Related papers: Leaky Integrate-and-Fire Neuron under Poisson Stim…
Many systems are modulated by unknown slow processes. This hinders analysis in highly non-linear systems, such as excitable systems. We show that for such systems, if the input matches the sparse `spiky' nature of the output, the spiking…
Spintronics is an important emerging technology for data storage and computation. In this field, magnetic skyrmion-based devices are attractive due to their small size and energy consumption. However, controlling the creation, deletion and…
Compared with rate-based artificial neural networks, Spiking Neural Networks (SNN) provide a more biological plausible model for the brain. But how they perform supervised learning remains elusive. Inspired by recent works of Bengio et al.,…
A compound Poisson process whose randomized time is an independent Poisson process is called compound Poisson process with Poisson subordinator. We provide its probability distribution, which is expressed in terms of the Bell polynomials,…
Spike-train responses of single Hodgkin-Huxley (HH) and integrate-and-fire (IF) neurons with and without the refractory period, are calculated and compared. The HH and IF neurons are assumed to receive spike-train inputs with the constant…
In an all-to-all network of integrate-fire oscillators in which there is a disorder in the intrinsic firing rates of the neurons, we show that through spike timing-dependent plasticity the links which have the faster oscillators as…
Starting from a spectral expansion of the Fokker-Plank equation for the membrane potential density in a network of spiking neurons, a low-dimensional dynamics of the collective firing rate is derived. As a result a $n$-order ordinary…
This paper suggests a learning-theoretic perspective on how synaptic plasticity benefits global brain functioning. We introduce a model, the selectron, that (i) arises as the fast time constant limit of leaky integrate-and-fire neurons…
Non-homogeneous Poisson processes are used in a wide range of scientific disciplines, ranging from the environmental sciences to the health sciences. Often, the central object of interest in a point process is the underlying intensity…
We consider a finite system of interacting point processes with memory of variable length modeling a finite but large network of spiking neurons with two different leakage mechanisms. Associated to each neuron there are two point processes,…
Striatal projection neurons form a sparsely-connected inhibitory network, and this arrangement may be essential for the appropriate temporal organization of behavior. Here we show that a simplified, sparse inhibitory network of…
Spiking Neural Networks (SNN) exhibit higher energy efficiency compared to Artificial Neural Networks (ANN) due to their unique spike-driven mechanism. Additionally, SNN possess a crucial characteristic, namely the ability to process…
By recording multiple cells simultaneously, electrophysiologists have found evidence for repeating spatiotemporal spike patterns, which can carry information. How this information is extracted by downstream neurons is unclear. In this…
We report about the main dynamical features of a model of leaky-integrate-and fire excitatory neurons with short term plasticity defined on random massive networks. We investigate the dynamics by a Heterogeneous Mean-Field formulation of…
Neurons fire irregularly on multiple timescales when stimulated with a periodic pulse train. This raises two questions: Does this irregularity imply significant intrinsic stochasticity? Can existing neuron models be readily extended to…
We show that \emph{stochastic bursting} is observed in a ring of unidirectional delay-coupled noisy excitable systems, thanks to the combinational action of time-delayed coupling and noise. Under the approximation of timescale separation,…
We consider a sparse random network of excitatory leaky integrate-and-fire neurons with short-term synaptic depression. Furthermore to mimic the dynamics of a brain circuit in its first stages of development we introduce for each neuron…
We present a first-order non-homogeneous Markov model for the interspike-interval density of a continuously stimulated spiking neuron. The model allows the conditional interspike-interval density and the stationary interspike-interval…
In this work, based on a realization of an inhomogeneous Poisson process whose intensity function depends on a real unknown parameter, we consider a simple hypothesis against a sequence of close (contiguous) alternatives. Under certain…
A recent study on the effect of colored driving noise on the escape from a metastable state derives an analytic expression of the transfer function of the leaky integrate-and-fire neuron model subject to colored noise. Here we present an…