Rigorous results on the threshold network model

More rigorous results on the NK model

A discrete time neural network model with spiking neurons. Rigorous results on the spontaneous dynamics.

We derive rigorous results describing the asymptotic dynamics of a discrete time model of spiking neurons introduced in Soula et al. (Neural Comput. 18, 1, 2006). Using symbolic dynamic techniques we show how the dynamics of membrane potential has a one to one correspondence with sequences of spikes patterns ("raster plots"). Moreover, though the dynamics is generically periodic, it has a weak ...

Some rigorous results for the Hopfield Model

For the Hopfield model with the Hebb connection matrix we investigate the case of p memorized patterns that are distorted copies of the same standard. In other words, we try to simulate that learning always takes place by means of repeating presentations of one and the same standard, and the presentations are accompanied by distortions of the standard. We obtain some rigorous results relating t...

Rigorous Results for the Nk Model

Motivated by the problem of the evolution of DNA sequences, Kauffman and Levin introduced a model in which fitnesses were assigned to strings of 0’s and 1’s of length N based on the values observed in a sliding window of length K + 1. When K ≥ 1, the landscape is quite complicated with many local maxima. Its properties have been extensively investigated by simulation but until our work and the ...

Some Rigorous Results on the Sherrington-Kirkpatrick Spin Glass Model

We prove that in the high temperature regime (T/J > 1) the deviation of the total free energy of the Sherrington-Kirkpatrick (S-K) spin glass model from the easily computed logAv(ZN({βJ})) converges in distribution, as ΛΓ-KX), to a (shifted) Gaussian variable. Some weak results about the low temperature regime are also obtained.