Related papers: A Fourier-invariant method for locating point-mass…
We propose to measure the weak cosmic shear using the spatial derivatives of the galaxy surface brightness field. The measurement should be carried out in Fourier space, in which the point spread function (PSF) can be transformed to a…
Context. There are typically two different approaches to inferring the mass formation history (MFH) of a given galaxy from its luminosity in different bands. Non-parametric methods are known for their flexibility and accuracy, while…
We study the density of the invariant measure of the Hurwitz complex continued fraction from a computational perspective. It is known that this density is piece-wise real-analytic and so we provide a method for calculating the Taylor…
When using Laguerre and Hermite spectral methods to numerically solve PDEs in unbounded domains, the number of collocation points assigned inside the region of interest is often insufficient, particularly when the region is expanded or…
This paper determines how to define a discretely implemented Fourier transform when analysing an observed spatial point process. To develop this transform we answer four questions; first what is the natural definition of a Fourier…
We study the possibility of using quadrupole moments of auto-convolved galaxy images to measure cosmic shear. The autoconvolution of an image corresponds to the inverse Fourier transformation of its power spectrum. The new method has the…
Interferometers play an increasingly important role for spatially resolved observations. If employed at full potential, interferometry can probe an enormous dynamic range in spatial scale. Interpretation of the observed visibilities…
Because the magnitude of inner products with its basis functions are invariant to rotation and scale change, the Fourier-Mellin transform has long been used as a component in Euclidean invariant 2D shape recognition systems. Yet…
In many practical applications, spatial data are often collected at areal levels (i.e., block data) and the inferences and predictions about the variable at points or blocks different from those at which it has been observed typically…
The investigation of the pulsation properties of pre-main-sequence intermediate-mass stars is a promising tool to evaluate the intrinsic properties of these stars and to constrain current evolutionary models. Many new candidates of this…
We propose a quantum algorithm for finding eigenvalues of non-unitary matrices. We show how to construct, through interactions in a quantum system and projective measurements, a non-Hermitian or non-unitary matrix and obtain its eigenvalues…
A new method of quantum state tomography for quantum information processing is described. The method based on two-dimensional Fourier transform technique involves detection of all the off-diagonal elements of the density matrix in a…
Algebraic tools in statistics have recently been receiving special attention and a number of interactions between algebraic geometry and computational statistics have been rapidly developing. This paper presents another such connection,…
We introduce a diffusion-based generative model to describe the distribution of galaxies in our Universe directly as a collection of points in 3-D space (coordinates) optionally with associated attributes (e.g., velocities and masses),…
Two-point correlation functions (2PCF) are widely used to characterize how points cluster in space. In this work, we study the problem of measuring the 2PCF over a large set of points, restricted to a subset satisfying a property of…
Compressive sensing has become a powerful addition to uncertainty quantification in recent years. This paper identifies new bases for random variables through linear mappings such that the representation of the quantity of interest is more…
We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices, by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the…
We consider space-saving versions of several important operations on univariate polynomials, namely power series inversion and division, division with remainder, multi-point evaluation, and interpolation. Now-classical results show that…
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…
The efficient creation and detection of spatial modes of light has become topical of late, driven by the need to increase photon-bit-rates in classical and quantum communications. Such mode creation/detection is traditionally achieved with…