Distances over hyper graphs
A new class of hypergraphs is defined, fractal hypertrees, which make it possible to understand the concept of complexity of a system and to define non-trivial metrics.
On the B-differential of the componentwise minimum of two affine vector functions
This paper focuses on the description and computation of the B-differential of the componentwise minimum of two affine vector functions. This issue arises in the reformulation of the linear complementarity problem with the Min C-function. The question has many equivalent formulations and we identify some of them in linear algebra, convex analysis a...
On the B-differential of the componentwise minimum of two affine vector functions - The full report
This paper focuses on the description and computation of the B-differential of the componentwise minimum of two affine vector functions. This issue arises in the reformulation of the linear complementarity problem with the Min C-function. The question has many equivalent formulations and we identify some of them in linear algebra, convex analysis a...
Modèles et métaphores dans les projets système d’information
En France, J.-L. Le Moigne a apporté une nouvelle perspective à l’ingénierie des systèmes d’information (SI), en promouvant l’analyse et la modélisation des systèmes. L’utilisation de modèles a apporté une contribution majeure à la conception des SI. Les méthodologies systémiques se sont multipliées à partir des années 1980, avant de céder la place...
Agir en écologue de l'action
Dans le sillage des Objectifs de Développement Durable (ODD) de l'ONU, et des rapports du Groupe d'experts Intergouvernemental sur l'Evolution du Climat (GIEC), les incitations à répondre à l'urgence de la lutte contre le réchauffement climatique et à la préservation de la biodiversité, se font de plus en plus pressantes. A partir de la pensée comp...
Complexity Methods in Physics-Guided Machine Learning
Complexity is easy to recognize but difficult to define: there are a host of measures of complexity, each relevant for a particular application.In Surface engineering, self-organization drives the formation of patterns on matter by femtosecond laser irradiation, which have important biomedical applications. Pattern formation details are not fully u...
Kernels and quasi-kernels in digraphs.
An important concept in directed graph theory is that of a kernel. This notion was introduced by Morgenstern and von Neumann for studying winning strategies in combinatorial games and now has numerous applications in various fields such as graph theory, game theory, economics, and logic.In a directed graph, D=(V,A), a kernel is a subset N of vertic...
On the algorithmic complexity of two player zero-sum games of finite duration with imperfect information
In this thesis we study the complexity of computing optimal strategies in two player zero-sum games with imperfect information. In games with Imperfect information players only have partial knowledge about their position in the game. This makes the task of computing optimal strategies hard especially when players forget previously gained informatio...
Reachability problems for general rotor walks in graphs
In this thesis, we focus on the algorithmic properties of a cellular automaton known as rotor walks. This model has been introduced in two distinct ways. Firstly, as a fundamental operation within another cellular automaton known as Sandpiles, which models the collapse of a sand pile when it becomes too high. Secondly, due to its resemblance to wel...
Algorithms for Promise Coloring Problems on Tournaments and Graphs
The first part of this thesis is on the subject of coloring tournaments, from analgorithmic, complexity and structural perspective. A k-coloring of a directed graph,and in particular a tournament, is a partition of its vertices into k acyclic sets. Thechromatic number of a directed graph or a tournament is then the minimum k suchthat it is k-colora...
