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Article Dans Une Revue Journal of Computational Neuroscience Année : 2018

An integrate-and-fire model to generate spike trains with long memory

Résumé

Long-range dependence (LRD) has been observed in a variety of phenomena in nature, and for several years also in the spiking activity of neurons. Often, this is interpreted as originating from a non-Markovian system. Here we show that a purely Markovian integrate-and-re (IF) model, with a noisy slow adaptation term, can generate data that appears as having LRD with a Hurst exponent (H) greater than 0.5. A proper analysis shows that the asymptotic value of H is 0.5 if a long enough sequence of events is taken into account. For comparison, we also consider a new model of individual IF neuron with fractional noise. The correlations of its spike trains are studied and proved to have long memory, unlike classical IF models. On the other hand, to correctly measure long-range dependence, it is usually necessary to know if the data are stationary. Thus, a methodology to evaluate stationarity of the interspike intervals (ISIs) is presented and applied to the various IF models. In conclusion, the spike trains of our fractional model have the long-range dependence property, while those from classical Markovian models do not. However, Markovian IF models may seem to have it because of apparent non-stationarities.
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Dates et versions

hal-01521891 , version 1 (12-05-2017)
hal-01521891 , version 2 (28-03-2018)

Identifiants

Citer

Alexandre Richard, Patricio Orio, Etienne Tanré. An integrate-and-fire model to generate spike trains with long memory. Journal of Computational Neuroscience, inPress, ⟨10.1007/s10827-018-0680-1⟩. ⟨hal-01521891v1⟩

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