论文标题
随机强迫下旋转器网络的自洽分析理论：内在噪声和共同输入的影响
A self-consistent analytical theory for rotator networks under stochastic forcing: effects of intrinsic noise and common input
论文作者
论文摘要
尽管我们大脑的神经网络的复杂性令人难以置信，但对神经动态的理论描述导致了对可能的网络状态和动态的深刻见解。开发适用于尖峰网络的理论仍然充满挑战，因此使人们可以表征生物学上更现实的网络的动态属性。在这里，我们基于Van Meegen＆Lindner的最新工作，他们表明了“旋转器网络”，虽然比真实的尖峰网络要简单得多，因此更适合数学分析，但仍然允许捕获尖峰神经元网络的动态属性。该框架可以很容易地扩展到单个单元接收不相关的随机输入的情况，而随机输入可以解释为固有的噪声。但是，当单个旋转器收到的输入在单位之间密切相关时，该理论的假设不再适用。如我们所示，在这种情况下，网络波动变得显着非高斯，这要求对该理论进行重新加工。使用累积扩展，我们开发了一种自洽的分析理论，该理论解释了观察到的非高斯统计。我们的理论为进一步研究这些网络的更通用网络设置和信息传输属性提供了一个起点。
Despite the incredible complexity of our brains' neural networks, theoretical descriptions of neural dynamics have led to profound insights into possible network states and dynamics. It remains challenging to develop theories that apply to spiking networks and thus allow one to characterize the dynamic properties of biologically more realistic networks. Here, we build on recent work by van Meegen & Lindner who have shown that "rotator networks," while considerably simpler than real spiking networks and therefore more amenable to mathematical analysis, still allow to capture dynamical properties of networks of spiking neurons. This framework can be easily extended to the case where individual units receive uncorrelated stochastic input which can be interpreted as intrinsic noise. However, the assumptions of the theory do not apply anymore when the input received by the single rotators is strongly correlated among units. As we show, in this case the network fluctuations become significantly non-Gaussian, which calls for a reworking of the theory. Using a cumulant expansion, we develop a self-consistent analytical theory that accounts for the observed non-Gaussian statistics. Our theory provides a starting point for further studies of more general network setups and information transmission properties of these networks.
