Related papers: Fast Sparsely Synchronized Brain Rhythms in A Scal…
Sparse neural networks attract increasing interest as they exhibit comparable performance to their dense counterparts while being computationally efficient. Pruning the dense neural networks is among the most widely used methods to obtain a…
We present a simple Markov model of spiking neural dynamics that can be analytically solved to characterize the stochastic dynamics of a finite-size spiking neural network. We give closed-form estimates for the equilibrium distribution,…
We study in this paper the effect of an unique initial stimulation on random recurrent networks of leaky integrate and fire neurons. Indeed given a stochastic connectivity this so-called spontaneous mode exhibits various non trivial…
A complete self-control mechanism is proposed in the dynamics of neural networks through the introduction of a time-dependent threshold, determined in function of both the noise and the pattern activity in the network. Especially for…
We consider a pair of collectively oscillating networks of dynamical elements and optimize their internetwork coupling for efficient mutual synchronization based on the phase reduction theory developed in Ref. [H. Nakao, S. Yasui, M. Ota,…
Using a stochastic generalization of the Hodgkin–Huxley model, we consider the influence of intrinsic channel noise on the synchronization between the spiking activity of the excitable membrane and an externally applied periodic…
In this report trial-to-trial variations in the synchronized responses of neural networks are offered as evidence for excitation-inhibition ratio being a dynamic variable over time scales of minutes. Synchronized network responses to…
We report a new mechanism through which extreme events with a dragon king-like distribution emerge in a network of unidirectional ring of Hindmarsh-Rose bursting neurons interacting through chemical synapses. We establish and substantiate…
We consider two coupled populations of leaky integrate-and-fire neurons. Depending on the coupling strength, mean fields generated by these populations can have incommensurate frequencies, or become frequency locked. In the observed 2:1…
A population of firing neurons is expected to carry not only mean firing rate but also its fluctuation and synchrony among neurons. In order to examine this possibility, we have studied responses of neuronal ensembles to three kinds of…
Recent experiments suggest that inhibitory networks of interneurons can synchronize the neuronal discharge in in vitro hippocampal slices. Subsequent theoretical work has shown that strong synchronization by mutual inhibition is only…
It has been recently reported that explosive synchronization transitions can take place in networks of phase oscillators [G\'omez-Garde\~nes \emph{et al.} Phys.Rev.Letts. 106, 128701 (2011)] and chaotic oscillators [Leyva \emph{et al.}…
Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon…
Suppression of excessively synchronous beta-band oscillatory activity in the brain is believed to suppress hypokinetic motor symptoms of Parkinson's disease. Recently, a lot of interest has been devoted to desynchronizing delayed feedback…
The dynamics of spatially-structured networks of $N$ interacting stochastic neurons can be described by deterministic population equations in the mean-field limit. While this is known, a general question has remained unanswered: does…
Small world networks interpolate between fully regular and fully random topologies and simultaneously exhibit large local clustering as well as short average path length. Small world topology has therefore been suggested to support network…
In this work we study the detection of weak stimuli by spiking neurons in the presence of certain level of noisy background neural activity. Our study has focused in the realistic assumption that the synapses in the network present…
Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can display substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level…
The mathematical theory of pattern formation in electrically coupled networks of excitable neurons forced by small noise is presented in this work. Using the Freidlin-Wentzell large deviation theory for randomly perturbed dynamical systems…
Despite impressive performance, deep neural networks require significant memory and computation costs, prohibiting their application in resource-constrained scenarios. Sparse training is one of the most common techniques to reduce these…