Neuroimaging of Epilepsy Laboratory, McConnell Brain Imaging Center, McGill University, Montreal Neurological Institute and Hospital, H3A 2B4, Montreal, Quebec, Canada.
Departamento de Física, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil.
Phys Rev E. 2018 Apr;97(4-1):042415. doi: 10.1103/PhysRevE.97.042415.
Power-law-shaped avalanche-size distributions are widely used to probe for critical behavior in many different systems, particularly in neural networks. The definition of avalanche is ambiguous. Usually, theoretical avalanches are defined as the activity between a stimulus and the relaxation to an inactive absorbing state. On the other hand, experimental neuronal avalanches are defined by the activity between consecutive silent states. We claim that the latter definition may be extended to some theoretical models to characterize their power-law avalanches and critical behavior. We study a system in which the separation of driving and relaxation time scales emerges from its structure. We apply both definitions of avalanche to our model. Both yield power-law-distributed avalanches that scale with system size in the critical point as expected. Nevertheless, we find restricted power-law-distributed avalanches outside of the critical region within the experimental procedure, which is not expected by the standard theoretical definition. We remark that these results are dependent on the model details.
幂律形的雪崩大小分布被广泛用于探测许多不同系统中的临界行为，特别是在神经网络中。雪崩的定义是模糊的。通常，理论上的雪崩被定义为刺激和松弛到非活跃的吸收状态之间的活动。另一方面，实验神经元的雪崩则由连续的沉默状态之间的活动来定义。我们声称，后者的定义可以扩展到某些理论模型，以描述它们的幂律雪崩和临界行为。我们研究了一个系统，其中驱动和松弛时间尺度的分离源自其结构。我们将两种雪崩的定义都应用于我们的模型。两种定义都产生了幂律分布的雪崩，其在临界点上与系统大小成比例，这是预期的。然而，我们在实验过程中发现了在临界区域之外的受限幂律分布的雪崩，这是标准理论定义所不期望的。我们注意到，这些结果取决于模型的细节。
