De nombreux phénomènes de physique quantique ne peuvent être compris que par l'analyse des systèmes ouverts. Un appareil de mesure, par exemple, est un système macroscopique en contact avec un système quantique. Ainsi, tout modèle d'expérience doit prendre en compte les dynamiques propres aux systèmes ouverts. Ces dynamiques peuvent être complexes : l'interaction du système avec son environnement peut modifier ses propriétés, l'interaction peu créer des effets de mémoire dans l'évolution du système, . . . Ces dynamiques sont particulièrement importantes dans l'étude des expériences d'optique quantique. Nous sommes aujourd'hui capables de manipuler individuellement des particules. Pour cela la compréhension et le contrôle de l'influence de l'environnement est crucial. Dans cette thèse nous étudions d'un point de vue théorique quelques procédures communément utilisées en optique quantique. Avant la présentation de nos résultats, nous introduisons et motivons l'utilisation de la description markovienne des systèmes quantiques ouverts. Nous présentons a la fois les équations maîtresses et le calcul stochastique quantique. Nous introduisons ensuite la notion de trajectoire quantique pour la description des mesures indirectes continues. C'est dans ce contexte que l'on présente les résultats obtenus au cours de cette thèse. Dans un premier temps, nous étudions la convergence des mesures non destructives. Nous montrons qu'elles reproduisent la réduction du paquet d'onde du système mesuré. Nous montrons que cette convergence est exponentielle avec un taux fixe. Nous bornons le temps moyen de convergence. Dans ce cadre, en utilisant les techniques de changement de mesure par martingale, nous obtenons la limite continue des trajectoires quantiques discrètes. Dans un second temps, nous étudions l'influence de l'enregistrement des résultats de mesure sur la préparation d'état par ingénierie de réservoir. Nous montrons que l'enregistrement des résultats de mesure n'a pas d'influence sur la convergence proprement dite. Cependant, nous trouvons que l'enregistrement des résultats de mesure modifie le comportement du système avant la convergence. Nous retrouvons une convergence exponentielle avec un taux équivalent au taux sans enregistrement. Mais nous trouvons aussi un nouveau taux de convergence correspondant a une stabilité asymptotique. Ce dernier taux est interprété comme une mesure non destructive ajoutée. Ainsi l'état du système ne converge qu'après un temps aléatoire. A partir de ce temps la convergence peut être bien plus rapide. Nous obtenons aussi une borne sur le temps moyen de convergence. / Many quantum physics phenomena can only be understood in the context of open system analysis. For example a measurement apparatus is a macroscopic system in contact with a quantum system. Therefore any experiment model needs to take into account open system behaviors. These behaviors can be complex: the interaction of the system with its environment might modify its properties, the interaction may induce memory effects in the system evolution, ... These dynamics are particularly important when studying quantum optic experiments. We are now able to manipulate individual particles. Understanding and controlling the environment influence is therefore crucial. In this thesis we investigate at a theoretical level some commonly used quantum optic procedures. Before the presentation of our results, we introduce and motivate the Markovian approach to open quantum systems. We present both the usual master equation and quantum stochastic calculus. We then introduce the notion of quantum trajectory for the description of continuous indirect measurements. It is in this context that we present the results obtained during this thesis. First, we study the convergence of non demolition measurements. We show that they reproduce the system wave function collapse. We show that this convergence is exponential with a fixed rate. We bound the mean convergence time. In this context, we obtain the continuous time limit of discrete quantum trajectories using martingale change of measure techniques. Second, we investigate the influence of measurement outcome recording on state preparation using reservoir engineering techniques. We show that measurement outcome recording does not influence the convergence itself. Nevertheless, we find that measurement outcome recording modifies the system behavior before the convergence. We recover an exponential convergence with a rate equivalent to the rate without measurement outcome recording. But we also find a new convergence rate corresponding to an asymptotic stability. This last rate is interpreted as an added non demolition measurement. Hence, the system state converges only after a random time. At this time the convergence can be much faster. We also find a bound on the mean convergence time.

Dans le cadre de l’informatique décisionnelle, la programmation physico-financière doit permettre à des acteurs d’une collectivité provenant de divers domaines de faire converger leurs problématiques vers un objectif commun. L’une des principales difficultés de la modélisation d’une programmation physico-financière est que chaque acteur exprime ses problématiques dans des échelles de temps différentes. Dans cette thèse CIFRE, un métamodèle de calcul en temps continu appliqué à la programmation physico-financière est proposé afin de permettre aux acteurs de regrouper leurs visions dans un modèle unique, tout en se plaçant sur des échelles de temps différentes. La modélisation continue développée est confrontée à la modélisation discrète (représentative de l’état de l’art) au travers d’un cas d’étude, montrant les avancées de la première vis-à-vis de la seconde. Ce métamodèle innovant a été implémenté au sein de la société MGDIS, dans le cadre d’une convention CIFRE, à l’aide d’une architecture orientée service. Cette architecture se base sur un style innovant conçu dans cette thèse afin de maximiser la capacité à paralléliser l’évaluation des modèles. La solution développée dans cette thèse a été conçue pour permettre la programmation physico-financière de gros volumes de données à l’échelle réelle. Elle a été validée sur un cas d’étude et répond aux exigences exprimées par les experts de la modélisation de programmation physico-financière de MGDIS qui ont émis un avis positif quant à l’applicabilité de la solution proposée. / In the scope of Business Intelligence, planning aims to support multiple actors in their process of converging different views and problematics from different domains to get a shared business planning model. A major difficulty in business planning is that each actor states her/his views and problematics with a different time scale. Integrating them into a unique model that represents a common state of reality becomes very costly and awkward to manage when basing the construction of these models on discrete modeling techniques used by current tools of business planning. This doctorate thesis proposes a novel solution, beyond the state-of-the-art, for addressing these issues: it conceives a novel metamodel based on a continuous time calculus. Through the developed approach, it allows multiple actors to integrate the different business logics of their planning domain in a shared model as well as to observe it from different time scales. The advantages of our solution based on continuous time against solutions based on discrete time are presented through a case study. The conceived metamodel was implemented within a real industrial set in MGDIS (a company specialized in business planning for local governments) following an innovative service oriented architecture: this architecture segregates the modeling from the evaluation to allow the parallelization of model evaluation for big volumes of data. The overall solution conceived and implemented in this thesis was designed to be a real scale prototype to be applied to real scale problems. Besides the case study, it was validated by MGDIS experts on business planning against real requirements.

This thesis investigates a technique to estimate the risk of the mean-variance (MV) portfolio optimization problem. We call this technique the Scaling technique. It provides a better estimator of the risk of the MV optimal portfolio. We obtain this result for a general estimator of the covariance matrix of the returns which includes the correlated sampling case as well as the independent sampling case and the exponentially weighted moving average case. This gave rise to the paper, [CMcS]. Our result concerning the Scaling technique relies on the moments of the inverse of compound Wishart matrices. This is an open problem in the theory of random matrices. We actually tackle a much more general setup, where we consider any random matrix provided that its distribution has an appropriate invariance property (orthogonal or unitary) under an appropriate action (by conjugation, or by a left-right action). Our approach is based on Weingarten calculus. As an interesting byproduct of our study - and as a preliminary to the solution of our problem of computing the moments of the inverse of a compound Wishart random matrix, we obtain explicit moment formulas for the pseudo-inverse of Ginibre random matrices. These results are also given in the paper, [CMS]. Using the moments of the inverse of compound Wishart matrices, we obtain asymptotically unbiased estimators of the risk and the weights of the MV portfolio. Finally, we have some numerical results which are part of our future work.

The thesis deals about methods widely used for life insurance products evaluation from the clients perspective. These methods of evaluation are important mainly for comparisons of several insurance products. One of goals of the thesis is to analyze existing methods used for evaluation of insurance products and discuss their suitability for comparing life insurance products. These methods are based mainly on cost analyses because they were originally developed especially for investments projects comparisons. The main goal of the thesis is to create new indices for comparing life insurance products. These new indices are supposed to resolve imperfections of regularly used evaluation methods. They are also designed to cover all functions of life insurance therefore they are supposed to provide with more coherent information for comparisons. The indices are based on knowledge of life insurance products, probability, demography, financial and insurance calculus.

Dans cette thèse, j'étudie deux aspects distincts de la cryptographie basée sur les courbes elliptiques et hyperelliptiques. Dans une première partie, je confronte deux méthodes de calcul de couplages, originales car ne reposant pas sur le traditionnel algorithme de Miller. Ainsi, dans [42], K. Stange calcula le couplage de Tate sur une courbe elliptique à partir d'un nouvel outil, les elliptic nets. Y. Uchida et S. Uchiyama généralisèrent ces objets au cas hyperelliptique ([47]), mais ne donnèrent un algorithme pour le calcul de couplages que dans le cas des courbes de genre 2. Mon premier travail dans cette thèse fut de donner cet algorithme pour le cas général. De leur côté, D. Lubicz et D. Robert donnèrent dans [28] une autre méthode de calcul de couplage, basée sur les fonctions thêta. Le second résultat de ma thèse est de réunifier ces deux méthodes : je montre que la formule de récurrence à la base des nets est une conséquence des formules d'addition des fonctions thêta utilisées dans l'algorithme de Lubicz et Robert. Dans la seconde partie de ma thèse, je me suis intéressé à l'algorithme de calcul d'index attaquant le problème du logarithme discret sur les courbes elliptiques et hyperelliptiques. Dans le cas elliptique, une des étapes principales de cette attaque repose sur les polynômes de Semaev. Je donne une nouvelle construction ces polynômes en utilisant la fonction sigma de Weierstrass, pour pouvoir ensuite les généraliser pour la première fois au cas hyperelliptique. / In this thesis, I study two different aspects of elliptic and hyperelliptic curves based cryptography.In the first part, I confront two methods of pairings computation, whose original feature is that they are not based the traditional Miller algorithm. Therefore, in [42], K. Stange computed Tate pairings on elliptic curves using a new tool, the elliptic nets. Y. Uchida and S. Uchiyama generalized these objects to hyperelliptic case ([47]), but they gave an algorithm for pairing computation only for the genus 2 case. My first work in this thesis was to give this algorithm for the general case. Meanwhile, D. Lubicz and D. Robert gave in [28] an other pairing computation method, based on theta functions. The second result of my thesis is the reunification of these two methods : I show that the recurrence equation which is the basis of nets theory is a consequence of the addition law of theta functions used in the Lubicz and Robert’s algorithm. In the second part, I study the index calculus algorithm attacking the elliptic and hyperelliptic curve discrete logarithm problem. In the elliptic case, one of the main steps of this attack requires the Semaev polynomials. I reconstruct these polynomials using Weierstrass sigma function, with the purpose of giving their first hyperelliptic generalization.

Orientador: Lee Luan Ling / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-08T01:26:33Z (GMT). No. of bitstreams: 1 Vieira_FlavioHenriqueTeles_D.pdf: 4214611 bytes, checksum: 755dfe9865aff1214f8e551afde7541d (MD5) Previous issue date: 2006 / Resumo: A modelagem multifractal generaliza os modelos de tráfego existentes na literatura e se mostra apropriada para descrever as características encontradas nos fluxos de tráfego das redes atuais. A presente tese investiga abordagens para alocação de banda, predição de tráfego e estimação de probabilidade de perda de bytes considerando as características multifractais de tráfego. Primeiramente, um Modelo Multifractal baseado em Wavelets (MMW) é proposto. Levando em consideração as propriedades deste modelo, são derivados o parâmetro de escala global, a função de autocorrelação e a banda efetiva para processos multifractais. A capacidade de atualização em tempo real do MMW aliada à banda efetiva proposta permite o desenvolvimento de um algoritmo de estimação adaptativa de banda efetiva. Através deste algoritmo é introduzido um esquema de provisão adaptativo de banda efetiva. Estuda-se também a alocação de banda baseada em predição de tráfego. Para este fim, propõe-se um preditor adaptativo fuzzy de tráfego, o qual é aplicado em uma nova estratégia de alocação de banda. O preditor fuzzy adaptativo proposto utiliza funções de base ortonormais baseadas nas propriedades do MMW. Com relação à probabilidade de perda para tráfego multifractal, derivase uma expressão analítica para a estimação da probabilidade de perda de bytes considerando que o tráfego obedece ao MMW. Além disso, uma caracterização mais completa do comportamento de fila é efetuada pela obtenção de limitantes para a probabilidade de perda e para a ocupação média do buffer em termos da banda efetiva do MMW. Por fim, é apresentado um esquema de controle de admissão usando o envelope efetivo proposto para o MMW oriundo do cálculo de rede estatístico, que garante que os fluxos admitidos obedeçam simultaneamente aos requisitos de perda e de retardo. As simulações realizadas evidenciam a relevância das propostas apresentadas / Abstract: Multifractal modeling generalizes the existing traffic models and is believed to be appropriate to describe the characteristics of traffic flows of modern communication networks. This thesis investigates some novel approaches for bandwidth allocation, traffic prediction and byte loss probability estimation, by considering the multifractal characteristics of the network traffic. Firstly, a Wavelet based Multifractal Model (WMM) is proposed. Taking into account the properties of this multifractal model, we derive the global scaling parameter, the autocorrelation function and the effective bandwidth for multifractal processes. The real time updating capacity of the WMM in connection with our effective bandwidth proposal allows us to develop an algorithm for adaptive effective bandwidth estimation. Then, through this algorithm, an adaptive bandwidth provisioning scheme is introduced. In this work, we also study a prediction-based bandwidth allocation case. For this end, we develop an adaptive fuzzy predictor, which is incorporated into a novel bandwidth allocation scheme. The proposed adaptive fuzzy predictor makes use of orthonormal basis functions based on the properties of the WMM. Additionally, we derive an analytical expression for the byte loss probability estimation assuming that the traffic obeys the MMW. Besides, a more complete characterization of the queuing behavior is carried out through the estimation of the bounds for the loss probability and mean queue length in buffer in terms of the WMM based effective bandwidth. Finally, an admission control scheme is presented that uses the WMM based effective envelope derived through the statistical network calculus, guaranteeing that the admitted flows simultaneously attend the loss and delay requirements. The computer simulation results confirm the relevance of the presented proposals / Doutorado / Telecomunicações e Telemática / Doutor em Engenharia Elétrica

Orientador: Francisco Odair Vieira de Paiva, Aloisio Freiria Neves / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-08T02:49:07Z (GMT). No. of bitstreams: 1 Malavazi_MazilioCoronel_M.pdf: 786706 bytes, checksum: 9e4d9aae3bd0fdd46d7adf64ce8958ef (MD5) Previous issue date: 2007 / Resumo: Nesta dissertação obtemos resultados de multiplicidade de soluções fracas não triviais para o problema -Du + V (x)u = f (x; u); x 2 RN; onde V é contínua, f é C1, com f (x; 0) = 0 e f é assintoticamente linear. Utilizamos métodos variacionais e a teoria de grupos críticos, para obtermos e distinguirmos as soluções. Apresentamos também resultados de existência de solução não trivial para o problema -Du + V (x)u = f (u); x 2 RN; onde V e f são funções contínuas. Utilizamos as técnicas de concentração de compacidade e de aproximação do domínio por subconjuntos limitados, para obtermos a solução / Abstract: In this dissertation we get resulted of multiplicity of not trivial weak solutions for the problem -Du + V (x)u = f (x; u); x 2 RN; where V is continuous, f is C1, with f (x; 0) = 0 and f is asymptotically linear. We use variationals methods and the theory of critical groups, to get and to distinguish the solutions. We also present results of existence of not trivial solution for the problem -Du + V (x)u = f (u); x 2 RN; where V and f are continuous functions. We use the techniques of concentration of compactness and approximation of the domain for bounded subsets, to get the solution / Mestrado / Mestre em Matemática

Orientador: Diego Sebastian Ledesma / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T22:36:25Z (GMT). No. of bitstreams: 1 Paula_PedroManfrimMagalhaesde_M.pdf: 1130226 bytes, checksum: bbd8d375ddf7846ed2eafe024103e682 (MD5) Previous issue date: 2015 / Resumo: Este trabalho apresenta um estudo sobre variedades Riemannianas que possuem um tensor de Bakry-Émery-Ricci com limitações. Inicialmente abordamos tanto aspectos da geometria Riemanniana tradicional como métricas e geodésicas, quanto aspectos mais avançados como as fórmulas de Bochner, Weitzenböck e o teorema de Hodge. Em seguida discutimos a convergência de Gromov-Hausdorff e suas propriedades, além de serem apresentados alguns teoremas como os de Kasue e Fukaya. Por fim estudamos as propriedades topológicas e geométricas de variedades com limitação no tensor de Bakry-Émery-Ricci e o comportamento de tais limitações com respeito à submersões e à convergência de Gromov-Hausdorff / Abstract: This work presents a study about Riemannian manifolds having a Bakry-Émery-Ricci tensor with bounds. Initially we approached both the traditional aspects of Riemannian geometry like metrics and geodesics, as more advanced aspects like the Bochner, Weitzenböck formulas and the Hodge's theorem. Then we discussed the Gromov-Hausdorff convergence and its properties, in addition to showing some theorems as those from Kasue and Fukaya. Lastly we studied the topological and geometric properties of manifolds with bounds on the Bakry-Émery-Ricci tensor and the behavior of these bounds with respect to submersions and the Gromov-Hausdorff convergence / Mestrado / Matematica / Mestre em Matemática

Made available in DSpace on 2016-07-18T17:54:15Z (GMT). No. of bitstreams: 1 Mikelli_DISSERTACAO_10_08_2011.pdf: 1426547 bytes, checksum: b10606d3e1c92ec94ba352eb9d78bd91 (MD5) Previous issue date: 2011-06-22 / The teaching of mathematics has become the subject of constant discussion among students and researchers. Most of the researches and studies on the subject has revealed that the major difficulty is related to what is taught to students in the school and what is needed to confront the difficulties in their daily routine. The parameters for a national mathematics curriculum (BRAZIL, 1997) approach the issue by presenting a new perspective on teaching based on the significant knowledge, suggesting procedures that were done in the early years of elementary school that promote understanding of mathematical concepts and particularly the mental calculus and estimate. In this study, it aims to investigate the procedures adopted by the professor for teaching mental calculus in the early years of elementary school. The study was developed in the early years of elementary school in a public school in Presidente Prudente. The research was developed within a qualitative approach in the ethnographic case study, involving literature, documentary and field researches. Data collection was conducted through interviews with teachers looking for information on how is the teaching and learning of mental calculus, and analysis of official documents, diaries and records written in the student s notebook by the students. The qualitative data were collected in the content analysis proposed by Bardin (2008) which involves the interpretation of the messages having as parameter the theoretical reference on the subject. / O ensino da Matemática tem se tornado objeto de reflexão constante entre os estudiosos e pesquisadores sobre o assunto. Grande parte das pesquisas e dos estudos realizados sobre o tema tem revelado que a grande dificuldade dos alunos está em relacionar o que lhe é ensinado na escola com o que é necessário para o enfrentamento das dificuldades no seu cotidiano. Os Parâmetros Curriculares Nacionais de Matemática (BRASIL,1997) abordam o tema apresentando uma nova perspectiva de ensino baseada no conhecimento significativo, sugerindo procedimentos que, trabalhados nos anos iniciais do Ensino Fundamental, venham favorecer a compreensão dos conceitos matemáticos e, em específico, o trabalho com o cálculo mental e a estimativa. No presente estudo, buscou-se investigar os procedimentos adotados pelo docente para o ensino do cálculo mental nos anos iniciais do Ensino Fundamental. O trabalho foi desenvolvido nos anos iniciais do Ensino Fundamental de uma escola pública municipal de Presidente Prudente. A pesquisa foi desenvolvida dentro da abordagem qualitativa do tipo estudo de caso etnográfico, envolvendo pesquisa bibliográfica, documental e pesquisa de campo. A coleta de dados foi realizada por meio de entrevistas com professores procurando obter informações sobre como se dá o ensino e aprendizagem do cálculo mental, além de análise de documentos oficiais, diários e registros feitos no caderno pelo aluno. Os dados qualitativos obtidos foram tratados à luz da análise de conteúdo proposta por Bardin (2008) que envolve a interpretação do significado das mensagens tendo como parâmetro o referencial teórico levantado sobre o assunto.

Dans la première partie de cette thèse, nous obtenons l’existence d’une densité et des estimées gaussiennes pour la solution d’une équation différentielle stochastique rétrograde. C’est une application du calcul de Malliavin et plus particulièrement d’une formule d’I. Nourdin et de F. Viens. La deuxième partie de cette thèse est consacrée à la simulation d’une équation aux dérivées partielles stochastique par une méthode probabiliste qui repose sur la représentation de l’équation aux dérivées partielles stochastique en terme d’équation différentielle doublement stochastique rétrograde, introduite par E. Pardoux et S. Peng. On étend dans ce cadre les idées de F. Zhang et E. Gobet et al. sur la simulation d’une équation différentielle stochastique rétrograde. Dans la dernière partie, nous étudions l’erreur faible du schéma d’Euler implicite pour les processus de diffusion et l’équation de la chaleur stochastique. Dans le premier cas, nous étendons les résultats de D. Talay et L. Tubaro. Dans le second cas, nous étendons les travaux de A. Debussche. / No English summary available.