Related papers: Using fractional differentiation in astronomy
With an exponentially increasing amount of astronomical data, the complexity and dimension of astronomical data are likewise growing rapidly. Extracting information from such data becomes a critical and challenging problem. For example,…
In this article we would like to consider some approaches to non-integer integro-differentiations and its implementation in computer algebra system Wolfram Mathematics.
In many astrophysical systems, smoothly-varying large-scale variations coexist with small-scale fluctuations. For example, a large-scale velocity or density gradient can exist in molecular clouds that exhibit small-scale turbulence. In…
The shapelets method for image analysis is based upon the decomposition of localised objects into a series of orthogonal components with convenient mathematical properties. We extend the "Cartesian shapelet" formalism from earlier work, and…
I introduce a straightforward technique for the filtering of extended astronomical images into components of different spatial scales. For a positive original image, each component is positive definite, and the sum of all components equals…
We describe our ongoing work on, and future plans for, searches in bulk matter for fractional charge elementary particles and very massive elementary particles. Our primary interest is in searching for such particles that may have been…
We present a generic algorithm for performing astronomical image registration and pointing refinement. The method is based on matching the positions and fluxes of available point sources in image overlap regions. This information is used to…
The theory of fractional calculus in the complex plane was not built with a specific application in mind. The main obstacle to application was the difficulty with obtaining analytic continuations of fractional derivatives and integrals. It…
Astronomical images suffer a constant presence of multiple defects that are consequences of the intrinsic properties of the acquisition equipments, and atmospheric conditions. One of the most frequent defects in astronomical imaging is the…
Astronomical images often have regions with missing or unwanted information, such as bad pixels, bad columns, cosmic rays, masked objects, or residuals from imperfect model subtractions. In certain situations it can be essential, or…
It is demonstrated that non-constant kernel solution, that can fit the spatial variations of the kernel can be obtained with minimum computing time. The CPU cost required with this new extension of the image subtraction method is almost the…
Astrophysics and cosmology are rich with data. The advent of wide-area digital cameras on large aperture telescopes has led to ever more ambitious surveys of the sky. Data volumes of entire surveys a decade ago can now be acquired in a…
We discuss the use of galaxies to trace the large-scale structure of the universe and thereby to make cosmological inferences. We put special emphasis on our lack of knowledge about the relative distribution of galaxies and the dynamically…
Plasma fractals is a technique to generate random and realistic clouds, textures and terrains~-- traditionally using recursive subdivision. We demonstrate a new approach, based on iterative expansion. It gives a family of algorithms that…
Semantic segmentation is a critical task in computer vision aiming to identify and classify individual pixels in an image, with numerous applications in for example autonomous driving and medical image analysis. However, semantic…
Photometric redshifts play an important role as a measure of distance for various cosmological topics. Spectroscopic redshifts are only available for a very limited number of objects but can be used for creating statistical models. A broad…
I discuss recent progress in dark matter searches, focusing in particular on how rigorous modeling the dark matter distribution in the Galaxy and in its satellite galaxies improves our interpretation of the limits on the annihilation and…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
We present an algorithm implemented in the astroalign Python module for image registration in astronomy. Our module does not rely on WCS information and instead matches 3-point asterisms (triangles) on the images to find the most accurate…
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…