Volume 15 Supplement 1

## Abstracts from the Twenty Third Annual Computational Neuroscience Meeting: CNS*2014

# Fluctuation scaling in neural spike trains

- Shinsuke Koyama
^{1, 2, 3}Email author

**15(Suppl 1)**:P119

https://doi.org/10.1186/1471-2202-15-S1-P119

© Koyama; licensee BioMed Central Ltd. 2014

**Published: **21 July 2014

## Keywords

The fluctuation scaling (FS) law has been observed in a wide variety of phenomena. It states that the variance of a quantity has a power function relation with the mean. Since Taylor found it in ecological systems [1], the FS law has been demonstrated in many natural and social systems, showing a universality of the law [2]. In this study, The FS law for neural spike trains is formulated using the framework of renewal point processes.

The scaling exponent $\phantom{\rule{0.5em}{0ex}}\alpha $ characterizes the 'intrinsic' dispersion of neuronal firing. For a Poisson (random) process, $\alpha =2$. On the other hand, $\alpha >2\left(\alpha <2\right)$ implies the tendency for the timing of spikes to be over (under) dispersed for large means, and under (over) dispersed for small means.

with $\beta =3-\alpha $ for $\text{\Delta}>>1$.

In the presentation, I show the following two results:

The fluctuation scaling law emerges in the first-passage time to a threshold of certain diffusion processes (i.e., integrate-and-fire models).

The likelihood function of spike trains is constructed, based on which I propose a method for extracting the scaling exponent from nonstationary spike trains. This method is applied to biological spike train data to characterize the variability of neuronal firing.

Possible implications of these results are discussed in terms of characterizing intrinsic dynamics of neuronal discharge.

## Declarations

### Acknowledgements

This work was supported by JSPS KAKENHI Grant Number 24700287.

## Authors’ Affiliations

## References

- Taylor LR: Aggregation, variance and the mean. Nature. 1961, 189: 732-735. 10.1038/189732a0.View ArticleGoogle Scholar
- Eisler Z, Bartos I, Kertesz J: Fluctuation scaling in complex systems: Taylor's law and beyond. Advances in Physics. 2008, 57: 89-142. 10.1080/00018730801893043.View ArticleGoogle Scholar

## Copyright

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