11 research outputs found
Neuroelectric source localization by random spatial sampling
The magnetoencephalography (MEG) aims at reconstructing the unknown
neuroelectric activity in the brain from the measurements of the neuromagnetic field in the outer space.
The localization of neuroelectric sources from MEG data results in an ill-posed and ill-conditioned
inverse problem that requires regularization techniques to be solved.
In this paper we propose a new inversion method based on random spatial sampling that is
suitable to localize focal neuroelectric sources. The method is fast, efficient and requires
little memory storage. Moreover, the numerical tests show that the random sampling method has a high spatial resolution even in the case of deep source localization from noisy magnetic data
On the effective interfacial resistance through quasi-filling fractal layers
This paper concerns the periodic homogenization of the stationary heat equation in a domain with two connected components, separated by an oscillating interface defined on prefractal Koch type curves. The problem depends both on the parameter ε that defines the periodic structure of the interface and on n, which is the index of the prefractal iteration. First, we study the limit as ε vanishes, showing that the homogenized problem is strictly dependent on the amplitude of the oscillations and the parameter appearing in the transmission condition. Finally, we perform the asymptotic behaviour as n goes to infinity, giving rise to a limit problem defined on a domain with fractal interface
MIXED NORMS, FUNCTIONAL INEQUALITIES, AND HAMILTON-JACOBI EQUATIONS
In this paper we generalize the notion of hypercontractivity for nonlinear semigroups allowing the functions to belong to mixed spaces. As an application of this notion, we consider a class of Hamilton-Jacobi equations and we establish functional inequalities. More precisely, we get hypercontractivity for viscosity solutions given in terms of Hopf-Lax type formulas. In this framework, we consider different measures associated with the variables; consequently, using mixed norms, we find new inequalities. The novelty of this approach is the study of functional inequalities with mixed norms for semigroups
MATLAB for applications in economics and finance
The book offers a clear and easy introduction to MATLAB and to tis main applications in the economic and financial environment