Can Power-Law Scaling and Neuronal Avalanches Arise from Stochastic Dynamics?

Abstract

The presence of self-organized criticality in biology is often evidenced by a power-law scaling of event size distributions, which can be measured by linear regression on logarithmic axes. We show here that such a procedure does not necessarily mean that the system exhibits self-organized criticality. 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. However, this result is not robust to change in detection threshold, or when tested using more rigorous statistical analyses such as the Kolmogorov-Smirnov 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, stochastic processes can produce spurious power-law scaling without the presence of underlying self-organized criticality. However, this power-law is only apparent in logarithmic representations, and does not survive more rigorous analysis such as the Kolmogorov-Smirnov test. The same analysis was also performed on an artificial network known to display self-organized criticality. In this case, both the graphical representations and the rigorous statistical analysis reveal with no ambiguity that the avalanche size is distributed as a power-law. We conclude that logarithmic representations can lead to spurious power-law scaling induced by the stochastic nature of the phenomenon. This apparent power-law scaling does not constitute a proof of self-organized criticality, which should be demonstrated by more stringent statistical tests.

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Cited by papers we hold 7

• Why Brain Criticality Is Clinically Relevant: A Scoping Review · 2020
  No notice
• Computing the Local Field Potential (LFP) from Integrate-and-Fire Network Models · 2015
  No notice
• Self-organized criticality as a fundamental property of neural systems · 2014
  No notice
• Extracting functionally feedforward networks from a population of spiking neurons · 2012
  Not checked
• Statistical Analyses Support Power Law Distributions Found in Neuronal Avalanches · 2011
  No notice
• Neurobiologically Realistic Determinants of Self-Organized Criticality in Networks of Spiking Neurons · 2011
  No notice
• Avalanches in a Stochastic Model of Spiking Neurons · 2010
  No notice

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