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Haplotype-based methods offer a powerful approach to disease gene mapping, based on the association between causal mutations and the ancestral haplotypes on which they arose. As part of The SNP Consortium Allele Frequency Projects, we characterized haplotype patterns across 51 autosomal regions (spanning 13 megabases of the human genome) in samples from(More)
We describe the Phase II HapMap, which characterizes over 3.1 million human single nucleotide polymorphisms (SNPs) genotyped in 270 individuals from four geographically diverse populations and includes 25-35% of common SNP variation in the populations surveyed. The map is estimated to capture untyped common variation with an average maximum r2 of between(More)
With the advent of dense maps of human genetic variation, it is now possible to detect positive natural selection across the human genome. Here we report an analysis of over 3 million polymorphisms from the International HapMap Project Phase 2 (HapMap2). We used 'long-range haplotype' methods, which were developed to identify alleles segregating in a(More)
Despite great progress in identifying genetic variants that influence human disease, most inherited risk remains unexplained. A more complete understanding requires genome-wide studies that fully examine less common alleles in populations with a wide range of ancestry. To inform the design and interpretation of such studies, we genotyped 1.6 million common(More)
We present a technique for transforming classical approximation algorithms into constant-time algorithms that approximate the size of the optimal solution. Our technique is applicable to a certain subclass of algorithms that compute a solution in a constant number of phases. The technique is based on greedily considering local improvements in random(More)
We introduce a new tool for approximation and testing algorithms called partitioning oracles. We develop methods for constructing them for any class of bounded-degree graphs with an excluded minor, and in general, for any hyperfinite class of bounded-degree graphs. These oracles utilize only local computation to consistently answer queries about a global(More)
We study the problem of estimating the Earth Mover's Distance (EMD) between probability distributions when given access only to samples. We give closeness testers and additive-error estimators over domains in [0, ∆] d , with sample complexities independent of domain size – permitting the testability even of continuous distributions over infinite domains.(More)
Ocular involvement in muscular dystrophy ranges from structural defects to abnormal electroretinograms. While the mechanisms underlying the abnormal retinal physiology in patients are not understood, it is thought that alpha-dystroglycan extracellular interactions are critical for normal visual function. Here we show that beta-dystroglycan anchors(More)
Presenilin 1 (PS1) and Presenilin 2 (PS2) are the enzymatic component of the γ-secretase complex that cleaves amyloid precursor protein (APP) to release amyloid beta (Aβ) peptide. PS deficiency in mice results in neuroinflammation and neurodegeneration in the absence of accumulated Aβ. We hypothesize that PS influences neuroinflammation through its(More)