Critical states are sometimes identified experimentally through power-law statistics or
universal scaling functions. We show here that such features naturally emerge from …

The neural dynamics generating sensory, motor, and cognitive functions are commonly
understood through field theories for neural population activity. Classic neural field theories …

The dynamics of exchangeable or spatially-structured networks of $ N $ interacting
stochastic neurons can be described by deterministic population equations in the mean-field …

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 …

The spiking activity of neocortical neurons exhibits a striking level of variability, even when
these networks are driven by identical stimuli. The approximately Poisson firing of neurons …

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 …

Motivated by several applications, including neuronal models, we consider the McKean–
Vlasov limit for a general class of mean-field systems of interacting diffusions characterized …

Neural computations emerge from myriad neuronal interactions occurring in intricate spiking
networks. Due to the inherent complexity of neural models, relating the spiking activity of a …

We study a stochastic process describing the continuous time evolution of the membrane
potentials of finite system of neurons in the absence of external stimuli. The values of the …

In neuroscience, learning and memory are usually associated with long-term changes in
neuronal connectivity. In this context, synaptic plasticity refers to the set of mechanisms …