Related papers: Sampling patterns for Zernike-like bases in non-st…
Rational function approximations find applications in many areas including macro-modeling of high-frequency circuits, model order reduction for controller design, interpolation and extrapolation of system responses, surrogate models for…
The method of wavefront shaping to control optical properties of opaque media is a promising technique for authentication applications. One of the main challenges of this technique is the sensitivity of the wavefront-sample coupling to…
The decomposition of the polynomials on the quaternionic unit sphere in $\Hd$ into irreducible modules under the action of the quaternionic unitary (symplectic) group and quaternionic scalar multiplication has been studied by several…
The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…
Highly directional radiation from photonic structures is important for many applications, including high power photonic crystal surface emitting lasers, grating couplers, and light detection and ranging devices. However, previous…
We extend Zeilberger's approach to special function identities to cases that are not holonomic. The method of creative telescoping is thus applied to definite sums or integrals involving Stirling or Bernoulli numbers, incomplete Gamma…
Advanced wavefront sensors (WFS) are essential for enabling new science cases for telescopes that utilize adaptive optics (AO) systems. While complex field WFS -- those that estimate the electric field phase and amplitude through…
Deep convolutional neural networks are hindered by training instability and feature redundancy towards further performance improvement. A promising solution is to impose orthogonality on convolutional filters. We develop an efficient…
Metagratings have been shown to form an agile and efficient platform for extreme wavefront manipulation, going beyond the limitations of gradient metasurfaces. Previous approaches for transmissive metagratings have resorted on compound…
Inference for statistics of a stationary time series often involve nuisance parameters and sampling distributions that are difficult to estimate. In this paper, we propose the method of orthogonal samples, which can be used to address some…
We present a method using Zernike moments for quantifying rotational and reflectional symmetries in scanning transmission electron microscopy (STEM) images, aimed at improving structural analysis of materials at the atomic scale. This…
We investigate methods to calibrate the non-common path aberrations at an adaptive optics system having a wavefront-correcting device working at an extremely high resolution (larger than 150x150). We use focal-plane images collected…
For orthogonal polynomials defined by compact Jacobi matrix with exponential decay of the coefficients, precise properties of orthogonality measure is determined. This allows showing uniform boundedness of partial sums of orthogonal…
To directly image Earth-like planets, contrast levels of 10^-8 - 10^-10 are required. The next generation of instruments will need wavefront control below the nanometer level to achieve these goals. The Zernike wavefront sensor (ZWFS) is a…
We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon satisfying simple geometric criteria, our construction produces 2n…
Circumstellar disks play a key role in the understanding of stellar systems. Direct imaging of such extended structures is a challenging task. Current post-processing techniques, first tailored for exoplanets imaging, tend to produce…
This paper is concerned with the problem of sampling and interpolation involving derivatives in shift-invariant spaces and the error analysis of the derivative sampling expansions for fundamentally large classes of functions. A new type of…
We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the…
We study central configurations when the set of positions is symmetric. We use a theorem from representation theory of finite groups to explore the symmetry properties of equations for central configurations. This approach simplifies…
We show that several families of classical orthogonal polynomials on the real line are also orthogonal on the interior of an ellipse in the complex plane, subject to a weighted planar Lebesgue measure. In particular these include Gegenbauer…