A Distributed and Incremental SVD Algorithm for Agglomerative Data Analysis on Large Networks

In this paper, we show that the SVD of a matrix can be constructed efficiently in a hierarchical approach. Our algorithm is proven to recover the singular values and left singular vectors if the rank of the input matrix $A$ is known. Further, the hierarchical algorithm can be used to recover the $d$ largest singular values and left singular vectors with bounded error. We also show that the proposed method is stable with respect to roundoff errors or corruption of the original matrix entries. Numerical experiments validate the proposed algorithms and parallel cost analysis

Modewise Johnson-Lindenstrauss Embeddings for Nuclear Many-Body Theory

In this work, we explore modewise Johnson-Lindenstrauss embeddings (JLEs) as a tool to reduce the computational cost and memory requirements of nuclear many-body methods. JLEs are randomized projections of high-dimensional data tensors onto low-dimensional subspaces that preserve key structural features. Such embeddings allow for the oblivious and incremental compression of large tensors, e.g., the nuclear Hamiltonian, into significantly smaller random sketches that still allow for the accurate calculation of ground-state energies and other observables. Their oblivious character makes it possible to compress a tensor without knowing in advance exactly what observables one might want to approximate at a later time. This opens the door for the use of tensors that are much too large to store in memory, e.g., complete two-plus three-nucleon Hamiltonians in large, symmetry-unrestricted bases. Such compressed Hamiltonians can be stored and used later on with relative ease. As a first step, we analyze the JLE's impact on the second-order Many-Body Perturbation Theory (MBPT) corrections for nuclear ground-state observables. Numerical experiments for a wide range of closed-shell nuclei, model spaces and state-of-the-art nuclear interactions demonstrate the validity and potential of the proposed approach: We can compress nuclear Hamiltonians hundred- to thousand-fold while only incurring mean relative errors of 1\% or less in ground-state observables. Importantly, we show that JLEs capture the relevant physical information contained in the highly structured Hamiltonian tensor despite their random characteristics. In addition to the significant storage savings, the achieved compressions imply multiple order-of magnitude reductions in computational effort when the compressed Hamiltonians are used in higher-order MBPT or nonperturbative many-body methods.Comment: 23 pages, 14 figure

Functional redundancy of two C. elegans homologs of the histone chaperone Asf1 in germline DNA replication

AbstractEukaryotic genomes contain either one or two genes encoding homologs of the highly conserved histone chaperone Asf1, however, little is known of their in vivo roles in animal development. UNC-85 is one of the two Caenorhabditis elegans Asf1 homologs and functions in post-embryonic replication in neuroblasts. Although UNC-85 is broadly expressed in replicating cells, the specificity of the mutant phenotype suggested possible redundancy with the second C. elegans Asf1 homolog, ASFL-1. The asfl-1 mRNA is expressed in the meiotic region of the germline, and mutants in either Asf1 genes have reduced brood sizes and low penetrance defects in gametogenesis. The asfl-1, unc-85 double mutants are sterile, displaying defects in oogenesis and spermatogenesis, and analysis of DNA synthesis revealed that DNA replication in the germline is blocked. Analysis of somatic phenotypes previously observed in unc-85 mutants revealed that they are neither observed in asfl-1 mutants, nor enhanced in the double mutants, with the exception of enhanced male tail abnormalities in the double mutants. These results suggest that the two Asf1 homologs have partially overlapping functions in the germline, while UNC-85 is primarily responsible for several Asf1 functions in somatic cells, and is more generally involved in replication throughout development

Quantization and Compressive Sensing

Quantization is an essential step in digitizing signals, and, therefore, an indispensable component of any modern acquisition system. This book chapter explores the interaction of quantization and compressive sensing and examines practical quantization strategies for compressive acquisition systems. Specifically, we first provide a brief overview of quantization and examine fundamental performance bounds applicable to any quantization approach. Next, we consider several forms of scalar quantizers, namely uniform, non-uniform, and 1-bit. We provide performance bounds and fundamental analysis, as well as practical quantizer designs and reconstruction algorithms that account for quantization. Furthermore, we provide an overview of Sigma-Delta ($\Sigma\Delta$) quantization in the compressed sensing context, and also discuss implementation issues, recovery algorithms and performance bounds. As we demonstrate, proper accounting for quantization and careful quantizer design has significant impact in the performance of a compressive acquisition system.Comment: 35 pages, 20 figures, to appear in Springer book "Compressed Sensing and Its Applications", 201

Genomic Deletion Marking an Emerging Subclone of \u3ci\u3eFrancisella tularensis\u3c/i\u3e subsp. \u3ci\u3eholarctica\u3c/i\u3e in France and the Iberian Peninsula

Francisella tularensis subsp. holarctica is widely disseminated in North America and the boreal and temperate regions of the Eurasian continent. Comparative genomic analyses identified a 1.59-kb genomic deletion specific to F. tularensis subsp. holarctica isolates from Spain and France. Phylogenetic analysis of strains carrying this deletion by multiple-locus variable-number tandem repeat analysis showed that the strains comprise a highly related set of genotypes, implying that these strains were recently introduced or recently emerged by clonal expansion in France and the Iberian Peninsula

Genomic Deletion Marking an Emerging Subclone of Francisella tularensis subsp. holarctica in France and the Iberian Peninsula

P. 7465-7470Francisella tularensis subsp. holarctica is widely disseminated in North America and the boreal and temperate regions of the Eurasian continent. Comparative genomic analyses identified a 1.59-kb genomic deletion specific to F. tularensis subsp. holarctica isolates from Spain and France. Phylogenetic analysis of strains carrying this deletion by multiple-locus variable-number tandem repeat analysis showed that the strains comprise a highly related set of genotypes, implying that these strains were recently introduced or recently emerged by clonal expansion in France and the Iberian PeninsulaS