Abstract
The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to −1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesis for neuronal avalanches by using more stringent statistical analyses. In particular, we performed the following steps: (i) analysis of finite-size scaling to identify scale-free dynamics in neuronal avalanches, (ii) model parameter estimation to determine the specific exponent of the power law, and (iii) comparison of the power law to alternative model distributions. Consistent with critical state dynamics, avalanche size distributions exhibited robust scaling behavior in which the maximum avalanche size was limited only by the spatial extent of sampling (“finite size” effect). This scale-free dynamics suggests the power law as a model for the distribution of avalanche sizes. Using both the Kolmogorov-Smirnov statistic and a maximum likelihood approach, we found the slope to be close to −1.5, which is in line with previous reports. Finally, the power law model for neuronal avalanches was compared to the exponential and to various heavy-tail distributions based on the Kolmogorov-Smirnov distance and by using a log-likelihood ratio test. Both the power law distribution without and with exponential cut-off provided significantly better fits to the cluster size distributions in neuronal avalanches than the exponential, the lognormal and the gamma distribution. In summary, our findings strongly support the power law scaling in neuronal avalanches, providing further evidence for critical state dynamics in superficial layers of cortex.
Highlights
Complex systems, when poised at the transition between order and disorder, exhibit scale-free dynamics [1]
Good fits were obtained by the inverse Gaussian distribution, which describes a power law with fixed exponent 21.5 and additional cut-off function. These results indicate that cluster size distributions in neuronal avalanches scale according to a power law with particular exponent a close to 21.5, which provides strong support for critical state dynamics in superficial layers of cortex
The results will be presented in the following order: First, finite-size scaling analysis, which is required to determine whether the power law model is an appropriate model for neuronal avalanches
Summary
Complex systems, when poised at the transition between order and disorder, exhibit scale-free dynamics [1]. The size of neuronal activity cascades in superficial layers of cortex, measured by the number of negative threshold crossings of the local field potential (nLFP), has been suggested to be distributed according to a power law with exponent a close to 21.5 [2,3,4,5] (Figure 1). This activity was termed ‘‘neuronal avalanches.’’ The exponent of 21.5 indicates that neuronal avalanches reflect longrange spatial and temporal correlations in the network as expected from critical dynamics [2,6,7,8]. Avalanche dynamics fulfill the theoretical predictions for critical branching processes that exhibit both a power law in cascade size distributions with a slope of 21.5 and a critical branching parameter equal to unity [2,10]
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