标题： 神经活动的统计模型、临界性和齐普夫定律 显示英文标题

标题： Statistical models of neural activity, criticality, and Zipf's law

摘要： 在本概述中，我们讨论了神经元网络中临界动力学的观测与通常用作神经活动统计模型的最大熵模型之间的联系，特别关注“统计”和“动力学”临界性之间的关系。 我们给出了在一种方式上临界但在另一种方式上不临界的系统示例，从而说明了这两个概念的不同之处。 然后我们讨论了神经活动中的Zipf定律的出现，并在多种不同条件下验证了视网膜活动中的存在。 在章节的第二部分，我们回顾了统计临界性与参数空间结构之间的联系，如Fisher信息所描述的那样。 我们注意到，基于模型的临界性特征，即比热的发散，独立于所研究的数据集而出现；我们认为这与之前的理论结果相容。 显示英文摘要

摘要： In this overview, we discuss the connections between the observations of critical dynamics in neuronal networks and the maximum entropy models that are often used as statistical models of neural activity, focusing in particular on the relation between "statistical" and "dynamical" criticality. We present examples of systems that are critical in one way, but not in the other, exemplifying thus the difference of the two concepts. We then discuss the emergence of Zipf laws in neural activity, verifying their presence in retinal activity under a number of different conditions. In the second part of the chapter we review connections between statistical criticality and the structure of the parameter space, as described by Fisher information. We note that the model-based signature of criticality, namely the divergence of specific heat, emerges independently of the dataset studied; we suggest this is compatible with previous theoretical findings.