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École thématique; Signal is an "alternative" synchronous language, with the following features: it addresses open systems and puts clocks ans synchronization at the forefront. To this end, synchronization is synthesized, not verified. We will emphasize the clock and causality calculus and show its use in modular compilation. Then, we'll show how we can extend the clock calculus and improve the power of the language, and extend the causality calculus toward supporting constraint solving (instead of evaluating signal expressions). The latter extension may be suited to physical system modeling.; Conçu et développé à la même période que les autres langages synchrones, Signal, avec le recul, apparaît comme étant à part dans le paysage. Il est dédié aux systèmes dits "ouverts" et se focalise sur la synchronisation et les horloges. La synchronisation d'un programme est synthétisée et non pas vérifiée. Nous expliquerons les principes de cette approche, et, en premier, le calcul d'horloges et de causalité, qui permet de dégager une notion d'interface utile pour la compilation modulaire. Notre objectif, au-delà du langage, est de montrer l'intérêt de ces principes. Nous expliquerons comment exploiter les avancées récentes des techniques de preuve pour augmenter la puissance du calcul d'horloges. Et, surtout, nous expliquerons comment une extension du calcul de causalité permet de traiter des programmes incluant des contraintes numériques, extension utile lorsqu'on s'intéresse à la modélisation de systèmes physiques.

Lecture notes for a course given at the Algebraic Coding Theory (ACT) summer school 2022; Doctoral; These lecture notes have been written for a course at the Algebraic Coding Theory (ACT) summer school 2022 that took place in the university of Zurich. The objective of the course propose an in-depth presentation of the proof of one of the most striking results of coding theory: Tsfasman Vl\u{a}du\c{t} Zink Theorem, which asserts that for some prime power $q$, there exist sequences of codes over $\mathbb{F}_q$ whose asymptotic parameters beat random codes.

Doctoral; Classifying lattice walks in restricted lattices is an important problem in enumerative combinatorics. Recently, computer algebra methods have been used to explore and solve a number of difficult questions related to lattice walks. In this course, we will give an overview of recent results on structural properties and explicit formulas for generating functions of walks in the quarter plane, with an emphasis on the algorithmic methodology.

Doctoral; In this note we introduce and discuss a few concentration tools for the study of concentration inequalities on the real line. After recalling versions of the Chernoff method, we move to concentration inequalities for predictable processes. We especially focus on bounds that enable to handle the sum of real-valued random variables, where the number of summands is itself a random stopping time, and target fully explicit and empirical bounds. We then discuss some important other tools, such as the Laplace method and the transportation lemma.

Doctoral; In this tutorial, we focus on data arriving sequentially by block in a stream. A semiparametric regression model involving a common EDR (Effective Dimension Reduction) direction β is assumed in each block. Our goal is to estimate this direction at each arrival of a new block. A simple direct approach consists of pooling all the observed blocks and estimating the EDR direction by the SIR (Sliced Inverse Regression) method. But in practice, some disadvantages become apparent such as the storage of the blocks and the running time for high dimensional data. To overcome these drawbacks, we propose an adaptive SIR estimator of β. The proposed approach is faster both in terms of computational complexity and running time, and provides data storage benefits. A graphical tool is provided in order to detect changes in the underlying model such as a drift in the EDR direction or aberrant blocks in the data stream. This is a joint work with Marie Chavent, Vanessa Kuentz-Simonet, Benoit Liquet,Thi Mong Ngoc Nguyen and Jérôme Saracco.

National audience; Doctoral

Doctoral

Doctoral

Master; These are the lecture notes of a course on logic and commonsense reasoning given to master students in philosophy of the University of Rennes 1. N.B.: Some parts of these lectures notes are sometimes largely based on or copied verbatim from publications of other authors. When this is the case, these parts are mentioned at the end of each chapter in the section “Further reading”.

Doctoral