The notion of smooth entropy allows a unifying, generalized formulation of privacy ampli-cation and entropy smoothing. Smooth entropy is a measure for the number of almost uniform random bits that can be extracted from a random source by probabilistic algorithms. It is known that the R enyi entropy of order at least 2 of a random variable is a lower bound for its smooth entropy. On the other ha...

Abstract For over two decades entropy theory has been applied to groundwater modeling with particular regard to (1) groundwater head, (2) parameter estimation, and (3) contaminant transport. Entropy theory is formulated in two domains: real domain and frequency domain. In the real domain, the theory comprises (a) Shannon entropy or another form, (2) principle of maximum entropy, (3) relative en...

Entropy has been launched as a scientific journal to provide an advanced forum for the community of entropy and information researchers. There are many types of entropy reported in the scientific literature [1]. The great diversity in the concept and definition may cause tremendous problems. My own humble suggestion is the following regarding the main two kinds of entropy: 1. Any information-th...

We give an explicit construction of a function that is almost a 2-source extractor for linear entropy, it is a condenser where the output has almost full entropy. Given 2 sources with entropy δn, the output of the condenser is a distribution on m-bit strings that is ǫ-close to having min-entropy m− poly(log(1/ǫ), 1/δ), where here m is linear in n.

We calculate the quantum corrections to the entropy of a very large black hole, coming from the theory of a D-dimensional, non-critical bosonic string. We show that, for D > 2, as a result of modular invariance the entropy is ultraviolet finite, although it diverges in the infrared (while for D = 2 the entropy contains both ultraviolet and infrared divergences). The issue of modular invariance ...

fluids for various industrial applications because of their excellent thermal performance. This study analytically and experimentally examines the effects of nanoparticle dispersion on the entropy generation of EG–Al2O3 ...

Lecture 1. Free Independence and Free Harmonic Analysis. 2 1.1. Probability spaces. 2 1.2. Non-commutative probability spaces. 3 1.3. Classical independence. 4 1.4. Free products of non-commutative probability spaces. 5 1.5. Free Fock space. 6 1.6. Free Central Limit Theorem. 8 1.7. Free Harmonic Analysis. 10 1.8. Further topics. 16 Lecture 2. Random Matrices and Free Probability. 17 2.1. Rando...

congestive heart failure (chf) remains to be one of the major cardiovascular disorders in the world. due to the prevalence of chf related issues, it is prudent to seek out new prognostic predictors that would facilitate the prevention, monitoring, and treatment of the disease on a daily basis. a detection approach using entropy measures extracted from surface electrocardiograms (ecgs) and class...

A proposal for a new method of classification of objects of various nature, named “2”-soft classification, which allows for referring objects to one of two types with optimal entropy probability for available collection of learning data with consideration of additive errors therein. A decision rule of randomized parameters and probability density function (PDF) is formed, which is determined by...

We show that for any amenable group Γ and any ZΓ-module M of type FL with vanishing Euler characteristic, the entropy of the natural Γ-action on the Pontryagin dual of M is equal to the L-torsion of M. As a particular case, the entropy of the principal algebraic action associated with the module ZΓ/ZΓf is equal to the logarithm of the Fuglede-Kadison determinant of f whenever f is a non-zero-di...