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We propose a decomposition method for the spectral peaks in an observed frequency spectrum, which is efficiently acquired by utilizing the Fast Fourier Transform. In contrast to the traditional methods of waveform fitting on the spectrum,…

Existing feature selection methods fail to properly account for interactions between features when evaluating feature subsets. In this paper, we attempt to remedy this issue by using orthogonal variance decomposition to evaluate features.…

This work is concerned with variational analysis of so-called spectral functions and spectral sets of matrices that only depend on eigenvalues of the matrix. Based on our previous work [H. T. B\`ui, M. N. B\`ui, and C. Clason, Convex…

The study of the differential rotation in the chromosphere of the Sun is of significant importance as it provides valuable insights into the rotational behaviour of the solar atmosphere at higher altitudes and the coupling mechanism between…

Symmetric trace-free tensors are used in many areas of physics, including electromagnetism, relativistic celestial mechanics and geodesy, as well as in the study of gravitational radiation and gravitational lensing. Their use allows…

Model-based decompositions have gained considerable attention after the initial work of Freeman and Durden. This decomposition which assumes the target to be reflection symmetric was later relaxed in the Yamaguchi et al. decomposition with…

We study orthogonal decompositions of symmetric and ordinary tensors using methods from linear algebra. For the field of real numbers we show that the sets of decomposable tensors can be defined be equations of degree 2. This gives a new…

To perform precise and accurate photometric catalogue cross-matches -- assigning counterparts between two separate datasets -- we need to describe all possible sources of uncertainty in object position. With ever-increasing time baselines…

We apply the method of orbit harmonics to the set of break divisors and orientable divisors on graphs to obtain the central and external zonotopal algebras respectively. We then relate a construction of Efimov in the context of…

This paper presents a method for the accurate and efficient computations on scalar, vector and tensor fields in three-dimensional spherical polar coordinates. The methods uses spin-weighted spherical harmonics in the angular directions and…

We present a covariant formulation for constructing general quadratic actions for cosmological perturbations, invariant under a given set of gauge symmetries for a given field content. This approach allows us to analyse scalar, vector and…

We present a new method for the analysis of images, a fundamental task in observational astronomy. It is based on the linear decomposition of each object in the image into a series of localised basis functions of different shapes, which we…

We survey the construction of a range of function spaces used in harmonic analysis of PDE, including classical results as well as recent developments. We frame these constructions in a common conceptual framework, where these function…

In Delta Scuti star models, the calculated amplitude ratios and phase differences for multi-colour photometry exhibit a strong dependence on convection. These observables are tools for determination of the spherical harmonic degree of the…

We investigate of the systems of proper motions of stars in the ground-based catalogues HSOY, UCAC5, GPS1 and PMA derived by combining with the Gaia DR1 space data. Assuming the systematic differences of stellar proper motions of two…

The geometric Langlands program is distinguished in assigning spectral decompositions to all representations, not only the irreducible ones. However, it is not even clear what is meant by a spectral decomposition when one works with…

Observations of stellar surfaces - except for the Sun - are hampered by their tiny angular extent, while observed spectral lines are smeared by averaging over the stellar surface, and by stellar rotation. Exoplanet transits can be used to…

We present a sub-arcsecond cross-match of Gaia DR2 against the INT Photometric H-alpha Survey of the Northern Galactic Plane Data Release 2 (IPHAS DR2) and the Kepler-INT Survey (KIS). The resulting value-added catalogues (VACs) provide…

Multipole expansion methods have been primarily used for analyzing the electromagnetic scattering from non-magnetic isotropic dielectric scatterers, and studies about the scattering from magnetic objects seem to be lacking. In this work, we…

We consider f(Q) extended symmetric teleparallel cosmologies, where Q is the non-metricity scalar, and constrain its functional form through the order reduction method. By using this technique, we are able to reduce and integrate the field…