A multiresolution wavelet representation in two or more dimensions

In the multiresolution approximation, a signal is examined on a hierarchy of resolution scales by projection onto sets of smoothing functions. Wavelets are used to carry the detail information connecting adjacent sets in the resolution hierarchy. An algorithm has been implemented to perform a multiresolution decomposition in n greater than or equal to 2 dimensions based on wavelets generated from products of 1-D wavelets and smoothing functions. The functions are chosen so that an n-D wavelet may be associated with a single resolution scale and orientation. The algorithm enables complete reconstruction of a high resolution signal from decomposition coefficients. The signal may be oversampled to accommodate non-orthogonal wavelet systems, or to provide approximate translational invariance in the decomposition arrays

Transverse excitations of ultracold matter waves upon propagation past abrupt waveguide changes

The propagation of ultracold atomic gases through abruptly changing waveguide potentials is examined in the limit of non-interacting atoms. Time-independent scattering calculations of microstructured waveguides with discontinuous changes in the transverse harmonic binding potentials are used to mimic waveguide perturbations and imperfections. Three basic configurations are examined: step-like, barrier-like and well-like with waves incident in the ground mode. At low energies, the spectra rapidly depart from single-moded, with significant transmission and reflection of excited modes. The high-energy limit sees 100 percent transmission, with the distribution of the transmitted modes determined simply by the overlap of the mode wave functions and interference.Comment: 20 pages, 7 figures, under review PR

How Do Communities Use a Participatory Public Health Approach to Build Resilience? The Los Angeles County Community Disaster Resilience Project.

Community resilience is a key concept in the National Health Security Strategy that emphasizes development of multi-sector partnerships and equity through community engagement. Here, we describe the advancement of CR principles through community participatory methods in the Los Angeles County Community Disaster Resilience (LACCDR) initiative. LACCDR, an initiative led by the Los Angeles County Department of Public Health with academic partners, randomized 16 community coalitions to implement either an Enhanced Standard Preparedness or Community Resilience approach over 24 months. Facilitated by a public health nurse or community educator, coalitions comprised government agencies, community-focused organizations and community members. We used thematic analysis of data from focus groups (n = 5) and interviews (n = 6 coalition members; n = 16 facilitators) to compare coalitions' strategies for operationalizing community resilience levers of change (engagement, partnership, self-sufficiency, education). We find that strategies that included bidirectional learning helped coalitions understand and adopt resilience principles. Strategies that operationalized community resilience levers in mutually reinforcing ways (e.g., disseminating information while strengthening partnerships) also secured commitment to resilience principles. We review additional challenges and successes in achieving cross-sector collaboration and engaging at-risk groups in the resilience versus preparedness coalitions. The LACCDR example can inform strategies for uptake and implementation of community resilience and uptake of the resilience concept and methods