LAUSR

We consider a class of spiking neuronal models, defined by a set of conditions typical for basic threshold-type models, such as the leaky integrate-and-fire or the binding neuron model and also for some artificial neurons. A neuron is fed with a Poisson process. Each output impulse is applied to the neuron itself after a finite delay Δ. This impulse acts as being delivered through a fast Cl-type inhibitory synapse. We derive a general relation which allows calculating exactly the probability density function (pdf) p(t) of output interspike intervals of a neuron with feedback based on known pdf p0(t) for the same neuron without feedback and on the properties of the feedback line (the Δ value). Similar relations between corresponding moments are derived. Furthermore, we prove that the initial segment of pdf p0(t) for a neuron with a fixed threshold level is the same for any neuron satisfying the imposed conditions and is completely determined by the input stream. For the Poisson input stream, we calculate t...