Cardanobile Stefano, Rotter Stefan
BCCN & Faculty of Biology, Albert-Ludwig University Freiburg, Freiburg, Germany.
J Comput Neurosci. 2010 Apr;28(2):267-84. doi: 10.1007/s10827-009-0204-0. Epub 2010 Jan 6.
We introduce a nonlinear modification of the classical Hawkes process allowing inhibitory couplings between units without restrictions. The resulting system of interacting point processes provides a useful mathematical model for recurrent networks of spiking neurons described as Wiener cascades with exponential transfer function. The expected rates of all neurons in the network are approximated by a first-order differential system. We study the stability of the solutions of this equation, and use the new formalism to implement a winner-takes-all network that operates robustly for a wide range of parameters. Finally, we discuss relations with the generalised linear model that is widely used for the analysis of spike trains.
我们引入了经典霍克斯过程的非线性修正，允许单元之间无限制地存在抑制性耦合。由此产生的相互作用点过程系统为作为具有指数传递函数的维纳级联描述的脉冲神经元递归网络提供了一个有用的数学模型。网络中所有神经元的预期速率由一个一阶微分系统近似。我们研究了该方程解的稳定性，并使用新形式主义实现了一个赢家通吃网络，该网络在广泛的参数范围内都能稳健运行。最后，我们讨论了与广泛用于分析脉冲序列的广义线性模型的关系。
