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

Alexandre Richard 1 Patricio Orio 2 Etienne Tanré 3
3 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : 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.
Type de document :
Pré-publication, Document de travail
2017
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  • HAL Id : hal-01521891, version 1
  • ARXIV : 1702.03762

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Alexandre Richard, Patricio Orio, Etienne Tanré. An integrate-and-fire model to generate spike trains with long memory. 2017. 〈hal-01521891〉

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