Related papers: A method for testing the cosmic homogeneity with S…
Mutidimensional cosmological models with $n\left( n\geq 2\right) $ Einstein spaces $M_i\left( i=1,\ldots ,n\right) $ are investigated. The cosmological constant and homogeneous minimally coupled scalar field as a matter sources are…
Most of current cosmological theories are built combining an isotropic and homogeneous manifold with a scale factor that depends on time. If one supposes a hyperconical universe with linear expansion, an inhomogeneous metric can be obtained…
We examine the properties of a recently proposed observationally viable alternative to homogeneous cosmology with smooth dark energy, the timescape cosmology. In the timescape model cosmic acceleration is realized as an apparent effect…
I consider the effect of a finite sample size on the entropy of a sample of independent events. I propose formula for entropy which satisfies Shannon's axioms, and which reduces to Shannon's entropy when sample size is infinite. I discuss…
We analyze two different algorithms for constructing weakly inhomogeneous models for the low-redshift Universe, in order to provide a tool for testing the geodesic dynamics, within the sphere of validity for the Universe acceleration. We…
The scaling properties of various composite information-theoretic measures (Shannon and R\'enyi entropy sums, Fisher and Onicescu information products, Tsallis entropy ratio, Fisher-Shannon product and shape complexity) are studied in…
This paper is devoted to the study the $m$-point homogeneity property and the point homogeneity degree for finite metric spaces. Since the vertex sets of regular polytopes, as well as of some their generalizations, are homogeneous, we pay…
Testing the homogeneity between two samples of functional data is an important task. While this is feasible for intensely measured functional data, we explain why it is challenging for sparsely measured functional data and show what can be…
In this paper, we consider testing the homogeneity for proportions in independent binomial distributions especially when data are sparse for large number of groups. We provide broad aspects of our proposed tests such as theoretical studies,…
Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given…
We consider the problem of reconstructing inhomogeneities in an isotropic elastic body using time harmonic waves. Here we extend the so called monotonicity method for inclusion detection and show how to determine certain types of…
We present a new methodology and accompanying theory to test for separability of spatio-temporal functional data. In spatio-temporal statistics, separability is a common simplifying assumption concerning the covariance structure which, if…
We present cosmological-scale numerical simulations of an evolving universe in full general relativity (GR) and introduce a new numerical tool, {\sc CosmoGRaPH}, which employs the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formalism on a…
New measurements of galaxy clustering and background radiations provide improved constraints on the isotropy and homogeneity of the Universe on large scales. In particular, the angular distribution of radio sources and the X-Ray Background…
The Shannon entropy of a random variable $X$ has much behaviour analogous to a signed measure. Previous work has concretized this connection by defining a signed measure $\mu$ on an abstract information space $\tilde{X}$, which is taken to…
The so-called Darboux III oscillator is an exactly solvable $N$-dimensional nonlinear oscillator defined on a radially symmetric space with non-constant negative curvature. This oscillator can be interpreted as a smooth (super)integrable…
In this paper a new method of detection of homogeneous zones and singularity parts of a 1D signal is proposed. The entropy function is used to transform signal in piecewise linear one. The multiple regression permits to detect lines and…
Shannon entropy in position ($S_{\rvec}$) and momentum ($S_{\pvec}$) spaces, along with their sum ($S_t$) are presented for unit-normalized densities of He, Li$^+$ and Be$^{2+}$ ions, spatially confined at the center of an impenetrable…
Isomorph theory is one of the promising theories to understand the quasi-universal relationship between thermodynamic, dynamic and structural characteristics. Based on the hidden scale invariance of the inverse power law potentials, it…
We define a one-parameter family of entropies, each assigning a real number to any probability measure on a compact metric space (or, more generally, a compact Hausdorff space with a notion of similarity between points). These entropies…