A Canonical Form for Positive Definite Matrices

We exhibit an explicit, deterministic algorithm for finding a canonical form for a positive definite matrix under unimodular integral transformations. We use characteristic sets of short vectors and partition-backtracking graph software. The algorithm runs in a number of arithmetic operations that is exponential in the dimension $n$, but it is practical and more efficient than canonical forms based on Minkowski reduction

A canonical form for positive definite matrices

We exhibit an explicit, deterministic algorithm for finding a canonical form for a positive definite matrix under unimodular integral transformations. We use characteristic sets of short vectors and partition-backtracking graph software. The algorithm runs in a number of arithmetic operations that is exponential in the dimension n, but it is practical and more efficient than canonical forms based on Minkowski reduction

Computing classical modular forms

We discuss practical and some theoretical aspects of computing a database of classical modular forms in the L-functions and Modular Forms Database (LMFDB).Comment: 62 pages; minor edit

The scale of population structure in Arabidopsis thaliana

The population structure of an organism reflects its evolutionary history and influences its evolutionary trajectory. It constrains the combination of genetic diversity and reveals patterns of past gene flow. Understanding it is a prerequisite for detecting genomic regions under selection, predicting the effect of population disturbances, or modeling gene flow. This paper examines the detailed global population structure of Arabidopsis thaliana. Using a set of 5,707 plants collected from around the globe and genotyped at 149 SNPs, we show that while A. thaliana as a species self-fertilizes 97% of the time, there is considerable variation among local groups. This level of outcrossing greatly limits observed heterozygosity but is sufficient to generate considerable local haplotypic diversity. We also find that in its native Eurasian range A. thaliana exhibits continuous isolation by distance at every geographic scale without natural breaks corresponding to classical notions of populations. By contrast, in North America, where it exists as an exotic species, A. thaliana exhibits little or no population structure at a continental scale but local isolation by distance that extends hundreds of km. This suggests a pattern for the development of isolation by distance that can establish itself shortly after an organism fills a new habitat range. It also raises questions about the general applicability of many standard population genetics models. Any model based on discrete clusters of interchangeable individuals will be an uneasy fit to organisms like A. thaliana which exhibit continuous isolation by distance on many scales

Fifteen new risk loci for coronary artery disease highlight arterial-wall-specific mechanisms

Coronary artery disease (CAD) is a leading cause of morbidity and mortality worldwide. Although 58 genomic regions have been associated with CAD thus far, most of the heritability is unexplained, indicating that additional susceptibility loci await identification. An efficient discovery strategy may be larger-scale evaluation of promising associations suggested by genome-wide association studies (GWAS). Hence, we genotyped 56,309 participants using a targeted gene array derived from earlier GWAS results and performed meta-analysis of results with 194,427 participants previously genotyped, totaling 88,192 CAD cases and 162,544 controls. We identified 25 new SNP-CAD associations (P < 5 × 10(-8), in fixed-effects meta-analysis) from 15 genomic regions, including SNPs in or near genes involved in cellular adhesion, leukocyte migration and atherosclerosis (PECAM1, rs1867624), coagulation and inflammation (PROCR, rs867186 (p.Ser219Gly)) and vascular smooth muscle cell differentiation (LMOD1, rs2820315). Correlation of these regions with cell-type-specific gene expression and plasma protein levels sheds light on potential disease mechanisms

Biological, clinical and population relevance of 95 loci for blood lipids.

Plasma concentrations of total cholesterol, low-density lipoprotein cholesterol, high-density lipoprotein cholesterol and triglycerides are among the most important risk factors for coronary artery disease (CAD) and are targets for therapeutic intervention. We screened the genome for common variants associated with plasma lipids in >100,000 individuals of European ancestry. Here we report 95 significantly associated loci (P < 5 x 10(-8)), with 59 showing genome-wide significant association with lipid traits for the first time. The newly reported associations include single nucleotide polymorphisms (SNPs) near known lipid regulators (for example, CYP7A1, NPC1L1 and SCARB1) as well as in scores of loci not previously implicated in lipoprotein metabolism. The 95 loci contribute not only to normal variation in lipid traits but also to extreme lipid phenotypes and have an impact on lipid traits in three non-European populations (East Asians, South Asians and African Americans). Our results identify several novel loci associated with plasma lipids that are also associated with CAD. Finally, we validated three of the novel genes-GALNT2, PPP1R3B and TTC39B-with experiments in mouse models. Taken together, our findings provide the foundation to develop a broader biological understanding of lipoprotein metabolism and to identify new therapeutic opportunities for the prevention of CAD

Variants in KCNQ1 increase type II diabetes susceptibility in South Asians: A study of 3,310 subjects from India and the US

<p>Abstract</p> <p>Background</p> <p>Polymorphisms in intron 15 of potassium voltage-gated channel, KQT-like subfamily member 1 (<it>KCNQ1</it>) gene have been associated with type II diabetes (T2D) in Japanese genome-wide association studies (GWAS). More recently a meta-analysis of European GWAS has detected a new independent signal associated with T2D in intron 11 of the <it>KCNQ1 </it>gene. The purpose of this investigation is to examine the role of these variants with T2D in populations of Asian Indian descent from India and the US.</p> <p>Methods</p> <p>We examined the association between four variants in the <it>KCNQ1 </it>gene with T2D and related quantitative traits in a total of 3,310 Asian Indian participants from two different cohorts comprising 2,431 individuals of the Punjabi case-control cohort from the Sikh Diabetes Study and 879 migrant Asian Indians living in the US.</p> <p>Results</p> <p>Our data confirmed the association of a new signal at the <it>KCNQ1 </it>locus (rs231362) with T2D showing an allelic odds ratio (OR) of 1.24 95%CI [1.08-1.43], p = 0.002 in the Punjabi cohort. A moderate association with T2D was also seen for rs2237895 in the Punjabi (OR 1.14; p = 0.036) and combined cohorts (meta-analysis OR 1.14; p = 0.018). Three-site haplotype analysis of rs231362, rs2237892, rs2237895 exhibited considerably stronger evidence of association of the GCC haplotype with T2D showing OR of 1.24 95%CI [1.00-1.53], p = 0.001, permutation p = 8 × 10^-4in combined cohorts. The 'C' risk allele carriers of rs2237895 had significantly reduced measures of HOMA-B in the US cohort (p = 0.008) as well as in combined cohort in meta-analysis (p = 0.009).</p> <p>Conclusions</p> <p>Our investigation has confirmed that the variation within the <it>KCNQ1 </it>locus confers a significant risk to T2D among Asian Indians. Haplotype analysis further suggested that the T2D risk associated with <it>KCNQ1 </it>SNPs may be derived from 'G' allele of rs231362 and 'C' allele of rs2237895 and this appears to be mediated through β cell function.</p

Erratum: Sequence data and association statistics from 12,940 type 2 diabetes cases and controls.

This corrects the article DOI: 10.1038/sdata.2017.179

A study of common Mendelian disease carriers across ageing British cohorts: meta-analyses reveal heterozygosity for alpha 1-antitrypsin deficiency increases respiratory capacity and height

Background: Several recessive Mendelian disorders are common in Europeans, including cystic fibrosis (CFTR), medium-chain-acyl-Co-A-dehydrogenase deficiency (ACADM), phenylketonuria (PAH) and alpha 1-antitrypsin deficiency (SERPINA1). Methods: In a multicohort study of > 19 000 older individuals, we investigated the relevant phenotypes in heterozygotes for these genes: lung function (forced expiratory volume in 1 second (FEV1), forced vital capacity (FVC)) for CFTR and SERPINA1; cognitive measures for ACADM and PAH; and physical capability for ACADM, PAH and SERPINA1. Results: Findings were mostly negative but lung function in SERPINA1 ( protease inhibitor (PI) Z allele, rs28929474) showed enhanced FEV1 and FVC (0.13 zscore increase in FEV1 (p=1.7×10-5) and 0.16 z-score increase in FVC (p=5.2×10-8)) in PI-MZ individuals. Height adjustment (a known, strong correlate of FEV1 and FVC) revealed strong positive height associations of the Z allele (1.50 cm increase in height (p=3.6×10-10)). Conclusions: The PI-MZ rare (2%) SNP effect is nearly four times greater than the 'top' common height SNP in HMGA2. However, height only partially attenuates the SERPINA1-FEV1 or FVC association (around 50%) and vice versa. Height SNP variants have recently been shown to be positively selected collectively in North versus South Europeans, while the Z allele high frequency is localised to North Europe. Although PI-ZZ is clinically disadvantageous to lung function, PI-MZ increases both height and respiratory function; potentially a balanced polymorphism. Partial blockade of PI could conceivably form part of a future polytherapeutic approach in very short children. The notion that elastase inhibition should benefit patients with chronic obstructive pulmonary disease may also merit reevaluation. PI is already a therapeutic target: our findings invite a reconsideration of the optimum level in respiratory care and novel pathway potential for development of agents for the management of growth disorders