1967
DOI: 10.1016/s0006-3495(67)86596-2
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Neuronal Spike Trains and Stochastic Point Processes

Abstract: In a growing class of neurophysiological experiments, the train of impulses ("spikes") produced by a nerve cell is subjected to statistical treatment involving the time intervals between spikes. The statistical techniques available for the analysis of single spike trains are described and related to the underlying mathematical theory, that of stochastic point processes, i.e., of stochastic processes whose realizations may be described as series of point events occurring in time, separated by random intervals. … Show more

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Cited by 1,139 publications
(447 citation statements)
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“…One property of this function is that it asymptotes to a constant limiting value so that highly regular spike trains reach this value more slowly than spike trains with a higher degree of variability. Thus, the number of peaks in the autocorrelogram that occur at integral multiples of the mean interspike interval, before reaching a constant limiting value, represent an index of regularity of firing (31). Neurons that exhibit an initial peak with a decay to a steady-state level are classified as bursty, whereas neurons that exhibit a random firing pattern display an autocorrelation function characterized by an initial trough that rises to a steady-state value (6).…”
Section: Methodsmentioning
confidence: 99%
“…One property of this function is that it asymptotes to a constant limiting value so that highly regular spike trains reach this value more slowly than spike trains with a higher degree of variability. Thus, the number of peaks in the autocorrelogram that occur at integral multiples of the mean interspike interval, before reaching a constant limiting value, represent an index of regularity of firing (31). Neurons that exhibit an initial peak with a decay to a steady-state level are classified as bursty, whereas neurons that exhibit a random firing pattern display an autocorrelation function characterized by an initial trough that rises to a steady-state value (6).…”
Section: Methodsmentioning
confidence: 99%
“…In a model with fall times of the coupling between the oscillators, Tsodyks et al [40] showed that the complete synchronized state is unstable to inhomogeneity in the oscillators frequencies. Finally Gerstner [43,17] achieved a synthesis of results on IF oscillators models by introducing a general model containing various versions of IF models as special cases and an analytical approach from the point of view of a renewal theory [44,45,46]. In the previous studies the oscillators are typically model neurons described as leaky integrator on a membrane potential.…”
Section: Introductionmentioning
confidence: 99%
“…The coefficient of reliability ¶ is a quantitative measure of the variance of spike time firing to repeated identical stimuli, adapted from multiple crosscorrelation analysis (13). Each single trial recording, considered as a point process (14), was convolved with a Gaussian smoothing function (standard deviation of 10 msec) truncated with a total width of three standard deviations. The reliability coefficient is the mean crosscorrelation of each smoothed single-trial spike train with every other smoothed single-trial spike train in a block of trials.…”
Section: Methodsmentioning
confidence: 99%