Among the presently known numerical solvers of integral equations, two main categories of approaches can be traced: mesh-free approaches, mesh-based approaches. We will propose some techniques to process geometric data so that they can be efficiently used in subsequent numerical treatments of integral equations. In order to prepare geometric information so that the above two approaches can be automatically applied, we need the following items: (1) Splitting a given surface into several four-sided patches, (2) Generating a diffeomorphism from the unit square to a foursided patch, (3) Generating a mesh M on a given surface, (4) Patching of a given triangulation. In order to have a splitting, we need to approximate the surfaces first by polygonal regions. We use afterwards quadrangulation techniques by removing quadrilaterals repeatedly. We will generate the diffeomorphisms by means of transfinite interpolations of Coons and Gordon types. The generation of a mesh M from a piecewise Riemannian surface will use some generalized Delaunay techniques in which the mesh size will be determined with the help of the Laplace-Beltrami operator. We will describe our experiences with the IGES format because of two reasons. First, most of our implementations have been done with it. Next, some of the proposed methodologies assume that the curve and surface representations are similar to those of IGES. Patching a mesh consists in approximating or interpolating it by a set of practical surfaces such as B-spline patches. That approach proves useful when we want to utilize a mesh-free integral equation solver but the input geometry is represented as a mesh.

L’intérêt principal de cette recherche porte sur la validation d’une méthode statistique en pharmaco-épidémiologie. Plus précisément, nous allons comparer les résultats d’une étude précédente réalisée avec un devis cas-témoins niché dans la cohorte utilisé pour tenir compte de l’exposition moyenne au traitement : – aux résultats obtenus dans un devis cohorte, en utilisant la variable exposition variant dans le temps, sans faire d’ajustement pour le temps passé depuis l’exposition ; – aux résultats obtenus en utilisant l’exposition cumulative pondérée par le passé récent ; – aux résultats obtenus selon la méthode bayésienne. Les covariables seront estimées par l’approche classique ainsi qu’en utilisant l’approche non paramétrique bayésienne. Pour la deuxième le moyennage bayésien des modèles sera utilisé pour modéliser l’incertitude face au choix des modèles. La technique utilisée dans l’approche bayésienne a été proposée en 1997 mais selon notre connaissance elle n’a pas été utilisée avec une variable dépendante du temps. Afin de modéliser l’effet cumulatif de l’exposition variant dans le temps, dans l’approche classique la fonction assignant les poids selon le passé récent sera estimée en utilisant des splines de régression. Afin de pouvoir comparer les résultats avec une étude précédemment réalisée, une cohorte de personnes ayant un diagnostique d’hypertension sera construite en utilisant les bases des données de la RAMQ et de Med-Echo. Le modèle de Cox incluant deux variables qui varient dans le temps sera utilisé. Les variables qui varient dans le temps considérées dans ce mémoire sont iv la variable dépendante (premier évènement cérébrovasculaire) et une des variables indépendantes, notamment l’exposition / The main interest of this research is the validation of a statistical method in pharmacoepidemiology. Specifically, we will compare the results of a previous study performed with a nested case-control which took into account the average exposure to treatment to : – results obtained in a cohort study, using the time-dependent exposure, with no adjustment for time since exposure ; – results obtained using the cumulative exposure weighted by the recent past ; – results obtained using the Bayesian model averaging. Covariates are estimated by the classical approach and by using a nonparametric Bayesian approach. In the later, the Bayesian model averaging will be used to model the uncertainty in the choice of models. To model the cumulative effect of exposure which varies over time, in the classical approach the function assigning weights according to recency will be estimated using regression splines. In order to compare the results with previous studies, a cohort of people diagnosed with hypertension will be constructed using the databases of the RAMQ and Med-Echo. The Cox model including two variables which vary in time will be used. The time-dependent variables considered in this paper are the dependent variable (first stroke event) and one of the independent variables, namely the exposure.

CETTE THESE TRAITE DU PROBLEME DE LA LOCALISATION DANS UN ENVIRONNEMENT TRIDIMENSIONNEL (3D) D'UN ROBOT MOBILE AUTONOME, AINSI QUE DE CELUI DE LA MODELISATION DE TERRAIN. DEUX DOMAINES TYPIQUES D'APPLICATION DE CE TRAVAIL SONT LA ROBOTIQUE MOBILE D'INTERVENTION (SECURITE CIVILE,) ET L'EXPLORATION PLANETAIRE. LA CONTRIBUTION DE LA THESE SE SITUE SURTOUT AU NIVEAU DE LA LOCALISATION D'UN ROBOT DANS UN ENVIRONNEMENT SEMI-STRUCTURE OU NON STRUCTURE. UN ETAT DE L'ART CONCERNANT D'UNE PART LES PRINCIPAUX CAPTEURS UTILISABLES, ET D'AUTRE PART LA MODELISATION, EST PRESENTE. L'ACCENT EST MIS SUR LES CAPTEURS INERTIELS ET SUR LA MODELISATION DE FORMES NON STRUCTUREES ; LE CHOIX DES CAPTEURS UTILISES, AINSI QUE CELUI DES PRIMITIVES GEOMETRIQUES RETENUES, SONT JUSTIFIES. DANS UN PREMIER TEMPS, UNE APPROCHE POUR LA LOCALISATION DU ROBOT A L'AIDE D'AMERS DE TYPE STRUCTURE, MAIS EVENTUELLEMENT NATURELS, EST PRESENTEE. LE PROBLEME DE LA FUSION INCREMENTALE D'UN MODELE DE LOCALISATION BASE SUR DES PRIMITIVES HETEROGENES, A PARTIR DE LA DETECTION DE LIGNES VERTICALES (ARBRES, COLONNES) OU DE MURS, EST TRAITE. PLUSIEURS APPROCHES POUR LE RECALAGE DE LA POSITION DU ROBOT ET LA FUSION DES DONNEES HETEROGENES SONT COMPAREES. UNE STRATEGIE DE CHOIX DES DIFFERENTS AMERS EST ENFIN PROPOSEE. DANS UN DEUXIEME TEMPS, LE PROBLEME DE LA MODELISATION DE TERRAIN ACCIDENTE ET DU RECALAGE SUR DES CARACTERISTIQUES NON STRUCTUREES DE L'ENVIRONNEMENT EST ABORDE. UNE METHODE DE MODELISATION DU TERRAIN PAR HIERARCHIE DE B-SPLINES EST PROPOSEE, ET LA CONSTRUCTION INCREMENTALE DU MODELE DE TERRAIN EST TRAITEE. LE MODELE ANALYTIQUE OBTENU PERMET D'EXTRAIRE DIVERS INVARIANTS 3D, COMME DES MAXIMA D'ALTITUDE OU DES POINTS DE FORTE COURBURE ; L'ASPECT MULTI-RESOLUTION PERMET DE FOCALISER PROGRESSIVEMENT LA RECHERCHE DE TELLES CARACTERISTIQUES. FINALEMENT, UNE METHODE DE LOCALISATION FAISANT COOPERER L'EXTRACTION DE CARACTERISTIQUES AVEC DES TECHNIQUES DE TYPE CORRELATION EST PROPOSEE. LES DIFFERENTES METHODES DEVELOPPEES ONT FAIT L'OBJET D'UNE VALIDATION SUR PLUSIEURS ROBOTS MOBILES EXPERIMENTAUX

Advances in numerical optimization have raised the possibility that efficient and novel aircraft configurations may be ``discovered'' by an algorithm. To begin exploring this possibility, a fast and robust set of tools for aerodynamic shape optimization is developed. Parameterization and mesh-movement are integrated to accommodate large changes in the geometry. This integrated approach uses a coarse B-spline control grid to represent the geometry and move the computational mesh; consequently, the mesh-movement algorithm is two to three orders faster than a node-based linear elasticity approach, without compromising mesh quality. Aerodynamic analysis is performed using a flow solver for the Euler equations. The governing equations are discretized using summation-by-parts finite-difference operators and simultaneous approximation terms, which permit nonsmooth mesh continuity at block interfaces. The discretization results in a set of nonlinear algebraic equations, which are solved using an efficient parallel Newton-Krylov-Schur strategy. A gradient-based optimization algorithm is adopted. The gradient is evaluated using adjoint variables for the flow and mesh equations in a sequential approach. The flow adjoint equations are solved using a novel variant of the Krylov solver GCROT. This variant of GCROT is flexible to take advantage of non-stationary preconditioners and is shown to outperform restarted flexible GMRES. The aerodynamic optimizer is applied to several studies of induced-drag minimization. An elliptical lift distribution is recovered by varying spanwise twist, thereby validating the algorithm. Planform optimization based on the Euler equations produces a nonelliptical lift distribution, in contrast with the predictions of lifting-line theory. A study of spanwise vertical shape optimization confirms that a winglet-up configuration is more efficient than a winglet-down configuration. A split-tip geometry is used to explore nonlinear wake-wing interactions: the optimized split-tip demonstrates a significant reduction in induced drag relative to a single-tip wing. Finally, the optimal spanwise loading for a box-wing configuration is investigated.

[pt] No processo de perfilagem de poços de petróleo e gás, as propriedades entre duas camadas axiais podem apresentar diferenças. Estas descontinuidades das propriedades algumas vezes trazem dificuldades na representação do comportamento dos campos electromagnéticos. Nas análises eletromagnéticas de perfilagem de poço de petróleo, o Método de Casamento de Modos (NMM) vem sendo utilizado a partir da combinação de técnicas numéricas com analíticas e da resolução das equações de Maxwell em meios heterogêneos, cujos campos eletromagnéticos, na direção axial, são representados via decomposição espectral, e, na direção radial, por meio de solução das equações diferenciais ordinárias. Assim, com o objetivo de explorar a representação dos campos eletromagnéticos sobre as interfaces axiais via NMM, este trabalho propõe a utilização de funções B-Splines cúbicas na expansão dos campos, na direção axial, bem como a incorporação da multiplicidade de nós, que permitem uma melhor representação do comportamento dos campos nas interfaces axiais. O algoritmo implementado foi validado nas suas diversas etapas ao comparar os autovalores da representação modal com os obtidos analiticamente em problemas canônicos, e os resultados finais comparados com exemplos apresentados na literatura e calculados com o Método de Diferenças Finitas no Tempo (FDTD). O método NMM, combinado às funções B-Splines cúbicas, foi aplicado a vários perfis de poços de petroléo que serviram de exemplo neste estudo. Um estudo comparativo mostrou que o uso das funções B-Splines cúbicas com multiplicidade dos nós sobre as descontinuidades permitiu uma redução no número total de nós nas expansões dos campos eletromagnéticos. / [en] In the logging process of gas and oil wells, differences in the properties between two axial layers can usually be found. These property discontinuities can bring difficulties for the representation of electromagnetic fields behavior. For electromagnetic analysis of well logging, the Numerical Mode-Matching - NMM method has been used. It combines numerical and analytical techniques, by solving equations Maxwell s in a heterogeneous media. There, the electromagnetic fields in the axial direction are represented by spectral decomposition and in the radial direction are represented by the solution of Ordinary Differential Equations (ODE). With the objective of explorer the representation of the electromagnetic fields on axial interfaces in the Numerical Mode Matched Method, this work explores the use of B-Splines cubic functions to expand the fields in the axial direction, as well as the incorporation of the multiple knots fetching to become the representation of fields behavior most optimized and realistic on axial interfaces. The NMM algorithm was implemented and it was validated by comparing the final results with those obtained by using Finite Difference Time-Domain – FDTD to analyse examples shown in the literature. To validate the results obtained for the eigenvalues, they were compared with the analytical solutions obtained for canonical configurations. The use of NMM Method combined with B-Spline cubic has been applied to several well profiles shown in the literature. The comparative study showed that the use B-Spline cubic with multiple knots near the discontinuities allows a reduction in the overall number of knots employed in the field expansion.

La thèse porte sur la segmentation spatio-temporelle et interactive d'images cardiaquesdynamiques. Elle s'inscrit dans le projet ANR 3DSTRAIN du programme"Technologies pour la Santé et l'Autonomie" qui a pour objectif d'estimer de façoncomplète, dense et sur plusieurs modalités d'imagerie 3D+t (telles que l'imageriepar résonance magnétique (IRM), la tomographie par émission monophotonique(TEMP) et l'échocardiographie) l'indice de déformation du muscle cardiaque : lestrain. L'estimation du strain nécessite une étape de segmentation qui doit être laplus précise possible pour fournir une bonne évaluation de cet indice. Nos travauxse sont orientés sur deux axes principaux : (1) le développement d'un modèle desegmentation conforme à la morphologie du muscle cardiaque et (2) la possibilitéde corriger interactivement et intuitivement le résultat de la segmentation obtenuegrâce à ce modèle. / This thesis focuses on the spatio-temporal and interactive segmentation of dynamiccardiac images. It is a part of the ANR 3DSTRAIN project of program "Technologiesfor Health and Autonomy" which aims to estimate full, dense and on several3D+t imaging modalities (such as Magnetic Resonance Imaging (MRI), Single PhotonEmission Computed Tomography (SPECT) and echocardiography) the indexof deformation of the heart muscle : the strain. The strain estimation requires asegmentation step which must be as precise as possible to provide a good estimationof this index. Our work was focused on two main areas : (1) the development of asegmentation model conforms to the shape of the heart muscle and (2) the abilityto interactively and intuitively correct the segmentation's result obtained with thismodel.

The aim of this thesis is to analyze two major indicators representing the processes of natural changes in population, which are not influenced by age structure -- age specific fertility rate and age specific mortality rate and to introduce functional data analysis, which has recently become increasingly applied in many scientific fields. The functional data analysis is introduced on the Czech demographic data set for more than last sixty years. The thesis briefly describes historical development of mortality and fertility and also describes selected methods of functional data analysis by using statistical program R. Functional data analysis provides a wide variety of graphics tools to explore the data which we called functional and help us to explore all typical and atypical features, identify outliers etc.

Diploma thesis deals with image interpolation. The aim of this work is to study theoretically and then describe the nature of the various methods of image interpolation and some of them implemented in the program MATLAB. The introductory part of this work theoretically closer to important terms that are closely related to this topic of digital image processing sufficient to understand the principle. In the following of the thesis will be discussed all of today's commonly used method of image interpolation. Will hear all about the method of image interpolation using nearest neightbor interpolation and image help of polynimals such as (bi)linear, (bi)quadratic and (bi)kubic method. Then work theoretically analyzes the theory of individual species curves and splines. More specifically, coming to their most frequently used variants of B-spline curves and ther generalizations called NURBS, with addressing the problem of interpolating these curves. The final chapter consists of the results achieved in the program MATLAB.

This study focuses on the numerical solution of a fourth-order cell problem obtained through a two- scale expansion approach applied to a higher gradient heat equation microscopic problem involving temperature distributions. The main objective is to investigate the temperature field within the macroscale domain and compute the effective conductivity using finite element methods. The research utilizes numerical techniques, specifically finite element methods, to solve the fourth-order cell problem and obtain the temperature distribution.

This thesis develops an algorithm to decrease high-curvature sections in tool paths for complex parts to achieve shorter machining times resulting in higher production rates. In the research sample cases, the algorithm decreased machining times by 1% to 9% for design-induced sections of high curvature and by 16% to 75% for CAM induced ripples using high path tolerances. High-curvature sections in tool paths are caused by complex part geometry, noise, and discontinuities in the model. The curvature is decreased by deviating the tool path within an allowable path tolerance. The feedrate along the tool path is directly related to the curvature of the tool path. High-curvature sections cause the NC machine to reduce the feedrate along the tool path due to acceleration and jerk limits. These lower feedrates increase machining time and slow production rates. This new algorithm decreases curvature, which increases feedrates and decreases machining times, thereby increasing production rates for manufacturing companies. The tool paths are represented by cubic B-splines. The algorithm is based on the basic principle that the curvature of a B-spline directly relates to the geometry of its control polygon. If the control polygon's geometry has many tight corners then the B-spline will have high curvature. If the control polygon's geometry is a straight line then the B-spline will be a straight line with zero curvature. The algorithm deviates the control polygon's points so that they move towards forming a straight line. The control polygon will rarely form a straight line because the spline is limited by the path tolerance. However, as the control polygon moves towards forming a straight line, the curvature decreases, which allows the feedrate to increase. Six sample cases are explored in which the machining time is decreased. Three of the cases are tool paths that contain curvature sections with a range of unnecessary curvature from low to high. One sample is the tool path for the complex geometry in a snow tire mold. Another sample tool path contains ripples caused by noise in the CAD model. The last tool path contains ripples caused by tangency discontinuities in the CAD model. The percent of time saved directly relates to the severity of the curvature in the part. This thesis provides a quick and efficient means to reduce curvature in complex parts, resulting in decreased machining times and increased production rates.