# American Institute of Mathematical Sciences

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2016, 13(3): 537-550. doi: 10.3934/mbe.2016006

## Fluctuation scaling in neural spike trains

 1 Department of Statistical Modeling, The Institute of Statistical Mathematics, 10-3 Midoricho, Tachikawa, Tokyo, Japan 2 Principles of Informatics Research Division, National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, Japan

Received  March 2015 Revised  November 2015 Published  January 2016

Fluctuation scaling has been observed universally in a wide variety of phenomena. In time series that describe sequences of events, fluctuation scaling is expressed as power function relationships between the mean and variance of either inter-event intervals or counting statistics, depending on measurement variables. In this article, fluctuation scaling has been formulated for a series of events in which scaling laws in the inter-event intervals and counting statistics were related. We have considered the first-passage time of an Ornstein-Uhlenbeck process and used a conductance-based neuron model with excitatory and inhibitory synaptic inputs to demonstrate the emergence of fluctuation scaling with various exponents, depending on the input regimes and the ratio between excitation and inhibition. Furthermore, we have discussed the possible implication of these results in the context of neural coding.
Citation: Shinsuke Koyama, Ryota Kobayashi. Fluctuation scaling in neural spike trains. Mathematical Biosciences & Engineering, 2016, 13 (3) : 537-550. doi: 10.3934/mbe.2016006
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