# École doctorale mathématiques, information et ingénierie des systèmes (Caen)

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Works: 134 works in 225 publications in 2 languages and 225 library holdings Other, 996
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Most widely held works by information et ingénierie des systèmes (Caen) École doctorale mathématiques
Estimation and feature selection in high-dimensional mixtures-of-experts models by Bao Tuyen Huynh( )

2 editions published in 2019 in English and held by 2 WorldCat member libraries worldwide

This thesis deals with the problem of modeling and estimation of high-dimensional MoE models, towards effective density estimation, prediction and clustering of such heterogeneous and high-dimensional data. We propose new strategies based on regularized maximum-likelihood estimation (MLE) of MoE models to overcome the limitations of standard methods, including MLE estimation with Expectation-Maximization (EM) algorithms, and to simultaneously perform feature selection so that sparse models are encouraged in such a high-dimensional setting. We first introduce a mixture-of-experts' parameter estimation and variable selection methodology, based on l1 (lasso) regularizations and the EM framework, for regression and clustering suited to high-dimensional contexts. Then, we extend the method to regularized mixture of experts models for discrete data, including classification. We develop efficient algorithms to maximize the proposed l1 -penalized observed-data log-likelihood function. Our proposed strategies enjoy the efficient monotone maximization of the optimized criterion, and unlike previous approaches, they do not rely on approximations on the penalty functions, avoid matrix inversion, and exploit the efficiency of the coordinate ascent algorithm, particularly within the proximal Newton-based approach
Analyse spectrale et calcul numérique pour l'équation de Boltzmann by Ibrahim Jrad( )

2 editions published in 2018 in French and held by 2 WorldCat member libraries worldwide

In this thesis, we study the solutions of the Boltzmann equation. We are interested in the homogeneous framework in which the solution f(t; x; v) depends only on the time t and the velocity v. We consider singular crosssections (non cuto_ case) in the Maxwellian case. For the study of the Cauchy problem, we consider a uctuation of the solution around the Maxwellian distribution then a decomposition of this uctuation in the spectral base associated to the quantum harmonic oscillator At first, we solve numerically the solutions using symbolic computation methods and spectral decomposition of Hermite functions. We consider regular initial data and initial conditions of distribution type. Next, we prove that there is no longer a global solution in time for a large initial condition that changes sign (which does not contradict the global existence of a weak solution for a positive initial condition - see for example Villani Arch. Rational Mech. Anal 1998)
Mathematical analysis and numerical approximation of flow models in porous media by Sarra Brihi( )

2 editions published in 2018 in English and held by 2 WorldCat member libraries worldwide

This thesis is devoted to Darcy Brinkman Forchheimer (DBF) equations with a non standard boundary conditions. We prove first the existence of different type of solutions (weak, strong) of the stationary DBF problem in a simply connected domain with boundary conditions on the normal component of the velocity field and the tangential component of the vorticity. Next, we consider Brinkman Forchheimer (BF) system with boundary conditions on the pressure in a non simply connected domain. We prove the well-posedness and the existence of a strong solution of this problem. We establish the regularity of the solution in the L^p spaces, for p >= 2.The approximation of the non stationary DBF problem is based on the pseudo-compressibility approach. The second order's error estimate is established in the case where the boundary conditions are of type Dirichlet or Navier. Finally, the finite elements Galerkin Discontinuous method is proposed and the convergence is settled concerning the linearized DBF problem and the non linear DBF system with a non standard boundary conditions
Two problems in arithmetic geometry. Explicit Manin-Mumford, and arithmetic Bernstein-Kusnirenko by César Martinez Metzmeier( )

2 editions published in 2017 in English and held by 2 WorldCat member libraries worldwide

In the first part of this thesis we present sharp bounds on the number of maximal torsion cosets in a subvariety of a complex algebraic torus $(\mathbb{C}^{\times})^n$ and of an Abelian variety. In both cases, we give an explicit bound in terms of the degree of the defining polynomials and the ambient variety. Moreover, the dependence on the degree of the polynomials is sharp. In the case of the complex torus, we also give an effective bound in terms of the toric degree of the subvariety. As a consequence of the latter result, we prove the conjectures of Ruppert, and Aliev and Smyth on the number of isolated torsion points of a hypersurface. These conjectures bound this number in terms of the multidegree and the volume of the Newton polytope of a polynomial defining the hypersurface, respectively.In the second part of the thesis, we present an upper bound for the height of isolated zeros, in the torus, of a system of Laurent polynomials over an adelic field satisfying the product formula. This upper bound is expressed in terms of the mixed integrals of the local roof functions associated to the chosen height function and to the system of Laurent polynomials. We also show that this bound is close to optimal in some families of examples. This result is an arithmetic analogue of the classical Bern\v{s}tein-Ku\v{s}nirenko theorem
Contribution à la reconnaissance d'activités à partir d'un objet connecté by Romain Auber( )

2 editions published in 2019 in French and held by 2 WorldCat member libraries worldwide

This manuscript deals with the recognition of activities from accelerometric data. The device used to collect the accelerometer data is eTact, a device developed by Bodycap. Several solutions are proposed to optimize the autonomy of the connected object. These solutions are implemented and compared on different data sets. The originality of one of these solutions is to binarize the data of the accelerometer before transferring them to an external platform where they are analyzed. The use of binary data induces the loss of a lot of information, however it is shown in this manuscript that it is possible to estimate, among other things, the parameters of an Auto Regressive model of a time series from the binary information on this series. In this respect, an identification algorithm is proposed and analyzed
Contribution à l'évaluation opérationnelle des systèmes biométriques multimodaux by Antoine Cabana( )

2 editions published in 2018 in French and held by 2 WorldCat member libraries worldwide

Le développement et la multiplication de dispositifs connectés, en particulier avec les \textit{smartphones}, nécessitent la mise en place de moyens d'authentification. Dans un soucis d'ergonomie, les industriels intègrent massivement des systèmes biométrique afin de garantir l'identité du porteur, et ce afin d'autoriser l'accès à certaines applications et fonctionnalités sensibles (paiements, e-banking, accès à des données personnelles : correspondance électronique..). Dans un soucis de garantir, une adéquation entre ces systèmes d'authentification et leur usages, la mise en œuvre d'un processus d'évaluation est nécessaire.L'amélioration des performances biométriques est un enjeux important afin de permettre l'intégration de telles solutions d'authentification dans certains environnement ayant d'importantes exigences sur les performances, particulièrement sécuritaires. Afin d'améliorer les performances et la fiabilité des authentifications, différentes sources biométriques sont susceptibles d'être utilisées dans un processus de fusion. La biométrie multimodale réalise, en particulier, la fusion des informations extraites de différentes modalités biométriques
Continuum limits of evolution and variational problems on graphs by Yosra Hafiene( )

2 editions published in 2018 in English and held by 2 WorldCat member libraries worldwide

The non-local p-Laplacian operator, the associated evolution equation and variational regularization, governed by a given kernel, have applications in various areas of science and engineering. In particular, they are modern tools for massive data processing (including signals, images, geometry), and machine learning tasks such as classification. In practice, however, these models are implemented in discrete form (in space and time, or in space for variational regularization) as a numerical approximation to a continuous problem, where the kernel is replaced by an adjacency matrix of a graph. Yet, few results on the consistency of these discretization are available. In particular it is largely open to determine when do the solutions of either the evolution equation or the variational problem of graph-based tasks converge (in an appropriate sense), as the number of vertices increases, to a well-defined object in the continuum setting, and if yes, at which rate. In this manuscript, we lay the foundations to address these questions.Combining tools from graph theory, convex analysis, nonlinear semigroup theory and evolution equa- tions, we give a rigorous interpretation to the continuous limit of the discrete nonlocal p-Laplacian evolution and variational problems on graphs. More specifically, we consider a sequence of (determin- istic) graphs converging to a so-called limit object known as the graphon. If the continuous p-Laplacian evolution and variational problems are properly discretized on this graph sequence, we prove that the solutions of the sequence of discrete problems converge to the solution of the continuous problem governed by the graphon, as the number of graph vertices grows to infinity. Along the way, we provide a consistency/error bounds. In turn, this allows to establish the convergence rates for different graph models. In particular, we highlight the role of the graphon geometry/regularity. For random graph se- quences, using sharp deviation inequalities, we deliver nonasymptotic convergence rates in probability and exhibit the different regimes depending on p, the regularity of the graphon and the initial data
Approche basées sur l'apprentissage en profondeur pour la segmentation des organes à risques dans les tomodensitométries thoraciques. by Roger Trullo Ramirez( )

2 editions published in 2018 in English and held by 2 WorldCat member libraries worldwide

La radiothérapie est un traitement de choix pour le cancer thoracique, l'une des principales causes de décès dans le monde. La planification de la radiothérapie nécessite de contourer non seulement la tumeur, mais également les organes à risque (OAR) situés près de la tumeur dans le thorax, tels que le coeur, les poumons, l'oesophage, etc. Cette segmentation permet de minimiser la quantité d'irradiation reçue pendant le traitement. Aujourd'hui, la segmentation de OAR est réalisée principalement manuellement par des cliniciens sur des images scanner (CT), malgré une prise en charge logicielle partielle. C'est une tâche complexe, sujette à la variabilité intra et interobservateur. Dans ce travail, nous présentons plusieurs méthodologies utilisant des techniques d'apprentissage profond pour segmenter automatiquement le coeur, la trachée, l'aorte et l'oesophage. En particulier, l'oesophage est particulièrement difficile à segmenter, en raison de l'absence de contraste et de variabilité de forme entre différents patients. Les réseaux profonds convolutionnels offrent aujourd'hui des performances de pointe en matière desegmentation sémantique, nous montrons d'abord comment un type spécifique d'architecture basée sur des skip connections peut améliorer la précision des résultats, par rapport à un réseau pleinement convolutionnel (FCN) standard. Dans une deuxième contribution, nous avons intégré des informations de contexte spatial au processus de segmentation, par le biais de réseaux collaboratifs, permettant les segmentations de chaque organe individuellement. Troisièmement, nous proposons une représentation différente des données, basée sur une carte de distance, utilisée en conjointement avec des réseaux adversariaux (GAN), comme un autre moyen de contraindre le contexte anatomique. Les méthodes proposées ont été évaluées sur une base d'images scanner de 60 patients. Les résultats montrent des résultats encourageants pour l'application clinique et souligne le potentiel des méthodes prenant en compte le contexte spatial dans la segmentation
Effet du vieillissement par fatigue électrothermique sur la compatibilité électromagnétique des composants de puissance à base de SiC by Chawki Douzi( )

2 editions published in 2019 in French and held by 2 WorldCat member libraries worldwide

This research work focuses on the electrothermal aging effect on the electromagnetic compatibility of power components based on silicon carbide SiC. It focuses on two major parts ; an experimental part and another more oriented modelization. Experimentally, this thesis studies the aging effect of SiC transistors used in static converters on the electromagnetic interferences EMI generated by these converters. The second part deals with the modeling of these transistors in order to emulate the effect of their aging on the EMI of the modules they compose. This step made it possible to validate the methodology developed for the simulation of the conducted EMI of a healthy SiC MOFSET at first and of an aged SiC MOSFET in a second time. Overall, this innovative modeling approach developed in this work helps the designers of static converters to predict the conducted EMI before and after aging without going through the measurement. This provides additional information on the evolution of the EMC signatures of such modules during its lifetime and thus to estimate the risk associated with the aging of the components
Analyse d'un problème d'interaction fluide-structure avec des conditions aux limites de type frottement à l'interface by Hela Ayed( )

2 editions published in 2017 in French and held by 2 WorldCat member libraries worldwide

This PHD thesis is devoted to the theoretical and numerical analysis of a stationary fluid-structure interaction problem between an incompressible viscous Newtonian fluid, modeled by the 2D Stokes equations, and a deformable structure modeled by the 1D beam equations.The fluid and structure are coupled via a friction boundary condition at the fluid-structure interface.In the theoretical study, we prove the existence of a unique weak solution, under small displacements, of the fluid-structure interaction problem under a slip boundary condition of friction type (SBCF) by using Schauder fixed point theorem.In the numerical analysis, we first study a mixed finite element approximation of the Stokes equations under SBCF.We also prove an optimal a priori error estimate for regular data and we provide numerical examples.Finally, we present a fixed point algorithm for numerical simulation of the coupled problem under nonlinear boundary conditions
Caractériser et détecter les communautés dans les réseaux sociaux by Jean Creusefond( )

2 editions published in 2017 in French and held by 2 WorldCat member libraries worldwide

N this thesis, I first present a new way of characterising communities from a network of timestamped messages. I show that its structure is linked with communities : communication structures are over-represented inside communities while diffusion structures appear mainly on the boundaries.Then, I propose to evaluate communities with a new quality function, compacity, that measures the propagation speed of communications in communities. I also present the Lex-Clustering, a new community detection algorithm based on the LexDFS graph traversal that features some characteristics of information diffusion.Finally, I present a methodology that I used to link quality functions and ground-truths. I introduce the concept of contexts, sets of ground-truths that are similar in some way. I implemented this methodology in a software called CoDACom (Community Detection Algorithm Comparator, codacom.greyc.fr) that also provides many community detection tools
Contribution à la commande d'un onduleur multiniveaux, destinée aux énergies renouvelables, en vue de réduire le déséquilibre dans les réseaux électriques. by Léa Riachy( )

2 editions published in 2017 in French and held by 2 WorldCat member libraries worldwide

The work in this research thesis presents a contribution to voltage regulation in electrical networks. By considering adequate active and reactive powers injection into the grid, voltage control and load balancing are provided. These powers are generated from a grid connected renewable energy conversion system : a special attention was paid to the Wind Energy ConversionSystem (WECS) based on Doubly-Fed Induction Generator (DFIG).The typical control strategy for WECS is the maximum power coefficient tracking method. However, this method limits desirable ancillary power services, such as the participation of wind turbines in voltage regulation in the power grid. Therefore, a new method that derives the optimal power coefficient enhancing the participation of WTS in voltage regulation in the network (reactive and unbalanced power compensation), has been developed. The multilevel NPC (Neutral Point Clamped) converter, used for grid interface connection of renewable energy sources systems, has been studied. A predictive control method for the three-level NPC converter, capable of simultaneously compensating the problems of : DC link capacitors voltage balancing, load balancing and power factor correction in the power system, has been proposed. Then, the application of this predictive control was extended to simultaneously achieve multiple objectives: load balancing with power factor correction in the network, DC link capacitors voltage balancing, switching losses minimization and common mode voltage reduction. The switching losses minimization was obtained by proposing a new strategy which consists on exploiting the manufacturer datasheets that gives the evolution of the switching loss energy in function of the circulating current. The experimental curves of the datasheet are expressed in a mathematical model implemented in the predictive control. Simulation and experimental results are presented to evaluate the performance of the proposed method
Contributions to keystroke dynamics for privacy and security on the Internet by Denis Migdal( )

2 editions published in 2019 in English and held by 2 WorldCat member libraries worldwide

Interactions on the Internet require trust between each involved party. Internet entities assume, at the same time, several roles, each having their own interests and motivations; leading to conflicts that must be addressed to enable security and trust. In this thesis, we use, and focus on, Keystroke Dynamics (the way a user type on its keyboard) in an attempt to solve some of these conflicts.Keystroke Dynamics is a a costless and transparent biometric modality as it does not require neither additional sensors nor additional actions from the user. Unfortunately, Keystroke Dynamics also enables users profiling (s.a. identification, gender, age), against their knowledge and consent.In order to protect users privacy, we propose to anonymize Keystroke Dynamics. Still, such information can be legitimately needed by services in order to straighten user authentication. We then propose a Personal Identity Code Respecting Privacy, enabling biometric users authentication without threatening users privacy.We also propose a Social Proof of Identity enabling to verify claimed identities while respecting user privacy, as well as ensuring users past behaviors through a system of accountability. Generation of synthetic Keystroke Dynamics is also considered to augment existent Keystroke Dynamics datasets, and, in the end, enabling sharing of Keystroke Dynamics datasets without exposing biometric information of real users
Estimation de profondeur à partir d'images monoculaires par apprentissage profond by Michel Moukari( )

2 editions published in 2019 in French and held by 2 WorldCat member libraries worldwide

La vision par ordinateur est une branche de l'intelligence artificielle dont le but est de permettre à une machine d'analyser, de traiter et de comprendre le contenu d'images numériques. La compréhension de scène en particulier est un enjeu majeur en vision par ordinateur. Elle passe par une caractérisation à la fois sémantique et structurelle de l'image, permettant d'une part d'en décrire le contenu et, d'autre part, d'en comprendre la géométrie. Cependant tandis que l'espace réel est de nature tridimensionnelle, l'image qui le représente, elle, est bidimensionnelle. Une partie de l'information 3D est donc perdue lors du processus de formation de l'image et il est d'autant plus complexe de décrire la géométrie d'une scène à partir d'images 2D de celle-ci.Il existe plusieurs manières de retrouver l'information de profondeur perdue lors de la formation de l'image. Dans cette thèse nous nous intéressons à l'estimation d'une carte de profondeur étant donné une seule image de la scène. Dans ce cas, l'information de profondeur correspond, pour chaque pixel, à la distance entre la caméra et l'objet représenté en ce pixel. L'estimation automatique d'une carte de distances de la scène à partir d'une image est en effet une brique algorithmique critique dans de très nombreux domaines, en particulier celui des véhicules autonomes (détection d'obstacles, aide à la navigation).Bien que le problème de l'estimation de profondeur à partir d'une seule image soit un problème difficile et intrinsèquement mal posé, nous savons que l'Homme peut apprécier les distances avec un seul œil. Cette capacité n'est pas innée mais acquise et elle est possible en grande partie grâce à l'identification d'indices reflétant la connaissance a priori des objets qui nous entourent. Par ailleurs, nous savons que des algorithmes d'apprentissage peuvent extraire ces indices directement depuis des images. Nous nous intéressons en particulier aux méthodes d'apprentissage statistique basées sur des réseaux de neurones profond qui ont récemment permis des percées majeures dans de nombreux domaines et nous étudions le cas de l'estimation de profondeur monoculaire
Optimisation pour des problèmes industriels de tournées de véhicules : vers une transition énergétique by Abdelaziz Benantar( )

2 editions published in 2017 in French and held by 2 WorldCat member libraries worldwide

The thesis focuses on the study of real road transportation and distribution pro-blems. The question concerns in particular the optimization of two different vehicle routing problems arising in the distribution of petroleum products and the transfer of containers. The first problem, modelled as an application of the multi-compartment vehicle routing problem with time windows (MCVRPTW), is solved by using a tabu search method. The same method is then applied to two other variants. One introduces additional constraints related to loading operations for petroleum products on the compartments, while the other one includes the ad-justment concept in quantities applied for. Moreover, in the context of an energy transition, we addressed the container transfer problem using a fleet of electric trucks in the industrial port zone of Le Havre. The optimization involves two levels : the strategic level for dimensioning electrical infrastructures and the operational level for constructing the vehicle routes. Only the strategic level is tackled with a research project thanks to a coupling of optimization and simulation
Temporal planning with fuzzy constraints and preferences by Krystian Jobczyk( )

2 editions published in 2017 in English and held by 2 WorldCat member libraries worldwide

Temporal planning forms conceptually a part of temporal reasoning and it belongs to research area of Artificial Intelligence and it may be seen as an extension of classical planning by temporal aspects of acting. Temporal planing is usually complemented by considering preferences or different types of temporal constraints imposed on execution of actions. There exist many approaches to this issue. One one hand, there are different paradigms to temporal planning, such as: planning via search in graphs (STRIPS), planning via satisfiability or planning in terms of Markov processes. These approaches are mutually incompatible. In addition, temporal planning requires a subject-specification as it is rather defined in a methodological way. On the other hand, temporal constraints are represented and modeled in different ways dependently on their quantitative or qualitative nature. In particular, Allen's relations between temporal intervals - an important class of temporal constraints - do not have any quantitative aspects and cannot be considered in computational contexts. According to this situation, this PhD-thesis is aimed at the proposing a depth-analysis of temporal planning with fuzzy constraints which contains some remedies on these difficulties. Namely, two approaches to the representation and modeling of these issues are put forward. In the first one (chapter 2, chapter 3) - fuzzy Allen's relations as fuzzy temporal constraints are represented by norms of convolutions in a Banach space of Lebesgue integrable functions. It allows us immerse Allen's relations in the computational contexts of temporal planning (based on STRIPS and on DavisPutnam procedure) and to elucidate their quantitative nature. This approach is developed in a context of Multi-Agent Problem as a subject basis of this approach. In the second one (chapter 4, chapter 5) - fuzzy temporal constrains with fuzziness introduced by preferences are represented in a logical terms of Preferential Halpern-Shoham Logic. It allows us to adopt these result in a construction of the plan controller. This approach is developed in a context of Temporal Traveling Salesman Problem as a subject basis of this approach. Finally, an attempt to reconcile these two lines of representation of fuzzy temporal constraints was also proposed
Exponential weighted aggregation : oracle inequalities and algorithms by Duy tung Luu( )

2 editions published in 2017 in English and held by 2 WorldCat member libraries worldwide

In many areas of statistics, including signal and image processing, high-dimensional estimation is an important task to recover an object of interest. However, in the overwhelming majority of cases, the recovery problem is ill-posed. Fortunately, even if the ambient dimension of the object to be restored (signal, image, video) is very large, its intrinsic complexity'' is generally small. The introduction of this prior information can be done through two approaches: (i) penalization (very popular) and (ii) aggregation by exponential weighting (EWA). The penalized approach aims at finding an estimator that minimizes a data loss function penalized by a term promoting objects of low (simple) complexity. The EWA combines a family of pre-estimators, each associated with a weight exponentially promoting the same objects of low complexity.This manuscript consists of two parts: a theoretical part and an algorithmic part. In the theoretical part, we first propose the EWA with a new family of priors promoting analysis-group sparse signals whose performance is guaranteed by oracle inequalities. Next, we will analysis the penalized estimator and EWA, with a general prior promoting simple objects, in a unified framework for establishing some theoretical guarantees. Two types of guarantees will be established: (i) prediction oracle inequalities, and (ii) estimation bounds. We will exemplify them for particular cases some of which studied in the literature. In the algorithmic part, we will propose an implementation of these estimators by combining Monte-Carlo simulation (Langevin diffusion process) and proximal splitting algorithms, and show their guarantees of convergence. Several numerical experiments will be considered for illustrating our theoretical guarantees and our algorithms
Contribution aux graphes creux pour le problème de tournées sur arcs déterministe et robustes : théorie et algorithmes by Sara Tfaili( )

2 editions published in 2017 in French and held by 2 WorldCat member libraries worldwide

This dissertation consists of two main parts : in the first part, we study the detreministic capacitated arc routing problem over sparse underlying graphs wher we have developed a new transformation techniquevof sparse CARP into sparse CVRP. The second part is consecrated about the sparse CARP with travel costs uncertainty. We have given a mathematical formulation of the probleme in min-max. A worst scenario for the robust problem is then identified, and two algorithmic approaches are proposed to determine a solution of the studied problem
Mathematical analysis and numerical approximations of magnetohydrodynamics equations with several types of boundary conditions by Julien Poirier( )

2 editions published in 2021 in English and held by 2 WorldCat member libraries worldwide

Cette thèse est consacrée à l'étude des équations de la magnétohydrodynamique pour différentes conditions aux bords. Dans un premier temps nous effectuons une analyse de ces équations pour des conditions aux bords impliquant la pression dans un domaine qui peut être non simplement connexe, avec l'existence de solutions hilbertiennes par un point fixe de Schauder, puis les régularités W1,p pour p > 2 et W2,p pour p > frac{6}{5} à partir des régularités des problèmes de Stokes et du problème elliptique, et, par dualité après une étude du système linéarisé,W1,p pour frac{3}{2} < p < 2. Dans un second temps, nous effectuons une étude similaire du système, avec des conditions aux bords de type Navier pour la vitesse et le champ magnétique, et dans le cas simplement connexe. Ces différentes conditions aux bords impliquent des adaptations des espaces fonctionnels, en travaillant dans les espaces de Banach H(div) ou H(rot). Pour ces conditions de type Navier, nous travaillons sur une approximation numérique du système avec un schéma numérique de Galerkin discontinu, une méthode basée sur des fonctions de base complètement discontinue . Nous montrons que le problème est bien posé, et effectuons une analyse de l'erreur a priori de la vitesse, du champ magnétique et de la pression basée sur une inégalité discrète Lp que nous prouvons. Enfin, nous considérons l'approximation numérique du système de Navier-Stokes non stationnaire, avec des conditions aux limites de type Navier, en étudiant le système par deux méthodes de perturbation de l'incompressibilité div u = 0 la méthode de compressibilité artificielle et la méthode de pseudo-compressibilité
Ramification et points de petite hauteur by Arnaud Plessis( )

2 editions published in 2019 in French and held by 2 WorldCat member libraries worldwide

Dans cette thèse, on s'intéressera aux points de petite hauteur dans le groupe multiplicatif et sur une courbe elliptique.Dans le cas du groupe multiplicatif, on étudiera tout d'abord les corps dont les points de petites hauteurs sont les racines de l'unité.Ensuite, on localisera les points de petite hauteur dans un corps généré par certains groupes de rang fini.Pour cela, on aura besoin d'étudier les groupes de ramification de certaines extensions radicales.Ces résultats vont dans la direction d'une conjecture de Rémond.Il existe aussi un analogue de cette conjecture dans le cas des variétés abéliennes et il semblerait qu'on puisse même l'étendre au cas des variétés semi-abéliennes isotriviales.Cette nouvelle conjecture permet de relier entre eux certains théorèmes déjà présent dans la littérature.Cependant, ces résultats ne concerne que le cas où les points de petite hauteur sont des points de torsion.Pour conclure cette thèse, on donnera un premier exemple de cette conjecture dans le cas où les points de petite hauteur ne sont pas nécessairement des points de torsion

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Mathématiques, information et ingénierie des systèmes

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French (22)

English (18)