Horo-tight spheres in hyperbolic space

We study horo-tight immersions of manifolds into hyperbolic spaces. The main result gives several characterizations of horo-tightness of spheres, answering a question proposed by Cecil and Ryan. For instance, we prove that a sphere is horo-tight if and only if it is tight in the hyperbolic sense. For codimension bigger than one, it follows that horo-tight spheres in hyperbolic space are metric spheres. We also prove that horo-tight hyperspheres are characterized by the property that both of its total absolute horospherical curvatures attend their minimum value. We also introduce the notion of weak horo-tightness: an immersion is weak horo-tight if only one of its total absolute curvature attends its minimum. We prove a characterization theorem for weak horo-tight hyperspheres.

Cell-cell signal-dependent dynamic interactions between HD-GYP and GGDEF domain proteins mediate virulence in Xanthomonas campestris

RpfG is a paradigm for a class of widespread bacterial two-component regulators with a CheY-like receiver domain attached to a histidine-aspartic acid-glycine-tyrosine-proline (HD-GYP) cyclic di-GMP phosphodiesterase domain. In the plant pathogen Xanthomonas campestris pv. campestris (Xcc), a two-component system comprising RpfG and the complex sensor kinase RpfC is implicated in sensing and responding to the diffusible signaling factor (DSF), which is essential for cell-cell signaling. RpfF is involved in synthesizing DSF, and mutations of rpfF, rpfG, or rpfC lead to a coordinate reduction in the synthesis of virulence factors such as extracellular enzymes, biofilm structure, and motility. Using yeast two-hybrid analysis and fluorescence resonance energy transfer experiments in Xcc, we show that the physical interaction of RpfG with two proteins with diguanylate cyclase (GGDEF) domains controls a subset of RpfG-regulated virulence functions. RpfG interactions were abolished by alanine substitutions of the three residues of the conserved GYP motif in the HD-GYP domain. Changing the GYP motif or deletion of the two GGDEF-domain proteins reduced Xcc motility but not the synthesis of extracellular enzymes or biofilm formation. RpfG-GGDEF interactions are dynamic and depend on DSF signaling, being reduced in the rpfF mutant but restored by DSF addition. The results are consistent with a model in which DSF signal transduction controlling motility depends on a highly regulated, dynamic interaction of proteins that influence the localized expression of cyclic di-GMP.

Analysis of Optimum Location, Viability, and Potential Effects of Wind Farm Construction in Maine

Maine has the highest potential for wind energy in New England and falls within the top twenty states in the nation. It falls just behind Wisconsin and California with an estimate electrical output of 56 billion kWhs. The geological makeup of Maine’s mountains in the western part of the state, and the exposed coastline provide opportune areas to capture wind and convert it into energy. The information included in this poster will suggest the most likely areas for wind development based on a number of factors as recommended by the American Wind Energy Association.