Can power-law scaling and neuronal avalanches arise from
stochastic dynamics?
Jonathan Touboul and Alain Destexhe
PLoS One 5: e8982, 2010.
Online Version:
http://dx.plos.org/10.1371/journal.pone.0008982.
Abstract
The presence of self-organized criticality in biology is often
evidenced through the power-law scaling of event size distributions
represented in logarithmic scale. We show here that such a procedure
does not necessarily mean that the system exhibits power-law scaling.
We first provide an analysis of multisite local field potential (LFP)
recordings of brain activity and show that event size distributions
defined as negative LFP peaks can be close to power-law
distributions. This result is however not robust to change in
detection threshold, or to more severe statistical analyses such as
the Kolmogorov-Smirnoff test. Similar power-law scaling is observed
for surrogate signals, suggesting that power-law scaling may be a
generic property of thresholded stochastic processes. We next
investigate this problem analytically and show that indeed, spurious
power-law scaling can appear from stochastic processes without the
presence of underlying self-organized criticality. However, this
power-law is only apparent in logarithmic representations, but does
not resist to more severe analysis such as the Kolmogorov-Smirnoff
test. We conclude that logarithmic representations can lead to
spurious power-law scaling induced by the stochastic nature of the
phenomenon, and should be demonstrated by more stringent statistical
tests.
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