STOCHASTIC NEURAL FIELD THEORY AND THE SYSTEM-SIZE EXPANSION
STOCHASTIC NEURAL FIELD THEORY AND THE SYSTEM-SIZE EXPANSION
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DOI：
10.1137/090756971
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发表时间：
2009-01-01
影响因子：
1.9
通讯作者：
Bressloff, Paul C.
中科院分区：
文献类型：
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作者：
Bressloff, Paul C.
我们分析了一个主方程制定的随机神经动力学的突触耦合均匀的神经元群体的网络，每个组成的N个相同的神经元。网络的状态由每个群体中活跃或尖峰神经元的比例指定，并且选择转换速率，使得在热力学或确定性极限（N ->无穷大）中，我们恢复标准的基于活动或基于电压的速率模型。我们推导出最低阶修正这些速率方程大，但有限的N使用两种不同的近似方案，一个是基于货车坎彭系统大小的扩展和其他基于路径积分方法。这两种方法产生相同的级数展开的时刻方程，在O（1/N）可以截断，形成一个封闭的系统的方程的一阶和二阶矩。采取连续极限的时刻方程，同时保持系统的大小N固定生成一个系统的integodifferential方程的平均值和协方差的相应的随机神经场模型。我们还展示了如何路径积分的方法可以用来研究大偏差或罕见的事件统计基本逃离盆地的吸引力的一个稳定的不动点的平均场动力学，这样的分析是不可能使用系统的大小扩展，因为后者不能准确地确定指数小的过渡。
We analyze a master equation formulation of stochastic neurodynamics for a network of synaptically coupled homogeneous neuronal populations each consisting of N identical neurons. The state of the network is specified by the fraction of active or spiking neurons in each population, and transition rates are chosen so that in the thermodynamic or deterministic limit ( N -> infinity) we recover standard activity-based or voltage-based rate models. We derive the lowest order corrections to these rate equations for large but finite N using two different approximation schemes, one based on the Van Kampen system-size expansion and the other based on path integral methods. Both methods yield the same series expansion of the moment equations, which at O(1/N) can be truncated to form a closed system of equations for the first- and second-order moments. Taking a continuum limit of the moment equations while keeping the system size N fixed generates a system of integrodifferential equations for the mean and covariance of the corresponding stochastic neural field model. We also show how the path integral approach can be used to study large deviation or rare event statistics underlying escape from the basin of attraction of a stable fixed point of the mean-field dynamics; such an analysis is not possible using the system-size expansion since the latter cannot accurately determine exponentially small transitions.