Can power-law scaling and neuronal avalanches arise from stochastic dynamics?

Jonathan Touboul and Alain Destexhe

PLoS One 5: e8982, 2010.

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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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