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Based on Morse theory for the energy functional on path spaces we develop a deformation theory for mapping spaces of spheres into orthogonal groups. This is used to show that these mapping spaces are weakly homotopy equivalent, in a stable…
We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…
One of the main goals of modern observational cosmology is to map the large scale structure of the Universe. A potentially powerful approach for doing this would be to exploit three-dimensional spectral maps, i.e. the specific intensity of…
We present an analytic model of the lightcurve variation for stars with non-evolving starspots on a differentially rotating surface. The Fourier coefficients of the harmonics of the rotation period are expressed in terms of the latitude of…
The study of multiple extrasolar planetary systems has the opportunity to obtain constraints for the planetary masses and orbital inclinations via the detection of mutual perturbations. The analysis of precise radial velocity measurements…
Quantitative thermodynamical, dynamical and magnetic properties of the solar and stellar plasmas are obtained by interpreting their emergent non-polarized and polarized spectrum. This inference requires the selection of a set of spectral…
We conduct a thorough study into the feasibility of measuring large-scale correlated proper motions of galaxies with astrometric surveys. We introduce a harmonic formalism for analysing proper motions and their correlation functions on the…
Stellar and galactic systems are objects in dynamical equilibrium that are composed of ordinary baryonic matter hypothetically embedded in extended dominant dark matter halos. Our aim is to investigate the scaling relations and…
Complex phenomena can be better understood when broken down into a limited number of simpler "components". Linear statistical methods such as the principal component analysis and its variants are widely used across various fields of applied…
Future precision cosmology from large-scale structure experiments including the Dark Energy Spectroscopic Instrument (DESI) and Euclid will probe wider and deeper cosmic volumes than those covered by previous surveys. The Cartesian power…
We introduce the Stellar decomposition, a model for efficient topological data structures over a broad range of simplicial and cell complexes. A Stellar decomposition of a complex is a collection of regions indexing the complex's vertices…
In this paper, we adopt minimal gravitational decoupling scheme to extend a non-static spherically symmetric isotropic composition to anisotropic interior in…
Photometric and astrometric monitoring of directly imaged exoplanets will deliver unique insights into their rotational periods, the distribution of cloud structures, weather, and orbital parameters. As the host star is occulted by the…
Spherical harmonics provide a smooth, orthogonal, and symmetry-adapted basis to expand functions on a sphere, and they are used routinely in physical and theoretical chemistry as well as in different fields of science and technology, from…
We present a new approach for correcting instrumental polarization by modeling the non-depolarizing effects of a complex series of optical elements to determine physically realizable Mueller matrices. Provided that the Mueller matrix of the…
Recently, there have been studies of parametric resonance decay of oscillating real homogeneous cosmological scalar fields, in both the narrow-band and broad-band case, primarily within the context of inflaton decay and (p)reheating.…
Due to the exquisite photometric precision, transiting exoplanet discoveries from the Kepler mission are enabling several new techniques of confirmation and characterization. One of these newly accessible techniques analyzes the phase…
We perform an all-sky analysis of the general relativistic galaxy power spectrum using the well-developed spherical Fourier decomposition. Spherical Fourier analysis expresses the observed galaxy fluctuation in terms of the spherical…
Controllability and observability Gramians, along with their inverses, are widely used to solve various problems in control theory. This paper proposes spectral decompositions of the controllability Gramian and its inverse based on system…
We propose a conjectural semiorthogonal decomposition for the derived category of the moduli space of stable rank 2 bundles with fixed determinant of odd degree, independently formulated by Narasimhan. We discuss some evidence for, and…