Related papers: A method for testing the cosmic homogeneity with S…
Aim of this short note is to study Shannon's entropy power along entropic interpolations, thus generalizing Costa's concavity theorem. We shall provide two proofs of independent interest: the former by $\Gamma$-calculus, hence applicable to…
Statements of Shannon's Noiseless Coding Theorem by various authors, including the original, are reviewed and clarified. Traditional statements of the theorem are often unclear as to when it applies. A new notation is introduced and the…
Assuming the universe is spatially homogeneous on the largest scales lays the foundation for almost all cosmology. This idea is based on the Copernican principle, that we are not at a particularly special place in the universe.…
This article looks at how inhomogeneous spacetime models may be significant for cosmology. First it looks at how the averaging process may affect large scale dynamics, with backreaction effects leading to effective contributions to the…
In this paper, we provide the proof of $L^2$ consistency for the $k$th nearest neighbour distance estimator of the Shannon entropy for an arbitrary fixed $k\geq 1.$ We construct the non-parametric test of goodness-of-fit for a class of…
In this thesis we investigate cosmological models more general than the isotropic and homogeneous Friedmann-Lemaitre models. We focus on cosmologies with one spatial degree of freedom, whose matter content consists of a perfect fluid and…
We describe and analyze some Monte Carlo methods for manifolds in Euclidean space defined by equality and inequality constraints. First, we give an MCMC sampler for probability distributions defined by un-normalized densities on such…
3D image processing constitutes nowadays a challenging topic in many scientific fields such as medicine, computational physics and informatics. Therefore, development of suitable tools that guaranty a best treatment is a necessity.…
Shannon's information entropies in position- and momentum- space and their sum $S$ are calculated for various $s$-$p$ and $s$-$d$ shell nuclei using a correlated one-body density matrix depending on the harmonic oscillator size $b_0$ and…
The Shannon entropy is used as a basis for applying different lemmas and conjectures concerning the set of gaps between prime numbers G_p , thus estimating several measures of it. The same procedures are applied to artificially created…
We quantify the physical memory of the cosmic density field using mutual information between $N$-body snapshots at different redshifts, removing a random baseline to isolate gravitational correlations. The shared mutual information rises…
The Cram\'er-Rao, Fisher-Shannon and LMC shape complexity measures have been recently shown to play a relevant role to study the internal disorder of finite many-body systems (e.g., atoms, molecules, nuclei). They highlight amongst the…
We present a general approach to the study of the local distribution of measures on Euclidean spaces, based on local entropy averages. As concrete applications, we unify, generalize, and simplify a number of recent results on local…
In this work we examine two different measures for inhomogeneity and complexity that are derived from nonextensive considerations a' la Tsallis. Their performance is then tested on theoretically generated patterns. All measures are found to…
We investigate a hybrid numerical algorithm aimed at the large-scale cosmological N-body simulation for the on-going and the future high precious sky surveys. It makes use of a truncated Fast Multiple Method (FMM) for short-range gravity,…
We show that an information-theoretic property of Shannon's entropy power, known as concavity of entropy power, can be fruitfully employed to prove inequalities in sharp form. In particular, the concavity of entropy power implies the…
The current standard model of cosmology, the LambdaCDM model, is based on the homogeneous FLRW solutions of the Einstein equations to which some perturbations are added to account for the CMB features and structure formation at large…
We consider possible tests of the Einstein Equivalence Principle for physical systems in which quantum-mechanical vacuum energies cannot be neglected. Specific tests include a search for the manifestation of non-metric effects in Lamb-shift…
In this paper, we obtain new measurements of the angular homogeneity scale ($\theta_H$) from the BOSS DR12 and eBOSS DR16 catalogs of Luminous Red Galaxies of the Sloan Digital Sky Survey. Considering the flat $\Lambda$CDM model, we use the…
Using joint Shannon entropy, we propose an inequality for a four-level system, which is satisfied in any non-contextual realist hidden variable model. We show that this entropic inequality is violated by quantum mechanics for a range of…