Related papers: Self-consistent formulations for stochastic nonlin…
We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar…
Stochastic resonance (SR) is a well known phenomenon in dynamical systems. It consists of the amplification and optimization of the response of a system assisted by stochastic noise. Here we carry out the first experimental study of SR in…
Noise can shape the firing behaviors of neurons. Here, we show that noise acting on the fast variable of the Hedgehog burster can tune the spike counts of bursts via the self-induced stochastic resonance (SISR) phenomenon. Using the…
Artificial neural networks can harness stochasticity in multiple ways to enable a vast class of computationally powerful models. Electronic implementation of such stochastic networks is currently limited to addition of algorithmic noise to…
We analyze the effects of spatiotemporal noise on stationary pulse solutions (bumps) in neural field equations on planar domains. Neural fields are integrodifferential equations whose integral kernel describes the strength and polarity of…
In this manuscript we analyze the collective behavior of mean-field limits of large-scale, spatially extended stochastic neuronal networks with delays. Rigorously, the asymptotic regime of such systems is characterized by a very intricate…
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 phenomena that emerge from the interaction of the stochastic opening and closing of ion channels (channel noise) with the non-linear neural dynamics are essential to our understanding of the operation of the nervous system. The effects…
We consider a system of nonlinear partial differential equations with stochastic dynamical boundary conditions that arises in models of neurophysiology for the diffusion of electrical potentials through a finite network of neurons.…
Intrinsic stochasticity can induce highly non-trivial effects on dynamical systems, including stochastic and coherence resonance, noise induced bistability, noise-induced oscillations, to name but a few. In this paper we revisit a mechanism…
While deep learning methods have achieved strong performance in time series prediction, their black-box nature and inability to explicitly model underlying stochastic processes often limit their generalization to non-stationary data,…
Stochastic resonance holds much promise for the detection of weak signals in the presence of relatively loud noise. Following the discovery of nondynamical and of aperiodic stochastic resonance, it was recently shown that the phenomenon can…
This paper is concerned with the stochastic thermodynamics of non-equilibrium Gaussian processes that can exhibit anomalous diffusion. In the systems considered, the noise correlation function is not necessarily related to friction. Thus,…
We consider a stochastic version of an excitable system based on the Morris-Lecar model of a neuron, in which the noise originates from stochastic Sodium and Potassium ion channels opening and closing. One can analyze neural excitability in…
Experimental research has shown that the brain's fast electrochemical dynamics, or neurodynamics (ND), is strongly stochastic, chaotic, and instanton (neuroavalanche)-dominated. It is also partly scale-invariant which has been loosely…
This paper is devoted to studying the Onsager-Machlup functional for stochastic differential equations with time-varying noise of the {\alpha}-H\"older, 0<{\alpha}<1/4, dXt =f(t,Xt)dt+g(t)dWt. Our study focuses on scenarios where the…
Populations of spiking neuron models have densities of their microscopic variables (e.g., single-cell membrane potentials) whose evolution fully capture the collective dynamics of biological networks, even outside equilibrium. Despite its…
Starting at the mesoscopic level with a general formulation of stochastic thermodynamics in terms of Markov jump processes, we identify the scaling conditions that ensure the emergence of a (typically nonlinear) deterministic dynamics and…
The ability of a brain or a neural network to efficiently learn depends crucially on both the task structure and the learning rule. Previous works have analyzed the dynamical equations describing learning in the relatively simplified…
The spatiotemporal nature of neuronal behavior in spiking neural networks (SNNs) make SNNs promising for edge applications that require high energy efficiency. To realize SNNs in hardware, spintronic neuron implementations can bring…