Predicted Residual Error Sum of Squares of Mixed Models: An Application for Genomic Prediction.

Genomic prediction is a statistical method to predict phenotypes of polygenic traits using high-throughput genomic data. Most diseases and behaviors in humans and animals are polygenic traits. The majority of agronomic traits in crops are also polygenic. Accurate prediction of these traits can help medical professionals diagnose acute diseases and breeders to increase food products, and therefore significantly contribute to human health and global food security. The best linear unbiased prediction (BLUP) is an important tool to analyze high-throughput genomic data for prediction. However, to judge the efficacy of the BLUP model with a particular set of predictors for a given trait, one has to provide an unbiased mechanism to evaluate the predictability. Cross-validation (CV) is an essential tool to achieve this goal, where a sample is partitioned into K parts of roughly equal size, one part is predicted using parameters estimated from the remaining K - 1 parts, and eventually every part is predicted using a sample excluding that part. Such a CV is called the K-fold CV. Unfortunately, CV presents a substantial increase in computational burden. We developed an alternative method, the HAT method, to replace CV. The new method corrects the estimated residual errors from the whole sample analysis using the leverage values of a hat matrix of the random effects to achieve the predicted residual errors. Properties of the HAT method were investigated using seven agronomic and 1000 metabolomic traits of an inbred rice population. Results showed that the HAT method is a very good approximation of the CV method. The method was also applied to 10 traits in 1495 hybrid rice with 1.6 million SNPs, and to human height of 6161 subjects with roughly 0.5 million SNPs of the Framingham heart study data. Predictabilities of the HAT and CV methods were all similar. The HAT method allows us to easily evaluate the predictabilities of genomic prediction for large numbers of traits in very large populations

Evidence for correlated states in a cluster of bosons with Rashba spin-orbit coupling

We study the ground state properties of spin-half bosons subjected to the Rashba spin-orbit coupling in two dimensions. Due to the enhancement of the low energy density of states, it is expected that the effect of interaction becomes more important. After reviewing several possible ideal condensed states, we carry out an exact diagonalization calculation for a cluster of the bosons in the presence of strong spin-orbit coupling on a two-dimensional disk and reveal strong correlations in its ground state. We derive a low-energy effective Hamiltonian to understand how states with strong correlations become energetically more favorable than the ideal condensed states.Comment: 23 pages, 6 figure

Mott-Superfluid Transition for Spin-Orbit Coupled Bosons in One-Dimensional Optical Lattices

We study the effects of spin-orbit coupling on the Mott-superfluid transition of bosons in a one-dimensional optical lattice. We determine the strong coupling magnetic phase diagram by a combination of exact analytic and numerical means. Smooth evolution of the magnetic structure into the superfluid phases are investigated with the density matrix renormalization group technique. Novel magnetic phases are uncovered and phase transitions between them within the superfluid regime are discussed. Possible experimental detection are discussed.Comment: 5 pages, 4 figure

Proof of the deadlock-freeness of ALD routing algorithm

This is the appendix to the paper Load-Balanced Adaptive Routing for Torus Networks to provide a detailed, formal proof of the deadlock-freeness of the routing algorithm proposed in the paper. The paper is submitted to Electronics Letters, and the abstract of which is as follows: A new routing algorithm for torus interconnection networks to achieve high throughput on various traffic patterns, Adaptive Load-balanced routing with cycle Detection (ALD), is presented. Instead of the -channels scheme adopted in a few recently proposed algorithms of the same category, a cycle detection scheme is employed in ALD to handle deadlock, which leads to higher routing adaptability. Simulation results demonstrate that ALD achieves higher throughput than the recently proposed algorithms on both benign and adversarial traffic patterns

2D association and integrative omics analysis in rice provides systems biology view in trait analysis.

The interactions among genes and between genes and environment contribute significantly to the phenotypic variation of complex traits and may be possible explanations for missing heritability. However, to our knowledge no existing tool can address the two kinds of interactions. Here we propose a novel linear mixed model that considers not only the additive effects of biological markers but also the interaction effects of marker pairs. Interaction effect is demonstrated as a 2D association. Based on this linear mixed model, we developed a pipeline, namely PATOWAS. PATOWAS can be used to study transcriptome-wide and metabolome-wide associations in addition to genome-wide associations. Our case analysis with real rice recombinant inbred lines (RILs) at three omics levels demonstrates that 2D association mapping and integrative omics are able to provide a systems biology view into the analyzed traits, leading toward an answer about how genes, transcripts, proteins, and metabolites work together to produce an observable phenotype

PROC QTL—A SAS Procedure for Mapping Quantitative Trait Loci

Statistical analysis system (SAS) is the most comprehensive statistical analysis software package in the world. It offers data analysis for almost all experiments under various statistical models. Each analysis is performed using a particular subroutine, called a procedure (PROC). For example, PROC ANOVA performs analysis of variances. PROC QTL is a user-defined SAS procedure for mapping quantitative trait loci (QTL). It allows users to perform QTL mapping for continuous and discrete traits within the SAS platform. Users of PROC QTL are able to take advantage of all existing features offered by the general SAS software, for example, data management and graphical treatment. The current version of PROC QTL can perform QTL mapping for all line crossing experiments using maximum likelihood (ML), least square (LS), iteratively reweighted least square (IRLS), Fisher scoring (FISHER), Bayesian (BAYES), and empirical Bayes (EBAYES) methods

Bayesian Mixture Model Analysis for Detecting Differentially Expressed Genes

Control-treatment design is widely used in microarray gene expression experiments. The purpose of such a design is to detect genes that express differentially between the control and the treatment. Many statistical procedures have been developed to detect differentially expressed genes, but all have pros and cons and room is still open for improvement. In this study, we propose a Bayesian mixture model approach to classifying genes into one of three clusters, corresponding to clusters of downregulated, neutral, and upregulated genes, respectively. The Bayesian method is implemented via the Markov chain Monte Carlo (MCMC) algorithm. The cluster means of down- and upregulated genes are sampled from truncated normal distributions whereas the cluster mean of the neutral genes is set to zero. Using simulated data as well as data from a real microarray experiment, we demonstrate that the new method outperforms all methods commonly used in differential expression analysis