This paper discusses some details of Vachaspati’s particle-monopole correspondence and their relation to a dual standard model. We show that contained within his correspondence are several sub-correspondences relating to electroweak, strong and hypercharge interactions. Associated with each of these we propose an analogous dual model; the use of these being to examine in isolation specific feat...

Hypercubes and star graphs are widespread topologies of interconnection networks. The class of hyper-stars was introduced as a new type of interconnection network to compete with both hypercubes and star graphs, and the class of folded hyper-stars is a strengthened variation of hyperstars with additional links to connect nodes with complemented 0/1-strings. Constructing independent spanning tre...

The double copy relates scattering amplitudes and classical solutions in Yang-Mills theory, gravity, related field theories. Previous work has shown that this an explicit realisation self-dual YM where the equation of motion can be written a form maps directly to Pleba\'nski's heavenly for gravity. involves area-preserving diffeomorphism algebra, two copies which appear equation. In paper, we s...

We pursue the study of the computational power of Piecewise Constant Derivative PCD systems started in PCD systems are dynamical systems de ned by a piecewise constant di erential equation and can be considered as computational machines working on a continuous space with a continuous time We prove that the languages recognized by rational PCD systems in dimension d k respectively d k k in nite ...

The dual simplex method is frequently the most efficient technique for solving linear programming (LP) problems. This thesis describes an efficient implementation of the sequential dual simplex method and the design and development of two parallel dual simplex solvers. In serial, many advanced techniques for the (dual) simplex method are implemented, including sparse LU factorization, hyper-spa...

Let L be the generalized mixed product ideal induced by a monomial ideal I. In this paper we compute powers of the genearlized mixed product ideals and show that Lk  have a linear resolution if and only if Ik have a linear resolution for all k. We also introduce the generalized mixed polymatroidal ideals and prove that powers and monomial localizations of a generalized mixed polymatroidal ideal...

A light Higgs portal scalar could be abundantly produced in the earth's atmosphere and decay large-volume neutrino detectors. We point out that Hyper-Kamiokande detector bears a strong discovery potential of probing such particles an uncharted parameter space is actively explored by intensity frontier experiments including rare kaon decays. The signal we propose to look for electron-positron pa...