190 research outputs found
Computing and deflating eigenvalues while solving multiple right hand side linear systems in Quantum Chromodynamics
We present a new algorithm that computes eigenvalues and eigenvectors of a
Hermitian positive definite matrix while solving a linear system of equations
with Conjugate Gradient (CG). Traditionally, all the CG iteration vectors could
be saved and recombined through the eigenvectors of the tridiagonal projection
matrix, which is equivalent theoretically to unrestarted Lanczos. Our algorithm
capitalizes on the iteration vectors produced by CG to update only a small
window of vectors that approximate the eigenvectors. While this window is
restarted in a locally optimal way, the CG algorithm for the linear system is
unaffected. Yet, in all our experiments, this small window converges to the
required eigenvectors at a rate identical to unrestarted Lanczos. After the
solution of the linear system, eigenvectors that have not accurately converged
can be improved in an incremental fashion by solving additional linear systems.
In this case, eigenvectors identified in earlier systems can be used to
deflate, and thus accelerate, the convergence of subsequent systems. We have
used this algorithm with excellent results in lattice QCD applications, where
hundreds of right hand sides may be needed. Specifically, about 70 eigenvectors
are obtained to full accuracy after solving 24 right hand sides. Deflating
these from the large number of subsequent right hand sides removes the dreaded
critical slowdown, where the conditioning of the matrix increases as the quark
mass reaches a critical value. Our experiments show almost a constant number of
iterations for our method, regardless of quark mass, and speedups of 8 over
original CG for light quark masses.Comment: 22 pages, 26 eps figure
Vibration stimuli and the differentiation of musculoskeletal progenitor cells: Review of results in vitro and in vivo
Due to the increasing burden on healthcare budgets of musculoskeletal system disease and injury, there is a growing need for safe, effective and simple therapies. Conditions such as osteoporosis severely impact on quality of life and result in hundreds of hours of hospital time and resources. There is growing interest in the use of low magnitude, high frequency vibration (LMHFV) to improve bone structure and muscle performance in a variety of different patient groups. The technique has shown promise in a number of different diseases, but is poorly understood in terms of the mechanism of action. Scientific papers concerning both the in vivo and in vitro use of LMHFV are growing fast, but they cover a wide range of study types, outcomes measured and regimens tested. This paper aims to provide an overview of some effects of LMHFV found during in vivo studies. Furthermore we will review research concerning the effects of vibration on the cellular responses, in particular for cells within the musculoskeletal system. This includes both osteogenesis and adipogenesis, as well as the interaction between MSCs and other cell types within bone tissue
Towards Real-Time Detection and Tracking of Spatio-Temporal Features: Blob-Filaments in Fusion Plasma
A novel algorithm and implementation of real-time identification and tracking
of blob-filaments in fusion reactor data is presented. Similar spatio-temporal
features are important in many other applications, for example, ignition
kernels in combustion and tumor cells in a medical image. This work presents an
approach for extracting these features by dividing the overall task into three
steps: local identification of feature cells, grouping feature cells into
extended feature, and tracking movement of feature through overlapping in
space. Through our extensive work in parallelization, we demonstrate that this
approach can effectively make use of a large number of compute nodes to detect
and track blob-filaments in real time in fusion plasma. On a set of 30GB fusion
simulation data, we observed linear speedup on 1024 processes and completed
blob detection in less than three milliseconds using Edison, a Cray XC30 system
at NERSC.Comment: 14 pages, 40 figure
Probing for the Trace Estimation of a Permuted Matrix Inverse Corresponding to a Lattice Displacement
In this work, we study probing for the more general problem of computing the
trace of a permutation of , say . The motivation comes from
Lattice QCD where we need to construct "disconnected diagrams" to extract
flavor-separated Generalized Parton functions. In Lattice QCD, where the matrix
has a 4D toroidal lattice structure, these non-local operators correspond to a
where is the permutation relating to some displacement
in one or more dimensions. We focus on a single dimension displacement ()
but our methods are general. We show that probing on or do not
annihilate the largest magnitude elements. To resolve this issue, our
displacement-based probing works on using a new coloring scheme that
works directly on appropriately displaced neighborhoods on the lattice. We
prove lower bounds on the number of colors needed, and study the effect of this
scheme on variance reduction, both theoretically and experimentally on a
real-world Lattice QCD calculation. We achieve orders of magnitude speedup over
the unprobed or the naively probed methods
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