Fast Genome-Wide QTL Association Mapping on Pedigree and Population Data

Since most analysis software for genome-wide association studies (GWAS) currently exploit only unrelated individuals, there is a need for efficient applications that can handle general pedigree data or mixtures of both population and pedigree data. Even data sets thought to consist of only unrelated individuals may include cryptic relationships that can lead to false positives if not discovered and controlled for. In addition, family designs possess compelling advantages. They are better equipped to detect rare variants, control for population stratification, and facilitate the study of parent-of-origin effects. Pedigrees selected for extreme trait values often segregate a single gene with strong effect. Finally, many pedigrees are available as an important legacy from the era of linkage analysis. Unfortunately, pedigree likelihoods are notoriously hard to compute. In this paper we re-examine the computational bottlenecks and implement ultra-fast pedigree-based GWAS analysis. Kinship coefficients can either be based on explicitly provided pedigrees or automatically estimated from dense markers. Our strategy (a) works for random sample data, pedigree data, or a mix of both; (b) entails no loss of power; (c) allows for any number of covariate adjustments, including correction for population stratification; (d) allows for testing SNPs under additive, dominant, and recessive models; and (e) accommodates both univariate and multivariate quantitative traits. On a typical personal computer (6 CPU cores at 2.67 GHz), analyzing a univariate HDL (high-density lipoprotein) trait from the San Antonio Family Heart Study (935,392 SNPs on 1357 individuals in 124 pedigrees) takes less than 2 minutes and 1.5 GB of memory. Complete multivariate QTL analysis of the three time-points of the longitudinal HDL multivariate trait takes less than 5 minutes and 1.5 GB of memory

A Framework for Structured Quantum Search

A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to the underlying structure of abstract search spaces, and is analytically simpler than previous structured search methods. The algorithm is evaluated empirically with a variety of search problems, and shown to be particularly effective for searches with many constraints. Furthermore, the algorithm provides a simple framework for utilizing search heuristics. It also exhibits the same phase transition in search difficulty as found for sophisticated classical search methods, indicating it is effectively using the problem structure.Comment: 18 pages, Latex, 7 figures, further information available at ftp://parcftp.xerox.com/pub/dynamics/quantum.htm

Extracting HI cosmological signal with Generalized Needlet Internal Linear Combination

HI intensity mapping is a new observational technique to map fluctuations in the large-scale structure of matter using the 21 cm emission line of atomic hydrogen (HI). Sensitive radio surveys have the potential to detect Baryon Acoustic Oscillations (BAO) at low redshifts (z < 1) in order to constrain the properties of dark energy. Observations of the HI signal will be contaminated by instrumental noise and, more significantly, by astrophysical foregrounds, such as Galactic synchrotron emission, which is at least four orders of magnitude brighter than the HI signal. Foreground cleaning is recognised as one of the key challenges for future radio astronomy surveys. We study the ability of the Generalized Needlet Internal Linear Combination (GNILC) method to subtract radio foregrounds and to recover the cosmological HI signal for a general HI intensity mapping experiment. The GNILC method is a new technique that uses both frequency and spatial information to separate the components of the observed data. Our results show that the method is robust to the complexity of the foregrounds. For simulated radio observations including HI emission, Galactic synchrotron, Galactic free-free, radio sources and 0.05 mK thermal noise, we find that we can reconstruct the HI power spectrum for multipoles 30 < l < 150 with 6% accuracy on 50% of the sky for a redshift z ~ 0.25.Comment: 20 pages, 13 figures. Updated to match version accepted by MNRA