860 research outputs found
An Analysis of Some Refractive Error Trends in US Air Force Pilots and Navigators
Refractive error trends with age in US Air Force pilots and navigator
Complexity and capacity bounds for quantum channels
We generalise some well-known graph parameters to operator systems by
considering their underlying quantum channels. In particular, we introduce the
quantum complexity as the dimension of the smallest co-domain Hilbert space a
quantum channel requires to realise a given operator system as its
non-commutative confusability graph. We describe quantum complexity as a
generalised minimum semidefinite rank and, in the case of a graph operator
system, as a quantum intersection number. The quantum complexity and a closely
related quantum version of orthogonal rank turn out to be upper bounds for the
Shannon zero-error capacity of a quantum channel, and we construct examples for
which these bounds beat the best previously known general upper bound for the
capacity of quantum channels, given by the quantum Lov\'asz theta number
Computing the entropy of user navigation in the web
Navigation through the web, colloquially known as "surfing", is one of the main activities of users during web interaction. When users follow a navigation trail they often tend to get disoriented in terms of the goals of their original query and thus the discovery of typical user trails could be useful in providing navigation assistance. Herein, we give a theoretical underpinning of user navigation in terms of the entropy of an underlying Markov chain modelling the web topology. We present a novel method for online incremental computation of the entropy and a large deviation result regarding the length of a trail to realize the said entropy. We provide an error analysis for our estimation of the entropy in terms of the divergence between the empirical and actual probabilities. We then indicate applications of our algorithm in the area of web data mining. Finally, we present an extension of our technique to higher-order Markov chains by a suitable reduction of a higher-order Markov chain model to a first-order one
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