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The energy of solutions of the scalar damped wave equation decays uniformly exponentially fast when the geometric control condition is satisfied. A theorem of Lebeau [leb93] gives an expression of this exponential decay rate in terms of the…
Electromagnetic ion cyclotron (EMIC) waves lead to rapid scattering of relativistic electrons in Earth's radiation belts, due to their large amplitudes relative to other waves that interact with electrons of this energy range. A central…
We study the statistical properties of wave scattering in a disordered waveguide. The statistical properties of a "building block" of length (delta)L are derived from a potential model and used to find the evolution with length of the…
Recently, spectral CT has been drawing a lot of attention in a variety of clinical applications primarily due to its capability of providing quantitative information about material properties. The quantitative integrity of the reconstructed…
Global observations of ocean swell, from satellite Synthetic Aperture Radar data, are used to estimate the dissipation of swell energy for a number of storms. Swells can be very persistent with energy e-folding scales exceeding 20,000 km.…
In this paper we propose a scalable version of a state-of-the-art deterministic time-invariant feature extraction approach based on consecutive changes of basis and nonlinearities, namely, the scattering network. The first focus of the…
Phenomena of wave propagation in dynamically varying structures have reemerged as the temporal variations of the medium's properties can extend the possibilities for electromagnetic wave manipulation. While the dynamical change of the…
This paper presents a comprehensive analysis of the information-energy capacity region for simultaneous lightwave information and power transfer (SLIPT) systems over lognormal fading channels. Unlike conventional studies that primarily…
The effects of different filtering strategies on the statistical properties of the resolved-to-sub-filter scale (SFS) energy transfer are analyzed in forced homogeneous and isotropic turbulence. We carry out a priori analyses of statistical…
We prove that the scattering matrix at a fixed quasi--energy determines uniquely a time--periodic potential that decays exponentially at infinity. We consider potentials that for each fixed time belong to $L^{3/2}$ in space. The exponent…
Orthogonal wavelet transforms are a cornerstone of modern signal and image denoising because they combine multiscale representation, energy preservation, and perfect reconstruction. In this paper, we show that these advantages can be…
Deep convolutional networks are well-known for their high computational and memory demands. Given limited resources, how does one design a network that balances its size, training time, and prediction accuracy? A surprisingly effective…
We consider two-dimensional periodic gravity water waves with constant nonzero vorticity $\gamma$, in infinite depth and with periodic boundary conditions. We prove that, if the characteristic wave number $\frac{\gamma^2}{g}$ is rational,…
Capturing high-frequency data concerning the condition of complex systems, e.g. by acoustic monitoring, has become increasingly prevalent. Such high-frequency signals typically contain time dependencies ranging over different time scales…
The paper studies properties of continuous time processes with spectrum degeneracy at a single point where their Fourier transforms vanish with a certain rate. It appears that these processes are linearly predictable in some weak sense,…
We study detection and imaging of small reflectors in heavy clutter, using an array of transducers that emits and receives sound waves. Heavy clutter means that multiple scattering of the waves in the heterogeneous host medium is strong and…
The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…
The last decade has shown a tremendous success in solving various computer vision problems with the help of deep learning techniques. Lately, many works have demonstrated that learning-based approaches with suitable network architectures…
We develop a Machine Learning Inversion method for analyzing scattering functions of mechanically driven polymers and extracting the corresponding feature parameters, which include energy parameters and conformation variables. The polymer…
The scattering-matrix product SS+ of a weakly absorbing medium is related by a unitary transformation to the time-delay matrix without absorption. It follows from this relationship that the eigenvalues of SS+ for a weakly absorbing chaotic…