The Maslov index in weak symplectic functional analysis

We recall the Chernoff-Marsden definition of weak symplectic structure and give a rigorous treatment of the functional analysis and geometry of weak symplectic Banach spaces. We define the Maslov index of a continuous path of Fredholm pairs of Lagrangian subspaces in continuously varying Banach spaces. We derive basic properties of this Maslov index and emphasize the new features appearing.Comment: 34 pages, 13 figures, 45 references, to appear in Ann Glob Anal Geom. The final publication will be available at http://www.springerlink.com. arXiv admin note: substantial text overlap with arXiv:math/040613

Genome-wide association study identifies WNT7B as a novel locus for central corneal thickness in Latinos

The cornea is the outermost layer of the eye and is a vital component of focusing incoming light on the retina. Central corneal thickness (CCT) is now recognized to have a significant role in ocular health and is a risk factor for various ocular diseases, such as keratoconus and primary open angle glaucoma. Most previous genetic studies utilized European and Asian subjects to identify genetic loci associated with CCT. Minority populations, such as Latinos, may aid in identifying additional loci and improve our understanding of the genetic architecture of CCT. In this study, we conducted a genome-wide association study (GWAS) in Latinos, a traditionally understudied population in genetic research, to further identify loci contributing to CCT. Study participants were genotyped using either the Illumina OmniExpress BeadChip (~730K markers) or the Illumina Hispanic/SOL BeadChip (~2.5 million markers). All study participants were 40 years of age and older. We assessed the association between individual single nucleotide polymorphisms (SNPs) and CCT using linear regression, adjusting for age, gender and principal components of genetic ancestry. To expand genomic coverage and to interrogate additional SNPs, we imputed SNPs from the 1000 Genomes Project reference panels. We identified a novel SNP, rs10453441 (P=6.01E-09), in an intron of WNT7B that is associated with CCT. Furthermore, WNT7B is expressed in the human cornea. We also replicated 11 previously reported loci, including IBTK, RXRA-COL5A1, COL5A1, FOXO1, LRRK1 and ZNF469 (P < 1.25E-3). These findings provide further insight into the genetic architecture of CCT and illustrate that the use of minority groups in GWAS will help identify additional loci

Genome-wide association study for refractive astigmatism reveals genetic co-determination with spherical equivalent refractive error : the CREAM consortium

Peer reviewe

The genetics of myopia

Myopia is the most common eye condition worldwide and its prevalence is increasing. While changes in environment, such as time spent outdoors, have driven myopia rates, within populations myopia is highly heritable. Genes are estimated to explain up to 80% of the variance in refractive error. Initial attempts to identify myopia genes relied on family studies using linkage analysis or candidate gene approaches with limited progress. More genome-wide association study (GWAS) approaches have taken over, ultimately resulting in the identification of hundreds of genes for refractive error and myopia, providing new insights into its molecular machinery. These studies showed myopia is a complex trait, with many genetic variants of small effect influencing retinal signaling, eye growth and the normal process of emmetropization. The genetic architecture and its molecular mechanisms are still to be clarified and while genetic risk score prediction models are improving, this knowledge must be expanded to have impact on clinical practice

IMI - Myopia Genetics Report

The knowledge on the genetic background of refractive error and myopia has expanded dramatically in the past few years. This white paper aims to provide a concise summary of current genetic findings and defines the direction where development is needed. We performed an extensive literature search and conducted informal discussions with key stakeholders. Specific topics reviewed included common refractive error, any and high myopia, and myopia related to syndromes. To date, almost 200 genetic loci have been identified for refractive error and myopia, and risk variants mostly carry low risk but are highly prevalent in the general population. Several genes for secondary syndromic myopia overlap with those for common myopia. Polygenic risk scores show overrepresentation of high myopia in the higher deciles of risk. Annotated genes have a wide variety of functions, and all retinal layers appear to be sites of expression. The current genetic findings offer a world of new molecules involved in myopiagenesis. As the missing heritability is still large, further genetic advances are needed. This Committee recommends expanding large-scale, in-depth genetic studies using complementary big data analytics, consideration of gene-environment effects by thorough measurement of environmental exposures, and focus on subgroups with extreme phenotypes and high familial occurrence. Functional characterization of associated variants is simultaneously needed to bridge the knowledge gap between sequence variance and consequence for eye growth

IMI - Myopia Genetics Report

The knowledge on the genetic background of refractive error and myopia has expanded dramatically in the past few years. This white paper aims to provide a concise summary of current genetic findings and defines the direction where development is needed.We performed an extensive literature search and conducted informal discussions with key stakeholders. Specific topics reviewed included common refractive error, any and high myopia, and myopia related to syndromes.To date, almost 200 genetic loci have been identified for refractive error and myopia, and risk variants mostly carry low risk but are highly prevalent in the general population. Several genes for secondary syndromic myopia overlap with those for common myopia. Polygenic risk scores show overrepresentation of high myopia in the higher deciles of risk. Annotated genes have a wide variety of functions, and all retinal layers appear to be sites of expression.The current genetic findings offer a world of new molecules involved in myopiagenesis. As the missing heritability is still large, further genetic advances are needed. This Committee recommends expanding large-scale, in-depth genetic studies using complementary big data analytics, consideration of gene-environment effects by thorough measurement of environmental exposures, and focus on subgroups with extreme phenotypes and high familial occurrence. Functional characterization of associated variants is simultaneously needed to bridge the knowledge gap between sequence variance and consequence for eye growth

Meta-analysis of gene-environment-wide association scans accounting for education level identifies additional loci for refractive error

Myopia is the most common human eye disorder and it results from complex genetic and environmental causes. The rapidly increasing prevalence of myopia poses a major public health challenge. Here, the CREAM consortium performs a joint meta-analysis to test single-nucleotide polymorphism (SNP) main effects and SNP x education interaction effects on refractive error in 40,036 adults from 25 studies of European ancestry and 10,315 adults from 9 studies of Asian ancestry. In European ancestry individuals, we identify six novel loci (FAM150B-ACP1, LINC00340, FBN1, DIS3L-MAP2K1, ARID2-SNAT1 and SLC14A2) associated with refractive error. In Asian populations, three genome-wide significant loci AREG, GABRR1 and PDE10A also exhibit strong interactions with education (P <8.5 x 10(-5)), whereas the interactions are less evident in Europeans. The discovery of these loci represents an important advance in understanding how gene and environment interactions contribute to the heterogeneity of myopia.Peer reviewe