O processo evolutivo deixa vieses no sistema nervoso de forma a optimizar nossas capacidades cognitivas para o ambiente em que evoluímos. Nosso objetivo é criar modelos de vida artificial nos quais a atenção seletiva, a tomada de decisão em sequências binárias e o tempo de reação ao aparecimento abrupto de um alvo precedido por pista emerjam como consequência da evolução. Em nossos experimentos, a atenção seletiva enviesava o processamento de estímulos de forma a dar prioridade aos mais relevantes quando eles tinham relevâncias diferentes. Nossos experimentos de tomada de decisão apóiam a teoria de que o pareamento de probabilidades, estratégia adotada por seres humanos neste tipo de experimento, é consequência da busca de padrões, que decorre da importância que isto teve durante a evolução humana. No estudo do tempo de reação, o comportamento observado em seres humanos só pôde ser modelado em populações de animais artificiais quando existia ruído e eles tinham que selecionar uma ação apropriada entre duas possíveis. / The evolutionary process leaves biases in the nervous system so as to optimize our cognitive capacities to the environment where we evolved. Our objective is to create artificial life models wherein selective attention, decision making in binary sequences and reaction time to the abrupt appearance of a target preceded by a cue emerge as a consequence of evolution. In our experiments, selective attention biased stimuli processing so as to give priority to the most relevant stimuli when they had different relevances. Our decision making experiments support the theory that probability matching, the strategy adopted by humans in this kind of experiment, is a consequence of a search for patterns, which results from the importance that finding regularities in our environment had during human evolution. In the study of reaction time, the behavior observed in humans could only be modeled in populations of artificial animal when there was noise and they had to select an appropriate action between two possible ones.

Au cours des dernières années, les fournisseurs de contenu ont connu une forte augmentation des demandes de contenus vidéo et de services riches en média. Compte tenu des limites de la mise à l'échelle du réseau et au-delà des réseaux de diffusion de contenu, les fournisseurs de services Internet développent leurs propres systèmes de mise en cache afin d'améliorer la performance du réseau. Ces facteurs expliquent l'enthousiasme à l'égard du concept de réseau centré sur le contenu et de sa fonction de mise en cache en réseau. La quantification analytique de la performance de la mise en cache n'est toutefois pas suffisamment explorée dans la littérature. De plus, la mise en place d'un système de caching efficace au sein d'une infrastructure réseau est très complexe et demeure une problématique ouverte. Pour traiter ces questions, nous présentons d'abord dans cette thèse un modèle générique et précis de cache nommé MACS (Markov chain-based Approximation of Caching Systems) qui peut être adapté très facilement pour représenter différents schémas de mise en cache et qui peut être utilisé pour calculer différentes mesures de performance des réseaux multi-cache. Nous avons ensuite abordé le problème de l'allocation des ressources de cache dans les réseaux avec capacité de caching. Moyennant notre outil analytique MACS, nous présentons une approche permettant de résoudre le compromis entre différentes mesures de performance en utilisant l'optimisation multi-objectif et nous proposons une adaptation de la métaheuristique GRASP pour résoudre le problème d'optimisation. / In the last few years, Content Providers (CPs) have experienced a high increase in requests for video contents and rich media services. In view of the network scaling limitations and beyond Content Delivery Networks (CDNs), Internet Service Providers (ISPs) are developing their own caching systems in order to improve the network performance. These factors explain the enthusiasm around the Content-Centric Networking (CCN) concept and its in-network caching feature. The analytical quantification of caching performance is, however, not sufficiently explored in the literature. Moreover, setting up an efficient caching system within a network infrastructure is very complex and remains an open problem. To address these issues, we provide first in this thesis a fairly generic and accurate model of caching nodes named MACS (Markov chain-based Approximation of Caching Systems) that can be adapted very easily to represent different caching schemes and which can be used to compute different performance metrics of multi-cache networks. We tackled after that the problem of cache resources allocation in cache-enabled networks. By means of our analytical tool MACS, we present an approach that solves the trade-off between different performance metrics using multi-objective optimization and we propose an adaptation of the metaheuristic GRASP to solve the optimization problem.

A hipertensão arterial sistêmica (HAS) é um fator de risco para 9,4 milhões de mortes em todo o mundo. No Brasil, a HAS atribui um custo anual de aproximadamente R$ 969,231,436,00 ao Sistema Único de Saúde (SUS). Alguns estudos têm mostrado uma grande efetividade da Atenção Farmacêutica (ATF) para melhorar os parâmetros clínicos de pacientes com HAS. Diante desse contexto, este trabalho teve o objetivo de desenvolver uma ferramenta econômica considerando custos e desfechos para auxiliar os gestores de saúde a implantar a ATF no SUS e reduzir a morbi-mortalidade ocasionada pela HAS. Para isso, foi conduzido um estudo farmacoeconômico de modelagem com análises de custo-efetividade, custo-benefício e custo-utilidade. Em duas unidades básicas do SUS, em Ribeirão Preto, 104 pacientes foram acompanhados por um programa de ATF durante o ano de 2009. Foram coletados dados clínicos, assistenciais e econômicos referentes aos anos de 2006 a 2012. Os dados foram divididos por períodos, 2006-2008 (pré ATF), 2009 (ATF) e 2010-2012 (pós ATF). A análise econômica foi realizada em cinco etapas: análise direta dos custos, análise indireta dos custos com modelagem de Markov, análise de custo-benefício com obtenção do valor presente líquido (VPL), análise de sensibilidade dos custos, e análise do impacto epidemiológico. O controle pressórico foi alcançado em 54,4%, 98,2% e 93,0% dos pacientes nos períodos pré ATF, ATF e pós ATF, respectivamente. Na análise direta dos custos houve diferença dos custos totais de -R$307,23 e R$4.053,32 e a razão de custo efetividade incremental foi R$1.124,24 e R$100,98, nos períodos ATF e pós ATF, respectivamente. Na projeção por modelagem de Markov houve 46 complicações da HAS e 17 mortes; e 15 complicações e 5 mortes ao longo de dez anos para a assistência a saúde sem a ATF e com a ATF, respectivamente. Houve o custo por paciente de R$ 17,09 / anos de vida ajustados por qualidade e R$ 28,98 por anos de vida ganhos após a alta da ATF. O VPL obtido com o investimento nesta prática farmacêutica foi R$ 3.791.111,13 e a razão benefício - custo (RBC) foi 30,03 (26,74 - 34,28), RBC > 1 com taxa de retorno de investimento de 303%. Conclui-se que a ATF foi capaz de melhorar o controle pressórico e os níveis de colesterol total reduzindo o risco cardiovascular, o que ocasionou a redução de gastos com a saúde e o impacto positivo epidemiológico. Essa análise foi suficiente para fundamentar uma ferramenta farmacoeconômica capaz de auxiliar os gestores na tomada de decisão quanto à implementação da ATF para a redução da morbi-mortalidade ocasionada pela HAS. / Systemic Arterial Hypertension (SAH) is a risk factor for 9.4 million deaths worldwide. In Brazil, SAH assigns an annual cost of approximately R$969,231,436,00 the Public Health System (PHS). Some studies have shown a great effectiveness of pharmaceutical care (PC) to improve clinical parameters of patients with SAH. In this context, this study aimed to develop an economic tool considering costs and outcomes to help health managers to deploy the PC in the PHS and reduce the morbidity and mortality caused by hypertension. For this, a pharmacoeconomic modeling study of cost-effectiveness analysis, cost-benefit and cost-utility was conducted. Into two basic units of PHS, in Ribeirão Preto, 104 patients were followed for an PC program during 2009. Clinical, healthcare and economic data were collected for the years 2006 to 2012. The data were divided into periods, 2006-2008 pre PC, 2009 PC and 2010-2012 post-PC. The economic analysis was carried out in five stages: Direct cost analysis; indirect cost analysis with Markov modeling; Cost-benefit analysis to obtain the net present value (NPV); Sensitivity analysis of the costs and analysis of epidemiological impact. The pressure control of patients was 54.4%, 98.2% and 93% in the pre PC, PC and post-PC, respectively. In direct cost analysis the difference between the total cost was -R$ 307.23 and R$ 4,053.32; the Incremental Cost Effectiveness Ratio was R$ 1,124.24 and R$ 100.98 for the periods PC and post-PC, respectively. There were 46 complications of hypertension and 17 deaths; and 15 complications and 5 deaths over ten years for health care without the PC and with PC, respectively. The cost per patient was R$ 17.09 / quality-adjusted life years and R$ 28.98 per year of life saved after discharge from the PC. The NPV obtained with the investment in this pharmaceutical practice was R$ 3,791,111.13 and the Benefit-cost Ratio (BCR) was 30.03 (26.74 - 34.28), BCR > 1 and investment return rate was 303%. It was concluded that the PC was able to improve the blood pressure control and total cholesterol level reducing the cardiovascular risk. That meant reduction spending on health and a positive epidemiological impact. This analysis was enough to develop a pharmacoeconomic tool that can assist managers in making decisions regarding the implementation of PC to reduce morbidity and mortality caused by SAH.

Introdução: A curva de crescimento é um modelo empírico da evolução de uma quantidade ao longo do tempo. As curvas de crescimento são utilizadas em muitas disciplinas , em particular no domínio da estatística, onde há uma grande literatura sobre o assunto relacionado a modelos não lineares. Método:No desenvolvimento dessa dissertação de mestrado, foi realizado um estudo baseado em dados de crescimento nas áreas biológica e médica para comparar os dois tipos de inferência (Clássica e Bayesiana), na busca de melhores estimativas e resultados para modelos de regressão não lineares, especialmente considerando alguns modelos de crescimento introduzidos na literatura. No método Bayesiano para a modelagem não linear assumimos erros normais uma suposição usual e também distribuições estáveis para a variável resposta. Estudamos também alguns aspectos de robustez dos modelos de regressão não linear para a presença de outliers ou observações discordantes considerando o uso de distribuições estáveis para a resposta no lugar da suposição de normalidade habitual. Resultados e Conclusões: Análise dos dois exemplos pode-se observar melhores ajustes quando utilizada o método Bayesiano de ajustes de modelos não lineares de curvas de crescimento. É bem sabido que, em geral, não há nenhuma forma fechada para a função densidade de probabilidade de distribuições estáveis. No entanto, sob uma abordagem Bayesiana, a utilização de uma variável aleatória latente ou auxiliar proporciona uma simplificação para obter qualquer distribuição a posteriori quando relacionado com distribuições estáveis. Esses resultados poderiam ser de grande interesse para pesquisadores e profissionais, ao lidar com dados não Gauss. Para demonstrar a utilidade dos aspectos computacionais, a metodologia é aplicada a um exemplo relacionado com as curvas de crescimento intra-uterino para prematuros. Resumos a posteriori de interesse são obtidos utilizando métodos MCMC (Markov Chain Monte Carlo) e o software OpenBugs. / Introduction: The growth curve is an empirical model of the evolution of a quantity over time. Growth curves are used in many disciplines, particularly in the field of statistics, where there is a large literature on the subject related to nonlinear models. Method: In the development of this dissertation, a study based on data growth in biological areas and medical was conducted to compare two types of inferences (Classical and Bayesian), in search of better estimates and results for nonlinear regression models, especially considering some growth models introduced in the literature. The Bayesian method for nonlinear modeling assume normal errors an usual assumption and also stable distributions for the response variable. We also study some aspects of robustness of nonlinear regression models for the presence of outliers or discordant observations regarding the use of stable distributions to the response in place of the usual assumption of normality. Results and Conclusions: In the analysis of two examples it can be seen best results using Bayesian methodology for non linear models of growth curves. It is well known that, in general, there is no closed form for the probability density function of stable distributions. However, under a Bayesian approach, the use of a latent random variable or auxiliary variable provides a simplification to get every conditional posterior related to stable distributions. These results could be of great interest to researchers and practitioners when dealing with non-Gaussian data. To demonstrate the utility of the computational aspects, the methodology is also applied to an example related to intrauterine growth curves for premature infants. Posterior summaries of interest are obtained using MCMC methods (MCMC) and the OpenBugs software.

Nesta dissertação foram estudados alguns modelos vetoriais que pretendem modelar e descrever alguns aspectos de sistemas sociais e de sua organização cultural. Partimos do modelo de Axelrod, um processo estocástico definido em uma rede, e introduzimos uma pequena alteração no modelo que desencadeou mudanças qualitativas interessantes, especialmente o surgimento de uma tensão superficial, que leva ao aparecimento de estados metaestáveis e de regiões culturais mais fixamente localizadas no espaço. Através da ótica da mecânica estatística e de extensas simulações computacionais, exploramos alguns dos aspectos que julgamos mais importantes na caracterização desse rico modelo. / Axelrod\'s model for cultural dissemination is a discrete vector representation for modeling social and cultural systems. In this work we have studied it and other related models, and a subtle change in the model\'s rule was proposed. Our slight alterations to the model yielded significant qualitative changes, specifically the emergence of surface tension, driving the system to metastable states. Using concepts from statistical mechanics and extensive numerical simulations, we explored some of the aspects that better describe the rich model devised, such as its transient and stationary behaviour.

Parameter estimation techniques have been successfully and extensively applied to deterministic models based on ordinary differential equations but are in early development for stochastic models. In this thesis, we first investigate using parameter estimation techniques for a deterministic model to approximate parameters in a corresponding stochastic model. The basis behind this approach lies in the Kurtz limit theorem which implies that for large populations, the realizations of the stochastic model converge to the deterministic model. We show for two example models that this approach often fails to estimate parameters well when the population size is small. We then develop a new method, the MCR method, which is unique to stochastic models and provides significantly better estimates and smaller confidence intervals for parameter values. Initial analysis of the new MCR method indicates that this method might be a viable method for parameter estimation for continuous time Markov chain models.

Le modèle ROF (Rudin, Osher, Fatemi), introduit en 1992 en utilisant la variation totale comme terme de régularisation pour la restauration d'images, a fait l'objet de nombreuses recherches théoriques et numériques depuis. Dans cette thèse, nous présentons de nouveaux modèles inspirés de la variation totale mais construits par analogie avec une méthode de débruitage beaucoup plus récente et radicalement différente : les moyennes non locales (NL-means). Dans une première partie, nous transposons le modèle ROF dans un cadre bayésien, et montrons que l'estimateur associé à un risque quadratique (moyenne a posteriori) peut être calculé numériquement à l'aide d'un algorithme de type MCMC (Monte Carlo Markov Chain), dont la convergence est soigneusement contrôlée compte tenu de la dimension élevée de l'espace des images. Nous montrons que le débruiteur associé permet notamment d'éviter le phénomène de "staircasing", défaut bien connu du modèle ROF. Dans la deuxième partie, nous proposons tout d'abord une version localisée du modèle ROF et en analysons certains aspects : compromis biais-variance, EDP limite, pondération du voisinage, etc. Enfin, nous discutons le choix de la variation totale en tant que modèle a priori, en confrontant le point de vue géométrique (modèle ROF) au cadre statistique (modélisation bayésienne).

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This thesis is based on four papers investigating properties of split trees and also introducing new methods for studying such trees. Split trees comprise a large class of random trees of logarithmic height and include e.g., binary search trees, m-ary search trees, quadtrees, median of (2k+1)-trees, simplex trees, tries and digital search trees. Split trees are constructed recursively, using “split vectors”, to distribute n “balls” to the vertices/nodes. The vertices of a split tree may contain different numbers of balls; in computer science applications these balls often represent “key numbers”. In the first paper, it was tested whether a recently described method for determining the asymptotic distribution of the number of records (or cuts) in a deterministic complete binary tree could be extended to binary search trees. This method used a classical triangular array theorem to study the convergence of sums of triangular arrays to infinitely divisible distributions. It was shown that with modifications, the same approach could be used to determine the asymptotic distribution of the number of records (or cuts) in binary search trees, i.e., in a well-characterized type of random split trees. In the second paper, renewal theory was introduced as a novel approach for studying split trees. It was shown that this theory is highly useful for investigating these types of trees. It was shown that the expected number of vertices (a random number) divided by the number of balls, n, converges to a constant as n tends to infinity. Furthermore, it was demonstrated that the number of vertices is concentrated around its mean value. New results were also presented regarding depths of balls and vertices in split trees. In the third paper, it was tested whether the methods of proof to determine the asymptotic distribution of the number of records (or cuts) used in the binary search tree, could be extended to split trees in general. Using renewal theory it was demonstrated for the overall class of random split trees that the normalized number of records (or cuts) has asymptotically a weakly 1-stable distribution. In the fourth paper, branching Markov chains were introduced to investigate split trees with immigration, i.e., CTM protocols and their generalizations. It was shown that there is a natural relationship between the Markov chain and a multi-type (Galton-Watson) process that is well adapted to study stability in the corresponding tree. A stability condition was presented to de­scribe a phase transition deciding when the process is stable or unstable (i.e., the tree explodes). Further, the use of renewal theory also proved to be useful for studying split trees with immi­gration. Using this method it was demonstrated that when the tree is stable (i.e., finite), there is the same type of expression for the number of vertices as for normal split trees.

Given the result $v_0$ of a survey and a nested collection of summary statistics that could be used to describe that result, it is natural to ask which of these summary statistics best describe $v_0$. In 1998 Diaconis and Sturmfels presented an approach for determining the conditional significance of a higher order statistic, after sampling a space conditioned on the value of a lower order statistic. Their approach involves the computation of a Markov basis, followed by the use of a Markov process with stationary hypergeometric distribution to generate a sample.This technique for data analysis has become an accepted tool of algebraic statistics, particularly for the study of fully ranked data. In this thesis, we explore the extension of this technique for data analysis to the study of partially ranked data, focusing on data from surveys in which participants are asked to identify their top $k$ choices of $n$ items. Before we move on to our own data analysis, though, we present a thorough discussion of the Diaconis–Sturmfels algorithm and its use in data analysis. In this discussion, we attempt to collect together all of the background on Markov bases, Markov proceses, Gröbner bases, implicitization theory, and elimination theory, that is necessary for a full understanding of this approach to data analysis.