Related papers: A new method for testing isotropy with Shannon ent…
(Abridged) We study the properties of anisotropic and axisymmetric velocity ellipsoids from maps of the gas velocity dispersion in nearby galaxies. This data allow us to measure the azimuthal-to-radial axis ratio of gas velocity ellipsoids,…
The cosmological principle assumes that the universe is homogeneous and isotropic on cosmic scales. There exist many works testing the cosmic homogeneity and/or the cosmic isotropy of the universe in the literature. In fact, some…
The statistical tests - done by the authors - are surveyed, which verify the null-hypothesis of the intrinsic randomness in the angular distribution of gamma-ray bursts collected at BATSE Catalog. The tests use the counts-in-cells method,…
Using the 2MASS Photometric Redshift catalogue we perform a number of statistical tests aimed at detecting possible departures from statistical homogeneity and isotropy in the large-scale structure of the Universe. Making use of the angular…
A spatial point pattern is called anisotropic if its spatial structure depends on direction. Several methods for anisotropy analysis have been introduced in the literature. In this paper, we give an overview of nonparametric methods for…
Motivated by the central role played by rotationally symmetric distributions in directional statistics, we consider the problem of testing rotational symmetry on the hypersphere. We adopt a semiparametric approach and tackle problems where…
This paper addresses the problem of detecting and estimating the anisotropy of a stationary real-valued random field from a single realization of one of its excursion sets. This setting is challenging as it relies on observing a binary…
AIMS. To check whether the polar angle distribution of QSOs around nearby spiral galaxies is isotropic or not. METHODS. A statistical analysis of the polar angle distribution of large samples of QSOs from the SDSS survey and Monte Carlo…
A new method for analyzing point patterns produced by the evolution of gravitational clustering is presented. The method is taken from the study of molecular liquids, where it has been introduced for making a statistical description of…
It is not obvious how to extend Shannon's original information entropy to higher dimensions, and many different approaches have been tried. We replace the English text symbol sequence originally used to illustrate the theory by a discrete,…
In parallel with advances in microscale imaging techniques, the fields of biology and materials science have focused on precisely extracting particle properties based on their diffusion behavior. Although the majority of real-world…
We test claims of large-scale anisotropy in the local expansion rate using cluster scaling relations as distance indicators. Using a Bayesian forward model, we jointly fit the X-ray luminosity--temperature (LT) and thermal…
The Shannon entropy is a fundamental measure for quantifying diversity and model complexity in fields such as information theory, ecology, and genetics. However, many existing studies assume that the number of species is known, an…
We investigate the observational effects of a quintessence model in an anisotropic spacetime. The anisotropic metric is a non-rotating particular case of a generalized Godel's metric and is classified as Bianchi III. This metric is an exact…
We investigate distributional properties of a class of spectral spatial statistics under irregular sampling of a random field that is defined on $\mathbb{R}^d$, and use this to obtain a test for isotropy. Within this context, edge effects…
Recently, a Monte Carlo method has been presented which allows for the form-free retrieval of size distributions from isotropic scattering patterns, complete with uncertainty estimates linked to the data quality. Here, we present an…
The cosmological principle, as the cornerstone of the standard cosmological model, requires that the Universe be homogeneous and isotropic on large scales. As a fundamental assumption, it is constantly subjected to testing via various…
Recent observational analyses have suggested possible evidence of hemisphere asymmetry in cosmological datasets. Parameterizations of this kind place observers in a privileged position-specifically on the plane that divides the two…
We analyze a set of volume limited samples from SDSS DR12 to quantify the degree of inhomogeneity at different length scales using Shannon entropy. We find that the galaxy distributions exhibit a higher degree of inhomogeneity as compared…
We evaluate reflected entropy in certain anisotropic boundary theories dual to nonrelativistic geometries using holography. It is proposed that this quantity is proportional to the minimal area of the entanglement wedge cross section. Using…