Invariants and Labels in Lie-Poisson Systems

Reduction is a process that uses symmetry to lower the order of a Hamiltonian system. The new variables in the reduced picture are often not canonical: there are no clear variables representing positions and momenta, and the Poisson bracket obtained is not of the canonical type. Specifically, we give two examples that give rise to brackets of the noncanonical Lie-Poisson form: the rigid body and the two-dimensional ideal fluid. From these simple cases, we then use the semidirect product extension of algebras to describe more complex physical systems. The Casimir invariants in these systems are examined, and some are shown to be linked to the recovery of information about the configuration of the system. We discuss a case in which the extension is not a semidirect product, namely compressible reduced MHD, and find for this case that the Casimir invariants lend partial information about the configuration of the system.Comment: 11 pages, RevTeX. To appear in Proceedings of the 13th Florida Workshop in Astronomy and Physic

Description of the inelastic collision of two solitary waves for the BBM equation

We prove that the collision of two solitary waves of the BBM equation is inelastic but almost elastic in the case where one solitary wave is small in the energy space. We show precise estimates of the nonzero residue due to the collision. Moreover, we give a precise description of the collision phenomenon (change of size of the solitary waves).Comment: submitted for publication. Corrected typo in Theorem 1.

Predicting oral anticoagulant response using a pharmacodynamic model

We developed a pharmacokinetic and pharmacodynamic model of warfarin absorption, metabolism, and anticoagulant action appropriate for guiding anticoagulant therapy. The model requires only two independently adjustable parameters to describe warfarin's effect on individual patients. For any given individual, these parameters are rapidly and inexpensively identified using a computer program based on the model. Test data were generated by superimposing Gaussian noise on dose-response curves calculated with the model. Then the computer program was applied to the test data. Future prothrombin complex activities (PCA's) and maintenance doses were predicted accurately early in the course of drug administration. In addition, the program accurately predicted PCA response in two groups of normal volunteers.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44006/1/10439_2006_Article_BF02363455.pd

Genome-Wide Association Study for Incident Myocardial Infarction and Coronary Heart Disease in Prospective Cohort Studies: The CHARGE Consortium

Background Data are limited on genome-wide association studies (GWAS) for incident coronary heart disease (CHD). Moreover, it is not known whether genetic variants identified to date also associate with risk of CHD in a prospective setting. Methods We performed a two-stageGWAS analysis of incident myocardial infarction (MI) and CHD in a total of 64,297 individuals (including 3898MI cases, 5465 CHD cases). SNPs that passed an arbitrary threshold of 5×10-6 in Stage I were taken to Stage II for further discovery. Furthermore, in an analysis of prognosis, we studied whether known SNPs from former GWAS were associated with totalmortality in individuals who experienced MI during follow-up. Results In Stage I 15 loci passed the threshold of 5×10-6; 8 loci for MI and 8 loci for CHD, for which one locus overlapped and none were reported in previous GWAS meta-analyses. We took 60 SNPs representing these 15 loci to Stage II of discovery. Four SNPs near QKI showed nominally significant association with MI (p-value<8.8×10-3) and three exceeded the genome-wide significance threshold when Stage I and Stage II results were combined (top SNP rs6941513: p = 6.2×10-9). Despite excellent power, the 9p21 locus SNP (rs1333049) was only modestly associated with MI (HR = 1.09, p-value = 0.02) and marginally with CHD (HR = 1.06, p-value = 0.08). Among an inception cohort of those who experienced MI during follow-up, the risk allele of rs1333049 was associated with a decreased risk of subsequent mortality (HR = 0.90, p-value = 3.2×10-3). Conclusions QKI represents a novel locus that may serve as a predictor of incident CHD in prospective studies. The association of the 9p21 locus both with increased risk of first myocardial infarction and longer survival after MI highlights the importance of study design in investigating genetic determinants of complex disorders

Meta-analysis of exome array data identifies six novel genetic loci for lung function

Background: Over 90 regions of the genome have been associated with lung function to date, many of which have also been implicated in chronic obstructive pulmonary disease. Methods: We carried out meta-analyses of exome array data and three lung function measures: forced expiratory volume in one second (FEV1), forced vital capacity (FVC) and the ratio of FEV1 to FVC (FEV1/FVC). These analyses by the SpiroMeta and CHARGE consortia included 60,749 individuals of European ancestry from 23 studies, and 7,721 individuals of African Ancestry from 5 studies in the discovery stage, with follow-up in up to 111,556 independent individuals. Results: We identified significant (P<2·8x10-7) associations with six SNPs: a nonsynonymous variant in RPAP1, which is predicted to be damaging, three intronic SNPs (SEC24C, CASC17 and UQCC1) and two intergenic SNPs near to LY86 and FGF10. Expression quantitative trait loci analyses found evidence for regulation of gene expression at three signals and implicated several genes, including TYRO3 and PLAU. Conclusions: Further interrogation of these loci could provide greater understanding of the determinants of lung function and pulmonary disease

RANTES/CCL5 and risk for coronary events: Results from the MONICA/KORA Augsburg case-cohort, Athero-express and CARDIoGRAM studies

Background: The chemokine RANTES (regulated on activation, normal T-cell expressed and secreted)/CCL5 is involved in the pathogenesis of cardiovascular disease in mice, whereas less is known in humans. We hypothesised that its relevance for atherosclerosis should be reflected by associations between CCL5 gene variants, RANTES serum concentrations and protein levels in atherosclerotic plaques and risk for coronary events. Methods and Findings: We conducted a case-cohort study within the population-based MONICA/KORA Augsburg studies. Baseline RANTES serum levels were measured in 363 individuals with incident coronary events and 1,908 non-cases (mean follow-up: 10.2±

Meta-analysis of 49 549 individuals imputed with the 1000 Genomes Project reveals an exonic damaging variant in ANGPTL4 determining fasting TG levels

Background So far, more than 170 loci have been associated with circulating lipid levels through genomewide association studies (GWAS). These associations are largely driven by common variants, their function is often not known, and many are likely to be markers for the causal variants. In this study we aimed to identify more new rare and low-frequency functional variants associated with circulating lipid levels. Methods We used the 1000 Genomes Project as a reference panel for the imputations of GWAS data from ~60 000 individuals in the discovery stage and ~90 000 samples in the replication stage. Results Our study resu

Multiethnic meta-analysis identifies ancestry-specific and cross-ancestry loci for pulmonary function

Nearly 100 loci have been identified for pulmonary function, almost exclusively in studies of European ancestry populations. We extend previous research by meta-analyzing genome-wide association studies of 1000 Genomes imputed variants in relation to pulmonary function in a multiethnic population of 90,715 individuals of European (N = 60,552), African (N = 8429), Asian (N = 9959), and Hispanic/Latino (N = 11,775) ethnicities. We identify over 50 additional loci at genome-wide significance in ancestry-specific or multiethnic meta-analyses. Using recent fine-mapping methods incorporating functional annotation, gene expression, and differences in linkage disequilibrium between ethnicities, we further shed light on potential causal variants and genes at known and newly identified loci. Several of the novel genes encode proteins with predicted or established drug targets, including KCNK2 and CDK12. Our study highlights the utility of multiethnic and integrative genomics approaches to extend existing knowledge of the genetics of l