Related papers: Characterizing variability in nonlinear recurrent …
Recurrently coupled oscillators that are sufficiently heterogeneous and/or randomly coupled can show an asynchronous activity in which there are no significant correlations among the units of the network. The asynchronous state can…
We have constructed a simple semiclassical model of neural network where neurons have quantum links with one another in a chosen way and affect one another in a fashion analogous to action potentials. We have examined the role of…
Large-scale white matter pathways crisscrossing the cortex create a complex pattern of connectivity that underlies human cognitive function. Generative mechanisms for this architecture have been difficult to identify in part because little…
Realistic networks display heterogeneous transmission delays. We analyze here the limits of large stochastic multi-populations networks with stochastic coupling and random interconnection delays. We show that depending on the nature of the…
A central question in neuroscience is to understand how noisy firing patterns are used to transmit information. Because neural spiking is noisy, spiking patterns are often quantified via pairwise correlations, or the probability that two…
We consider a system of $N$ neurons, each spiking randomly with rate depending on its membrane potential. When a neuron spikes, its potential is reset to $0$ and all other neurons receive an additional amount $h/N$ of potential, where $ h >…
In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature…
We study the stochastic dynamics of strongly-coupled excitable elements on a tree network. The peripheral nodes receive independent random inputs which may induce large spiking events propagating through the branches of the tree and leading…
The Nonlinear Noisy Leaky Integrate and Fire neuronal models are mathematical models that describe the activity of neural networks. These models have been studied at a microscopic level, using Stochastic Differential Equations, and at a…
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…
This paper proposes a flexible framework for inferring large-scale time-varying and time-lagged correlation networks from multivariate or high-dimensional non-stationary time series with piecewise smooth trends. Built on a novel and unified…
We analyze transport on a graph with multiple constraints and where the weight of the edges connecting the nodes is a dynamical variable. The network dynamics results from the interplay between a nonlinear function of the flow, dissipation,…
Stochastic resonance is a non-linear phenomenon, in which the sensitivity of signal detectors can be enhanced by adding random noise to the detector input. Here, we demonstrate that noise can also improve the information flux in recurrent…
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…
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…
Identifying the spatio-temporal network structure of brain activity from multi-neuronal data streams is one of the biggest challenges in neuroscience. Repeating patterns of precisely timed activity across a group of neurons is potentially…
Networks of neurons in some brain areas are flexible enough to encode new memories quickly. Using a standard firing rate model of recurrent networks, we develop a theory of flexible memory networks. Our main results characterize networks…
We present a complete mean field theory for a balanced state of a simple model of an orientation hypercolumn. The theory is complemented by a description of a numerical procedure for solving the mean-field equations quantitatively. With our…
We develop a unified theory that encompasses the macroscopic dynamics of recurrent interactions of binary units within arbitrary network architectures. Using the martingale theory, our mathematical analysis provides a complete description…
Sensory neurons often have variable responses to repeated presentations of the same stimulus, which can significantly degrade the stimulus information contained in those responses. This information can in principle be preserved if…