
Entropy, neutroentropy and antientropy for neutrosophic information
This approach presents a multivalued representation of the neutrosophic...
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Fractional hypergraph isomorphism and fractional invariants
Fractional graph isomorphism is the linear relaxation of an integer prog...
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From SharmaMittal to vonNeumann Entropy of a Graph
In this article, we introduce the SharmaMittal entropy of a graph, whic...
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A System of Billiard and Its Application to InformationTheoretic Entropy
In this article, we define an informationtheoretic entropy based on the...
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Linear Size Sparsifier and the Geometry of the Operator Norm Ball
The Matrix Spencer Conjecture asks whether given n symmetric matrices in...
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Reshaping Convex Polyhedra
Given a convex polyhedral surface P, we define a tailoring as excising f...
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Information theoretic parameters of noncommutative graphs and convex corners
We establish a second antiblocker theorem for noncommutative convex corners, show that the antiblocking operation is continuous on bounded sets of convex corners, and define optimisation parameters for a given convex corner that generalise wellknown graph theoretic quantities. We define the entropy of a state with respect to a convex corner, characterise its maximum value in terms of a generalised fractional chromatic number and establish entropy splitting results that demonstrate the entropic complementarity between a convex corner and its antiblocker. We identify two extremal tensor products of convex corners and examine the behaviour of the introduced parameters with respect to tensoring. Specialising to noncommutative graphs, we obtain quantum versions of the fractional chromatic number and the clique covering number, as well as a notion of noncommutative graph entropy of a state, which we show to be continuous with respect to the state and the graph. We define the Witsenhausen rate of a noncommutative graph and compute the values of our parameters in some specific cases.
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