Mathematics Consortium for Science and Industry, Department of Mathematics and Statistics, University of Limerick, Limerick V94 T9PX, Ireland.
Center for Complex Networks and Systems Research, School of Informatics, Computing, and Engineering, Indiana University, Bloomington, Indiana 47408, USA.
Phys Rev E. 2019 Jul;100(1-1):010401. doi: 10.1103/PhysRevE.100.010401.
Experimental and computational studies provide compelling evidence that neuronal systems are characterized by power-law distributions of neuronal avalanche sizes. This fact is interpreted as an indication that these systems are operating near criticality, and, in turn, typical properties of critical dynamical processes, such as optimal information transmission and stability, are attributed to neuronal systems. The purpose of this Rapid Communication is to show that the presence of power-law distributions for the size of neuronal avalanches is not a sufficient condition for the system to operate near criticality. Specifically, we consider a simplistic model of neuronal dynamics on networks and show that the degree distribution of the underlying neuronal network may trigger power-law distributions for neuronal avalanches even when the system is not in its critical regime. To certify and explain our findings we develop an analytical approach based on percolation theory and branching processes techniques.
实验和计算研究提供了令人信服的证据，表明神经元系统的神经元爆发大小呈幂律分布。这一事实被解释为这些系统接近临界状态的迹象，因此，临界动力过程的典型特性，如最优信息传输和稳定性，被归因于神经元系统。本快速通讯的目的是表明，神经元爆发大小的幂律分布并不是系统接近临界状态的充分条件。具体来说，我们考虑了一个神经元动力学在网络上的简化模型，并表明即使在系统不在其临界状态时，基础神经元网络的度分布也可能引发神经元爆发的幂律分布。为了证明和解释我们的发现，我们开发了一种基于渗流理论和分支过程技术的分析方法。
