9 research outputs found
Delayed feedback makes neuronal firing statistics non-Markovian
The instantaneous state of a neural network consists of both the degree of excitation of each neuron and the positions of impulses in communication lines between the neurons. In neurophysiological experiments, the times of neuronal firing are recorded but not the state of communication lines. However, future spiking moments substantially depend on the past positions of impulses in the lines. This suggests that the sequence of intervals between firing moments (interspike intervals, ISI) in the network can be non-Markovian. In the present paper, we analyze this problem for the simplest possible neural “network,” namely, for a single neuron with delayed feedback.Стан нейронної мережi складається як з величини збудження в кожному з нейронiв, так i зi значень положення iмпульсiв у лiнiях зв’язку. В нейрофiзiологiчних експериментах реєструються моменти пострiлiв окремих нейронiв, а не стани лiнiй зв’язку. Але моменти наступних пострiлiв iстотним чином залежать вiд положення iмпульсiв у лiнiях зв’язку в попереднi моменти. Це наводить на думку, що послiдовнiсть iнтервалiв мiж послiдовними пострiлами окремого нейрона в мережi (мiжспайковi iнтервали, МСI) може складати немарковський точковий стохастичний процес. У цiй роботi дослiджується така можливiсть для найпростiшої з можливих нейронної „мережi”, а саме, поодинокого нейрона з затриманим зворотним зв’язком
Firing statistics of inhibitory neuron with delayed feedback. I. Output ISI probability density
Activity of inhibitory neuron with delayed feedback is considered in the
framework of point stochastic processes. The neuron receives excitatory input
impulses from a Poisson stream, and inhibitory impulses from the feedback line
with a delay. We investigate here, how does the presence of inhibitory feedback
affect the output firing statistics. Using binding neuron (BN) as a model, we
derive analytically the exact expressions for the output interspike intervals
(ISI) probability density, mean output ISI and coefficient of variation as
functions of model's parameters for the case of threshold 2. Using the leaky
integrate-and-fire (LIF) model, as well as the BN model with higher thresholds,
these statistical quantities are found numerically. In contrast to the
previously studied situation of no feedback, the ISI probability densities
found here both for BN and LIF neuron become bimodal and have discontinuity of
jump type. Nevertheless, the presence of inhibitory delayed feedback was not
found to affect substantially the output ISI coefficient of variation. The ISI
coefficient of variation found ranges between 0.5 and 1. It is concluded that
introduction of delayed inhibitory feedback can radically change neuronal
output firing statistics. This statistics is as well distinct from what was
found previously (Vidybida & Kravchuk, 2009) by a similar method for excitatory
neuron with delayed feedback.Comment: 23 pages, 8 figure