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Entropy and random feedback
Convex function matrix spectrum application linear controller design
2015/8/11
The gamma-entropy is a convex function of matrices that is closely related to the Frobenius and spectral (maximum singular value) norms. It comes up in several applications such as central H-infinity ...
Empirical estimation of entropy functionals with confidence
Empirical estimation of entropy functionals confidence
2011/2/23
Nonparametric estimation of functionals of density from nite number of samples is an important tool in domains such as statistics, signal processing and machine learning.While several estimators have...
Natural extensions and entropy of $\alpha$-continued fractions
Natural extensions entropy
2010/11/23
We construct a natural extension for each of Nakada's $\alpha$-continued fractions and show the continuity as a function of $\alpha$ of both the entropy and the measure of the natural extension domai...
New entropy conditions for scalar conservation laws with discontinuous flux
New entropy conditions scalar conservation laws discontinuous flux
2010/11/23
We propose new Kruzhkov type entropy conditions for one dimensional scalar conservation law with a discontinuous flux. We prove existence and uniqueness of the entropy admissible weak solution to the ...
Asymptotic estimates on the time derivative of entropy on a Riemannian manifold
the time derivative entropy Riemannian manifold
2010/11/23
We consider the entropy of the solution to the heat equation on a Riemannian manifold. When the manifold is compact, we provide two estimates on the rate of change of the entropy in terms of the lower...
Approximating the Hard Square Entropy Constant with Probabilistic Methods
Square Entropy Constant Probabilistic Methods
2010/11/15
For any two-dimensional nearest neighbor shift of finite type X and any integer n > 0, one can define the horizontal strip shift H_n(X) to be the set of configurations on Z x {1,...,n} which do not c...
Entropy for symbolic dynamics with overlapping alphabets
Entropy for symbolic dynamics overlapping alphabets
2010/11/22
We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and s...