Self-similarity in sensory neural signals

A variety of statistical measures are useful for identifying the form of the point process that describes the maintained discharge of retinal-ganglion-cell (RGC) and lateral-geniculate-nucleus (LGN) neurons in the cat visual system. These measures are based on both interevent intervals and counts, and include the interevent-interval histogram, rescaled range analysis, the event-number histogram, Fano factor, Allan factor, and periodogram. All of these measures have been applied to data sets derived from both RGC and LGN neurons, and to surrogate versions thereof generated by randomly shuffling the order of the interevent intervals. The counting statistics reveal multiscale (1/f-type) fluctuations in the data (long-duration power-law correlation), which can be identified with neuronal facilitation. These fractal fluctuations are eliminated by the process of shuffling. Certain short-term features of the RGC and LGN spike trains are well described by the gamma-r renewal process that is often used to model visual-system action-potential interevent intervals. However, this model fails to accommodate the long-duration correlation. The authors present a new model for visual-system action-potential firings comprising a gamma-r renewal process compounded with fractal binomial noise. This fractal doubly stochastic point process characterizes the statistical behavior of both RGC and LGN spike trains exceedingly well.