Shape analysis plays an important role in many applications. In particular, in molecular biology, analyzing molecular shapes is essential to the fundamental problem of understanding how molecules interact. This project aims at developing efficient and effective algorithms to characterize and analyze molecular structures using geometric and topological methods. Two main components of this project are (1) developing novel molecular shape descriptors; and (2) identifying and representing meaningful features based on those descriptors. The project also produces accompanying (visualization) software. Results from this project (09/2006–10/2009) include the following publications. We have also set up web-servers for the software developed in this period, so that our new methods are accessible to a broader scientific community. The web sites are given below as well. In this final technical report, we first list publications and software resulted from this project. We then briefly explain the research conducted and main accomplishments during the period of this project.

The ARM Climate Research Facility currently operates more than 300 instrument systems that provide ground-based observations of the atmospheric column. To keep ARM at the forefront of climate observations, the ARM infrastructure depends heavily on instrument scientists and engineers, also known as Instrument Mentors. Instrument Mentors must have an excellent understanding of in situ and remote-sensing instrumentation theory and operation and have comprehensive knowledge of critical scale-dependent atmospheric processes. They also possess the technical and analytical skills to develop new data retrievals that provide innovative approaches for creating research-quality data sets.

The work reported is in pursuit of these goals: high-quality unstructured, non-uniform Voronoi and Delaunay grids; improved finite element and finite volume discretization schemes; and improved finite element and finite volume discretization schemes. These are sought for application to spherical and three-dimensional applications suitable for ocean, atmosphere, ice-sheet, and other climate modeling applications.

The objective of the ARM Science Board is to promote the Nation’s scientific enterprise by ensuring that the best quality science is conducted at the DOE’s User Facility known as the ARM Climate Research Facility. The goal of the User Facility is to serve scientific researchers by providing unique data and tools to facilitate scientific applications for improving understanding and prediction of climate science.

For the support of a new technology high energy collider ("4th") for potential use at a new lepton collider. In addition, support for dual-readout calorimetry, CERN RD52.