Nos últimos anos têm sido desenvolvidos modelos de regressão beta, que têm uma variedade de aplicações práticas como, por exemplo, a modelagem de taxas, razões ou proporções. No entanto, é comum que dados na forma de proporções apresentem zeros e/ou uns, o que não permite admitir que os dados provêm de uma distribuição contínua. Nesta tese, são propostas, distribuições de mistura entre uma distribuição beta e uma distribuição de Bernoulli, degenerada em zero e degenerada em um para modelar dados observados nos intervalos [0, 1], [0, 1) e (0, 1], respectivamente. As distribuições propostas são inflacionadas no sentido de que a massa de probabilidade em zero e/ou um excede o que é permitido pela distribuição beta. Propriedades dessas distribuições são estudadas, métodos de estimação por máxima verossimilhança e momentos condicionais são comparados. Aplicações a vários conjuntos de dados reais são examinadas. Desenvolvemos também modelos de regressão beta inflacionados assumindo que a distribuição da variável resposta é beta inflacionada. Estudamos estimação por máxima verossimilhança. Derivamos expressões em forma fechada para o vetor escore, a matriz de informação de Fisher e sua inversa. Discutimos estimação intervalar para diferentes quantidades populacionais (parâmetros de regressão, parâmetro de precisão) e testes de hipóteses assintóticos. Derivamos expressões para o viés de segunda ordem dos estimadores de máxima verossimilhança dos parâmetros, possibilitando a obtenção de estimadores corrigidos que são mais precisos que os não corrigidos em amostras finitas. Finalmente, desenvolvemos técnicas de diagnóstico para os modelos de regressão beta inflacionados, sendo adotado o método de influência local baseado na curvatura normal conforme. Ilustramos a teoria desenvolvida em um conjuntos de dados reais. / The last years have seen new developments in the theory of beta regression models, which are useful for modelling random variables that assume values in the standard unit interval such as proportions, rates and fractions. In many situations, the dependent variable contains zeros and/or ones. In such cases, continuous distributions are not suitable for modeling this kind of data. In this thesis we propose mixed continuous-discrete distributions to model data observed on the intervals [0, 1],[0, 1) and (0, 1]. The proposed distributions are inflated beta distributions in the sense that the probability mass at 0 and/or 1 exceeds what is expected for the beta distribution. Properties of the inflated beta distributions are given. Estimation based on maximum likelihood and conditional moments is discussed and compared. Empirical applications using real data set are provided. Further, we develop inflated beta regression models in which the underlying assumption is that the response follows an inflated beta law. Estimation is performed by maximum likelihood. We provide closed-form expressions for the score function, Fishers information matrix and its inverse. Interval estimation for different population quantities (such as regression parameters, precision parameter, mean response) is discussed and tests of hypotheses on the regression parameters can be performed using asymptotic tests. We also derive the second order biases of the maximum likelihood estimators and use them to define bias-adjusted estimators. The numerical results show that bias reduction can be effective in finite samples. We also develop a set of diagnostic techniques that can be employed to identify departures from the postulated model and influential observations. To that end, we adopt the local influence approach based in the conformal normal curvature. Finally, we consider empirical examples to illustrate the theory developed.

Dans ce Manuscrit, nous étudions l'influence de la géométrie sur les équations de Hardy-Sobolev perturbées ou non sur toute variété Riemannienne compacte sans bord de dimension supérieure ou égale à 3. Plus précisément, dans le cas non perturbé nous démontrons que pour toute dimension de la variété strictement supérieure à, l'existence d'une solution (ou plutôt une condition suffisante d'existence) dépendra de la géométrie locale autour de la singularité. En revanche, dans le cas où la dimension est égale à 3, c'est la géométrie globale (particulièrement, la masse de la fonction de Green) de la variété qui comptera. Dans le cas d'une équation à terme perturbatif sous-critique, nous démontrons que l'existence d'une solution dépendra uniquement de la perturbation pour les grandes dimensions et qu'une interaction entre la géométrie globale de la variété et la perturbation apparaîtra en dimension 3. Enfin, nous établissons une inégalité optimale de Hardy-Sobolev Riemannienne, la variété étant avec ou sans bord, où nous démontrons que la première meilleure constante est celle des inégalités Euclidiennes et est atteinte / In this Manuscript, we investigate the influence of geometry on the Hardy-Sobolev equations on the compact Riemannian manifolds without boundary of dimension greateror equal to 3. More precisely, we prove in the non perturbative case that the existence of solutions depends only on the local geometry around the singularity when the dimension is greater or equal to 4 while it is the global geometry of the manifold when the dimension is equal to 3 that matters. In the presence of a perturbative subcritical term, we prove that the existence of solutions depends only on the perturbation when the dimension is greater or equal to 4 while an interaction between the perturbation and the global geometry appears in dimension 3. Finally, we establish an Optimal Hardy-Sobolev inequality for all compact Riemannian manifolds, with or without boundary, where we prove that the Riemannian sharp constant is the one for the Euclidean inequality and is achieved

Les travaux présentés dans cette thèse portent sur le rôle que peuvent jouer les différentes courbures extrinsèques d’une hypersurface dans l’étude de sa géométrie, en particulier dans le cas des variétés spinorielles. Dans un premier temps, nous nous intéressons au cas de la courbure moyenne et construisons une nouvelle famille de surfaces minimales non simplement connexes dans le groupe de Lie Sol3, en adaptant une méthode déjà utilisée par Daniel et Hauswirth dans Nil3 et utilisant les propriétés de l’application de Gauss d’une surface. Ensuite, nous démontrons le Théorème d’Alexandrov généralisé aux Hr-courbures dans l’espace euclidien Rn+1 et dans l’espace hyperbolique Hn+1 en testant un spineur adéquat dans des inégalités de type holographiques établies récemment par Hijazi, Montiel et Raulot. Grâce à ces inégalités, nous démontrons également l'Inégalité de Heintze-Karcher dans l'espace euclidien. Enfin, nous donnons des majorations extrinsèques de la première valeur propre de l’opérateur de Dirac des surfaces de S2 x S1(r) et des sphères de Berger Sb3 (τ) grâce aux restrictions de spineurs ambiants construits par Roth, et nous en caractérisons les cas d’égalité. / In this thesis we are interested in the role played by the extrinsic curvatures of a hypersurface in the study of its geometry, especially in the case of spin manifolds. First, we focus our attention on the mean curvature and construct a new family of non simply connected minimal surfaces in the Lie group Sol3, by adapting a method used by Daniel and Hauswirth in Nil3 based on the properties of the Gauss map of a surface. Then we give a new spinorial proof of the Alexandrov Theorem extended to all Hr-curvatures in the euclidean space Rn+1 and in the hyperbolic space Hn+1, using a well-chosen test-spinor in the holographic inequalities recently obtained by Hijazi, Montiel and Raulot. These inequalities lead to a new proof of the Heintze-Karcher Inequality as well. Finally we use restrictions of particular ambient spinor fields constructed by Roth to give some extrinsic upper bounds for the first nonnegative eigenvalue of the Dirac operator of surfaces immersed into S2 x S1(r) and into the Berger spheres Sb3 (τ), and we describe the equality cases.

This thesis is devoted to the optical properties of low-dimensional structures based on such two-dimensional materials as graphene, silicene and phosphorene. We investigate optical properties of a variety of quasi-one dimensional and quasi-zero-dimensional structures, which are promising for future optoelectronics. Primarily we focus on their low-energy optical properties and how these properties are influenced by the structures’ geometry, external fields, intrinsic strain and edge disorder. As a consequence of this endeavor, we find several interesting effects such as correlation between the optical properties of tubes and ribbons whose periodic and ‘hard wall’ boundary conditions are matched and a universal value of matrix element in narrow-gap tubes and ribbons characterizing probability of transitions across the band gap opened up by intrinsic strain originating from the tube’s surface curvature or ribbon’s edge relaxation. The analytical study of the gapped 2D Dirac materials such as silicene and germanene, which have some similarity to the aforementioned quasi-one-dimensional systems in terms of physical description, reveals a valley- and polarization-dependent selection rules. It was also found that absorption coefficient should change in gapped materials with increasing frequency and become a half of its value for gap edge transitions when the spectrum is linear. Our analysis of the electronic properties of flat clusters of silicene and phosphorene relates the emergence and the number of the peculiar edge states localized at zero energy, so-called zero-energy states, which are know to be of topological origin, to the cluster’s structural characteristics such as shape and size. This allows to predict the presence and the number of such states avoiding complicated topological arguments and provides a recipes for design of metallic and dielectric clusters. We show that zero-energy states are optically active and can be efficiently manipulated by external electric field. However, the edge disorder is important to take into account. We present a new fractal-based methodology to study the effects of the edge disorder which can be applied also to modeling of composite materials. These finding should be useful in design of optoelectronic devices such as tunable emitters and detectors in a wide region of electromagnetic spectrum ranging form the mid-infrared and THz to the optical frequencies.

Les voies d’endocytose qui régissent l’internalisation d’éléments extracellulaires peuvent être classées selon que la protéine de manteau, la clathrine, est impliquée ou non dans le processus. Les voies indépendantes de la clathrine sont utilisées par de nombreuses toxines, des virus et des protéines endogènes. Les mécanismes permettant d’induire le recrutement des protéines cargoes et la déformation de la membrane plasmique dans le contexte de l'endocytose clathrine-indépendant restent encore mal compris. Cette étude montre que la galectine 3, une protéine humaine qui se lie aux glucides, induit la formation d’invaginations de la membrane plasmique de manière indépendante de la clathrine. Les glycosphingolipides (molécules jouant un rôle majeur dans la physiologie de la cellule) sont essentielles pour permettre à la galectine 3 d’induire ces invaginations et d’être internalisée dans la cellule. Les structures tubulaires induites par la galectine 3 présentent une morphologie étonnamment similaire à celle de compartiments intermédiaires de transport décrits dans la littérature pour l’endocytose indépendante de la clathrine. Des cargos utilisant la voie indépendante de la clathrine, tels que CD44 et les intégrines α5 et β1, sont retrouvés dans les tubules induits par la galectine 3. De plus, cette dernière est nécessaire à l’internalisation de CD44. Cela indique donc que la galectine 3 pourrait relier des protéines cargos glycosylés à des glycosphyngolipides de la membrane plasmique et ainsi induire une déformation de la membrane et leur internalisation dans les cellules. Ce mécanisme diffère de celui utilisé par la toxine pentamérique de Shiga et par la toxine cholérique, qui sont leur protéines cargos propores et interagissant directement avec le glycosphyngolipide leur servant de récepteur. Les tubules induits par la galectine 3 sont distincts de ceux induit par les autres lectines. Celles-ci présentent des spécificités différentes de liaison aux glucides, montrant ainsi la l'importance des interactions entre les lectines et les sucres dans ce processus. De plus, nous avons constaté que la galectine 3 module l’équilibre à l’état basal de l’intégrine β1 à la surface de la cellule. Cette protéine étant capitale pour les phénomènes d’adhésion et de migration cellulaires, nous avons donc exploré le rôle conjoint de la galectine 3 et des glycosphingolipides dans la migration cellulaire. La galectine 3 inhibe la migration des cellules humaines de carcinomes mammaires alors qu’elle stimule au contraire celle de cellules de tumeurs mammaires murines. Or, nous avons montré que la régulation par la galactine 3 de la migration de différentes lignées cellulaires est dépendante des glycosphingolipides. Il ressort donc de cette étude que la galectine 3 et les glycosphingolipides contribuent de manière synergique au processus d’induction de déformation de la membrane, à l’endocytose de protéines cargos et à la migration cellulaire. / Endocytic processes which govern the uptake of extracellular material into the cell can be classified based on their dependence on the coat protein, clathrin. Clathrin-independent mechanisms are used by many toxins, viruses and endogenous proteins. How cargo is recruited and membranes are bent is not well understood in these cases. Here, we discovered that galectin 3, a human carbohydrate binding protein induced the clathrin-independent formation of endocytic plasma membrane invaginations. Glycosphingolipids, which have established functions in key physiological processes, were found to be essential for the formation of galectin 3-induced invaginations and for the efficient uptake of the protein into the cell. Galectin 3-induced tubular structures were found to have a strikingly similar morphology to that of the clathrin-independent carriers described in literature. Clathrin-independent endocytic cargoes such as CD44, α5 and β1 integrin were present in galectin 3-induced tubules, and galectin activity and glycosphingolipids were required for the uptake of CD44. This indicated that galectin 3 could link glycosylated cargoes with glycosphingolipids for cargo recruitment and membrane bending. In contrast, the pentameric Shiga and cholera toxins are their own cargoes and drive membrane deformations by directly binding to their respective glycosphingolipid receptors. Galectin 3-induced tubules were distinct from those induced by lectins with different carbohydrate binding specificities, which revealed the importance of lectin-glycan interaction in this process. Further, we observed that galectin 3 modulated the steady state surface dynamics of β1 integrin, a protein which like CD44 is critical for cell adhesion and migration. Subsequently, we explored the interplay of galectins and glycosphingolipids in cell migration. Galectin 3 inhibited cell migration in human breast carcinoma cells, and stimulated migration in a mouse mammary tumor cell line. However, the regulation of migration by galectin 3 was in both cases found to be dependent on glycosphingolipids. In conclusion, galectin 3 and glycosphingolipids synergistically contribute to the clathrin-independent curvature generation process, cargo endocytosis and cell migration.

Esta dissertação tem como objetivo discutir sob quais condições uma G- estrutura é integrável. Primeiro apresentam-se fibrados principais, vetoriais e outras estruturas a elas associados como torção, espaços verticais, espaços horizontais e conexões. Depois apresentam-se a definição de G-estrutura, de integrabilidade de G-estruturas, com exemplos e as respectivas versões de integrabilidade e equivalência de G-estruturas. Finalmente, são descritas condições mais gerais que garantem a integrabilidade de G-estruturas. / This dissertation aims to discuss what are the conditions for the inte- grability of a G-structure. We begin presenting principal bundles, vectoer bundles, associated bundles and other structures related to them like torsion, vertical spaces, horizontal spaces and connections. After this, we present the definition of G-structure, integrability os G-structures with examples ans respectives versions of integrabilities and the equivalence of G-estructures. Finally, we describe more general conditions that ensure the integrability of G-structures.

Sur l’île de Majorque (Espagne), l’exploitation en continue de la nappe aquifère a favoriséla formation d’un biseau salé et l’épuisement de la ressource en eau potable. En 2002, un projet nommé ALIANCE, financé par l’Union européenne, a été lancé pour permettre une meilleure caractérisation des réservoirs. L’objectif est de concevoir un plan de gestion durable des ressources en eau dans les zones côtières aquifères sujets aux problèmes d’intrusion d’eau salée. Dans cet optique, un site expérimental près de la ville de Campos (Majorque) a été créé, avec la mise en place de plusieurs puits au sein d’un milieu karstique carbonaté. Des études pétrophysiques sur des échantillons ont été réalisées ainsi que différentes prospections géophysiques dans la zone saturée (tomographie puits à puits). Ce type d’études est utile pour déterminer certaines propriétés réservoirs telles que la porosité, mais sont limitées à la zone saturée au voisinage des puits. Ainsi, une étude sismique 3D haute résolution a été réalisée pour localiser les principaux réflecteurs, leurs répartitions sur la zone et imager les hétérogénéités du réservoir dans la zone non saturée. L’acquisition et le traitement de données sismiques lors de prospection de subsurface est une tâche difficile en raison de plusieurs facteurs, notamment logistique et technique. Cependant, cette acquisition 3D haute résolution a été optimisée pour imager une structure peu profonde, à savoir une centaine de mètres. Différentes stratégies de traitement de données ont été appliquées pour éliminer de manière efficace le bruit sur les données, et une technique de calcul de correction statique, basée sur l’inversion des temps de premières arrivées, a été mise au point. Différents attributs sismiques ont été extraits et utilisés pour la caratérisation du réservoir. La propagation des ondes sismiques est limitée par la nature des roches carbonatées et la création d’ondes de Rayleigh. Un obstacle majeur rencontré lors du traitement des données sismiques a été la présence d’ondes de Rayleigh de fortes amplitudes, d’une part due à l’utilisation d’une source en surface et d’autre part en raison des hétérogénéités de petite tailles. Un "mute" de ces ondes de surface a été réalisé avant d’imager la structure profonde. De multiples problèmes d’interférences sont également dus aux nombreuses hétérogénéités, à l’atténuation rapide du contenu hautes-fréquences des signaux et au contraste d’impédance avec les couches sous-jacentes. L’interprétation finale nous amène à observer que le réflecteur principal est très irrégulier sur une zone d’étude de petite taille à l’échelle d’un réservoir. L’analyse de différents attributs sismiques révèle clairement des structures et hétérogénéités typiques des systèmes karstiques. / Continuous water extraction and intrusion of salt water in the coastal aquifer of the islandof Mallorca (Spain) is depleting the fresh water aquifers. In 2002 a project named ALIANCE,funded by European Union, was initiated for better reservoir characterization and to devisethe sustainable management plan of the water resources in coastal aquifers suffering from salt water intrusion. For this purpose an experimental site near the Campos town on the island of Mallorca (Spain) was developed. Several wells on the site were drilled and cored. Extensive studies are carried out to characterize the reservoir by studying the well cores. Different geophysical tomographic studies are also carried out for these drilled wells in the saturated zone. Laboratory study of cores, petrophysical studies and several tomographic studies were helpful to construct the reservoir porosity system and other reservoir properties. But these all studies are restricted to saturated zone and in the vicinity of the wells. High resolution 3D seismic survey is carried out on this site to locate the different characteristic reflectors, their spatial presence over the area and reservoir heterogeneity in the unsaturated zone. Seismic data acquisition and processing for the shallow surveys is a difficult task due to number of factors including logistic and technical. Nonetheless high resolution 3D seismic survey is acquired with optimized parameters to image the required zone. Different data processing strategies are applied to get a noise free high resolution image. A technique for static correction calculation based on the delay time inversion is developed.Energy penetration in the subsurface was hampered due to carbonate rock nature and forced generation of Rayleigh waves. The processing of the seismic data was difficult due to overwhelming high amplitude Rayleigh waves that are generated partly due to use of the surface source and partly due to the small scale heterogeneities. Rayleigh wave muting is performed to obtain the meaningful image. Due to heterogeneities, attenuation of high frequency content of the signals and impedance contrast of the underlying layers result in interference. Different seismic attributes are extracted and used for reservoir characterization. From the interpretation of data it is evident that even for this small area the shape of the main reflector varies considerably in the area. Seismic attributes reveal karsts and other structural heterogeneities in the area.

Para analisar características de interesse a respeito de um conjunto de dados reais da área de Odontologia apresentado em Hadgu & Koch (1999), ajustaremos um modelo de regressão linear multivariado com erros nas variáveis com intercepto nulo. Este conjunto de dados é caracterizado por medições de placa bacteriana em três grupos de voluntários, antes e após utilizar dois líquidos de bochecho experimentais e um líquido de bochecho controle, com medições (sujeitas a erros de medição) no início do estudo, após três e seis meses de utilização dos líquidos. Neste caso, uma possível estrutura de dependência entre as medições feitas em um mesmo indivíduo deve ser incorporada ao modelo e, além disto, temos duas variáveis resposta para cada indivíduo. Após a apresentação do modelo estatístico, iremos obter estimativas de máxima verossimilhança dos parâmetros utilizando o algoritmo iterativo EM e testaremos as hipóteses de interesse utilizando testes assintóticos de Wald, razão de verossimilhanças e score. Como neste caso não existe um teste ótimo, faremos um estudo de simulação para verificar o comportamento das três estatísticas de teste em relação a diferentes tamanhos amostrais e diferentes valores de parâmetros. Finalmente, faremos um estudo de diagnóstico buscando identificar possíveis pontos influentes no modelo, considerando o enfoque de influência local proposto por Cook (1986) e a medida de curvatura normal conformal desenvolvida por Poon & Poon (1999). / To analyze some characteristics of interest in a real odontological data set presented in Hadgu & Koch (1999), we propose the use of a multivariate null intercept errors-in-variables regression model. This data set is composed by measurements of dental plaque index (with measurement errors), which were measured in volunteers who were randomized to two experimental mouth rinses (A and B) or a control mouth rinse. The measurements were taken in each individual, before and after the use of the respective mouth rinses, in the beginning of the study, after three months from the baseline and after six months from the baseline. In this case, a possible structure of dependency between the measurements taken within the same individual must be incorporated in the model. After presenting the statistical model, we obtain the maximum likelihood estimates of the parameters using the numerical algorithm EM, and we test the hypotheses of interest considering asymptotic tests (Wald, likelihood ratio and score). Also, a simulation study to verify the behavior of these three test statistics is presented, considering diferent sample sizes and diferent values for the parameters. Finally, we make a diagnostic study to identify possible influential observations in the model, considering the local influence approach proposed by Cook (1986) and the conformal normal curvature proposed by Poon & Poon (1999).

O objetivo central desta dissertação é apresentar as folheações infinitesimalmente polares, fornecendo uma demonstração para o teorema que as caracteriza. Seguimos a abordagem original encontrada em Lytchak e Thorbergsson [25], de 2010. Diretamente da definição e do teorema principal obtem-se dois exemplos: folheações polares e folheações riemannianas singulares de codimensão 1 ou 2. Dedicamos especial atenção a um terceiro exemplo: folheações sem pontos horizontalmente conjugados. A demonstração deste resultado utiliza resultados obtidos anteriormente pelos mesmos autores em 2007, Lytchak e Thorbergsson [24]. Abordamos também, brevemente, as implicações do teorema caracterizador (que é um resultado local) sobre o quociente global de uma folheação infinitesimalmente polar. Variedades com folheações infinitesimalmente polares podem ser encaradas como um objeto que apresenta aspectos clássicos do teorema do toro maximal para grupos de Lie compactos, em um contexto mais amplo. / The present work aims at introducing infinitesimally polar foliations -- as defined by Lytchak and Thorbergsson [25] -- providing a proof for the classification theorem. Polar foliations and low codimension singular Riemannian foliations are two immediate examples. A third example is given by foliations without horizontally conjugate points. The proof of this assertion relies on previous results established by the same authors in Lytchak and Thorbergsson [24]. The classification theorem for infinitesimally polar foliations is a local result; we also derive from it some global consequences on the quotient space of such foliations. Infinitesimally polar foliations may be regarded as a generalised setting where one can find characteristic features from the maximal torus theorem for compact Lie groups.

O objetivo central desta dissertação é apresentar as folheações infinitesimalmente polares, fornecendo uma demonstração para o teorema que as caracteriza. Seguimos a abordagem original encontrada em Lytchak e Thorbergsson [25], de 2010. Diretamente da definição e do teorema principal obtem-se dois exemplos: folheações polares e folheações riemannianas singulares de codimensão 1 ou 2. Dedicamos especial atenção a um terceiro exemplo: folheações sem pontos horizontalmente conjugados. A demonstração deste resultado utiliza resultados obtidos anteriormente pelos mesmos autores em 2007, Lytchak e Thorbergsson [24]. Abordamos também, brevemente, as implicações do teorema caracterizador (que é um resultado local) sobre o quociente global de uma folheação infinitesimalmente polar. Variedades com folheações infinitesimalmente polares podem ser encaradas como um objeto que apresenta aspectos clássicos do teorema do toro maximal para grupos de Lie compactos, em um contexto mais amplo. / The present work aims at introducing infinitesimally polar foliations -- as defined by Lytchak and Thorbergsson [25] -- providing a proof for the classification theorem. Polar foliations and low codimension singular Riemannian foliations are two immediate examples. A third example is given by foliations without horizontally conjugate points. The proof of this assertion relies on previous results established by the same authors in Lytchak and Thorbergsson [24]. The classification theorem for infinitesimally polar foliations is a local result; we also derive from it some global consequences on the quotient space of such foliations. Infinitesimally polar foliations may be regarded as a generalised setting where one can find characteristic features from the maximal torus theorem for compact Lie groups.