Infinite-message Interactive Function Computation in Collocated Networks

An interactive function computation problem in a collocated network is studied in a distributed block source coding framework. With the goal of computing a desired function at the sink, the source nodes exchange messages through a sequence of error-free broadcasts. The infinite-message minimum sum-rate is viewed as a functional of the joint source pmf and is characterized as the least element in a partially ordered family of functionals having certain convex-geometric properties. This characterization leads to a family of lower bounds for the infinite-message minimum sum-rate and a simple optimality test for any achievable infinite-message sum-rate. An iterative algorithm for evaluating the infinite-message minimum sum-rate functional is proposed and is demonstrated through an example of computing the minimum function of three sources.Comment: 5 pages. 2 figures. This draft has been submitted to IEEE International Symposium on Information Theory (ISIT) 201

Unified Parametrization of Quark and Lepton Mixing Matrices

We present a unified parametrization of quark and lepton mixing matrices. By using some simple relations between the mixing angles of quarks and leptons, i.e., the quark-lepton complementarity, we parametrize the lepton mixing matrix with the Wolfenstein parameters $\lambda$ and $A$ of the quark mixing matrix. It is shown that the Wolfenstein parameter $\lambda$ can measure both the deviation of the quark mixing matrix from the unit matrix, and the deviation of the lepton mixing matrix from the exactly bimaximal mixing pattern.Comment: 4 Latex pages, notation revised, no change in physical content, final version for publicatio

Superluminal Neutrinos in the Minimal Standard Model Extension

Most recently, the measurement of the neutrino velocity with the OPERA detector in the CNGS beam shows unexpected indication, that the muon neutrino velocity, $v_{\nu}$, exceeds the velocity of light in the vacuum, $c$, which is obviously in contradiction with the most basic hypothesis of modern physics. Within the framework of minimal Standard Model Extension, we discuss the modified dispersion relation and consequently the velocity-energy relation of muon neutrinos. The simplified models are fit to the OPERA data, Fermilab experiment and MINO data. We find that minimal Standard Extension can describe these long baseline superluminal neutrinos to a good accuracy. For the well-known tension between the OPERA measurement and the Supernova 1987A neutrino observation, we discussed two ways out of the contradiction.Comment: 7 pages, 2 figure