Higher Order Connections

The purpose of this article is to present the theory of higher order connections on vector bundles from a viewpoint inspired by projective differential geometry

Formal Adjoints and a Canonical Form for Linear Operators

We describe a canonical form for linear differential operators that are formally self-adjoint or formally skew-adjoint.Comment: 3 page

The Research of Thomas P. Branson

The Midwest Geometry Conference 2007 was devoted to the substantial mathematical legacy of Thomas P. Branson who passed away unexpectedly the previous year. This contribution to the Proceedings briefly introduces this legacy. We also take the opportunity of recording his bibliography. Thomas Branson was on the Editorial Board of SIGMA and we are pleased that SIGMA is able to publish the Proceedings.Comment: This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Protein Structure Prediction: The Next Generation

Over the last 10-15 years a general understanding of the chemical reaction of protein folding has emerged from statistical mechanics. The lessons learned from protein folding kinetics based on energy landscape ideas have benefited protein structure prediction, in particular the development of coarse grained models. We survey results from blind structure prediction. We explore how second generation prediction energy functions can be developed by introducing information from an ensemble of previously simulated structures. This procedure relies on the assumption of a funnelled energy landscape keeping with the principle of minimal frustration. First generation simulated structures provide an improved input for associative memory energy functions in comparison to the experimental protein structures chosen on the basis of sequence alignment

A combinatorial formula for homogeneous moments

We establish a combinatorial formula for homogeneous moments and give some examples where it can be put to use. An application to the statistical mechanics of interacting gauged vortices is discussed.Comment: 8 pages, LaTe