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Statistical Analyses Support Power Law Distributions Found in Neuronal Avalanches

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  • Andreas Klaus
  • Shan Yu
  • Dietmar Plenz

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.

Suggested Citation

  • Andreas Klaus & Shan Yu & Dietmar Plenz, 2011. "Statistical Analyses Support Power Law Distributions Found in Neuronal Avalanches," PLOS ONE, Public Library of Science, vol. 6(5), pages 1-12, May.
  • Handle: RePEc:plo:pone00:0019779
    DOI: 10.1371/journal.pone.0019779
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    Cited by:

    1. Safari, Muhammad Aslam Mohd & Masseran, Nurulkamal & Ibrahim, Kamarulzaman & AL-Dhurafi, Nasr Ahmed, 2020. "The power-law distribution for the income of poor households," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    2. Forough Habibollahi & Brett J. Kagan & Anthony N. Burkitt & Chris French, 2023. "Critical dynamics arise during structured information presentation within embodied in vitro neuronal networks," Nature Communications, Nature, vol. 14(1), pages 1-13, December.
    3. Todd Zorick & Mark A Mandelkern, 2013. "Multifractal Detrended Fluctuation Analysis of Human EEG: Preliminary Investigation and Comparison with the Wavelet Transform Modulus Maxima Technique," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-7, July.
    4. Okorie, Idika E. & Nadarajah, Saralees, 2021. "A note on “The distribution of union size: Canada, 1913–2014”," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).
    5. Liang, Sai & Qi, Zhengling & Qu, Shen & Zhu, Ji & Chiu, Anthony S.F. & Jia, Xiaoping & Xu, Ming, 2016. "Scaling of global input–output networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 311-319.
    6. Ayana Aspembitova & Ling Feng & Valentin Melnikov & Lock Yue Chew, 2019. "Fitness preferential attachment as a driving mechanism in bitcoin transaction network," PLOS ONE, Public Library of Science, vol. 14(8), pages 1-20, August.
    7. Michael P. Leung, 2022. "Dependence‐robust inference using resampled statistics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(2), pages 270-285, March.
    8. Salvador Pueyo, 2014. "Ecological Econophysics for Degrowth," Sustainability, MDPI, vol. 6(6), pages 1-53, May.
    9. Pachon, Angelica & Polito, Federico & Sacerdote, Laura, 2020. "On the continuous-time limit of the Barabási–Albert random graph," Applied Mathematics and Computation, Elsevier, vol. 378(C).

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