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I was reading a journal article on modeling the interaction between different neural networks and I am confused about the follwoing method (cited below). It is describing the spike rate output of a neuron based on oscillating firing rates of excitatory (E) and inhibitory (I) inputs:

"Consider two local circuits, both projecting to a third circuit ... each comprised of E and I cells, with at least a projection from the local I cells to the E cells. When an input network is synchronized it produces periodic E cell activity at a specific global phase set by its local I cells. These two sources of E volleys together with the local inhibition drive the E cells in the receiving circuit. Here we are interested in modeling the impact of E and I streams that are out of phase.

We studied the effect of synchronized E and I inputs on a model neuron with Hodgkin–Huxley-type channels.... Periodic and synchronous activity was modeled as a Poisson process with a time-varying firing rate comprised of a periodic sequence of Gaussian peaks. Each Gaussian peak generated a so-called volley: a set of input spike times tightly centered on the location of the peak."

and

"The number of incoming I and E spikes varied from cycle to cycle because the E and I inputs were generated as Poisson processes with a spike density comprised of a periodic sequence of Gaussian peaks."

Is it describing a non-homogeneous Poisson process which, due to the nature of the time-varying probability of a spike occurrence, produces a firing rate for the inputs that looks like a series of (approximate) 'Gaussian-shaped' curves? Or is there something I am missing in the "Gaussian peak" part? I initially thought that the peaks were generated through a Poisson process, and then 'something else happened', involving generating "volleys" via a different probability distribution. But the peaks are evenly spaced at a constant 25 ms period, and the actual number of spikes, as described above, varies due to it being a Poisson process. So, I figured that the actual spike occurrence at any point in time is given by the time-varying Poisson distribution, and the nature of the function, with time-varying λ(t), produces a series of spikes that looks like, as mentioned before, a series of 'Gaussian-shaped curves'. Otherwise, I don't see where the Poisson process part comes in.

Paper: Mechanisms for Phase Shifting in Cortical Networks and their Role in Communication through Coherence by Paul H. Tiesinga and Terrence J. Sejnowski.

Any help appreciated.

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# Neuroscience: poisson and gauss in neuron firing rate model

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