A crescente disponibilidade de recursos computacionais para o cálculo, simulação e aquisição de dados permite que cientistas e engenheiros produzam enormes conjuntos de dados, bi ou tridimensionais, em geral multivariados. A aplicação de técnicas de Computação Gráfica com o objetivo de ganhar compreensão desses dados compreende o objeto de estudo da área conhecida por Visualização Científica. Texturização é uma forma de variar as propriedades de uma superfície ponto a ponto de forma que esta simule detalhes que não estão de fato presentes na sua geometria. A texturização pode ser aplicada usando as técnicas de mapeamento de textura, e a textura procedimental . Conjuntos de dados vetoriais tridimensionais necessitam de técnicas complexas e computacionalmente caras para que sejam visualizadas com sucesso. No caso de dados vetoriais densos, a visualização torna-se mais difícil, uma vez que as técnicas convencionais não produzem uma visualização adequada desse dados. A técnica conhecida por Line Integral Convolution (LIC) produz bons resultados para conjunto de dados vetoriais densos a um custo computacional aceitável. Esta técnica utiliza uma textura de ruído branco e o cálculo de streamlines como base para a geração da imagem LIC. Esta técnica produz assim uma imagem bidimensional de uma fatia selecionada desse conjunto de dados, interpolando a textura ruído segundo o campo vetorial a ser visualizado. Este trabalho propõe-se a invertigar a técnica LIC e sua relevância no contexto de visualização científica, através da implementação da classe vtkImageLIC. Esta classe segue os princípios de orientação a objetos podendo, assim, ser integrada à biblioteca de visualização VTK, conferindo-lhe portabilidade e capacidade de extensão. / The increasing availability of computational resources for calculus, simulation and data acquisition allow scientists and engineers to generate enormous datasets, bi or tridimensional, generally, multi-varied. The application of Computer Graphics techniques aiming at gathering a better understanding of these data is the target of an area known as Scientific Visualization (ViSC). Texturing is a means of changing the surface’s properties step by step in such a way that it simulates details which are not present in the surface´s geometry. Texturing can be applied through texturing mapping and procedural techniques. Tridimensional vectorial datasets require complex and computer-demanding techniques to be successfully visualized. For dense vectorial dataset, the visualization becomes more difficult, since conventional techniques do not generated an adequate visualization of data. The technique known as Line Integral Convolution (LIC) produces better results for dense vectorial dataset within acceptable computational costs. This technique uses a white noise texture and streamline calculus as the foundation for LIC image generation. As a result, the technique produces a bidimensional image of a selected slice of the dataset, by interpolating the white noise texture according to the vector field to be visualized. This work aims to investigate the LIC technique and its relevance in the context of Scientific Visualization, culminating with the implementation of the vtkImageLIC class. This class is bound to object oriented programming principles and can be integrated with the VTK visualization Library, allowing it to be portable and easily extensible.

A crescente disponibilidade de recursos computacionais para o cálculo, simulação e aquisição de dados permite que cientistas e engenheiros produzam enormes conjuntos de dados, bi ou tridimensionais, em geral multivariados. A aplicação de técnicas de Computação Gráfica com o objetivo de ganhar compreensão desses dados compreende o objeto de estudo da área conhecida por Visualização Científica. Texturização é uma forma de variar as propriedades de uma superfície ponto a ponto de forma que esta simule detalhes que não estão de fato presentes na sua geometria. A texturização pode ser aplicada usando as técnicas de mapeamento de textura, e a textura procedimental . Conjuntos de dados vetoriais tridimensionais necessitam de técnicas complexas e computacionalmente caras para que sejam visualizadas com sucesso. No caso de dados vetoriais densos, a visualização torna-se mais difícil, uma vez que as técnicas convencionais não produzem uma visualização adequada desse dados. A técnica conhecida por Line Integral Convolution (LIC) produz bons resultados para conjunto de dados vetoriais densos a um custo computacional aceitável. Esta técnica utiliza uma textura de ruído branco e o cálculo de streamlines como base para a geração da imagem LIC. Esta técnica produz assim uma imagem bidimensional de uma fatia selecionada desse conjunto de dados, interpolando a textura ruído segundo o campo vetorial a ser visualizado. Este trabalho propõe-se a invertigar a técnica LIC e sua relevância no contexto de visualização científica, através da implementação da classe vtkImageLIC. Esta classe segue os princípios de orientação a objetos podendo, assim, ser integrada à biblioteca de visualização VTK, conferindo-lhe portabilidade e capacidade de extensão. / The increasing availability of computational resources for calculus, simulation and data acquisition allow scientists and engineers to generate enormous datasets, bi or tridimensional, generally, multi-varied. The application of Computer Graphics techniques aiming at gathering a better understanding of these data is the target of an area known as Scientific Visualization (ViSC). Texturing is a means of changing the surface’s properties step by step in such a way that it simulates details which are not present in the surface´s geometry. Texturing can be applied through texturing mapping and procedural techniques. Tridimensional vectorial datasets require complex and computer-demanding techniques to be successfully visualized. For dense vectorial dataset, the visualization becomes more difficult, since conventional techniques do not generated an adequate visualization of data. The technique known as Line Integral Convolution (LIC) produces better results for dense vectorial dataset within acceptable computational costs. This technique uses a white noise texture and streamline calculus as the foundation for LIC image generation. As a result, the technique produces a bidimensional image of a selected slice of the dataset, by interpolating the white noise texture according to the vector field to be visualized. This work aims to investigate the LIC technique and its relevance in the context of Scientific Visualization, culminating with the implementation of the vtkImageLIC class. This class is bound to object oriented programming principles and can be integrated with the VTK visualization Library, allowing it to be portable and easily extensible.

This thesis describes the development of the real-time convolution system (RTCS) for a little-studied talker/listener in virtual acoustic environments. We include descriptions of the high-resolution directivity measurements of human speech, the RTCS system components, the measurement and characterization of oral-binaural room impulse responses (OBRIRs) for a variety of acoustic environments, and the compensation filter necessary for its validity. In addition to incorporating the high-resolution directivity measurements, this RTCS improved on that developed by Cabrera et al. [1] through the derivation and inclusion of the compensation filter. Objective measures in the time- and frequency-domains, as well as subjective measures, were developed to asses the validity of the RTCS. The utility of the RTCS is demonstrated in the study on vocal effort, and the results of an initial investigation into the vocal effort data are presented.

Cette thèse porte sur les lois stables réelles au sens large et comprend deux parties indépendantes. La première partie concerne les lois stables généralisées introduites par Schneider dans un contexte physique et étudiées ensuite par Pakes. Elles sont définies par une équation différentielle fractionnaire dont on caractérise ici l'existence et l'unicité des solutions densité à l'aide de deux paramètres positifs, l'un de stabilité et l'autre de biais. On montre ensuite diverses identités en loi pour les variables aléatoires sous-jacentes. On étudie le comportement asymptotique précis de la densité aux deux extrémités du support. Dans certains cas, on donne des représentations exactes de ces densités comme fonctions de Fox. Enfin, on résout entièrement les questions ouvertes autour de l'infinie divisibilité des lois stables généralisées. La seconde partie, plus longue, porte sur l'analyse classique des lois alpha-stables libres réelles. Introduites par Bercovici et Pata, ces lois ont ensuite étudiées par Biane, Demni et Hasebe-Kuznetsov sous divers points de vue. Nous montrons qu'elles sont classiquement infiniment divisibles pour alpha inférieur ou égal à 1 et qu'elles appartiennent à la classe de Thorin étendue pour alpha inférieur ou égal à 3/4. La mesure de Lévy est calculée explicitement pour alpha = 1 et ce calcul entraîne que les lois 1-stables libres n'appartiennent pas à la classe de Thorin, sauf dans le cas de la loi de Cauchy avec dérive. Dans le cas symétrique, nous montrons que les densités alpha-stables libres ne sont pas infiniment divisibles quand alpha supérieur à 1. Dans le cas de signe constant nous montrons que les densités stables libres ont une courbe en baleine, autrement dit que leurs dérivées successives ne s'annulent qu'une seule fois sur leurs supports, ce qui constitue un raffinement de l'unimodalité et fait écho à la courbe en cloche des densités stables classiques récemment montrée rigoureusement. Nous établissons enfin plusieurs propriétés précises des densités stables libres spectralement de signe constant, parmi lesquelles une analyse détaillée de la variable aléatoire de Kanter, des expansions asymptotiques complètes en zéro, ainsi que plusieurs propriétés intrinsèques des courbes en baleine. Nous montrons enfin une nouvelle identité en loi pour l'algèbre Beta-Gamma, diverses propriétés d'ordre stochastique et nous étudions le problème classique de Van Dantzig pour la loi semi-circulaire généralisée. / This thesis deals with real stable laws in the broad sense and consists of two independent parts. The first part concerns the generalized stable laws introduced by Schneider in a physical context and then studied by Pakes. They are defined by a fractional differential equation, whose existence and uniqueness of the density solutions is here characterized via two positive parameters, a stability parameter and a bias parameter. We then show various identities in law for the underlying random variables. The precise asymptotic behaviour of the density at both ends of the support is investigated. In some cases, exact representations as Fox functions of these densities are given. Finally, we solve entirely the open questions on the infinite divisibility of the generalized stable laws. The second and longer part deals with the classical analysis of the free alpha-stable laws. Introduced by Bercovici and Pata, these laws were then studied by Biane, Demni and Hasebe-Kuznetsov, from various points of view. We show that they are classically infinitely divisible for alpha less than or equal to 1 and that they belong to the extended Thorin class extended for alpha less than or equal to 3/4. The Lévy measure is explicitly computed for alpha = 1, showing that free 1-stable distributions are not in the Thorin class except in the drifted Cauchy case. In the symmetric case we show that the free alpha-stable densities are not infinitely divisible when alpha larger than 1. In the one-sided case we prove, refining unimodality, that the densities are whale-shaped, that is their successive derivatives vanish exactly once on their support. This echoes the bell shape property of the classical stable densities recently rigorously shown. We also derive several fine properties of spectrally one-sided free stable densities, including a detailed analysis of the Kanter random variable, complete asymptotic expansions at zero, and several intrinsic features of whale-shaped functions. Finally, we display a new identity in law for the Beta-Gamma algebra, various stochastic order properties, and we study the classical Van Danzig problem for the generalized semi-circular law.

The arithmetic operations such as multiplication and division in binary number system are computationally complex in terms of area, delay and power. Logarithmic Number Systems (LNS) offer a viable alternative combining the simplicity of fixed point number systems and the precision of floating point number systems. However, the computations in LNS result in some loss of accuracy and thus, are limited to mostly signal processing applications; where in certain amount of error is tolerable. In LNS, the cost of computations can be tradeoff with the level of accuracy needed. The Mitchell algorithm proposed incite[mitchell], is a simple approach commonly used for logarithmic multiplication. The method involves a high error margin due to a piecewise straight line approximation of the logarithm curve. Thus, several methods have been proposed in the literature for improving the accuracy of Mitchell's algorithm. In this thesis, we propose a new method for improving the accuracy of Mitchell's logarithmic multiplication using operand decomposition. The operand decomposition process decreases the number of bits with the value of '1' in the multiplicands and reduces the amount of approximation. The proposed method brings down the average error percentage of Mitchell's logarithmic multiplication by around 45%. It can be combined with previous methods to further improve the accuracy. Experimental results are presented to show that both the error range and the average error percentage can be significantly improved by using operand decomposition.

Motivated by the work of Hognas and Mukherjea on semigroups,we study semihypergroups, which are structures closer to semigroups than hypergroups in the sense that they do not require an identity or an involution. Dunkl[Du73] calls them hypergroups (without involution), and Jewett[Je75] calls them semiconvos. A semihypergroup does not assume any algebraic operation on itself. To generalize results from semigroups to semihypergroups, we first put together the fundamental algebraic concept a semihypergroup inherits from its measure algebra. Among other things, we define the Rees convolution product, and prove that if X; Y are non-empty sets and H is a hypergroup, then with the Rees convolution product, X x H x Y is a completely simple semihypergroup which has all its idempotent elements in its center. We also point out striking differences between semigroups and semihypergroups. For instance, we construct an example of a commutative simple semihypergroup, which is not completely simple. In a commutative semihypergroup S, we solve the Choquet equation μ * v = v, under certain mild conditions.We also give the most general result for the non-commutative case.We give an example of an idempotent measure on a commutative semihypergroup whose support does not contain an idempotent element and so could not be completely simple. This is in contrast with the context of semigroups, where idempotent measures have completely simple supports. The results of Hognas and Mukherjea [HM95] on the weak convergence of the sequence of averages of convolution powers of probability measures is generalized to semihypergroups. We use these results to give an alternative method of solving the Choquet equation on hypergroups (which was initially solved in [BH95] with many steps). We show that If S is a compact semihypergroup and μ is a probability measure with S = [ U∞n=1 Supp(μ)n], then for any open set G ⊃ K where K is the kernel of S limn-→∞μn(G) = 1. Finally, we extend to hypergroups basic techniques on multipliers set forth for groups in [HR70], namely propositions 5.2.1 and 5.2.2 , we give a proof of an extended version of Wendel's theorem for locally compact commutative hypergroups and show that this version also holds for compact non-commutative hypergroups. For a compact commutative hypergroup H, we establish relationships between semigroup S = S = {T(ξ) : ξ > 0} of operators on Lp(H), 1 ≤ p < 1 < ∞, which commutes with translations, and semigroup M = {Eξ : ξ > 0} of Lp(H) multipliers. These results generalize those of [HP57] for the circle groups and [B074] for compact abelian groups.

The unsteady nature of coastal hydrodynamics is associated with complex boundary layer dynamics and hence engineering predictions of shear stresses and sediment transport are difficult. This thesis explores some of the complex hydrodynamic problems and boundary layer behaviour in the coastal zone and seeks to provide new and improved modelling approaches. The latest experimental results are used to inform the model development process. New laboratory experiments carried out as part of this thesis illustrate the value of convolution integral calculations for both pressure and skin friction forces on particles on the bed. The experiments also highlight the importance of the phase differences between free stream velocity and boundary layer shear stresses. The use of a “bed” shear stress as a model input is found to be problematic whenever there is a large vertical gradient in the boundary layer shear stress. New experimental and modelling work has helped to improve our understanding of sheet flow boundary layer dynamics. This thesis builds on some of these new discoveries to propose a new simplified model framework for sheet flow sediment transport prediction using convolution integrals. This time domain technique has the advantage of simplicity while incorporating the most important physical processes from more detailed models. The new model framework could be incorporated into any depth averaged coastal hydrodynamic modelling software package. Boundary layer analysis techniques presented in the thesis provide an improved understanding of the effective roughness of mobile beds and can be used to calculate instantaneous shear stress profiles throughout the mobile bed boundary layer. New solutions for swash zone hydrodynamics are presented which illustrate the limitations of the previous benchmark analytical model for swash hydrodynamics. It is shown that real swash necessarily involves a much larger influx of mass and momentum than the analytical solution which was previously used by many in the swash sediment transport research community. Models for swash boundary layer development are also presented.

Je présente dans ce manuscrit mes travaux de recherche effectués depuis la thèse. Mes thèmes de recherche sont principalement motivés par des applications en génomique ou post-génomique. Mon domaine de recherche est assez vaste, mais le dénominateur commun de mes travaux est la présence de variables latentes (non observées) dans les modèles étudiés. Mes préoccupations sont majoritairement théoriques : éudes asymptotiques, convergence des estimateurs, vitesses, identifiabilité... Les modèles considérés peuvent être aussi bien paramétriques que semi ou non paramétriques, et les outils statistiques utilisés sont donc relativement variés.<br /><br />Ma présentation s'organise en trois grandes thématiques : les travaux portant sur des séquences, notamment sur la modélisation de leur distribution et des processus d'évolution sous-jacents ; les travaux de statistique semi ou non paramétrique portant sur des signaux observés avec du bruit ; et enfin les travaux (en partie en cours) portant sur les graphes aléatoires.

Ce travail se décompose en trois parties distinctes. Dans la première partie, on introduit un algorithme du type Gauss-Seidel pour la minimisation de fonctionnelles symétriques semi-définies positives. La convergence de cet algorithme est démontrée. En application, on donne deux méthodes de lissage de surfaces. Ces méthodes sont basées sur l'idée de ramener un probleme de lissage a deux dimensions a la resolution d'une suite de problèmes a une dimension faciles a résoudre. Pour cela on utilise l'opération d'inf-convolution spline. Dans la deuxième partie, on introduit une nouvelle methode pour la conception d'un verre progressif. Ce verre est représente par une surface suffisamment régulière, a laquelle on impose des conditions sur ses courbures principales dans certaines zones (zone de vision de loin et zone de vision de pres), et des conditions sur ses directions principales de courbure dans d'autres zones (zone nasale et zone temporale). La surface est écrite sous forme de produit tensoriel de b-splines de degré quatre. Pour la calculer, on est amené a minimiser un opérateur non quadratique. Cette minimisation est alors effectuée par un procédé itératif dont on a teste numériquement la convergence rapide

Développement d'un algorithme de telles surfaces en utilisant la théorie de l'inf-convolution spline. Ceci est réalisé grâce à un choix de base traduisant les discontinuités. Un algorithme original de trace de courbes isovaleurs pour ces surfaces base sur une méthode de suivi des courbes de niveau est présente. Proposition d'un logiciel regroupant différents algorithmes