Two-player turn-based zero-sum games on (finite or infinite) graphs are a central framework in theoretical computer science — notably as a tool for controller synthesis, but also due to their connection with logic and automata theory. A crucial challenge in the field is to understand how complex strategies need to be to play optimally, given a type of game and a winning objective. I will give a tour of recent advances aiming to characterize games where finite-memory strategies suffice (i.e., using a limited amount of information about the past). We mostly focus on so-called chromatic memory, which is limited to using colors — the basic building blocks of objectives — seen along a play to update itself. Chromatic memory has the advantage of being usable in different game graphs, and the corresponding class of strategies turns out to be of great interest to both the practical and the theoretical sides.[-]

Quel rapport entre la forme d'un chou-fleur des côtes de Bretagne, des vaisseaux sanguins et les structures fractales ?
Quel rapport entre une maladie génétique et un fichier de musique mp3 ?
Quel rapport entre des dessins faits par Léonard de Vinci et les lois mathématiques gouvernant la forme des plantes ou la reproduction des lapins ?
Quel rapport entre la forme de la terre, le GPS de ma voiture et un vieux puits d'Egypte ?
Pourquoi les météorologues sont capables de prédire une hausse du niveau des océans dans 100 ans mais incapables de prévoir s'il va pleuvoir dans 15 jours ?
Quel rapport entre le cerveau humain et le cerveau d'un ordinateur ?
Nous répondrons à toutes ces questions via des mathématiques simples et élégantes, accessibles à tous.[-]

The introduction of wavelets in the mid 80's has significantly reshaped some areas of the scientific landscape by establishing bridges between previously disconnected domains, and eventually leading to a new paradigm. This generally accepted-yet loose-claim can be given a more precise form by exploiting bibliometric databases such as the ISI Web of Science. Preliminary results in this direction will be reported here, based on multiple entries where authors, references, keywords and disciplines are used as nodes of a network in which the links correspond to their co-appearance in the same paper. While the evolution in time of such an « heterogeneous net » gives a quantified perspective on the birth and growth of wavelets as a well-identified scientific field of its own, it also raises many interpretation issues (related, e.g., to automation vs. expertise) whose implications go beyond this peculiar case study.

Keywords : wavelets - history - bibliometry - network, paradigm[-]