The paper provides a quantitative algebraic analysis of a BB’84-type quantum key distribution protocol. The analysis is done in an algebraic setting, where classical and quantum variables form a module for the quantale formed from the communication and quantum actions. The module-quantale pair is endowed with sup-maps that encode uncertainties of agents involved in the protocol, about the varia...

An essential spanning forest of an infinite graph G is a spanning forest of G in which all trees have infinitely many vertices. Let Gn be an increasing sequence of finite connected subgraphs of G for which ∪Gn = G. Pemantle’s arguments (1991) imply that the uniform measures on spanning trees of Gn converge weakly to an Aut(G)-invariant measure μG on essential spanning forests of G. We show that...

Several ways of assigning probabilities to runs of timed automata (TA) have been proposed recently. When only the TA is given, a relevant question is to design a probability distribution which represents in the best possible way the runs of the TA. This question does not seem to have been studied yet. We give an answer to it using a maximal entropy approach. We introduce our variant of stochast...

Tzu-Chieh Wei, Kae Nemoto, Paul M. Goldbart, Paul G. Kwiat, William J. Munro, and Frank Verstraete Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080 Informatics, Bangor University, Bangor LL57 1UT, United Kingdom Hewlett-Packard Laboratories, Filton Road, Stoke Gifford, Bristol, BS34 SQ2, United Kingdom Department of Mathemati...

Point mutations in the phosphorylation domain of the Bcr-Abl fusion oncogene give rise to drug resistance in chronic myelogenous leukemia patients. These mutations alter kinase-mediated signaling function and phenotypic outcome. An information theoretic analysis of the correlation of phosphoproteomic profiling and transformation potency of the oncogene in different mutants is presented. The the...

The notions of “limiting entropy” and “independence entropy” for one-dimensional subshifts were introduced by Louidor, Marcus, and the second author in [15]. It was also implicitly conjectured there that these two quantities are always equal. We verify this conjecture, which implies, among other things, that the limiting entropy of any one-dimensional SFT is of the form 1 n log k for k, n ∈ N. ...

We introduce smooth entropy as a measure for the number of almost uniform random bits that can be extracted from a source by probabilistic algorithms. The extraction process should be universal in the sense that it does not require the distribution of the source to be known. Rather, it should work for all sources with a certain structural property, such as a bound on the maximal probability of ...

In this paper we investigate the support of the unique measure of maximal entropy of complex Hénon maps, J∗. The main question is whether this set is the same as the analogue of the Julia set J .

The concept of C-space entropy was recently introduced in [1, 2, 3], as a measure of knowledge of C-space for sensor-based path planning and exploration for general robot-sensor systems. The robot plans the next sensing action to maximally reduce the expected C-space entropy, also called the maximal expected entropy reduction, or MER criterion. The expected C-space entropy computation, however,...

In this paper, the matrix variate ^-generalized normal distribution is introduced. Then its properties are studied. In particular, it is proved that this distribution has maximal entropy in a certain class of distributions.