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One of the problems of producing spectrographs for Extremely Large Telescopes (ELTs) is that the beam size is required to scale with telescope aperture if all other parameters are held constant, leading to enormous size and implied cost.…

Weak lensing by large-scale structure is a powerful probe of cosmology if the apparent alignments in the shapes of distant galaxies can be accurately measured. Most studies have therefore focused on improving the fidelity of the shape…

A novel phase retrieval method, motivated by ptychographic imaging, is proposed for the approximate recovery of a compactly supported specimen function $f:\mathbb{R}\rightarrow\mathbb{C}$ from its continuous short time Fourier transform…

We study the class of Lorentzian symmetric polynomials and Lorentzian symmetric functions, which are defined to be symmetric functions for which every truncation of variables is Lorentzian. Similar to the space of Lorentzian polynomials, we…

I present a new algorithm, CALCLENS, for efficiently computing weak gravitational lensing shear signals from large N-body light cone simulations over a curved sky. This new algorithm properly accounts for the sky curvature and boundary…

There are now several comprehensive web applications, stand-alone computer programs and computer algebra functions that, given a floating point number such as 6.518670730718491, can return concise nonfloat constants such as 3 arctan 2 + ln…

This paper offers a newly created integral approach for operators employing the orthogonal modified Laguerre polynomials and P\u{a}lt\u{a}nea basis. These operators approximate the functions over the interval $[0,\infty)$. Further, the…

The degrees of polynomials representing or approximating Boolean functions are a prominent tool in various branches of complexity theory. Sherstov recently characterized the minimal degree deg_{\eps}(f) among all polynomials (over the…

We compare theoretical, experimental, and computational approaches to random rough surfaces. The aim is to produce rough surfaces with desirable correlations and to analyze the correlation functions extracted from the surface profiles.…

Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we…

This paper introduces a reformulation of the classical convergence theorem for spectral sequences of filtered complexes which provides an algorithm to effectively compute the induced filtration on the total (co)homology, as soon as the…

A general theory of inhomogeneous broadening is rarely applied to nonlinear spectroscopy in lieu of either a simple Lorentzian or Gaussian model. In this work, we generalize all the important third-order nonlinear susceptibility expressions…

A few iterations of alternating least squares with a random starting point provably suffice to produce nearly optimal spectral- and Frobenius-norm accuracies of low-rank approximations to a matrix; iterating to convergence is unnecessary.…

Using Fisher information and the Cram\'er-Rao lower bound, we analyse fundamental precision limits in the determination of spectral parameters in inelastic optical scattering. General analytic formulae are derived which account for the…

Grothendieck inequalities are fundamental inequalities which are frequently used in many areas of mathematics and computer science. They can be interpreted as upper bounds for the integrality gap between two optimization problems: a…

Obtaining accurate distributions of galaxy redshifts is a critical aspect of weak lensing cosmology experiments. One of the methods used to estimate and validate redshift distributions is apply weights to a spectroscopic sample so that…

Astrobot swarms are used to capture astronomical signals to generate the map of the observable universe for the purpose of dark energy studies. The convergence of each swarm in the course of its coordination has to surpass a particular…

INTEGRAL observations provide a large amount of data on accreting binary systems. The interpretation of the spectral emission of these sources needs timing analysis and phase resolved spectroscopy, which are really cumbersome tasks if…

We derive a spectral interpretation of the pivot operation on a graph and generalise this operation to hypergraphs. We establish lower bounds on the number of flat spectra of a Boolean function, depending on internal structures, with…

The estimation of probability density functions (PDF) using approximate maps is a fundamental building block in computational probability. We consider forward problems in uncertainty quantification: the inputs or the parameters of a…