All roots of unity are detected by the A-polynomial

For an arbitrary positive integer n, we construct infinitely many one-cusped hyperbolic 3-manifolds where each manifold's A-polynomial detects every n-th root of unity. This answers a question of Cooper, Culler, Gillet, Long, and Shalen as to which roots of unity arise in this manner.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-11.abs.htm

Low level measurements of atmospheric DMS, H2S, and SO2 for GTE/CITE-3

This project involved the measurement of atmospheric dimethylsulfide (DMS) and hydrogen sulfide (H2S) as part of the GTE/CITE-3 instrument intercomparison program. The two instruments were adapted for use on the NASA Electra aircraft and participated in all phases of the mission. This included ground-based measurements of NIST-provided standard gases and a series of airborne missions over the Western Atlantic Ocean. Analytical techniques used are described and the results are summarized

Selection of quasi-stationary states in the Navier-Stokes equation on the torus

The two dimensional incompressible Navier-Stokes equation on $D_\delta := [0, 2\pi\delta] \times [0, 2\pi]$ with $\delta \approx 1$, periodic boundary conditions, and viscosity $0 < \nu \ll 1$ is considered. Bars and dipoles, two explicitly given quasi-stationary states of the system, evolve on the time scale $\mathcal{O}(e^{-\nu t})$ and have been shown to play a key role in its long-time evolution. Of particular interest is the role that $\delta$ plays in selecting which of these two states is observed. Recent numerical studies suggest that, after a transient period of rapid decay of the high Fourier modes, the bar state will be selected if $\delta \neq 1$, while the dipole will be selected if $\delta = 1$. Our results support this claim and seek to mathematically formalize it. We consider the system in Fourier space, project it onto a center manifold consisting of the lowest eight Fourier modes, and use this as a model to study the selection of bars and dipoles. It is shown for this ODE model that the value of $\delta$ controls the behavior of the asymptotic ratio of the low modes, thus determining the likelihood of observing a bar state or dipole after an initial transient period. Moreover, in our model, for all $\delta \approx 1$, there is an initial time period in which the high modes decay at the rapid rate $\mathcal{O}(e^{-t/\nu})$, while the low modes evolve at the slower $\mathcal{O}(e^{-\nu t})$ rate. The results for the ODE model are proven using energy estimates and invariant manifolds and further supported by formal asymptotic expansions and numerics.Comment: 29 pages, 4 figure

Development of a machine vision system for automated structural assembly

Research is being conducted at the LaRC to develop a telerobotic assembly system designed to construct large space truss structures. This research program was initiated within the past several years, and a ground-based test-bed was developed to evaluate and expand the state of the art. Test-bed operations currently use predetermined ('taught') points for truss structural assembly. Total dependence on the use of taught points for joint receptacle capture and strut installation is neither robust nor reliable enough for space operations. Therefore, a machine vision sensor guidance system is being developed to locate and guide the robot to a passive target mounted on the truss joint receptacle. The vision system hardware includes a miniature video camera, passive targets mounted on the joint receptacles, target illumination hardware, and an image processing system. Discrimination of the target from background clutter is accomplished through standard digital processing techniques. Once the target is identified, a pose estimation algorithm is invoked to determine the location, in three-dimensional space, of the target relative to the robots end-effector. Preliminary test results of the vision system in the Automated Structural Assembly Laboratory with a range of lighting and background conditions indicate that it is fully capable of successfully identifying joint receptacle targets throughout the required operational range. Controlled optical bench test results indicate that the system can also provide the pose estimation accuracy to define the target position

User interface issues in supporting human-computer integrated scheduling

Explored here is the user interface problems encountered with the Operations Missions Planner (OMP) project at the Jet Propulsion Laboratory (JPL). OMP uses a unique iterative approach to planning that places additional requirements on the user interface, particularly to support system development and maintenance. These requirements are necessary to support the concepts of heuristically controlled search, in-progress assessment, and iterative refinement of the schedule. The techniques used to address the OMP interface needs are given

Selection of quasi-stationary states in the stochastically forced Navier-Stokes equation on the torus

The stochastically forced vorticity equation associated with the two dimensional incompressible Navier-Stokes equation on $D_\delta:=[0,2\pi\delta]\times [0,2\pi]$ is considered for $\delta\approx 1$, periodic boundary conditions, and viscocity $0<\nu\ll 1$. An explicit family of quasi-stationary states of the deterministic vorticity equation is known to play an important role in the long-time evolution of solutions both in the presence of and without noise. Recent results show the parameter $\delta$ plays a central role in selecting which of the quasi-stationary states is most important. In this paper, we aim to develop a finite dimensional model that captures this selection mechanism for the stochastic vorticity equation. This is done by projecting the vorticity equation in Fourier space onto a center manifold corresponding to the lowest eight Fourier modes. Through Monte Carlo simulation, the vorticity equation and the model are shown to be in agreement regarding key aspects of the long-time dynamics. Following this comparison, perturbation analysis is performed on the model via averaging and homogenization techniques to determine the leading order dynamics for statistics of interest for $\delta\approx1$.Comment: 23 pages, 27 figure

DEFEATING AND DETERRING DOMESTIC TERRORISM THROUGH EVIDENCE-BASED POLICYMAKING

This thesis investigates how evidence-based policymaking can be employed to improve policy decisions and resource allocations aimed at deterring and defeating domestic terrorism. The executive and legislative branches of government have mandated that evidence-based policymaking be implemented in federal governmental decisional processes, including the National Strategy for Countering Domestic Terrorism. However, there is no federal guidance that specifies how to use evidence and data to combat domestic terrorism. This thesis investigates the numerous challenges of using evidence in domestic counterterrorism initiatives and analyzes three case studies to provide recommendations for an integrated approach to the implementation of the Strategy. The findings of this thesis supplement OMB’s guidance on the four components of evidence-based policymaking. Among others, it recommends that the government should institute standardized data collection, provide improved guidelines, generate a cadre of professionals trained in evaluation, establish evidence-based policymaking centers of excellence, designate a bipartisan Congressionally mandated oversight office, and create a repository that captures the methodologies and results of ongoing and completed evidence-based programs for countering domestic terrorism.Outstanding ThesisCaptain, United States Coast GuardApproved for public release. Distribution is unlimited