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Biomedical subjects

D Bollé

Publications and source records attributed to D Bollé.

At least 19 recordsLinked to original sources
PubMed2006

Metastable configurations of small-world networks.

We calculate the number of metastable configurations of Ising small-world networks that are constructed upon superimposing sparse Poisson random graphs onto a one-dimensional chain. Our solution is based on replicated transfer-matrix techniques. We examine the denegeracy of the ground state and find a jump in the entropy of metastable configurations exactly at the crossover between the small-world and the Poisson random graph structures. We also examine the difference in entropy between metastable and all possible configurations, for both ferromagnetic and bond-disordered long-range couplings.

Journal Article↗
PubMed2003

Time evolution of the extremely diluted Blume-Emery-Griffiths neural network.

A study of the time evolution and a stability analysis of the phases in the extremely diluted Blume-Emery-Griffiths neural network model are shown to yield new phase diagrams in which fluctuation retrieval may drive pattern retrieval. It is shown that saddle-point solutions associated with fluctuation overlaps slow down the flow of the network states towards the retrieval fixed points. A comparison of the performance with other three-state networks is also presented.

Biophysical Phenomena↗
PubMed2003

Optimal capacity of the Blume-Emery-Griffiths perceptron.

A Blume-Emery-Griffiths perceptron model is introduced and its optimal capacity is calculated within the replica-symmetric Gardner approach, as a function of the pattern activity and the embedding stability parameter. The stability of the replica-symmetric approximation is studied via the analog of the de Almeida-Thouless line. A comparison is made with other three-state perceptrons.

Journal Article↗
PubMed2002

Gap structure of the local field in symmetric Q Ising neural networks.

The time evolution of the local field in symmetric Q-Ising neural networks is studied for arbitrary Q. In particular, the structure of the noise and the appearance of gaps in the probability distribution are discussed. Results are presented for several values of Q and compared with numerical simulations.

Journal Article↗
PubMed2001

Optimal colored perceptrons.

Ashkin-Teller type perceptron models are introduced. Their maximal capacity per number of couplings is calculated within a first-step replica-symmetry-breaking Gardner approach. The results are compared with extensive numerical simulations using several algorithms.

Algorithms↗
PubMed1996

Optimal nonlinear training in the multi-class proximity problem.

Using a signal-to-noise analysis, the effects of nonlinear modulation of the Hebbian learning rule in the multi-class proximity problem are investigated. Both random classification and classification provided by a Gaussian and a binary teacher are treated. Analytic expressions are derived for the learning and generalization rates around an old and a new prototype. For the proximity problem with binary inputs but Q'-state outputs, it is shown that the optimal modulation is a combination of a hyperbolic tangent and a linear function. As an illustration, numerical results are presented for the two-class and the Q' = 3 multi-class problem.

Learning↗