Related papers: An integrate-and-fire model to generate spike trai…

Recent years have seen significant progress in developing spiking neural networks (SNNs) as a potential solution to the energy challenges posed by conventional artificial neural networks (ANNs). However, our theoretical understanding of…

This article contains two main theoretical results on neural spike train models. The first assumes that the spike train is modeled as a counting or point process on the real line where the conditional intensity function is a product of a…

We consider a wide class of spiking neuron models, defined by rather general set of conditions typical for basic models like leaky integrate and fire, or binding neuron model. A neuron is fed with a point renewal process. A relation between…

We consider processes with second order long range dependence resulting from heavy tailed durations. We refer to this phenomenon as duration-driven long range dependence (DDLRD), as opposed to the more widely studied linear long range…

Fiber nonlinearities, that lead to nonlinear signal interference (NLI), are typically regarded as an instantaneous material response with respect to the optical field. However, in addition to an instantaneous part, the nonlinear fiber…

There is a wide range of mathematical models that describe populations of large numbers of neurons. In this article, we focus on nonlinear noisy leaky integrate-and-fire (NNLIF) models that describe neuronal activity at the level of the…

Stability arguments are often used to prevent learning algorithms from having ever increasing activity and weights that hinder generalization. However, stability conditions can clash with the sparsity required to augment the energy…

The relative timing of action potentials in neurons recorded from local cortical networks often shows a non-trivial dependence, which is then quantified by cross-correlation functions. Theoretical models emphasize that such spike train…

Measures of linear dependence (coherence) and nonlinear dependence (phase synchronization) between any number of multivariate time series are defined. The measures are expressed as the sum of lagged dependence and instantaneous dependence.…

Spiking Neural Networks (SNNs), inspired by the brain, are characterized by minimal power consumption and swift inference capabilities on neuromorphic hardware, and have been widely applied to various visual perception tasks. Current…

The time elapsed model describes the firing activity of an homogeneous assembly of neurons thanks to the distribution of times elapsed since the last discharge. It gives a mathematical description of the probability density of neurons…

We investigate numerically the collective dynamical behavior of pulse-coupled non-leaky integrate-and-fire-neurons that are arranged on a two-dimensional small-world network. To ensure ongoing activity, we impose a probability for…

We extensively explore networks of weakly unbalanced, leaky integrate-and-fire (LIF) neurons for different coupling strength, connectivity, and by varying the degree of refractoriness, as well as the delay in the spike transmission. We find…

We describe a method to train spiking deep networks that can be run using leaky integrate-and-fire (LIF) neurons, achieving state-of-the-art results for spiking LIF networks on five datasets, including the large ImageNet ILSVRC-2012…

The adaptive leaky integrate-and-fire (ALIF) model is fundamental within computational neuroscience and has been instrumental in studying our brains $\textit{in silico}$. Due to the sequential nature of simulating these neural models, a…

Discrimination between non-stationarity and long-range dependency is a difficult and long-standing issue in modelling financial time series. This paper uses an adaptive spectral technique which jointly models the non-stationarity and…

In this paper we introduce a model, the stochastic fractional delay differential equation (SFDDE), which is based on the linear stochastic delay differential equation and produces stationary processes with hyperbolically decaying…

Measures of multiple spike train synchrony are essential in order to study issues such as spike timing reliability, network synchronization, and neuronal coding. These measures can broadly be divided in multivariate measures and averages…

We establish a general linear response relation for spiking neuronal networks, based on chains with unbounded memory. This relation allows us to predict the influence of a weak amplitude time-dependent external stimuli on spatio-temporal…

For a class of fast {\it Cl-}type inhibitory spiking neuron models with delayed feedback fed with a Poisson stochastic process of excitatory impulses, it is proven that the stream of output interspike intervals cannot be presented as a…