Multiresolution kernel matrix algebra

We propose a sparse arithmetic for kernel matrices, enabling efficient scattered data analysis. The compression of kernel matrices by means of samplets yields sparse matrices such that assembly, addition, and multiplication of these matrices can be performed with essentially linear cost. Since the inverse of a kernel matrix is compressible, too, we have also fast access to the inverse kernel matrix by employing exact sparse selected inversion techniques. As a consequence, we can rapidly evaluate series expansions and contour integrals to access, numerically and approximately in a data-sparse format, more complicated matrix functions such as $A^\alpha$ and $\exp(A)$. By exploiting the matrix arithmetic, also efficient Gaussian process learning algorithms for spatial statistics can be realized. Numerical results are presented to quantify and quality our findings

Device Therapies Among Patients Receiving Primary Prevention Implantable Cardioverterâ Defibrillators in the Cardiovascular Research Network

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143721/1/jah33061_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/143721/2/jah33061.pd

Massively Parallel RNA Sequencing Identifies a Complex Immune Gene Repertoire in the lophotrochozoan Mytilus edulis

The marine mussel Mytilus edulis and its closely related sister species are distributed world-wide and play an important role in coastal ecology and economy. The diversification in different species and their hybrids, broad ecological distribution, as well as the filter feeding mode of life has made this genus an attractive model to investigate physiological and molecular adaptations and responses to various biotic and abiotic environmental factors. In the present study we investigated the immune system of Mytilus, which may contribute to the ecological plasticity of this species. We generated a large Mytilus transcriptome database from different tissues of immune challenged and stress treated individuals from the Baltic Sea using 454 pyrosequencing. Phylogenetic comparison of orthologous groups of 23 species demonstrated the basal position of lophotrochozoans within protostomes. The investigation of immune related transcripts revealed a complex repertoire of innate recognition receptors and downstream pathway members including transcripts for 27 toll-like receptors and 524 C1q domain containing transcripts. NOD-like receptors on the other hand were absent. We also found evidence for sophisticated TNF, autophagy and apoptosis systems as well as for cytokines. Gill tissue and hemocytes showed highest expression of putative immune related contigs and are promising tissues for further functional studies. Our results partly contrast with findings of a less complex immune repertoire in ecdysozoan and other lophotrochozoan protostomes. We show that bivalves are interesting candidates to investigate the evolution of the immune system from basal metazoans to deuterostomes and protostomes and provide a basis for future molecular work directed to immune system functioning in Mytilus

Bembel: The fast isogeometric boundary element C++ library for Laplace, Helmholtz, and electric wave equation

In this article, we present Bembel, the C++ library featuring higher order isogeometric Galerkinboundary element methods for Laplace, Helmholtz, and Maxwell problems. Bembel is compatible withgeometriesfromtheOctaveNURBSpackage,andprovidesaninterfacetotheEigentemplatelibraryforlinear algebra operations. For computational efficiency, it applies an embedded fast multipole methodtailored to the isogeometric analysis framework and a parallel matrix assembly based on OpenMP

Bembel: The fast isogeometric boundary element C++ library for Laplace, Helmholtz, and electric wave equation

In this article, we present Bembel, the C++ library featuring higher order isogeometric Galerkinboundary element methods for Laplace, Helmholtz, and Maxwell problems. Bembel is compatible withgeometriesfromtheOctaveNURBSpackage,andprovidesaninterfacetotheEigentemplatelibraryforlinear algebra operations. For computational efficiency, it applies an embedded fast multipole methodtailored to the isogeometric analysis framework and a parallel matrix assembly based on OpenMP