Related papers: Autonomous learning of nonlocal stochastic neuron …
White noise methods are a powerful tool for characterizing the computation performed by neural systems. These methods allow one to identify the feature or features that a neural system extracts from a complex input, and to determine how…
In a recent study the initial rise of the mutual information between the firing rates of N neurons and a set of p discrete stimuli has been analytically evaluated, under the assumption that neurons fire independently of one another to each…
Neural populations exposed to a certain stimulus learn to represent it better. However, the process that leads local, self-organized rules to do so is unclear. We address the question of how can a neural periodic input be learned and use…
Determining evolution equations governing the probability density function (pdf) of non-Markovian responses to random differential equations (RDEs) excited by coloured noise, is an important issue arising in various problems of stochastic…
Stochastic differential equations are commonly used to describe the evolution of stochastic processes. The state uncertainty of such processes is best represented by the probability density function (PDF), whose evolution is governed by the…
Many systems of partial differential equations have been proposed as simplified representations of complex collective behaviours in large networks of neurons. In this survey, we briefly discuss their derivations and then review the…
Classical nonlinear dynamical systems are often characterized by their steady-state probability distribution functions (PDFs). Typically, PDFs are accumulated from numerical simulations that involve solving the underlying dynamical…
The response of neurons is highly sensitive to the stimulus. The stimulus can be associated with a direct injection in vitro experimentation (e.g., time dependent and independent inputs); or post-synaptic potentials resulting from the…
The Fokker-Planck (FP) equation is a linear partial differential equation which governs the temporal and spatial evolution of the probability density function (PDF) associated with the response of stochastic dynamical systems. An exact…
The response of a neural cell to an external stimulus can follow one of the two patterns: Nonresonant neurons monotonously relax to the resting state after excitation while resonant ones show subthreshold oscillations. We investigate how do…
The Fokker-Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines but it requires specification of the coefficients for each case, which can be functions of space-time and…
We continue the analysis of models of spontaneous wave function collapse with stochastic dynamics driven by non-white Gaussian noise. We specialize to a model in which a classical "noise" field, with specified autocorrelator, is coupled to…
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…
Single neuron models have a long tradition in computational neuroscience. Detailed biophysical models such as the Hodgkin-Huxley model as well as simplified neuron models such as the class of integrate-and-fire models relate the input…
Spiking neural network is a type of artificial neural network in which neurons communicate between each other with spikes. Spikes are identical Boolean events characterized by the time of their arrival. A spiking neuron has internal…
We study a Langevin equation describing the stochastic motion of a particle in one dimension with coordinate $x$, which is simultaneously exposed to a space-dependent friction coefficient $\gamma(x)$, a confining potential $U(x)$ and…
We consider stochastic dynamics of a particle on a plane in presence of two noises and a confining parabolic potential - an analog of the experimentally-relevant Brownian Gyrator (BG) model. In contrast to the standard BG model, we suppose…
Many systems in nature and laboratories are far from equilibrium and exhibit significant fluctuations, invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability…
Neuronal membrane potentials fluctuate stochastically due to conductance changes caused by random transitions between the open and close states of ion channels. Although it has previously been shown that channel noise can nontrivially…
We propose a stochastic dynamical model of noisy neural networks with complex architectures and discuss activation of neural networks by a stimulus, pacemakers and spontaneous activity. This model has a complex phase diagram with…