Finite-sided deformation spaces of complete affine 3-manifolds

A Margulis spacetime is a complete affine 3-manifold M with nonsolvable fundamental group. Associated to every Margulis spacetime is a noncompact complete hyperbolic surface S. We show that every Margulis spacetime is orientable, even though S may be nonorientable. We classify Margulis spacetimes when S is homeomorphic to a two-holed cross-surface, that is, the complement of two disjoint discs in the real projective plane. We show that every such manifold is homeomorphic to a solid handlebody of genus two, and admits a fundamental polyhedron bounded by crooked planes. Furthermore, the deformation space is a bundle of convex quadrilateral cones over the space of marked hyperbolic structures. The sides of each quadrilateral cone are defined by invariants of the two boundary components and the two orientation-reversing simple curves. The two-holed cross-surface, together with the three-holed sphere, are the only topologies for which the deformation space of complete affine structures is finite-sided.Comment: 29 pages, 8 figures. Accepted for publication in the Journal of Topolog

Correlating the Energetics and Atomic Motions of the Metal-Insulator Transition of M1 Vanadium Dioxide

Materials that undergo reversible metal-insulator transitions are obvious candidates for new generations of devices. For such potential to be realised, the underlying microscopic mechanisms of such transitions must be fully determined. In this work we probe the correlation between the energy landscape and electronic structure of the metal-insulator transition of vanadium dioxide and the atomic motions occurring using first principles calculations and high resolution X-ray diffraction. Calculations find an energy barrier between the high and low temperature phases corresponding to contraction followed by expansion of the distances between vanadium atoms on neighbouring sub-lattices. X-ray diffraction reveals anisotropic strain broadening in the low temperature structure's crystal planes, however only for those with spacings affected by this compression/expansion. GW calculations reveal that traversing this barrier destabilises the bonding/anti-bonding splitting of the low temperature phase. This precise atomic description of the origin of the energy barrier separating the two structures will facilitate more precise control over the transition characteristics for new applications and devices.Comment: 11 Pages, 8 Figure

The Influence of Genetics on Cystic Fibrosis Phenotypes

Technological advances in genetics have made feasible and affordable large studies to identify genetic variants that cause or modify a trait. Genetic studies have been carried out to assess variants in candidate genes, as well as polymorphisms throughout the genome, for their associations with heritable clinical outcomes of cystic fibrosis (CF), such as lung disease, meconium ileus, and CF-related diabetes. The candidate gene approach has identified some predicted relationships, while genome-wide surveys have identified several genes that would not have been obvious disease-modifying candidates, such as a methionine sulfoxide transferase gene that influences intestinal obstruction, or a region on chromosome 11 proximate to genes encoding a transcription factor and an apoptosis controller that associates with lung function. These unforeseen associations thus provide novel insight into disease pathophysiology, as well as suggesting new therapeutic strategies for CF