Related papers: Fighting seizures with seizures: diffusion and sta…

Metastable brain dynamics are characterized by abrupt, jump-like modulations so that the neural activity in single trials appears to unfold as a sequence of discrete, quasi-stationary states. Evidence that cortical neural activity unfolds…

For spiking neural networks we consider the stability problem of global synchrony, arguably the simplest non-trivial collective dynamics in such networks. We find that even this simplest dynamical problem -- local stability of synchrony --…

Based on a system-reservoir model, where the system is nonlinearly coupled to a heat bath and the heat bath is modulated by an external stationary Gaussian noise, we derive the generalized Langevin equation with space dependent friction and…

We study the effects of noise on stationary pulse solutions (bumps) in spatially extended neural fields. The dynamics of a neural field is described by an integrodifferential equation whose integral term characterizes synaptic interactions…

The collective dynamics of excitatory pulse coupled neurons with spike timing dependent plasticity (STDP) is studied. The introduction of STDP induces persistent irregular oscillations between strongly and weakly synchronized states,…

The time elapsed model describes the firing activity of an homogeneous assembly of neurons thanks to the distribution of times elapsed since the last discharge. It gives a mathematical description of the probability density of neurons…

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…

In this paper, we consider an opioid epidemic dynamical model with random perturbation that typically describes the interplay between regular prescription use, addictive use, and the process of rehabilitation from addiction and vice-versa.…

The brain can be understood as a collection of interacting neuronal oscillators, but the extent to which its sustained activity is due to coupling among brain areas is still unclear. Here we study the joint dynamics of two cortical columns…

We introduce and solve a general model of dynamic response under external perturbations. This model captures a wide range of systems out of equilibrium including Ising models of physical systems, social opinions, and population genetics.…

Biological systems use neural circuits to integrate input information and produce outputs. Synaptic convergence, where multiple neurons converge their inputs onto a single downstream neuron, is common in natural neural circuits. However,…

Balance of excitation and inhibition is a fundamental feature of in vivo network activity and is important for its computations. However, its presence in the neocortex of higher mammals is not well established. We investigated the dynamics…

We study the statistical physics of a surprising phenomenon arising in large networks of excitable elements in response to noise: while at low noise, solutions remain in the vicinity of the resting state and large-noise solutions show…

Robust information representation and its persistent maintenance are fundamental for higher cognitive functions. Existing models employ distinct neural mechanisms to separately address noise-resistant processing or information maintenance,…

Persistent activity is postulated to drive neural network plasticity and learning. To investigate its underlying cellular mechanisms, we developed a biophysically tractable model that explains the emergence, sustenance, and eventual…

The Nonlinear Noisy Leaky Integrate and Fire neuronal models are mathematical models that describe the activity of neural networks. These models have been studied at a microscopic level, using Stochastic Differential Equations, and at a…

This article describes a numerical procedure designed to tune the parameters of periodically-driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic…

The removal of multiplicative Gamma noise is a critical research area in the application of synthetic aperture radar (SAR) imaging, where neural networks serve as a potent tool. However, real-world data often diverges from theoretical…

We apply sonification strategies and quantum computing to the analysis of an episode of seizure. We first sonify the signal from a selection of channels (from real ECoG data), obtaining a polyphonic sequence. Then, we propose two quantum…

We consider the long-time dynamics of a general class of nonlinear Fokker-Planck equations, describing the large population behavior of mean-field interacting units. The main motivation of this work concerns the case where the individual…