152 research outputs found
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
is known. Further, the hierarchical algorithm can be used to recover the
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
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
() 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 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
- …