  Here we demonstrate that the activity of neural ensembles can be
quantitatively modeled. We first show that an ensemble dynamical model (EDM)
accurately approximates the distribution of voltages and average firing rate
per neuron of a population of simulated integrate-and-fire neurons. EDMs are
high-dimensional nonlinear dynamical models. To faciliate the estimation of
their parameters we present a dimensionality reduction method and study its
performance with simulated data. We then introduce and evaluate a
maximum-likelihood method to estimate connectivity parameters in networks of
EDMS. Finally, we show that this model an methods accurately approximate the
high-gamma power evoked by pure tones in the auditory cortex of rodents.
Overall, this article demonstrates that quantitatively modeling brain activity
at the ensemble level is indeed possible, and opens the way to understanding
the computations performed by neural ensembles, which could revolutionarize our
understanding of brain function.
