Related papers: Poisson Hypothesis and large-population limit for …
Neural computations arising from myriads of interactions between spiking neurons can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this…
Network dynamics with point-process-based interactions are of paramount modeling interest. Unfortunately, most relevant dynamics involve complex graphs of interactions for which an exact computational treatment is impossible. To circumvent…
Many phenomena can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this difficulty, the Poisson Hypothesis regime replaces interaction…
We study the mean-field limit of a model of biological neuron networks based on the so-called stochastic integrate-and-fire (IF) dynamics. Our approach allows to derive a continuous limit for the macroscopic behavior of the system, the…
We investigate the dynamics of large-scale interacting neural populations, composed of conductance based, spiking model neurons with modifiable synaptic connection strengths, which are possibly also subjected to external noisy currents. The…
Neural computations emerge from myriads of neuronal interactions occurring in intricate spiking networks. Due to the inherent complexity of neural models, relating the spiking activity of a network to its structure requires simplifying…
This article presents a biological neural network model driven by inhomogeneous Poisson processes accounting for the intrinsic randomness of synapses. The main novelty is the introduction of local interactions: each firing neuron triggers…
We continue the work of a series of previous studies of a mathematical model that describes the mean-field limit behavior of a homogeneous network of excitatory point spiking neurons. Contrary to other models, here noise is intrinsic to the…
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…
Population equations for infinitely large networks of spiking neurons have a long tradition in theoretical neuroscience. In this work, we analyze a recent generalization of these equations to populations of finite size, which takes the form…
In this paper we prove the Poisson Hypothesis for the limiting behavior of the large queueing systems in some simple ("mean-field") cases. We show in particular that the corresponding dynamical systems, defined by the non-linear Markov…
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…
A key problem in computational neuroscience is to find simple, tractable models that are nevertheless flexible enough to capture the response properties of real neurons. Here we examine the capabilities of recurrent point process models…
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…
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,…
The activity of a sparse network of leaky integrate-and-fire neurons is carefully revisited with reference to a regime of a bona-fide asynchronous dynamics. The study is preceded by a finite-size scaling analysis, carried out to identify a…
We study the solutions of a McKean-Vlasov stochastic differential equation (SDE) driven by a Poisson process. In neuroscience, this SDE models the mean field limit of a system of $N$ interacting excitatory neurons with $N$ large. Each…
We investigate a stochastic network composed of Integrate-and-Fire spiking neurons, focusing on its mean-field asymptotics. We consider an invariant probability measure of the McKean-Vlasov equation and establish an explicit sufficient…
We prove that the general mean-field type networks at low load behave in accordance with the Poisson Hypothesis. That means that the network equilibrates in time independent of its size. This is a "high-temperature" counterpart of our…
Coarse-graining microscopic models of biological neural networks to obtain mesoscopic models of neural activities is an essential step towards multi-scale models of the brain. Here, we extend a recent theory for mesoscopic population…