This thesis explores data assimilation techniques for ocean models, and particularly for stochastic models. The stochastic framework of interest is called location uncertainty (LU) and aims at incorporating the stochasticity in geophysical systems through a velocity decomposition into a large-scale smooth in time component, and a highly oscillating...
We introduce for any Poisson structure π on a manifold M the notion of bi-realisation and illustrate it by examples. We define Hamiltonian Poisson integrators as Poisson integrators for which discrete trajectory follows the flow of a time-dependent Hamiltonian. Next, a construction of a Hamiltonian Poisson integrator for generics Poisson structure ...
Dans cette thèse, on étudie des marches aléatoires induites par des actions de groupes probabilisés sur des espaces de courbure négative ou nulle. On décrit en particulier le cas d'actions sur des espaces CAT(0) admettant des éléments contractants, c'est-à-dire dont les propriétés imitent ceux des isométries loxodromiques dans les espaces Gromov-hy...
The ability to make adequate decisions under time constraints is crucial in daily life. To this purpose, humans establish strategies to optimize their speed-accuracy trade-off, as theorized by models of decision-making (Ratcliff, 1978; Bogacz et al., 2006). Perceptual anticipation can be beneficial to that aim, as correct anticipation results in a ...
This thesis deals with the aeroelastic modeling of an aircraft, and its active control. By using the aircraft's control surfaces appropriately, it is possible to reduce loads due to wind gusts and turbulence. This reduces the mass of the structures responsible for maintaining the integrity of the aircraft, and thus improves the performance of the o...
In this thesis, we describe and analyze an interplay between dynamical systems, sparse structures, convex analysis, and functional analysis. We approach global attractors through an infinite dimensional linear programming problem (LP), investigate the Koopman and Perron-Frobenius semigroups of linear operators associated with a dynamical system, an...
The aim of the poster is to showcase the interplay between group theory, algebraic topology and combinatorics on words. A result that allows to display this is the return theorem by Berté et al. in 2015. The poster will contain an introduction to fundamental groups of graphs, dendric words as well as a new result concerning return groups of eventua...
Since 2015, dendric shifts (a generalisation of Sturmian words) have been widely studied. One of the results concerning these shift spaces is the return theorem. It describes the groups generated by the return words of a dendric shift. The proof uses the fundamental group of the Rauzy graph of the shift space. Later, eventually dendric shifts were ...
This thesis aims to make a contribution to the study of a somehow large class of partially hyperbolic diffeomorphisms denoted as ‘discretized Anosov flows’. This class is shown to comprise whole connected components of partially hyperbolic diffeomorphisms with one dimensional center in any dimension. Several general properties of discretized Anosov...
Dans cette thèse, nous étudions sous l'angle de la modélisation mathématique l'hématopoïèse, le développement des hémopathies malignes que sont les néoplasmes myéloprolifératifs (NMP) puis leur traitement à l'Interféron alpha (IFN⍺).L'hématopoïèse est le processus de création de nos cellules sanguines à partir de cellules souches situées dans la mo...
