相关论文: Homogenization of a Wilson-Cowan model for neural …
The Wilson-Cowan model for metapopulation, a Neural Mass Network Model, treats different subcortical regions of the brain as connected nodes, with connections representing various types of structural, functional, or effective neuronal…
The paper deals with homogenization and higher order approximations of solutions to nonlocal evolution equations of convolution type whose coefficients are periodic in the spatial variables and random stationary in time. We assume that the…
The paper deals with the homogenization of a linear Boltzmann equation by the means of the sigma-convergence method. Under a general deterministic assumption on the coefficients of the equation, we prove that the density of the particles…
In this study we consider limit theorems for microscopic stochastic models of neural fields. We show that the Wilson-Cowan equation can be obtained as the limit in probability on compacts for a sequence of microscopic models when the number…
In this paper we provide a rate of convergence for periodic homogenization of Hamilton-Jacobi-Bellman equations with nonlocal diffusion. The result is based on the regularity of the associated effective problem, where the convexity plays a…
Neural fields are evolving towards a general-purpose continuous representation for visual computing. Yet, despite their numerous appealing properties, they are hardly amenable to signal processing. As a remedy, we present a method to…
We address the homogenization of a semilinear hyperbolic stochastic partial differential equation with highly oscillating coefficients, in the context of ergodic algebras with mean value. To achieve our goal, we use a suitable variant of…
The compatibility between the conformal symmetry and the closure of conformal algebras is discussed on the nonlinear sigma model. The present approach, above the basis of field redefinition employed in the Hamiltonian scheme, attempts the…
In this work, we review the connection between the subjects of homogenization and nonlocal modeling and discuss the relevant computational issues. By further exploring this connection, we hope to promote the cross fertilization of ideas…
The metaplectic covariance for all forms of the Weyl-Wigner-Groenewold-Moyal quantization is established with different realizations of the inhomogeneous symplectic algebra. Beyond that, in its most general form $W_{\infty}$ -covariance of…
We construct novel conformal sigma models in three dimensions. Nonlinear sigma models in three dimensions are nonrenormalizable in perturbation theory. We use Wilsonian renormalization group equation method to find the fixed points.…
We consider the homogenization of Hamilton-Jacobi equations and degenerate Bellman equations in stationary, ergodic, unbounded environments. We prove that, as the microscopic scale tends to zero, the equation averages to a deterministic…
A generalized version of the Wilson-Cowan (WC) model is proposed which accounts for the evolution of the synaptic resources. Adiabatic elimination of the fast variables is performed to yield a simplified framework for the coupled…
In several works, the theory of strongly continuous groups is used to build a framework for solving stochastic homogenization problems. Following this idea, we construct a detailed and comprehensive theory of homogenization. This enables to…
It is known that all the vector bundles of the title can be obtained by holomorphic induction from representations of a certain parabolic Lie algebra on finite dimensional inner product spaces. The representations, and the induced bundles,…
We study random homogenization of second-order, degenerate and quasilinear Hamilton-Jacobi equations which are positively homogeneous in the gradient. Included are the equations of forced mean curvature motion and others describing…
A particular form of non-linear $\sigma$-model, having a global gauge invariance, is studied. The detailed discussion on current algebra structures reveals the non-abelian nature of the invariance, with {\it{field dependent structure…
We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics and provide a unified treatment for (non-)periodic homogenization problems in thermodynamics,…
This paper investigates homogenization problems for the nonlocal operators with rapidly oscillating coefficients in the cases of periodic and random statistically homogeneous micro-structures. These operators involve the fractional…
The continuous dependence of solutions to certain (non-autonomous, partial, integro-differential-algebraic, evolutionary) equations on the coefficients is addressed. We give criteria that guarantee that convergence of the coefficients in…