Pabble: parameterised Scribble

© 2014, The Author(s).Many parallel and distributed message-passing programs are written in a parametric way over available resources, in particular the number of nodes and their topologies, so that a single parallel program can scale over different environments. This article presents a parameterised protocol description language, Pabble, which can guarantee safety and progress in a large class of practical, complex parameterised message-passing programs through static checking. Pabble can describe an overall interaction topology, using a concise and expressive notation, designed for a variable number of participants arranged in multiple dimensions. These parameterised protocols in turn automatically generate local protocols for type checking parameterised MPI programs for communication safety and deadlock freedom. In spite of undecidability of endpoint projection and type checking in the underlying parameterised session type theory, our method guarantees the termination of end point projection and type checking

Quasi-Degenerate Neutrino Masses with Normal and Inverted Hierarchy

The effects of CP-phases on the three absolute quasi-degenerate Majorana neutrino (QDN) masses are stud-ied with neutrino mass matrices obeying {\mu} - {\tau} symmetry for normal as well as inverted hierarchical mass patterns. We have made further investigations on 1) the prediction of solar mixing angle which lies below tri-bimaximal mixing value in consistent with neutrino oscillation observational data, 2) the prediction on absolute neutrino mass parameter (mee) in 0{\nu}{\beta}{\beta} decay, and 3) cosmological bound on the sum of the three absolute neutrino masses. The numerical analysis is carried out through the parameterization of neu- trino mass matrices using only two unknown parameters ({\epsilon}, {\eta}) within {\mu} - {\tau} symmetry. The results show the validity of QDN mass models in both normal and inverted hierarchical patterns. These models are far from discrimination and hence not yet ruled out. The results presented in this article are new and have subtle ef- fects in the discrimination of neutrino mass models.Comment: 8 pages, gave a contributory Talk at Ist IAS-CERN Singpore, Jan 2012; Journal of Modern Physics (JMP), Vol 2. No.11, November 2011 US