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Modeling neural activity with cumulative damage distributions

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Abstract

Neurons transmit information as action potentials or spikes. Due to the inherent randomness of the inter-spike intervals (ISIs), probabilistic models are often used for their description. Cumulative damage (CD) distributions are a family of probabilistic models that has been widely considered for describing time-related cumulative processes. This family allows us to consider certain deterministic principles for modeling ISIs from a probabilistic viewpoint and to link its parameters to values with biological interpretation. The CD family includes the Birnbaum–Saunders and inverse Gaussian distributions, which possess distinctive properties and theoretical arguments useful for ISI description. We expand the use of CD distributions to the modeling of neural spiking behavior, mainly by testing the suitability of the Birnbaum–Saunders distribution, which has not been studied in the setting of neural activity. We validate this expansion with original experimental and simulated electrophysiological data.

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Acknowledgments

The authors thank the Editor-in-Chief, Prof. Dr. J. Leo van Hemmen, and two anonymous referees for their valuable comments on an earlier version of this manuscript, which resulted in this improved version. The authors thank Rosie Gronthos from Australia for proofreading the first revised version of this manuscript and Patricia Van Roon from Canada for proofreading its second version. The research of V. Leiva was supported by FONDECYT 1120879 grant from the Chilean government; of M. Tejo by FONDECYT 3140613 postdoctorate grant; of P. Guiraud by PIA-Anillo ACT1112 grant from the Chilean government; of P. Orio by FONDECYT 1130862 and PIA-Anillo ACT-1113; and of P. Orio and O. Schmachtenberg by The Centro Interdisciplinario de Neurociencia de Valparaíso, which is a Millennium Institute supported by the Millennium Scientific Initiative of the Ministerio de Economía, Fomento y Turismo of the Chilean government.

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Leiva, V., Tejo, M., Guiraud, P. et al. Modeling neural activity with cumulative damage distributions. Biol Cybern 109, 421–433 (2015). https://doi.org/10.1007/s00422-015-0651-9

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