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Hierarchical networks, power laws, and neuronal avalanches

机译:分层网络,幂律和神经元雪崩

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摘要

We show that in networks with a hierarchical architecture, critical dynamical behaviors can emerge even when the underlying dynamical processes are not critical. This finding provides explicit insight into current studies of the brain's neuronal network showing power-law avalanches in neural recordings, and provides a theoretical justification of recent numerical findings. Our analysis shows how the hierarchical organization of a network can itself lead to power-law distributions of avalanche sizes and durations, scaling laws between anomalous exponents, and universal functions-even in the absence of self-organized criticality or critical points. This hierarchy-induced phenomenon is independent of, though can potentially operate in conjunction with, standard dynamical mechanisms for generating power laws.
机译:我们表明,在具有分层体系结构的网络中,即使基本的动态过程并不关键,也会出现关键的动态行为。这一发现提供了对大脑神经元网络当前研究的清晰见解,该研究显示了神经记录中的幂律雪崩,并为最近的数字发现提供了理论依据。我们的分析表明,网络的层次结构本身如何导致雪崩大小和持续时间的幂律分布,异常指数之间的缩放定律以及通用功能,即使没有自组织的临界点或临界点也是如此。这种层次结构引起的现象与生成功率定律的标准动力学机制无关,尽管可以潜在地与其结合使用。

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