-multifunctions and their properties.
L'article traite des liens entre la syntaxe et la sémantique formelle (de nature logique) des jugements perceptifs et leur contenu proprement perceptif (de nature géométrique). Dans les situations les plus élémentaires le contenu perceptif se ramène à des remplissements de domaines spatiaux (l'extension des objets) par des qualités sensibles (couleurs, textures, etc.). Ces remplissements sont descriptibles par des sections de fibrations appropriées, qui sont des cas particuliers de faisceaux. Il...
Nous distinguons deux étapes dans l'activité de compréhension d'un problème additif : la compréhension de l'énoncé et la réduction à un problème prototypique. Après avoir mis en évidence, à partir de résultats de recherches cognitives et didactiques, certains processus cognitifs élémentaires dans l'activité de compréhension d'énoncés additifs, nous proposons une modélisation cognitive de la compréhension des problèmes additifs basée sur la notion d'opérateur qui permet de prendre en compte et d'articuler...
The geometry of complex networks is closely related with their structure and function. In this paper, we investigate the Gromov-hyperbolicity of the Newman-Watts model of small-world networks. It is known that asymptotic Erdős-Rényi random graphs are not hyperbolic. We show that the Newman-Watts ones built on top of them by adding lattice-induced clustering are not hyperbolic as the network size goes to infinity. Numerical simulations are provided to illustrate the effects of various parameters...
Large games of kind considered in the present paper (LSF-games) directly generalize the usual concept of n-matrix games; the notion is related to games with a continuum of players and anonymous games with finitely many types of players, finitely many available actions and distribution dependent payoffs; however, there is no need to introduce a distribution on the set of types. Relevant features of equilibrium distributions are studied by means of fixed point, nonlinear complementarity and constrained...
The games of type considered in the present paper (LSE-games) extend the concept of LSF-games studied by Wieczorek in [2004], both types of games being related to games with a continuum of players. LSE-games can be seen as anonymous games with finitely many types of players, their action sets included in Euclidean spaces and payoffs depending on a player's own action and finitely many integral characteristics of distributions of the players' (of all types) actions. We prove the existence of equilibria...
Stochastic token theory is a new branch of mathematical psychology. In this paper we investigate algebraic properties of token systems defined on finite lattices.