Related papers: First passage time distribution for spiking neuron…
Spiking neural networks (SNNs) process time-series data via internal event-driven neural dynamics. The energy consumption of an SNN depends on the number of spikes exchanged between neurons over the course of the input presentation.…
Often sharp changes in cellular behavior are triggered by thresholded events, i.e., by the attainment of a threshold value of a relevant cellular or molecular dynamical variable. Since the governing variable itself typically undergoes noisy…
We consider a bivariate diffusion process and we study the first passage time of one component through a boundary. We prove that its probability density is the unique solution of a new integral equation and we propose a numerical algorithm…
The paper addresses the problem of calculating the noise-induced switching rates in systems with delay-distributed kernels and Gaussian noise. A general variational formulation for the switching rate is derived for any distribution kernel,…
We examine how the prior probability distribution of a sensory variable in the environment influences the optimal allocation of neurons and spikes in a population that represents that variable. We start with a conventional response model,…
Neural computations arising from myriads of interactions between spiking neurons can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this…
Spiking neural networks (SNNs) are distributed trainable systems whose computing elements, or neurons, are characterized by internal analog dynamics and by digital and sparse synaptic communications. The sparsity of the synaptic spiking…
We derive expressions for the first three moments of the decision time (DT) distribution produced via first threshold crossings by sample paths of a drift-diffusion equation. The "pure" and "extended" diffusion processes are widely used to…
In Part I of this paper, we presented a mathematical model for communication subject to both network interference and noise, where the interferers are scattered according to a spatial Poisson process, and are operating asynchronously in a…
Permutation tests have been proposed by Albert et al. (2015) to detect dependence between point processes, modeling in particular spike trains, that is the time occurrences of action potentials emitted by neurons. Our present work focuses…
The biologically inspired spiking neurons used in neuromorphic computing are nonlinear filters with dynamic state variables -- very different from the stateless neuron models used in deep learning. The next version of Intel's neuromorphic…
Spiking Neural Networks (SNNs) are distributed trainable systems whose computing elements, or neurons, are characterized by internal analog dynamics and by digital and sparse synaptic communications. The sparsity of the synaptic spiking…
Cortical neurons include many sub-cellular processes, operating at multiple timescales, which may affect their response to stimulation through non-linear and stochastic interaction with ion channels and ionic concentrations. Since new…
An inverse procedure is proposed and tested which aims at recovering the a priori unknown functional and structural information from global signals of living brains activity. To this end we consider a Leaky-Integrate and Fire (LIF) model…
Spiking Neural Networks (SNNs) are a promising framework for event-driven temporal processing. Prior work has improved temporal modeling through richer neuron dynamics and network-level mechanisms such as recurrence and delays, but it…
This study proposes a framework that extends existing time-coding time-to-first-spike spiking neural network (SNN) models to allow processing information changing over time. We explain spike propagation through a model with multiple input…
The first-passage time (FPT), i.e., the moment when a stochastic process reaches a given threshold value for the first time, is a fundamental mathematical concept with immediate applications. In particular, it quantifies the statistics of…
The result of computational operations performed at the single cell level are coded into sequences of action potentials (APs). In the cerebral cortex, due to its columnar organization, large number of neurons are involved in any individual…
We study the dynamics of excitable integrate-and-fire neurons in a small-world network. At low densities $p$ of directed random connections, a localized transient stimulus results in either self-sustained persistent activity or in a brief…
We consider here a single-compartment model of these neurons which is capable of describing many of the known features of spike generation, particularly the slow rhythmic pacemaking activity often observed in these cells in a variety of…