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

Alexandre Richard (1, 2) , Patricio Orio (3) , Etienne Tanré (4)

1 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes
2 FR3487 - Fédération de Mathématiques de l'Ecole Centrale Paris
3 CINV - Centro Interdisciplinario de Neurociencia de Valparaiso
4 TOSCA - TO Simulate and CAlibrate stochastic models

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-fire (IF) model, with a noisy slow adaptation term, can generate interspike intervals (ISIs) that appear as having LRD. However a proper analysis shows that this is not the case asymptotically. For comparison, we also consider a new model of individual IF neuron with fractional (non-Markovian) noise. The correlations of its spike trains are studied and proven to have LRD, 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 ISIs is presented and applied to the various IF models. We explain that Markovian IF models may seem to have LRD because of non-stationarities.

Mots clés: Long-range dependence; Stochastic Integrate-and-Fire model; Interspike interval statistics; Stationarity

Domaines: Probabilités [math.PR]

Alexandre Richard, Patricio Orio, Etienne Tanré. An integrate-and-fire model to generate spike trains with long-range dependence. Journal of Computational Neuroscience, 2018, 44 (3), pp.297-312. ⟨10.1007/s10827-018-0680-1⟩. ⟨hal-01521891v2⟩