Biologically plausible statistics from a Markov model of spiking cortical networks

Understanding the spatio-temporal correlations observed in nervous tissue is a major challenge in computational neuroscience. We approach this challenge by modeling the global network state as a single Markov process [1,2]. Each neuron is modeled as a two (active or inactive) – or three-state (active, inactive, or refractory) random variable, with each neuron's spike probability a function of its input current and internal threshold, updated at time steps dependent upon the current network state. Using the stochastic simulation algorithm [3], we simulate the network model with excitatory and inhibitory neurons and with random connectivity tuned so that each spike triggers on average one new spike, i.e. in the critical regime.