Institut de mathématiques de Toulouse (2007....).
Overview
Works:  91 works in 175 publications in 2 languages and 172 library holdings 

Roles:  Other, Degree grantor, 981 
Publication Timeline
.
Most widely held works by
Institut de mathématiques de Toulouse (2007....).
Marches quantiques ouvertes by
Hugo Bringuier(
Book
)
2 editions published in 2018 in French and held by 2 WorldCat member libraries worldwide
This thesis is devoted to the study of stochastic models derived from open quantum systems. In particular, this work deals with open quantum walks that are the quantum analogues of classical random walks. The first part consists in giving a general presentation of open quantum walks. The mathematical tools necessary to study open quan tum systems are presented, then the discrete and continuous time models of open quantum walks are exposed. These walks are respectively governed by quantum channels and Lindblad operators. The associated quantum trajectories are given by Markov chains and stochastic differential equations with jumps. The first part concludes with discussions over some of the research topics such as the Dirichlet problem for open quantum walks and the asymptotic theorems for quantum non demolition measurements. The second part collects the articles written within the framework of this thesis. These papers deal with the topics associated to the irreducibility, the recurrencetransience duality, the central limit theorem and the large deviations principle for continuous time open quantum walks
2 editions published in 2018 in French and held by 2 WorldCat member libraries worldwide
This thesis is devoted to the study of stochastic models derived from open quantum systems. In particular, this work deals with open quantum walks that are the quantum analogues of classical random walks. The first part consists in giving a general presentation of open quantum walks. The mathematical tools necessary to study open quan tum systems are presented, then the discrete and continuous time models of open quantum walks are exposed. These walks are respectively governed by quantum channels and Lindblad operators. The associated quantum trajectories are given by Markov chains and stochastic differential equations with jumps. The first part concludes with discussions over some of the research topics such as the Dirichlet problem for open quantum walks and the asymptotic theorems for quantum non demolition measurements. The second part collects the articles written within the framework of this thesis. These papers deal with the topics associated to the irreducibility, the recurrencetransience duality, the central limit theorem and the large deviations principle for continuous time open quantum walks
Apprentissage statistique : application au trafic routier à partir de données structurées et aux données massives by
Brendan Guillouet(
Book
)
2 editions published in 2016 in French and held by 2 WorldCat member libraries worldwide
This thesis focuses on machine learning techniques for application to big data. We first consider trajectories defined as sequences of geolocalized data. A hierarchical clustering is then applied on a new distance between trajectories (Symmetrized SegmentPath Distance) producing groups of trajectories which are then modeled with Gaussian mixture in order to describe individual movements. This modeling can be used in a generic way in order to resolve the following problems for road traffic : final destination, trip time or next location predictions. These examples show that our model can be applied to different traffic environments and that, once learned, can be applied to trajectories whose spatial and temporal characteristics are different. We also produce comparisons between different technologies which enable the application of machine learning methods on massive volumes of data
2 editions published in 2016 in French and held by 2 WorldCat member libraries worldwide
This thesis focuses on machine learning techniques for application to big data. We first consider trajectories defined as sequences of geolocalized data. A hierarchical clustering is then applied on a new distance between trajectories (Symmetrized SegmentPath Distance) producing groups of trajectories which are then modeled with Gaussian mixture in order to describe individual movements. This modeling can be used in a generic way in order to resolve the following problems for road traffic : final destination, trip time or next location predictions. These examples show that our model can be applied to different traffic environments and that, once learned, can be applied to trajectories whose spatial and temporal characteristics are different. We also produce comparisons between different technologies which enable the application of machine learning methods on massive volumes of data
Strichartz estimates and the nonlinear Schrödingertype equations by
Van Duong Dinh(
Book
)
2 editions published in 2018 in English and held by 2 WorldCat member libraries worldwide
Cette thèse est consacrée à l'étude des aspects linéaires et nonlinéaires des équations de type Schrödinger [ i partial_t u + nabla^sigma u = F, quad nabla = sqrt {Delta}, quad sigma in (0, infty).] Quand dollar sigma = 2 dollar, il s'agit de l'équation de Schrödinger bien connue dans de nombreux contextes physiques tels que la mécanique quantique, l'optique nonlinéaire, la théorie des champs quantiques et la théorie de HartreeFock. Quand dollar sigma in (0,2) backslash {1} dollar, c'est l'équation Schrödinger fractionnaire, qui a été découverte par Laskin (voir par exemple cite{Laskin2000} et cite{Laskin2002}) en lien avec l'extension de l'intégrale de Feynman, des chemins quantiques de type brownien à ceux de Lévy. Cette équation apparaît également dans des modèles de vagues (voir par exemple cite{IonescuPusateri} et cite{Nguyen}). Quand dollar sigma = 1 dollar, c'est l'équation des demiondes qui apparaît dans des modèles de vagues (voir cite{IonescuPusateri}) et dans l'effondrement gravitationnel (voir cite{ElgartSchlein}, cite{FrohlichLenzmann}). Quand dollar sigma = 4 dollar, c'est l'équation Schrödinger du quatrième ordre ou biharmonique introduite par Karpman cite{Karpman} et par KarpmanShagalov cite{KarpmanShagalov} pour prendre en compte le rôle de la dispersion du quatrième ordre dans la propagation d'un faisceau laser intense dans un milieu massif avec nonlinéarité de Kerr. Cette thèse est divisée en deux parties. La première partie étudie les estimations de Strichartz pour des équations de type Schrödinger sur des variétés comprenant l'espace plat euclidien, les variétés compactes sans bord et les variétés asymptotiquement euclidiennes. Ces estimations de Strichartz sont utiles pour l'étude de l'équations dispersives nonlinéaire à régularité basse. La seconde partie concerne l'étude des aspects nonlinéaires tels que les caractères localement puis globalement bien posés sous l'espace d'énergie, ainsi que l'explosion de solutions peu régulières pour des équations nonlinéaires de type Schrödinger. [...]
2 editions published in 2018 in English and held by 2 WorldCat member libraries worldwide
Cette thèse est consacrée à l'étude des aspects linéaires et nonlinéaires des équations de type Schrödinger [ i partial_t u + nabla^sigma u = F, quad nabla = sqrt {Delta}, quad sigma in (0, infty).] Quand dollar sigma = 2 dollar, il s'agit de l'équation de Schrödinger bien connue dans de nombreux contextes physiques tels que la mécanique quantique, l'optique nonlinéaire, la théorie des champs quantiques et la théorie de HartreeFock. Quand dollar sigma in (0,2) backslash {1} dollar, c'est l'équation Schrödinger fractionnaire, qui a été découverte par Laskin (voir par exemple cite{Laskin2000} et cite{Laskin2002}) en lien avec l'extension de l'intégrale de Feynman, des chemins quantiques de type brownien à ceux de Lévy. Cette équation apparaît également dans des modèles de vagues (voir par exemple cite{IonescuPusateri} et cite{Nguyen}). Quand dollar sigma = 1 dollar, c'est l'équation des demiondes qui apparaît dans des modèles de vagues (voir cite{IonescuPusateri}) et dans l'effondrement gravitationnel (voir cite{ElgartSchlein}, cite{FrohlichLenzmann}). Quand dollar sigma = 4 dollar, c'est l'équation Schrödinger du quatrième ordre ou biharmonique introduite par Karpman cite{Karpman} et par KarpmanShagalov cite{KarpmanShagalov} pour prendre en compte le rôle de la dispersion du quatrième ordre dans la propagation d'un faisceau laser intense dans un milieu massif avec nonlinéarité de Kerr. Cette thèse est divisée en deux parties. La première partie étudie les estimations de Strichartz pour des équations de type Schrödinger sur des variétés comprenant l'espace plat euclidien, les variétés compactes sans bord et les variétés asymptotiquement euclidiennes. Ces estimations de Strichartz sont utiles pour l'étude de l'équations dispersives nonlinéaire à régularité basse. La seconde partie concerne l'étude des aspects nonlinéaires tels que les caractères localement puis globalement bien posés sous l'espace d'énergie, ainsi que l'explosion de solutions peu régulières pour des équations nonlinéaires de type Schrödinger. [...]
Champs de vecteurs quadratiques avec solutions univaluées en dimension 3 et supérieure by
Daniel De La Rosa Gómez(
Book
)
2 editions published in 2019 in English and held by 2 WorldCat member libraries worldwide
It is a remarkable fact that among the known examples of quadratic semicomplete vector fields on C^3, it is always possible to find linear coordinates where the corresponding vector field has allor "almost all"coefficients in the real numbers. Indeed, the coefficients are very often integral. The space of quadratic vector fields on C^3, up to linear equivalence, is a complex 9dimensional family. The main result of this thesis establishes that the degree of freedom in determining the coefficients of a semicomplete vector field (under very mild generic assumptions) is at most 3. In other words, there are 3 parameters from which all remaining parameters are determined. Moreover if these 3 parameters are real, then so is the vector field. We start by considering a generic quadratic vector field Z on C^n that is homogeneous and is not a multiple of the radial vector field. The first step in our work will be to construct a canonical form for the induced vector field X on CP(n1). This canonical form will be invariant under the action of a specific group of symmetries. When n=3, we then push further our approach by studying the singularities not lying on the exceptional divisor but at the hyperplane at infinity Delta=CP(2). In this setting the dynamics of the foliation turn out to be quite simple while the singularities tend to be degenerated. The advantage is that we can deal with degenerated singularities with the technique of successive blowups. This leads to simple expressions for the eigenvalues directly in terms of the coefficients of X
2 editions published in 2019 in English and held by 2 WorldCat member libraries worldwide
It is a remarkable fact that among the known examples of quadratic semicomplete vector fields on C^3, it is always possible to find linear coordinates where the corresponding vector field has allor "almost all"coefficients in the real numbers. Indeed, the coefficients are very often integral. The space of quadratic vector fields on C^3, up to linear equivalence, is a complex 9dimensional family. The main result of this thesis establishes that the degree of freedom in determining the coefficients of a semicomplete vector field (under very mild generic assumptions) is at most 3. In other words, there are 3 parameters from which all remaining parameters are determined. Moreover if these 3 parameters are real, then so is the vector field. We start by considering a generic quadratic vector field Z on C^n that is homogeneous and is not a multiple of the radial vector field. The first step in our work will be to construct a canonical form for the induced vector field X on CP(n1). This canonical form will be invariant under the action of a specific group of symmetries. When n=3, we then push further our approach by studying the singularities not lying on the exceptional divisor but at the hyperplane at infinity Delta=CP(2). In this setting the dynamics of the foliation turn out to be quite simple while the singularities tend to be degenerated. The advantage is that we can deal with degenerated singularities with the technique of successive blowups. This leads to simple expressions for the eigenvalues directly in terms of the coefficients of X
Sur la notion d'optimalité dans les problèmes de bandit stochastique by
Pierre Ménard(
Book
)
2 editions published in 2018 in English and held by 2 WorldCat member libraries worldwide
The topics addressed in this thesis lie in statistical machine learning and sequential statistic. Our main framework is the stochastic multiarmed bandit problems. In this work we revisit lower bounds on the regret. We obtain nonasymptotic, distributiondependent bounds and provide simple proofs based only on wellknown properties of KullbackLeibler divergence. These bounds show in particular that in the initial phase the regret grows almost linearly, and that the wellknown logarithmic growth of the regret only holds in a final phase. Then, we propose algorithms for regret minimization in stochastic bandit models with exponential families of distributions or with distribution only assumed to be supported by the unit interval, that are simultaneously asymptotically optimal (in the sense of Lai and Robbins lower bound) and minimax optimal. We also analyze the sample complexity of sequentially identifying the distribution whose expectation is the closest to some given threshold, with and without the assumption that the mean values of the distributions are increasing. This work is motivated by phase I clinical trials, a practically important setting where the arm means are increasing by nature. Finally we extend Fano's inequality, which controls the average probability of (disjoint) events in terms of the average of some KullbackLeibler divergences, to work with arbitrary unitvalued random variables. Several novel applications are provided, in which the consideration of random variables is particularly handy. The most important applications deal with the problem of Bayesian posterior concentration (minimax or distributiondependent) rates and with a lower bound on the regret in nonstochastic sequential learning
2 editions published in 2018 in English and held by 2 WorldCat member libraries worldwide
The topics addressed in this thesis lie in statistical machine learning and sequential statistic. Our main framework is the stochastic multiarmed bandit problems. In this work we revisit lower bounds on the regret. We obtain nonasymptotic, distributiondependent bounds and provide simple proofs based only on wellknown properties of KullbackLeibler divergence. These bounds show in particular that in the initial phase the regret grows almost linearly, and that the wellknown logarithmic growth of the regret only holds in a final phase. Then, we propose algorithms for regret minimization in stochastic bandit models with exponential families of distributions or with distribution only assumed to be supported by the unit interval, that are simultaneously asymptotically optimal (in the sense of Lai and Robbins lower bound) and minimax optimal. We also analyze the sample complexity of sequentially identifying the distribution whose expectation is the closest to some given threshold, with and without the assumption that the mean values of the distributions are increasing. This work is motivated by phase I clinical trials, a practically important setting where the arm means are increasing by nature. Finally we extend Fano's inequality, which controls the average probability of (disjoint) events in terms of the average of some KullbackLeibler divergences, to work with arbitrary unitvalued random variables. Several novel applications are provided, in which the consideration of random variables is particularly handy. The most important applications deal with the problem of Bayesian posterior concentration (minimax or distributiondependent) rates and with a lower bound on the regret in nonstochastic sequential learning
Le problème de Dirichlet pour les équations de MongeAmpère complexes by
Mohamad Charabati(
Book
)
2 editions published in 2016 in English and held by 2 WorldCat member libraries worldwide
In this thesis we study the regularity of solutions to the Dirichlet problem for complex MongeAmpère equations and also for complex Hessian equations in a bounded domain of Cn. In the first chapter, we give basic facts in pluripotential theory. In the second chapter, we study the modulus of continuity of solutions to the Dirichlet problem for complex MongeAmpère equations when the right hand side is a measure with continuous density with respect to the Lebesgue measure in a bounded strongly hyperconvex Lipschitz domain. In the third chapter, we prove the Hölder continuity of solutions to this problem for some general measures. In the fourth chapter, we consider the Dirichlet problem for complex Hessian equations when the right hand side depends on the unknown function. We give a sharp estimate of the modulus of continuity of the solution as the density is continuous. Moreover, for the case of Lpdensity we demonstrate that the solution is Hölder continuous up to the boundary
2 editions published in 2016 in English and held by 2 WorldCat member libraries worldwide
In this thesis we study the regularity of solutions to the Dirichlet problem for complex MongeAmpère equations and also for complex Hessian equations in a bounded domain of Cn. In the first chapter, we give basic facts in pluripotential theory. In the second chapter, we study the modulus of continuity of solutions to the Dirichlet problem for complex MongeAmpère equations when the right hand side is a measure with continuous density with respect to the Lebesgue measure in a bounded strongly hyperconvex Lipschitz domain. In the third chapter, we prove the Hölder continuity of solutions to this problem for some general measures. In the fourth chapter, we consider the Dirichlet problem for complex Hessian equations when the right hand side depends on the unknown function. We give a sharp estimate of the modulus of continuity of the solution as the density is continuous. Moreover, for the case of Lpdensity we demonstrate that the solution is Hölder continuous up to the boundary
Etude d'un problème d'interaction fluidestructure : modélisation, analyse, stabilisation et simulations numériques by
Guillaume Delay(
Book
)
2 editions published in 2018 in French and held by 2 WorldCat member libraries worldwide
Ce travail de thèse porte sur l'étude d'un système d'interaction fluidestructure. Nous en traitons de nombreux aspects allant de sa modélisation jusqu'à l'étude de sa stabilisation et de sa simulation numérique. Le premier chapitre du manuscrit aborde la modélisation du système ainsi que l'existence de solutions fortes en temps petits. Le fluide est représenté par les équations de NavierStokes incompressibles. La structure est déformable et dépend d'un nombre fini de paramètres. Nous obtenons ses équations en appliquant un principe des travaux virtuels. Le système d'équations final est non linéaire. Nous prouvons l'existence locale d'une solution à ce système, dans un premier temps sur le système linéarisé autour de l'état nul. Puis, nous prouvons l'existence de solutions en temps petits au système non linéaire grâce à un argument de point fixe. Le deuxième chapitre traite de la stabilisation par feedback autour d'un état stationnaire non nul du système présenté dans le Chapitre 1. L'opérateur de feedback est déterminé à partir de l'analyse du problème linéarisé autour de l'état stationnaire et de la résolution d'une équation de Riccati. Le résultat de stabilisation portant sur le système non linéaire requiert des données petites et est obtenu par un argument de point fixe. Le troisième chapitre se concentre sur les aspects numériques de ce problème. La construction de l'opérateur de feedback correspond à la version discrétisée de celle proposée dans le Chapitre 2. Le système fluidestructure est simulé en utilisant une méthode de domaines fictifs
2 editions published in 2018 in French and held by 2 WorldCat member libraries worldwide
Ce travail de thèse porte sur l'étude d'un système d'interaction fluidestructure. Nous en traitons de nombreux aspects allant de sa modélisation jusqu'à l'étude de sa stabilisation et de sa simulation numérique. Le premier chapitre du manuscrit aborde la modélisation du système ainsi que l'existence de solutions fortes en temps petits. Le fluide est représenté par les équations de NavierStokes incompressibles. La structure est déformable et dépend d'un nombre fini de paramètres. Nous obtenons ses équations en appliquant un principe des travaux virtuels. Le système d'équations final est non linéaire. Nous prouvons l'existence locale d'une solution à ce système, dans un premier temps sur le système linéarisé autour de l'état nul. Puis, nous prouvons l'existence de solutions en temps petits au système non linéaire grâce à un argument de point fixe. Le deuxième chapitre traite de la stabilisation par feedback autour d'un état stationnaire non nul du système présenté dans le Chapitre 1. L'opérateur de feedback est déterminé à partir de l'analyse du problème linéarisé autour de l'état stationnaire et de la résolution d'une équation de Riccati. Le résultat de stabilisation portant sur le système non linéaire requiert des données petites et est obtenu par un argument de point fixe. Le troisième chapitre se concentre sur les aspects numériques de ce problème. La construction de l'opérateur de feedback correspond à la version discrétisée de celle proposée dans le Chapitre 2. Le système fluidestructure est simulé en utilisant une méthode de domaines fictifs
Optimal uncertainty quantification of a risk measurement from a computer code by
Jérôme Stenger(
Book
)
2 editions published in 2020 in English and held by 2 WorldCat member libraries worldwide
Uncertainty quantification in a safety analysis study can be conducted by considering the uncertain inputs of a physical system as a vector of random variables. The most widespread approach consists in running a computer model reproducing the physical phenomenon with different combinations of inputs in accordance with their probability distribution. Then, one can study the related uncertainty on the output or estimate a specific quantity of interest (QoI). Because the computer model is assumed to be a deterministic blackbox function, the QoI only depends on the choice of the input probability measure. It is formally represented as a scalar function defined on a measure space. We propose to gain robustness on the quantification of this QoI. Indeed, the probability distributions characterizing the uncertain input may themselves be uncertain. For instance, contradictory expert opinion may make it difficult to select a single probability distribution, and the lack of information in the input variables affects inevitably the choice of the distribution. As the uncertainty on the input distributions propagates to the QoI, an important consequence is that different choices of input distributions will lead to different values of the QoI. The purpose of this thesis is to account for this second level uncertainty. We propose to evaluate the maximum of the QoI over a space of probability measures, in an approach known as optimal uncertainty quantification (OUQ). Therefore, we do not specify a single precise input distribution, but rather a set of admissible probability measures defined through moment constraints. The QoI is then optimized over this measure space. After exposing theoretical results showing that the optimization domain of the QoI can be reduced to the extreme points of the measure space, we present several interesting quantities of interest satisfying the assumption of the problem. This thesis illustrates the methodology in several application cases, one of them being a real nuclear engineering case that study the evolution of the peak cladding temperature of fuel rods in case of an intermediate break loss of coolant accident
2 editions published in 2020 in English and held by 2 WorldCat member libraries worldwide
Uncertainty quantification in a safety analysis study can be conducted by considering the uncertain inputs of a physical system as a vector of random variables. The most widespread approach consists in running a computer model reproducing the physical phenomenon with different combinations of inputs in accordance with their probability distribution. Then, one can study the related uncertainty on the output or estimate a specific quantity of interest (QoI). Because the computer model is assumed to be a deterministic blackbox function, the QoI only depends on the choice of the input probability measure. It is formally represented as a scalar function defined on a measure space. We propose to gain robustness on the quantification of this QoI. Indeed, the probability distributions characterizing the uncertain input may themselves be uncertain. For instance, contradictory expert opinion may make it difficult to select a single probability distribution, and the lack of information in the input variables affects inevitably the choice of the distribution. As the uncertainty on the input distributions propagates to the QoI, an important consequence is that different choices of input distributions will lead to different values of the QoI. The purpose of this thesis is to account for this second level uncertainty. We propose to evaluate the maximum of the QoI over a space of probability measures, in an approach known as optimal uncertainty quantification (OUQ). Therefore, we do not specify a single precise input distribution, but rather a set of admissible probability measures defined through moment constraints. The QoI is then optimized over this measure space. After exposing theoretical results showing that the optimization domain of the QoI can be reduced to the extreme points of the measure space, we present several interesting quantities of interest satisfying the assumption of the problem. This thesis illustrates the methodology in several application cases, one of them being a real nuclear engineering case that study the evolution of the peak cladding temperature of fuel rods in case of an intermediate break loss of coolant accident
Formes effectives de la conjecture de ManinMumford et réalisations du polylogarithme abélien by
Danny Scarponi(
Book
)
2 editions published in 2016 in English and held by 2 WorldCat member libraries worldwide
In this thesis we approach two independent problems in the field of arithmetic geometry, one regarding the torsion points of abelian varieties and the other the motivic polylogarithm on abelian schemes. The ManinMumford conjecture (proved by Raynaud in 1983) states that if A is an abelian variety and X is a subvariety of A not containing any translate of an abelian subvariety of A, then X can only have a finite number of points that are of finite order in A. In 1996, Buium presented an effective form of the conjecture in the case of curves. In this thesis, we show that Buium's argument can be made applicable in higher dimensions to prove a quantitative version of the conjecture for a class of subvarieties with ample cotangent studied by Debarre. Our proof also generalizes to any dimension a result on the sparsity of pdivisible unramified liftings obtained by Raynaud in the case of curves. In 2014, Kings and Roessler showed that the realisation in analytic Deligne cohomology of the degree zero part of the motivic polylogarithm on abelian schemes can be described in terms of the BismutKoehler higher analytic torsion form of the Poincaré bundle. In this thesis, using the arithmetic intersection theory in the sense of Burgos, we give a refinement of Kings and Roessler's result in the case in which the base of the abelian scheme is proper
2 editions published in 2016 in English and held by 2 WorldCat member libraries worldwide
In this thesis we approach two independent problems in the field of arithmetic geometry, one regarding the torsion points of abelian varieties and the other the motivic polylogarithm on abelian schemes. The ManinMumford conjecture (proved by Raynaud in 1983) states that if A is an abelian variety and X is a subvariety of A not containing any translate of an abelian subvariety of A, then X can only have a finite number of points that are of finite order in A. In 1996, Buium presented an effective form of the conjecture in the case of curves. In this thesis, we show that Buium's argument can be made applicable in higher dimensions to prove a quantitative version of the conjecture for a class of subvarieties with ample cotangent studied by Debarre. Our proof also generalizes to any dimension a result on the sparsity of pdivisible unramified liftings obtained by Raynaud in the case of curves. In 2014, Kings and Roessler showed that the realisation in analytic Deligne cohomology of the degree zero part of the motivic polylogarithm on abelian schemes can be described in terms of the BismutKoehler higher analytic torsion form of the Poincaré bundle. In this thesis, using the arithmetic intersection theory in the sense of Burgos, we give a refinement of Kings and Roessler's result in the case in which the base of the abelian scheme is proper
Kstabilité et variétés kähleriennes avec classe transcendante by
Zakarias Sjöström Dyrefelt(
Book
)
2 editions published in 2017 in English and held by 2 WorldCat member libraries worldwide
In this thesis we are interested in questions of geometric stability for constant scalar curvature Kähler (cscK) manifolds with transcendental cohomology class. As a starting point we develop generalized notions of Kstability, extending a classical picture for polarized manifolds due to G. Tian, S. Donaldson, and others, to the setting of arbitrary compact Kähler manifolds. We refer to these notions as cohomological Kstability. By contrast to the classical theory, this formalism allows us to treat stability questions for nonprojective compact Kähler manifolds as well as projective manifolds endowed with nonrational polarizations. As a first main result and a fundamental tool in this thesis, we study subgeodesic rays associated to test configurations in our generalized sense, and establish formulas for the asymptotic slope of a certain family of energy functionals along these rays. This is related to the Deligne pairing construction in algebraic geometry, and covers many of the classical energy functionals in Kähler geometry (including Aubin's Jfunctional and the Mabuchi Kenergy functional). In particular, this yields a natural potentialtheoretic aproach to energy functional asymptotics in the theory of Kstability. Building on this foundation we establish a number of stability results for cscK manifolds: First, we show that cscK manifolds are Ksemistable in our generalized sense, extending a result due to S. Donaldson in the projective setting. Assuming that the automorphism group is discrete we further show that Kstability is a necessary condition for existence of constant scalar curvature Kähler metrics on compact Kähler manifolds. More precisely, we prove that coercivity of the Mabuchi functional implies uniform Kstability, generalizing results of T. Mabuchi, J. Stoppa, R. Berman, R. Dervan as well as S. Boucksom, T. Hisamoto and M. Jonsson for polarized manifolds. This gives a new and more general proof of one direction of the YauTianDonaldson conjecture in this setting. The other direction (sufficiency of Kstability) is considered to be one of the most important open problems in Kähler geometry. We finally give some partial results in the case of compact Kähler manifolds admitting nontrivial holomorphic vector fields, discuss some further perspectives and applications of the theory of Kstability for compact Kähler manifolds with transcendental cohomology class, and ask some questions related to stability loci in the Kähler cone
2 editions published in 2017 in English and held by 2 WorldCat member libraries worldwide
In this thesis we are interested in questions of geometric stability for constant scalar curvature Kähler (cscK) manifolds with transcendental cohomology class. As a starting point we develop generalized notions of Kstability, extending a classical picture for polarized manifolds due to G. Tian, S. Donaldson, and others, to the setting of arbitrary compact Kähler manifolds. We refer to these notions as cohomological Kstability. By contrast to the classical theory, this formalism allows us to treat stability questions for nonprojective compact Kähler manifolds as well as projective manifolds endowed with nonrational polarizations. As a first main result and a fundamental tool in this thesis, we study subgeodesic rays associated to test configurations in our generalized sense, and establish formulas for the asymptotic slope of a certain family of energy functionals along these rays. This is related to the Deligne pairing construction in algebraic geometry, and covers many of the classical energy functionals in Kähler geometry (including Aubin's Jfunctional and the Mabuchi Kenergy functional). In particular, this yields a natural potentialtheoretic aproach to energy functional asymptotics in the theory of Kstability. Building on this foundation we establish a number of stability results for cscK manifolds: First, we show that cscK manifolds are Ksemistable in our generalized sense, extending a result due to S. Donaldson in the projective setting. Assuming that the automorphism group is discrete we further show that Kstability is a necessary condition for existence of constant scalar curvature Kähler metrics on compact Kähler manifolds. More precisely, we prove that coercivity of the Mabuchi functional implies uniform Kstability, generalizing results of T. Mabuchi, J. Stoppa, R. Berman, R. Dervan as well as S. Boucksom, T. Hisamoto and M. Jonsson for polarized manifolds. This gives a new and more general proof of one direction of the YauTianDonaldson conjecture in this setting. The other direction (sufficiency of Kstability) is considered to be one of the most important open problems in Kähler geometry. We finally give some partial results in the case of compact Kähler manifolds admitting nontrivial holomorphic vector fields, discuss some further perspectives and applications of the theory of Kstability for compact Kähler manifolds with transcendental cohomology class, and ask some questions related to stability loci in the Kähler cone
Quelques retombées de la géométrie des surfaces toriques sur un corps fini sur l'arithmétique et la théorie de l'information by
Jade Nardi(
Book
)
2 editions published in 2019 in English and held by 2 WorldCat member libraries worldwide
Cette thèse, à la frontière entre les mathématiques et l'informatique, est consacrée en partie à l'étude des paramètres et des propriétés des codes de Goppa sur les surfaces de Hirzebruch. D'un point de vue arithmétique, la théorie des codes correcteurs a ravivé la question du nombre de points rationnels d'une variété définie sur un corps fini, qui semblait résolue par la formule de Lefschetz. La distance minimale de codes géométriques donne un majorant du nombre de points rationnels d'une hypersurface d'une variété donnée et de classe de Picard fixée. Ce majorant étant le plus souvent atteint pour les courbes très réductibles, il est naturel de se concentrer sur les courbes irréductibles pour affiner les bornes. On présente une stratégie globale pour majorer le nombre de points d'une variété en fonction de son ambiant et d'invariants géométriques, notamment liés à la théorie de l'intersection. De plus, une méthode de ce type pour les courbes d'une surface torique est développée en adaptant l'idée de F.J Voloch et K.O. Sthör aux variétés toriques. Enfin, on s'intéresse aux protocoles de Private Information Retrivial, qui visent à assurer qu'un utilisateur puisse accéder à une entrée d'une base de données sans révéler d'information sur l'entrée au propriétaire de la base de données. Un protocole basé sur des codes sur des plans projectifs pondérés est proposé ici. Il améliore les protocoles existants en résistant à la collusion de serveurs, au prix d'une grande perte de capacité de stockage. On pallie ce problème grâce à la méthode du lift qui permet la construction de familles de codes asymptotiquement bonnes, avec les mêmes propriétés locales
2 editions published in 2019 in English and held by 2 WorldCat member libraries worldwide
Cette thèse, à la frontière entre les mathématiques et l'informatique, est consacrée en partie à l'étude des paramètres et des propriétés des codes de Goppa sur les surfaces de Hirzebruch. D'un point de vue arithmétique, la théorie des codes correcteurs a ravivé la question du nombre de points rationnels d'une variété définie sur un corps fini, qui semblait résolue par la formule de Lefschetz. La distance minimale de codes géométriques donne un majorant du nombre de points rationnels d'une hypersurface d'une variété donnée et de classe de Picard fixée. Ce majorant étant le plus souvent atteint pour les courbes très réductibles, il est naturel de se concentrer sur les courbes irréductibles pour affiner les bornes. On présente une stratégie globale pour majorer le nombre de points d'une variété en fonction de son ambiant et d'invariants géométriques, notamment liés à la théorie de l'intersection. De plus, une méthode de ce type pour les courbes d'une surface torique est développée en adaptant l'idée de F.J Voloch et K.O. Sthör aux variétés toriques. Enfin, on s'intéresse aux protocoles de Private Information Retrivial, qui visent à assurer qu'un utilisateur puisse accéder à une entrée d'une base de données sans révéler d'information sur l'entrée au propriétaire de la base de données. Un protocole basé sur des codes sur des plans projectifs pondérés est proposé ici. Il améliore les protocoles existants en résistant à la collusion de serveurs, au prix d'une grande perte de capacité de stockage. On pallie ce problème grâce à la méthode du lift qui permet la construction de familles de codes asymptotiquement bonnes, avec les mêmes propriétés locales
Ergodicité des équations différentielles stochastiques fractionnaires et problèmes liés by
Maylis Varvenne(
Book
)
2 editions published in 2019 in English and held by 2 WorldCat member libraries worldwide
In this thesis, we focus on three problems related to the ergodicity of stochastic dynamics with memory (in a discretetime or continuoustime setting) and especially of Stochastic Differential Equations (SDE) driven by fractional Brownian motion. In the first chapter, we study the longtime behavior of a general class of discretetime stochastic dynamics driven by an ergodic and stationary Gaussian noise. Following the seminal paper written by Hairer (2005) on the ergodicity of fractional SDE (see also FontbonaPanloup (2017) and DeyaPanloupTindel (2019)), we first build a Markovian structure above the dynamics, we show existence and uniqueness of the invariant distribution and then we exhibit some upperbounds on the rate of convergence to equilibrium in terms of the asymptotic behavior of the covariance function of the Gaussian noise (or more precisely, of the asymptotic behavior of the coefficients appearing in its moving average representation). The second chapter establishes longtime concentration inequalities both for functionals of the whole solution on an interval [0,T] of an additive fractional SDE and for functionals of discretetime observations of this process. Then, we apply this general result to specific functionals related to discrete and continuoustime occupation measures of the process. The last chapter, which uses the results developed in Chapter 2, is a joint work with Panloup and Tindel which focuses on the parametric estimation of the (nonlinear) drift term in an additive fractional SDE. We use a minimum contrast estimation based on the identification of the invariant distribution (for which we build an approximation from discretetime observations of the SDE). We provide consistency results as well as nonasymptotic estimates of the corresponding quadratic error. Some of our results are illustrating through numerical discussions. We also give some examples for which the identifiability condition related to our estimation procedure (intrinsically linked to the invariant distribution) is fulfilled
2 editions published in 2019 in English and held by 2 WorldCat member libraries worldwide
In this thesis, we focus on three problems related to the ergodicity of stochastic dynamics with memory (in a discretetime or continuoustime setting) and especially of Stochastic Differential Equations (SDE) driven by fractional Brownian motion. In the first chapter, we study the longtime behavior of a general class of discretetime stochastic dynamics driven by an ergodic and stationary Gaussian noise. Following the seminal paper written by Hairer (2005) on the ergodicity of fractional SDE (see also FontbonaPanloup (2017) and DeyaPanloupTindel (2019)), we first build a Markovian structure above the dynamics, we show existence and uniqueness of the invariant distribution and then we exhibit some upperbounds on the rate of convergence to equilibrium in terms of the asymptotic behavior of the covariance function of the Gaussian noise (or more precisely, of the asymptotic behavior of the coefficients appearing in its moving average representation). The second chapter establishes longtime concentration inequalities both for functionals of the whole solution on an interval [0,T] of an additive fractional SDE and for functionals of discretetime observations of this process. Then, we apply this general result to specific functionals related to discrete and continuoustime occupation measures of the process. The last chapter, which uses the results developed in Chapter 2, is a joint work with Panloup and Tindel which focuses on the parametric estimation of the (nonlinear) drift term in an additive fractional SDE. We use a minimum contrast estimation based on the identification of the invariant distribution (for which we build an approximation from discretetime observations of the SDE). We provide consistency results as well as nonasymptotic estimates of the corresponding quadratic error. Some of our results are illustrating through numerical discussions. We also give some examples for which the identifiability condition related to our estimation procedure (intrinsically linked to the invariant distribution) is fulfilled
Algorithmes stochastiques pour l'apprentissage, l'optimisation et l'approximation du régime stationnaire by
Sofiane Saadane(
Book
)
2 editions published in 2016 in French and held by 2 WorldCat member libraries worldwide
In this thesis, we are studying severa! stochastic algorithms with different purposes and this is why we will start this manuscript by giving historicals results to define the framework of our work. Then, we will study a bandit algorithm due to the work of Narendra and Shapiro whose objectif was to determine among a choice of severa! sources which one is the most profitable without spending too much times on the wrong orres. Our goal is to understand the weakness of this algorithm in order to propose an optimal procedure for a quantity measuring the performance of a bandit algorithm, the regret. In our results, we will propose an algorithm called NS overpenalized which allows to obtain a minimax regret bound. A second work will be to understand the convergence in law of this process. The particularity of the algorith is that it converges in law toward a nondiffusive process which makes the study more intricate than the standard case. We will use coupling techniques to study this process and propose rates of convergence. The second work of this thesis falls in the scope of optimization of a function using a stochastic algorithm. We will study a stochastic version of the socalled heavy bali method with friction. The particularity of the algorithm is that its dynamics is based on the ali past of the trajectory. The procedure relies on a memory term which dictates the behavior of the procedure by the form it takes. In our framework, two types of memory will investigated : polynomial and exponential. We will start with general convergence results in the nonconvex case. In the case of strongly convex functions, we will provide upperbounds for the rate of convergence. Finally, a convergence in law result is given in the case of exponential memory. The third part is about the McKeanVlasov equations which were first introduced by Anatoly Vlasov and first studied by Henry McKean in order to mode! the distribution function of plasma. Our objective is to propose a stochastic algorithm to approach the invariant distribution of the McKean Vlasov equation. Methods in the case of diffusion processes (and sorne more general pro cesses) are known but the particularity of McKean Vlasov process is that it is strongly nonlinear. Thus, we will have to develop an alternative approach. We will introduce the notion of asymptotic pseudotrajectory in odrer to get an efficient procedure
2 editions published in 2016 in French and held by 2 WorldCat member libraries worldwide
In this thesis, we are studying severa! stochastic algorithms with different purposes and this is why we will start this manuscript by giving historicals results to define the framework of our work. Then, we will study a bandit algorithm due to the work of Narendra and Shapiro whose objectif was to determine among a choice of severa! sources which one is the most profitable without spending too much times on the wrong orres. Our goal is to understand the weakness of this algorithm in order to propose an optimal procedure for a quantity measuring the performance of a bandit algorithm, the regret. In our results, we will propose an algorithm called NS overpenalized which allows to obtain a minimax regret bound. A second work will be to understand the convergence in law of this process. The particularity of the algorith is that it converges in law toward a nondiffusive process which makes the study more intricate than the standard case. We will use coupling techniques to study this process and propose rates of convergence. The second work of this thesis falls in the scope of optimization of a function using a stochastic algorithm. We will study a stochastic version of the socalled heavy bali method with friction. The particularity of the algorithm is that its dynamics is based on the ali past of the trajectory. The procedure relies on a memory term which dictates the behavior of the procedure by the form it takes. In our framework, two types of memory will investigated : polynomial and exponential. We will start with general convergence results in the nonconvex case. In the case of strongly convex functions, we will provide upperbounds for the rate of convergence. Finally, a convergence in law result is given in the case of exponential memory. The third part is about the McKeanVlasov equations which were first introduced by Anatoly Vlasov and first studied by Henry McKean in order to mode! the distribution function of plasma. Our objective is to propose a stochastic algorithm to approach the invariant distribution of the McKean Vlasov equation. Methods in the case of diffusion processes (and sorne more general pro cesses) are known but the particularity of McKean Vlasov process is that it is strongly nonlinear. Thus, we will have to develop an alternative approach. We will introduce the notion of asymptotic pseudotrajectory in odrer to get an efficient procedure
Modélisation stochastique de processus d'agrégation en chimie by
Daniel Paredes Moreno(
Book
)
2 editions published in 2017 in English and held by 2 WorldCat member libraries worldwide
Nous concentrons notre intérêt sur l'Équation du Bilan de la Population (PBE). Cette équation décrit l'évolution, au fil du temps, des systèmes de particules en fonction de sa fonction de densité en nombre (NDF) où des processus d'agrégation et de rupture sont impliqués. Dans la première partie, nous avons étudié la formation de groupes de particules et l'importance relative des variables dans la formation des ces groupes en utilisant les données dans (Vlieghe 2014) et des techniques exploratoires comme l'analyse en composantes principales, le partitionnement de données et l'analyse discriminante. Nous avons utilisé ce schéma d'analyse pour la population initiale de particules ainsi que pour les populations résultantes sous différentes conditions hydrodynamiques. La deuxième partie nous avons étudié l'utilisation de la PBE en fonction des moments standard de la NDF, et les méthodes en quadrature des moments (QMOM) et l'Extrapolation Minimale Généralisée (GME), afin de récupérer l'évolution, d'un ensemble fini de moments standard de la NDF. La méthode QMOM utilise une application de l'algorithme Produit Différence et GME récupère une mesure discrète nonnégative, étant donnée un ensemble fini de ses moments standard. Dans la troisième partie, nous avons proposé un schéma de discrétisation afin de trouver une approximation numérique de la solution de la PBE. Nous avons utilisé trois cas où la solution analytique est connue (Silva et al. 2011) afin de comparer la solution théorique à l'approximation trouvée avec le schéma de discrétisation. La dernière partie concerne l'estimation des paramètres impliqués dans la modélisation des processus d'agrégation et de rupture impliqués dans la PBE. Nous avons proposé une méthode pour estimer ces paramètres en utilisant l'approximation numérique trouvée, ainsi que le Filtre Étendu de Kalman. La méthode estime interactivement les paramètres à chaque instant du temps, en utilisant un estimateur de Moindres Carrés nonlinéaire
2 editions published in 2017 in English and held by 2 WorldCat member libraries worldwide
Nous concentrons notre intérêt sur l'Équation du Bilan de la Population (PBE). Cette équation décrit l'évolution, au fil du temps, des systèmes de particules en fonction de sa fonction de densité en nombre (NDF) où des processus d'agrégation et de rupture sont impliqués. Dans la première partie, nous avons étudié la formation de groupes de particules et l'importance relative des variables dans la formation des ces groupes en utilisant les données dans (Vlieghe 2014) et des techniques exploratoires comme l'analyse en composantes principales, le partitionnement de données et l'analyse discriminante. Nous avons utilisé ce schéma d'analyse pour la population initiale de particules ainsi que pour les populations résultantes sous différentes conditions hydrodynamiques. La deuxième partie nous avons étudié l'utilisation de la PBE en fonction des moments standard de la NDF, et les méthodes en quadrature des moments (QMOM) et l'Extrapolation Minimale Généralisée (GME), afin de récupérer l'évolution, d'un ensemble fini de moments standard de la NDF. La méthode QMOM utilise une application de l'algorithme Produit Différence et GME récupère une mesure discrète nonnégative, étant donnée un ensemble fini de ses moments standard. Dans la troisième partie, nous avons proposé un schéma de discrétisation afin de trouver une approximation numérique de la solution de la PBE. Nous avons utilisé trois cas où la solution analytique est connue (Silva et al. 2011) afin de comparer la solution théorique à l'approximation trouvée avec le schéma de discrétisation. La dernière partie concerne l'estimation des paramètres impliqués dans la modélisation des processus d'agrégation et de rupture impliqués dans la PBE. Nous avons proposé une méthode pour estimer ces paramètres en utilisant l'approximation numérique trouvée, ainsi que le Filtre Étendu de Kalman. La méthode estime interactivement les paramètres à chaque instant du temps, en utilisant un estimateur de Moindres Carrés nonlinéaire
Modèles intègres dérivés et ses applications à l'étude de certains espaces des modules rigides analytiques dérivés by
Jorge Ferreira Antonio(
Book
)
2 editions published in 2019 in English and held by 2 WorldCat member libraries worldwide
In this thesis, we study different aspects of derived kanalytic geometry. Namely, we extend the theory of classical formal models for rigid kanalytic spaces to the derived setting. Having a theory of derived formal models at our disposal we proceed to study certain applications such as the representability of derived Hilbert stack in the derived kanalytic setting. We construct a moduli stack of derived kadic representations of profinite spaces and prove its geometricity as a derived kanalytic stack. Under certain hypothesis we show the existence of a natural shifted symplectic structure on it. Our main applications is to study proétale kadic local systems on smooth schemes in positive characteristic. Finally, we study at length an analytic analogue (both over the field of complex numbers C and over a nonarchimedean field k) of the structured algebraic HKR, proved by Toen and Vezzosi
2 editions published in 2019 in English and held by 2 WorldCat member libraries worldwide
In this thesis, we study different aspects of derived kanalytic geometry. Namely, we extend the theory of classical formal models for rigid kanalytic spaces to the derived setting. Having a theory of derived formal models at our disposal we proceed to study certain applications such as the representability of derived Hilbert stack in the derived kanalytic setting. We construct a moduli stack of derived kadic representations of profinite spaces and prove its geometricity as a derived kanalytic stack. Under certain hypothesis we show the existence of a natural shifted symplectic structure on it. Our main applications is to study proétale kadic local systems on smooth schemes in positive characteristic. Finally, we study at length an analytic analogue (both over the field of complex numbers C and over a nonarchimedean field k) of the structured algebraic HKR, proved by Toen and Vezzosi
Flots de MongeAmpère complexes sur les variétés hermitiennes compactes by
Tat Dat Tô(
Book
)
2 editions published in 2018 in English and held by 2 WorldCat member libraries worldwide
In this thesis we study the complex MongeAmpère flows, and their generalizations and geometric applications on compact Hermitian manifods. In the first two chapters, we prove that a general complex MongeAmpère flow on a compact Hermitian manifold can be run from an arbitrary initial condition with zero Lelong number at all points. Using this property, we confirm a conjecture of Tosatti Weinkove: the ChernRicci flow performs a canonical surgical contraction. Finally, we study a generalization of the ChernRicci flow on compact Hermitian manifolds, namely the twisted ChernRicci flow. This part gave rise to two independent publications. In the third chapter, a notion of parabolic C subsolution is introduced for parabolic nonlinear equations, extending the theory of C subsolutions recently developed by B. Guan and more specifically G. Székelyhidi for elliptic equations. The resulting parabolic theory provides a convenient unified approach for the study of many geometric flows. This part is a joint work with Duong H. Phong (Columbia University) In the fourth chapter, a viscosity approach is introduced for the Dirichlet problem associated to complex Hessian type equations on domains in Cn. The arguments are modelled on the theory of viscosity solutions for real Hessian type equations developed by Trudinger. As consequence we solve the Dirichlet problem for the Hessian quotient and special Lagrangian equations. We also establish basic regularity results for the solutions. This part is a joint work with Slawomir Dinew (Jagiellonian University) and HoangSon Do (Hanoi Institute of Mathematics)
2 editions published in 2018 in English and held by 2 WorldCat member libraries worldwide
In this thesis we study the complex MongeAmpère flows, and their generalizations and geometric applications on compact Hermitian manifods. In the first two chapters, we prove that a general complex MongeAmpère flow on a compact Hermitian manifold can be run from an arbitrary initial condition with zero Lelong number at all points. Using this property, we confirm a conjecture of Tosatti Weinkove: the ChernRicci flow performs a canonical surgical contraction. Finally, we study a generalization of the ChernRicci flow on compact Hermitian manifolds, namely the twisted ChernRicci flow. This part gave rise to two independent publications. In the third chapter, a notion of parabolic C subsolution is introduced for parabolic nonlinear equations, extending the theory of C subsolutions recently developed by B. Guan and more specifically G. Székelyhidi for elliptic equations. The resulting parabolic theory provides a convenient unified approach for the study of many geometric flows. This part is a joint work with Duong H. Phong (Columbia University) In the fourth chapter, a viscosity approach is introduced for the Dirichlet problem associated to complex Hessian type equations on domains in Cn. The arguments are modelled on the theory of viscosity solutions for real Hessian type equations developed by Trudinger. As consequence we solve the Dirichlet problem for the Hessian quotient and special Lagrangian equations. We also establish basic regularity results for the solutions. This part is a joint work with Slawomir Dinew (Jagiellonian University) and HoangSon Do (Hanoi Institute of Mathematics)
Spectre de matrices de permutation aléatoires by
Valentin Bahier(
Book
)
2 editions published in 2018 in English and held by 2 WorldCat member libraries worldwide
In this thesis, our goal is to study random matrices related to permutations. We tackle the study of their spectra in various ways, and at different scales. First, we extend the work of Wieand about the numbers of eigenvalues lying in some fixed arcs of the unit circle. We take advantage of the results of Ben Arous and Dang on the linear statistics of the spectrum of permutation matrices for a oneparameter family of deformations of the uniform law on the symmetric group, called Ewens' measures. One of the most innovative parts of our work is the generalization to nonfixed arcs. Indeed we get similar results when we let the lengths of the arcs decrease to zero slower than 1/n. Then, we look at the spectrum at microscopic scale. Inspired by the work of Najnudel and Nikeghbali about the convergence of empirical measures of rescaled eigenangles, we give a meaning to the convergence in terms of indicator functions of intervals. From the limiting point process, we show that the number of points in any interval is asymptotically normal as the length of the interval goes to infinity. Finally, we adapt some results of Chhaibi, Najnudel and Nikeghbali on the characteristic polynomial of the CUE at microscopic scale, and develop them in our framework. Analogously but with different techniques of proof, we get that the characteristic polynomials converge to entire functions, and this for a large family of laws including the Ewens' measures
2 editions published in 2018 in English and held by 2 WorldCat member libraries worldwide
In this thesis, our goal is to study random matrices related to permutations. We tackle the study of their spectra in various ways, and at different scales. First, we extend the work of Wieand about the numbers of eigenvalues lying in some fixed arcs of the unit circle. We take advantage of the results of Ben Arous and Dang on the linear statistics of the spectrum of permutation matrices for a oneparameter family of deformations of the uniform law on the symmetric group, called Ewens' measures. One of the most innovative parts of our work is the generalization to nonfixed arcs. Indeed we get similar results when we let the lengths of the arcs decrease to zero slower than 1/n. Then, we look at the spectrum at microscopic scale. Inspired by the work of Najnudel and Nikeghbali about the convergence of empirical measures of rescaled eigenangles, we give a meaning to the convergence in terms of indicator functions of intervals. From the limiting point process, we show that the number of points in any interval is asymptotically normal as the length of the interval goes to infinity. Finally, we adapt some results of Chhaibi, Najnudel and Nikeghbali on the characteristic polynomial of the CUE at microscopic scale, and develop them in our framework. Analogously but with different techniques of proof, we get that the characteristic polynomials converge to entire functions, and this for a large family of laws including the Ewens' measures
Modélisations des écoulements fluviaux adaptées aux observations spatiales et assimilations de données altimétriques by
Thibault Malou(
Book
)
2 editions published in 2022 in French and held by 2 WorldCat member libraries worldwide
This PhD work focuses on river modelling adapted to spatial altimetry, which allows the measurement of the height of water in rivers. In order to estimate the discharge using these data, the mathematical models need to be consistent with the spatiotemporal scale of the observations (hundreds of metres and tens of days) and an estimate of some quantities not measured by these altimetry satellites, notably the bottom elevation and a physical parametrization (friction coefficient).The difficulty in estimating the discharge from altimetric data comes in particular from the slope of the free surface, which is also not measured at a fine enough scale.A new methodology to determine local and algebraic discharge estimation laws (StageFallDischarge laws, SFD) from altimetry data from several satellites (e.g. Jason3, Sentinel3A and Sentinel3B) is proposed. The method is based on a hydrodynamic model calibrated by assimilation of altimetry data. These SFD laws are determined to reproduce the discharge estimated by the hydrodynamic model from noisy altimetry data and physically consistent simulated hydraulic quantities.These laws are successfully obtained on the complex hydrographic network of the Rio NegroRio Branco.The method should be applicable for operational estimation of discharge.Modelling adapted to spatial observations therefore requires choosing models that are coherent with the available data and with the observed spatiotemporal scales. As a result, the diffusive wave equation has the advantage of having the water height as state variable, which is directly measured in contrast to the discharge.In this work, a double spatiotemporal scale is introduced to take into account the scale of physics (small scale) and the scale of observations (large scale). The width variations are negligible on the scale of physics, which is not the case on the scale of observations. A diffusive wave equation adapted to the scale of satellite observations is derived. This new diffusive wave equation takes into account width variations through two additional terms compared to the classical equation.A numerical study shows that the observationscale equation estimates the slope of the free surface and thus the discharge with better accuracy than the classical equation. One of the additional terms in the observationscale equation is also highlighted by quantifying the importance of the terms of a dictionary based on sparse regression.In order to obtain an estimate of the bottom elevation and the friction coefficient (nonobserved by the altimetry satellites), altimetric data are assimilated into the hydrodynamic models by minimising the gap between the modelled height and the measured height. The quality of this data assimilation depends in particular on the estimation of the covariance of the background error, i.e. the error between the background value and the true value of the parameter, that preconditiones the Hessian of the cost function. However, this covariance is usually defined in an empirical manner.Thus, this work proposes a method for estimating the covariance of the background error and the correlation length from the equations governing the physics (here the diffusive wave equations) using the Green kernels.These new operators and the physically consistent correlation length coupled with a decreasing exponential kernel give better results than the empirical operators
2 editions published in 2022 in French and held by 2 WorldCat member libraries worldwide
This PhD work focuses on river modelling adapted to spatial altimetry, which allows the measurement of the height of water in rivers. In order to estimate the discharge using these data, the mathematical models need to be consistent with the spatiotemporal scale of the observations (hundreds of metres and tens of days) and an estimate of some quantities not measured by these altimetry satellites, notably the bottom elevation and a physical parametrization (friction coefficient).The difficulty in estimating the discharge from altimetric data comes in particular from the slope of the free surface, which is also not measured at a fine enough scale.A new methodology to determine local and algebraic discharge estimation laws (StageFallDischarge laws, SFD) from altimetry data from several satellites (e.g. Jason3, Sentinel3A and Sentinel3B) is proposed. The method is based on a hydrodynamic model calibrated by assimilation of altimetry data. These SFD laws are determined to reproduce the discharge estimated by the hydrodynamic model from noisy altimetry data and physically consistent simulated hydraulic quantities.These laws are successfully obtained on the complex hydrographic network of the Rio NegroRio Branco.The method should be applicable for operational estimation of discharge.Modelling adapted to spatial observations therefore requires choosing models that are coherent with the available data and with the observed spatiotemporal scales. As a result, the diffusive wave equation has the advantage of having the water height as state variable, which is directly measured in contrast to the discharge.In this work, a double spatiotemporal scale is introduced to take into account the scale of physics (small scale) and the scale of observations (large scale). The width variations are negligible on the scale of physics, which is not the case on the scale of observations. A diffusive wave equation adapted to the scale of satellite observations is derived. This new diffusive wave equation takes into account width variations through two additional terms compared to the classical equation.A numerical study shows that the observationscale equation estimates the slope of the free surface and thus the discharge with better accuracy than the classical equation. One of the additional terms in the observationscale equation is also highlighted by quantifying the importance of the terms of a dictionary based on sparse regression.In order to obtain an estimate of the bottom elevation and the friction coefficient (nonobserved by the altimetry satellites), altimetric data are assimilated into the hydrodynamic models by minimising the gap between the modelled height and the measured height. The quality of this data assimilation depends in particular on the estimation of the covariance of the background error, i.e. the error between the background value and the true value of the parameter, that preconditiones the Hessian of the cost function. However, this covariance is usually defined in an empirical manner.Thus, this work proposes a method for estimating the covariance of the background error and the correlation length from the equations governing the physics (here the diffusive wave equations) using the Green kernels.These new operators and the physically consistent correlation length coupled with a decreasing exponential kernel give better results than the empirical operators
Flots rugueux et inclusions différentielles perturbées by
Antoine Brault(
Book
)
2 editions published in 2018 in French and held by 2 WorldCat member libraries worldwide
This thesis consists of three independent chapters in the theme of rough path theory. Introduced in 1998 by Terry Lyons, this pathwise approach to stochastic differential equations (SDE) allows one to study SDE driven by processes that do not have the semimartingale property which is required to apply the framework of the Itô integral. This is for example the case of the fractional Brownian motion for a Hurst index different from onehalf. The first chapter deals with the links between rough path and regularity structure theories. The latter was recently introduced by Martin Hairer to solve a large class of stochastic partial differential equations. With the tools of this new theory, we show how to build the rough integral and the signature of an irregular path, which leads to solve a rough differential equation (RDE). In the second chapter, we focus on building RDE flows from their approximations at small scale, called almost flows. We show that under weak conditions on regularity of almost flows, although the uniqueness of the associated RDE solutions does not hold, we are able to select a measurable flow. Our general framework unifies the previous approaches by flow due to I. Bailleul, A. M. Davie, P. Friz and N. Victoir. In the last chapter, we study of a differential inclusion perturbed by a rough path, i.e. a RDE whose drift is a multivalued function. We prove, without convexity hypothesis and several conditions on the regularity of the drift, the existence of a solution
2 editions published in 2018 in French and held by 2 WorldCat member libraries worldwide
This thesis consists of three independent chapters in the theme of rough path theory. Introduced in 1998 by Terry Lyons, this pathwise approach to stochastic differential equations (SDE) allows one to study SDE driven by processes that do not have the semimartingale property which is required to apply the framework of the Itô integral. This is for example the case of the fractional Brownian motion for a Hurst index different from onehalf. The first chapter deals with the links between rough path and regularity structure theories. The latter was recently introduced by Martin Hairer to solve a large class of stochastic partial differential equations. With the tools of this new theory, we show how to build the rough integral and the signature of an irregular path, which leads to solve a rough differential equation (RDE). In the second chapter, we focus on building RDE flows from their approximations at small scale, called almost flows. We show that under weak conditions on regularity of almost flows, although the uniqueness of the associated RDE solutions does not hold, we are able to select a measurable flow. Our general framework unifies the previous approaches by flow due to I. Bailleul, A. M. Davie, P. Friz and N. Victoir. In the last chapter, we study of a differential inclusion perturbed by a rough path, i.e. a RDE whose drift is a multivalued function. We prove, without convexity hypothesis and several conditions on the regularity of the drift, the existence of a solution
Modèles de diffusion nonconventionnelle en écologie et biologie évolutive impliquant des environnements fragmentés by
Alexis Léculier(
Book
)
2 editions published in 2020 in English and held by 2 WorldCat member libraries worldwide
Dans cette thèse nous nous intéressons à une étude mathématique qualitative de problèmes issus d'écologie et de biologie évolutive. Nous étudions l'influence d'une dispersion nonlocale pour une espèce biologique vivant dans un environnement fragmenté. Plus précisément, dans une première partie, nous établissons un critère de survie pour une espèce biologique dont la dynamique est régie par une équation de FisherKPP fractionnaire dans un domaine fragmenté avec des conditions extérieures de Dirichlet. Ce critère repose sur le signe de la valeur propre principale de sousensembles inclus dans le domaine. De plus, nous démontrons un résultat d'existence et d'unicité de la solution stationnaire d'une équation de FisherKPP dans des domaines fragmentés généraux appartenant à la classe des solutions positives, bornées et nontriviales. Dans le cas particulier d'un domaine périodique et fragmenté, nous établissons l'existence d'un phénomène d'invasion à vitesse exponentielle. Enfin, dans une seconde partie, nous considérons un modèle traitant d'une espèce biologique organisée phénotypiquement vivant dans un environnement fragmenté. Cette espèce est sujette à des mutations à petits effets phénotypiques ainsi qu'à une dispersion spatiale à la fois locale et nonlocale. Nous démontrons l'émergence de traits phénotypiques dominants lorsque les mutations ont de petits effets
2 editions published in 2020 in English and held by 2 WorldCat member libraries worldwide
Dans cette thèse nous nous intéressons à une étude mathématique qualitative de problèmes issus d'écologie et de biologie évolutive. Nous étudions l'influence d'une dispersion nonlocale pour une espèce biologique vivant dans un environnement fragmenté. Plus précisément, dans une première partie, nous établissons un critère de survie pour une espèce biologique dont la dynamique est régie par une équation de FisherKPP fractionnaire dans un domaine fragmenté avec des conditions extérieures de Dirichlet. Ce critère repose sur le signe de la valeur propre principale de sousensembles inclus dans le domaine. De plus, nous démontrons un résultat d'existence et d'unicité de la solution stationnaire d'une équation de FisherKPP dans des domaines fragmentés généraux appartenant à la classe des solutions positives, bornées et nontriviales. Dans le cas particulier d'un domaine périodique et fragmenté, nous établissons l'existence d'un phénomène d'invasion à vitesse exponentielle. Enfin, dans une seconde partie, nous considérons un modèle traitant d'une espèce biologique organisée phénotypiquement vivant dans un environnement fragmenté. Cette espèce est sujette à des mutations à petits effets phénotypiques ainsi qu'à une dispersion spatiale à la fois locale et nonlocale. Nous démontrons l'émergence de traits phénotypiques dominants lorsque les mutations ont de petits effets
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Related Identities
 École doctorale Mathématiques, informatique et télécommunications (Toulouse) Other Degree grantor
 Université Toulouse 3 Paul Sabatier (1969....). Degree grantor
 Institut national des sciences appliquées (Toulouse / 1961....). Degree grantor
 Gamboa, Fabrice Opponent Thesis advisor
 Loubès, JeanMichel (19......; mathématicien) Opponent Thesis advisor
 Raymond, JeanPierre (mathématicien) Thesis advisor
 Klein, Thierry (1975....). Thesis advisor
 Ervedoza, Sylvain (1984....). Opponent Thesis advisor
 Miclo, Laurent (19......; mathématicien) Thesis advisor
 Coutin, Laure Thesis advisor
Alternative Names
Centre de recherche mathématique (Toulouse)
IMT
IMTCEREMATH
Institut de Mathématiques de Toulouse facility in Toulouse, France
Institut Mathématique de Toulouse
Institut national des sciences appliquées Toulouse Institut de mathématiques
Institutu de Matemátiques de Toulouse
Toulouse Mathematics Institute
UMR 5219
UMR 5640
Unité mixte de recherche 5219
Université des sciences sociales (Toulouse). Centre de recherche mathématique
Université des sciences sociales Toulouse Institut de mathématiques
Université des sciences sociales (Toulouse). Institut de mathématiques de Toulouse
Université Paul Sabatier Toulouse Institut de mathématiques
Université Toulouse 1 Capitole. Centre de recherche mathématique
Université Toulouse 1 Capitole. Institut de mathématiques de Toulouse
Université Toulouse III  Paul Sabatier Institut de Mathématiques de Toulouse
Université ToulouseJean Jaurès. Centre de recherche mathématique
Université ToulouseJean Jaurès. Institut de mathématiques de Toulouse
UPS (Toulouse). Centre de recherche mathématique
UPS (Toulouse). Institut de mathématiques de Toulouse
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