Quasi-period collapse and GL_n(Z)-scissors congruence in rational polytopes

Quasi-period collapse occurs when the Ehrhart quasi-polynomial of a rational polytope has a quasi-period less than the denominator of that polytope. This phenomenon is poorly understood, and all known cases in which it occurs have been proven with ad hoc methods. In this note, we present a conjectural explanation for quasi-period collapse in rational polytopes. We show that this explanation applies to some previous cases appearing in the literature. We also exhibit examples of Ehrhart polynomials of rational polytopes that are not the Ehrhart polynomials of any integral polytope. Our approach depends on the invariance of the Ehrhart quasi-polynomial under the action of affine unimodular transformations. Motivated by the similarity of this idea to the scissors congruence problem, we explore the development of a Dehn-like invariant for rational polytopes in the lattice setting.Comment: 8 pages, 3 figures, to appear in the proceedings of Integer points in polyhedra, June 11 -- June 15, 2006, Snowbird, U

A network approach to parts provisioning for apollo prelaunch operations

Network approach to replacement-parts policy for Apollo prelaunch operation

Calibration, optimization, and deployment of PTR-MS instruments during the AIRMAP project

Proton Transfer Reaction Mass Spectrometry (PTR-MS) is an increasingly popular technique for monitoring volatile organic compounds with high sensitivity and time resolution. This dissertation encompasses three different projects, sharing the common theme of expanding the knowledge and utility of the technique. The first project focuses on elucidating the ion chemistry that occurs within the PTR-MS drift tube reaction chamber. The PTR-MS uses a differentially pumped skimmer to prevent excess water from the ion source from entering the drift tube reaction chamber. By placing a metering valve in between the skimmer region and the pump, it was possible to control the amount of water entering the drift tube. The valve made it possible to parameterize the impact of the pumping speed of the skimmer on ion source performance, cluster formation, and sensitivity. These results are compared with a kinetics model that simulates the protonated cluster distributions in the drift tube. The second part of this dissertation describes the process for calibrating and deploying the instrument to measure acetic acid. Generating calibrations and measurements of ambient levels acetic acid are challenging because it adsorbs on instrument surfaces and transfer lines. To overcome the challenge of calibrating, a special permeation oven was used to generate a stable flow of acetic acid in the range of 7.0 to 26.5 ppbv, yielding calibration factors of 7.0 +/- 0.3 ncps·ppbv-1 to 10.9 +/- 0.7 ncps·ppbv-1 at 132 Td. At 88 Td, the calibration factor was found to be 30.8 +/- 2.6 ncps·ppbv-1. Measurements made on Appledore Island during ICARTT show that the PTR-MS measurements correlate well with those from the MC/IC technique, with a correlation coefficient of 0.78. The final project uses the high time resolution of PTR-MS measurements to quantify the impact of storm systems on monoterpene mixing ratios in rural New Hampshire. Analysis of five years of monoterpene measurements at Thompson Farm (in Durham, NH) show storm events with intense precipitation correlate with brief periods of enhanced monoterpene mixing ratios. These events are classified based on duration and intensity, finding that storms can temporarily increase emissions by as much as 4260 g·km-2·hr -1

A distinct sortase SrtB anchors and processes a streptococcal adhesin AbpA with a novel structural property.

Surface display of proteins by sortases in Gram-positive bacteria is crucial for bacterial fitness and virulence. We found a unique gene locus encoding an amylase-binding adhesin AbpA and a sortase B in oral streptococci. AbpA possesses a new distinct C-terminal cell wall sorting signal. We demonstrated that this C-terminal motif is required for anchoring AbpA to cell wall. In vitro and in vivo studies revealed that SrtB has dual functions, anchoring AbpA to the cell wall and processing AbpA into a ladder profile. Solution structure of AbpA determined by NMR reveals a novel structure comprising a small globular α/β domain and an extended coiled-coil heliacal domain. Structural and biochemical studies identified key residues that are crucial for amylase binding. Taken together, our studies document a unique sortase/adhesion substrate system in streptococci adapted to the oral environment rich in salivary amylase

Existence of Monetary Steady States in a Matching Model: Indivisible Money

Existence of a monetary steady state is established for a random matching model with divisible goods, indivisible money, and take-it-or-leave-it offers by consumers. There is no restriction on individual money holdings. The background environment is that in papers by Shi and by Trejos and Wright. The monetary steady state shown to exist has nice properties: the value function, defined on money holdings, is increasing and strictly concave, and the measure over money holdings has full support.