Commensurability Classes of Fake Quadrics

A fake quadric is a smooth projective surface that has the same rational cohomology as a smooth quadric surface but is not biholomorphic to one. We provide an explicit classification of all irreducible fake quadrics according to the commensurability class of their fundamental group. To accomplish this task, we develop a number of new techniques that explicitly bound the arithmetic invariants of a fake quadric and more generally of an arithmetic manifold of bounded volume arising from a form of SL_2 over a number field

Confounding from Cryptic Relatedness in Case-Control Association Studies

Case-control association studies are widely used in the search for genetic variants that contribute to human diseases. It has long been known that such studies may suffer from high rates of false positives if there is unrecognized population structure. It is perhaps less widely appreciated that so-called “cryptic relatedness” (i.e., kinship among the cases or controls that is not known to the investigator) might also potentially inflate the false positive rate. Until now there has been little work to assess how serious this problem is likely to be in practice. In this paper, we develop a formal model of cryptic relatedness, and study its impact on association studies. We provide simple expressions that predict the extent of confounding due to cryptic relatedness. Surprisingly, these expressions are functions of directly observable parameters. Our analytical results show that, for well-designed studies in outbred populations, the degree of confounding due to cryptic relatedness will usually be negligible. However, in contrast, studies where there is a sampling bias toward collecting relatives may indeed suffer from excessive rates of false positives. Furthermore, cryptic relatedness may be a serious concern in founder populations that have grown rapidly and recently from a small size. As an example, we analyze the impact of excess relatedness among cases for six phenotypes measured in the Hutterite population

Serum calcium and risk of migraine : a Mendelian randomization study

Migraine affects similar to 14% of the world's population, though not all predisposing causal risk factors are known. We used electronic health records, genetic co-heritability analysis, and a two-sampleMendelian Randomization (MR) design to determine if elevated serum calcium levels were associated with risk of migraine headache. Co-morbidity was evaluated using electronic health records obtained from the PennOmics database comprising>1 million patient entries. Genetic co-heritability and causality via MR was assessed using data from the International Headache Consortium (23,285 cases, 95,425 controls) and circulating serum calcium levels (39,400 subjects). We observed co-occurrence of migraine and hypercalcaemia ICD-9 diagnoses (OR = 1.58, P = 4 x 10-(13)), even after inclusion of additional risk factors for migraine (OR = 1.23, P = 2 x 10 -(3)). Second, we observed co-heritability (r(g) =0.191, P = 0.03) between serum calcium and migraine headache, indicating that these traits have a genetic basis in common. Finally, we found that elevation of serum calcium levels by 1 mg/dl resulting from our genetic score was associated with an increase in risk of migraine (OR = 1.80, 95% CI: 1.31-2.46, P = 2.5 x 10 -(4)), evidence supporting a causal hypothesis. We also present multiple MR sensitivity analyses in support of this central finding. Our results provide evidence that hypercalcaemia is comorbid with migraine headache diagnoses, and that genetically elevated serum calcium over lifetime appears to increase risk for migraine. Further studies will be required to understand the biologicalmechanism, pathways, and clinical implication for riskmanagement.Peer reviewe

Coverage and Characteristics of the Affymetrix GeneChip Human Mapping 100K SNP Set

Improvements in technology have made it possible to conduct genome-wide association mapping at costs within reach of academic investigators, and experiments are currently being conducted with a variety of high-throughput platforms. To provide an appropriate context for interpreting results of such studies, we summarize here results of an investigation of one of the first of these technologies to be publicly available, the Affymetrix GeneChip Human Mapping 100K set of single nucleotide polymorphisms (SNPs). In a systematic analysis of the pattern and distribution of SNPs in the Mapping 100K set, we find that SNPs in this set are undersampled from coding regions (both nonsynonymous and synonymous) and oversampled from regions outside genes, relative to SNPs in the overall HapMap database. In addition, we utilize a novel multilocus linkage disequilibrium (LD) coefficient based on information content (analogous to the information content scores commonly used for linkage mapping) that is equivalent to the familiar measure r (2) in the special case of two loci. Using this approach, we are able to summarize for any subset of markers, such as the Affymetrix Mapping 100K set, the information available for association mapping in that subset, relative to the information available in the full set of markers included in the HapMap, and highlight circumstances in which this multilocus measure of LD provides substantial additional insight about the haplotype structure in a region over pairwise measures of LD

Expressions 2014

https://openspace.dmacc.edu/expressions/1028/thumbnail.jp

A Map of Recent Positive Selection in the Human Genome

The identification of signals of very recent positive selection provides information about the adaptation of modern humans to local conditions. We report here on a genome-wide scan for signals of very recent positive selection in favor of variants that have not yet reached fixation. We describe a new analytical method for scanning single nucleotide polymorphism (SNP) data for signals of recent selection, and apply this to data from the International HapMap Project. In all three continental groups we find widespread signals of recent positive selection. Most signals are region-specific, though a significant excess are shared across groups. Contrary to some earlier low resolution studies that suggested a paucity of recent selection in sub-Saharan Africans, we find that by some measures our strongest signals of selection are from the Yoruba population. Finally, since these signals indicate the existence of genetic variants that have substantially different fitnesses, they must indicate loci that are the source of significant phenotypic variation. Though the relevant phenotypes are generally not known, such loci should be of particular interest in mapping studies of complex traits. For this purpose we have developed a set of SNPs that can be used to tag the strongest ∼250 signals of recent selection in each population