Orthogonal rational functions and rational modifications of a measure on the unit circle

AbstractIn this paper we present formulas expressing the orthogonal rational functions associated with a rational modification of a positive bounded Borel measure on the unit circle, in terms of the orthogonal rational functions associated with the initial measure. These orthogonal rational functions are assumed to be analytic inside the closed unit disc, but the extension to the case of orthogonal rational functions analytic outside the open unit disc is easily made. As an application we obtain explicit expressions for the orthogonal rational functions associated with a rational modification of the Lebesgue measure

Down on the Brandywine

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High genotypic diversity and a novel variant of human cytomegalovirus revealed by combined UL33/UL55 genotyping with broad-range PCR

The known strains of human cytomegalovirus (HCMV) represent genotypic variants of a single species, and HCMV genotypic variability has been studied in order to reveal correlations between different disease patterns and the presence of certain HCMV genotypes, either as single or as multiple infections. The methods used for the detection of HCMV genotypes have not always been sophisticated enough to achieve complete comprehensiveness, mainly because only one genotype is usually detected in a certain specimen, due to primer specificity and genome copy number. To improve detection of variant HCMV genotypes in mixed infections, we developed PCR assays with degenerate primers targeting two variable HCMV genes, glycoprotein B (gB, UL55) and the G-protein-coupled receptor gene UL33. Primers were designed to bind conserved sites in the genomes of HCMV variants and great ape CMVs. To analyse if samples contained one or more HCMV genotypic variants, PCR assays were supplemented with oligonucleotides containing locked nucleic acids. This broad-range PCR methodology and subsequent sequence analysis detected all gB/UL55 and UL33 genotypic variants known to date in primary clinical specimens, but also revealed that many samples contained genotype mixtures. Importantly, a novel UL33 genotypic variant could be discovered in several specimens, and one HCMV isolate was plaque-purified containing the novel UL33 genotype and a so far undescribed variant of gB

Large-scale genome-wide analysis identifies genetic variants associated with cardiac structure and function

BACKGROUND: Understanding the genetic architecture of cardiac structure and function may help to prevent and treat heart disease. This investigation sought to identify common genetic variations associated with inter-individual variability in cardiac structure and function. METHODS: A GWAS meta-analysis of echocardiographic traits was performed, including 46,533 individuals from 30 studies (EchoGen consortium). The analysis included 16 traits of left ventricular (LV) structure, and systolic and diastolic function. RESULTS: The discovery analysis included 21 cohorts for structural and systolic function traits (n = 32,212) and 17 cohorts for diastolic function traits (n = 21,852). Replication was performed in 5 cohorts (n = 14,321) and 6 cohorts (n = 16,308), respectively. Besides 5 previously reported loci, the combined meta-analysis identified 10 additional genome-wide significant SNPs: rs12541595 near MTSS1 and rs10774625 in ATXN2 for LV end-diastolic internal dimension; rs806322 near KCNRG, rs4765663 in CACNA1C, rs6702619 near PALMD, rs7127129 in TMEM16A, rs11207426 near FGGY, rs17608766 in GOSR2, and rs17696696 in CFDP1 for aortic root diameter; and rs12440869 in IQCH for Doppler transmitral A-wave peak velocity. Findings were in part validated in other cohorts and in GWAS of related disease traits. The genetic loci showed associations with putative signaling pathways, and with gene expression in whole blood, monocytes, and myocardial tissue. CONCLUSION: The additional genetic loci identified in this large meta-analysis of cardiac structure and function provide insights into the underlying genetic architecture of cardiac structure and warrant follow-up in future functional studies. FUNDING: For detailed information per study, see Acknowledgments.This work was supported by a grant from the US National Heart, Lung, and Blood Institute (N01-HL-25195; R01HL 093328 to RSV), a MAIFOR grant from the University Medical Center Mainz, Germany (to PSW), the Center for Translational Vascular Biology (CTVB) of the Johannes Gutenberg-University of Mainz, and the Federal Ministry of Research and Education, Germany (BMBF 01EO1003 to PSW). This work was also supported by the research project Greifswald Approach to Individualized Medicine (GANI_MED). GANI_MED was funded by the Federal Ministry of Education and Research and the Ministry of Cultural Affairs of the Federal State of Mecklenburg, West Pomerania (contract 03IS2061A). We thank all study participants, and the colleagues and coworkers from all cohorts and sites who were involved in the generation of data or in the analysis. We especially thank Andrew Johnson (FHS) for generation of the gene annotation database used for analysis. We thank the German Center for Cardiovascular Research (DZHK e.V.) for supporting the analysis and publication of this project. RSV is a member of the Scientific Advisory Board of the DZHK. Data on CAD and MI were contributed by CARDIoGRAMplusC4D investigators. See Supplemental Acknowledgments for consortium details. PSW, JFF, AS, AT, TZ, RSV, and MD had full access to all of the data in the study and take responsibility for the integrity of the data and the accuracy of the data analysis

Genetic associations at 53 loci highlight cell types and biological pathways relevant for kidney function.

Reduced glomerular filtration rate defines chronic kidney disease and is associated with cardiovascular and all-cause mortality. We conducted a meta-analysis of genome-wide association studies for estimated glomerular filtration rate (eGFR), combining data across 133,413 individuals with replication in up to 42,166 individuals. We identify 24 new and confirm 29 previously identified loci. Of these 53 loci, 19 associate with eGFR among individuals with diabetes. Using bioinformatics, we show that identified genes at eGFR loci are enriched for expression in kidney tissues and in pathways relevant for kidney development and transmembrane transporter activity, kidney structure, and regulation of glucose metabolism. Chromatin state mapping and DNase I hypersensitivity analyses across adult tissues demonstrate preferential mapping of associated variants to regulatory regions in kidney but not extra-renal tissues. These findings suggest that genetic determinants of eGFR are mediated largely through direct effects within the kidney and highlight important cell types and biological pathways

Celestijnenlaan 200A – B-3001 Heverlee (Belgium) Orthogonal rational functions with complex poles: The Favard theorem

Let {ϕn} be a sequence of rational functions with arbitrary complex poles, generated by a certain three-term recurrence relation. In this paper we show that under some mild conditions, the rational functions ϕn form an orthonormal system with respect to a Hermitian positive-definite inner product