Dependency Representing Markov Properties of Spike Trains Recorded from Central Single Neurons

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Abstract
Neuronal spike trains are regarded as stochastic point processes. To estimate the order and the value of Markov properties of the adjacent interspike interval sequences, new statistics were proposed: dependency ~Dm for discrete variable, simplified dependency .cxa.Dm for continuous variable in the stationary point processes and ~Dm(t) for discrete variable in the non-stationary point processes. With the use of .cxa.Dm it was shown that the maintained activity of the neurons of the [cat] mesencephalic reticular formation and red nucleus (tonic neuron groups) revealed higher order and larger values of Markov properties than that of the optic tract (OT) fibers and lateral geniculate nucleus neurons (phasic neuron groups) in cats. By employing ~Dm(t) it was shown that the value of the 1st order Markov properties of OT spike trains induced by the light spot presentation increased earlier in Y-fibers than in X-fibers; and that the value for Y-fibers returned to the maintained level in a short time, while the maximum value for X-fibers continued up to the light-off. The differentiation may have a decided functional significance. Dependency code apparently represents the stability of neuronal functions.

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