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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.

Master

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

Doctoral

Doctoral

Context of the tutorial: the IEEE CIS Summer School on Computational Intelligence and Applications (IEEE CIS SSoCIA 2022), associated with the 8th IEEE Latin American Conference on Computational Intelligence (IEEE LA-CCI 2022).; Doctoral; Random Neural Networks are a class of Neural Networks coming from Stochastic Processes and, in particular, from Queuing Models. They have some nice properties and they have reached good performances in several application areas. They are, in fact, queuing systems seen as Neural machines, and the two uses (probabilistic models for the performance evaluation of systems, or learning machines similar as the other more standard families of Neural Networks) refer to the same mathematical objects. They have the appealing that, as other special models that are unknown for most experts in Machine Learning, their testing in and/or adaptation to the many areas where standard Machine Learning techniques have obtained great successes is totally open.In the tutorial, we will introduce Random Neurons and the networks we can build with them, plus some details about the numerical techniques needed to learn with them. We will also underline the reasons that make them at least extremely interesting. We will also describe some of their successful applications, including our examples. We will focus on learning, but we will mention other uses of these models in performance evaluation, in the analysis of biological systems, and in optimization.

Doctoral

Master; These notes present a project in numerical optimization dealing with the implementation of an interior-point method for solving a self-dual conic optimization (SDCO) problem. The cone is the Cartesian product of cones of positive semidefinite matrices of various dimensions (imposing to matrices to be positive semidefinite) and of a positive orthant. Therefore, the solved problem encompasses semidefinite and linear optimization.The project was given in a course entitled 'Advanced Continuous Optimization II' at the University Paris-Saclay, in 2016-2020. The solver is designed step by step during a series of 5 sessions of 4 hours each. Each session corresponds to a chapter of these notes (or a part of it). The correctness of the SDCO solver is verified during each session on small academic problems, having diverse properties. During the last session, the developed piece of software is used to minimize a univariate polynomial on an interval and to solve a few small size rank relaxations of QCQO (quadratically constrained quadratic optimization) problems, modeling various instances of the OPF (optimal power flow) problem. The student has to master not ony the implementation of the interior-point solver, but is also asked to understand the underliying theory by solving exercises consisting in proving some properties of the implemented algorithms.The goal of the project is not to design an SDCO solver that would beat the best existing solver but to help the students to understand and demystify what there is inside such a piece of software. As a side outcome, this course also shows that a rather performent SDCO solver can be realized in a relatively short time.; Ces notes présentent un projet d'optimisation numérique dans lequel on implémente une méthode de points intérieurs pour résoudre un problème d'optimisation conique auto-duale (OCAD). Le cône est le produit cartésien de cônes de matrices semi-définies positives de dimensions variables et d'un orthant positif. Dès lors, le problème contient l'optimisation semi-défiinie et l'optimisation linéaire.Ce projet a été proposé dans un cours intitulé 'Advanced Continuous Optimization II' à l'université Paris-Saclay, en 2016-1020. Le solveur est conçu pas à pas durant une suite de 5 leçons de 4 heures chacune. Chaque session fait l'objet d'un chapitre de ces notes. La bonne marche du solveur OCAD est vérifiée à chaque session sur de petits problèmes académiques, ayant diverses propriétés. Durant la dernière session, le code développé est utilisé pour minimiser un polynôme d'une variable sur un intervalle et pour résoudre la relaxation de rang de la formulation QCQP (quadratically constrained quadratic programming) de quelques problèmes d'optimisation de flux d'énergie (OPF) dans de petits réseaux de distribution d'électricité. L'étudiant doit maîtriser non seulement l'implémentation du solveur de points-intérieurs, mais aussi la théorie sous-jacente de manière à pouvoir résoudre des exercices qui consistent à démontrer des propriétés des algorithmes implémentés.Le but de ce cours n'est pas de concevoir un solveur OCAD qui surpasserait le meilleur solveur existant, mais d'aider l'étudiant à comprendre et à démythifier ce que contient un tel solveur. Une conséquence secondaire de cet exercice est de montrer qu'un code OCAD assez performant peut être réalisé en très peu de temps.

Doctoral