On Optimal Partitioning For Sparse Matrices In Variable Block Row Format

The Variable Block Row (VBR) format is an influential blocked sparse matrix format designed to represent shared sparsity structure between adjacent rows and columns. VBR consists of groups of adjacent rows and columns, storing the resulting blocks that contain nonzeros in a dense format. This reduces the memory footprint and enables optimizations such as register blocking and instruction-level parallelism. Existing approaches use heuristics to determine which rows and columns should be grouped together. We adapt and optimize a dynamic programming algorithm for sequential hypergraph partitioning to produce a linear time algorithm which can determine the optimal partition of rows under an expressive cost model, assuming the column partition remains fixed. Furthermore, we show that the problem of determining an optimal partition for the rows and columns simultaneously is NP-Hard under a simple linear cost model. To evaluate our algorithm empirically against existing heuristics, we introduce the 1D-VBR format, a specialization of VBR format where columns are left ungrouped. We evaluate our algorithms on all 1626 real-valued matrices in the SuiteSparse Matrix Collection. When asked to minimize an empirically derived cost model for a sparse matrix-vector multiplication kernel, our algorithm produced partitions whose 1D-VBR realizations achieve a speedup of at least 1.18 over an unblocked kernel on 25% of the matrices, and a speedup of at least 1.59 on 12.5% of the matrices. The 1D-VBR representation produced by our algorithm had faster SpMVs than the 1D-VBR representations produced by any existing heuristics on 87.8% of the test matrices

Weighted Radon transforms for which the Chang approximate inversion formula is precise

We describe all weighted Radon transforms on the plane for which the Chang approximate inversion formula is precise. Some subsequent results, including the Cormack type inversion for these transforms, are also given

A Parallel Solver for Graph Laplacians

Problems from graph drawing, spectral clustering, network flow and graph partitioning can all be expressed in terms of graph Laplacian matrices. There are a variety of practical approaches to solving these problems in serial. However, as problem sizes increase and single core speeds stagnate, parallelism is essential to solve such problems quickly. We present an unsmoothed aggregation multigrid method for solving graph Laplacians in a distributed memory setting. We introduce new parallel aggregation and low degree elimination algorithms targeted specifically at irregular degree graphs. These algorithms are expressed in terms of sparse matrix-vector products using generalized sum and product operations. This formulation is amenable to linear algebra using arbitrary distributions and allows us to operate on a 2D sparse matrix distribution, which is necessary for parallel scalability. Our solver outperforms the natural parallel extension of the current state of the art in an algorithmic comparison. We demonstrate scalability to 576 processes and graphs with up to 1.7 billion edges.Comment: PASC '18, Code: https://github.com/ligmg/ligm

Serum eosinophil cationic protein (S-ECP) in a population with low prevalence of atopy

AbstractThe study is a part of the European Community Respiratory Health Survey. A random sample (n=351) of 20–44-year olds and persons of the same age with asthma-like symptoms or current asthma medication according to a postal questionnaire (n=95) were studied. Interview was taken, methacholine challenge was done and ECP, total and specific IgE were measured from serum. The median S-ECP value was 8.0 μg/l in the random sample. The geometric mean of S-ECP was higher in subjects with, than without atopy (10.2. vs 8.9 μg/l, P<0.01) and in subjects with bronchial hyperresponsiveness (BHR) than in subjects without BHR (9.9 vs 8.0 μg/l,P <0.01). The levels correlated weakly to forced expiratory volume in one second (FEV1) (r=0.13, P<0.01) and were not independently correlated with respiratory symptoms, asthma or FEV1 after adjusting for BHR, IgE, sensitisation and smoking. Our results indicate that the level of eosinophil activation is low in a population with a low prevalence of atopy, even when BHR is common

Do Foreigners Need Title Insurance in Mexico? - An Analysis of U.S. Title Insurance and Mexican Real Estate Law

This paper analyzes the title insurance industry in the United States and comparable institutions in Mexico. It begins with an overview of the history of title in both counties, followed by a description of their respective real estate systems. Finally, a summary of the laws that affect holding title to property in Mexico reveals that, although title insurance may provide other benefits for foreign investors, it provides duplicitous coverage for property in Mexico

Comment on ``Density-matrix renormalization-group method for excited states''

In a Physical Review B paper Chandross and Hicks claim that an analysis of the density-density correlation function in the dimerised Hubbard model of polyacetylene indicates that the optical exciton is bound, and that a previous study by Boman and Bursill that concluded otherwise was incorrect due to numerical innacuracy. We show that the method used in our original paper was numerically sound and well established in the literature. We also show that, when the scaling with lattice size is analysed, the interpretation of the density-density correlation function adopted by Chandross and Hicks in fact implies that the optical exciton is unbound.Comment: RevTeX, 10 pages, 4 eps figures fixed and included now in tex

Insect immunity: cDNA clones coding for the precursor forms of cecropins A and D, antibacterial proteins from Hyalophora cecropia

AbstractUsing synthetic probes cDNA clones were isolated correponding to the precursor forms of cecropins A and D. The sequences obtained were compared to earlier data for preprocecropin B. A processing scheme in three or four steps is discussed

Jet: Multilevel Graph Partitioning on GPUs

The multilevel heuristic is the dominant strategy for high-quality sequential and parallel graph partitioning. Partition refinement is a key step of multilevel graph partitioning. In this work, we present Jet, a new parallel algorithm for partition refinement specifically designed for Graphics Processing Units (GPUs). We combine Jet with GPU-aware coarsening to develop a $k$-way graph partitioner. The new partitioner achieves superior quality when compared to state-of-the-art shared memory graph partitioners on a large collection of test graphs.Comment: Submitted as a non-archival track paper for SIAM ACDA 202