Related papers: Projections, Entropy and Sumsets
We generalize the weighted cumulative entropies (WCRE and WCE), introduced in [5], for a system or component lifetime. Representing properties of cumulative entropies, several bounds and inequalities for the WCRE is proposed
In this perspective review, we present a concise yet multifaceted overview of the pivotal role played by the the shear viscosity to entropy density ratio across various physical contexts. After summarizing some of the main aspects of the…
This paper is twofold. In the first part, we present a refinement of the R\'enyi Entropy Power Inequality (EPI) recently obtained in \cite{BM16}. The proof largely follows the approach in \cite{DCT91} of employing Young's convolution…
The category of metric spaces is a subcategory of quasi-metric spaces. In this paper the notion of entropy for the continuous maps of a quasi-metric space is extended via spanning and separated sets. Moreover, two metric spaces that are…
We consider the technique introduced in a recent work by Ashtekar, Campiglia and Henderson, which generate a spinfoam-like sum from a Hamiltonian theory. We study the possibility of using it for finding the generalized projector of a…
This paper represents an extended version of an earlier note [10]. The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. We analyse analogs of…
Projection theorems of divergences enable us to find reverse projection of a divergence on a specific statistical model as a forward projection of the divergence on a different but rather "simpler" statistical model, which, in turn, results…
Some related results to Pecaric's inequality in inner product spaces that generalises Bombieri's inequality, are given.
Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…
We present two new estimators for estimating the entropy of absolutely continuous random variables. Some properties of them are considered, specifically consistency of the first is proved. The introduced estimators are compared with the…
The notion of the ultrametrics can be considered as a zero-dimensional analogue of ordinary metrics, and it is expected to prove ultrametric versions of theorems on metric spaces. In this paper, we provide ultrametric versions of the…
We compute R\'enyi entropies for the statistics of a noisy simultaneous observation of two complementary observables in two-dimensional quantum systems. The relative amount of uncertainty between two states depends on the uncertainty…
Entropy is the measure of uncertainty in any data and is adopted for maximisation of mutual information in many remote sensing operations. The availability of wide entropy variations motivated us for an investigation over the suitability…
In this article we discuss a generalized Wirtinger inequality.
We generalize several theorems of R\'enyi, Parry, Dar\'oczy and K\'atai by characterizing the greedy and quasi-greedy expansions in non-integer bases.
We extend the recent $L^{1}$ uncertainty inequalities obtained by Dall'ara-Trevisan to the metric setting. For this purpose we introduce a new class of weights, named *isoperimetric weights*, for which the growth of the measure of their…
Entropic uncertainty relations play an important role in both fundamentals and applications of quantum theory. Although they have been well-investigated in quantum theory, little is known about entropic uncertainty in generalized…
We establish some weighted $L^2$ inequalities for Fourier extension operators in the setting of orthonormal systems. In the process we develop a direct approach to such inequalities based on generalised Wigner distributions, complementing…
The entropy power inequality for independent random vectors is a foundational result of information theory, with deep connections to probability and geometric functional analysis. Several extensions of the entropy power inequality have been…
In this note a notion of generalized topological entropy for arbitrary subsets of the space of all sequences in a compact topological space is introduced. It is shown that for a continuous map on a compact space the generalized topological…