The Hitchin-Witten Connection and Complex Quantum Chern-Simons Theory

We give a direct calculation of the curvature of the Hitchin connection, in geometric quantization on a symplectic manifold, using only differential geometric techniques. In particular, we establish that the curvature acts as a first-order operator on the quantum spaces. Projective flatness follows if the K\"ahler structures do not admit holomorphic vector fields. Following Witten, we define a complex variant of the Hitchin connection on the bundle of prequantum spaces. The curvature is essentially unchanged, so projective flatness holds in the same cases. Finally, the results are applied to quantum Chern-Simons theory, both for compact and complex gauge groups

A gentle introduction to the discrete Laplace method for estimating Y-STR haplotype frequencies

Y-STR data simulated under a Fisher-Wright model of evolution with a single-step mutation model turns out to be well predicted by a method using discrete Laplace distributions.Comment: 18 pages, 5 figure

A Hyperstable Miniprotein: Additive Effects of D- and L-Ala Substitutions

The effects of alanine substitutions in each helical segment of the structure, and Gly to D-Ala mutations at sites where glycines have positive phi angles in the Trp-cage miniprotein are reported. The effects of the stabilizing mutation were additive, yielding a 20-residue construct (Tm = 83^o^C). Gly to L-Ala substitutions were uniformly destabilizing ([DELTA][DELTA]G~F~ > 11 kJ/mol): the preference for a D-Ala can be as large as 16 kJ/mol. Glycine to D-Ala mutations are validated as a strategy for the design of hyperstable miniprotein scaffolds suitable for stereospecific pharmacophore display

Bio-inspired metal-coordination: Using more of nature’s tricks to assemble hydrogel materials with multi-functional properties

A variety of dynamic bonds have been employed as reversible crosslinks in polymer materials in efforts to obtain desirable properties such as stimuli-response, self-healing and shape-memory. Many dynamic bonds utilized so far however, have poor compatibility with aqueous solvents, thereby limiting their use in polymer materials intended for environmental, medical and personal care applications. Inspired by marine biological materials, we have been exploring metal-coordinate dynamic crosslinks that allow unique control over metal-binding polymer network properties in aqueous conditions. These early bio-mimetic explorations revealed that certain metal-ligand coordination complexes allow aqueous polymer solutions to be finely tuned between fluids and strong viscoelastic gels, simply by the choice of the coordinating metal ion. More recently we have begun exploring stimuli-responsive properties of metal-coordinate polymer networks and have found that temperature, pH, magnetic and mechanical stimuli all can induce strong responses in metal-ligand coordinate crosslink dynamics. These demonstrations open the door to design of multi-stimuli-response controlled polymer hydrogel materials. Early lessons from this pursuit will be presented

A Neolithic Causewayed Camp at Trelleborg near Slagelse, West Zealand

A Neolithic Causewayed Camp at Trelleborg near Slagelse, West Zealan