A model to describe spike-trains with power-law Fano factor.

There have been reports of cortical cells showing a Fano factor that scales with the size of the interval in which the spikes are being counted, with a power law dependence. A simple argument shows that, if this scaling is power-like, its value should be bounded between 0 and 1. This scaling constrains the behavior of the auto-correlation function of the spike train. If the variable describing the time of a spike were continuous, by fixing the first and second moment of the count, one would get a gaussian distribution. However if the spike-train is treated as a binary string of msec intervals, with site variables that can only take two discrete values according to whether there is or there is not a spike present in the corresponding time bin, the two-point and multi-point functions produced by the model become much more interesting. The resulting model resembles a magnetic system very popular in physics known as an Ising model. Constraining the auto-correlation function of the model to be the same as the spike-train data enforces a constraint on the parameters of the model. I will discuss why and how to choose the interaction in the Ising model in order to reproduce the behavior expected in the two-point function.

1:30pm -3:00pm, HSE 810.