Weyl group multiple Dirichlet series constructed from quadratic characters

We construct multiple Dirichlet series in several complex variables whose coefficients involve quadratic residue symbols. The series are shown to have an analytic continuation and satisfy a certain group of functional equations. These are the first examples of an infinite collection of unstable Weyl group multiple Dirichlet series in greater than two variables.Comment: incorporated referee's comment

Crystal constructions in Number Theory

Weyl group multiple Dirichlet series and metaplectic Whittaker functions can be described in terms of crystal graphs. We present crystals as parameterized by Littelmann patterns and we give a survey of purely combinatorial constructions of prime power coefficients of Weyl group multiple Dirichlet series and metaplectic Whittaker functions using the language of crystal graphs. We explore how the branching structure of crystals manifests in these constructions, and how it allows access to some intricate objects in number theory and related open questions using tools of algebraic combinatorics

Metaplectic Ice

Spherical Whittaker functions on the metaplectic n-fold cover of GL(r+1) over a nonarchimedean local field containing n distinct n-th roots of unity may be expressed as the partition functions of statistical mechanical systems that are variants of the six-vertex model. If n=1 then in view of the Casselman-Shalika formula this fact is related to Tokuyama's deformation of the Weyl character formula. It is shown that various properties of these Whittaker functions may be expressed in terms of the commutativity of row transfer matrices for the system. Potentially these properties (which are already proved by other methods, but very nontrivial) are amenable to proof by the Yang-Baxter equation

Metabolic Control Analysis in a Cellular Model of Elevated MAO-B: Relevance to Parkinson’s Disease

We previously demonstrated that spare respiratory capacity of the TCA cycle enzyme alpha-ketoglutarate dehydrogenase (KGDH) was completely abolished upon increasing levels of MAO-B activity in a dopaminergic cell model system (Kumar et al., J Biol Chem 278:46432–46439, 2003). MAO-B mediated increases in H2O2 also appeared to result in direct oxidative inhibition of both mitochondrial complex I and aconitase. In order to elucidate the contribution that each of these components exerts over metabolic respiratory control as well as the impact of MAO-B elevation on their spare respiratory capacities, we performed metabolic respiratory control analysis. In addition to KGDH, we assessed the activities and substrate-mediated respiration of complex I, pyruvate dehydrogenase (PDH), succinate dehydrogenase (SDH), and mitochondrial aconitase in the absence and presence of complex-specific inhibitors in specific and mixed substrate conditions in mitochondria from our MAO-B elevated cells versus controls. Data from this study indicates that Complex I and KGDH are the most sensitive to inhibition by MAO-B mediated H2O2 generation, and could be instrumental in determining the fate of mitochondrial metabolism in this cellular PD model system

Determinants of Natural Mating Success in the Cannibalistic Orb-Web Spider Argiope bruennichi

Monogynous mating systems (low male mating rates) occur in various taxa and have evolved several times independently in spiders. Monogyny is associated with remarkable male mating strategies and predicted to evolve under a male-biased sex ratio. While male reproductive strategies are well documented and male mating rates are easy to quantify, especially in sexually cannibalistic species, female reproductive strategies, the optimal female mating rate, and the factors that affect the evolution of female mating rates are still unclear. In this study, we examined natural female mating rates and tested the assumption of a male-biased sex ratio and female polyandry in a natural population of Argiope bruennichi in which we controlled female mating status prior to observations. We predicted variation in female mating frequencies as a result of spatial and temporal heterogeneity in the distribution of mature females and males. Females had a low average mating rate of 1.3 and the majority copulated only once. Polyandry did not entirely result from a male-biased sex-ratio but closely matched the rate of male bigamy. Male activity and the probability of polyandry correlated with factors affecting pheromone presence such as virgin females' density. We conclude that a strong sex ratio bias and high female mating rates are not necessary components of monogynous mating systems as long as males protect their paternity effectively and certain frequencies of bigyny stabilise the mating system

Bioactivity, biocompatibility and antimicrobial properties of a chitosan-mineral composite for periodontal tissue regeneration

A composite membrane of the polymer, chitosan, and the silver-exchanged mineral phase, tobermorite, was prepared by solvent casting and characterised by scanning electron microscopy and Fourier transform infrared spectroscopy. The in vitro bioactivity, cytocompatibility and antimicrobial activity of the composite were evaluated with respect to its potential application as a guided tissue regeneration (GTR) membrane. The in vitro bioactivity was verified by the formation of hydroxyapatite on the surface of the membrane in simulated body fluid and its cytocompatibility was established using MG63 human osteosarcoma cells. The presence of silver ions conferred significant antimicrobial activity against S. aureus, P. aeruginosa and E. coli. The findings of this investigation have indicated that the chitosansilver-tobermorite composite is a prospective candidate for GTR applications