The moment-entropy inequality shows that a continuous random variable with given second moment and maximal Shannon entropy must be Gaussian. Stam’s inequality shows that a continuous random variable with given Fisher information and minimal Shannon entropy must also be Gaussian. The CramérRao inequality is a direct consequence of these two inequalities. In this paper the inequalities above are ...

Given an irreducible subshift of finite type X , a subshift Y , a factor map π : X → Y , and an ergodic invariant measure ν on Y , there can exist more than one ergodic measure on X which projects to ν and has maximal entropy among all measures in the fiber, but there is an explicit bound on the number of such maximal entropy preimages.

One important issue in the theory of Ordered Weighted Averaging (OWA) operators is the determination of the associated weights. One of the first approaches, suggested by O’Hagan, determines a special class of OWA operators having maximal Shannon entropy of the OWA weights for a given level of orness; algorithmically it is based on the solution of a constrained optimization problem. In this pape...

In this paper, we study the variation of ergodic measures maximal $ u $-entropy among set diffeomorphisms factoring over Anosov and having c $-mostly contracting center. By using concept skeleton introduced in [6] prove that number such is upper semi-continuous C^1 $-topology. We also give an example to show how these collapse under small perturbations.

Quantum computation has been growing rapidly in both theory and experiments. In particular, quantum computing devices with a large number of qubits have developed by IBM, Google, IonQ, others. The current are noisy intermediate-scale devices, so approaches to validate processing on these needed. One the most common ways validation for an n-qubit system is tomography, which tries reconstruct sys...

We consider topological Markov chains (also called Markov shifts) on countable graphs. We show that a transient graph can be extended to a recurrent graph of equal entropy which is either positive recurrent of null recurrent, and we give an example of each type. We extend the notion of local entropy to topological Markov chains and prove that a transitive Markov chain admits a measure of maxima...