Minimizing Communication in Linear Algebra

In 1981 Hong and Kung proved a lower bound on the amount of communication needed to perform dense, matrix-multiplication using the conventional $O(n^3)$ algorithm, where the input matrices were too large to fit in the small, fast memory. In 2004 Irony, Toledo and Tiskin gave a new proof of this result and extended it to the parallel case. In both cases the lower bound may be expressed as $\Omega$(#arithmetic operations / $\sqrt{M}$), where M is the size of the fast memory (or local memory in the parallel case). Here we generalize these results to a much wider variety of algorithms, including LU factorization, Cholesky factorization, $LDL^T$ factorization, QR factorization, algorithms for eigenvalues and singular values, i.e., essentially all direct methods of linear algebra. The proof works for dense or sparse matrices, and for sequential or parallel algorithms. In addition to lower bounds on the amount of data moved (bandwidth) we get lower bounds on the number of messages required to move it (latency). We illustrate how to extend our lower bound technique to compositions of linear algebra operations (like computing powers of a matrix), to decide whether it is enough to call a sequence of simpler optimal algorithms (like matrix multiplication) to minimize communication, or if we can do better. We give examples of both. We also show how to extend our lower bounds to certain graph theoretic problems. We point out recently designed algorithms for dense LU, Cholesky, QR, eigenvalue and the SVD problems that attain these lower bounds; implementations of LU and QR show large speedups over conventional linear algebra algorithms in standard libraries like LAPACK and ScaLAPACK. Many open problems remain.Comment: 27 pages, 2 table

Effect of calcium supplements on risk of myocardial infarction and cardiovascular events : meta-analysis

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Operation Moshtarak and the manufacture of credible, “heroic” warfare

Richard Lance Keeble argues that Fleet Street’s coverage of the Afghan conflict has served largely to promote the interests of the military/industrial/media complex – and marginalise the views of the public who have consistently appealed in polls for the troops to be brought back hom

Analytical performance assessment of a novel active mooring system for load reduction in marine energy converters

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.Reliability and storm survival of Marine Energy Converters are critical to their commercial development and deployment. The Intelligent Active Mooring System (IAMS) is a novel device intended to minimise extreme and fatigue loading in mooring lines through a non-linear load–extension curve that is variable in operation to adjust to the prevailing metocean conditions. An analytical model of IAMS, validated by physical model tests at the Dynamic Marine Component test facility at the University of Exeter, is used in a numerical simulation of the performance of IAMS as part of the mooring system of the South West Mooring Test Facility buoy. A 10 m length of IAMS can reduce the rms line tension in normal operating conditions by up to 21% and the peak line tension in storm conditions by up to 21% when compared to braided nylon mooring lines. Peak line tension reductions of over 50% can be achieved if a longer IAMS unit is used. The resulting mooring system can be optimised to give load reductions in a wide range of metocean conditions; while variable pre-tension could be used for tidal range compensation or to ease access for installation and maintenance.The work reported here is part of a joint project between AWS Ocean Ltd., Teqniqa Systems Ltd. and the University of Exeter. The project was funded in part by the Technology Strategy Board (now Innovate UK) grant number 101970

Immunodepletion and hypoxia preconditioning of mouse vompact bone cells as a novel protocol to isolate highly immunosuppressive mesenchymal stem cells

Prepublished on Liebert Instant Online December 21, 2016Compact bones (CB) are major reservoirs of mouse mesenchymal stem cells (mMSC). Here, we established a protocol to isolate MSC from CB and tested their immunosuppressive potential. Collagenase type II digestion of BM-flushed CB from C57B/6 mice was performed to liberate mMSC precursors from bone surfaces to establish nondepleted mMSC. CB cells were also immunodepleted based on the expression of CD45 (leukocytes) and TER119 (erythroid cells) to eliminate hematopoietic cells. CD45-TER119- CB cells were subsequently used to generate depleted mMSC. CB nondepleted and depleted mMSC progenitors were cultured under hypoxic conditions to establish primary mMSC cultures. CB depleted mMSC compared to nondepleted mMSC showed greater cell numbers at subculturing and had increased functional ability to differentiate into adipocytes and osteoblasts. CB depleted mMSC had high purity and expressed key mMSC markers (>85% Sca-1, CD29, CD90) with no mature hematopoietic contaminating cells (<5% CD45, CD11b) when subcultured to passage 5 (P5). Nondepleted mMSC cultures, however, were less pure and heterogenous with <72% Sca-1+, CD29+, and CD90+ cells at early passages (P1 or P2), along with high percentages of contaminating CD11b+ (35.6%) and CD45+ (39.2%) cells that persisted in culture long term. Depleted and nondepleted mMSC nevertheless exhibited similar potency to suppress total (CD3+), CD4+ and CD8+ T cell proliferation, in a dendritic cell allostimulatory one-way mixed lymphocyte reaction. CB depleted mMSC, pretreated with proinflammatory cytokines IFN-γ, TNF-α, and IL-17A, showed superior suppression of CD8+ T cell, but not CD4+ T cell proliferation, relative to untreated-mMSC. In conclusion, CB depleted mMSC established under hypoxic conditions and treated with selective cytokines represent a novel source of potent immunosuppressive MSC. As these cells have enhanced immune modulatory function, they may represent a superior product for use in clinical allotransplantation.Kisha Nandini Sivanathan, Stan Gronthos, Shane T. Grey, Darling Rojas-Canales, and Patrick T. Coate

Morphological phylogeny of Megachilini and the evolution of leaf-cutter behavior in bees (Hymenoptera: Megachilidae): Evolution of leaf-cutter behavior in bees

A unique feature among bees is the ability of some species of Megachile Latreille s.l. to cut and process fresh leaves for nest construction. The presence of a razor between the female mandibular teeth (interdental laminae) to facilitate leaf-cutting (LC) is a morphological novelty that might have triggered a subsequent diversification in this group. However, we have a limited understanding of the phylogeny of this group despite the large number of described species and the origins and patterns of variations of this mandibular structure are unknown. Herein, using a cladistic analysis of adult external morphological characters, we explored the relationships of all genera of Megachilini and the more than 50 subgenera of Megachile s.l. We coded 272 characters for 8 outgroups and 114 ingroup species. Depending on the weighting scheme (equal or implied weighting), our parsimony analyses suggested the monophyly of Megachile s.l. and that either Noteriades Cockerell or the clade Coelioxys Latreille + Radoszkowskiana Popov is the extant sister group of all other Megachilini. In addition, we conducted Bayesian total-evidence tip-dating analyses to examine other possible hypotheses of relationships and patterns of variation of the interdental lamina. Our analyses suggest that interdental laminae developed asynchronicaly from two different structures in the mandible, and differ in their phenotypic plasticity. Character correlation tests using phylogenetic pairwise comparisons indicated that the presence of interdental lamina is not associated with head size, mandible size and shape, and pubescence on the adductor interspace. We discuss the implications of our findings for the classification of Megachilini and the development of novel evolutionary, ecological, and functional hypotheses on this behavior. New taxa established are Pseudoheriadini Gonzalez &amp; Engel, new tribe, Ochreriadini Gonzalez &amp; Engel, new tribe, Cremnomegachile Gonzalez &amp; Engel, new genus, Rozenapis Gonzalez &amp; Engel, new genus, and Saucrochile Gonzalez &amp; Engel, new genus, along with the following new combinations: Cremnomegachile dolichosoma (Benoist), new combination, Rozenapis ignita (Smith), new combination, and Saucrochile heriadiformis (Smith), new combination

Calcium supplements and cancer risk : a meta-analysis of randomised controlled trials

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