Related papers: Varentropy Decreases Under the Polar Transform
The Varentropy is a measure of the variability of the information content of random vector and it is invariant under affine transformations. We introduce the statistical estimate of varentropy of random vector based on the nearest neighbor…
Entropy is a fundamental thermodynamic quantity that is a measure of the accessible microstates available to a system, with the stability of a system determined by the magnitude of the total entropy of the system. This is valid across truly…
Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…
Transfer entropy (TE) captures the directed relationships between two variables. Partial transfer entropy (PTE) accounts for the presence of all confounding variables of a multivariate system and infers only about direct causality. However,…
In this work, we consider a recently proposed entropy S (called varentropy) defined by a variational relationship dI=beta*(d<x>-<dx>) as a measure of uncertainty of random variable x. By definition, varentropy underlies a generalized…
Transfer entropy (TE) is an attractive model-free method to detect causality and infer structural connectivity of general digital systems. However it relies on high dimensions used in its definition to clearly remove the memory effect and…
We study some properties of binary sequences generated by random substitutions of constant length. Specifically, assuming the alphabet $\{0,1\}$, we consider the following asymmetric substitution rule of length $k$: $0 \to \langle 0, 0,…
Transfer entropy is capable of capturing nonlinear source-destination relations between multi-variate time series. It is a measure of association between source data that are transformed into destination data via a set of linear…
In classical information theory, a causal relationship between two variables is typically modelled by assuming that, for every possible state of one of the variables, there exists a particular distribution of states of the second variable.…
Transfer Entropy (TE), the primary method for determining directed information flow within a network system, can exhibit bias - either in deficiency or excess - during both pairwise and conditioned calculations, owing to high-order…
A statistical model of homopolymer DNA, coupling internal base pair states (unbroken or broken) and external thermal chain fluctuations, is exactly solved using transfer kernel techniques. The dependence on temperature and DNA length of the…
In Reliability Theory, uncertainty is measured by the Shannon entropy. Recently, in order to analyze the variability of such measure, varentropy has been introduced and studied. In this paper we define a new concept of varentropy for past…
We consider a simple transformation (coding) of an iid source called a bit-shift channel. This simple transformation occurs naturally in magnetic or optical data storage. The resulting process is not Markov of any order. We discuss methods…
The ratio of shear viscosity to entropy density, $\eta/s$, is computed in various holographic geometries that break translation invariance (but are isotropic). The shear viscosity does not have a hydrodynamic interpretation in such…
Memory or transistor devices based on electron's spin rather than its charge degree of freedom offer certain distinct advantages and comprise a cornerstone of spintronics. Recent years have witnessed the emergence of a new field,…
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…
We prove a lower estimate on the increase in entropy when two copies of a conditional random variable $X | Y$, with $X$ supported on $\mathbb{Z}_q=\{0,1,\dots,q-1\}$ for prime $q$, are summed modulo $q$. Specifically, given two i.i.d copies…
A full calculation of lepton-pair angular characteristics is carried out for $e^+e^-$ pairs created in $pp$, $pn$ and $pd$ collisions at intermediate energies. It is demonstrated that the proposed new observable, the dilepton decay…
Recently, there has been growing attention to study uncertainty measures for doubly truncated random variables. In this paper, the concept of varextropy for doubly truncated random variables is introduced. The changes of this measure under…
Entropy plays a key role in statistical physics of complex systems, which in general exhibit diverse aspects of emergence on different scales. However, it still remains not fully resolved how entropy varies with the coarse-graining level…