovian transition probability matrices, however restricts the application of the Markov Chain methodology. The durability and degradation factors, defined as design and maintenance levels, material and workmanship quality, external and internal climate, and operational environment, similar to the factors identified in the state-of-the–art ‘Factor Method’ for service life prediction, and current condition are rated on a uniform colour-coded five-point rating system and used to develop “IF-THEN” rules based on expert knowledge and reasoning. Fuzzy logic artificial intelligence is then used to translate these rules into crisp probability values to populate the Markovian transitional probability matrices. Historic performance data from previous condition assessments of six academic hospitals are used to calibrate and test the model. There is good correlation between the transitional probability matrices developed for the proposed model and other Markov applications in concrete bridge deck deterioration and roof maintenance models, based on historic performance data collected over extended periods, which makes the correlation more significant. Proof is presented that the Markov Chain can be used to calculate the estimated service life of a building or component, quantify changes in condition over time and determine the effect of maintenance levels on service life. It is also illustrated that the limited availability of historic performance data on degradation of building materials can be supplemented with expert knowledge, translated into probability values through the application of Fuzzy Logic Artificial Intelligence, to develop transition probability matrices for the Markov Chain. The proposed model can also be used to determine the estimated loss of or gain in service life of a building or component for various levels of maintenance. / Thesis (PhD(Civil Engineering))--University of Pretoria, 2007. / Civil Engineering / unrestricted

The objective of the study is to apply Markov chain analysis to analyze student flow through King Abdul Aziz University (KAU) in Saudi Arabia, and to predict important metrics such as graduation and dropout rates. This objective arises from examination of the policies of KAU University. We begin with background information detailing the subject of study, then move into a general outline of stochastic processes. We then use these methods to construct a specific matrix of transition probabilities with data from the university student population. Finally, we discuss the calculation of the possibilities of transition between each level of study and the average time a student takes to complete each stage. The study uses Markov chains with these outcomes to analyze student retention data from the Department of Mathematics at KAU. From this analysis, the study will provide university policy recommendations that can be generalized to examine other universities.

Estudamos o comportamento da familia aresta-triangulo de grafos aleatorios exponenciais (ERG) usando metodos de Monte Carlo baseados em Cadeias de Markov. Comparamos contagens de subgrafos e correlacoes entre arestas de ergs as de Grafos Aleatorios Binomiais (BRG, tambem chamados de Erdos-Renyi). E um resultado teorico conhecido que para algumas parametrizacoes os limites das contagens de subgrafos de ERGs convergem para os de BRGs, assintoticamente no numero de vertices [BBS11, CD11]. Observamos esse fenomeno em grafos com poucos (20) vertices em nossas simulacoes. / We study the behavior of the edge-triangle family of exponential random graphs (ERG) using the Markov Chain Monte Carlo method. We compare ERG subgraph counts and edge correlations to those of the classic Binomial Random Graph (BRG, also called Erdos-Renyi model). It is a known theoretical result that for some parameterizations the limit ERG subgraph counts converge to those of BRGs, as the number of vertices grows [BBS11, CD11]. We observe this phenomenon on graphs with few (20) vertices in our simulations.

Species conservation initiatives play an important role in ecological studies. Occupancy models have been a useful tool for ecologists to make inference about species distribution and occurrence. Bayesian methodology is a popular framework used to model the relationship between species and environmental variables. In this dissertation we develop a Gibbs sampling method using a logit link function in order to model posterior parameters of the single-season spatial occupancy model. We incorporate the widely used Intrinsic Conditional Autoregressive (ICAR) prior model to specify the spatial random effect in our sampler. We also develop OccuSpytial, a statistical package implementing our Gibbs sampler in the Python programming language. The aim of this study is to highlight the computational efficiency that can be obtained by employing several techniques, which include exploiting the sparsity of the precision matrix of the ICAR model and also making use of Polya-Gamma latent variables to obtain closed form expressions for the posterior conditional distributions of the parameters of interest. An algorithm for efficiently sampling from the posterior conditional distribution of the spatial random effects parameter is also developed and presented. To illustrate the sampler's performance a number of simulation experiments are considered, and the results are compared to those obtained by using a Gibbs sampler incorporating Restricted Spatial Regression (RSR) to specify the spatial random effect. Furthermore, we fit our model to the Helmeted guineafowl (Numida meleagris) dataset obtained from the 2nd South African Bird Atlas Project database in order to obtain a distribution map of the species. We compare our results with those obtained from the RSR variant of our sampler, those obtained by using the stocc statistical package (written using the R programming language), and those obtained from not specifying any spatial information about the sites in the data. It was found that using RSR to specify spatial random effects is both statistically and computationally more efficient that specifying them using ICAR. The OccuSpytial implementations of both ICAR and RSR Gibbs samplers has significantly less runtime compared to other implementations it was compared to.

京都大学 / 0048 / 新制・課程博士 / 博士(農学) / 甲第22514号 / 農博第2418号 / 新制||農||1078(附属図書館) / 学位論文||R2||N5294(農学部図書室) / 京都大学大学院農学研究科地域環境科学専攻 / (主査)教授 村上 章, 教授 藤原 正幸, 教授 磯 祐介 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DGAM

This thesis is focused on possibilities of a project development prediction and a decision support for managers of those projects, which is an up to date topic in the present time turbulent environment. Project is understood as a stochastic process with discrete states and discrete time in this thesis. This approach could be represented by discrete moments of finding out project state. Project is compared to a finite automaton and Markovs chains are subsequently used. State model of the project based on Earned Value Management method is created in the proposal part of this thesis and there are state transitions probabilities. There are adjustments of the model designed consequently so the model is capable to fit some concrete situation closely. Designed proposals are tested in different situations to prove their value in the experimental part of this work.

Dans cette thèse nous essayons de comprendre pourquoi le Principe de Maximisation de Production d'Entropie (MEP) donne de très bons résultats dans de nombreux domaines de la physique hors équilibre et notamment en climatologie. Pour ce faire nous étudions ce principe sur des systèmes jouets de la physique statistique qui reproduisent les comportements des modèles climatiques. Nous avons notamment travaillé sur l'Asymmetric Simple Exclusion Process (ASEP) et le Zero Range Process (ZRP). Ceci nous a permis tout d'abord de relier MEP à un autre principe qui est le principe de maximisation d'entropie de Kolmogorov-Sinai (MKS). De plus, l'application de MEP à ces systèmes jouets donne des résultats physiquement cohérents. Nous avons ensuite voulu étendre le lien entre MEP et MKS dans des systèmes plus compliqués avant de montrer que, pour les chaines de Markov, maximiser l'entropie de KS revenait à minimiser le temps que le système prend pour atteindre son état stationnaire (mixing time). En fin nous avons appliqué MEP à la convection atmosphérique. / In this thesis we try to understand why the maximum entropy production principlegives really good results in a wide range of Physics fields and notably in climatology. Thus we study this principle on classical toy models which mimic the behaviour of climat models. In particular we worked on the Asymmetric Simple Exclusion Process(ASEP) and on the Zero Range Process (ZRP). This enabled us first to connect MEP to an other principle which is the maximum Kolmogorov-Sinaï entropy principle (MKS). Moreover the application of MEP on these systems gives results that are physically coherent. We then wanted to extend this link between MEP and MKS in more complicated systems, before showing that, for Markov Chains, maximise the KS entropy is the same as minimise the time the system takes to reach its stationnary state (mixing time). Thus, we applied MEP to the atmospheric convection.

This thesis investigates dierent types of Monte Carlo estimators for use in computationof chemical system, mainly to be used in calculating surface growthand evolution of SiC. Monte Carlo methods are a class of algorithms using randomsampling to numerical solve problems and are used in many cases. Threedierent types of Monte Carlo methods are studied, a simple Monte Carlo estimatorand two types of Markov chain Monte Carlo Metropolis algorithm MonteCarlo and kinetic Monte Carlo. The mathematical background is given for allmethods and they are tested both on smaller system, with known results tocheck their mathematical and chemical soundness and on larger surface systemas an example on how they could be used

One of the most significant changes in the evolution of modern business management is that organizations no longer compete as individual entities in the market, but as interlocking supply chains. Markets are no longer simply trading desks but dynamic ecosystems where people, organizations and the environment interact. Products and associated materials and resources are links that bridge supply chains from upstream (sourcing and manufacturing) to downstream (delivering and consuming). The lifecycle of a product plays a critical role in supply chains. Supply chains may be composed by, designed around, and modified for products. Product-related issues greatly impact supply chains. Existing studies have advanced product management and product lifecycle management literature through dimensions of product innovation, product growth, product line extensions, product efficiencies, and product acquisition. Product deletion, rationalization, or reduction research is limited but is a critical issue for many reasons. Sustainability is an important reason for this managerial decision. This study, grounded from multiple literature streams in both marketing and supply chain fields, identified relations and propositions to form a firm-level analysis on the role of supply chains in organizational product deletion decisions. Interviews, observational and archival data from international companies (i.e.: Australia, China, India, and Iran) contributed to the empirical support as case studies through a grounded theory approach. Bayesian analysis, an underused empirical analysis tool, was utilized to provide insights into this underdeveloped research stream; and its relationship to qualitative research enhances broader methodological understanding. Gibbs sampler and reversible jump Markov chain Monte Carlo (MCMC) simulation were used for Bayesian analysis based on collected data. The integrative findings are exploratory but provide insights for a number of research propositions.