Spatiotemporal correlations in brain activity are functionally important and have been implicated in perception, learning and plasticity, exploratory behavior, and various aspects of cognition. Neurons in the cerebral cortex are strongly interacting. Their activity is temporally irregular and can exhibit substantial correlations. However, how the collective dynamics of highly recurrent and strongly interacting neurons can evolve into a state in which the activity of individual cells is highly irregular yet macroscopically correlated is an open question. Here, we develop a general theory that relates the strength of pairwise correlations to the anatomical features of networks of strongly coupled neurons. To this end, we investigate networks of binary units. When interactions are strong, the activity is irregular in a large region of parameter space. We find that despite the strong interactions, the correlations are generally very weak. Nevertheless, we identify architectural features, which if present, give rise to strong correlations without destroying the irregularity of the activity. For networks with such features, we determine how correlations scale with the network size and the number of connections. Our work shows the mechanism by which strong correlations can be consistent with highly irregular activity, two hallmarks of neuronal dynamics in the central nervous system.

中文翻译：

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强循环神经元网络中的相关强度。

大脑活动的时空相关在功能上很重要，并且与感知，学习和可塑性，探索行为以及认知的各个方面有关。大脑皮层中的神经元相互作用强烈。它们的活动在时间上是不规则的，并且可能表现出实质的相关性。然而，高度复发和强烈相互作用的神经元的集体动力学如何演变成单个细胞的活性高度不规则而宏观相关的状态是一个悬而未决的问题。在这里，我们发展了一个一般的理论，将成对相关的强度与强耦合神经元网络的解剖特征相关联。为此，我们研究了二进制单位的网络。当交互作用很强时，活动在很大的参数空间区域中是不规则的。我们发现，尽管相互作用很强，但相关性通常非常弱。但是，我们确定了体系结构特征，如果存在这些特征，则会在不破坏活动不规则性的情况下产生很强的相关性。对于具有此类功能的网络，我们确定相关性如何随网络规模和连接数扩展。我们的工作显示了强相关性可以与高度不规则活动相一致的机制，高度不规则活动是中枢神经系统中神经元动力学的两个标志。我们确定相关性如何随网络规模和连接数扩展。我们的工作显示了强相关性可以与高度不规则活动相一致的机制，高度不规则活动是中枢神经系统中神经元动力学的两个标志。我们确定相关性如何随网络规模和连接数扩展。我们的工作显示了强相关性可以与高度不规则活动相一致的机制，高度不规则活动是中枢神经系统中神经元动力学的两个标志。