[pt] A escolha de uma carreira é uma das decisões mais importantes na vida de uma pessoa, e é feita em um ambiente repleto de incertezas em relação ao futuro. Este trabalho analisa o aspecto financeiro da escolha entre uma carreira numa empresa privada e uma carreira em um órgão público, com ingresso por meio de um concurso. A análise pelo tradicional fluxo de caixa descontado apresenta uma série de limitações por não captar aspectos como a incerteza e a flexibilidade da tomada de decisão. Assim é aplicada uma abordagem segundo a teoria das Opções Reais, que se mostra mais adequada a este caso, pois permite que a flexibilidade de escolha seja modelada e considerada na escolha de carreira de um indivíduo. Neste estudo, os ganhos em uma empresa privada são modelados por meio de um processo estocástico enquanto a carreira pública tem um valor determinístico. Existe flexibilidade de data em relação ao ingresso na carreira pública, porém esta decisão é irreversível. Os resultados sugerem que a opção de ingressar na carreira pública pode ter valor significativo em relação à carreira privada. / [en] Choosing a career is one of the most important decisions in a person s life, and is done in an environment full of uncertainties about the future. This study analyzes the financial aspect of a career choice between a private company and a career in the government, with admission through a contest. The analysis through the traditional discounted cash flow would bring a lot of limitations, not capturing aspects such as uncertainty and flexibility of decision making. So real options theory approach is applied, which appears more appropriate in this case because it allows the flexibility of choice to be modeled and considered in the choice of an individual s career. In this study earnings in a private company are modeled through a stochastic process while public career has a deterministic value. There is flexibility regarding the date of entry into public career, but this decision is irreversible. The results suggest that the option of joining the public career may have significant value in relation to private career.

Cette thèse vise à caractériser la dynamique stochastique hors-équilibre de particules browniennes sous l’effet de confinement. Ce confinement est appliqué ici par des potentiels attractifs ou des frontières imperméables créant des barrières entropiques. Dans un premier temps, nous regardons la dispersion de particules sans interactions dans les milieux hétérogènes. Un nuage de particules browniennes s’étale au cours du temps sans atteindre la distribution d’équilibre de Boltzmann, et son étalement est alors caractérisé par une diffusivité effective inférieure à la diffusivité microscopique. Dans un premier chapitre, nous nous intéressons au lien entre la géométrie de confinement et la dispersion dans le cas particulier des microcanaux périodiques. Pour cela, nous calculons la diffusivité effective sans hypothèse de réduction de dimensionnalité, contrairement à l’approche standard dite de Fick-Jacobs. Une classification des différents régimes de dispersion est alors réalisée, pour toute géométrie autant pour les canaux continus que discontinus. Dans un second chapitre, nous étendons cette analyse à la dispersion dans les réseaux périodiques d’obstacles sphériques attractifs à courte portée. La présence d’un potentiel attractif peut, de manière surprenante, augmenter la dispersion. Nous quantifions cet effet dans le régime dilué, et montrons alors son optimisation pour plusieurs potentiels ainsi que pour une diffusion médiée par la surface des sphères. Ensuite, nous étudions la dynamique stochastique de particules browniennes dans un piège optique en présence d’une force non conservative créée par la pression de radiation du laser. L’expression perturbative des courants stationnaires, décrivant les vortex browniens, est dérivée pour les basses pressions en conservant le terme inertiel dans l’équation de Langevin sous-amortie. L’expression de la densité spectrale est également calculée permettant d’observer les anisotropies du piège et les effets de la force non conservative.La plupart des expressions analytiques obtenues durant cette thèse sont asymptotiquement exactes et vérifiées par des analyses numériques basées sur l’intégration de l’équation de Langevin ou la résolution d’équation aux dérivées partielles. / This thesis aims to characterize the out-of-equilibrium stochastic dynamics of Brownian particles under the effectof confinement. This confinement is applied here by attractive potentials or impermeable boundaries creatingentropic barriers. First, we look at the dispersion of particles without interaction in heterogeneous media. Acloud of Brownian particles spreads over time without reaching the Boltzmann equilibrium distribution, andits spreading is then characterized by an effective diffusivity lower than the microscopic diffusivity. In a firstchapter, we are interested in the link between the confinement geometry and the dispersion in the particularcase of periodic microchannels. For this, we calculate the effective diffusivity without dimensionality reductionassumption, instead of the standard Fick-Jacobs’ approach. A classification of the different dispersion regimesis then performed for any geometry for both continuous and discontinuous channels. In a second chapter, weextend this analysis to dispersion in periodic networks of short-range attractive spherical obstacles. The presenceof an attractive potential can surprisingly increase the dispersion. We quantify this effect in the dilute regimeand then show its optimization for several potentials as well as for diffusion mediated by the surface of thespheres. Later, we study the stochastic dynamics of Brownian particles in an optical trap in the presence ofa non-conservative force created by the radiation pressure of the laser. The perturbative expression of thestationary currents describing Brownian vortices is derived for the low pressures keeping the inertial term in theunderdamped Langevin equation. The expression of the power spectrum density is also calculated to observe thetrap anisotropies and the effects of the non-conservative force. Most of analytical expressions obtained duringthis thesis are asymptotically exact and verified by numerical analysis based on the integration of the Langevinequation or the resolution of partial differential equation.

Cette thèse porte sur divers aspects de lois et de processus non-gaussiens qui partagent des propriétés de changement d'échelle où intervient l'exposant 2/3. Les deux principaux objets probabilistes que nous allons présenter sont : 1) La loi de Tracy-Widom : C'est la loi limite de la plus grande valeur propre de matrices aléatoires appartenant aux beta-ensembles lorsque leur dimension tend vers l'infini. Dans un travail en commun avec Balint Virag, nous avons établi le comportement asymptotique de la queue droite de cette loi pour tout beta strictement positif, en utilisant des outils d'analyse de diffusions du type Girsanov. 2) Le ''vrai'' processus auto-répulsif (''true self repelling motion'') TSRM : C'est un processus auto-interagissant qui a été introduit par Balint Toth et Wendelin Werner. Nous nous sommes intéressés à des propriétés de cet objet liées à ses trajectoires (grandes déviations, lois du logarithme itéré) et à des calculs explicites de lois marginales (travail en collaboration avec Balint Toth). Cette étude nous a aussi amenés à aborder des questions liées à la théorie des jeux. / This thesis focuses on various aspects of non-Gaussian distributions and processes sharing scaling properties where the exponent 2/3 appears. The two probabilistic objects that we will introduce are: 1) Tracy-Widom distribution: This is the large dimensional limit of the top eigenvalue of random matrices in beta-ensembles. In a joint work with Balint Virag, we studied the asymptotic behavior of its right tail for all positive beta, using tools coming from diffusion analysis, such as the Girsanov formula. 2) The “true self repelling motion” (TSRM): This is a self-interacting process which was introduced by Balint Toth and Wendelin Werner. We have been interested in properties related to trajectories of this motion (large deviations, law of the iterated logarithm) and explicit distribution computations (joint work with Balint Toth). During this study, we have also dealt with questions related to game theory.

Une interface est une zone de l'espace qui sépare deux régions possédant des propriétés physiques différentes. La plupart des interfaces de la nature résultent d'un processus de croissance, mêlant une composante aléatoire et une dynamique déterministe régie par les symétries du problème. Le résultat du processus de croissance est un objet présentant des corrélations à longue portée. Dans cette thèse, nous nous proposons d'étudier la statistique d'extrême de différents types d'interfaces. Une première motivation est de raffiner la compréhension géométrique de tels objets, via leur maximum. Une seconde motivation s'inscrit dans la démarche plus générale de la statistique d'extrême de variables aléatoires fortement corrélées. A l'aide de méthodes analytiques d'intégrales de chemin nous analysons la distribution du maximum d'interfaces à l'équilibre, dont l'énergie es t purement élastique à courte portée. Nous attaquons ensuite le problème d'interfaces élastiques en milieu désordonné, principalement à l'aide de simulations numériques. Enfin nous étudierons une interface hors-équilibre dans son régime de croissance. L'équivalence de ce type d'interface avec le polymère dirigé en milieu aléatoire, un des paradigmes de la physique statistique des systèmes désordonnés, donne une portée étendue aux résultats concernant la statistique du maximum de l'interface. Nous exposerons les résultats que nous avons obtenus sur un modèle de mouvements browniens qui ne se croisent pas, tout en explicitant le lien entre ce modèle, l'interface en croissance et le polymère dirigé. / An interface is an area of space that separates two regions having different physical properties. Most interfaces in nature are the result of a growth process, mixing a random behavior and a deterministic dynamic derived from the symmetries of the problem. This growth process gives an object with extended correlations. In this thesis, we focus on the study of the extremum of different kinds of interfaces. A first motivation is to refine the geometric properties of such objects, looking at their maximum. A second motivation is to explore the extreme value statistics of strongly correlated random variables. Using path integral techniques we analyse the probability distribution of the maximum of equilibrium interfaces, possessing short range elastic energy. We then extend this to elastic interfaces in random media, with essentially numerical simulations. Finally we study a particular type of out-of-equilibrium interface, in its growing regime. Such interface is equivalent to the directed polymer in random media, a paradigm of the statistical mechanics of disordered systems. This equivalence reinforces the interest in the extreme value statistics of the interface. We will show the exact results we obtained for a non-intersecting Brownian motion model, explaining precisely the link with the growing interface and the directed polymer.

[pt] O objetivos desta dissertação é fazer uma análise de investimentos usando a teoria das Opções Reais de uma planta GTL. Está análise é a mais indicada, pois se verificam várias flexibilidades nesta planta em relação aos inputs (pode ser usado mais de um produto como matéria- prima) e em relação aos outputs (existem várias combinações possíveis de produção). Torna-se de grande importância neste caso saber calcular o valor destas opções e verificar se vale a pena ou não a construção de uma planta que possa usar como matéria prima mais de um produto e/ou que possa produzir mais de uma possível combinação de produção. A construção de uma planta que possua a possibilidade de trocar de insumo e/ou trocar a combinação de produção só será viável caso o valor criado pela flexibilidade seja maior do que o custo necessário para implementá-la (investimento adicional e custos operacionais extras). Sendo assim, o objetivo desta dissertação é calcular até quanto a Petrobras estaria disposta a pagar para ter uma planta que possua a opção de swicth use dos inputs e/ou outputs, o valor que ela teria que investir para usufruir desta flexibilidade, e através da diferença entre estes valores verificar se vale a pena ou não a construção da planta com flexibilidade de input e/ou output. / [en] The objective of this dissertation is to do a analysis of investiment using the real option theory for the plant GTL. This analysis is the best because there are many flexibilities in this plant in relation the inputs (the plant can operate with several inputs) and in relation the outputs (there are many possible combination of production). In this case is very important to know how to calculate the value of these options and to verify if it is worthwhile or not the construction of a plant that could use two inputs and/or is able to procuce several possible combinations of production. The construction of the plant that change the input abd /or can changer the production combination is viable if the value created by flexibility is large than the necessary cost to implement its (additional investiment and extra operational costs). So, the objective of this dissertation is to calculate until hen Petrobras would be avaible to pay in order to have a plant that has the option of swicth use of inputs and/or outputs, the value it would have to invest to use this flexibility, and through the difference between these values verify if is worthwhile or not the construction of the plant with the flexibility of input and/or output.

Dans le cadre d’un projet de drug design, l’amélioration de la prédiction de l’affinité représente toujours un défi malgré les nombreux efforts déployés dans ce sens. De plus, les constantes cinétiques d’association et de dissociation sont d'un intérêt majeur pour la découverte de nouveaux médicaments, notamment au stade précoce de l'optimisation des molécules afin de mieux évaluer leurs tolérances et efficacités. De par la récente émergence des études de constantes cinétiques, il existe peu de méthodes de prédiction de ces dernières et aucune approche efficace n'a encore été développée pour estimer correctement ces paramètres cinétiques.En relevant ces deux défis, le premier volet de cette thèse consiste au développement de nouvelles méthodes qui permettent dans un premier temps d’améliorer la prédiction de l’affinité par docking flexible et dans un deuxième temps la prédiction des constantes cinétiques d’association et de dissociations (kon et koff) grâce à des simulations de dynamique moléculaire accélérées.Dans le second volet de cette thèse, nous avons conçu de nouveaux inhibiteurs des LIM kinases, cibles émergentes impliquées dans plusieurs physiopathologies incluant la neurofibromatose et le cancer. Nos composés ont de bonnes affinités et sélectivités in vitro, et d’excellentes activités et tolérances évaluées sur des tests cellulaires. / In a drug design project, improving the prediction of affinity is still an issue despite the considerable efforts made in this direction. In addition, binding kinetic constants are of major interest for the discovery of new drugs, in particular at the early stage of molecules optimization to better evaluate their tolerance and efficacy. Due to the recent emergence of the importance of binding kinetics, methods of kinetic rates prediction remain scarce and no efficient computational approach has still been developed to correctly estimate kinetic parameters.In order to challenge these two problematics, the first part of this thesis consists in the development of new methods that allow, first, to improve the prediction of affinity by a flexible docking and, second, to predict the ligand binding/unbinding pathways and binding kinetic rates (kon and koff) by enhanced molecular dynamics simulations.In the second part of this thesis, we have designed novel inhibitors of LIM kinases, emerging targets involved in several pathophysiologies including neurofibromatosis and cancer. Our compounds have good affinities and selectivities in vitro, and excellent activities and tolerances evaluated on cellular tests.

Neben ihrer Bedeutung in industriellen Anwendungen dienen Kolloide als Modellsysteme in Experimenten und in der Theorie, um die Struktur und Dynamik von kondensierter Materie zu untersuchen. Kürzlich wurde experimentell gezeigt, dass eine kleine Anisotropie ausreicht, um die viskoelastische Antwort im Vergleich zu harten Kugeln drastisch zu ändern. Die mikroskopischen Ursachen hierfür sind bisher nicht verstanden. In dieser Arbeit werden daher Nichtgleichgewichts-Brownsche-Dynamik-Simulationen (NEBD) von harten kolloidalen Dumbbells in oszillatorischen Scherfeldern entwickelt und eingesetzt, um diese Resultate mit Verbindung zu Rheologie- und Neutronenstreuexperimenten zu erklären. Weiterhin wird die Bedeutung der Anisotropie für Struktur und Dynamik von solchen Suspensionen im Gleichgewicht mit Hilfe von "Linear-Response"-Theorie und Brownsche-Dynamik-Simulationen analysiert. Im linearen Limit zeigt die Scherviskosität bei hohen Packungsdichten einen dramatischen Anstieg jenseits eines kritischen Anisotropieparameters. Dies weist darauf hin, dass schon bei den kleinen Anisotropien kollektive Rotations-Translations-Kopplungen für langsame Zeitskalen verantwortlich sind. Weiterhin wird ein Nichtgleichgewichtsübergang mittels NEBD-Simulationen von Suspensionen harter Dumbbells im PC unter oszillatorischer Scherung ersichtlich. Es wird gezeigt, dass der kontinuierliche Übergang nur für sehr kleine Aspektverhältnisse erhalten bleibt. Oberhalb eines bestimmten Aspektverhältnisses wird der Übergang durch einen ungeordneten Zustand vermittelt. Außerdem wird ein Sliding-Layer Zustand mit kollektiver Ordnung der Teilchenausrichtung bei hohen Scheramplituden beobachtet. Somit zeigt diese Arbeit, dass die NEBD-Simulationen Phänomene in Rheologie- und Streuexperimenten erklären. Angesichts dieser Experimente wird gezeigt, dass der Orientierungsfreiheitsgrad einen starken Einfluss auf den strukturellen Übergang bei steigenden Amplituden hat. / Besides being important for industrial applications, colloidal suspensions have long served as model systems for investigating the structure and dynamics of condensed matter. Recently, it has been demonstrated experimentally that apparently a small particle anisotropy is sufficient to dramatically change the viscoelastic response under external shearing fields, of which the microscopic mechanisms are not yet sufficiently understood. In the present work, NEBD simulations of colloidal hard dumbbells in oscillatory shear fields are developed and employed to elucidate the novel findings in close connection with comprehensive rheology and SANS experiments. Furthermore, by utilising BD simulations and linear response theory, the impact of anisotropy on structure and dynamics of such suspensions in equilibrium is analysed. In the linear response limit, the shear viscosity exhibits a dramatic increase at high packing fractions beyond a critical anisotropy of the particles. This indicates that newly occurring, collective rotational-translational couplings must be made responsible for slow time scales appearing in the PC. Moreover, a non-equilibrium transition emerging at moderate aspect ratios is revealed by NEBD of plastic crystalline suspensions under oscillatory shear. This transition behaviour is systematically studied. It is demonstrated that the continuous nature of the transition is retained for very low aspect ratios only. Above a certain aspect ratio, the transition is mediated by an intermediate disordered state. Furthermore, a partially oriented sliding layer state featuring a finite collective order in the particles'' orientations is observed at high strains. Hence, this thesis demonstrates that the NEBD simulations explain novel phenomena in rheology and scattering experiments. In the light of these experiments, it is shown that the orientational degree of freedom has a vigorous impact on the structural transition under increasing oscillatory shear.

Nous considérons le cas d’un assureur qui doit indemniser une banque à la suite de pertes liées à un défaut de remboursement de ses emprunteurs. Les modèles couramment utilisés sont collectifs et ne permettent pas de prendre en compte les comportements individuels des emprunteurs. Dans une première partie nous définissons un modèle pour étudier le montant des pertes liées à ces défauts de paiement (provision) pour une période donnée. La quantité clé de notre modèle est le montant d’un défaut. Pour un emprunteur j et une date de fin de prêt Tj , ce montant vaut max(Sj Tj -Rj Tj ; 0), où Sj Tj est le montant dû par l’emprunteur et dépend de la durée et du montant du prêt, et Rj Tj est le montant de la revente du bien immobilier financé par le prêt. Rj Tj est proportionnel au montant emprunté; le coefficient de proportionnalité est modélisé par un mouvement Brownien géométrique et représente les fluctuations des prix de l’immobilier. La loi des couples (Date de fin du prêt, Durée du prêt) est modélisée par un processus ponctuel de Poisson. La provision Ph, où h est la durée maximale des contrats considérés, est alors définie comme la somme d’un nombre aléatoire de montants de défauts individuels. Nous pouvons ainsi calculer l’espérance et la variance de la provision mais aussi donner un algorithme de simulation. Il est également possible d’estimer les paramètres liés au modèle et de fournir une valeur numérique aux quantiles de la provision. Dans une deuxième partie nous nous intéresserons au besoin de solvabilité associé au risque de provisionnement (problématique imposée par la réforme européenne Solvabilité 2). La question se ramène à étudier le comportement asymptotique de Ph lorsque h ! +1. Nous montrons que Ph, convenablement normalisée, converge en loi vers une variable aléatoire qui est la somme de deux variables dont l’une est gaussienne / We consider an insurance company which has to indemnify a bank against losses related to a borrower defaulting on payments. Models normally used by insurers are collectives and do not allows to take into account the personal characteristics of borrowers. In a first part, we defined a model to evaluate potential future default amounts (provision) over a fixed period.The amount of default is the key to our model. For a borrower j and an associated maturity Tj, this amount is max(Sj Tj -Rj Tj ; 0), where Sj Tj is the outstanding amount owed by the borrower and depends on the borrowed amount and the term of the loan, and Rj Tj is the property sale amount. Rj Tj is proportionate to the borrowed amount; the proportionality coefficient is modeled by a geometric Brownian motion and represents the fluctuation price of real estate. The couples (Maturity of the loan, Term of the loan) are modeled by a Poisson point process. The provision Ph, where h is the maximum duration of the loans, is defined as the sum of the random number of individual defaults amounts. We can calculate the mean and the variance of the provision and also give an algorithm to simulate the provision. It is also possible to estimate the parameters of our model and then give a numerical value of the provision quantile. In the second part we will focus on the solvency need due to provisioning risk (topic imposed by the european Solvency 2 reform). The question will be to study the asymptotic behaviour of Ph when h ! +1. We will show that Ph, well renormalized, converges in law to a random variable which is the sum of two random variables whose one is a Gaussian

O aumento pelo interesse na teoria de integração estocástica é, basicamente, consequência da acirrada competição para entender, desenvolver e aplicar a matemática subjacente ao mercado mobiliário. Neste trabalho desenvolvemos, de maneira didática e visando aplicações, tal teoria. Para tanto, começamos apresentando um desenvolvimento cuidadoso da teoria dos martingais e dos principais resultados de medida e probabilidade relacionados. Depois apresentamos de maneira formal a teoria de integração estocástica com respeito aos semi-martingais contínuos. Finalizamos com um tratamento das principais aplicações dessa teoria como a fórmula de Itô, uma introdução às equações diferenciais estocásticas e a fórmula de Feynman-Kac. Apresentamos também, em um apêndice, a teoria de mudança de medida e o teorema de Girsanov. Tentamos durante o trabalho apresentar exemplos relacionados com finanças e ilustrar a importância do movimento Browniano. / The increasing interest in the theory of Stochastic Integration is due mainly to the competitive pressure to understand, develop and apply the underlying mathematics of security markets. In this work, we attempt to develop part of the theory in a didactical approach and focused toward some particular applications. For this purpose, we begin by introducing a thorough development of Martingale theory and the main related results on Measure and Probability theory. We then present in a formal way the Stochastic Integration Theory with respect to continuous Semimartingales. Subsequentially, we show some of the theory\'s main applications, such as Itô\'s formula, an introduction to the theory of Stochastic Differential Equations and Feynman-Kac\'s formula. We also present in the appendix Girsanov\'s theorem and a construction of Brownian motion. During the development of this text we endeavored to enrich it by including examples relevant to finance and emphasizing the importance of the ubiquitous Brownian motion.

O objetivo do presente trabalho foi propor métodos de processamento de sinais e reconhecimento de padrões dos sinais de respostas de sensores de gás, utilizando técnicas e modelos da geometria fractal. Foram analisados e estudados os sinais de resposta de dois tipos de sensores. O primeiro sensor foi um dispositivo de óxido de estanho, cujo princípio de funcionamento baseia-se na mudança da resistividade do filme. Este forneceu sinais de respostas com características ruidosas como resposta à interação com as moléculas de gás. O segundo sensor foi um dispositivo Metal-Óxido-Semicondutor (MOS) com princípio de funcionamento baseado na geração de foto corrente, fornecendo respostas imagens bidimensionais. Para as análises dos sinais ruidosos do sensor de óxido de estanho, foi proposto um método de processamento baseado no modelo do movimento Browniano fracionário. Com este método foi possível a discriminação de gases combustíveis com uma taxa de acerto igual a 100%. Para as análises das respostas do tipo imagem do sensor MOS, foram propostos dois diferentes métodos. O primeiro foi embasado no princípio de compressão fractal de imagens e o segundo método proposto, foi baseado na análise e determinação da dimensão fractal multiescala. Ambos os métodos propostos mostram-se eficazes para a determinação da assinatura, como o reconhecimento, de todos os gases que foram utilizados nos experimentos. Os resultados obtidos no presente trabalho abrem novas fronteiras e perspectivas nos paradigmas de processamento de sinais e reconhecimento de padrões, quando utilizada a teoria da geometria fractal. / The aim of the present work was to propose methods for signal possessing and pattern, recognition from the signals response of gas sensors using models and techniques from the fractal geometry. The data studied and analyzed were obtained from two kinds of sensors. The first sensor was the tin oxide device, which detection principle is based on the resistivity changes of the tin oxide film and it provides noisy signals as response to the gas interaction. The second sensor was a metal-oxide-semiconductor (MOS) device, which has as the working principle the photocurrent generation. This sensor provides two-dimensional images signals. A method using a fractional Brownian motion was proposed to analyze the noise signal from the tin oxide device. The fuel gases discrimination employing this model was 100% successful. Two different methods were proposed to analyze the signal response from the MOS device. The first method was based on the fractal image compression technique and the second one was based on the analysis and determination of the multiscale fractal dimension. Both proposed methods have shown to be efficient tools for signature determination as the pattern recognition of all gases that were used in the experiment. The results obtained in the present work open new frontiers and perspectives inside the paradigms of the signal processing and pattern recognition by using the fractal theory.