La radiothérapie utilise des faisceaux de particules dans le but d'irradier et d'éliminer les tumeurs cancéreuses tout en épargnant au maximum les tissus sains. La perte d'énergie en forme de pic de Bragg des protons dans la matière permet une amélioration balistique du dépôt de la dose par rapport aux rayons X. Le volume irradié peut ainsi être précisément ajusté au volume tumoral. Cette thèse, dans le cadre du projet RACCAM, vise à étudier et à mettre au point le design d'une installation de protonthérapie basée sur un accélérateur de particules à champ fixe et à gradient alterné FFAG dans le but de construire un aimant FFAG à secteur spiral pour validation. Nous présentons tout d'abord la protonthérapie pour définir un cahier des charges médicales définissant les critères techniques d'une installation de protonthérapie. Puis nous introduisons les accélérateurs FFAG par une présentation des projets passés et en cours dans le monde avant de développer la théorie de la dynamique faisceau dans le cas de l'optique à focalisation invariante. Nous décrivons ensuite les outils de modélisation et simulation mis au point pour étudier cette dynamique faisceau dans une optique FFAG à focalisation invariante et à secteur spiral. Nous expliquons par la suite la recherche des paramètres de l'optique ayant abouti à la construction d'un aimant prototype. Enfin, nous décrivons l'installation de protonthérapie du projet RACCAM depuis le cyclotron injecteur jusqu'au système d'extraction.

<p>In this thesis, we give two constructions for Riemannian metrics on Seiberg-Witten moduli spaces. Both these constructions are naturally induced from the L2-metric on the configuration space. The construction of the so called quotient L2-metric is very similar to the one construction of an L2-metric on Yang-Mills moduli spaces as given by Groisser and Parker. To construct a Riemannian metric on the total space of the Seiberg-Witten bundle in a similar way, we define the reduced gauge group as a subgroup of the gauge group. We show, that the quotient of the premoduli space by the reduced gauge group is isomorphic as a U(1)-bundle to the quotient of the premoduli space by the based gauge group. The total space of this new representation of the Seiberg-Witten bundle carries a natural quotient L2-metric, and the bundle projection is a Riemannian submersion with respect to these metrics. We compute explicit formulae for the sectional curvature of the moduli space in terms of Green operators of the elliptic complex associated with a monopole. Further, we construct a Riemannian metric on the cobordism between moduli spaces for different perturbations. The second construction of a Riemannian metric on the moduli space uses a canonical global gauge fixing, which represents the total space of the Seiberg-Witten bundle as a finite dimensional submanifold of the configuration space.</p> <p>We consider the Seiberg-Witten moduli space on a simply connected K&auml;uhler surface. We show that the moduli space (when nonempty) is a complex projective space, if the perturbation does not admit reducible monpoles, and that the moduli space consists of a single point otherwise. The Seiberg-Witten bundle can then be identified with the Hopf fibration. On the complex projective plane with a special Spin-C structure, our Riemannian metrics on the moduli space are Fubini-Study metrics. Correspondingly, the metrics on the total space of the Seiberg-Witten bundle are Berger metrics. We show that the diameter of the moduli space shrinks to 0 when the perturbation approaches the wall of reducible perturbations. Finally we show, that the quotient L2-metric on the Seiberg-Witten moduli space on a K&auml;hler surface is a K&auml;hler metric.</p> / <p>In dieser Dissertationsschrift geben wir zwei Konstruktionen Riemannscher Metriken auf Seiberg-Witten-Modulr&auml;umen an. Beide Metriken werden in nat&uuml;rlicher Weise durch die L2-Metrik des Konfiguartionsraumes induziert. Die Konstruktion der sogenannten Quotienten-L2-Metrik entspricht der durch Groisser und Parker angegebenen Konstruktion einer L2-Metrik auf Yang-Mills-Modulr&auml;umen. Zur Konstruktion einer Quotienten-Metrik auf dem Totalraum des Seiberg-Witten-B&uuml;ndels f&uuml;hren wir die sogenannte reduzierte Eichgruppe ein. Wir zeigen, dass der Quotient des Pr&auml;modulraumes nach der reduzierten Eichgruppe als U(1)-B&uuml;ndel isomorph ist zu dem Quotienten nach der basierten Eichgruppe. Dadurch tr&auml;gt der Totalraum des Seiberg-Witten B&uuml;ndels eine nat&uuml;rliche Quotienten-L2-Metrik, bzgl. derer die B&uuml;ndelprojektion eine Riemannsche Submersion ist. Wir berechnen explizite Formeln f&uuml;r die Schnittr&uuml;mmung des Modulraumes in Ausdr&uuml;cken der Green-Operatoren des zu einem Monopol geh&ouml;rigen elliptischen Komplexes. Ferner konstruieren wir eine Riemannsche Metrik auf dem Kobordismus zwischen Modulr&auml;umen zu verschiedenen St&ouml;rungen. Die zweite Konstruktion einer Riemannschen Metrik auf Seiberg-Witten-Modulr&auml;umen benutzt eine kanonische globale Eichfixierung, verm&ouml;ge derer der Totalraum des Seiberg-Witten-B&uuml;ndels als endlich-dimensionale Untermannigfaltigkeit des Konfigurationsraumes dargestellt werden kann.</p> <p>Wir betrachten speziell die Seiberg-Witten-Modulr&auml;ume auf einfach zusammenh&auml;ngenden K&auml;hler-Mannigfaltigkeiten. Wir zeigen, dass der Seiberg-Witten-Modulraum (falls nicht-leer) im irreduziblen Fall ein komplex projektiver Raum its und im reduziblen Fall aus einem einzelnen Punkt besteht. Das Seiberg-Witten-B&uuml;ndel l&auml;&szlig;t sich mit der Hopf-Faserung identifizieren. Die L2-Metrik des Modulraumes auf der komplex projektiven Fl&auml;che CP2 (mit einer speziellen Spin-C-Struktur) ist die Fubini-Study-Metrik; entsprechend sind die Metriken auf dem Totalraum Berger-Metriken. Wir zeigen, dass der Durchmesser des Modulraumes gegen 0 konvergiert, wenn die St&ouml;rung sich dem reduziblen Fall n&auml;hert. Schlie&szlig;lich zeigen wir, dass die Quotienten-L2-Metrik auf dem Seiberg-Witten-Modulraum einer K&auml;hlerfl&auml;che eine K&auml;hler-Metrik ist.</p>

The aim of this thesis is to introduce a general framework for what is informally referred to as finite-time dynamics. Within this framework, we study hyperbolicity of reference trajectories, existence of invariant manifolds as well as normal hyperbolicity of invariant manifolds called Lagrangian Coherent Structures. We focus on a simple derivation of analytical results. At the same time, our approach together with the analytical results has strong impact on the numerical implementation by providing calculable expressions for known functions and continuity results that ensure robust computation. The main results of the thesis are robustness of finite-time hyperbolicity in a very general setting, finite-time analogues to classical linearization theorems, an approach to the computation of so-called growth rates and the generalization of the variational approach to Lagrangian Coherent Structures.

This paper describes some results of a research study on conjecturing and proving in a dynamic geometry environment (DGE), and it focuses on particular cognitive processes that seem to be induced by certain uses of tools available in Cabri (a particular DGE). Building on the work of Arzarello and Olivero (Arzarello et al., 1998, 2002; Olivero, 2002), we have conceived a model describing some cognitive processes that may occur during the production of conjectures and proofs in a DGE and that seem to be related to the use of specific dragging schemes, in particular to the use of the scheme we refer to as maintaining dragging. This paper contains a description of aspects of the theoretical model we have elaborated for describing such cognitive processes, with specific attention towards the role of the dragging schemes, and an example of how the model can be used to analyze students’ explorations.

The dynamics of Hamiltonian systems (e.g. planetary motion, electron dynamics in nano-structures, molecular dynamics) can be investigated by symplectic maps. While a lot of work has been done for 2D maps, much less is known for higher dimensions. For a generic 4D map regular 2D-tori are organized around a skeleton of families of elliptic 1D-tori, which can be visualized by 3D phase-space slices. An analysis of the different bifurcations of the families of 1D-tori in phase space and in frequency space by computing the involved hyperbolic and elliptic 1D-tori is presented. Applying known results of normal form analysis, both the local and the global structure can be understood: Close to a bifurcation of a 1D-torus, the phase-space structures are surprisingly similar to bifurcations of periodic orbits in 2D maps. Far away the phase-space structures can be explained by remnants of broken resonant 2D-tori. / Die Dynamik Hamilton'scher Syteme (z.B. Planetenbewegung, Elektronenbewegung in Nanostrukturen, Moleküldynamik) kann mit Hilfe symplektischer Abbildungen untersucht werden. Bezüglich 2D Abbildungen wurde bereits umfassende Forschungsarbeit geleistet, doch für Systeme höherer Dimension ist noch vieles unverstanden. In einer generischen 4D Abbildung sind reguläre 2D-Tori um ein Skelett aus Familien von elliptischen 1D-Tori organisiert, was in 3D Phasenraumschnitten visualisiert werden kann. Durch die Berechnung der beteiligten hyperbolischen und elliptischen 1D-Tori werden die verschiedenen Bifurkationen der Familien von 1D-Tori im Phasenraum und im Frequenzraum analysiert. Die Anwendung bekannter Ergebnisse aus Normalformanalysen ermöglicht das Verständnis sowohl des lokalen, als auch des globalen Regimes. Nahe an der Bifurkation eines 1D-Torus sind die Phasenraumstrukturen denen von Bifurkationen periodischer Orbits in 2D Abbildungen überraschend ähnlich. Weit entfernt können die Phasenraumstrukturen als Überreste eines zerplatzten resonanten 2D-Torus erklärt werden.

We will show that the only connected Euclidean spheres admitting a structure of Lie group are S1 and S3, for all n greater than or equal to 1. We will do this through the study of properties of the De Rham cohomology groups of sphere Sn and of compact connected Lie groups. / Fundação de Amparo a Pesquisa do Estado de Alagoas / Mostraremos que as únicas esferas euclidianas conexas que admitem uma estrutura de grupo de Lie são S1 e S3, para todo n maior ou igual a 1. Faremos isso por intermédio do estudo de propriedades dos grupos de cohomologia de De Rham das esfereas Sn e dos grupos de Lie compactos e conexos.

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, 2016. / Neste trabalho analisamos uma versão simplificada do jogo Monopoly utilizando um modelo de Cadeia de Markov com parâmetro de tempo discreto. No primeiro capítulo discorremos sobre a Teoria Clássica das Probabilidades, trazendo os resultados mais importantes para este estudo, precedida por uma breve introdução acerca das ideias sobre o acaso ao longo da história da humanidade e os principais pensadores envolvidos no desenvolvimento dessa Teoria. No segundo capítulo fazemos uma introdução histórica aos processos estocásticos e às Cadeias de Markov; em seguida, explicamos os conceitos fundamentais sobre Cadeias de Markov, colocando alguns exemplos e por fim discutindo a ergodicidade de uma Cadeia de Markov. No terceiro capítulo, após uma breve explicação sobre o surgimento e posterior evolução do jogo Monopoly ao longo do século XX, analisamos a dinâmica do jogo pelo modelo de uma Cadeia de Markov, utilizando como objeto de estudo uma versão mais simples do jogo em questão. / In this work we analyze a simplified version of the Monopoly game using a Markov chain model with discrete time parameter. In the first chapter we discuss on the Classical Theory of Probability, bringing the most important results for this study, preceded by a brief introduction about the ideas of chance throughout the history of mankind and leading thinkers involved in the development of this theory. In the second chapter we make a historical introduction to stochastic processes and Markov chains; then we explain the fundamental concepts of Markov Chains, putting some examples and finally discussing the ergodicity of a Markov chain. In the third chapter, after a brief explanation of the emergence and subsequent evolution of the Monopoly game throughout the twentieth century, we analyze the dynamics of the game by the model of a Markov chain, using as an object of study a simpler version of the game in question.

De plus en plus d’applications ont pour objectif d’automatiser l’analyse des comportements humains afin d’aider les experts qui réalisent actuellement ces analyses. Cette thèse traite de l’analyse des expressions faciales qui fournissent des informations clefs sur ces comportements.Les travaux réalisés portent sur une solution innovante, basée sur l’organisation des expressions, permettant de définir efficacement une expression d’un visage.Nous montrons que l’organisation des expressions, telle que définie, est universelle : une expression est alors caractérisée par son intensité et sa position relative par rapport aux autres expressions. La solution est comparée aux méthodes classiques et montre une augmentation significative des résultats de reconnaissance sur 14 expressions non basiques. La méthode a été étendue à des sujets inconnus. L’idée principale est de créer un espace d’apparence plausible spécifique à la personne inconnue en synthétisant ses expressions basiques à partir de déformations apprises sur d’autres sujets et appliquées sur le neutre du sujet inconnu. La solution est aussi mise à l’épreuve dans un environnement multimodal dont l’objectif est la reconnaissance d’émotions lors de conversations spontanées. Notre méthode a été mise en œuvre dans le cadre du challenge international AVEC 2012 (Audio/Visual Emotion Challenge) où nous avons fini 2nd, avec des taux de reconnaissance très proches de ceux obtenus par les vainqueurs. La comparaison des deux méthodes (la nôtre et celles des vainqueurs) semble montrer que l’extraction des caractéristiques pertinentes est la clef de tels systèmes. / More and more applications aim at automating the analysis of human behavior to assist or replace the experts who are conducting these analyzes. This thesis deals with the analysis of facial expressions, which provide key information on these behaviors.Our work proposes an innovative solution to effectively define a facial expression, regardless of the morphology of the subject. The approach is based on the organization of expressions.We show that the organization of expressions, such as defined, is universal and can be effectively used to uniquely define an expression. One expression is given by its intensity and its relative position to the other expressions. The solution is compared with the conventional methods based on appearance data and shows a significant increase in recognition results of 14 non-basic expressions. The method has been extended to unknown subjects. The main idea is to create a plausible appearance space dedicated to the unknown person by synthesizing its basic expressions from deformations learned on other subjects and applied to the neutral face of the unknown subject. The solution is tested in a more comprehensive multimodal environment, whose aim is the recognition of emotions in spontaneous conversations. Our method has been implemented in the international challenge AVEC 2012 (Audio / Visual Emotion Challenge) where we finished 2nd, with recognition rates very close to the winners’ ones. Comparison of both methods (ours and the winners’ one) seems to show that the extraction of relevant features is the key to such systems.

Neste trabalho apresentamos uma descrição geométrica do grupo de tranças no disco Bpnq e sua apresentação em termos de geradores e relatores no famoso teorema da apresentação de Artin. Mostraremos também que o grupo de tranças puras PBpnq, grupo que possui a permutação trivial das cordas, é bi-ordenável, ou seja, exibiremos uma ordenação para PBpnq que será invariante pela multiplicação em ambos os lados. Esse processo é dado a partir da combinação da técnica de pentear Artin e a expansão Magnus para grupos livres. / In this work, we present a geometric description of the braids groups of the disk Bpnq and its presentation in terms of generators and relations in the famous theorem of Artin\'s presentation. We also show that groups of pure braids, denoted by PBpnq, groups that have the trivial permutation of the strings, are bi-orderable, that is, we will present the explicit construction of a strict total ordering of pure braids PBpnq which is invariant under multiplying on both sides. This process is given from the combination of the techniques of combing Artin and Magnus expansion to free groups.

Made available in DSpace on 2016-12-12T20:15:50Z (GMT). No. of bitstreams: 1 Antonio J Fidelis.pdf: 14922669 bytes, checksum: 6b0a7e53941481a93d4afce451520db9 (MD5) Previous issue date: 2013-03-08 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work we present a study of the logistic map xn+1 = rxn(1 xn) based on the supertracks, a set of continuous functions of the fixed parameter r recursively generated from the map s critical point Xmax = 1/2. This functions determine some iriternal and externa! boundaries of the orbit diagram of the map and provide information about the dynamics of the orbits. The iritersections of these functions can be periodic points or Misiurewicz points. We analyze the dynamics of the orbit in a particular Misiurewicz point, originated from the first coilision between the unstable fixed point and the chaotic attractor. As inedited results, we present algebraically the Lyapunov exponent and the invariant measure for this fixed parameter s value r. Algebraical orbits from the birth and the death of the famous period 3 window are presented as inedited result too. / Neste trabalho apresentamos um estudo do mapa logístico xn + 1 = rxn(1 xn) através do formalismo de supertracks, um conjunto de funções contínuas do parâmetro fixo r geradas recursivamente a partir do ponto crítico do mapa Xmax = 1/2. Essas funções determinam algumas fronteiras internas e externas no diagrama de bifurcação do mapa e fornecem informações sobre a dinâmica das órbitas. As interseções dessas funções podem ser pontos periódicos ou pontos de Misiurewicz. Analisamos a dinâmica da órbita num ponto de Misiurewicz em particular, originado da primeira colisão do ponto fixo instável com o atrator caótico. Como resultados inéditos, apresentamos de forma algébrica o expoente de Lyapunov e a medida invariante para este valor do parâmetro r. As órhitas algébricas do nascimento e da morte da famosa janela de período 3 são também ineditamente apresentados.