Institut für Physik, Humboldt-Universität zu Berlin, Germany.
Phys Rev E. 2017 Nov;96(5-1):052306. doi: 10.1103/PhysRevE.96.052306. Epub 2017 Nov 6.
We develop a statistical framework for studying recurrent networks with broad distributions of the number of synaptic links per neuron. We treat each group of neurons with equal input degree as one population and derive a system of equations determining the population-averaged firing rates. The derivation rests on an assumption of a large number of neurons and, additionally, an assumption of a large number of synapses per neuron. For the case of binary neurons, analytical solutions can be constructed, which correspond to steps in the activity versus degree space. We apply this theory to networks with degree-correlated topology and show that complex, multi-stable regimes can result for increasing correlations. Our work is motivated by the recent finding of subnetworks of highly active neurons and the fact that these neurons tend to be connected to each other with higher probability.
我们开发了一个统计框架，用于研究具有广泛神经元突触连接数分布的递归网络。我们将每个具有相同输入度的神经元群体视为一个种群，并推导出一组确定种群平均发放率的方程组。该推导基于神经元数量很大的假设，并且还基于神经元中每个神经元的突触数量很大的假设。对于二进制神经元的情况，可以构建解析解，它们对应于活动与度空间中的步骤。我们将此理论应用于具有度相关拓扑的网络，并表明随着相关性的增加，可能会产生复杂的多稳定状态。我们的工作是由最近发现的高度活跃神经元的子网以及这些神经元彼此之间连接的概率更高的事实所驱动的。
