First-order transition resulting from asymmetric input distribution in a neuron population model

FERNANDO MONTANI; BARAVALLE, ROMAN

Buenos Aires

Conferencia; 27th International Conference on Statistical Physics, StatPhys 27; 2019

IUPAP

It is usually assumed that the output variables of functional and structural brain parameters, such as the firing rates of individual neurons or the synchronous discharge of neural populations have a bell-shaped input distribution. However, at many physiological and anatomical levels in the brain, the distribution of numerous parameters is in fact strongly skewed with a heavy tail, suggesting that skewed distributions are fundamental to structural and functional brain organization. Importantly, populations of neurons show synchronous activity patterns as they share common correlated inputs. The Dichotomized Gaussian framework refers to the case in which these inputs are considered as Gaussians distributed.  We present an extension to the Dichotomized Gaussian input model considering a skewed input distribution. The skewness of the distribution induces a first-order transition in the model and we show analytically how small changes in the correlation inputs can lead to large changes in the interactions of the outputs leading to a phase transition. More specifically, we present an exact quantification of output variables of functional and structural brain parameters by estimating the different orders of the cumulants. In particular, the Binder cumulative estimation allows us to identify a possible phase transition in the correlation statistics of the spikes characterizing the scaling properties of the system.