Lattices and automorphisms of compact complex manifolds

This work makes use of well-known integral lattices to construct complex algebraic varieties reflecting properties of the lattices. In particular the automorphism groups of the lattices are closely related to the symmetries of varieties. The constructions are to two types: generalised Kummer manifolds and toric varieties. In both cases the examples are of the most interest. A generalised Kummer manifold is the resolution of the quotient of a complex torus by some finite group G. A description of the construction for certain cyclic groups G by given in terms of holomorphic surgery of disc bundles. The action of the automorphism groups is given explicitly. The most important example is a compact complex 12-dimensinoal manifold associated to the Leech lattice admitting an action of the finite simple Suzuki group. All these generalised Kummer manifolds are shown to be simply connected. Toric varieties are associated to certain decompositions of Rn into convex cones. The automorphism groups of those associated to Weyl group decompositions of Rn are calculated. These are used to construct 24-dimensional singular varieties from some Neimeier lattices. Their symmetries are extensions of Mathieu groups and their singularities closely related to the Golay codes

The development of a tin whisker mitigating conformal coating

The development of a tin whisker mitigating conformal coatin

Chinese Postman Problem on edge-colored multigraphs

It is well-known that the Chinese postman problem on undirected and directed graphs is polynomial-time solvable. We extend this result to edge-colored multigraphs. Our result is in sharp contrast to the Chinese postman problem on mixed graphs, i.e., graphs with directed and undirected edges, for which the problem is NP-hard

Successful Cognitive Aging in Rats: A Role for mGluR5 Glutamate Receptors, Homer 1 Proteins and Downstream Signaling Pathways

Normal aging is associated with impairments in cognition, especially learning and memory. However, major individual differences are known to exist. Using the classical Morris Water Maze (MWM) task, we discriminated a population of 24-months old Long Evans aged rats in two groups - memory-impaired (AI) and memory-unimpaired (AU) in comparison with 6-months old adult animals. AI rats presented deficits in learning, reverse memory and retention. At the molecular level, an increase in metabotropic glutamate receptors 5 (mGluR5) was observed in post-synaptic densities (PSD) in the hippocampus of AU rats after training. Scaffolding Homer 1b/c proteins binding to group 1 mGluR facilitate coupling with its signaling effectors while Homer 1a reduces it. Both Homer 1a and 1b/c levels were up-regulated in the hippocampus PSD of AU animals following MWM task. Using immunohistochemistry we further demonstrated that mGluR5 as well as Homer 1b/c stainings were enhanced in the CA1 hippocampus sub-field of AU animals. In fact mGluR5 and Homer 1 isoforms were more abundant and co-localized in the hippocampal dendrites in AU rats. However, the ratio of Homer 1a/Homer 1b/c bound to mGluR5 in the PSD was four times lower for AU animals compared to AI rats. Consequently, AU animals presented higher PKCγ, ERK, p70S6K, mTOR and CREB activation. Finally the expression of immediate early gene Arc/Arg3.1 was shown to be higher in AU rats in accordance with its role in spatial memory consolidation. On the basis of these results, a model of successful cognitive aging with a critical role for mGluR5, Homer 1 proteins and downstream signalling pathways is proposed here

Systematic experimental charge density analysis of anion receptor complexes

The first systematic electronic resolution study of a series of urea-based anion receptor complexes is presented. The hydrogen bonding in these multi-component systems was fully characterised using Bader’s Quantum Theory of Atoms In Molecules (QTAIM) with the strength of the various N?H…anion hydrogen bonds quantified and the individual contributions of different intermolecular forces to the overall receptor: anion interaction derived by comparison of the charge densities in the related complexes. The strength of the N?H…anion hydrogen bonds was correlated to the basicity of the anion and related to modifications applied to the structure of the receptors. The geometric criteria used to identify hydrogen bonding interactions in standard resolution X-ray diffraction studies were shown to be valid for stronger interactions. However, these geometric criteria are less reliable and lead to assumptions that are not necessarily upheld when applied to weaker intermolecular interactions and the presence of these could only be confirmed by charge density studies. The effect that changes to the receptor substitution pattern have on the entire supramolecular system is illustrated by the differences in the electrostatic potential distributions and atomic charges across the series. The application of systematic high resolution studies to rationalise a variety of host-guest systems has been demonstrated

Modular functors in homotopy quantum field theory and tortile structures

AbstractWe study a version of a modular functor for Turaev's homotopy quantum field theories using 2-categories of surfaces. We define the homotopy surface 2-category of a space X and define an SX-structure to be a monoidal 2-functor from this to the 2-category of idempotent-complete additive k-linear categories. We initiate the study of the algebraic structure arising from these functors. In particular we show that a unitary SX-structure gives rise to a lax tortile π-category when the background space is an Eilenberg–Maclane space X=K(π,1), and to a tortile category with lax π2X-action when the background space is simply connected