复杂动力系统演化现象的极值理论：神经网络模型中的点火级联
Extreme value theory of evolving phenomena in complex dynamical systems: firing cascades in a model of neural network
摘要：
我们扩展了极值动力学理论的范围，以涵盖那些不是瞬间发生的现象，而是在有限的时间间隔内演变的，尽管在开始时是未知的。我们考虑复杂的动力系统，由许多独立的子系统连接的网络的相互作用。作为一般理论的一个具体例子，本文详细分析了描述大脑皮层电活动的神经网络模型：在此基础上，我们提出了神经元级联这一重要生理现象的新定义。我们得出极值法律的统计这些级联，无论是从角度来看的concernances（满足临界尺度理论）和块极大值。
英文摘要：
We extend the scope of the dynamical theory of extreme values to cover phenomena that do not happen instantaneously, but evolve over a finite, albeit unknown at the onset, time interval. We consider complex dynamical systems, composed of many individual subsystems linked by a network of interactions. As a specific example of the general theory, a model of neural network, introduced to describe the electrical activity of the cerebral cortex, is analyzed in detail: on the basis of this analysis we propose a novel definition of neuronal cascade, a physiological phenomenon of primary importance. We derive extreme value laws for the statistics of these cascades, both from the point of view of exceedances (that satisfy critical scaling theory) and of block maxima.
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