Submitted by Ana Paula Camara Leal de Sá Lucas Hasenclever (anapaulasalucas@gmail.com) on 2016-10-25T21:46:24Z No. of bitstreams: 1 Dissertação_Ana Paula Sá Lucas Hasenclever_assinada.pdf: 919502 bytes, checksum: be5b234607137d01de09758fc414a429 (MD5) / Approved for entry into archive by GILSON ROCHA MIRANDA (gilson.miranda@fgv.br) on 2016-11-01T15:25:00Z (GMT) No. of bitstreams: 1 Dissertação_Ana Paula Sá Lucas Hasenclever_assinada.pdf: 919502 bytes, checksum: be5b234607137d01de09758fc414a429 (MD5) / Approved for entry into archive by Maria Almeida (maria.socorro@fgv.br) on 2016-11-08T13:29:50Z (GMT) No. of bitstreams: 1 Dissertação_Ana Paula Sá Lucas Hasenclever_assinada.pdf: 919502 bytes, checksum: be5b234607137d01de09758fc414a429 (MD5) / Made available in DSpace on 2016-11-08T13:30:10Z (GMT). No. of bitstreams: 1 Dissertação_Ana Paula Sá Lucas Hasenclever_assinada.pdf: 919502 bytes, checksum: be5b234607137d01de09758fc414a429 (MD5) Previous issue date: 2015-08-24 / Propomos um modelo econométrico reduzido para explicar a variação mensal dos preços de minério de ferro para o período entre janeiro de 2008 e julho de 2015 e o utilizamos para realizar projeções mensais a partir de janeiro de 2012. Em seguida, foram realizadas quarenta e quatro projeções de seis meses cada usando um VAR reduzido para estimar regressores incluídos no modelo. Os resultados mostram que os preços gerados pelo modelo objetivo deste estudo apresentam incerteza inferior aos preços gerados através do random walk. Estes resultados se mantêm para o horizonte de seis meses considerado. Adicionalmente, a média de preços de minério de ferro para 2015, considerando os preços realizados entre janeiro e julho e a projeção para os últimos cinco meses corresponde à média das expectativas do mercado, proporcionando uma tese para relatórios de banco.

Orientador: Prof. Dr. Rafael de Mattos Grisi / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional, 2014. / O presente trabalho tem por objetivo relacionar o estudo de Passeios Aleatórios em uma e duas dimensões com o funcionamento de redes elétricas, por meio de modelagem matemática, para que tal relação possa ser aplicada ao estudo de conteúdos relativos ao ensino da matemática no Ensino Médio, em especial no que se refere a Probabilidade, Matrizes e Funções. Visando uma melhor organização dos conceitos e conteúdos abordados, o trabalho foi dividido em quatro capítulos. No primeiro capítulo serão apresentados os conceitos de Passeios Aleatórios em uma e duas dimensões, abordando o estudo de funções hamrônicas e de representação matricial de uma função harmônica. No segundo capítulo veremos métodos de resolução de funções harmônicas, em especial os métodos de relaxamentos, fazendo uma descrição e gerando uma motivação para o estudo do método, e o método de reolução por cadeias de Markov. O terceiro capítulo relaciona os conceitos até então estudados com redes elétricas, apresentando redes elétricas em uma e em duas dimensões, e também dando uma interpretação de voltagem e corrente, para na sequência apresentar uma interpretação probabilística de ambos. Por fim, no quarto capítulo são apresentadas atividades que podem ser realizadas em sala de aula, com alunos do Ensino Médio, para o estudo de Passeios Aleatórios, de forma simples e rápida, visando sua efetiva utilização em sala de aula. / This work aims to relate the Random Walks study in one and two dimensions with the operation of electrical networks, through mathematical modeling, that such a relationship can be applied to the study of material related to the teaching of mathematics in high school, in particular refers to Probability, Arrays and functions. For a better organization of the concepts covered and content, the work was divided into four chapters. Random Walks in the first chapter of the concepts will be presented in one and two dimensions, addressing the study hamrÃ'nicas functions and matrix representation of a harmonic function. In the second chapter we resolution methods of harmonic functions, particularly the relaxation methods, thereby generating a description and a motivation for the study of the method and reolução method of Markov chains. The third chapter lists the concepts studied hitherto grids, grids having in one and in two dimensions, and also giving an interpretation of voltage and current in response to forward a probabilistic interpretation of both. Finally, in the fourth chapter contains activities that can be performed in the classroom, with high school students to the study of Random Walks, simply and quickly, for their effective use in the classroom.

Les patrons récursifs de déplacement, où l’individu revient à des sites déjà visités, sont très répandus. L’utilisation de la mémoire, supposée être avantageuse lorsque l’environnement est prévisible, pourrait être sous-jacente à l’émergence de ces patrons. Cependant, notre compréhension de l’interface mémoire-déplacement a jusqu'à présent été limitée par un manque de méthodes adaptées et d’investigation théorique des avantages de l’utilisation de la mémoire et des patrons qui en émergent. Au cours de cette thèse j’ai cherché à combler en partie ces manques. Je propose ici trois nouveaux cadres d'analyse des patrons récursifs de déplacement. Le premier délimite les zones les plus fréquemment revisitées par un individu, le deuxième détecte la périodicité dans les revisites de sites connus, et le troisième définit formellement et quantifie la routine de déplacement en termes de répétitivité de la séquence de déplacement, et propose un algorithme pour détecter les sous-séquences répétées. A l'aide d'un modèle individu-centré, nous montrons que l'utilisation de la mémoire dans un environnement prévisible est très avantageuse énergétiquement comparée à une stratégie de recherche sans mémoire, y compris en situation de compétition, et qu'elle mène à l'émergence de domaines vitaux stables et à la ségrégation spatiale entre individus. L'utilisation de la mémoire invalide plusieurs hypothèses très courantes faites par les études populationnelles, en menant à une forte déplétion de l’environnement, à une augmentation de la taille de la population à l’équilibre, et à une relation non linéaire entre la taille de population totale et l’intensité de compétition localement ressentie par les individus. Ainsi, ma thèse contribue à une meilleure compréhension des conséquences de la mémoire sur la valeur sélective des individus, sur les patrons de déplacement, et sur la démographie des populations. Elle propose des méthodes innovantes pour quantifier et caractériser les patrons récursifs de déplacement pouvant émerger de son utilisation. Ces méthodes devraient ouvrir de nouvelles opportunités de comparaisons entre individus de différentes populations ou espèces qui permettront le test d'hypothèses sur les pressions de sélection favorisant l'utilisation de la mémoire. / Recursive movement patterns, by which an individual returns to already visited sites, are very common. Memory use, hypothesized to be advantageous when the environment is predictable, could underlie the emergence of these patterns. However, our understanding of the memory-movement interface has been limited by two knowledge gaps. We still lack appropriate methodologies and theoretical knowledge of the advantages of memory use and of the patterns that emerge from it. During this PhD project, I aimed at filling in some of these gaps. I present here three new frameworks for the analysis of recursive movement patterns. The first one delimits the areas most frequently revisited by an individual, the second one detects periodic revisit patterns, and the third one formally defines and quantifies routine movement behaviour in terms of movement sequence repetitiveness, and presents an algorithm that detects the sub-sequences that are repeated. Using an individual-based model, we show that memory use, when the environment is predictable, is very energetically advantageous compared to foraging strategies that do not use memory, including in a situation of competition, and that it leads to the emergence of stable Home Ranges and spatial segregation between individuals. Memory use invalidates several hypotheses very commonly made in population studies, by leading to a stronger environmental depletion, to a higher equilibrium population size, and to a nonlinear relationship between the total population size and the individually-experienced intensity of competition. Therefore, my PhD thesis contributes to a better understanding of the consequences of memory use for the fitness of individuals, for movement patterns, and for population dynamics. It offers innovative methodologies that quantify and characterize recursive movement patterns that can emerge from its use. These methods should open new opportunities for the comparison of the movements of individuals from different populations and species, and thus the testing of hypotheses about the pressures that select for memory use.

Les suspensions d'objets microscopiques ayant la faculté de se déplacer par eux-mêmes dans le fluide qui les entoure sont des systèmes qui présentent un intérêt croissant dans la communauté scientifique. Du fait de leur dynamique intrinsèquement hors-équilibre au sens de la physique statistique, ils génèrent des effets particulièrement complexes. Parmi les micro-objets autopropulsés existants, les micro-algues vertes représentent une part importante de la biomasse de la Terre et participent activement au retraitement du CO2 par leur activité photosynthétique. Elles présentent de plus un remarquable potentiel dans les domaines de la production de bio-carburants, du retraitement des déchets, de la fabrication de cosmétiques et de compléments alimentaires. La compréhension de la dynamique de nage de ce type de microorganisme est d'un intérêt primordial d'un point de vue industriel. Cet ouvrage présente l'étude de la dynamique de la micro-algue Chlamydomonas Reinhardtii. En utilisant un système de suivi de particules en imagerie optique que nous avons développé, nous analysons ici le mécanisme fondamental de nage utilisé par cette algue jusqu'à ses implications en terme d'effets collectifs sur la dynamique de nage d'une suspension semi-diluée. / The suspensions of microscopic objects with the ability to propel themselves into the surrounding fluid are systems of growing interest in the scientific community. Due to their intrinsic out-of-equilibrium dynamics in the sense of statistical physics, they generate complex effects. Among the existing self-propelled micro-objects, green micro-algae are an important part of the biomass of Earth and they actively participate to the recycling of CO2 by their photosynthetic activity. Moreover they have remarkable potential for the production of bio-fuels, waste reprocessing, cosmetics and dietary supplements production. From an industrial point of view, understanding the dynamics of this type of swimming microorganism is of primary interest. This work presents the study of the dynamics of microalgae Chlamydomonas Reinhardtii. Using a system of particle tracking with optical imaging that we have developed, we analyze the mechanism of stroke used by the algae up to its implications in terms of collective effects on the dynamics of swimming in a semi-dilute suspension.

Les marches aléatoires en milieu aléatoire ont suscité un vif intérêt au cours de ces dernières années, tant en sciences appliquées, comme moyen notamment d'affiner des modèles par une prise en compte des fluctuations de l'environnement, qu'en mathématiques, de par la multiplicité et la richesse des comportements qu'elles présentent. Cette thèse est dédiée à l'étude de divers aspects de la transience des marches aléatoires en milieu aléatoire. Elle est composée de deux parties, la première consacrée au cas des environnements de Dirichlet sur Z^d, la seconde au régime transient sous-diffusif sur Z. La loi de Dirichlet apparaît naturellement du fait de son lien avec les marches renforcées. Certaines de ses spécificités permettent de plus d'obtenir des résultats sensiblement plus précis qu'en général. On démontre ainsi tout d'abord une caractérisation de l'intégrabilité des temps de sortie de parties finies de graphes quelconques, qui permet de raffiner un critère de balisticité dans Z^d. On prouve également que les marches aléatoires en environnement de Dirichlet sont transientes directionnellement, avec probabilité positive, dès que les paramètres ne sont pas symétriques. En dimension 1, la thèse se focalise sur le rôle des vallées profondes de l'environnement, en fournissant une nouvelle preuve du théorème de Kesten-Kozlov-Spitzer dans le cas sous-diffusif basée sur l'étude fine du comportement de la marche. Outre une meilleure compréhension de l'émergence de la loi limite, cette preuve a l'avantage de fournir la valeur explicite de ses paramètres. / Random walks in random environment have raised a great interest in the last few years, both among applied scientists, notably as a way to refine models by taking fluctuations of the surrounding environment into account, and among mathematicians, because of the variety and wealth of behaviours they display. This thesis aims at the study of miscellaneous aspects of the transience of random walks in random environment. A first part is dedicated to Dirichlet environments on Z^d and a second one to the transient subdiffusive regime on Z. Random walks in Dirichlet environment arise naturally as an equivalent model for oriented-edge reinforced reinforced random walks. Its specificities also allow for sensibly sharper results than in the general case. We thus prove a characterization of the integrability of exit times out of finite subsets of arbitrary graphs, which enables us to refine a ballisticity criterion on Z^d. We also prove that these random walks are transient with positive probability as soon as the parameters are non-symmetric. In dimension 1, the thesis focuses on the role of the deep valleys of the environment. We give a new proof of Kesten-Kozlov-Spitzer theorem in the subdiffusive regime based on a fine study of the behaviour of the walk. Together with a better understanding of the origin of the limit law, this proof also provides its explicit parameters.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / One of the greatest reasons to use robotics rather than human beings is to avoid hazardous situations such as activities related to search, surveillance and rescue. The pursuit-evasion problem is a fundamental theoretical base to apply robotics on these cases. This dissertation presents an approach to solve the pursuit-evasion problem with no previous knowledge of the map, which must be simply connected, using multi-robots systems with limited sensing. The approach is based on the random walk, since it is a mathematical formalization probabilistically complete, considering plane and obstacle free environments that shall be treated discretely through a regular occupation grid. This dissertation also presents a variation of this approach, though it considers random walk probabilities, to enhance the previous approach, decreasing the amount of iterations needed to solve the problem. In order to validate what is proposed, a discrete multi-robot simulation environment was developed. Finally, the results obtained on the tests that were performed and possible future works that could improve this approach are discussed. / Uma das principais motivações do uso de sistemas robóticos em detrimento de seres humanos é evitar situações de risco, como as encontradas em atividades de busca, vigilância e resgate. O problema de perseguição-evasão é uma base teórica fundamental para a aplicação da robótica nestes casos. Esta dissertação apresenta uma abordagem para solução do problema de perseguição-evasão sem um conhecimento a priori do mapa, que deverá ser simplesmente conectado, através da coordenação de múltiplos robôs com visão limitada. A abordagem aqui proposta é baseada na random walk, por esta ser uma formalização matemática probabilisticamente completa, sendo contemplados ambientes planos e sem obstáculos, que serão tratados discretamente por meio de uma grade de ocupação regular. Ainda nesta dissertação, foi proposta uma variação dessa abordagem, porém com a ponderação de probabilidades da random walk, com o objetivo de aprimorar a anterior, diminuindo número de iterações necessárias para solução do problema. Para a validação da abordagem proposta, foi desenvolvido um ambiente de simulações para abordagens discretas de múltiplos robôs. Finalmente, são discutidos os resultados obtidos nos testes realizados e propostos trabalhos futuros para melhoria desta abordagem.

La nécessité de protéger les véhicules de rentrée atmosphérique a conduit à la sélection des matériaux carbonés pour les applications les plus extrêmes [1, 2]. Au vu du coût prohibitif des essais en conditions réelles [1], la simulation permet de prédire et comprendre le comportement du matériau lors de la rentrée atmosphérique. Les modèles de l’ablation du carbone n’ont cessé de se complexifier [1, 3, 4, 5, 6]. Cependant, ils ne donnent pas de descriptions fines de la surface du matériau. C’est pour remédier à cela que plusieurs études ont été lancées au Laboratoire des Composites Thermostructuraux (LCTS) [7, 8]. Le Plasmatron du VKI est le moyen à haut flux de chaleur et à haute vitesse utilisé pour cette thèse [9, 10]. Dans cette étude, des échantillons sont testés sous des flux de chaleur allant jusqu’à 2800 kW/m2. Ces essais sur le composite 3D carbone/carbone (Cf/C) ont mené à des résultats très intéressants sur la morphologie du composite lors de l’ablation. Le four à image d’arc est le moyen à très haut flux de chaleur et à convection nulle utilisé au cours de cette thèse. Des flux de chaleurs de 10 MW m-2 ont pu être appliqués à des échantillons de 3D Cf/C. Les observations MEB couplées à la reconstruction numérique du four ont permis de noter les différences entre l’oxydation et la sublimation du composite. Un code de diffusion/ablation est développé depuis plusieurs années au LCTS [7, 11, 12, 13, 14] : AMA. Il permet de simuler l’ablation d’un matériau en carbone. Ce code a été validé par J. Lachaud sans prise en compte de l’écoulement [7]. Un nouveau couplage avec le code Open-Foam [15] a été développé et validé. Le code AMA a été utilisé afin de déterminer les paramètres influençant la rugosité du 3D Cf/C sous un écoulement laminaire. / Carbonaceous materials have been selected to protect atmospheric re-entry vehicles under the most extremes conditions [1, 2]. Because real flight experiments are very expensive [1], simulation is an important means to predict and understand the material behaviour during atmospheric re-entry. The models of carbonaceous materials ablation have become more and more complex [1, 3, 4, 5, 6]. However, they are not accurate to describe finely the material surface. To find a solution to this problem, several studies have been conducted at the Laboratoire des Composites Thermostructuraux (LCTS) [7, 8]. The Plasmatron of the VKI is the experimental means which has been used in this doctoral thesis. It can reach moderately high heat flux under high speed flow [9, 10]. In this study, several samples have been tested under an heat flux up to 2800 kW/m2. These tests on the 3D carbon/carbon (Cf/C) composite have given very interesting results about the material morphology during ablation. An arc image furnace, which can reach very high heat flux but without important flow field, has been used during this doctoral study. 3D Cf/C samples have been ablated under heat flux up to 10 MW m-2. SEM observations with the help of a numerical simulation of the furnace, have put the differences between oxidation and sublimation forward. A diffusion/ablation code has been developed at LCTS for several years [7, 11, 12, 13, 14] : AMA. This piece of software is designed to simulate the ablation of a carbonaceous material. It has been validated without flow field by J. Lachaud [7]. A new coupling method between AMA and Open-Foam [15] has been developed and validated. Finally, AMA has been used to point out the parameters which drive the 3D Cf/C surface recession under laminar flow field.

In this dissertation, we study integrodifference equations in patchy landscapes. Specifically, we provide a framework for linking individual dispersal behavior with population-level dynamics in patchy landscapes by integrating recent advances in modeling dispersal into an integrodifference equation. First, we formulate a random-walk model in a patchy landscape with patch-dependent diffusion, settling, and mortality rates. We incorporate mechanisms for individual behavior at an interface which, in general, results in the probability-density function of the random walker being discontinuous at an interface. We show that the dispersal kernel can be characterized as the Green's function of a second-order differential operator and illustrate the kind of (discontinuous) dispersal kernels that arise from our approach. We examine the dependence of obtained kernels on model parameters. Secondly, we analyze integrodifference equations in patchy landscapes equipped with discontinuous kernels. We obtain explicit formulae for the critical-domain-size problem, as well as, explicit formulae for the analogous critical size of good patches on an infinite, periodic, patchy landscape. We examine the dependence of obtained formulae on individual behavior at an interface. Through numerical simulations, we observe that, if the population can persist on an infinite, periodic, patchy landscape, its spatial profile can evolve into a discontinuous traveling periodic wave. We derive a dispersion relation for the speed of the wave and illustrate how interface behavior affects invasion speeds. Lastly, we develop a strategic model for the spread of the emerald ash borer and its interaction with host trees. A thorough literature search provides point estimates and interval ranges for model parameters. Numerical simulations show that the spatial profile of an emerald ash borer invasion evolves into a pulse-like solution that moves with constant speed. We employ Latin hypercube sampling to obtain a plausible collection of parameter values and use a sensitivity analysis technique, partial rank correlation coefficients, to identify model parameters that have the greatest influence on obtained speeds. We illustrate the applicability of our framework by exploring the effectiveness of barrier zones on slowing the spread of the emerald ash borer invasion.

The key objective of this thesis is the outline of an alternative capital market modeling framework, the Volatility Asset Pricing Model, VAPM, inspired by the innovative dual approach of Mandelbrot and Hudson using the method based on synthesis of two seemingly antagonistic factors -- the volatility of market prices and their serial dependence determining the capital markets' dynamics. The pilot tests of this model in various periods using the market index as well as a portfolio of selected securities delivered generally satisfactory results. Firstly, the work delivers a brief recapitulation regarding the concepts of a consumer/investor choice under general conditions of hypothetical certainty. Secondly, this outline is then followed by a description of the "classical" methodologies in the risky environment of uncertainty, with assessment of their corresponding key models, i.e. the CAPM, SIM, MIM, APTM, etc., notwithstanding results of the related testing approaches. Thirdly, this assessment is based on evaluation of the underlying doctrine of Efficient Market Hypothesis in relation to the so called Random Walk Model. Fourthly, in this context the work also offers a brief exposure to a few selected tests of these contraversial concepts. Fifthly, the main points of conteporary approaches such as the Fractal Dimension and the Hurst Exponent in the dynamic framework of information entropy are subsequently described as the theoretical tools leading to development of the abovementioned model VAPM. The major contribution of this thesis is considered its attempt to apply the abovementioned concepts in practice, with the intention to possibly inspire a further analytical research.

Ce travail est consacré à l'étude de limites d'échelle de différentes fonctionnelles de marches aléatoires sur un arbre de Galton-Watson, potentiellement en milieu aléatoire. La marche aléatoire que nous considérons sur cet arbre est une marche aux plus proches voisins récurrente nulle, dont les probabilités de transition dépendent de l'environnement. Plus particulièrement, nous étudions la trace de la marche, c'est-à-dire le sous-arbre constitué des sommets visités par celle-ci. Nous considérons d'abord le cas où dans un certain sens l'environnement est à variance finie, et nous montrons que bien renormalisée la trace converge vers la forêt brownienne. Nous considérons ensuite des hypothèses plus faibles, et nous montrons que la fonction de hauteur de la marche (c'est-à-dire la suite des hauteurs prises par la marche) converge vers le processus de hauteur en temps continu d'un processus de Lévy spectralement positif strictement stable, et que la trace de la marche converge vers l'arbre réel codé par ce même processus. La stratégie employée pour établir ces résultats repose sur l'étude d'un type d'arbres que nous introduisons dans cette thèse : ceux-ci sont des arbres de Galton-Watson à deux types, l'un des types étant stérile, et à longueur d'arête. Notre principal résultat concernant ces arbres assure que leur fonction de hauteur satisfait un principe d'invariance, similaire à celui vérifié par les arbres de Galton-Watson simples. Ces arbres trouvent également une application directe dans les arbres de Galton-Watson multitype à infinité de types, un lien explicite entre les deux nous permettant de montrer qu'ils satisfont également le même principe d'invariance. / This work is devoted to the study of scaling limits of different functionals of random walks on a Galton-Watson tree, potentially in random environment. The randow walk we consider is a null recurrent nearest-neigbout random walk, the probability transition of which depend on the environment. More precisely, we study the trace of the walk, that is the sub-tree made up of the vertices visited by the walk. We first consider the case where in a certain sense the environment has finite variance, and we show that when well-renormalised, the trace converges towards the Brownian forest. We then consider hypotheses of regular variation on the environement, and we show that the height function of the walk (that is the sequence of heights in the tree of the walk) converges towards the continuous time height process of a spectrally positive strictly stable Lévy process, and that the trace of the walk converges towards the real tree coded by this very process. The strategy used to prove these two results is based on the study of a certain kind of trees that we introduce in this thesis: they are Galton-Watson trees with two types, one of which being sterile, and with edge lengths. Our main result about these trees states that their height functions satisfies an invariance principle, similar to that verified by simple Galton-Watson trees. These trees also find a direct application in multitype Galton-Watson trees with infinitely many types, as an explicit link between these two kind of trees allow us to show that they satisfy also the same invariance principle.