Results 11 to 20 of about 564 (79)
International Journal of Stochastic Analysis, Volume 16, Issue 3, Page 209-231, 2003., 2003 Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst‐case design settings, the disturbance is considered random with imprecisely known probability distribution.
Phil Diamond +2 more
wiley +1 more source
Weighted additive information measures
International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 3, Page 417-423, 1990., 1990 We determine all measurable functions I, G, L : [0, 1] → ℝ satisfying the functional equation for P ∈ Γn, Q ∈ Γm and for a fixed pair (n, m), n ≥ 3, m ≥ 3, where G(0) = L(0) = 0 and G(1) = L(1) = 1. This functional equation has interesting applications in information theory.
Wolfgang Sander
wiley +1 more source
A measure of mutual divergence among a number of probability distributions
International Journal of Mathematics and Mathematical Sciences, Volume 10, Issue 3, Page 597-607, 1987., 1986 The principle of optimality of dynamic programming is used to prove three major inequalities due to Shannon, Renyi and Holder. The inequalities are then used to obtain some useful results in information theory. In particular measures are obtained to measure the mutual divergence among two or more probability distributions.
J. N. Kapur, Vinod Kumar, Uma Kumar
wiley +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 9, Issue 3, Page 545-550, 1986., 1986 In this series, this paper is devoted to the study of a functional equation connected with the characterization of weighted entropy and weighted entropy of degree β. Here, we find the general solution of the functional equation (2) on an open domain, without using 0‐probability and 1‐probability.
Pl. Kannappan, P. K. Sahoo
wiley +1 more source
Remainder Terms for Some Quantum Entropy Inequalities
, 2014 We consider three von Neumann entropy inequalities: subadditivity; Pinsker's inequality for relative entropy; and the monotonicity of relative entropy.
Carlen, Eric A., Lieb, Elliott H.
core +1 more source
Relative entropy via non-sequential recursive pair substitutions
, 2010 The entropy of an ergodic source is the limit of properly rescaled 1-block entropies of sources obtained applying successive non-sequential recursive pairs substitutions (see P. Grassberger 2002 ArXiv:physics/0207023 and D. Benedetto, E.
Benedetto D +7 more
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Variational representations related to Tsallis relative entropy
, 2019 We develop variational representations for the deformed logarithmic and exponential functions and use them to obtain variational representations related to the quantum Tsallis relative entropy.
Hansen, Frank, Shi, Guanghua
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Entropy and a generalisation of `Poincare's Observation'
, 2002 Consider a sphere of radius root(n) in n dimensions, and consider X, a random variable uniformly distributed on its surface. Poincare's Observation states that for large n, the distribution of the first k coordinates of X is close in total variation ...
Johnson, Oliver
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Scientific AfricanExtropy has recently become a focal point of study as a measure of uncertainty in probability distributions and serves as the dual complement to entropy.
Amal S. Hassan +3 more
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New Jensen's bounds for HA-convex mappings with applications to Shannon entropy
Demonstratio MathematicaThe aim of this article is to establish some new extensions and variants of Jensen’s discrete and Simic-type inequalities for HA-convex and uniformly HA-convex functions.
Sayyari Yamin +4 more
doaj +1 more source