How round is a protein? Exploring protein structures for globularity using conformal mapping.

We present a new algorithm that automatically computes a measure of the geometric difference between the surface of a protein and a round sphere. The algorithm takes as input two triangulated genus zero surfaces representing the protein and the round sphere, respectively, and constructs a discrete conformal map f between these surfaces. The conformal map is chosen to minimize a symmetric elastic energy E S (f) that measures the distance of f from an isometry. We illustrate our approach on a set of basic sample problems and then on a dataset of diverse protein structures. We show first that E S (f) is able to quantify the roundness of the Platonic solids and that for these surfaces it replicates well traditional measures of roundness such as the sphericity. We then demonstrate that the symmetric elastic energy E S (f) captures both global and local differences between two surfaces, showing that our method identifies the presence of protruding regions in protein structures and quantifies how these regions make the shape of a protein deviate from globularity. Based on these results, we show that E S (f) serves as a probe of the limits of the application of conformal mapping to parametrize protein shapes. We identify limitations of the method and discuss its extension to achieving automatic registration of protein structures based on their surface geometry

Distortion-free Displacement Mapping

Displacement mapping is routinely used to add geometric details in a fast and easy‐to‐control way, both in offline rendering as well as recently in interactive applications such as games. However, it went largely unnoticed (with the exception of McGuire and Whitson [MW08]) that, when applying displacement mapping to a surface with a low‐distortion parametrization, this parametrization is distorted as the geometry was changed by the displacement mapping. Typical resulting artifacts are “rubber band”‐like distortion patterns in areas of strong displacement change where a small isotropic area in texture space is mapped to a large anisotropic area in world space. We describe a fast, fully GPU‐based two‐step procedure to resolve this problem. First, a correction deformation is computed from the displacement map. Second, two variants to apply this correction when computing displacement mapping are proposed. The first variant is backward‐compatible and can resolve the artifact in any rendering pipeline without modifying it and without requiring additional computation at render time, but only works for bijective parametrizations. The second variant works for more general parametrizations, but requires to modify the rendering code and incurs a very small computational overhead

The Precision Array for Probing the Epoch of Reionization: 8 Station Results

We are developing the Precision Array for Probing the Epoch of Reionization (PAPER) to detect 21cm emission from the early Universe, when the first stars and galaxies were forming. We describe the overall experiment strategy and architecture and summarize two PAPER deployments: a 4-antenna array in the low-RFI environment of Western Australia and an 8-antenna array at our prototyping site in Green Bank, WV. From these activities we report on system performance, including primary beam model verification, dependence of system gain on ambient temperature, measurements of receiver and overall system temperatures, and characterization of the RFI environment at each deployment site. We present an all-sky map synthesized between 139 MHz and 174 MHz using data from both arrays that reaches down to 80 mJy (4.9 K, for a beam size of 2.15e-5 steradians at 154 MHz), with a 10 mJy (620 mK) thermal noise level that indicates what would be achievable with better foreground subtraction. We calculate angular power spectra ($C_\ell$) in a cold patch and determine them to be dominated by point sources, but with contributions from galactic synchrotron emission at lower radio frequencies and angular wavemodes. Although the cosmic variance of foregrounds dominates errors in these power spectra, we measure a thermal noise level of 310 mK at $\ell=100$ for a 1.46-MHz band centered at 164.5 MHz. This sensitivity level is approximately three orders of magnitude in temperature above the level of the fluctuations in 21cm emission associated with reionization.Comment: 13 pages, 14 figures, submitted to AJ. Revision 2 corrects a scaling error in the x axis of Fig. 12 that lowers the calculated power spectrum temperatur