Related papers: On a finite-size neuronal population equation
A complex interplay of single-neuron properties and the recurrent network structure shapes the activity of cortical neurons. The single-neuron activity statistics differ in general from the respective population statistics, including…
Long-range dependence (LRD) has been observed in a variety of phenomena in nature, and for several years also in the spiking activity of neurons. Often, this is interpreted as originating from a non-Markovian system. Here we show that a…
The efficient coding theory postulates that single cells in a neuronal population should be optimally configured to efficiently encode information about a stimulus subject to biophysical constraints. This poses the question of how multiple…
We have proposed a generalized Langevin-type rate-code model subjected to multiplicative noise, in order to study stationary and dynamical properties of an ensemble containing {\it finite} $N$ neurons. Calculations using the Fokker-Planck…
Motivated by applications in reinforcement learning (RL), we study a nonlinear stochastic approximation (SA) algorithm under Markovian noise, and establish its finite-sample convergence bounds under various stepsizes. Specifically, we show…
We consider spatially extended conductance based neuronal models with noise described by a stochastic reaction diffusion equation with additive noise coupled to a control variable with multiplicative noise but no diffusion. We only assume a…
In this paper, we present new results for the synchronization and consensus of networks described by Ito stochastic differential equations. From the methodological viewpoint, our results are based on the use of stochastic Lyapunov…
We analyze the macroscopic behavior of multi-populations randomly connected neural networks with interaction delays. Similar to cases occurring in spin glasses, we show that the sequences of empirical measures satisfy a large deviation…
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…
Maximum entropy methods provide a principled path connecting measurements of neural activity directly to statistical physics models, and this approach has been successful for populations of $N\sim 100$ neurons. As $N$ increases in new…
In this paper, we formulate a stochastic logistic fish growth model driven by both white noise and non-Gaussian noise. We focus our study on the mean time to extinction, escape probability to measure the noise-induced extinction probability…
We consider a pair of stochastic integrate and fire neurons receiving correlated stochastic inputs. The evolution of this system can be described by the corresponding Fokker-Planck equation with non-trivial boundary conditions resulting…
The spiking activity of single neurons can be well described by a nonlinear integrate-and-fire model that includes somatic adaptation. When exposed to fluctuating inputs sparsely coupled populations of these model neurons exhibit stochastic…
We present a stochastic version of the Cucker-Smale flocking dynamics based on a markovian $N$-particle system of pair interactions with unbounded and, in general, non-Lipschitz continuous interaction potential. We establish the infinite…
Spiking Neural Networks (SNNs) draw inspiration from biological neurons to enable brain-like computation, demonstrating effectiveness in processing temporal information with energy efficiency and biological realism. Most existing SNNs are…
Spiking neural networks (SNNs) are posited as a computationally efficient and biologically plausible alternative to conventional neural architectures, with their core computational framework primarily using the leaky integrate-and-fire…
Motivated by experimental observations, we investigate a variant of the cocktail party problem: the detection of a weak periodic stimulus in the presence of fluctuations and another periodic stimulus which is stronger than the periodic…
We demonstrate that waves in distinct layers of a neuronal network can become phase-locked by common spatiotemporal noise. This phenomenon is studied for stationary bumps, traveling waves, and breathers. A weak noise expansion is used to…
We study the mean-field limit and stationary distributions of a pulse-coupled network modeling the dynamics of a large neuronal assemblies. Our model takes into account explicitly the intrinsic randomness of firing times, contrasting with…
In this note, we develop semi-analytical techniques to obtain the full correlational structure of a stochastic network of nonlinear neurons described by rate variables. Under the assumption that pairs of membrane potentials are jointly…