Langlois Dominic, Cousineau Denis, Thivierge J P
School of Psychology, University of Ottawa, 136 Jean Jacques Lussier, Ottawa, Ontario, Canada K1N 6N5.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jan;89(1):012709. doi: 10.1103/PhysRevE.89.012709. Epub 2014 Jan 15.
The coordination of activity amongst populations of neurons in the brain is critical to cognition and behavior. One form of coordinated activity that has been widely studied in recent years is the so-called neuronal avalanche, whereby ongoing bursts of activity follow a power-law distribution. Avalanches that follow a power law are not unique to neuroscience, but arise in a broad range of natural systems, including earthquakes, magnetic fields, biological extinctions, fluid dynamics, and superconductors. Here, we show that common techniques that estimate this distribution fail to take into account important characteristics of the data and may lead to a sizable misestimation of the slope of power laws. We develop an alternative series of maximum likelihood estimators for discrete, continuous, bounded, and censored data. Using numerical simulations, we show that these estimators lead to accurate evaluations of power-law distributions, improving on common approaches. Next, we apply these estimators to recordings of in vitro rat neocortical activity. We show that different estimators lead to marked discrepancies in the evaluation of power-law distributions. These results call into question a broad range of findings that may misestimate the slope of power laws by failing to take into account key aspects of the observed data.
大脑中神经元群体之间活动的协调对于认知和行为至关重要。近年来被广泛研究的一种协调活动形式是所谓的神经元雪崩，即持续的活动爆发遵循幂律分布。遵循幂律的雪崩并非神经科学所特有，而是出现在广泛的自然系统中，包括地震、磁场、生物灭绝、流体动力学和超导体。在这里，我们表明，估计这种分布的常用技术没有考虑到数据的重要特征，可能会导致幂律斜率的相当大的错误估计。我们针对离散、连续、有界和删失数据开发了一系列替代的最大似然估计器。通过数值模拟，我们表明这些估计器能够对幂律分布进行准确评估，比常用方法有所改进。接下来，我们将这些估计器应用于体外大鼠新皮质活动的记录。我们表明，不同的估计器在幂律分布的评估中会导致显著差异。这些结果对广泛的研究结果提出了质疑，这些研究结果可能由于没有考虑观测数据的关键方面而错误估计了幂律的斜率。
