A Quadratically Regularized Functional Canonical Correlation Analysis for Identifying the Global Structure of Pleiotropy with NGS Data

Investigating the pleiotropic effects of genetic variants can increase statistical power, provide important information to achieve deep understanding of the complex genetic structures of disease, and offer powerful tools for designing effective treatments with fewer side effects. However, the current multiple phenotype association analysis paradigm lacks breadth (number of phenotypes and genetic variants jointly analyzed at the same time) and depth (hierarchical structure of phenotype and genotypes). A key issue for high dimensional pleiotropic analysis is to effectively extract informative internal representation and features from high dimensional genotype and phenotype data. To explore multiple levels of representations of genetic variants, learn their internal patterns involved in the disease development, and overcome critical barriers in advancing the development of novel statistical methods and computational algorithms for genetic pleiotropic analysis, we proposed a new framework referred to as a quadratically regularized functional CCA (QRFCCA) for association analysis which combines three approaches: (1) quadratically regularized matrix factorization, (2) functional data analysis and (3) canonical correlation analysis (CCA). Large-scale simulations show that the QRFCCA has a much higher power than that of the nine competing statistics while retaining the appropriate type 1 errors. To further evaluate performance, the QRFCCA and nine other statistics are applied to the whole genome sequencing dataset from the TwinsUK study. We identify a total of 79 genes with rare variants and 67 genes with common variants significantly associated with the 46 traits using QRFCCA. The results show that the QRFCCA substantially outperforms the nine other statistics.Comment: 64 pages including 12 figure

On whether or not L(E, F) = Lr(E, F) for some classical Banach lattices E and F

AbstractFor Banach lattices E and F, L(E,F) is the space of all continuous linear operators E→F, Lr(E,F) is the vector space of all regular continuous linear operators E→F which is endowed with the r-norm. This paper concerns the problems: (1) is every continuous linear operator E→F regular? (2) if the answer to (1) is “yes”, there is a further problem: is its operator norm in L(E,F) equal to its r-norm in Lr(E,F)? A series of conclusions is obtained for cases in which each of E and F is one of Banach lattices lp (1≤p < ∞), l∞, c0, c, C[0,1] and C(X)

A characterization of Riesz spaces which are Riesz isomorphic to C(X) for some completely regular space X

AbstractLet E be an Archimedean Riesz space possessing a weak unit e and let Ω be the collection of all Riesz homomorphisms ø from E onto ℝ such that ø(e)=1. The Gelfand mapping G :x→x^ on E is defined by x^(ø) = ø(x) for all ø∈Ω. We endow Ω with the topology induced by E (i.e., the weakest topology such that each x^ is continuous on Ω). The principal ideal in E generated by e is denoted by Id(e). The main theorem in this paper says that the following statements (A) and (B) are equivalent.(A)There exists a completely regular space X such that E is Riesz isomorphic to the space C(X) of all real continuous functions on X.(B)The following conditions for the Riesz space E hold: (1) E is Archimedean and has a weak unit e; (2) Ω separates the points of E; (3) E is uniformly complete; (4) G(Id(e)) is norm dense in the space Cb(Ω) of all real bounded continuous functions on Ω; (5) E is 2-universally complete with carrier space Ω.Some other conditions are mentioned and an example is given to show that condition (5) is necessary for (B) ⇒(A)

Homocoupling of CO and isocyanide mediated by a C,C′-bis(silylenyl)-substituted ortho-carborane

The unexpected reactivity of the o-carborane supported bis-silylene [(LSi:)C]2B10H101 {L= PhC(tBuN)2} towards carbon monoxide and 2,6-dimethylphenyl isocyanide is reported. While the reaction of 1 with CO leads selectively to the novel head-to-head coupling and C–O cleavage product 2 from two molecules 1 and four molecules CO, the reaction of 1 with 2,6-dimethylphenyl isocyanide affords solely the 1 : 2 molar head-to-tail coupling product 3 with a Si[double bond, length as m-dash]C bond.TU Berlin, Open-Access-Mittel - 201