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Simple random walks on various types of partially horizontally oriented regular lattices are considered. The horizontal orientations of the lattices can be of various types (deterministic or random) and depending on the nature of the orientation the asymptotic behaviour of the random walk is shown to be recurrent or transient. In particular, for randomly(More)
Random walks on general graphs play an important role in the understanding of the general theory of stochastic processes. Beyond their fundamental interest in probability theory, they arise also as simple models of physical systems. A brief survey of the physical relevance of the notion of random walk on both undirected and directed graphs is given followed(More)
Microarray technology is a widely used approach to gene expression analysis. Many tools for microarray management and data analysis have been developed, and recently new methods have been proposed for deciphering biological pathways by integrating microarray data with other data sources. However, to improve microarray analysis and provide meaningful gene(More)
After a rapid introduction to the physical motivations and a succinct presentation of heuristic results, this survey summarises the main mathematical results known on the Edwards-Anderson and the Sherrington-Kirkpatrick models of spin glasses. Although not complete proofs but rather sketches of the relevant steps and important ideas are given, only results(More)
Neural networks are systems of interconnected processors mimicking some of the brain functions. After a rapid overview of neural computing, the thermodynamic formalism of the learning procedure is introduced. Besides its use in introducing eecient stochas-tic learning algorithms, it gives an insight in terms of information theory. Main emphasis is given in(More)
We consider a directed random walk making either 0 or +1 moves and a Brownian bridge, independent of the walk, conditionned to arrive at point b on time T. The Hamiltonian is deened as the sum of the square of increments of the bridge between the moments of jump of the random walk and interpreted as an energy function over the bridge connguration; the(More)
Simple random walks on a partially directed version of Z 2 are considered. More precisely, vertical edges between neighbouring vertices of Z 2 can be traversed in both directions (they are undirected) while horizontal edges are one-way. The horizontal orientation is prescribed by a random perturbation of a periodic function, the perturbation probability(More)
We report on a work in progress aiming at automatically analysing electrocardiograms with the help of wavelet bases. The objective we have fixed was to introduce a parsimonious and computationally efficient method --- that can be ultimately incorporated on standard ECG recording devices --- to automatically localise points of interest and decide whether(More)