Abstract closed patterns beyond lattices

National audienceLa recherche en fouille de motifs a porté ces dernières années en particulier sur les opérateurs de fermeture sur des langages partiellement ordonnés, isomorphes à un sous ensemble d'un ensemble d'attributs, ne formant pas nécessairement un treillis. Un résultat de M. Boley et co-auteurs définit une propriété qui garantit qu'un opérateur de fermeture existe quel que soit l'ensemble d'objets dans lequel on cherche le support des motifs. Nous relions ce travail au cadre classique de l'analyse de Galois et des concepts formels, détaillons la structure des ensemble de fermés, ainsi que les implications associées, et montrons que la simplification par abstraction extensionnelle reste applicable dans ce cas

Statistical Complexity and Nontrivial Collective Behavior in Electroencephalografic Signals

We calculate a measure of statistical complexity from the global dynamics of electroencephalographic (EEG) signals from healthy subjects and epileptic patients, and are able to stablish a criterion to characterize the collective behavior in both groups of individuals. It is found that the collective dynamics of EEG signals possess relative higher values of complexity for healthy subjects in comparison to that for epileptic patients. To interpret these results, we propose a model of a network of coupled chaotic maps where we calculate the complexity as a function of a parameter and relate this measure with the emergence of nontrivial collective behavior in the system. Our results show that the presence of nontrivial collective behavior is associated to high values of complexity; thus suggesting that similar dynamical collective process may take place in the human brain. Our findings also suggest that epilepsy is a degenerative illness related to the loss of complexity in the brain.Comment: 13 pages, 3 figure

Operational and Goal-Independent Denotational Semantics for Prolog with Cut

In this paper we propose an operational and a denotational semantics for Prolog. We deal with the control rules of Prolog and the cut operator. Our denotational semantics provides a goal--independent semantics. This means that the behaviour of a goal in a program is defined as the evaluation of the goal in the denotation (semantics) of the program. We show how our denotational semantics can be specialised into a computed answer semantics and into a call pattern semantics. Our work provides a basis for a precise abstract interpretation of Prolog programs

Bose - Einstein Condensate Superfluid-Mott Insulator Transition in an Optical Lattice

We present in this paper an analytical model for a cold bosonic gas on an optical lattice (with densities of the order of 1 particle per site) targeting the critical regime of the Bose - Einstein Condensate superfluid - Mott insulator transition. We focus on the computation of the one - body density matrix and its Fourier transform, the momentum distribution which is directly obtainable from `time of flight'' measurements. The expected number of particles with zero momentum may be identified with the condensate population, if it is close to the total number of particles. Our main result is an analytic expression for this observable, interpolating between the known results valid for the two regimes separately: the standard Bogoliubov approximation valid in the superfluid regime and the strong coupling perturbation theory valid in the Mott regime.Comment: 40 pages, 6 figure

Random Walks on Stochastic Temporal Networks

In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly understood. In this chapter, we develop a mathematical framework for random walks on temporal networks using an approach that provides a compromise between abstract but unrealistic models and data-driven but non-mathematical approaches. To do this, we introduce a stochastic model for temporal networks in which we summarize the temporal and structural organization of a system using a matrix of waiting-time distributions. We show that random walks on stochastic temporal networks can be described exactly by an integro-differential master equation and derive an analytical expression for its asymptotic steady state. We also discuss how our work might be useful to help build centrality measures for temporal networks.Comment: Chapter in Temporal Networks (Petter Holme and Jari Saramaki editors). Springer. Berlin, Heidelberg 2013. The book chapter contains minor corrections and modifications. This chapter is based on arXiv:1112.3324, which contains additional calculations and numerical simulation

Representing Isabelle in LF

LF has been designed and successfully used as a meta-logical framework to represent and reason about object logics. Here we design a representation of the Isabelle logical framework in LF using the recently introduced module system for LF. The major novelty of our approach is that we can naturally represent the advanced Isabelle features of type classes and locales. Our representation of type classes relies on a feature so far lacking in the LF module system: morphism variables and abstraction over them. While conservative over the present system in terms of expressivity, this feature is needed for a representation of type classes that preserves the modular structure. Therefore, we also design the necessary extension of the LF module system.Comment: In Proceedings LFMTP 2010, arXiv:1009.218