arXiv subjects

Nestor Parga

Publications and source records attributed to Nestor Parga.

4 recordsLinked to original sources

arXiv2007

Theory of input spike auto- and cross-correlations and their effect on the response of spiking neurons

Spike correlations between neurons are ubiquitous in the cortex, but their role is at present not understood. Here we describe the firing response of a leaky integrate-and-fire neuron (LIF) when it receives a temporarily correlated input generated by presynaptic correlated neuronal populations. Input correlations are characterized in terms of the firing rates, Fano factors, correlation coefficients and correlation timescale of the neurons driving the target neuron. We show that the sum of the presynaptic spike trains cannot be well described by a Poisson process. Solutions of the output firing rate are found in the limit of short and long correlation time scales.

q-bio.NC↗

arXiv2007

Auto and crosscorrelograms for the spike response of LIF neurons with slow synapses

An analytical description of the response properties of simple but realistic neuron models in the presence of noise is still lacking. We determine completely up to the second order the firing statistics of a single and a pair of leaky integrate-and-fire neurons (LIFs) receiving some common slowly filtered white noise. In particular, the auto- and cross-correlation functions of the output spike trains of pairs of cells are obtained from an improvement of the adiabatic approximation introduced in \cite{Mor+04}. These two functions define the firing variability and firing synchronization between neurons, and are of much importance for understanding neuron communication.

q-bio.NC↗

arXiv1999

The mutual information of a stochastic binary channel: validity of the Replica Symmetry Ansatz

We calculate the mutual information (MI) of a two-layered neural network with noiseless, continuous inputs and binary, stochastic outputs under several assumptions on the synaptic efficiencies. The interesting regime corresponds to the limit where the number of both input and output units is large but their ratio is kept fixed at a value $α$. We first present a solution for the MI using the replica technique with a replica symmetric (RS) ansatz. Then we find an exact solution for this quantity valid in a neighborhood of $α= 0$. An analysis of this solution shows that the system must have a phase transition at some finite value of $α$. This transition shows a singularity in the third derivative of the MI. As the RS solution turns out to be infinitely differentiable, it could be regarded as a smooth approximation to the MI. This is checked numerically in the validity domain of the exact solution.

cond-mat.dis-nn↗

arXiv1997

Complex-Field Zeros of the random-energy model

The complex-field zeros of the Random Energy Model are analytically determined. For T T_c a region is found which is free of zeros and is associated to the paramagnetic phase of the system. This region is separated from the former by a line of zeros. The real axis is found to be enclosed in a cloud of zeros in the whole frozen phase of the system.

cond-mat.dis-nn↗