Related papers: Linear response for spiking neuronal networks with…
Models of neural responses to stimuli with complex spatiotemporal correlation structure often assume that neurons are only selective for a small number of linear projections of a potentially high-dimensional input. Here we explore recent…
Although recent neurophysiological experiments suggest that synchronous neural activity is involved in some perceptual and cognitive processes, the functional role of such coherent neuronal behavior is not well understood. As a first step…
The synergy between spiking neural networks and neuromorphic hardware holds promise for the development of energy-efficient AI applications. Inspired by this potential, we revisit the foundational aspects to study the capabilities of…
Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…
One of the fundamental characteristics of a nonlinear system is how it transfers correlations in its inputs to correlations in its outputs. This is particularly important in the nervous system, where correlations between spiking neurons are…
The present paper provides exact mathematical expressions for the high-order moments of spiking activity in a recurrently-connected network of linear Hawkes processes. It extends previous studies that have explored the case of a (linear)…
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…
Stochastic integrate-and-fire (IF) neuron models have found widespread applications in computational neuroscience. Here we present results on the white-noise-driven perfect, leaky, and quadratic IF models, focusing on the spectral…
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…
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…
Spike generation in neurons produces a temporal point process, whose statistics is governed by intrinsic phenomena and the external incoming inputs to be coded. In particular, spike-evoked adaptation currents support a slow temporal process…
The binding neuron model is inspired by numerical simulation of Hodgkin-Huxley-type point neuron, as well as by the leaky integrate-and-fire model. In the binding neuron, the trace of an input is remembered for a fixed period of time after…
Spiking neural networks (SNNs) are posited as a computationally efficient and biologically plausible alternative to conventional neural architectures, with their core computational framework primarily using the leaky integrate-and-fire…
The dynamical responses of complex neuronal networks to external stimulus injected on a \emph{single} neuron are investigated. Stimulating the largest-degree neuron in the network, it is found that as the intensity of the stimulus…
Implementations of spiking neural networks on neuromorphic hardware promise orders of magnitude less power consumption than their non-spiking counterparts. The standard neuron model for spike-based computation on such systems has long been…
We construct a model that predicts the statistical properties of spike trains generated by a sensory neuron. The model describes the combined effects of the neuron's intrinsic properties, the noise in the surrounding, and the external…
Many neural systems display cascading behavior characterized by uninterrupted sequences of neuronal firing. This gap precludes an understanding of how variations in network structure manifest in neural dynamics and either support or impinge…
This is a continuation of a recent study on the modeling of the information coding in sensory system in the brain. The data from a sensory neurons are available as discrete spike timings with no amplitude information. In the simulations,…
Generalized linear models are one of the most efficient paradigms for predicting the correlated stochastic activity of neuronal networks in response to external stimuli, with applications in many brain areas. However, when dealing with…
We consider a conductance based neural network inspired by the generalized Integrate and Fire model introduced by Rudolph and Destexhe. We show the existence and uniqueness of a unique Gibbs distribution characterizing spike train…