Construction of Almost Disjunct Matrices for Group Testing

In a \emph{group testing} scheme, a set of tests is designed to identify a small number $t$ of defective items among a large set (of size $N$) of items. In the non-adaptive scenario the set of tests has to be designed in one-shot. In this setting, designing a testing scheme is equivalent to the construction of a \emph{disjunct matrix}, an $M \times N$ matrix where the union of supports of any $t$ columns does not contain the support of any other column. In principle, one wants to have such a matrix with minimum possible number $M$ of rows (tests). One of the main ways of constructing disjunct matrices relies on \emph{constant weight error-correcting codes} and their \emph{minimum distance}. In this paper, we consider a relaxed definition of a disjunct matrix known as \emph{almost disjunct matrix}. This concept is also studied under the name of \emph{weakly separated design} in the literature. The relaxed definition allows one to come up with group testing schemes where a close-to-one fraction of all possible sets of defective items are identifiable. Our main contribution is twofold. First, we go beyond the minimum distance analysis and connect the \emph{average distance} of a constant weight code to the parameters of an almost disjunct matrix constructed from it. Our second contribution is to explicitly construct almost disjunct matrices based on our average distance analysis, that have much smaller number of rows than any previous explicit construction of disjunct matrices. The parameters of our construction can be varied to cover a large range of relations for $t$ and $N$.Comment: 15 Page

Search for Light Higgs Boson at LHC via Production Through Weak Boson Fusion

The LHC potential for observing a light Higgs boson produced through Weak Boson Fusion mode, ${\rm qq}\to {\rm qqH}$, is presented. For non-hadronic decays modes of the Higgs boson the process is identified with a final state containing two energetic forward-backward jets, separated with a large rapidity and a hadronically quiet central region. The use of these properties, combined with special features of some of the decay modes enhances the potential of an early discovery of a light Higgs boson both in the Standard Model and beyond. The recent studies done in the context of CMS experiment are discussed.Comment: 4 pages, 6 figures, Presented at Les XXXVIII Recontres de Moriond,QCD and High Energy Hadronic Interactions}, Les Arcs,Savoie, France, 22-29 March 200

On a Duality Between Recoverable Distributed Storage and Index Coding

In this paper, we introduce a model of a single-failure locally recoverable distributed storage system. This model appears to give rise to a problem seemingly dual of the well-studied index coding problem. The relation between the dimensions of an optimal index code and optimal distributed storage code of our model has been established in this paper. We also show some extensions to vector codes.Comment: A small new section and new references added. A minor error corrected from the previous versio

Chromosomal mutational algebra: a new algebra to manipulate chromosomal mutation

This study leads to a new algebra. An algebra is defined on the common mechanisms of chromosomal mutation. The algebra (_S^[PSI](C)_^, ~*~, ', [DELTA], _D_) is constructed for a given _C_ and [PSI]. This algebra represents the most common chromosomal mutational mechanisms. This can lead to a new way to manipulate chromosomal mutation with higher structures of abstract mathematics. The first proposal of the algebra was reported in Mazumdar _et al._, 2007