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- Dimitri PETRITIS
- 2001

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)

- M Campanino, D Petritis
- 2002

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)

In this paper we study a regular rooted coloured tree with random labels assigned to its edges, where the distribution of the label assigned to an edge depends on the colours of its endpoints. We obtain some new results relevant to this model and also show how our model generalizes many other probabilistic models, including random walk in random environment… (More)

- Antony Le Béchec, Pierre-Joachim Zindy, +5 authors Nathalie Théret
- In Silico Biology
- 2008

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)

- Dimitri Petritis
- 1996

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)

- Dimitri Petritis
- 1995

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)

- Dimitri Petritis
- 2001

We study random walks in a random environment on a regular, rooted, coloured tree. The asymptotic behaviour of the walks is classified for ergodicity/transience in terms of the geometric properties of the matrix describing the random environment. A related problem, with only one type of vertices and quite stringent conditions on the transition probabilities… (More)

- Servet Mart Nez, Dimitri Petritis
- 1995

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)

- Massimo Campanino, Dimitri Petritis
- J. Applied Probability
- 2014

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)

- Ahmad Khoureich Ka, Dimitri Petritis
- ISABEL '11
- 2011

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)