The Inhomogeneous Hall's Ray

We show that the inhomogenous approximation spectrum, associated to an irrational number \alpha\ always has a Hall's Ray; that is, there is an \epsilon>0 such that [0,\epsilon) is a subset of the spectrum. In the case when \alpha\ has unbounded partial quotients we show that the spectrum is just a ray.Comment: Fixed typos in bibliograph

Spectra of Maser Radiation from a Turbulent, Circumnuclear Accretion Disk. III. Circular polarization

Calculations are performed for the circular polarization of maser radiation from a turbulent, Keplerian disk that is intended to represent the sub-parsec disk at the nucleus of the galaxy NGC4258. The polarization in the calculations is a result of the Zeeman effect in the regime in which the Zeeman splitting is much less than the spectral linebreadth. Plausible configurations for turbulent magnetic and velocity fields in the disk are created by statistical methods. This turbulence, along with the Keplerian velocity gradients and the blending of the three hyperfine components to form the $6_{16} - 5_{23}$ masing transition of water, are key ingredients in determining the appearance of the polarized spectra that are calculated. These spectra are quite different from the polarized spectra that would be expected for a two-level transition where there is no hyperfine structure. The effect of the hyperfine structure on the polarization is most striking in the calculations for the maser emission that represents the central (or systemic) features of NGC4258. Information about magnetic fields is inferred from observations for polarized maser radiation and bears on the structure of accretion disks.Comment: Latex, uses aastex, eucal, to be published in the Astrophysical Journa

An Information-geometric Approach to Sensor Management

An information-geometric approach to sensor management is introduced that is based on following geodesic curves in a manifold of possible sensor configurations. This perspective arises by observing that, given a parameter estimation problem to be addressed through management of sensor assets, any particular sensor configuration corresponds to a Riemannian metric on the parameter manifold. With this perspective, managing sensors involves navigation on the space of all Riemannian metrics on the parameter manifold, which is itself a Riemannian manifold. Existing work assumes the metric on the parameter manifold is one that, in statistical terms, corresponds to a Jeffreys prior on the parameter to be estimated. It is observed that informative priors, as arise in sensor management, can also be accommodated. Given an initial sensor configuration, the trajectory along which to move in sensor configuration space to gather most information is seen to be locally defined by the geodesic structure of this manifold. Further, divergences based on Fisher and Shannon information lead to the same Riemannian metric and geodesics.Comment: 4 pages, 3 figures, to appear in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, March 201

Microbial diversity in the thermal springs within Hot Springs National Park

The thermal water systems of Hot Springs National Park (HSNP) in Hot Springs, Arkansas exist in relative isolation from other North American thermal systems. The HSNP waters could therefore serve as a unique center of thermophilic microbial biodiversity. However, these springs remain largely unexplored using culture-independent next generation sequencing techniques to classify species of thermophilic organisms. Additionally, HSNP has been the focus of anthropogenic development, capping and diverting the springs for use in recreational bathhouse facilities. Human modification of these springs may have impacted the structure of these bacterial communities compared to springs left in a relative natural state. The goal of this study was to compare the community structure in two capped springs and two uncapped springs in HSNP, as well as broadly survey the microbial diversity of the springs. We used Illumina 16S rRNA sequencing of water samples from each spring, the QIIME workflow for sequence analysis, and generated measures of genera and phyla richness, diversity, and evenness. In total, over 700 genera were detected and most individual samples had more than 100 genera. There were also several uncharacterized sequences that could not be placed in known taxa, indicating the sampled springs contain undescribed bacteria. There was great variation both between sites and within samples, so no significant differences were detected in community structure between sites. Our results suggest that these springs, regardless of their human modification, contain a considerable amount of biodiversity, some of it potentially unique to the study site

A computational method to model radar return range in a polygonally based, computer-generated-imagery simulation

Described is a method for modeling a ground-mapping radar system for use in simulations where the terrain is in a polygonal form commonly used with computer generated imagery (CGI). The method employs a unique approach for rapidly rejecting polygons not visible to the radar to facilitate the real-time simulation of the radar return. This rapid rejection of the nonvisible polygons requires the precalculation and storage of a set of parameters that do not vary during the simulation. The calculation of a radar range as a function of the radar forward-looking angle to the CGI terrain is carried out only for the visible polygons. This method was used as part of a simulation for terrain-following helicopter operations on the vertical motion simulator at the NASA Ames Research Center. It proved to be an efficient means for returning real-time simulated radar range data

Flight test of navigation and guidance sensor errors measured on STOL approaches

Navigation and guidance sensor error characteristics were measured during STOL approach-flight investigations. Data from some of the state sensors of a digital avionics system were compared to corresponding outputs from an inertial navigation system. These sensors include the vertical gyro, compass, and accelerometers. Barometric altimeter data were compared to altitude measured by a tracking radar. Data were recorded with the Augmentor Wing Jet STOL Research Aircraft parked and in flight

Operator-Valued Frames for the Heisenberg Group

A classical result of Duffin and Schaeffer gives conditions under which a discrete collection of characters on $\mathbb{R}$, restricted to $E = (-1/2, 1/2)$, forms a Hilbert-space frame for $L^2(E)$. For the case of characters with period one, this is just the Poisson Summation Formula. Duffin and Schaeffer show that perturbations preserve the frame condition in this case. This paper gives analogous results for the real Heisenberg group $H_n$, where frames are replaced by operator-valued frames. The Selberg Trace Formula is used to show that perturbations of the orthogonal case continue to behave as operator-valued frames. This technique enables the construction of decompositions of elements of $L^2(E)$ for suitable subsets $E$ of $H_n$ in terms of representations of $H_n$