Didier Aussel
Summary:
The aim of this course is fourfold, namely :
1. to introduce multi-leader-follower games
2. to explore the recent theoretical advances
3. to present some of the numerous applications of these optimization model
4. to present, in the case of Single-Leader-Follower games (SLMFG), the very recently tested SOS1-numerical scheme to determine, numerically, some solutions of these difficult problems.
Patrick Tchepmo Djomegni
Summary: De ce cours, nous espérons que les étudiants auront des outils minimums pour modéliser la propagation des maladies épidémiques, et étudier des stratégies de contrôle. Les étudiants acquerront de connaissances nouvelles qui les prépareront pour leurs travaux thèse (mémoire). L’université en bénéficiera aussi à travers le renforcement des capacités de ses futurs enseignants.
Etienne Pardoux
Summary: On présente les mesures aléatoires de Poisson, et comment celles-ci permettent de construire les processus de Lévy, mais aussi les équations différentielles stochastiques à sauts, ainsi que les processus de branchement à espace d’état continu
Didier Jean CAUCAL
Summary: In this automaticity course we will teach the recognition of infinite words by automata. We will study the complexity of these infinite words and the non-algebraicity of the irrational numbers they represent. We will discuss its extension via battery-powered automata.
Ibrahima Drame
Summary: Galton Watson process :
- without immigration
- with immigration
- multitype (with a finite number of types)
Continuous time branching process :
- with exponential lifetime distributions, i.e markovian branching process
Patrick Tchepmo Djomegni
Summary: In this course, students will be introduced to the mathematical modeling of infectious diseases. Basic knowledge on certain diseases (tuberculosis, HIV/AIDS, hepatitis, malaria…) will be provided. Only deterministic mathematical models will be studied. Since the models are expressed in the form of ordinary differential equations, most of them cannot be solved explicitly. The qualitative characteristics of the solutions will be studied.
Coordinator: Ramesh Gautam, Mathematical Biology Research Centre (MBRC), Nepal
Gourav Arora (India), Youcef Mammeri (France)
Frédérique Oggier
Summary: In this course, we taught show how lattices and codes, both independently and jointly, are used in the context of communication systems. The course was structured as follows :
Ibrahima Drame
Summary: In this course, we will study Galton- Watson processes, which are the simplest prototype of branching processes and are characterized by the fact that time is discrete and represents successive generations. On the other hand, we will consider branching processes in continuous time, that is, populations that reproduce and die at random times, continuously over time.