Symmetric Subgroup Actions on Isotropic Grassmannians

Let G be the group preserving a nondegenerate sesquilinear form on a vector space V, and H a symmetric subgroup of G of the type G1 x G2. We explicitly parameterize the H-orbits in the Grassmannian of r-dimensional isotropic subspaces of V by a complete set of H-invariants. We describe the Bruhat order in terms of the majorization relationship over a diagram of these H-invariants. The inclusion order, the stabilizer, the orbit dimension, the open H-orbits, the decompositions of an H orbit into H\cap G_0 and H_0 orbits are also explicitly described.Comment: 30 page

Learning Face Age Progression: A Pyramid Architecture of GANs

The two underlying requirements of face age progression, i.e. aging accuracy and identity permanence, are not well studied in the literature. In this paper, we present a novel generative adversarial network based approach. It separately models the constraints for the intrinsic subject-specific characteristics and the age-specific facial changes with respect to the elapsed time, ensuring that the generated faces present desired aging effects while simultaneously keeping personalized properties stable. Further, to generate more lifelike facial details, high-level age-specific features conveyed by the synthesized face are estimated by a pyramidal adversarial discriminator at multiple scales, which simulates the aging effects in a finer manner. The proposed method is applicable to diverse face samples in the presence of variations in pose, expression, makeup, etc., and remarkably vivid aging effects are achieved. Both visual fidelity and quantitative evaluations show that the approach advances the state-of-the-art.Comment: CVPR 2018. V4 and V2 are the same, i.e. the conference version; V3 is a related but different work, which is mistakenly submitted and will be submitted as a new arXiv pape

The role of heritability in mapping expression quantitative trait loci

Gene expression, as a heritable complex trait, has recently been used in many genome-wide linkage studies. The estimated overall heritability of each trait may be considered as evidence of a genetic contribution to the total phenotypic variation, which implies the possibility of mapping genome regions responsible for the gene expression variation via linkage analysis. However, heritability has been found to be an inconsistent predictor of significant linkage signals. To investigate this issue in human studies, we performed genome-wide linkage analysis on the 3554 gene expression traits of 194 Centre d'Etude du Polymorphisme Humain individuals provided by Genetic Analysis Workshop 15. Out of the 422 expression traits with significant linkage signals identified (LOD > 5.3), 89 traits have low estimated heritability (h2 < 10%), among which 23 traits have an estimated heritability equal to 0. The linkage analysis on individual pedigree shows that the overall LOD scores may result from a few pedigrees with strong linkage signals. Screening gene expressions before linkage analysis using a relatively low heritability (h2 < 20%) may result in a loss of significant linkage signals, especially for trans-acting expression quantitative trait loci (49%)

A Penalized Multi-trait Mixed Model for Association Mapping in Pedigree-based GWAS

In genome-wide association studies (GWAS), penalization is an important approach for identifying genetic markers associated with trait while mixed model is successful in accounting for a complicated dependence structure among samples. Therefore, penalized linear mixed model is a tool that combines the advantages of penalization approach and linear mixed model. In this study, a GWAS with multiple highly correlated traits is analyzed. For GWAS with multiple quantitative traits that are highly correlated, the analysis using traits marginally inevitably lose some essential information among multiple traits. We propose a penalized-MTMM, a penalized multivariate linear mixed model that allows both the within-trait and between-trait variance components simultaneously for multiple traits. The proposed penalized-MTMM estimates variance components using an AI-REML method and conducts variable selection and point estimation simultaneously using group MCP and sparse group MCP. Best linear unbiased predictor (BLUP) is used to find predictive values and the Pearson's correlations between predictive values and their corresponding observations are used to evaluate prediction performance. Both prediction and selection performance of the proposed approach and its comparison with the uni-trait penalized-LMM are evaluated through simulation studies. We apply the proposed approach to a GWAS data from Genetic Analysis Workshop (GAW) 18