Related papers: Quantitative and qualitative analysis of asynchron…
Large sparse circuits of spiking neurons exhibit a balanced state of highly irregular activity under a wide range of conditions. It occurs likewise in sparsely connected random networks that receive excitatory external inputs and recurrent…
Novel experimental techniques reveal the simultaneous activity of larger and larger numbers of neurons. As a result there is increasing interest in the structure of cooperative -- or correlated -- activity in neural populations, and in the…
We consider a ring network of quadratic integrate-and-fire neurons with nonlocal synaptic and gap junction coupling. The corresponding neural field model supports solutions such as standing and travelling waves, and also lurching waves. We…
Neural network dynamics emerge from the interaction of spiking cells. One way to formulate the problem is through a theoretical framework inspired by ideas coming from statistical physics, the so-called mean-field theory. In this document,…
Synchronous firing of neurons is thought to play important functional roles such as feature binding and switching of cognitive states. Although synchronization has mainly been investigated using model neurons with simple connection topology…
We present a mathematical analysis of a networks with Integrate-and-Fire neurons and adaptive conductances. Taking into account the realistic fact that the spike time is only known within some \textit{finite} precision, we propose a model…
We study mean-field descriptions for spatially-extended networks of linear (leaky) and quadratic integrate-and-fire neurons with stochastic spiking times. We consider large-population limits of continuous-time Galves-L\"ocherbach (GL)…
The highly variable dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference but stand in apparent contrast to the deterministic response of neurons measured in vitro.…
In a first step towards the comprehension of neural activity, one should focus on the stability of the various dynamical states. Even the characterization of idealized regimes, such as a perfectly periodic spiking activity, reveals…
The statistics of correlations are central quantities characterizing the collective dynamics of recurrent neural networks. We derive exact expressions for the statistics of correlations of nonlinear recurrent networks in the limit of a…
All higher order central nervous systems exhibit spontaneous neural activity, though the purpose and mechanistic origin of such activity remains poorly understood. We explore the ignition and spread of collective spontaneous…
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…
We show that \emph{stochastic bursting} is observed in a ring of unidirectional delay-coupled noisy excitable systems, thanks to the combinational action of time-delayed coupling and noise. Under the approximation of timescale separation,…
Networks of randomly connected neurons are among the most popular models in theoretical neuroscience. The connectivity between neurons in the cortex is however not fully random, the simplest and most prominent deviation from randomness…
In this paper, we clarify the mechanisms underlying a general phenomenon present in pulse-coupled heterogeneous inhibitory networks: inhibition can induce not only suppression of the neural activity, as expected, but it can also promote…
Neuronal ensemble activity, including coordinated and oscillatory patterns, exhibits hallmarks of nonequilibrium systems with time-asymmetric trajectories to maintain their organization. However, assessing time asymmetry from neuronal…
In a recent work, mean-field analysis and computer simulations were employed to analyze critical self-organization in networks of excitable cellular automata where randomly chosen synapses in the network were depressed after each spike (the…
Despite the huge number of neurons composing a brain network, ongoing activity of local cell assemblies composing cortical columns is intrinsically stochastic. Fluctuations in their instantaneous rate of spike firing $\nu(t)$ scale with the…
Mesoscopic models of finite-size neuronal populations are crucial to understand the dynamics of neural networks in the brain, especially their fluctuations and response to stimuli. However, current theories to derive such models are based…
The study of balanced networks of excitatory and inhibitory neurons has led to several open questions. On the one hand it is yet unclear whether the asynchronous state observed in the brain is autonomously generated, or if it results from…