SlabLU: A Two-Level Sparse Direct Solver for Elliptic PDEs

The paper describes a sparse direct solver for the linear systems that arise from the discretization of an elliptic PDE on a two dimensional domain. The solver is designed to reduce communication costs and perform well on GPUs; it uses a two-level framework, which is easier to implement and optimize than traditional multi-frontal schemes based on hierarchical nested dissection orderings. The scheme decomposes the domain into thin subdomains, or "slabs". Within each slab, a local factorization is executed that exploits the geometry of the local domain. A global factorization is then obtained through the LU factorization of a block-tridiagonal reduced coefficient matrix. The solver has complexity $O(N^{5/3})$ for the factorization step, and $O(N^{7/6})$ for each solve once the factorization is completed. The solver described is compatible with a range of different local discretizations, and numerical experiments demonstrate its performance for regular discretizations of rectangular and curved geometries. The technique becomes particularly efficient when combined with very high-order convergent multi-domain spectral collocation schemes. With this discretization, a Helmholtz problem on a domain of size $1000 \lambda \times 1000 \lambda$ (for which N=100 \mbox{M}) is solved in 15 minutes to 6 correct digits on a high-powered desktop with GPU acceleration

Randomized Strong Recursive Skeletonization: Simultaneous compression and factorization of H\mathcal{H}-matrices in the Black-Box Setting

The hierarchical matrix ($\mathcal{H}^{2}$-matrix) formalism provides a way to reinterpret the Fast Multipole Method and related fast summation schemes in linear algebraic terms. The idea is to tessellate a matrix into blocks in such as way that each block is either small or of numerically low rank; this enables the storage of the matrix and the application of it to a vector in linear or close to linear complexity. A key motivation for the reformulation is to extend the range of dense matrices that can be represented. Additionally, $\mathcal{H}^{2}$-matrices in principle also extend the range of operations that can be executed to include matrix inversion and factorization. While such algorithms can be highly efficient for certain specialized formats (such as HBS/HSS matrices based on ``weak admissibility''), inversion algorithms for general $\mathcal{H}^{2}$-matrices tend to be based on nested recursions and recompressions, making them challenging to implement efficiently. An exception is the \textit{strong recursive skeletonization (SRS)} algorithm by Minden, Ho, Damle, and Ying, which involves a simpler algorithmic flow. However, SRS greatly increases the number of blocks of the matrix that need to be stored explicitly, leading to high memory requirements. This manuscript presents the \textit{randomized strong recursive skeletonization (RSRS)} algorithm, which is a reformulation of SRS that incorporates the randomized SVD (RSVD) to simultaneously compress and factorize an $\mathcal{H}^{2}$-matrix. RSRS is a ``black box'' algorithm that interacts with the matrix to be compressed only via its action on vectors; this extends the range of the SRS algorithm (which relied on the ``proxy source'' compression technique) to include dense matrices that arise in sparse direct solvers

Parallel Optimizations for the Hierarchical Poincar\'e-Steklov Scheme (HPS)

Parallel optimizations for the 2D Hierarchical Poincar\'e-Steklov (HPS) discretization scheme are described. HPS is a multi-domain spectral collocation scheme that allows for combining very high order discretizations with direct solvers, making the discretization powerful in resolving highly oscillatory solutions to high accuracy. HPS can be viewed as a domain decomposition scheme where the domains are connected directly through the use of a sparse direct solver. This manuscript describes optimizations of HPS that are simple to implement, and that leverage batched linear algebra on modern hybrid architectures to improve the practical speed of the solver. In particular, the manuscript demonstrates that the traditionally high cost of performing local static condensation for discretizations involving very high local order $p$ can be reduced dramatically

SkelFMM: A Simplified Fast Multipole Method Based on Recursive Skeletonization

This work introduces the kernel-independent multi-level algorithm "skelFMM" for evaluating all pairwise interactions between $N$ points connected through a kernel such as the fundamental solution of the Laplace or the Helmholtz equations. The method is based on linear algebraic tools such as randomized low rank approximation and "skeleton representations" of far-field interactions. The work is related to previously proposed linear algebraic reformulations of the fast multipole method (FMM), but is distinguished by relying on simpler data structures. In particular, skelFMM does not require an "interaction list", as it relies instead on algebraically-modified kernel interactions between near-neighbors at every level. Like other kernel independent algorithms, it only requires evaluation of the kernel function, allowing the methodology to easily be extended to a range of different kernels in 2D and 3D. The simplicity of the algorithm makes it particularly amenable to parallel implementation on heterogeneous hardware architectures. The performance of the algorithm is demonstrated through numerical experiments conducted on uniform and non-uniform point distributions in 2D and 3D, involving Laplace and (low frequency) Helmholtz kernels. The algorithm relies on a precomputation stage that constructs a tailored representation for a given geometry of points. Once the precomputation has completed, the matrix-vector multiplication attains high speed through GPU acceleration that leverages batched linear algebra

Virtual identity as practice : exploring the relationship between role-players and their characters in the massively multiplayer online game 'Star Wars Galaxies'

The objective of this research is firstly, to evaluate claims that cyberspace, due to its inherent qualities, has had an unprecedented effect on how we construct, present and think about our collective and individual identities online and offline. Secondly, it will highlight how people use shared understandings of popular culture products in order to maintain social formations in cyberspace.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

A mutation in POLE predisposing to a multi-tumour phenotype

Somatic mutations in the POLE gene encoding the catalytic subunit of DNA polymerase epsilon have been found in sporadic colorectal cancers (CRCs) and are most likely of importance in tumour development and/or progression. Recently, families with dominantly inherited colorectal adenomas and colorectal cancer were shown to have a causative heterozygous germline mutation in the proofreading exonuclease domain of POLE. The highly penetrant mutation was associated with predisposition to CRC only and no extra-colonic tumours were observed. We have identified a mutation in a large family in which the carriers not only developed CRC, they also demonstrate a highly penetrant predisposition to extra-intestinal tumours such as ovarian, endometrial and brain tumours. The mutation, NM_006231.2:c.1089C>A, p.Asn363Lys, also located in the proofreading exonuclease domain is directly involved in DNA binding. Theoretical prediction of the amino acid substitution suggests a profound effect of the substrate binding capability and a more severe impairment of the catalytic activity compared to the previously reported germline mutation. A possible genotype to phenotype correlation for deleterious mutations in POLE might exist that needs to be considered in the follow-up of mutation carriers

A MUSE map of the central Orion Nebula (M 42)

We present a new integral-field spectroscopic dataset of the central part of the Orion Nebula (M 42), observed with the MUSE instrument at the ESO VLT. We reduced the data with the public MUSE pipeline. The output products are two FITS cubes with a spatial size of ~5.9'x4.9' (corresponding to ~0.76 pc x 0.63 pc) and a contiguous wavelength coverage of 4595...9366 Angstrom, spatially sampled at 0.2". We provide two versions with a sampling of 1.25 Angstrom and 0.85 Angstrom in dispersion direction. Together with variance cubes these files have a size of 75 and 110 GiB on disk. They represent one of the largest integral field mosaics to date in terms of information content. We make them available for use in the community. To validate this dataset, we compare world coordinates, reconstructed magnitudes, velocities, and absolute and relative emission line fluxes to the literature and find excellent agreement. We derive a two-dimensional map of extinction and present de-reddened flux maps of several individual emission lines and of diagnostic line ratios. We estimate physical properties of the Orion Nebula, using the emission line ratios [N II] and [S III] (for the electron temperature $T_e$) and [S II] and [Cl III] (for the electron density $N_e$), and show two-dimensional images of the velocity measured from several bright emission lines.Comment: Resubmitted to A&A after incorporating referee comments; access to full dataset via http://muse-vlt.eu/science/data-release

Comprehensive screening of genomic and metagenomic data reveals a large diversity of tetracycline resistance genes

Tetracyclines are broad-spectrum antibiotics used to prevent or treat a variety of bacterial infections. Resistance is often mediated through mobile resistance genes, which encode one of the three main mechanisms: active efflux, ribosomal target protection or enzymatic degradation. In the last few decades, a large number of new tetracycline-resistance genes have been discovered in clinical settings. These genes are hypothesized to originate from environmental and commensal bacteria, but the diversity of tetracycline-resistance determinants that have not yet been mobilized into pathogens is unknown. In this study, we aimed to characterize the potential tetracycline resistome by screening genomic and metagenomic data for novel resistance genes. By using probabilistic models, we predicted 1254 unique putative tetracycline resistance genes, representing 195 gene families (<70 % amino acid sequence identity), whereof 164 families had not been described previously. Out of 17 predicted genes selected for experimental verification, 7 induced a resistance phenotype in an Escherichia coli host. Several of the predicted genes were located on mobile genetic elements or in regions that indicated mobility, suggesting that they easily can be shared between bacteria. Furthermore, phylogenetic analysis indicated several events of horizontal gene transfer between bacterial phyla. Our results also suggested that acquired efflux pumps originate from proteobacterial species, while ribosomal protection genes have been mobilized from Firmicutes and Actinobacteria. This study significantly expands the knowledge of known and putatively novel tetracycline resistance genes, their mobility and evolutionary history. The study also provides insights into the unknown resistome and genes that may be encountered in clinical settings in the future

Antibodies to leukotoxin A from the periodontal pathogen Aggregatibacter actinomycetemcomitans in patients at an increased risk of rheumatoid arthritis

ObjectivesPeriodontitis and underlying bacteria have been linked to the development of rheumatoid arthritis (RA). One suggested pathogen is Aggregatibacter actinomycetemcomitans (A.a.), which expresses leukotoxin A (LtxA) that can citrullinate human proteins, providing a possible trigger for the production of anti-citrullinated protein antibodies (ACPA). In this study, we seek to determine the presence of antibodies toward LtxA in patients at risk of developing RA.MethodsTwo prospective observational patient cohorts (one Swedish and one British) with symptomatic at-risk patients were studied. Anti-LtxA antibodies were analyzed by a cell-based neutralization assay in baseline serum and compared to 100 Swedish blood donors that served as controls.ResultsSerum anti-LtxA levels or positivity did not differ between patients and blood donors. In the British cohort, anti-LtxA was more prevalent among ACPA-positive arthralgia patients compared with ACPA-negative arthralgia cases (24% vs. 13%, p < 0.0001). In the Swedish at-risk cohort, anti-LtxA positive patients were at increased risk of progression to arthritis (hazard ratio (HR) 2.10, 95% CI 1.04–4.20), but this was not confirmed in the UK at-risk cohort (HR 0.99, CI 0.60–1.65).ConclusionSerum anti-LtxA is not elevated before RA diagnosis, and associations with disease progression and ACPA levels differ between populations. Other features of the oral microbiome should be explored in upcoming periodontitis-related RA research