Spiking networks and their rate-based equivalents : does it make sense to use Siegert neurons ?
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Neuronal simulations fall in two broad classes: ones that use spiking neurons and ones that don’t. While spiking models match biology better than rate-based systems, computationally they can be quite expensive. The literature offers some attempts to find and use rate-based neuron models that capture important properties of spiking units. One of the most rigorous approaches [1] approximates the output rate of leaky integrate-and-fire neurons (LIF) for Poisson input trains by analyzing the subthreshold activity of the neuron [2]. This approach, the Siegert neuron, is shown in Fig. 1.
[1] R. Douglas,et al. Recurrent neuronal circuits in the neocortex , 2007, Current Biology.
[2] Nicolas Brunel,et al. Dynamics of a recurrent network of spiking neurons before and following learning , 1997 .
[3] Nicolas Brunel,et al. From Spiking Neuron Models to Linear-Nonlinear Models , 2011, PLoS Comput. Biol..
[4] A. Siegert. On the First Passage Time Probability Problem , 1951 .