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- 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)

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

Simple random walks on a partially directed version of Z are considered. More precisely, vertical edges between neighbouring vertices of Z 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 decays… (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)

We study a model of a polling system, that is, a collection of d queues with a single server that switches from queue to queue. The service time distribution and arrival rates change randomly every time a queue is emptied. This model is mapped to a mathematically equivalent model of a random walk with random choice of transition probabilities, a model which… (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)

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)

- 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)

- 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)

- Dimitri Petritis
- NICSO
- 2007

Techniques for data-mining, latent semantic analysis, contextual search of databases, etc. have long ago been developed by computer scientists working on information retrieval (IR). Experimental scientists, from all disciplines, having to analyse large collections of raw experimental data (astronomical, physical, biological, etc.) have developed powerful… (More)