نتایج جستجو برای: rényi
تعداد نتایج: 6772 فیلتر نتایج به سال:
Relations between Shannon entropy and Rényi entropies of integer order are discussed. For any N–point discrete probability distribution for which the Rényi entropies of order two and three are known, we provide an lower and an upper bound for the Shannon entropy. The average of both bounds provide an explicit extrapolation for this quantity. These results imply relations between the von Neumann...
A task is randomly drawn from a finite set of tasks and is described using a fixed number of bits. All the tasks that share its description must be performed. Upper and lower bounds on the minimum ρ-th moment of the number of performed tasks are derived. The case where a sequence of tasks is produced by a source and n tasks are jointly described using nR bits is considered. If R is larger than ...
One possibility of defining a quantum Rényi $\alpha $ -divergence two states is to optimize the classical their post-measurement probability distributions over all possible measurements (measured divergence), and maybe regularize thes...
Quantum-mechanical uncertainty relations for position and momentum are expressed in the form of inequalities involving the Rényi entropies. The proof of these inequalities requires the use of the exact expression for the p ,q -norm of the Fourier transformation derived by Babenko and Beckner. Analogous uncertainty relations are derived for angle and angular momentum and also for a pair of compl...
Recall that all the “Real-World” graphs we examined in Lecture 2 had one component containing a large constant fraction of the vertices. The second-largest component was smaller by many orders of magnitude. This property is shared by Erdös-Rényi random graphs and by many other graph models. In this lecture, we will see (mostly) why Erdös-Rényi random graphs have this property. The large compone...
We generalize the topological entanglement entropy to a family of topological Rényi entropies parametrized by a parameter alpha, in an attempt to find new invariants for distinguishing topologically ordered phases. We show that, surprisingly, all topological Rényi entropies are the same, independent of alpha for all nonchiral topological phases. This independence shows that topologically ordere...
EHS/NA22 Collaboration The entropy properties are analyzed by Ma's coincidence method in π + p and K + p collisions of the NA22 experiment at 250 GeV/c incident momentum. By using the Rényi entropies, we test the scaling law and additivity properties in rapidity space. The behavior of the Rényi entropies as a function of the average number of particles is investigated. The results are compared ...
Atar, Chowdhary and Dupuis have recently exhibited a variational formula for exponential integrals of bounded measurable functions in terms of Rényi divergences. We develop a variational characterization of the Rényi divergences between two probability distributions on a measurable space in terms of relative entropies. When combined with the elementary variational formula for exponential integr...
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