First passage time distribution for spiking neuron with delayed excitatory feedback
A class of spiking neuronal models with threshold 2 is considered. It is defined by a set of conditions typical for basic threshold-type models, such as the leaky integrate-and-fire (LIF) or the binding neuron model and also for some artificial neurons. A neuron is stimulated with a Poisson stream of excitatory impulses. Each output impulse is conveyed through the feedback line to the neuron input after finite delay $\Delta$. This impulse is identical to those delivered from the input stream. We have obtained a general relation allowing calculating exactly the probability density function (PDF) $p(t)$ for distribution of the first passage time of crossing the threshold, which is the distribution of output interspike intervals (ISI) values for this neuron. The calculation is based on known PDF $p^0(t)$ for that same neuron without feedback, intensity of the input stream $\lambda$ and properties of the feedback line. Also, we derive exact relation for calculating the moments of $p(t)$ based on known moments of $p^0(t)$. The obtained general expression for $p(t)$ is checked numerically using Monte Carlo simulation for the case of LIF model. The course of $p(t)$ has a $\delta$-function type peculiarity. This fact contributes to the discussion about the possibility to model neuronal activity with Poisson process, supporting the "no" answer.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
A `Rosetta stone' for the population dynamics of spiking neuron networks
Populations of spiking neuron models have densities of their microscopic variables (e.g., single-cell membrane potentials) whose evolution fully capture the collective dynamics of biological networks, even outside equili…
Matched transient and steady-state approximation of first-passage-time distributions of coloured noise driven leaky neurons
The first-passage-time distribution of a leaky integrate-and-fire neuron driven by a characteristically coloured noise is approximated by matching a transient and a steady-state solution of the membrane voltage distribut…
Ternary Spiking Neural Networks Enhanced by Complemented Neurons and Membrane Potential Aggregation
Spiking Neural Networks (SNNs) are promising energy-efficient models and powerful framworks of modeling neuron dynamics. However, existing binary spiking neurons exhibit limited biological plausibilities and low informat…
Counting to Ten with Two Fingers: Compressed Counting with Spiking Neurons
We consider the task of measuring time with probabilistic threshold gates implemented by bio-inspired spiking neurons. In the model of spiking neural networks, network evolves in discrete rounds, where in each round, neu…
Vocal Bursts Valence PredictionNeuronal calculus for the auditory pathway
The first steps in the neural processing of sound are located in the auditory nerve and in the cochlear nuclei. To model the signal processing efficiently, we propose a simple mathematical tool that takes the minute timi…