Applications of inertial-sensor high-inheritance instruments to DSN precision antenna pointing

Laboratory test results of the initialization and tracking performance of an existing inertial-sensor-based instrument are given. The instrument, although not primarily designed for precision antenna pointing applications, demonstrated an on-average 10-hour tracking error of several millidegrees. The system-level instrument performance is shown by analysis to be sensor limited. Simulated instrument improvements show a tracking error of less than 1 mdeg, which would provide acceptable performance, i.e., low pointing loss, for the Deep Space Network 70-m antenna subnetwork, operating at Ka-band (1-cm wavelength)

Gravity referenced elevation encoder development

Recent progress in the development of a gravity-sensor-based instrument for determining the elevation angle of DSN antennas is described. The benefits of such a system include the capability to locate the Gravity Referenced Elevation Encoder (GREE) directly on the primary reflector (thus bypassing structural flexure and deformation error sources), anticipated lower maintenance costs compared to the present gimbal encoders, direct replaceability, or supplementation of the present gimbal encoders and the utilization of off-the-shelf components to construct the GREE. This article includes a description of the nominal GREE design. Test results on a laboratory breadboard model are given. Rigid-body dynamics of the GREE are derived and the simulated performance in response to measured antenna vibrations is given

Estimating Effects and Making Predictions from Genome-Wide Marker Data

In genome-wide association studies (GWAS), hundreds of thousands of genetic markers (SNPs) are tested for association with a trait or phenotype. Reported effects tend to be larger in magnitude than the true effects of these markers, the so-called ``winner's curse.'' We argue that the classical definition of unbiasedness is not useful in this context and propose to use a different definition of unbiasedness that is a property of the estimator we advocate. We suggest an integrated approach to the estimation of the SNP effects and to the prediction of trait values, treating SNP effects as random instead of fixed effects. Statistical methods traditionally used in the prediction of trait values in the genetics of livestock, which predates the availability of SNP data, can be applied to analysis of GWAS, giving better estimates of the SNP effects and predictions of phenotypic and genetic values in individuals.Comment: Published in at http://dx.doi.org/10.1214/09-STS306 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Conformal Field Theories, Representations and Lattice Constructions

An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted and $Z_2$-twisted theories, $H(\Lambda)$ and $\tilde H(\Lambda)$ respectively, which may be constructed from a suitable even Euclidean lattice $\Lambda$. Similarly, one may construct lattices $\Lambda_C$ and $\tilde\Lambda_C$ by analogous constructions from a doubly-even binary code $C$. In the case when $C$ is self-dual, the corresponding lattices are also. Similarly, $H(\Lambda)$ and $\tilde H(\Lambda)$ are self-dual if and only if $\Lambda$ is. We show that $H(\Lambda_C)$ has a natural ``triality'' structure, which induces an isomorphism $H(\tilde\Lambda_C)\equiv\tilde H(\Lambda_C)$ and also a triality structure on $\tilde H(\tilde\Lambda_C)$. For $C$ the Golay code, $\tilde\Lambda_C$ is the Leech lattice, and the triality on $\tilde H(\tilde\Lambda_C)$ is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories $H(\Lambda)$ and $\tilde H(\Lambda)$ with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code.Comment: 65 page

Multi-locus models of genetic risk of disease

Background: Evidence for genetic contribution to complex diseases is described by recurrence risks to relatives of diseased individuals. Genome-wide association studies allow a description of the genetics of the same diseases in terms of risk loci, their effects and allele frequencies. To reconcile the two descriptions requires a model of how risks from individual loci combine to determine an individual's overall risk

On the fundamental representation of Borcherds algebras with one imaginary simple root

Borcherds algebras represent a new class of Lie algebras which have almost all the properties that ordinary Kac-Moody algebras have, and the only major difference is that these generalized Kac-Moody algebras are allowed to have imaginary simple roots. The simplest nontrivial examples one can think of are those where one adds ``by hand'' one imaginary simple root to an ordinary Kac-Moody algebra. We study the fundamental representation of this class of examples and prove that an irreducible module is given by the full tensor algebra over some integrable highest weight module of the underlying Kac-Moody algebra. We also comment on possible realizations of these Lie algebras in physics as symmetry algebras in quantum field theory.Comment: 8 page

Explicit determination of a 727-dimensional root space of the hyperbolic Lie algebra E10E_{10}

The 727-dimensional root space associated with the level-2 root \bLambda_1 of the hyperbolic Kac--Moody algebra $E_{10}$ is determined using a recently developed string theoretic approach to hyperbolic algebras. The explicit form of the basis reveals a complicated structure with transversal as well as longitudinal string states present.Comment: 12 pages, LaTeX 2

Prediction of individual genetic risk to disease from genome-wide association studies

Empirical studies suggest that the effect sizes of individual causal risk alleles underlying complex genetic diseases are small, with most genotype relative risks in the range of 1.1-2.0. Although the increased risk of disease for a carrier is small for any single locus, knowledge of multiple-risk alleles throughout the genome could allow the identification of individuals that are at high risk. In this study, we investigate the number and effect size of risk loci that underlie complex disease constrained by the disease parameters of prevalence and heritability. Then we quantify the value of prediction of genetic risk to disease using a range of realistic combinations of the number, size, and distribution of risk effects that underlie complex diseases. We propose an approach to assess the genetic risk of a disease in healthy individuals, based on dense genome-wide SNP panels. We test this approach using simulation. When the number of loci contributing to the disease is >50, a large case-control study is needed to identify a set of risk loci for use in predicting the disease risk of healthy people not included in the case-control study. For diseases controlled by 1000 loci of mean relative risk of only 1.04, a case-control study with 10,000 cases and controls can lead to selection of ∼75 loci that explain >50% of the genetic variance. The 5% of people with the highest predicted risk are three to seven times more likely to suffer the disease than the population average, depending on heritability and disease prevalence. Whether an individual with known genetic risk develops the disease depends on known and unknown environmental factors