Related papers: A new method for testing isotropy with Shannon ent…
The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for…
The impact of local space anisotropy on the transverse Doppler effect is examined. Two types of laboratory experiments aimed at seeking and measuring the local space anisotropy are proposed. In terms of the conventional special relativity…
We analyse the distribution of position angles of 1 million galaxies from the Hyperleda catalogue, a sample that presents the galaxies coordinates in the celestial sphere, information that allows us to look for a possible privileged…
Shannon entropy was defined for probability distributions and then its using was expanded to measure the uncertainty of knowledge for systems with complete information. In this article, it is proposed to extend the using of Shannon entropy…
An indentation testing method, which utilizes lateral contact of a long cylindrical indenter, is developed for a thin transversely isotropic incompressible elastic film deposited onto a smooth rigid substrate. It is assumed that the…
The assumption of isotropy -- that the Universe looks the same in all directions on large scales -- is fundamental to the standard cosmological model. This model forms the building blocks of essentially all of our cosmological knowledge to…
We present a new methodology for the characterization of the metric entropy of infinite-dimensional ellipsoids with exponentially decaying semi-axes. This procedure does not rely on the explicit construction of coverings or packings and…
Consider $M$-estimation in a semiparametric model that is characterized by a Euclidean parameter of interest and an infinite-dimensional nuisance parameter. As a general purpose approach to statistical inferences, the bootstrap has found…
Most linear dimension reduction methods proposed in the literature can be formulated using an appropriate pair of scatter matrices, see e.g. Ye and Weiss (2003), Tyler et al. (2009), Bura and Yang (2011), Liski et al. (2014) and Luo and Li…
Recently, the Shannon entropy, which was introduced originally as a measure of information amount, has been widely used as a useful index of various diversities such as biodiversity and geodiversity. In this work we have evaluated the…
An observation of the anisotropy of dark matter interactions in a direction-sensitive detector would provide decisive evidence for the discovery of galactic dark matter. Directional information would also provide a crucial input to…
A leading way to constrain physical theories from cosmological observations is to test their predictions for the angular clustering statistics of matter tracers, a technique that is set to become ever more central with the next generation…
Three methods for detecting and characterizing structure in point data, such as that generated by redshift surveys, are described: classification using self-organizing maps, segmentation using Bayesian blocks, and density estimation using…
We introduce a new mathematical tool (a direction-dependent probe) to analyse the randomness of purported isotropic Gaussian random fields on the sphere. We apply the probe to assess the full-sky cosmic microwave background (CMB)…
The entropic uncertainty measures of the multidimensional hydrogenic states quantify the multiple facets of the spatial delocalization of the electronic probability density of the system. The Shannon entropy is the most adequate uncertainty…
We present a new study concerning the application of the Schwarzschild orbit superposition method to model spherical galaxies. The method aims to recover the mass and the orbit anisotropy parameter profiles of the objects using measurements…
Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…
Starting from the central density slope-anisotropy theorem of An and Evans (2006), recent investigations have shown that the involved density slope-anisotropy inequality holds not only at the center, but at all radii (i.e. globally) in a…
The cosmological principle asserts that the Universe is homogeneous and isotropic on large enough scales. However, alternative cosmological models can bring about anisotropies through local inhomogeneities, anisotropic evolution, or exotic…
The measurements of CMB anisotropy have opened up a window for probing the global topology of the universe on length scales comparable to and beyond the Hubble radius. We have developed a new method for calculating the CMB anisotropy in…