Age features of the power spectrum of alpha-band eeg during complex mental activities

Urgency: Electroencephalographic analysis is one of the most informative methods of study of the systemic organization of integrative processes of the human brain in different functional States, mental activity, attention. Objective: to Study the age peculiarities of the organization of the cerebral cortex in the alpha sub-bands with complex mental activities with verbal and figurative components

In-plane elastic wave propagation and band-gaps in layered functionally graded phononic crystals

AbstractIn-plane wave propagation in layered phononic crystals composed of functionally graded interlayers arisen from the solid diffusion of homogeneous isotropic materials of the crystal is considered. Wave transmission and band-gaps due to the material gradation and incident wave-field are investigated. A classification of band-gaps in layered phononic crystals is proposed. The classification relies on the analysis of the eigenvalues of the transfer matrix for a unit-cell and the asymptotics derived for the transmission coefficient. Two kinds of band-gaps, where the transmission coefficient decays exponentially with the number of unit-cells are specified. The so-called low transmission pass-bands are introduced in order to identify frequency ranges, in which the transmission is sufficiently low for engineering applications, but it does not tend to zero exponentially as the number of unit-cells tends to infinity. A polyvalent analysis of the geometrical and physical parameters on band-gaps is presented

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Track A Basic Science

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138319/1/jia218438.pd

Spring boundary conditions and modeling of 2D wave propagation in composites with imperfect interfaces

The possibility of applying spring boundary conditions to model propagation of elastic waves in layered composites with nonperfect contact between layers in studied. The stiffnesses in the spring boundary conditions are determined by the crack density, the effective size of microdefects, and the elastic properties of the materials via the Baik-Thompson and Bostr\uf6m-Wickham approaches. The efficiency of the model is analyzed for periodic structures with damaged layers

Effective spring boundary conditions for a damaged interface between dissimilar media in three-dimensional case

Elastic waves in the presence of a damaged interface between two dissimilar elastic media is investigated in the three-dimensional case. The damaged is modeled as a stochastic distribution of equally sized circular cracks which is transformed into a spring boundary condition. First the scattering by a single circular interface crack between two dissimilar half-spaces is investigated and solved explicitly for normally incident waves in the low frequency limit. The transmission by a distribution of cracks is then determined and is transformed into a spring boundary condition, where effective spring stiffnesses are expressed in terms of elastic moduli and damage parameters. A comparison with previous results for a periodic distribution of cracks shows good agreement

Spring boundary conditions and modeling of 2D wave propagation in composites with imperfect interfaces

The possibility of applying spring boundary conditions to model propagation of elastic waves in layered composites with nonperfect contact between layers in studied. The stiffnesses in the spring boundary conditions are determined by the crack density, the effective size of microdefects, and the elastic properties of the materials via the Baik-Thompson and Bostr\uf6m-Wickham approaches. The efficiency of the model is analyzed for periodic structures with damaged layers