Related papers: A Test for Isotropy on a Sphere using Spherical Ha…
We propose and develop a formalism to describe and constrain statistically anisotropic primordial perturbations. Starting from a decomposition of the primordial power spectrum in spherical harmonics, we find how the temperature fluctuations…
Data uniformity is a concept associated with several semantic data characteristics such as lack of features, correlation and sample bias. This article introduces a novel measure to assess data uniformity and detect uniform pointsets on…
In modeling spatial processes, a second-order stationarity assumption is often made. However, for spatial data observed on a vast domain, the covariance function often varies over space, leading to a heterogeneous spatial dependence…
Despite its fundamental importance in cosmology, there have been very few straight-forward tests of the cosmological principle. Such tests are especially timely because of the hemispherical asymmetry in the cosmic microwave background…
Testing for dependence has been a well-established component of spatial statistical analyses for decades. In particular, several popular test statistics have desirable properties for testing for the presence of spatial autocorrelation in…
Statistical isotropy is often assumed in cosmology and should be tested rigorously against observational data. We construct simple quadratic estimators to reconstruct asymmetry in the primordial power spectrum from CMB temperature and…
Spatio-temporal covariances are important for describing the spatio-temporal variability of underlying random processes in geostatistical data. For second-order stationary processes, there exist subclasses of covariance functions that…
Modern cosmology rests on the cosmological principle, that on large enough scales the Universe is both homogeneous and isotropic. A corollary is that galaxies' spin vectors should be isotropically distributed on the sky. This has been…
Persistent Homology is a widely used topological data analysis tool that creates a concise description of the topological properties of a point cloud based on a specified filtration. Most filtrations used for persistent homology depend…
The statistical expectation values of the temperature fluctuations and polarization of cosmic microwave background (CMB) are assumed to be preserved under rotations of the sky. We investigate the statistical isotropy (SI) of the CMB maps…
We consider an analysis of variance type problem, where the sample observations are random elements in an infinite dimensional space. This scenario covers the case, where the observations are random functions. For such a problem, we propose…
For the accurate representation and reconstruction of band-limited signals on the sphere, an optimal-dimensionality sampling scheme has been recently proposed which requires the optimal number of samples equal to the number of degrees of…
We investigate how to derive an isotropic stellar model in the framework of mimetic gravitational theory. Recently, this theory has gained big interest due to its difference from Einstein's general relativity (GR), especially in the domain…
Reverberant sound fields are often modeled as isotropic. However, it has been observed that spatial properties change during the decay of the sound field energy, due to non-isotropic attenuation in non-ideal rooms. In this letter, a model…
We extend a previous analysis of spatial correlation functions for classical electromagnetic vector fields near a perfectly conducting boundary [PRE, vol. 73, 036604 (2006)] to the case of an isotropic semi-infinite medium with planar…
In this article, we study whether the slope functions of two scalar-on-function regression models in two samples are associated with any arbitrary transformation along the vertical axis. The problem is formally stated as a statistical…
This study presents a comprehensive investigation of anisotropy in a holographic p-wave superconductor model, revealing novel insights into the behavior of quantum information measures in strongly coupled systems. Through rigorous…
In this paper, we investigate a two dimensional isotropic harmonic oscillator on a time-dependent spherical background. The effect of the background can be represented as a minimally coupled field to the oscillator's Hamiltonian. For a…
Isotropic covariance structures can be unreasonable for phenomena in three-dimensional spaces such as the ocean. In the ocean, the variability of the response may vary with depth, and ocean currents may lead to spatially varying anisotropy.…
The Standard Inflationary model predicts an isotropic distribution of the Cosmic Microwave Background temperature fluctuations. Detection of deviations from statistical isotropy would call for a revision of the physics of the early…