Las Cadenas de Markov son sucesiones de variables aleatorias que permiten evaluar la probabilidad con la que un estado actual puede alcanzar uno inmediatamente posterior. Se ha utilizado en diversas aplicaciones como predicciones de escenarios económicos, patrones de compra, estimación de indicadores, administración de inventarios, proyecciones demográficas, pronósticos de votación, etc. En el presente trabajo se mostrarán aplicaciones no convencionales de Cadenas de Markov, las cuales han sido orientadas a disciplinas artísticas, con la finalidad de desmitificar la aparente incompatibilidad entre las matemáticas y las artes. Entre las mencionadas aplicaciones se encuentran dos composiciones musicales contemporáneas, creadas utilizando como referencia la obra musical de una banda predeterminada. Dichas composiciones obtenidas guardan notoria relación con el estilo musical de la banda referencial. Los archivos de audio se encuentran adjuntos al presente documento. Del mismo modo, se muestran poesías y textos generados con esta aplicación matemática y que guardan relación con el estilo literario de escritores tomados como referencia. Finalmente se mostrarán aplicaciones de las Cadenas de Markov para la Generación de Imágenes y Videos a través de sistemas generativos, disciplina denominada “Arte Procesual-Aleatorio”. / Tesis

This dissertation consists of three main essays in which we study important problems in engineering and finance. In the first part of this dissertation, we study the use of Information Relaxations to obtain dual bounds in the context of Partially Observable Markov Decision Processes (POMDPs). POMDPs are in general intractable problems and the best we can do is obtain suboptimal policies. To evaluate these policies, we investigate and extend the information relaxation approach developed originally for Markov Decision Processes. The use of information relaxation duality for POMDPs presents important challenges, and we show how change-of-measure arguments can be used to overcome them. As a second contribution, we show that many value function approximations for POMDPs are supersolutions. By constructing penalties from supersolutions we are able to achieve significant variance reduction when estimating the duality gap directly, and the resulting dual bounds are guaranteed to provide tighter bounds than those provided by the supersolutions themselves. Applications in robotic navigation and telecommunications are given in Chapter 2. A further application of this approach is provided in Chapter 5 in the context of personalized medicine. In the second part of this dissertation, we discuss a number of weaknesses inherent in traditional scenario analysis. For instance, the standard approach to scenario analysis aims to compute the P&L of a portfolio resulting from joint stresses to underlying risk factors, leaving all unstressed risk factors set to zero. This approach ignores thereby the conditional distribution of the unstressed risk factors given the stressed risk factors. We address these weaknesses by embedding the scenario analysis within a dynamic factor model for the underlying risk factors. We recur to multivariate state-space models that allow the modeling of real-world behavior of financial markets, like volatility clustering for example. Additionally, these models are sufficiently tractable to permit the computation (or simulation from) the conditional distribution of unstressed risk factors. Our approach permits the use of observable and unobservable risk factors. We provide applications to fixed income and options portfolios, where we are able to show the degree in which the two scenario analysis approaches can lead to dramatic differences. In the third part, we propose a framework to study a Human-Machine interaction system within the context of financial Robo-advising. In this setting, based on risk-sensitive dynamic games, the robo-advisor adaptively learns the preferences of the investor as the investor makes decisions that optimize her risk-sensitive criterion. The investor and machine's objectives are aligned but the presence of asymmetric information makes this joint optimization process a game with strategic interactions. By considering an investor with mean-variance risk preferences we are able to reduce the game to a POMDP. The human-machine interaction protocol features a trade-off between allowing the robo-advisor to learn the investors preferences through costly communications and optimizing the investor's objective relying on outdated information.

The increased globalisation of information and communication technologies has transformed the world into the internet of things (IoT), which is accomplished within the resources of wireless sensor networks (WSNs). Therefore, the future IoT networks will consist of high density of connected nodes that suffer from resource limitation, especially the energy one, and distribute randomly in a harsh and large-scale areas. Accordingly, the contributions in this thesis are focused on the development of energy efficient design protocols based on optimisation algorithms, with consideration of the resource limitations, adaptability, scalability, node density and random distribution of node density in the geographical area. One MAC protocol and two routing protocols, with both a static and mobile sink, are proposed. The first proposed protocol is an energy efficient hybrid MAC protocol with dynamic sleep/wake-up extension to the IEEE 802.15.4 MAC, namely, HSW-802.15.4. The model automates the network by enabling it to work exibly in low and high-density networks with a lower number of collisions. A frame structure that offers an enhanced exploitation for the TDMA time slots (TDMAslots) is provided. To implement these enhanced slots exploitation, this hybrid protocol rst schedules the TDMAsslots, and then allocates each slot to a group of devices. A three-dimensional Markov chain is developed to display the proposed model in a theoretical manner. Simulation results show an enhancement in the energy conservation by 40% - 60% in comparison to the IEEE 802.15.4 MAC protocol. Secondly, an efficient centralised clustering-based whale optimisation algorithm (CC- WOA) is suggested, which employs the concept of software de ned network (SDN) in its mechanism. The cluster formulation process in this algorithm considers the random di- versi cation of node density in the geographical area and involves both sensor resource restrictions and the node density in the tness function. The results offer an efficient con- servation of energy in comparison to other protocols. Another clustering algorithm, called centralised load balancing clustering algorithm (C-LBCA), is also developed that uses par- ticle swarm optimisation (PSO) and presents robust load-balancing for data gathering in IoT. However, in large scale networks, the nodes, especially the cluster heads (CHs), suffer from a higher energy exhaustion. Hence, in this thesis, a centralised load balanced and scheduling protocol is proposed utilising optimisation algorithms for large scale IoT net- works, named, optimised mobile sink based load balancing (OMS-LB). This model connects the impact of the Optimal Path for the MS (MSOpath) determination and the adjustable set of data aggregation points (SDG) with the cluster formulation process to de ne an op- timised routing protocol suitable for large scale networks. Simulation results display an improvement in the network lifespan of up to 54% over the other approaches.

by Liang Fa Ming. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (p. 150-161). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web.

Li, Chung Fai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (p. 43). / Abstracts in English and Chinese. / Acknowledgement --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Construction of the State Spaces --- p.5 / Chapter 2.1 --- The Sierpinski Gasket --- p.5 / Chapter 2.1.1 --- Neighbourhood in the Sierpinski Gasket --- p.7 / Chapter 2.2 --- The Sierpinski Carpet --- p.9 / Chapter 2.2.1 --- Neighbourhood in the Sierpinski Carpet --- p.10 / Chapter 3 --- Preliminary Random Processes on Each Level --- p.12 / Chapter 3.1 --- The Sierpinski Gasket --- p.12 / Chapter 3.1.1 --- Definitions --- p.12 / Chapter 3.1.2 --- Properties of the Random Walk --- p.13 / Chapter 3.1.3 --- Preparations for convergence and continuity --- p.16 / Chapter 3.2 --- The Sierpinski Carpet --- p.19 / Chapter 3.2.1 --- The Brownian Motion Bn on Cn --- p.19 / Chapter 3.2.2 --- Properties of Bm(t) --- p.20 / Chapter 3.2.3 --- Exit time for Bn --- p.27 / Chapter 4 --- The limiting process --- p.29 / Chapter 4.1 --- The Sierpinski Gasket --- p.29 / Chapter 4.1.1 --- Convergence and continuity --- p.29 / Chapter 4.1.2 --- Extension from to G --- p.31 / Chapter 4.1.3 --- Markov property --- p.33 / Chapter 4.2 --- The Sierpinski Carpet --- p.34 / Chapter 4.2.1 --- Continuity --- p.34 / Chapter 4.2.2 --- Existence of Markov process on C --- p.37 / Chapter 4.2.3 --- Piecing Together --- p.38 / Bibliography --- p.43

Diabetes mellitus is a chronic disease in which the body does not produce sufficient insulin or in which the body has high insulin resistance thus making the regulation of blood glucose metabolism difficult. Currently, diabetes is still incurable. All patients need to well manage their blood glucose levels to reduce the risk of complications. This dissertation is comprised of two major studies. In diabetes type I, the blood glucose can only be managed by multiple daily injection of insulin. However, most patients tend to have difficulty in deciding the right amount of insulin dose. The first study is the development of a mathematical model of blood glucose levels, which leads to the development of a decision support system for diabetes type I using the Markov theory. In some type II and gestational diabetes, blood glucose can be managed by choosing diet properly and by exercising regularly. However, people tend to overestimate their activity levels. The second study describes the design and development of a wearable device based on the triaxial accelerometer that estimates the energy levels of normal daily physical activity with comparable accuracy to the gas analysis. This device development leads to two clinical studies. The first clinical study investigates whether the energy monitor could help people with diabetes in promoting and managing their daily activity and help to improve the glycosylated haemoglobin and body mass index. The second clinical study investigates whether the energy monitor could help pregnant women with gestational diabetes in managing their daily activity, blood glucose levels and body weight gain. This thesis also develops a telemedicine system to automate the data collection during the clinical trial period. The system would securely transmit all diabetes and energy data from the participants' home to a remote server. A key finding of this study was that a higher activity score results in smaller fluctuations in blood glucose levels between measurements in both diabetes and gestational diabetes subjects. This suggests that higher activity levels would make the management of diabetes more effective by reducing the fluctuation in blood glucose levels.

For the prediction of chaotic time series, a dichotomy has arisen between local approaches and global approaches. Local approaches hold the reputation of simplicity and feasibility, but they generally do not produce a compact description of the underlying system and are computationally intensive. Global approaches have the advantage of requiring less computation and are able to yield a global representation of the studied time series. However, due to the complexity of the time series process, it is often not easy to construct a global model to perform the prediction precisely. In addition to these approaches, a combination of the global and local techniques, called mixture of experts (ME), is also possible, where a smaller number of models work cooperatively to implement the prediction. This thesis reports on research about ME models for chaotic time series prediction. Based on a review of the techniques in time series prediction, a HMM-based ME model called "Time-line" Hidden Markov Experts (THME) is developed, where the trajectory of the time series is divided into some regimes in the state space and regression models called local experts are applied to learn the mapping on the regimes separately. The dynamics for the expert combination is a HMM, however, the transition probabilities are designed to be time-varying and conditional on the "real time" information of the time series. For the learning of the "time-line" HMM, a modified Baum-Welch algorithm is developed and the convergence of the algorithm is proved. Different versions of the model, based on MLP, RBF and SVM experts, are constructed and applied to a number of chaotic time series on both one-step-ahead and multi-step-ahead predictions. Experiments show that in general THME achieves better generalization performance than the corresponding single models in one-step-ahead prediction and comparable to some published benchmarks in multi-step-ahead prediction. Various properties of THME, such as the feature selection for trajectory dividing, the clustering techniques for regime extraction, the "time-line" HMM for expert combination and the performance of the model when it has different number of experts, are investigated. A number of interesting future directions for this work are suggested, which include the feature selection for regime extraction, the model selection for transition probability modelling, the extension to distribution prediction and the application on other time series.

Precipitation is an important element in the hydrological cycle. To predict and simulate large-scale precipitation, Global Circulation Models (GCMs) are widely used. However, their grid scale is too big to apply to local hydrologic fields. In this study, non-homogenous hidden Markov models (NHMM) are explored as a means of generating the probability of precipitation occurrence in small scale given large-scaled weather patterns. Three different spatial models: (1) independent (2) auto-logistic (3) Chow-Liu tree, are also explored, along with methods and steps for parameter estimation. From this exploration, independent models with NHMM are recommended for very small precipitation networks, and the maximum likelihood method is found to be the most practical fitting method. If there are many points for downscaling, Chow-Liu tree models with the Expectation-Maximization (EM) algorithm are recommended. If more exact solutions are needed, auto-logistic models can be employed. If many points are considered in auto-logistic models, the (EM) algorithm should be used to estimate parameters separately and global optimization methods should be used for emission matrix. The major problem found with the NHMM model in this study is matching the rainfall amount for each year or month. This problem can be addressed by whether combining occurrence models with amount modes or by improving only occurrence models.

Reproduction de : Thèse de doctorat : Systèmes automatiques : Toulouse, INPT : 2006. / Titre provenant de l'écran-titre. Bibliogr. 83 réf.

Reproduction de : Thèse de doctorat : Informatique : Grenoble, INPG : 1992. / Titre provenant de l'écran-titre. Bibliogr. p. 225-228.