Derived from spiking neuron models via the diffusion approximation, the moment activation (MA) faithfully captures the nonlinear coupling of correlated neural variability. However, numerical evaluation of the MA faces significant challenges due to a number of ill-conditioned Dawson-like functions. By deriving asymptotic expansions of these functions, we develop an efficient numerical algorithm for evaluating the MA and its derivatives ensuring reliability, speed, and accuracy. We also provide exact analytical expressions for the MA in the weak fluctuation limit. Powered by this efficient algorithm, the MA may serve as an effective tool for investigating the dynamics of correlated neural variability in large-scale spiking neural circuits.
翻译:从通过扩散近似法跳出的神经模型中产生的神经模型,即激活(MA)时刻忠实地捕捉了相关神经变异的非线性连接。然而,由于若干条件不完善的道森类似功能,对MA的数值评估面临重大挑战。通过生成这些功能的无症状扩展,我们开发了一个高效的数字算法,用于评估MA及其衍生物,确保可靠性、速度和准确性。我们还在微弱的波动限度内为MA提供精确的分析表达。借助这一高效的算法,MA可以作为一个有效的工具,用于调查大规模神经循环中相互关联的神经变异动态。