Related papers: Estimating the interaction graph of stochastic neu…
Plasticity is one of the most important properties of the nervous system, which enables animals to adjust their behavior to the ever-changing external environment. Changes in synaptic efficacy between neurons constitute one of the major…
An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad…
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…
In this paper we present a numerical study of a mathematical model of spiking neurons introduced by Ferrari et al. in an article entitled Phase transition forinfinite systems of spiking neurons. In this model we have a countable number of…
In this paper we present a simple microscopic stochastic model describing short term plasticity within a large homogeneous network of interacting neurons. Each neuron is represented by its membrane potential and by the residual calcium…
This paper models the dynamics of a large set of interacting neurons within the framework of statistical field theory. We use a method initially developed in the context of statistical field theory [44] and later adapted to complex systems…
Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous spiking activity. We extend the analysis of balanced networks to include the known dependence of connection probability on the…
We study a stochastic system of interacting neurons and its metastable properties. The system consists of $N$ neurons, each spiking randomly with rate depending on its membrane potential. At its spiking time, the neuron potential is reset…
Understanding how stimuli and synaptic connectivity in uence the statistics of spike patterns in neural networks is a central question in computational neuroscience. Maximum Entropy approach has been successfully used to characterize the…
We consider a new class of non Markovian processes with a countable number of interacting components, both in discrete and continuous time. Each component is represented by a point process indicating if it has a spike or not at a given…
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…
One major challenge in neuroscience is the identification of interrelations between signals reflecting neural activity and how information processing occurs in the neural circuits. At the cellular and molecular level, mechanisms of signal…
We consider a continuous-time stochastic model of spiking neurons. In this model, we have a finite or countable number of neurons which are vertices in some graph $G$ where the edges indicate the synaptic connection between them. We focus…
Spiking activity of neurons engaged in learning and performing a task show complex spatiotemporal dynamics. While the output of recurrent network models can learn to perform various tasks, the possible range of recurrent dynamics that…
We present two Bayesian procedures to infer the interactions and external currents in an assembly of stochastic integrate-and-fire neurons from the recording of their spiking activity. The first procedure is based on the exact calculation…
We study the spike statistics of neurons in a network with dynamically balanced excitation and inhibition. Our model, intended to represent a generic cortical column, comprises randomly connected excitatory and inhibitory leaky…
Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for…
Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active…
The apparent stochasticity of in-vivo neural circuits has long been hypothesized to represent a signature of ongoing stochastic inference in the brain. More recently, a theoretical framework for neural sampling has been proposed, which…
We consider a model of interacting neurons where the membrane potentials of the neurons are described by a multidimensional piecewise deterministic Markov process (PDMP) with values in ${\mathbb R}^N, $ where $ N$ is the number of neurons…