Ce travail étudie les déviations de sommes ergodiques pour des systèmes dynamiques substitutifs avec une matrice qui admet des valeurs propres de module supérieur à 1. Précisément, nous nous concentrons sur les substitutions telle que ces valeurs propres ne sont pas conjuguées. Dans un premier temps, on défini les lettres a-minimales et dominantes d'un mot pour étudier sa ligne brisée associé. On défini la ligne brisée normalisée et sa fonction limite. Pour l'étude des sommes ergodiques, on défini le sous-automate des lettres minimales. On donne des conditions sur une substitution de sorte qu'il y ait un nombre infini des sommes ergodiques égales à zéro pour un point x 2 X. Enfin, en utilisant un boucle dans une classe de Rauzy, on prouve l'existence d'un nombre infini d'échanges d'intervalles auto-similaires, dont la matrice de Rauzy a deux valeurs propres non conjuguées de module supérieur à 1. Et tout échange d'intervalles affine semi-conjugué à cet échange d'intervalles est aussi conjugué. / This thesis focuses on the deviation of ergodic sums for a substitution dynamical systems with a matrix that admits eigenvalues of modulus larger than 1. Specifically, we concentrate on substitutions with non-conjugated eigenvalues. At first, we define the a-minimals letters and the dominant letters of a word to study its broken associated line. We define the normalize broken line and its limit function. For the study of ergodic sums, we define the sub-automaton of minimum letters. We give conditions on a substitution so that there is infinitely many zero sums ergodic for a point x 2 X. Finally, using a loop in a class of Rauzy, we prove the existence of infinitely many interval exchange transformation self-similar, whose Rauzy matrix has two non-conjugated eigenvalues larger than 1 and every affine interval exchange transformation that is semi-conjugated, is also conjugated.

Estudamos inicialmente resultados de classificação de difeomorfismos de produtos de esferas de mesma dimensão. Tratado isto, estudamos os mergulhos suaves de produtos de três esferas, sendo a primeira de dimensão um e as demais de dimensão maior ou igual a um, com a dimensão da última maior ou igual a da segunda, em uma esfera em codimensão um, e buscamos a total caracterização do fecho das duas componentes conexas do complementar de tais mergulhos. Tratamos com enfoque especial os mergulhos do produto de três esferas de dimensão um na esfera de dimensão quatro, e, finalmente, estudamos problemas de classificação de mergulhos PL localmente não-enodados de somas conexas de toros em codimensão um. / We study initially results of classification of difeomorfisms of Cartesian products of spheres of same dimension. Treated this, we study the smooth embeddings of cartesian products of three spheres, being the first one of dimension one and excessively of bigger or equal dimension to one, with the dimension of the last equal greater or of second, in a sphere in codimension one, and search the total characterization of the latch of the two connected components of complementing of such embeddings. We deal with special approach the embeddings of the product to three spheres to dimension one in the sphere dimension four, and, finally, we study problems of classification of PL locally unknotted embeddings of connected sums of torus on codimension one.

Estudamos inicialmente resultados de classificação de difeomorfismos de produtos de esferas de mesma dimensão. Tratado isto, estudamos os mergulhos suaves de produtos de três esferas, sendo a primeira de dimensão um e as demais de dimensão maior ou igual a um, com a dimensão da última maior ou igual a da segunda, em uma esfera em codimensão um, e buscamos a total caracterização do fecho das duas componentes conexas do complementar de tais mergulhos. Tratamos com enfoque especial os mergulhos do produto de três esferas de dimensão um na esfera de dimensão quatro, e, finalmente, estudamos problemas de classificação de mergulhos PL localmente não-enodados de somas conexas de toros em codimensão um. / We study initially results of classification of difeomorfisms of Cartesian products of spheres of same dimension. Treated this, we study the smooth embeddings of cartesian products of three spheres, being the first one of dimension one and excessively of bigger or equal dimension to one, with the dimension of the last equal greater or of second, in a sphere in codimension one, and search the total characterization of the latch of the two connected components of complementing of such embeddings. We deal with special approach the embeddings of the product to three spheres to dimension one in the sphere dimension four, and, finally, we study problems of classification of PL locally unknotted embeddings of connected sums of torus on codimension one.

We consider discrete and continuous symmetric random variables X taking values in [0; 1], and thus having expected value 1/2. The main thrust of this investigation is to study the correlation between the variance, Var(X) of X and the value of the expected maximum E(Mn) = E(X1,...,Xn) of n independent and identically distributed random variables X1,X2,...,Xn, each distributed as X. Many special cases are studied, some leading to very interesting alternating sums, and some progress is made towards a general theory.

Many papers have been presented on the study of change points detection.　Nonetheless, we would like to point out that in dealing with the time series with switching regimes, we should also take the characteristics of change periods into account.　Because many patterns of change structure in time series exhibit a certain kind of duration, those phenomena should not be treated as a mere sudden turning at a certain time. In this paper, we propose procedures about change periods detection for nonlinear time series.　One of the detecting statistical methods is an application of fuzzy classification and generalization of Inclan and Tiao’s result.　Moreover, we develop the genetic-based searching procedure, which is based on the concepts of leading genetic model.　Simulation results show that the performance of these procedures is efficient and successful.　Finally, two empirical applications about change periods detection for Taiwan monthly visitors arrival and exchange rate are demonstrated.

Dans ce travail, nous nous intéressons aux problèmes relatifs aux polylogarithmes et aux sommes harmoniques pris en les multiindices négatifs(au sens large, appelés dans la suite non-positifs) et en les indices mixtes. Notre étude donnera des résultats généraux sur ces objets en relation avec les algèbres de Hopf. Les techniques utilisées sont basées sur la combinatoire des séries formelles non commutatives, formes linéaires sur l’algèbre de Hopf de φ−Shuffle. Notre travail donnera aussi un processus global pour renormaliser les polyzetâs divergents. Enfin, nous appliquerons les structures mises en évidence aux systèmes dynamiques non linéaires avec entrées singulières. / In this memoir are studied the polylogarithms and the harmonic sums at non-positive (i.e. weakly negative) multi-indices. General results about these objects in relation with Hopf algebras are provided. The technics exploited here are based on the combinatorics of non commmutative generating series relative to the Hopf φ−Shuffle algebra. Our work will also propose a global process to renormalize divergent polyzetas. Finally, we will apply these ideas to non-linear dynamical systems with singular inputs.

Orientador: Clésio Luis Tozzi / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-16T06:32:57Z (GMT). No. of bitstreams: 1 Freitas_GreiceMartinsde_M.pdf: 16453422 bytes, checksum: fa0ae64561fd346237c57310fb0d0073 (MD5) Previous issue date: 2010 / Resumo: A crescente utilização de câmeras de vídeo para o monitoramento de ambientes, auxiliando no controle de entrada, saída e trânsito de indivíduos ou veículos tem aumentado a busca por sistemas visando a automatização do processo de monitoramento por vídeos. Como requisitos para estes sistemas identificam-se o tratamento da entrada e saída de objetos na cena, variações na forma e movimentação dos alvos seguidos, interações entre os alvos como encontros e separações, variações na iluminação da cena e o tratamento de ruídos presentes no vídeo. O presente trabalho analisa e avalia as principais etapas de um sistema de rastreamento de múltiplos objetos através de uma câmera de vídeo fixa e propõe um sistema de rastreamento baseado em sistemas encontrados na literatura. O sistema proposto é composto de três fases: identificação do foreground através de técnicas de subtração de fundo; associação de objetos quadro a quadro através de métricas de cor, área e posição do centróide - com o auxílio da aplicação do filtro de Kalman - e, finalmente, classificação dos objetos a cada quadro segundo um sistema de gerenciamento de objetos. Com o objetivo de verificar a eficiência do sistema de rastreamento proposto, testes foram realizados utilizando vídeos das bases de dados PETS e CAVIAR. A etapa de subtração de fundo foi avaliada através da comparação do modelo Eigenbackground, utilizado no presente sistema, com o modelo Mistura de Gaussianas, modelo de subtração de fundo mais utilizado em sistemas de rastreamento. O sistema de gerenciamento de objeto foi avaliado por meio da classificação e contagem manual dos objetos a cada quadro do vídeo. Estes resultados foram comparados à saída do sistema de gerenciamento de objetos. Os resultados obtidos mostraram que o sistema de rastreamento proposto foi capaz de reconhecer e rastrear objetos em movimento em sequências de vídeos, lidando com oclusões e separações, mostrando adequabilidade para aplicação em sistemas de segurança em tempo real / Abstract: There are immediate needs for the use of video cameras in environment monitoring, which can be verified by the task of assisting the entrance, exit and transit registering of people or vehicles in a area. In this context, automated surveillance systems based on video images are increasingly gaining interest. As requisites for these systems, it can be identified the treatment of entrances and exits of objects on a scene, shape variation and movement of followed targets, interactions between targets (such as meetings and splits), lighting variations and video noises. This work analyses and evaluates the main steps of a multiple target tracking system through a fixed video camera and proposes a tracking system based on approaches found in the literature. The proposed system is composed of three steps: foreground identification through background subtraction techniques; object association through color, area and centroid position matching, by using the Kalman filter to estimate the object's position in the next frame, and, lastly, object classification according an object management system. In order to assess the efficiency of the proposed tracking system, tests were performed by using videos from PETS and CAVIAR datasets. The background subtraction step was evaluated by means of a comparison between the Eigenbackground model, used in the proposed tracking system, and the Mixture of Gaussians model, one of the most used background subtraction models. The object management system was evaluated through manual classification and counting of objects on each video frame. These results were compared with the output of the object management system. The obtained results showed that the proposed tracking system was able to recognize and track objects in movement on videos, as well as dealing with occlusions and separations, and, at the same time, encouraging future studies in order for its application on real time security systems / Mestrado / Engenharia de Computação / Mestre em Engenharia Elétrica

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This thesis presents a technique for automatic vectorization of innermost single statement loops with a cross-iteration data dependence by analyzing data-flow to recognize frequently recurring program idioms. Recognition is carried out by matching the circular SSA data-flow found around the loop body’s φ-function against several primitive patterns, forming a tree representation of the relevant data-flow that is then pruned down to a single parameterized node, providing a high-level specification of the data-flow idiom at hand used to guide algorithmic replacement applied to the intermediate representation. The versatility of the technique is shown by presenting an implementation supporting vectorization of both a limited class of linear recurrences as well as prefix sums, where the latter shows how the technique generalizes to intermediate representations with memory state in SSA-form. Finally, a thorough performance evaluation is presented, showing the effectiveness of the vectorization technique.

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