Related papers: Autonomous learning of nonlocal stochastic neuron …
Many natural phenomena exhibit a stochastic nature that one attempts at modeling by using stochastic processes of different types. In this context, often one is interested in investigating the memory properties of the natural phenomenon at…
Despite the incredible complexity of our brains' neural networks, theoretical descriptions of neural dynamics have led to profound insights into possible network states and dynamics. It remains challenging to develop theories that apply to…
This work is devoted to the effective macroscopic dynamics of a weakly damped stochastic nonlinear wave equation with a random dynamical boundary condition. The white noises are taken into account not only in the model equation defined on a…
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.…
This paper focuses on the outline of some computational methods for the approximate solution of the integral equations for the neuronal firing probability density and an algorithm for the generation of sample-paths in order to construct…
Stochasticity plays a central role in nearly every biological process, and the noise power spectral density (PSD) is a critical tool for understanding variability and information processing in living systems. In steady-state, many such…
We analyze the dynamics of the FitzHugh-Nagumo (FHN) model in the presence of colored noise and a periodic signal. Two cases are considered: (i) the dynamics of the membrane potential is affected by the noise, (ii) the slow dynamics of the…
This paper is concerned with stochastic systems whose state is a diffusion process governed by an Ito stochastic differential equation (SDE). In the framework of a nominal white-noise model, the SDE is driven by a standard Wiener process.…
Many physical systems characterized by nonlinear multiscale interactions can be effectively modeled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative…
The presence of correlated noise, arising from a mixture of independent fluctuations and a common noisy input shared across the neural population, is a ubiquitous feature of neural circuits, yet its impact on collective network dynamics…
The correlated variability in the responses of a neural population to the repeated presentation of a sensory stimulus is a universally observed phenomenon. Such correlations have been studied in much detail, both with respect to their…
We introduce a novel differentially private algorithm for online federated learning that employs temporally correlated noise to enhance utility while ensuring privacy of continuously released models. To address challenges posed by DP noise…
A neuron transforms its input into output spikes, and this transformation is the basic unit of computation in the nervous system. The spiking response of the neuron to a complex, time-varying input can be predicted from the detailed…
Self-organizing memristive networks are physical circuits that dynamically reconfigure their circuitry in response to external input signals. Their adaptive behavior arises from intrinsic neuro-synaptic dynamics combined with a…
We consider the statics and dynamics of a single particle trapped in a one-dimensional harmonic potential, and subjected to a driving noise with memory, that is represented by a resetting stochastic process. The finite memory of this…
The full dynamics of a synchronous recurrent neural network model with Ising binary units and a Hebbian learning rule with a finite self-interaction is studied in order to determine the stability to synaptic and stochastic noise of…
Dynamical balance of excitation and inhibition is usually invoked to explain the irregular low firing activity observed in the cortex. We propose a robust nonlinear balancing mechanism for a random network of spiking neurons, which works…
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…
Chaos provides many interesting properties that can be used to achieve computational tasks. Such properties are sensitivity to initial conditions, space filling, control and synchronization. Chaotic neural models have been devised to…
Self-sustained neural activity in the absence of ongoing external input is a fundamental feature of nervous system dynamics, yet the conditions under which it can emerge in biophysically grounded network models remain incompletely…