Related papers: Power spectrum and diffusion of the Amari neural f…
Wilson-Cowan and Amari-type models capture nonlinear neural population dynamics, providing a fundamental framework for modeling how sensory and other exogenous inputs shape activity in neural tissue. We study the controllability properties…
Human brain response is the overall ability of the brain in analyzing internal and external stimuli in the form of transferred energy to the mind/brain phase-space and thus, making the proper decisions. During the last decade scientists…
A neural field models the large scale behaviour of large groups of neurons. We extend results of van Gils et al. [2013] and Dijkstra et al. [2015] by including a diffusion term into the neural field, which models direct, electrical…
Motivated by considerations from neuroscience (macroscopic behavior of large ensembles of interacting neurons), we consider a population of mean field interacting diffusions in $\mathbf {R}^m$ in the presence of a random environment and…
The classical biophysical Morris-Lecar model of neuronal excitability predicts that upon stimulation of the neuron with a sufficiently large constant depolarizing current there exists a finite interval of the current values where periodic…
The aim of this work is to present a mathematical framework for the study of flickering inputs in visual processing tasks. When combined with geometric patterns, these inputs influence and induce interesting psychophysical phenomena, such…
In this work we consider a class of nonlocal non-autonomous evolution equations, which generalizes the model of neuronal activity that arises in Amari (1979). Under suitable assumptions on the nonlinearity and on the parameters present in…
We discuss the diffusion equation resulting from a strong dissipation limit of the random wave equation arising in the models of warm inflation. We show that the long wave power spectrum of scalar perturbations in the model of an…
We develop a straightforward analytical framework for the propagation of spatial light modes through a turbulent atmosphere. Built upon the split-step approach with the mode-based optical field representation, it directly assesses how…
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time…
We study the planar front solution for a class of reaction diffusion equations in multidimensional space in the case when the essential spectrum of the linearization in the direction of the front touches the imaginary axis. At the linear…
We discuss the response of a quantum system to a time-dependent perturbation with spectrum \Phi(\omega). This is characterised by a rate constant D describing the diffusion of occupation probability between levels. We calculate the…
Diffusion MRI (dMRI) provides contrast that reflect diffusing spins' interactions with microstructural features of biological systems, but its specificity remains limited due to the ambiguity of its relation to the underlying…
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 neural mechanism of memory has a very close relation with the problem of representation in artificial intelligence. In this paper a computational model was proposed to simulate the network of neurons in brain and how they process…
This paper focuses on the modeling of experiments conducted by Billock and Tsou [V. A. Billock and B. H. Tsou, Proc. Natl. Acad. Sci. USA, 104 (2007), pp. 8490--8495] using an Amari-type neural field that models the average membrane…
We present a microscopic approach for the coupling of cortical activity, as resulting from proper dipole currents of pyramidal neurons, to the electromagnetic field in extracellular fluid in presence of diffusion and Ohmic conduction.…
We propose a novel learning framework using neural mean-field (NMF) dynamics for inference and estimation problems on heterogeneous diffusion networks. Our new framework leverages the Mori-Zwanzig formalism to obtain an exact evolution…
This paper proposes an effective phase diffusion method to analyze chemical exchange in nuclear magnetic resonance (NMR). The chemical exchange involves spin jumps around different sites where the spin angular frequencies vary, which leads…
We propose a novel learning framework based on neural mean-field dynamics for inference and estimation problems of diffusion on networks. Our new framework is derived from the Mori-Zwanzig formalism to obtain an exact evolution of the node…