Mergers are functions that transform k (possibly dependent) random sources into a single random source, in a way that ensures that if one of the input sources has minentropy rate δ then the output has min-entropy rate close to δ. Mergers have proven to be a very useful tool in explicit constructions of extractors and condensers, and are also interesting objects in their own right. In this work ...

The interrelationships of the fundamental biological processes natural selection, mutation, and stochastic drift are quantified by the entropy rate of Moran processes with mutation, measuring the long-run variation of a Markov process. The entropy rate is shown to behave intuitively with respect to evolutionary parameters such as monotonicity with respect to mutation probability (for the neutra...

Mergers are functions that transform k (possibly dependent) random sources into a single random source, in a way that ensures that if one of the input sources has min-entropy rate δ then the output has min-entropy rate close to δ. Mergers have proven to be a very useful tool in explicit constructions of extractors and condensers, and are also interesting objects in their own right. In this work...

In this paper, the two parameter ADK entropy, as a generalized of Re’nyi entropy, is considered and some properties of it, are investigated. We will see that the ADK entropy for continuous random variables is invariant under a location and is not invariant under a scale transformation of the random variable. Furthermore, the joint ADK entropy, conditional ADK entropy, and chain rule of this ent...

The change in entropy, S , associated with the quasi-static absorption of a particle of energy ε by a Schwarzschild black hole (ScBH) is approximately (ε/T )− s, where T is the Hawking temperature of the black hole and s is the entropy of the particle. Motivated by the statistical interpretation of entropy, it is proposed here that the absorption should be suppressed, but not forbidden, when S ...

We provide a new derivation of the log likelihood spectral distance measure for signal processing using the logarithm of the ratio of entropy rate powers. Using this interpretation, we show that the log likelihood ratio is equivalent to the difference of two differential entropies, and further that it can be written as the difference of two mutual informations. These latter two expressions allo...

16.1 Recap Last time (and also in Homework #3), we introduced the notion of covering and packing numbers. Definition 1. Given a set S and a metric ρ and tolerance ǫ, the ǫ-covering number is given by N(ǫ;S, ρ) = min { n | S ⊆ ∪i=1Bǫ(y), for some y(i) ∈ S} } . Here Bǫ(y) = {x | ρ(x, y) ≤ ǫ} is the ball of radius ǫ centered at y. Thus, the ǫ-covering number is the minimum number of balls of radiu...

Computational notions of entropy have recently found many applications, including leakageresilient cryptography, deterministic encryption or memory delegation. The two main types of results which make computational notions so useful are (1) Chain rules, which quantify by how much the computational entropy of a variable decreases if conditioned on some other variable (2) Transformations, which q...

The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation dependent on both short-run and long-run behavior, and allow the relationships between mutation, selection, and population size to be examined. Bounds for the ...