Criticality of the Exponential Rate of Decay for the Largest Nearest Neighbor Link in Random Geometric Graph

Let n points be placed independently in d-dimensional space according to the densities $f(x) = A_d e^{-\lambda \|x\|^{\alpha}}, \lambda > 0, x \in \Re^d, d \geq 2.$ Let $d_n$ be the longest edge length for the nearest neighbor graph on these points. We show that $(\log(n))^{1-1/\alpha}d_n -b_n$ converges weakly to the Gumbel distribution where $b_n \sim \log \log n.$ We also show that the strong law result, % \lim_{n \to \infty} \frac{(\lambda^{-1}\log(n))^{1-1/\alpha}d_n}{\sqrt{\log \log n}} \to \frac{d}{\alpha \lambda}, a.s. % Thus, the exponential rate of decay i.e. $\alpha = 1$ is critical, in the sense that for $\alpha > 1, d_n \to 0,$ where as $\alpha < 1, d_n \to \infty$ a.s. as $n \to \infty.$Comment: Communicated to 'Stochastic Processes and Their Applications'. Sep. 11, 2006: replaced paper uploaded on Apr. 27, 2006 by a corrected version; errors/corrections found by the authors themselve

Geometric Design and Stability of Power Networks

From the perspective of the network theory, the present work illustrates how the parametric intrinsic geometric description exhibits an exact set of pair correction functions and global correlation volume with and without the inclusion of the imaginary power flow. The Gaussian fluctuations about the equilibrium basis accomplish a well-defined, non-degenerate, curved regular intrinsic Riemannian surfaces for the purely real and the purely imaginary power flows and their linear combinations. An explicit computation demonstrates that the underlying real and imaginary power correlations involve ordinary summations of the power factors, with and without their joint effects. Novel aspect of the intrinsic geometry constitutes a stable design for the power systems.Comment: 23 pages, 11 figures, Keywords: Correlation; Geometry; Power Flow; Network; Stabilit

Molten-Salt-Assisted Annealing for Making Colloidal ZnGa2O4:Cr Nanocrystals with High Persistent Luminescence

Persistent luminescent nanocrystals (PLNCs) in the sub-10 nm domain are considered to be the most fascinating inventions in lighting technology owing to their excellent performance in anti-counterfeiting, luminous paints, bioimaging, security applications, etc. Further improvement of persistent luminescence (PersL) intensity and lifetime is needed to achieve the desired success of PLNCs while keeping the uniform sub-10 nm size. In this work, the concept of molten salt confinement to thermally anneal as-synthesized ZnGa2O4:Cr3+ (ZGOC) colloidal NCs (CNCs) in a molten salt medium at 650 °C is introduced. This method led to significantly monodispersed and few agglomerated NCs with a much improved photoluminescence (PL) and PersL intensity without much growth in the size of the pristine CNCs. Other strategies such as i) thermal annealing, ii) overcoating, and iii) the core–shell strategy have also been tried to improve PL and PersL but did not improve them simultaneously. Moreover, directly annealing the CNCs in air without the assistance of molten salt could significantly improve both PL and PersL but led to particle heterogeneity and aggregation, which are highly unsuitable for in vivo imaging. We believe this work provides a novel strategy to design PLNCs with high PL intensity and long PersL duration without losing their nanostructural characteristics, water dispersibility and biocompatibility

Isolation, cloning and characterization of phlB gene from an Indian strain of Gram negative soil bacteria Pseudomonas fluorescens

412-419Phloroglucinol (PHL) or 2,4-diacetylphloroglucinol (DAPG) is a polyketide compound that exhibits broad spectrum anti-bacterial and antifungal properties against soil-borne plant pathogens. It is produced by gram negative bacterium Pseudomonas (fluorescent Pseudomonad) which renders them a potential biological control agent. The process of PHL production is accomplished by a well coordinated activity of four (phlABCD) genes arranged in an operon. All four genes are essential and indispensable for biosynthesis of DAPG from precursor malonyl CoA. Here, we report cloning and analysis of phlB gene from an Indian strain of Pseudomonas fluorescens. Further, we predicted the structure of PHLB protein and analyzed its intrinsic details. Stereo-chemical properties were analyzed by Ramachandran plot and secondary structure was retrieved by PDB sum. Our study provides insight into the structure of PHLB protein and revealed that though Pseudomonas PHLB lacks conserved motifs and domains it is indispensable for monoacetyl phloroglucinol (MAPG) synthesis

Congestion Managed Multicast Routing in Wireless Mesh Network

To provide broad band connectivity to the mobile users and to build a self-structured network, where it is not possible to have wired network, “Wireless Mesh Networks” are the most vital suitable technology. Routing in Wireless Mesh Networks is a multi-objective nonlinear optimization problem with some constraints. We explore multicast routing for least-cost, delay-sensitive and congestion-sensitive in optimizing the routing in Wireless mesh networks (WMNs). In this work different parameters are associated like edge cost, edge delay and edge congestion. The aim is to create a tree traversing which the set of target nodes are spanned, so as to make the cost and congestion to be minimum with a bounded delay over the path between every pair of source and destination. Since searching optimal routing satisfying multi constraints concurrently is an NP complete problem, we have presented a competent estimated algorithm certified with experimental results, which shows that the performance of presented algorithm is nearly optimum