Related papers: A method for testing the cosmic homogeneity with S…
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 this paper, we present a new multi-scale information content calculation method based on Shannon information (and Shannon entropy). The original method described by Claude E. Shannon and based on the logarithm of the probability of…
Empirical researchers often use slope-homogeneity tests to assess whether slopes can be treated as common across units. A key difficulty is that heterogeneity may be concentrated in a small number of units, so that a failure to reject…
The standard Friedmann model of cosmology is based on the Copernican Principle, i.e. the assumption of a homogeneous background on which structure forms via perturbations. Homogeneity underpins both general relativistic and modified gravity…
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…
There are not many tools to quantitatively monitor the emergence of classical geometric features from a quantum spacetime, whose microscopic structure may be a highly quantum-fluctuating "spacetime foam". To improve this situation, we…
The test of homogeneity for normal mixtures has been conducted in diverse research areas, but constructing a theory of the test of homogeneity is challenging because the parameter set for the null hypothesis corresponds to singular points…
We analyze the SDSS DR12 quasar catalogue to test the large-scale smoothness in the quasar distribution. We quantify the degree of inhomogeneity in the quasar distribution using information theory based measures and find that the degree of…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
The uncertainty relation based on the Shannon entropies of the probability densities in position and momentum spaces is improved for quantum systems in arbitrary $D$-dimensional spherically symmetric potentials. To find it, we have used the…
We relate the information entropy and the mass variance of any distribution in the regime of small fluctuations. We use a set of Monte Carlo simulations of different homogeneous and inhomogeneous distributions to verify the relation and…
Exact cosmological solutions are obtained for a five dimensional inhomogeneous fluid distribution along with a Brans-Dicke type of scalar field. The set includes varied forms of matter field including $\rho+p=0$, where p is the 3D isotropic…
The problem of Shannon entropy estimation in countable infinite alphabets is addressed from the study and use of convergence results of the entropy functional, which is known to be discontinuous with respect to the total variation distance…
We present the Shannon entropy as an indicator of spatial resolution for morphology of resonance mode pattern in dielectric micro cavity. We obtain two types of optimized mesh point for the minimum and maximum sizes, respectively. The…
Model-independent methods in cosmology has become an essential tool in order to deal with an increasing number of theoretical alternatives for explaining the late-time acceleration of the Universe. In principle, this provides a way of…
The BOSS quasar sample is used to study cosmic homogeneity with a 3D survey in the redshift range $2.2<z<2.8$. We measure the count-in-sphere, $N(<\! r)$, i.e. the average number of objects around a given object, and its logarithmic…
The assumption of homogeneity and isotropy on large scales is one of the main hypotheses of the standard cosmological model. In this paper, we revisit a test of cosmological isotropy using type Ia supernova (SN Ia) distances provided by the…
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…
The Shannon entropy in the atomic, molecular and chemical physics context is presented by using as test cases the hydrogenic-like atoms $H_c$, ${He_c}^+$ and ${Li_c}^{2+}$ confined by an impenetrable spherical box. Novel expressions for…
The concept of entropy, firstly introduced in information theory, rapidly became popular in many applied sciences via Shannon's formula to measure the degree of heterogeneity among observations. A rather recent research field aims at…