Extraction and Characterization of Essential Discharge Patterns from Multisite Recordings of Spiking Ongoing Activity

Abstract

Conditional sampling, in comparison with the classical constant time-bin sampling, enables to reject, at least in most cases, the common mode modulation of the spiking frequency across different spiking sources. Here we consider a simple but significant example while a more general analysis is currently in preparation: Consider two spiking neurons and let n1, n2 the number of spikes emitted in a time period T. They both follow a Poisson process with parameters λcλ1T and λcλ2T respectively, being λc a common modulation term, λ1 and λ2 the independent component of their activity. Let n1 + n2 = k and Pn1,n2 = Pn1,k−n1 the probability of observing n1 and k − n1 spikes (respectively from the first and the second neuron) in a period T. Then Pn1,k−n1 = e−λcT (λ1+λ2) (T λc) k λn 1 1 λk−n 1 2 n1!(k−n1)! Now consider the conditional probability of observing n1 and k − n1 spikes i