Generalized Cylinders in Semi-Riemannian and Spin Geometry

We use a construction which we call generalized cylinders to give a new proof of the fundamental theorem of hypersurface theory. It has the advantage of being very simple and the result directly extends to semi-Riemannian manifolds and to embeddings into spaces of constant curvature. We also give a new way to identify spinors for different metrics and to derive the variation formula for the Dirac operator. Moreover, we show that generalized Killing spinors for Codazzi tensors are restrictions of parallel spinors. Finally, we study the space of Lorentzian metrics and give a criterion when two Lorentzian metrics on a manifold can be joined in a natural manner by a 1-parameter family of such metrics.Comment: 29 pages, 2 figure

A streamwise-constant model of turbulent pipe flow

A streamwise-constant model is presented to investigate the basic mechanisms responsible for the change in mean flow occuring during pipe flow transition. Using a single forced momentum balance equation, we show that the shape of the velocity profile is robust to changes in the forcing profile and that both linear non-normal and nonlinear effects are required to capture the change in mean flow associated with transition to turbulence. The particularly simple form of the model allows for the study of the momentum transfer directly by inspection of the equations. The distribution of the high- and low-speed streaks over the cross-section of the pipe produced by our model is remarkably similar to one observed in the velocity field near the trailing edge of the puff structures present in pipe flow transition. Under stochastic forcing, the model exhibits a quasi-periodic self-sustaining cycle characterized by the creation and subsequent decay of "streamwise-constant puffs", so-called due to the good agreement between the temporal evolution of their velocity field and the projection of the velocity field associated with three-dimensional puffs in a frame of reference moving at the bulk velocity. We establish that the flow dynamics are relatively insensitive to the regeneration mechanisms invoked to produce near-wall streamwise vortices and that using small, unstructured background disturbances to regenerate the streamwise vortices is sufficient to capture the formation of the high- and low-speed streaks and their segregation leading to the blunting of the velocity profile characteristic of turbulent pipe flow

Genetic prediction of quantitative traits: a machine learner's guide focused on height

Machine learning and deep learning have been celebrating many successes in the application to biological problems, especially in the domain of protein folding. Another equally complex and important question has received relatively little attention by the machine learning community, namely the one of prediction of complex traits from genetics. Tackling this problem requires in-depth knowledge of the related genetics literature and awareness of various subtleties associated with genetic data. In this guide, we provide an overview for the machine learning community on current state of the art models and associated subtleties which need to be taken into consideration when developing new models for phenotype prediction. We use height as an example of a continuous-valued phenotype and provide an introduction to benchmark datasets, confounders, feature selection, and common metrics

Alterações neuroendócrinas causadas por disruptores endócrinos: o exemplo do Bisfenol A

Los contaminantes ambientales, como los disruptores endocrinos,podrían provocar profundos cambios en los seres vivos. Aqui se analizan las alteraciones neuroendocrinas y reproductivas en mamíferos, incluyendo las descriptas en humanos, causadas por una molécula de origen industrial, el Bisfenol A.Exposure to endocrine disruptors may produce profound alterations in several species. As an example, the neuroendocrine and reproductive alterations due to Bisphenol A in mammals are summarized here.Os contaminantes ambientais, como os disruptores endócrinos, poderiam provocar profundas alterações nos seres vivos. Aqui são analisadas as alterações neuroendócrinas e reprodutivas em mamíferos, incluindo as descritas em humanos, causadas por uma molécula de origem industrial,o Bisfenol AFil: Bourguignon, Nadia. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental (i); ArgentinaFil: Fernández, Marina . Universidad de Buenos Aires. Facultad de Medicina; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental (i); ArgentinaFil: Lux, Victoria Adela R.. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental (i); ArgentinaFil: Libertun, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental (i); Argentina. Universidad de Buenos Aires. Facultad de Medicina; Argentin

A characterization of Dirac morphisms

Relating the Dirac operators on the total space and on the base manifold of a horizontally conformal submersion, we characterize Dirac morphisms, i.e. maps which pull back (local) harmonic spinor fields onto (local) harmonic spinor fields.Comment: 18 pages; restricted to the even-dimensional cas

Vanishing viscosity limit of navier-stokes equations in gevrey class

In this paper we consider the inviscid limit for the periodic solutions to Navier-Stokes equation in the framework of Gevrey class. It is shown that the lifespan for the solutions to Navier-Stokes equation is independent of viscosity, and that the solutions of the Navier-Stokes equation converge to that of Euler equation in Gevrey class as the viscosity tends to zero. Moreover the convergence rate in Gevrey class is presented

Vacuum Spacetimes with Future Trapped Surfaces

In this article we show that one can construct initial data for the Einstein equations which satisfy the vacuum constraints. This initial data is defined on a manifold with topology $R^3$ with a regular center and is asymptotically flat. Further, this initial data will contain an annular region which is foliated by two-surfaces of topology $S^2$. These two-surfaces are future trapped in the language of Penrose. The Penrose singularity theorem guarantees that the vacuum spacetime which evolves from this initial data is future null incomplete.Comment: 19 page