Related papers: Linear response in neuronal networks: from neurons…

When a neuron fires and the resulting action potential travels down its axon toward other neurons' dendrites, the effect on each of those neurons is mediated by the weight of the synapse that separates it from the firing neuron. This…

Local patterns of excitation and inhibition that can generate neural waves are studied as a computational mechanism underlying the organization of neuronal tunings. Sparse coding algorithms based on networks of excitatory and inhibitory…

The relation between spontaneous and stimulated brain activity is a fundamental question in neuroscience, which has received wide attention in experimental studies. Recently, it has been suggested that the evoked response to external…

One of the most important challenges in mathematical neuroscience is to properly illustrate the stochastic nature of neurons. Among different approaches, the noisy leaky integrate-and-fire and the escape rate models are probably the most…

Realizations of low firing rates in neural networks usually require globally balanced distributions among excitatory and inhibitory links, while feasibility of temporal coding is limited by neuronal millisecond precision. We show that…

Deep neural networks give us a powerful method to model the training dataset's relationship between input and output. We can regard that as a complex adaptive system consisting of many artificial neurons that work as an adaptive memory as a…

In many cases, the computation of a neural system can be reduced to a receptive field, or a set of linear filters, and a thresholding function, or gain curve, which determines the firing probability; this is known as a linear/nonlinear…

This paper presents an overview of some techniques and concepts coming from dynamical system theory and used for the analysis of dynamical neural networks models. In a first section, we describe the dynamics of the neuron, starting from the…

The dynamics of neural networks is often characterized by collective behavior and quasi-synchronous events, where a large fraction of neurons fire in short time intervals, separated by uncorrelated firing activity. These global temporal…

In this note, we develop semi-analytical techniques to obtain the full correlational structure of a stochastic network of nonlinear neurons described by rate variables. Under the assumption that pairs of membrane potentials are jointly…

This paper introduces a class of stochastic models of interacting neurons with emergent dynamics similar to those seen in local cortical populations, and compares them to very simple reduced models driven by the same mean excitatory and…

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…

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,…

A model for directed networks is proposed and power laws for their in-degree and/or out-degree distributions are derived from the model. It is based on the Barabasi-Albert model and contains two parameters. The parameters serve as…

We present a theoretical study aiming at model fitting for sensory neurons. Conventional neural network training approaches are not applicable to this problem due to lack of continuous data. Although the stimulus can be considered as a…

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…

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…

In this paper a theoretical model of functioning of a neural circuit during a behavioral response has been proposed. A neural circuit can be thought of as a directed multigraph whose each vertex is a neuron and each edge is a synapse. It…

The paper examines the discrete-time dynamics of neuron models (of excitatory and inhibitory types) with piecewise linear activation functions, which are connected in a network. The properties of a pair of neurons (one excitatory and the…

The mathematical theory of quantum feedback networks has recently been developed for general open quantum dynamical systems interacting with bosonic input fields. In this article we show, for the special case of linear dynamical systems…