Exact Computation of a Manifold Metric, via Lipschitz Embeddings and Shortest Paths on a Graph

Data-sensitive metrics adapt distances locally based the density of data points with the goal of aligning distances and some notion of similarity. In this paper, we give the first exact algorithm for computing a data-sensitive metric called the nearest neighbor metric. In fact, we prove the surprising result that a previously published $3$-approximation is an exact algorithm. The nearest neighbor metric can be viewed as a special case of a density-based distance used in machine learning, or it can be seen as an example of a manifold metric. Previous computational research on such metrics despaired of computing exact distances on account of the apparent difficulty of minimizing over all continuous paths between a pair of points. We leverage the exact computation of the nearest neighbor metric to compute sparse spanners and persistent homology. We also explore the behavior of the metric built from point sets drawn from an underlying distribution and consider the more general case of inputs that are finite collections of path-connected compact sets. The main results connect several classical theories such as the conformal change of Riemannian metrics, the theory of positive definite functions of Schoenberg, and screw function theory of Schoenberg and Von Neumann. We develop novel proof techniques based on the combination of screw functions and Lipschitz extensions that may be of independent interest.Comment: 15 page

The effects of New Cooperative Medicine Scheme coverage on health outcomes and health care in rural China

health insurance, rural population, China, Health Economics and Policy,

Redesigning pictographs for patients with low health literacy and establishing preliminary steps for delivery via smart phones.

BackgroundPictographs (or pictograms) have been widely utilized to convey medication related messages and to address nonadherence among patients with low health literacy. Yet, patients do not always interpret the intended messages on commonly used pictographs correctly and there are questions how they may be delivered on mobile devices.ObjectiveOur objectives are to refine a set of pictographs to use as medication reminders and to establish preliminary steps for delivery via smart phones.MethodsCard sorting was used to identify existing pictographs that focus group members found "not easy" to understand. Participants then explored improvements to these pictographs while iterations were sketched in real-time by a graphic artist. Feedback was also solicited on how selected pictographs might be delivered via smart phones in a sequential reminder message. The study was conducted at a community learning center that provides literacy services to underserved populations in Seattle, WA. Participants aged 18 years and older who met the criteria for low health literacy using S-TOFHLA were recruited.ResultsAmong the 45 participants screened for health literacy, 29 were eligible and consented to participate. Across four focus group sessions, participants examined 91 commonly used pictographs, 20 of these were ultimately refined to improve comprehensibility using participatory design approaches. All participants in the fifth focus group owned and used cell phones and provided feedback on preferred sequencing of pictographs to represent medication messages.ConclusionLow literacy adults found a substantial number of common medication label pictographs difficult to understand. Participative design processes helped generate new pictographs, as well as feedback on the sequencing of messages on cell phones, that may be evaluated in future research

Assessing and Ensuring GOES-R Magnetometer Accuracy

The GOES-R magnetometer accuracy requirement is 1.7 nanoteslas (nT). During quiet times (100 nT), accuracy is defined as absolute mean plus 3 sigma. During storms (300 nT), accuracy is defined as absolute mean plus 2 sigma. To achieve this, the sensor itself has better than 1 nT accuracy. Because zero offset and scale factor drift over time, it is also necessary to perform annual calibration maneuvers. To predict performance, we used covariance analysis and attempted to corroborate it with simulations. Although not perfect, the two generally agree and show the expected behaviors. With the annual calibration regimen, these predictions suggest that the magnetometers will meet their accuracy requirements

Assessing and Ensuring GOES-R Magnetometer Accuracy

The GOES-R magnetometer subsystem accuracy requirement is 1.7 nanoteslas (nT). During quiet times (100 nT), accuracy is defined as absolute mean plus 3 sigma. During storms (300 nT), accuracy is defined as absolute mean plus 2 sigma. Error comes both from outside the magnetometers, e.g. spacecraft fields and misalignments, as well as inside, e.g. zero offset and scale factor errors. Because zero offset and scale factor drift over time, it will be necessary to perform annual calibration maneuvers. To predict performance before launch, we have used Monte Carlo simulations and covariance analysis. Both behave as expected, and their accuracy predictions agree within 30%. With the proposed calibration regimen, both suggest that the GOES-R magnetometer subsystem will meet its accuracy requirements

Physical Structure of Small Wolf-Rayet Ring Nebulae

We have selected the seven most well-defined WR ring nebulae in the LMC (Br 2, Br 10, Br 13, Br 40a, Br 48, Br 52, and Br 100) to study their physical nature and evolutionary stages. New CCD imaging and echelle observations have been obtained for five of these nebulae; previous photographic imaging and echelle observations are available for the remaining two nebulae. Using the nebular dynamics and abundances, we find that the Br 13 nebula is a circumstellar bubble, and that the Br 2 nebula may represent a circumstellar bubble merging with a fossil main-sequence interstellar bubble. The nebulae around Br 10, Br 52, and Br 100 all show influence of the ambient interstellar medium. Their regular expansion patterns suggest that they still contain significant amounts of circumstellar material. Their nebular abundances would be extremely interesting, as their central stars are WC5 and WN3-4 stars whose nebular abundances have not been derived previously. Intriguing and tantalizing implications are obtained from comparisons of the LMC WR ring nebulae with ring nebulae around Galactic WR stars, Galactic LBVs, LMC LBVs, and LMC BSGs; however, these implications may be limited by small-number statistics. A SNR candidate close to Br 2 is diagnosed by its large expansion velocity and nonthermal radio emission. There is no indication that Br 2's ring nebula interacts dynamically with this SNR candidate.Comment: 20 pages, Latex (aaspp4.sty), 2 figures, accepted by the Astronomical Journal (March 99 issue

Electrodynamics of Media

Contains reports on four research projects.Joint Services Electronics Program (Contract DAAB07-74-C-0630)California Institute of Technology (Contract 953524

Electrodynamics of Media

Contains research objectives, summary of research and reports on three research projects.Joint Services Electronics Program (Contract DAAB07-75-C-1346)California Institute of Technology (Contract 953524