Thesis (M.Soc.Sc.)--University of Hong Kong, 1993. / Includes bibliographical references. Also available in print.

Thesis (Ph. D.)--Texas State University-San Marcos, 2007. / Vita. Appendices: leaves 194-207. Includes bibliographical references (leaves 208-209).

Thesis (doctoral)--Technical University of Delft, 2006 / Includes bibliographical references (p. 173-191) and index.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 115-119).

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Orientador: Simão Nicolau Stelmastchuk / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-17T21:13:11Z (GMT). No. of bitstreams: 1 Vieira_FranciscoZuiltonGoncalves_M.pdf: 2460011 bytes, checksum: bb34e809ab256fe3bb3b1bd74fc35eec (MD5) Previous issue date: 2011 / Resumo: Esta dissertação tem como tema o estudo das cadeias de Markov discretas com valores em um espaço de estados enumerável. Cadeias de Markov são processos estocásticos no seguinte sentido: dado o momento presente, o futuro não depende do passado, mas somente do momento presente. Nosso estudo é realizado sobre cadeias de Markov homogêneas (CMH) discretas. Inicialmente, introduzimos a definição e conceitos básicos das CMH discretas. Tais estudos nos conduzem ao conceito de topologia das matrizes de Transição associada as CMH. A topologia de tais cadeias é a ferramenta necessária para o estudo dos conjuntos recorrentes e transcientes, os quais são de grande importância nesta teoria. O estudo de estados estacionários e a propriedade forte de Markov também são abordados. Esta última propriedade serve para construção do conceito de estado recorrente. A partir deste último conceito trabalhamos com os conceitos de positivo e nulo recorrente. Por fim, estudamos o importante conceito de tempo absorção, o qual é entendido como o tempo que algum estado é absorvido a um conjunto recorrente / Abstract: This dissertation deals with the study of discrete Markov chains with values in a countable state space. Markov chains are processes stochastic in the following sense: given the present moment, the future does not depend on the past, but only in the present moment. Our study is conducted on homogeneous Markov chains (HMC) discrete. Initially, we introduced the definition and the basic concepts of discrete HMC. Such studies lead us to understand the concept of topology Transition matrices associated to HMC. The topology of these chains is a necessary tool for the study of the recurrent and transient sets, which are of great importance in this theory. The study of steady states and the strong Markov properties are also addressed. This latter property serves to build the concept of recurrent state. From this latter concept we work with the concepts of positive and null recurrent. Finally, we studied the important concept of absorption time, which is understood as the time that some state is absorbed to a set recurrent / Mestrado / Matematica / Mestre em Matemática

Point processes are mechanisms that beget point patterns. Realisations of point processes are observed in many contexts, for example, locations of stars in the sky, or locations of trees in a forest. Inferring the mechanisms that drive point processes relies on the development of models that appropriately account for the dependencies inherent in the data. Fitting models that adequately capture the complex dependency structures in either space, time, or both is often problematic. This is commonly due to—but not restricted to—the intractability of the likelihood function, or computational burden of the required numerical operations. This thesis primarily focuses on developing point process models with some hierarchical structure, and specifically where this is a latent structure that may be considered as one of the following: (i) some unobserved construct assumed to be generating the observed structure, or (ii) some stochastic process describing the structure of the point pattern. Model fitting procedures utilised in this thesis include either (i) approximate-likelihood techniques to circumvent intractable likelihoods, (ii) stochastic partial differential equations to model continuous spatial latent structures, or (iii) improving computational speed in numerical approximations by exploiting automatic differentiation. Moreover, this thesis extends classic point process models by considering multivariate dependencies. This is achieved through considering a general class of joint point process model, which utilise shared stochastic structures. These structures account for the dependencies inherent in multivariate point process data. These models are applied to data originating from various scientific fields; in particular, applications are considered in ecology, medicine, and geology. In addition, point process models that account for the second order behaviour of these assumed stochastic structures are also considered.

Atmospheric particles play a crucial role in climate, visibility, air pollution, and human health. Reactions between gas-phase molecules and particles (heterogeneous reactions) affect not only the particle composition and morphology, but also the composition of the atmosphere. This thesis investigates the heterogeneous chemistry of organic mixtures and inorganic solutions coated with organic monolayers as proxies for atmospheric particles. The first topic of interest was the reaction between N₂0₅ and aqueous inorganic solutions coated with organic monolayers. The goal of this work was to better understand how organic monolayers on aqueous particles affect the mass transport and kinetics of N₂0₅ uptake by aqueous aerosols, and consequently what effectthe monolayer can have on predicted concentrations of N₂0₅ in the atmosphere. To investigate heterogeneous reactions of inorganic solutions coated with an organic monolayer a new rectangular channel flow reactor was developed. This newly developed flow reactor was described in detail and validated. Subsequently, the new flow reactor was used to study the reactive uptake of N₂0₅ on sulfuric acid solutions in the presence of a variety of 1- and 2-component monolayers with varying functional groups, solubilities, chain lengths, surface pressures, and molecular surface areas. Reactive uptake of N₂0₅ on aqueous sulfuric acid solutions was found to correlate most strongly with the molecular surface area or packing density of the monolayer. These results provide a good foundation for determining the influence of monolayers on heterogeneous reactions in the atmosphere, and highlight the need for characterization of monolayer surface properties of organic monolayers present on atmospheric particles. The second topic of interest was reactions between 0₃ and proxies for meat cooking aerosols with the goal to better understand the effect of the phase and microstructure of the mixtures on the lifetime of oleic acid (OA) in atmospheric particles. The reactive uptake of 0₃ was approximately 1 order of magnitude slower on binarysolid-liquid mixtures and multicomponent mixtures that closely represent compositions of meat-cooking aerosols compared to the liquid solutions. Lifetimes up to 75 min were obtained for these mixtures. / Science, Faculty of / Chemistry, Department of / Graduate

This thesis mainly focuses on the statistical modelling of a selection of games, namely, the minority game, the urn model and the Hawk-Dove game. Chapters 1 and 2 give a brief introduction and survey of the field. In Chapter 3, the key characteristics of the minority game are reproduced. In addition, the minority game is extended to include wealth distribution and leverage effect. By assuming that each player has initial wealth which rises and falls according to profit and loss, with the potential of borrowing and bankruptcy, we find that modelled wealth distribution may be power law distributed and leverage increases the instability of the system. In Chapter 4, to explore the effects of memory, we construct a model where agents with memories of different lengths compete for finite resources. Using analytical and numerical approaches, our research demonstrates that an instability exists at a critical memory length; and players with different memory lengths are able to compete with each other and achieve a state of co-existence. The analytical solution is found to be connected to the well-known urn model. Additionally, our findings reveal that the temperature is related to the agent's memory. Due to its general nature, this memory model could potentially be relevant for a variety of other game models. In Chapter 5, our main finding is extended to the Hawk-Dove game, by introducing the memory parameter to each agent playing the game. An assumption is made that agents try to maximise their profits by learning from past experiences, stored in their finite memories. We show that the analytical results obtained from these two games are in agreement with the results from our simulations. It is concluded that the instability occurs when agents' memory lengths reach the critical value. Finally, Chapter 6 provides some concluding remarks and outlines some potential future work.

We develop several new algorithms using molecular simulation to investigate the nucleation barrier of a single, freely-jointed polymer chain. In the first part of the thesis, we use a free particle model to develop a new biasing technique, which uses an automated feedback mechanism to overcome the poor sampling of crystal states in a thermodynamic system. Our feedback technique does not require any prior knowledge of the nucleation barrier and enables good representative sampling of all available states of interest. In the second part of the thesis, we simulate the nucleation barrier of the single, freely-jointed, square-well chain. We use our feedback technique and parallel tempering with a nonstandard temperature distribution to overcome poor sampling of crystal states and configuration mixing issues respectively. We also provide some comparative analysis of different choices of configurational order parameters for the single chain. Finally, we apply stretching to the chain to approximate flow-induced crystallisation and investigate the effect of different degrees of stretch on the nucleation barrier. We verify the quality of our simulation with careful monitoring of several criteria, including the acceptance ratios of configuration swaps between simulations with adjacent temperatures, evolution of the energy traces as a result of configuration swaps between tempering levels, and ensuring effective de-correlation of configurations through reptation moves. Our simulations provide strong reproducible results for the base, the peak and beyond the peak of the barrier for the quiescent and stretched single chain. We observe a remarkably strong effect of modest stretching on the nucleation barrier for a single chain, which can potentially lead to dramatic effects on the nucleation rate. Our simulation code has been made publicly available, with details provided in an appendix.