Enthusiasm for Machine Learning is spreading to nearly all fields such as transportation, energy, medicine, banking or insurance as the ubiquity of sensors through IoT makes more and more data at disposal with an ever finer granularity. The abundance of new applications for monitoring of complex infrastructures (e.g. aircrafts, energy networks) tog...
The labour market is closely linked to the rental markets for professionals and for individuals. The purpose of this thesis is to study the interactions of these markets.In a first step, we develop and study a mean field game model that links the labour market with the rental market for professionals. In a specific framework where firms' production...
This thesis is devoted to the design of locally conservative and structure preserving schemes for Wasserstein gradient flows, i.e. steepest descent curves in the Wasserstein space. The time discretization is based on variational approaches that mimic at the discrete in time level the behavior of steepest descent curves. These discretizations involv...
Les champignons phytopathogènes sont à l'origine d'importantes pertes économiques. Parmi ces champignons, Botrytis cinerea est particulièrement destructeur. Afin de protéger les plantes, des molécules anti-fongiques sont développées. Elles sont classées selon leur Mode d'Action dont la compréhension permet d'élucider la façon dont les composés acti...
Many methods for statistical inference and generative modeling rely on a probability divergence to effectively compare two probability distributions. The Wasserstein distance, which emerges from optimal transport, has been an interesting choice, but suffers from computational and statistical limitations on large-scale settings. Several alternatives...
Les avancées technologiques émergentes de l’Internet des objets (IoT) ont conduit à une interférence significative des stratégies manufacturières. À cette fin, des concepts tels que "Industrie 4.0", "fabrication intelligente" et "usine numérique" ont vu le jour. Dans ces contextes, la maintenance prédictive joue de plus en plus un rôle crucial dans...
This thesis deals with the optimal transport problem, in particular with regularity properties shared by optimal transport maps. The first part of this manuscript provides a new proof of the Caffarelli contraction theorem, stating that the optimal transport map from the gaussian measure to a measure with a uniformly log-concave density with respect...
The optimal transportation problem originally introduced by G. Monge in 1781 and rediscovered by L. Kantorovich in 1942 consists in transformation of one mass distribution to another with the minimal amount of work. In this thesis, we consider some variational problems involving optimal transport. We are mainly motivated by the Wasserstein barycent...
An important goal of cognitive neurosciences is to understand the functional organization of the brain. It heavily relies on Functional Magnetic Resonance Imaging (fMRI), a powerful tool to investigate the link between brain function and anatomical structures at a high spatial-resolution. Functional inter-individual variability is a major obstacle ...
Topological data analysis (or TDA for short) consists in a set of methods aiming to extract topological and geometric information from complex nonlinear datasets. This field is here tackled from two different perspectives.First, we consider techniques from geometric inference, whose goal is to reconstruct geometric invariants of a manifold thanks t...
