J Huyghebaert

Mean-field theory for the Q-state Potts-glass neural network with biased patterns

A systematic study of the Q-state Potts model of neural networks, extended to include biased patterns, is made for extensive loading alpha . Mean-field equations are written down within the replica symmetric approximation, for general Q and arbitrary temperature T. For the Q=3 model and two classes of representative bias parameters, the storage capacity and retrieval quality at zero temperature are discussed as functions of the bias, taking into account the Mattis retrieval state and the lowest symmetric states. The T- alpha diagram is obtained and the stability properties of the retrieval state are analysed at finite temperatures. A comparison is made with the biased Hopfield model.

On the phase diagram of the Q-state Potts-glass neural network

The Q-state Potts model of neural networks, extended to include biased patterns, is studied for extensive loading α. Mean-field equations are written down for general Q and arbitrary temperature T. Within the replica symmetric approximation, the complete T-α phase diagram is discussed, especially for Q = 3. A study of the bifurcation diagrams for the overlap and the free clarifies the results obtained.

On the multi-neuron interaction model without truncating the interaction

A replica-symmetric mean-field theory approach is presented to the multi-neuron interaction model introduced by de Almeida and Iglesias (1990 Phys. Lett. 146A 239). Fixed-point equations are derived for the relevant order parameters of the model, extended to include biased patterns, without truncating the interaction. The capacity-bias and the temperature-capacity phase diagrams are discussed. Compared with the truncated version of the model, it is found that the capacity at zero temperature is infinite and that the retrieval states satisfy the de Almeida-Thouless stability condition.

Tunneling through Time-Modulated Barriers

Results are reported of extensive numerical simulations of the tunneling of a particle through a time-modulated barrier. It is demonstrated that the process of absorption and emission of modulation quanta depends sensitively on the modulation frequency and the modulation strength. The transmission coefficient develops a plateau at a crossover frequency which, for small to moderate modulation strength, corresponds to the frequency at which the energy of the first-order sideband becomes equal to the first resonance energy above the top of the barrier.