Related papers: Varentropy Decreases Under the Polar Transform
Maximum entropy distributions with discrete support in $m$ dimensions arise in machine learning, statistics, information theory, and theoretical computer science. While structural and computational properties of max-entropy distributions…
Inferring the directionality of interactions between cellular processes is a major challenge in systems biology. Time-lagged correlations allow to discriminate between alternative models, but they still rely on assumed underlying…
The chemical ordering transition in a binary alloy is examined using classical density functional theory for a binary mixture. The ordered lattice is assumed to be obtained from the disordered lattice by a volume change only, as in L1_2…
Various lower bounds are established for the entropy of sums, products and their combinations. First, we derive a prime-field analogue of a version of the entropy power inequality established by Tao over torsion-free groups. Next, we prove…
The variance of (relative) surprisal, also known as varentropy, so far mostly plays a role in information theory as quantifying the leading order corrections to asymptotic i.i.d.~limits. Here, we comprehensively study the use of it to…
The expected distributions of eclipse-depth versus period for eclipsing binaries of different luminosities are derived from large-scale population synthesis experiments. Using the rapid Hurley et al. BSE binary evolution code, we have…
We develop convergent variational perturbation theory for quantum statistical density matrices. The theory is applicable to polynomial as well as nonpolynomial interactions. Illustrating the power of the theory, we calculate the…
When presented with a data stream of two statistically dependent variables, predicting the future of one of the variables (the target stream) can benefit from information about both its history and the history of the other variable (the…
The glass transition is considered within two toys models, a mean field spin glass and a directed polymer in a correlated random potential. In the spin glass model there occurs a dynamical transition, where the system condenses in a state…
IIt is demonstrated that the entropy of statistical mechanics and of information theory, $S({\bf p}) = -\sum p_i \log p_i $ may be viewed as a measure of correlation. Given a probability distribution on two discrete variables, $p_{ij}$, we…
The polar transformation of a binary erasure channel (BEC) can be exactly approximated by other BECs. Ar{\i}kan proposed that polar codes for a BEC can be efficiently constructed by using its useful property. This study proposes a new class…
A general black-branes system under the T-duality transformation will become another smeared system with different dimensional black branes. We first use some simple examples to see that both systems have a same value of entropy and then…
We study the unfolding of a single polymer chain due to an external force. We use a simplified model which allows to perform all calculations in closed form without assuming a Boltzmann-Gibbs form for the equilibrium distribution.…
We establish a sharp estimate for a minimal number of binary digits (bits) needed to represent all bounded total generalized variation functions taking values in a general totally bounded metric space $(E,\rho)$ up to an accuracy of…
This paper describes an entropy equation, but one that should be used for measuring energy and not information. In relation to the human brain therefore, both of these quantities can be used to represent the stored information. The human…
We consider a soluble model of large $\phi^{4}$-graphs randomly embedded in one compactified dimension; namely the large-order behaviour of finite-temperature perturbation theory for the partition function of the anharmonic oscillator. We…
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…
So far the theory of Bose-Einstein condensates (BEC) of polar molecules was based on an ad hoc generalization of equations for spherical atoms. Here I adopt a rigorous pseudo-potential approach to low-energy dipolar interactions and derive…
In a feedforward network, Transfer Entropy (TE) can be used to measure the influence that one layer has on another by quantifying the information transfer between them during training. According to the Information Bottleneck principle, a…
Bounds on information combining are entropic inequalities that determine how the information, or entropy, of a set of random variables can change when they are combined in certain prescribed ways. Such bounds play an important role in…