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Spatial Frequency Domain Imaging can map tissue scattering and absorption properties over a wide field of view, making it useful for clinical applications such as wound assessment and surgical guidance. This technique has previously…
We bound the number of electromagnetic signals which may be observed over a frequency range $2W$ for a time $T$ within a region of space enclosed by a radius $R$. Our result implies that broadband fields in space cannot be arbitrarily…
Spatial variables can be observed in many different forms, such as regularly sampled random fields (lattice data), point processes, and randomly sampled spatial processes. Joint analysis of such collections of observations is clearly…
Pulse formation in passively mode locked lasers is often accompanied with dispersive waves that form of spectral sidebands due to spatial inhomogoneities in the laser cavity. Here we present an explicit calculation of the amplitude,…
We obtain sequences of inclusion sets for the spectrum, essential spectrum, and pseudospectrum of banded, in general non-normal, matrices of finite or infinite size. Each inclusion set is the union of the pseudospectra of certain…
The slopes of maximal subbundles of rank $s$ divided by the degree of the map under various pull backs form a bounded collection of numbers called the $s$-spectrum of the bundle. We study the supremum of the $s$-spectrum and determine it in…
Given an infinite iterated function system (IFS) $\mathcal{F}$, we define its dimension spectrum $D(\mathcal{F})$ to be the set of real numbers which can be realised as the dimension of some subsystem of $\mathcal{F}$. In the case where…
In their previous work, the authors studied the abelian sandpile model on graphs constructed from a growing piece of a plane or space tiling, given periodic or open boundary conditions, and identified spectral factors which govern the…
This paper addresses the difficulty of characterizing the time-varying nature of fading channels. The current time-invariant models often fall short of capturing and tracking these dynamic characteristics. To overcome this limitation, we…
A hybrid estimator of the log-spectral density of a stationary time series is proposed. First, a multiple taper estimate is performed, followed by kernel smoothing the log-multitaper estimate. This procedure reduces the expected mean square…
In this article we study the energy level spectrum of fractals which have block-hierarchical structures. We develop a method to study the spectral properties in terms of linearization of spectral decimation procedure and verify it…
Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…
We give a self-contained presentation of the theory of self-adjoint extensions using the technique of boundary triples. A description of the spectra of self-adjoint extensions in terms of the corresponding Krein maps (Weyl functions) is…
The subject of time-band-limiting, originating in signal processing, is dominated by the miracle that a naturally appearing integral operator admits a commuting differential one allowing for a numerically efficient way to compute its…
We examine the interplay between spectral bandwidth and illumination curvature in ptychography. By tailoring the divergence of the illumination, broader spectral bandwidths can be tolerated without requiring algorithmic modifications to the…
Multiple scattering of an electromagnetic wave as it passes through an object is a fundamental problem that limits the performance of current imaging systems. In this paper, we describe a new technique-called Series Expansion with…
The spectrum of a semi-infinite quantum graph tube with square period cells is analyzed. The structure is obtained by rolling up a doubly periodic quantum graph into a tube along a period vector and then retaining only a semi-infinite half…
The foundation of the theory presented here has already been proved to be effective for the case of curves belonging to the Koch family. The present paper extends the investigation to more complex curves, namely randomly generated curves…
Orthogonal time frequency space (OTFS) is a 2-dimensional (2D) modulation technique designed in the delay-Doppler domain. A key premise behind OTFS is the transformation of a time varying multipath channel into an almost non-fading 2D…
We propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the…