electromagnetic waves through localized resonances. In this talk we
introduce a rigorous mathematical framework for controlling localized
resonances and predicting exotic behavior inside optical metamaterials.
The theory is multiscale in nature and provides a rational basis for
designing microstructure using multiphase nonmagnetic materials to create
backward wave behavior across prescribed frequency ranges.
examples of the application of wavelet analysis to the understanding of mild Traumatic
Brain Injury (mTBI). First, the talk will focus on how wavelet-based features
can be used to define important characteristics of blast-related acceleration
and pressure signatures, and how these can be used to drive a Naïve Bayes
classifier using wavelet packets. Later, some recent progress on the use of
wavelets for data-driven clustering of brain regions and the characterization
of functional network dynamics related to mTBI will be discussed. In
particular, because neurological time series such as the ones obtained from an
fMRI scan belong to the class of long term memory processes
(also referred to as 1/f-like
processes), the use of wavelet
analysis guarantees optimal theoretical whitening properties and leads to
better clusters compared to classical seed-based approaches.
numerical methods (such as finite difference methods, Galerkin methods,
discontinuous Galerkin methods) for fully nonlinear second order PDEs
including Monge-Ampere type equations and Hamilton-Jacobi-Bellman
equations. The focus of this talk is to present a new framework for
constructing finite difference methods which can reliably approximate
viscosity solutions of these fully nonlinear PDEs. The
connection between this new framework with the well-known finite difference
theory for first order fully nonlinear Hamilton-Jacobi equations will be
explained. Extensions of these finite difference techniques
to discontinuous Galerkin settings will also be discussed.