  This paper introduces a class of stochastic models of interacting neurons
with emergent dynamics similar to those seen in local cortical populations, and
compares them to very simple reduced models driven by the same mean excitatory
and inhibitory currents. Discrepancies in firing rates between network and
reduced models were investigated, and mechanisms leading to these discrepancies
were identified. Chief among them is correlations in spiking, or partial
synchronization, working in concert with "nonlinearities" in the time evolution
of membrane potentials. Additionally, simple random walk models and their first
passage times were shown to reproduce well fluctuations in neuronal membrane
potentials and interspike times.
