Statistical analyses support power law distributions found in neuronal avalanches.
Statistical analyses support power law distributions found in neuronal avalanches.
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DOI：
10.1371/journal.pone.0019779
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发表时间：
2011
期刊：
影响因子：
3.7
通讯作者：
Plenz D
中科院分区：
文献类型：
--
作者：
Klaus A;Yu S;Plenz D
据报道，大脑皮层网络中神经元雪崩的大小分布服从指数接近−1.5的指数分布，这反映了神经元自发活动的长期空间相关性。然而，在经验数据中识别幂定律标度可能是困难的，有时还会引起争议。在目前的研究中，我们使用更严格的统计分析来检验神经元雪崩的幂定律假说。具体地说，我们执行了以下步骤：(I)有限尺寸标度分析以识别神经元雪崩中的无标度动力学，(Ii)模型参数估计以确定幂定律的特定指数，以及(Iii)幂定律与其他模型分布的比较。与临界状态动力学一致，雪崩大小分布显示出稳健的标度行为，其中最大雪崩大小仅受采样的空间范围限制(“有限大小”效应)。这种无标度的动力学表明，幂定律是雪崩大小分布的一个模型。使用柯尔莫戈洛夫-斯米尔诺夫统计量和最大似然法，我们发现斜率接近−1.5，这与之前的报道一致。最后，通过使用对数似然比检验，将神经元雪崩的幂定律模型与基于Kolmogorov-Smirnov距离的指数分布和各种重尾分布进行了比较。与指数分布、对数正态分布和伽马分布相比，无指数截止点和有指数截止点的幂分布对神经元雪崩的簇大小分布有更好的拟合效果。综上所述，我们的发现有力地支持了神经元雪崩的幂定律标度，为皮层浅层的临界状态动力学提供了进一步的证据。
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.
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