The Statistical Properties of Sequences of Stochastic Pulses

Lukes, Timothy J.

doi:10.1088/0370-1328/78/2/301

Cited by 25 publications

(9 citation statements)

References 8 publications

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“…64 For the HPP, the PSD of the point process simply assumes the value of the mean firing rate across all nonzero frequencies. For the DTMP, the point-process PSD asymptotically approaches the following limits, at low and at high frequencies, respectively [64][65][66] :…”

Section: Periodogrammentioning

confidence: 99%

Fractal character of the neural spike train in the visual system of the cat

et al. 1997

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We used a variety of statistical measures to identify the point process that describes the maintained discharge of retinal ganglion cells (RGC's) and neurons in the lateral geniculate nucleus (LGN) of the cat. These measures are based on both interevent intervals and event counts and include the interevent-interval histogram, rescaled range analysis, the event-number histogram, the Fano factor, Allan factor, and the periodogram. In addition, we applied these measures to surrogate versions of the data, generated by random shuffling of the order of interevent intervals. The continuing statistics reveal 1/f-type fluctuations in the data (long-duration power-law correlation), which are not present in the shuffled data. Estimates of the fractal exponents measured for RGC- and their target LGN-spike trains are similar in value, indicating that the fractal behavior either is transmitted form one cell to the other or has a common origin. The gamma-r renewal process model, often used in the analysis of visual-neuron interevent intervals, describes certain short-term features of the RGC and LGN data reasonably well but fails to account for the long-duration correlation. We present a new model for visual-system nerve-spike firings: a gamma-r renewal process whose mean is modulated by fractal binomial noise. This fractal, doubly stochastic point process characterizes the statistical behavior of both RGC and LGN data sets remarkably well.

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Section: Periodogrammentioning

confidence: 99%

Fractal character of the neural spike train in the visual system of the cat

et al. 1997

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“…This is possible because of our assumption of the phase resetting that accompanies the reset to the starting position, following each crossing of the barrier. Then, in terms of the FPTDF (8) we may write down the PSD at a frequency Q [31]: S(Q) = ( T) 5(Q/2m. )+( T) 'Re, (16) 1 -$(Q) $0(Q)=exp (p +p 2i QD-)--a (18) which yields, combined with (15), the PSD at the frequen- The behavior of the expression (19}as a function of the noise variance D is effectively dominated by the behavior of the real part of the characteristic function $0.…”

Section: Spectral Properties Of the Dynamicsmentioning

confidence: 99%

Cooperative behavior in the periodically modulated Wiener process: Noise-induced complexity in a model neutron

1994

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We consider a periodically modulated random walk (Wiener process) to an absorbing barrier with a deterministic reset to the starting point following each barrier crossing. Cooperative effects arising from the interplay between the noise and periodic modulation are analyzed as they manifest themselves in two statistical measures of the response: the passage time statistics of the process and the power spectral density of the output. Simple relationships exist between the extrema that occur in these two characterizations. The spectral properties of the response are seen to bear a striking resemblance to the stochastic resonance phenomenon that is known to occur in periodically driven noisy nonlinear systems.PACS number(s): 05.40.+j

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“…The final element which has been considered in this model is the repetitive pulse nature of the conductivity produced by channel opening and closing. The spectra for this type of process were worked out by Lukes (1961) and by Heiden (1969), and discussed more recently in terms of biological systems by Schick (1974). We will term their method the LHS model.…”

Section: Introductionmentioning

confidence: 99%

A model for channel noise, including the effect of diffusion

Green

1978

Acta Biotheor

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A model (based on a proposal by Schick (1974), is developed for channels composed of four species; the channels allow conduction when all species are in the correct configuration. Allowance is also made for diffusion resulting from depletion of ions in the neighbourhood of the channel. The result is a series of pulses in which the current falls as t -t/2 upon dosing the channel. The resulting power spectrum is calculated according to the method given by Schick and earlier workers, and is found to be, at least qualitatively, in agreement with many of the features of noise measured for certain types of nerve membranes. The calculations are not linearized, but are carried through numerically.

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The Statistical Properties of Sequences of Stochastic Pulses

Cited by 25 publications

References 8 publications

Fractal character of the neural spike train in the visual system of the cat

Fractal character of the neural spike train in the visual system of the cat

Cooperative behavior in the periodically modulated Wiener process: Noise-induced complexity in a model neutron

A model for channel noise, including the effect of diffusion

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