La Décomposition Modale Empirique (EMD) est un outil de traitement de signal piloté par les données et dédié aux signaux non-stationnaires issus ou non de systèmes linéaires. L'idée de base de l'EMD est l'interpolation des extrema par des splines pour extraire de composantes oscillantes appelées modes empiriques intrinsèques (IMFs) et un résidu. Dans cette thèse, un nouvel algorithme de l'EMD est introduit où au lieu d'une interpolation rigide, un lissage est utilisé pour la construction des enveloppes supérieures et inférieures du signal à décomposer. Ce nouvel algorithme est plus robuste au bruit que l'EMD conventionnelle et réduit le nombre d'IMFs "artificielles" (sur-décomposition). En combinant le nouvel algorithme et la méthode de séparation d'énergie (ESA) basée sur l'Opérateur d'Energie de Teager-Kaiser (OETK), un nouveau schéma de démodulation des signaux AM-FM multi-composante appelé EMD-ESA est introduit. Différentes versions de l'EMD-ESA sont analysées en terme de performance. Pour l'analyse Temps-Fréquence (TF), une nouvelle formulation de la carte TF de l'EMD-ESA appelée Transformation de Teager-Huang (THT) est présentée. Cette nouvelle Représentation TF (RTF) ne présentant pas de termes d'interférences est comparée aux RTF classiques telles que le spectrogramme, le scalogramme, la distribution de Wigner-Ville Distribution (WVD), la Pseudo-WVD et la réallocation de la Pseudo-WVD. En combinant la nouvelle formulation de la THT et la transformée de Hough, une nouvelle méthode de détection des signaux multi-composante à modulation linéaire de fréquence dans le plan TF est présentée. Cette méthode de détection est appelée transformation de Teager-Huang-Hough (THHT). Les résultats de la THHT sont comparés à ceux de la transformée WVD-Hough. Finalement, l'analyse TF par THT et par des RTF classiques (WVD, spectrogramme, etc.) de signaux réels de rétrodiffusion par des coques cylindriques de dimensions et de caractéristiques physiques différentes est présentée. Les résultats obtenus montrent l'apport de la THT comme un outil TF.

In dieser interdisziplinär geprägten Arbeit wird zunächst eine Übersicht über kugelbasierte Modelle und die algorithmischen Ansätze zur Generierung zufälliger Kugelpackungen gegeben. Ein Algorithmus aus der Gruppe der Kollektiven-Umordnungs-Algorithmen -- der Force-Biased-Algorithmus -- wird ausführlich erläutert und untersucht. Dabei werden die für den Force-Biased-Algorithmus als essenziell geltenden Verschiebungsfunktionen bezüglich ihres Einflusses auf den erreichbaren Volumenanteil der Packungen untersucht. Nicht nur aus der Literatur bekannte, sondern auch neu entwickelte Verschiebungsfunktionen werden hierbei betrachtet. Daran anschließend werden Empfehlungen zur Auswahl geeigneter Verschiebungsfunktionen gegeben. Einige mit dem Force-Biased-Algorithmus generierte Kugelpackungen, zum Beispiel hochdichte monodisperse Packungen, lassen den Schluss zu, dass insbesondere strukturelle Umbildungsvorgänge an solchen Packungen sehr gut zu untersuchen sind. Aus diesem Grund besitzt das Modell der mit dem Force-Biased-Algorithmus dicht gepackten harten Kugeln große Bedeutung in der Materialwissenschaft, insbesondere in der Strukturforschung. In einem weiteren Kapitel werden wichtige Kenngrößen kugelbasierter Modelle erläutert, wie z. B. spezifische Oberfläche, Volumenanteil und die Kontaktverteilungsfunktionen. Für einige besonders anwendungsrelevante Kenngrößen (z. B. die spezifische Oberfläche) werden Näherungsformeln entwickelt, an Modellsystemen untersucht und mit bekannten Näherungen aus der Literatur verglichen. Zur Generierung und Analyse der Kugelpackungen wurde im Rahmen dieser Arbeit die Simulationssoftware „SpherePack“ entwickelt, deren Aufbau unter dem Aspekt des Softwareengineerings betrachtet wird. Die Anforderungen an dieses Simulationssystem sowie dessen Architektur werden hier beschrieben, einschließlich der Erläuterung einzelner Berechnungsmodule. An ausgewählten praxisnahen Beispielen aus der Materialwissenschaft kann die Vielfalt der Einsatzmöglichkeiten eines Simulationssystems zur Generierung und Analyse von zufälligen dicht gepackten Kugelsystemen gezeigt werden. Vor allem die hohe Aussagekraft der Untersuchungen in Bezug auf Materialeigenschaften unterstreicht die Bedeutung des Modells zufällig dicht gepackter harter Kugeln in der Materialforschung und verwandten Forschungsgebieten.

Ce mémoire porte sur l’étude des équations d’évolution sur des variétés à coubure non nulle, plus particulièrement l’équation des ondes sur les espaces symétriques riemanniens de type non compact.Des propriétés de dispersion des solutions du problème de Cauchy homogène sont démontrées. Ces propriétés sont ensuite utilisées pour établir des estimations dites estimations de Strichartz. L’examen de ces estimées permet de déduire que le problème de Cauchy non linéaire avec des non-linéarités de type puissance est globalement bien posé pour des données initiales petites et localement bien posé pour des données arbitraires.Après un chapitre introductif dédié aux définitions, propriétés algébriques et géométriques des espaces symétriques et à quelques aspects élémentaires d’analyse harmonique sphérique sur ces espaces, un article est présenté : Wave equation on Riemannian symmetric spaces. Cet article contient nos résultats principaux. Dans le dernier chapitre nous présentons en détail deux problèmes ouverts qui prolongent nos travaux. Il s’agit respectivement d’établir le lien entre le comportement asymptotique des estimées et les orbites nilpotentes, et l’étude de l’équation des ondes pour les formes différentielles sur les espaces symétriques. / In this memoir we study evolution equations on curved manifolds. In particular we are interested in the wave equation on Riemannian symmetric spaces of the noncompact type.Dispersive properties of solutions of homogeneous Cauchy problem are proved. These properties are then used to establish Strichartz-type estimates. A closer study of these estimates shows that the nonlinear Cauchy problem with power-like nonlinearities is globally well posed for small initial data and locally well posed for arbitrary initial data.The first chapter is devoted to definitions, algebraic and geometric properties of symmetric spaces and to few elementary aspects of spherical analysis on these spaces. Then our main results are represented in an article : Wave equation on Riemannian symmetric spaces. In the last chapter we present in detail two open problems for future work. One issue is to establish a link between the asymptotic behavior of the estimates and nilpotent orbits, while another issue is the study of wave equation for differential forms on symmetric spaces.

L’apparition de la télé-échographie à la fin des années 1990 a largement contribué à l’améliorationdes capacités de prise en charge des patients. Aujourd’hui, le laboratoire PRISME bénéficie d’unsavoir faire reconnu dans la conception de systèmes de télé-échographie robotisée. L’objectif deces travaux de thèse est d’apporter une contribution scientifique et technique au projet ANR-PROSIT,qui vise à la mise en oeuvre d’un robot de télé-échographie innovant. Une étude du geste du praticienen milieu clinique a été menée afin d’en déterminer les caractéristiques cinématiques. Réalisée àl’aide du système de capture de mouvement Vicon Nexus, cette analyse a contribué à l’établissementdes spécifications du futur robot. Sa structure mécanique a fait l’objet d’une attention particulière. Unearchitecture parallèle sphérique a été sélectionnée, étudiée puis optimisée via un algorithmegénétique en fonction des critères d’espace de travail, de dextérité et de compacité. L’architectureainsi obtenue est ensuite analysée sur des aspects de collisions et d’inaccessibilité. Pour le contrôlede ce robot, l’utilisation d’une interface haptique à l’aspect proche d’une sonde d’échographie estproposée. Dotée d’un système de retour d’effort et d’une centrale inertielle fiabilisée par un filtre deKalman adaptatif, cette nouvelle interface a été testée et validée par le système Vicon Nexus. / Since the end of the nineties, the tele-echography has been contributing to improve the taking carecapacities of patients. Today, the PRISME laboratory has a recognized expertise in the design ofrobotic tele-echography systems. The objective of this thesis is to provide scientific and technicalsupport to the ANR-PROSIT project. It aims to design of an innovative tele-echography robot. Anexpert gesture study has been carried out in clinical environment to determine its kinematiccharacteristics. It has been performed using the motion capture system Vicon Nexus and itcontributed to establish the specifications of the future robot. The mechanic structure of this robot hasbeen minutely taken in consideration. The spherical parallel mechanism has been selected, studiedand optimized using a genetic algorithm with respect of criterion such as workspace, dexterity andcompacity. The resulted architecture is then analyzed regarding collisions and inaccessibilityaspects. To control this robot, the use of a haptic device with the same shape of an ultrasound probeis proposed. It provides force feedback and it is instrumented with an inertial measurement unit,processed by an adaptative Kalman filter. This new interface has been tested and validated by ViconNexus system.

O ganho crescen te de desempenho nos computadores modernos tem impulsionado os trabalhos científicos nas áreas de simulação computacional. Muitos autores utilizam em suas pesquisas ferramentas comerciais que limitam seus trabalhos ao esconder os algoritmos internos destas ferramentas e dificultam a adição de dados in-vivo nestes trabalhos. Este trabalho explora esta lacuna deixada por aqueles autores. Elaboramos um arcabouço computacional capaz de reproduzir os fenômenos óticos e fisiológicos do sistema visual. Construímos com superfícies quádricas os modelos esquemáticos do olho humano e propomos um algoritmo de traçado de raio realístico. Então realizamos um estudo nos modelos esquemáticos e a partir deles mais a adição de dados in-vivo obtidos de um topógrafo de córnea extraímos informações óticas destes modelos. Calculamos os coeficientes e Zernike dos modelos para tamanhos diversos de pupila e obtivemos medidas de aberração do olho humano. Os resultados encontrados estão de acordo com os trabalhos relacionados e as simulações com dados in-vivo estão consoantes com as produzidas por um aparelho de frente de onda comerciais. Este trabalho é um esforço em aproveitar as informações adquiridas pelos equipamentos modernos de oftalmologia, além de auxiliar o entendimento de sistemas visuais biológicos acabam também em auxiliar a elaboração de sistemas de visão artificial e os projetistas de sistemas óticos / The increase in performance of the modern computers has driven scientific work in the areas of computer simulation. Many authors use in their research commercial tools that use embedding algorithms, which sources are not provided, and it makes harder and sometimes impossible, the development of novel theories or experiments. This work explores this gap left for those authors. We present a computational framework capable to reproduce the optical and physiological phenomena of the human visual system. We construct schematical models of the human eye from quadrics surfaces and consider an algorithm of realistic ray tracing. Afterward, we performed a study on schematics models and in addition we introduce, in these models, in-vivo data obtained from corneal topography machine and extract optical information. We calculate the Zernike coefficients in the models for different sizes of pupil and measures of aberration of the human eye. The results are in agreement with related work and simulations with in-vivo data are according with the produced by a commercial wave-front device. This work is an effort in using to advantage the information acquired for the modern equipment of ophthalmology, besides assisting the understanding of biological visual systems, it also helps the development of artificial vision systems and the designing of optical systems

A maneira mais direta de detectar as anomalias da densidade é pelo estudo do potencial gravitacional e de suas derivadas. A disponibilidade global e a boa resolução dos dados do satélite GOCE, aliadas à disponibilidade de dados de gravimetria terrestre, são ideais para a comparação e classificação das bacias de larga escala, como as bacias sedimentares do Solimões e do Amazonas dentro do Craton amazônico. Foram processados um conjunto de dados, produtos GOCE EGG_TRF_2 Level 2, ao longo das trajetórias do satélite para remover o ruído (shift/drift) nos gradientes da gravidade a partir da técnica crossover (XO). Calculamos a redução das massas topográfica a fim de obter os componentes do gradiente da gravidade e anomalia da gravidade usando modelagem direta com prismas esféricos a partir do modelo de elevação digital, ETOPO1. Desta maneira, a comparação dos dados somente do satélite GOCE com as reduções das massas topográficas referentes aos componentes do gradiente da gravidade permitiram estimar quantidades invariantes que trouxeram uma melhoria na interpretação dos dados do tensor de gravidade. Além disso, comparamos dados terrestres do campo de gravidade com dados do campo de gravidade dos modelos geopotenciais EGM2008 e GOCE, uma vez que os dados terrestres podem ser afetados por erros em longos comprimentos de onda devido a erros de nivelamento, diferentes referenciais de altitudes, e aos problemas em interligar diferentes campanhas de medidas da gravidade. Portanto, estimamos uma melhora e uma nova representação dos mapas das anomalias de gravidade e do tensor gradiente da gravidade nas áreas inacessíveis do Craton Amazônico. As observações forneceram novas entradas para determinar campos regionais a partir dados brutos pre-processados (gradiente de gravidade EGG_TRF_2 L2), bem como a partir de um modelo geopotencial mais recente até grau e ordem 250 dos harmonicos esféricos derivados de dados somente do satélite GOCE para a representação do campo de gravidade como geóide, anomalias da gravidade e os componentes tensor da gravidade, os quais foram quantidades importantes para interpretação, modelagem e estudo dessas estruturas. Finalmente, obtivemos um modelo isostático considerando a estrutura de densidade litosférica estudada através de uma modelagem direta 3D da distribuição de densidade por prismas esféricos usando a geometria do embasamento e descontinuidade do Moho. Além do que, constatamos através da modelagem direta das soleiras de diabásios dentro dos sedimentos mostramos que somente as soleiras dentro da Bacia do Amazonas não são as únicas responsáveis pela anomalia de gravidade positiva que coincide aproximadamente com as espessuras máximas dos sedimentos da Bacia. Talvez, isso possa ser também um resultado de movimentos relativos do Escudo das Guianas situado ao norte da Bacia, e o Escudo Brasileiro situado ao sul. Embora isso seja apenas uma evidência adicional preliminar, não podemos confirmá-las a partir das estimativas do campo da gravidade. Portanto, é necessário outros tipos de dados geofísicos, como por exemplo, evidências mais claras advindas do paleomagnetismo. / The most direct way to detect density anomalies is the study of the gravity potential field and its derivatives. The global availability and good resolution of the GOCE mission coupled with the availability of terrestrial gravity data are ideal for the scope of intercomparison and classification of the two large-scale Amazon and Solimoes sedimentary basins into area of the Amazon Craton. The GOCE data set obtained in satellite tracks were processed from EGG_TRF_2 Level 2 Products generated with the correction needed to remove the noise (shift/drift), and so, to recover the individual components of the gravity gradient tensor using the crossover (XO) points technique. We calculated the topographic masses reductions in order to obtain the gravity gradient components and gravity anomaly (vertical component) using forward modelling from tesseroids from Digital Elevation Model, ETOPO1. Thus, the comparison of the only-satellite GOCE data with the reductions of the topographic masses for the gradient components allowed to estimate invariants quantities for bring an improvement in the interpretation of the gravity tensor data. Furthermore, we compared the terrestrial data gravity field with EGM2008 and GOCE-deduced gravity field because the terrestrial fields may be affected by errors at long wavelengths due to errors in leveling, different height references, and problems in connecting different measurement campaigns. However, we have estimated an improvement and new representations of the gravity anomalies maps and gravity gradient tensor components primary in inaccessible areas of the Amazon Craton. GOCE observations provide new inputs to determine the regional fields from the preprocessed raw data (EGG_TRF_2 L2 gravity gradients), as well from the most recent global geopotential model available up to degree and order 250 developed in spherical harmonics derived only-satellite GOCE data for representing of geoid and others gravity field as gravity anomaly and gravity gradient tensor components, which are important quantities for modelling and studying these structures. Finally, we obtained the isostatic model considering the lithospheric density structure studied through a 3D direct modelling of density distribution using the geometry of basement and Moho discontinuity, assumed to be known as initial constraint. In addition, we found through direct modeling sills and sediment has shown that the diabase sills are not the only ones responsible for positive gravity anomaly map that transects the Amazon Basin, roughly coincident with the maximum thickness of sedimentary rocks or the trough of the basin. Maybe, this could be the result of the relative movements of the Guiana Shield, situated at the north of the Amazon basin, and the Brazilian Shield, situated at the south. Although this is only a preliminary additional evidence, we cannot confirm it only from the data of gravity. It is necessary others types of geophysical data, for example, more clear evidences obtained from paleomagnetism.

The geometrical structure of a tree can consist of thousands, even millions, of branches, twigs and leaves in complex arrangements. The structure contains a lot of useful information and can be used for example to assess a tree's health or calculate parameters such as total wood volume or branch size distribution. Because of the complexity, capturing the structure of an entire tree used to be nearly impossible, but the increased availability and quality of particularly digital cameras and Light Detection and Ranging (LIDAR) instruments is making it increasingly possible. A set of digital images of a tree, or a point cloud of a tree from a LIDAR scan, contains a lot of data, but the information about the tree structure has to be extracted from this data through analysis. This work presents a method of reconstructing 3D models of trees from point clouds. The model is constructed from cylindrical segments which are added one by one. Bayesian inference is used to determine how to optimize the parameters of model segment candidates and whether or not to accept them as part of the model. A Hough transform for finding cylinders in point clouds is presented, and used as a heuristic to guide the proposals of model segment candidates. Previous related works have mainly focused on high density point clouds of sparse trees, whereas the objective of this work was to analyze low resolution point clouds of dense almond trees. The method is evaluated on artificial and real datasets and works rather well on high quality data, but performs poorly on low resolution data with gaps and occlusions.

Les malformations artério-­‐veineuses cérébrales (MAVc) sont des pathologies vasculaires agressives présentant un risque hémorragique lourd de conséquence en terme de morbi-­‐mortalité. Les outils d’imagerie disponibles actuellement ne permettent de comprendre que difficilement leur angio-­‐ architecture. Nous avons développé dans notre travail deux outils d’imagerie permettant d’affiner la compréhension de l’anatomie des ces malformations : un algorithme de segmentation semi-­‐automatisé et un algorithme d’anamorphose sphérique convexe. Ces algorithmes ont été élaborés pour être utilisés sur les acquisitions d’angiographie rotationnelle 3D ; ils permettent de mieux visualiser la veine de drainage principale des MAVc, notamment d’identifier une sténose ou une ectasie focale sur cette veine, et également de déceler de façon plus fiable la présence d’un anévrysme intra-­‐nidal. Ces améliorations dans l’analyse de l’angio-­‐architecture des MAVc permettront vraisemblablement de réduire le risque thérapeutique pour ces malformations. En vue de tester le potentiel des agents anti-­‐angiogéniques pour le traitement des MAVc, nous avons élaboré un modèle porcin simplifié de MAVc consistant en une occlusion unilatérale d’artère carotide primitive par voie endovasculaire. La comparaison entre le volume de rete mirabile à J0 et à 3 mois et les valeurs obtenues pour un groupe témoin a montré une augmentation significative du volume du rete mirabile chez les porcs ayant eu l’occlusion carotidienne. D’autre part, une tendance nette à l’augmentation des taux de VEGF (vascular endothelial growth factor) à proximité du rete mirabile était observée dans le groupe occlusion. Enfin, des modifications anatomopathologiques proches de celles des MAVc humaines étaient visualisées sur les pièces autopsiques des rete mirabile dans le groupe occlusion. / Brain arteriovenous malformations (bAVMs) are aggressive vascular malformations presenting a haemorrhagic complication risk that may lead to severe consequences in terms of morbi-­‐mortality. Available imaging tools poorly help in understanding their angio-­‐architecture. We have developed two imaging tools improving our understanding of the anatomy of these malformations: a semi-­‐automated segmentation algorithm and a convex spherical anamorphosis algorithm. These algorithms have been elaborated for use on 3D rotational angiography acquisitions; they provide a better visualisation of the bAVMs’ main draining vein, especially for venous stenosis or for focal ectasia. They also help in depicting accurately intranidal aneurysms. These improvements in the analysis of the bAVMs’ angioarchitecure may help in reducing the therapeutic risk for these malformations. For a further testing of the potential of anti-­‐angiogenic agents for the treatment of bAVMs, we have elaborated a simplified swine AVM model consisting in the occlusion of a common carotid artery by endovascular means. The comparison between the volume of the rete mirabile at D0 and 3 months and those measured in a control group showed a significant increasing of the retia in the occlusion group. Moreover, a tendency was observed concerning an increase in VEGF (vascular endothelial growth factor) serum levels close to the rete mirabile in the occlusion group. Finally, pathological changes close to those seen in human bAVMs were observed on autopsy samples in the occlusion group.

L'objectif de cette thèse est l'étude de la déformation, à l'échelle microscopique, de la phase MAX Ti2AlN, synthétisée par métallurgie des poudres. Ce travail se divise en trois parties : une première dans laquelle l'accent a été mis sur l'hystérèse mécanique des phases MAX via des essais cyclés, en nanoindentation sphérique et compression ex-situ de micro-piliers, sur des grains d'orientations différentes déterminées par l'EBSD. Dans la deuxième nous nous sommes intéressés à la déformation de micropiliers via des essais de compression cyclés in-situ couplés à la micro-diffraction Laue. L'objectif a été d'analyser les taches diffraction au cours de la déformation du pilier afin de mettre en évidence les mécanismes de déformation élémentaires mis en jeu et d'observer les structures finales via des images MEB post-mortem des piliers. Enfin, une dernière dans laquelle l'objectif a été l'étude des mécanismes de déformation en température à l'échelle microscopique via des essais de nano-indentation allant jusqu'à 800°C. La caractérisation des lignes de glissement en surface et des configurations microstructurales sous l'empreinte a été réalisée par AFM et MET respectivement. Toutes les données recueillies par ces divers essais aux petites échelles, ont permis d'affiner notre compréhension des mécanismes de déformation du monocristal de phase MAX, notamment vis à vis des modèles usuellement proposés dans la littérature. / The thesis's goal is to study the deformation, at microscopic scale, of the MAX phase Ti2AlN synthesized by powder metallurgy. This work is divided into three parts: in the first part, the interest has been put on the hysteretic behavior of the MAX phases via cyclic mechanical solicitations, during spherical indentation tests and ex-situ compression of micro-pillars, on differently orientated grains beforehand determined by EBSD. In the second part, we were interested into the micro-pillar's deformation via insitu cyclic compression tests coupled with Laue micro-diffraction. The goal was to analyse the evolution diffraction lines during the pillar's deformation in order to highlight the elementary deformation mechanisms and to observe the finale structures via the post-mortem SEM imaging of the pillars. Finally, a last part was devoted to study the deformation mechanisms in temperature at microscopic scale via nano-indentation tests up to 800°C. The characterization of the slip lines on the surface has been revealed by AFM and that of t he microstructural configurations (dislocations) under the indent has been done by TEM. All data collected by these various tests at the small scales have refined our understanding of the deformation mechanisms of crystal MAX phase, particularly with respect to the models usually proposed in the literature.

This thesis compares Weibull weakest link theory with inclusion of one and all three principal stresses. Principal stresses needed for this theory were calculated with finite element method. The informational research is in the introduction of this thesis. It includes ceramic materials, Weibull weakest link theory, Gaussian quadrature over spherical surface and ceramic head of hip joint endoprothesis. Theoretical part is used for next calculations of probability of failure. The probability of failure of ceramic rod loaded by four-point bending is calculated in first calculations. This task is solved as contact in the next step. Next part of this thesis is about selection of suitable method of numerical integration. This method will be used in the calculation with all three principal stresses. The results of calculation with all three principal stresses are compared with the results of the calculation which includes only first principal stress. Firstly, this is done for cylindrical body and then used on head of hip joint endoprothesis. In the last part of this thesis, probability of fracture of head hip joint endoprothesis with shape deviation of nominal conicity is calculated.