The covert set-cover problem with application to Network Discovery

We address a version of the set-cover problem where we do not know the sets initially (and hence referred to as covert) but we can query an element to find out which sets contain this element as well as query a set to know the elements. We want to find a small set-cover using a minimal number of such queries. We present a Monte Carlo randomized algorithm that approximates an optimal set-cover of size $OPT$ within $O(\log N)$ factor with high probability using $O(OPT \cdot \log^2 N)$ queries where $N$ is the input size. We apply this technique to the network discovery problem that involves certifying all the edges and non-edges of an unknown $n$-vertices graph based on layered-graph queries from a minimal number of vertices. By reducing it to the covert set-cover problem we present an $O(\log^2 n)$-competitive Monte Carlo randomized algorithm for the covert version of network discovery problem. The previously best known algorithm has a competitive ratio of $\Omega (\sqrt{n\log n})$ and therefore our result achieves an exponential improvement

Heat Transfer in Unsteady Squeezing Flow Between Parallel Plates

In this study, we investigated an unsteady MHD flow between parallel plates in the presence of viscous dissipation. The transformed governing equations are solved numerically using bvp5c Matlab package. The impact of different non-dimensional parameters on velocity and temperature profiles along with the local Nusselt number is discussed graphically. It is observed that the Nusselt number is a decreasing function of the radiation parameter and Hartmann number but it is an increasing function of squeeze number and Eckert number. Keywords:MHD, viscous dissipation, squeeze number, radiatio

Low Degree Metabolites Explain Essential Reactions and Enhance Modularity in Biological Networks

Recently there has been a lot of interest in identifying modules at the level of genetic and metabolic networks of organisms, as well as in identifying single genes and reactions that are essential for the organism. A goal of computational and systems biology is to go beyond identification towards an explanation of specific modules and essential genes and reactions in terms of specific structural or evolutionary constraints. In the metabolic networks of E. coli, S. cerevisiae and S. aureus, we identified metabolites with a low degree of connectivity, particularly those that are produced and/or consumed in just a single reaction. Using FBA we also determined reactions essential for growth in these metabolic networks. We find that most reactions identified as essential in these networks turn out to be those involving the production or consumption of low degree metabolites. Applying graph theoretic methods to these metabolic networks, we identified connected clusters of these low degree metabolites. The genes involved in several operons in E. coli are correctly predicted as those of enzymes catalyzing the reactions of these clusters. We independently identified clusters of reactions whose fluxes are perfectly correlated. We find that the composition of the latter `functional clusters' is also largely explained in terms of clusters of low degree metabolites in each of these organisms. Our findings mean that most metabolic reactions that are essential can be tagged by one or more low degree metabolites. Those reactions are essential because they are the only ways of producing or consuming their respective tagged metabolites. Furthermore, reactions whose fluxes are strongly correlated can be thought of as `glued together' by these low degree metabolites.Comment: 12 pages main text with 2 figures and 2 tables. 16 pages of Supplementary material. Revised version has title changed and contains study of 3 organisms instead of 1 earlie