Simple parallel and distributed algorithms for spectral graph sparsification

We describe a simple algorithm for spectral graph sparsification, based on iterative computations of weighted spanners and uniform sampling. Leveraging the algorithms of Baswana and Sen for computing spanners, we obtain the first distributed spectral sparsification algorithm. We also obtain a parallel algorithm with improved work and time guarantees. Combining this algorithm with the parallel framework of Peng and Spielman for solving symmetric diagonally dominant linear systems, we get a parallel solver which is much closer to being practical and significantly more efficient in terms of the total work.Comment: replaces "A simple parallel and distributed algorithm for spectral sparsification". Minor change

Multigrid Analysis of Scattering by Large Planar Structures

Abstract Fast iterative analysis of two-dimensional scattering by a large but finite array of perfectly conducting strips requires efficient evaluation of the electric field. We present a novel multigrid algorithm that carries out this task in CN computer operations, where C depends logarithmically on the desired accuracy in the field, and N is the number of spatial gridpoints. Numerical results are presented, and extensions of the algorithm are discussed

PRIMAL: Fast and Accurate Pedigree-based Imputation from Sequence Data in a Founder Population

Founder populations and large pedigrees offer many well-known advantages for genetic mapping studies, including cost-efficient study designs. Here, we describe PRIMAL (PedigRee IMputation ALgorithm), a fast and accurate pedigree-based phasing and imputation algorithm for founder populations. PRIMAL incorporates both existing and original ideas, such as a novel indexing strategy of Identity-By-Descent (IBD) segments based on clique graphs. We were able to impute the genomes of 1,317 South Dakota Hutterites, who had genome-wide genotypes for ~300,000 common single nucleotide variants (SNVs), from 98 whole genome sequences. Using a combination of pedigree-based and LD-based imputation, we were able to assign 87% of genotypes with >99% accuracy over the full range of allele frequencies. Using the IBD cliques we were also able to infer the parental origin of 83% of alleles, and genotypes of deceased recent ancestors for whom no genotype information was available. This imputed data set will enable us to better study the relative contribution of rare and common variants on human phenotypes, as well as parental origin effect of disease risk alleles in >1,000 individuals at minimal cost.</p

No Exit? Withdrawal Rights and the Law of Corporate Reorganizations

Bankruptcy scholarship is largely a debate about the comparative merits of a mandatory regime on one hand and bankruptcy by free design on the other. By the standard account, the current law of corporate reorganization is mandatory. Various rules that cannot be avoided ensure that investors’ actions are limited and they do not exercise their rights against specialized assets in a way that destroys the value of a business as a whole. These rules solve collective action problems and reduce the risk of bargaining failure. But there are costs to a mandatory regime. In particular, investors cannot design their rights to achieve optimal monitoring as they could in a system of bankruptcy by free design. This Article suggests that the academic debate has missed a fundamental feature of the law. Bankruptcy operates on legal entities, not on firms in the economic sense. For this reason, sophisticated investors do not face a mandatory regime at all. The ability of investors to place assets in separate entities gives them the ability to create specific withdrawal rights in the event the firm encounters financial distress. There is nothing mandatory about rules like the automatic stay when assets can be partitioned off into legal entities that are beyond the reach of the bankruptcy judge. Thus, by partitioning assets of one economic enterprise into different legal entities, investors can create a tailored bankruptcy regime. In this way, legal entities serve as building blocks that can be combined to create specific and varied but transparent investor withdrawal rights. This regime of tailored bankruptcy has been unrecognized and underappreciated and may be preferable to both mandatory and free design regimes. By allowing a limited number of investors to opt out of bankruptcy in a particular, discrete, and visible way, investors as a group may be able to both limit the risk of bargaining failure and at the same time enjoy the disciplining effect that a withdrawal right brings with it

Ethnic-specific associations of rare and low-frequency DNA sequence variants with asthma

Common variants at many loci have been robustly associated with asthma but explain little of the overall genetic risk. Here we investigate the role of rare (<1%) and low-frequency (1–5%) variants using the Illumina HumanExome BeadChip array in 4,794 asthma cases, 4,707 non-asthmatic controls and 590 case–parent trios representing European Americans, African Americans/African Caribbeans and Latinos. Our study reveals one low-frequency missense mutation in the GRASP gene that is associated with asthma in the Latino sample (P=4.31 × 10−6; OR=1.25; MAF=1.21%) and two genes harbouring functional variants that are associated with asthma in a gene-based analysis: GSDMB at the 17q12–21 asthma locus in the Latino and combined samples (P=7.81 × 10−8 and 4.09 × 10−8, respectively) and MTHFR in the African ancestry sample (P=1.72 × 10−6). Our results suggest that associations with rare and low-frequency variants are ethnic specific and not likely to explain a significant proportion of the ‘missing heritability’ of asthma

A new strategy for enhancing imputation quality of rare variants from next-generation sequencing data via combining SNP and exome chip data

Background: Rare variants have gathered increasing attention as a possible alternative source of missing heritability. Since next generation sequencing technology is not yet cost-effective for large-scale genomic studies, a widely used alternative approach is imputation. However, the imputation approach may be limited by the low accuracy of the imputed rare variants. To improve imputation accuracy of rare variants, various approaches have been suggested, including increasing the sample size of the reference panel, using sequencing data from study-specific samples (i.e., specific populations), and using local reference panels by genotyping or sequencing a subset of study samples. While these approaches mainly utilize reference panels, imputation accuracy of rare variants can also be increased by using exome chips containing rare variants. The exome chip contains 250 K rare variants selected from the discovered variants of about 12,000 sequenced samples. If exome chip data are available for previously genotyped samples, the combined approach using a genotype panel of merged data, including exome chips and SNP chips, should increase the imputation accuracy of rare variants. Results: In this study, we describe a combined imputation which uses both exome chip and SNP chip data simultaneously as a genotype panel. The effectiveness and performance of the combined approach was demonstrated using a reference panel of 848 samples constructed using exome sequencing data from the T2D-GENES consortium and 5,349 sample genotype panels consisting of an exome chip and SNP chip. As a result, the combined approach increased imputation quality up to 11 %, and genomic coverage for rare variants up to 117.7 % (MAF < 1 %), compared to imputation using the SNP chip alone. Also, we investigated the systematic effect of reference panels on imputation quality using five reference panels and three genotype panels. The best performing approach was the combination of the study specific reference panel and the genotype panel of combined data. Conclusions: Our study demonstrates that combined datasets, including SNP chips and exome chips, enhances both the imputation quality and genomic coverage of rare variants