论文标题
结构化旋转器网络的异步理论及其在兴奋性和抑制单位的复发网络中的应用
Theory of the asynchronous state of structured rotator networks and its application to recurrent networks of excitatory and inhibitory units
论文作者
论文摘要
反复耦合的振荡器是足够异质和/或随机耦合的振荡器，可以显示出异步活动，其中网络单位之间没有显着相关性。但是，异步状态仍然可以表现出丰富的时间相关统计数据，这通常很难在理论上捕获。对于随机耦合旋转器网络，可以得出确定网络噪声和网络中单个元素的自相关函数的微分方程。到目前为止，该理论仅限于统计上均匀的网络，因此很难将此框架应用于现实世界网络，这些框架是根据单个单元及其连接性构建的。一个特别引人注目的情况是神经网络必须区分兴奋性和抑制性神经元，这将其靶神经元推向或远离触发阈值。为了考虑到这样的网络结构，在这里我们将旋转器网络的理论扩展到多个人群的情况。具体而言，我们得出了一个微分方程的系统，该系统控制相应人群中网络波动的自洽自相关函数。然后，我们将这种一般理论应用于平衡案例中兴奋性和抑制单位的复发网络的特殊但重要的情况，并将我们的理论与数值模拟进行比较。我们通过将我们的结果与缺乏内部结构的等效均匀网络进行比较来检查网络结构对噪声统计的影响。我们的结果表明，振荡器类型的结构化连通性和异质性既可以增强或降低产生的网络噪声的总体强度并塑造其时间相关性。
Recurrently coupled oscillators that are sufficiently heterogeneous and/or randomly coupled can show an asynchronous activity in which there are no significant correlations among the units of the network. The asynchronous state can nevertheless exhibit a rich temporal correlation statistics, that is generally difficult to capture theoretically. For randomly coupled rotator networks, it is possible to derive differential equations that determine the autocorrelation functions of the network noise and of the single elements in the network. So far, the theory has been restricted to statistically homogeneous networks, making it difficult to apply this framework to real-world networks, which are structured with respect to the properties of the single units and their connectivity. A particularly striking case are neural networks for which one has to distinguish between excitatory and inhibitory neurons, which drive their target neurons towards or away from firing threshold. To take into account network structures like that, here we extend the theory for rotator networks to the case of multiple populations. Specifically, we derive a system of differential equations that govern the self-consistent autocorrelation functions of the network fluctuations in the respective populations. We then apply this general theory to the special but important case of recurrent networks of excitatory and inhibitory units in the balanced case and compare our theory to numerical simulations. We inspect the effect of the network structure on the noise statistics by comparing our results to the case of an equivalent homogeneous network devoid of internal structure. Our results show that structured connectivity and heterogeneity of the oscillator type can both enhance or reduce the overall strength of the generated network noise and shape its temporal correlations.
