A Gulf Unites Us: The Vietnamese Americans Of Black New Orleans East

Asian Studie

Geometric Aspects of Frame Representations of Abelian Groups

We consider frames arising from the action of a unitary representation of a discrete countable abelian group. We show that the range of the analysis operator can be determined by computing which characters appear in the representation. This allows one to compare the ranges of two such frames, which is useful for determining similarity and also for multiplexing schemes. Our results then partially extend to Bessel sequences arising from the action of the group. We apply the results to sampling on bandlimited functions and to wavelet and Weyl-Heisenberg frames. This yields a sufficient condition for two sampling transforms to have orthogonal ranges, and two analysis operators for wavelet and Weyl-Heisenberg frames to have orthogonal ranges. The sufficient condition is easy to compute in terms of the periodization of the Fourier transform of the frame generators.Comment: 20 pages; contact author: Eric Webe

Zolotarev Quadrature Rules and Load Balancing for the FEAST Eigensolver

The FEAST method for solving large sparse eigenproblems is equivalent to subspace iteration with an approximate spectral projector and implicit orthogonalization. This relation allows to characterize the convergence of this method in terms of the error of a certain rational approximant to an indicator function. We propose improved rational approximants leading to FEAST variants with faster convergence, in particular, when using rational approximants based on the work of Zolotarev. Numerical experiments demonstrate the possible computational savings especially for pencils whose eigenvalues are not well separated and when the dimension of the search space is only slightly larger than the number of wanted eigenvalues. The new approach improves both convergence robustness and load balancing when FEAST runs on multiple search intervals in parallel.Comment: 22 pages, 8 figure

Unleashing the Genome of Brassica Rapa

The completion and release of the Brassica rapa genome is of great benefit to researchers of the Brassicas, Arabidopsis, and genome evolution. While its lineage is closely related to the model organism Arabidopsis thaliana, the Brassicas experienced a whole genome triplication subsequent to their divergence. This event contemporaneously created three copies of its ancestral genome, which had diploidized through the process of homeologous gene loss known as fractionation. By the fractionation of homeologous gene content and genetic regulatory binding sites, Brassica’s genome is well placed to use comparative genomic techniques to identify syntenic regions, homeologous gene duplications, and putative regulatory sequences. Here, we use the comparative genomics platform CoGe to perform several different genomic analyses with which to study structural changes of its genome and dynamics of various genetic elements. Starting with whole genome comparisons, the Brassica paleohexaploidy is characterized, syntenic regions with A. thaliana are identified, and the TOC1 gene in the circadian rhythm pathway from A. thaliana is used to find duplicated orthologs in B. rapa. These TOC1 genes are further analyzed to identify conserved non-coding sequences that contain cis-acting regulatory elements and promoter sequences previously implicated in circadian rhythmicity. Each “cookbook style” analysis includes a step-by-step walk-through with links to CoGe to quickly reproduce each step of the analytical process