Symmetry breaking in general relativity

Bifurcation theory is used to analyze the space of solutions of Einstein's equations near a spacetime with symmetries. The methods developed here allow one to describe precisely how the symmetry is broken as one branches from a highly symmetric spacetime to nearby spacetimes with fewer symmetries, and finally to a generic solution with no symmetries. This phenomenon of symmetry breaking is associated with the fact that near symmetric solutions the space of solutions of Einstein's equations does not form a smooth manifold but rather has a conical structure. The geometric picture associated with this conical structure enables one to understand the breaking of symmetries. Although the results are described for pure gravity, they may be extended to classes of fields coupled to gravity, such as gauge theories. Since most of the known solutions of Einstein's equations have Killing symmetries, the study of how these symmetries are broken by small perturbations takes on considerable theoretical significance

St Paul\u27s Ethical Terminology

Because of the importance of Paul as missionary and as a teacher of doctrine and ethics and the past neglect of Pauline ethics; along with the changing conditions demand a constant study of the eternal principles of right and wrong

Alien Registration- Vincent, Arthur (Auburn, Androscoggin County)

https://digitalmaine.com/alien_docs/30496/thumbnail.jp

Aortic pulse wave velocity measurement via heart sounds and impedance plethysmography

Full abstract in the manuscript

Unconditional quantum cloning of coherent states with linear optics

A scheme for optimal Gaussian cloning of optical coherent states is proposed and experimentally demonstrated. Its optical realization is based entirely on simple linear optical elements and homodyne detection. The optimality of the presented scheme is only limited by detection inefficiencies. Experimentally we achieved a cloning fidelity of about 65%, which almost touches the optimal value of 2/3.Comment: Phys. Rev. Lett. Volume 94, Number 24, p. 24050

SHrinkage Covariance Estimation Incorporating Prior Biological Knowledge with Applications to High-Dimensional Data

In ``-omic data'' analysis, information on the structure of covariates are broadly available either from public databases describing gene regulation processes and functional groups such as the Kyoto encyclopedia of genes and genomes (KEGG), or from statistical analyses -- for example in form of partial correlation estimators. The analysis of transcriptomic data might benefit from the incorporation of such prior knowledge. In this paper we focus on the integration of structured information into statistical analyses in which at least one major step involves the estimation of a (high-dimensional) covariance matrix. More precisely, we revisit the recently proposed ``SHrinkage Incorporating Prior'' (SHIP) covariance estimation method which takes into account the group structure of the covariates, and suggest to integrate the SHIP covariance estimator into various multivariate methods such as linear discriminant analysis (LDA), global analysis of covariance (GlobalANCOVA), and regularized generalized canonical correlation analysis (RGCCA). We demonstrate the use of the resulting new methods based on simulations and discuss the benefit of the integration of prior information through the SHIP estimator. Reproducible R codes are available at http://www.ibe.med.uni-muenchen.de/organisation/mitarbeiter/020_professuren/boulesteix/shipproject/index.html

SHrinkage Covariance Estimation Incorporating Prior Biological Knowledge with Applications to High-Dimensional Data

In ``-omic data'' analysis, information on the structure of covariates are broadly available either from public databases describing gene regulation processes and functional groups such as the Kyoto encyclopedia of genes and genomes (KEGG), or from statistical analyses -- for example in form of partial correlation estimators. The analysis of transcriptomic data might benefit from the incorporation of such prior knowledge. In this paper we focus on the integration of structured information into statistical analyses in which at least one major step involves the estimation of a (high-dimensional) covariance matrix. More precisely, we revisit the recently proposed ``SHrinkage Incorporating Prior'' (SHIP) covariance estimation method which takes into account the group structure of the covariates, and suggest to integrate the SHIP covariance estimator into various multivariate methods such as linear discriminant analysis (LDA), global analysis of covariance (GlobalANCOVA), and regularized generalized canonical correlation analysis (RGCCA). We demonstrate the use of the resulting new methods based on simulations and discuss the benefit of the integration of prior information through the SHIP estimator. Reproducible R codes are available at http://www.ibe.med.uni-muenchen.de/organisation/mitarbeiter/020_professuren/boulesteix/shipproject/index.html

SU(2)SU(2) Gauge Theory with Two Fundamental Flavours: Scalar and Pseudoscalar Spectrum

We investigate the scalar and pseudoscalar spectrum of the $SU(2)$ gauge theory with $N_f=2$ flavours of fermions in the fundamental representation using non perturbative lattice simulations. We provide first benchmark estimates of the mass of the lightest $0(0^{+})$ ($\sigma$), $0(0^{-})$ ($\eta'$) and $1(0^+)$ ($a_0$) states, including estimates of the relevant disconnected contributions. We find $m_{a_0}/F_{\rm{PS}}= 16.7(4.9)$, $m_\sigma/F_{\rm{PS}}=19.2(10.8)$ and $m_{\eta'}/F_{\rm{PS}} = 12.8(4.7)$. These values for the masses of light scalar states provide crucial information for composite extensions of the Standard Model from the unified Fundamental Composi te Higgs-Technicolor theory \cite{Cacciapaglia:2014uja} to models of composite dark matter.Comment: 18 pages, 9 figure

The Term Lutron in the New Testament

It is the purpose of this paper to give a detailed study of the term lutron. For the purpose of e1ucidation or additional proof, the derivatives and their uses will be cited