Brane Resolution Through Fibration

We consider p-branes with one or more circular directions fibered over the transverse space. The fibration, in conjunction with the transverse space having a blown-up cycle, enables these p-brane solutions to be completely regular. Some such circularly-wrapped D3-brane solutions describe flows from SU(N)^3 N=2 theory, F_0 theory, as well as an infinite family of superconformal quiver gauge theories, down to three-dimensional field theories. We discuss the operators that are turned on away from the UV fixed points. Similarly, there are wrapped M2-brane solutions which describe smooth flows from known three-dimensional supersymmetric Chern-Simons matter theories, such as ABJM theory. We also consider p-brane solutions on gravitational instantons, and discuss various ways in which U-duality can be applied to yield other non-singular solutions.Comment: 35 pages, additional referenc

Advanced Silicon Avalanche Photodiodes on NASA's Global Ecosystem Dynamics Investigation (GEDI) Mission

Silicon Avalanche Photodiodes (APDs) are used in NASAs Global Ecosystem Dynamics Investigation (GEDI) which was launched in December 2018 and is currently measuring the Earths vegetation vertical structure from the International Space Station. The APDs were specially made for space lidar with a much lower hole-to-electron ionization coefficient ratio (k-factor ~0.008) than that of commercially available silicon APDs in order to reduce the APD excess noise from the randomness of the avalanche gain. A silicon heater resistor was used under the APD chip to heat the device up to 70C and improve its quantum efficiency at 1064 nm laser wavelength while maintaining a low dark current such that the overall signal to noise ratio is improved. Special APD protection circuits were used to raise the overload damage threshold to prevent device damage from strong laser return by specular surfaces, such as still water bodies, and space radiation events. The APD and a hybrid transimpedance amplifier circuit were hermetically sealed in a package with a sufficiently low leak rate to ensure multi-year operation lifetime in space. The detector assemblies underwent a series of pre-launch tests per NASA Goddard Environmental Verification Standard for space qualification. They have performed exactly as expected with GEDI in orbit. A detailed description of the GEDI detector design, signal and noise model, and test results are presented in this paper

Spectral geometry, homogeneous spaces, and differential forms with finite Fourier series

Let G be a compact Lie group acting transitively on Riemannian manifolds M and N. Let p be a G equivariant Riemannian submersion from M to N. We show that a smooth differential form on N has finite Fourier series if and only if the pull back has finite Fourier series on

The importance of the initial period of basal insulin titration in people with diabetes

Achieving target glycaemic control is essential in people with diabetes to minimize the risk of long-term complications, and many people with type 2 diabetes will ultimately require basal insulin (BI) therapy to achieve their individualized glycaemic targets. Usually, the first 12 weeks following initiation of BI therapy represents the period when the greatest dose increases and glycaemic reductions occur. Effective glycaemic control combined with minimizing the risk of hypoglycaemia is important to enable the achievement of glycaemic control in the longer term. However, substantial therapeutic inertia exists in clinical practice, both in initiation and up-titration of BI, owing to patient-, physician- and healthcare system-related barriers, including fear of hypoglycaemia and the perception of a burdensome regimen. The more prolonged duration of action, reduced glycaemic variability and lower risk of hypoglycaemia seen with second-generation versus first-generation BI analogues may help alleviate patients' and physicians' concerns and facilitate titration. In turn, optimal BI titration and subsequent metabolic benefits may help improve therapy adherence and self-management. This review details the clinical implications of prompt titration of BI to achieve early glycaemic control, and the importance of minimizing hypoglycaemia risk within the initial titration period. Facilitation of patients' self-management of BI is also addressed

Pseudo-Riemannian manifolds with recurrent spinor fields

The existence of a recurrent spinor field on a pseudo-Riemannian spin manifold $(M,g)$ is closely related to the existence of a parallel 1-dimensional complex subbundle of the spinor bundle of $(M,g)$. We characterize the following simply connected pseudo-Riemannian manifolds admitting such subbundles in terms of their holonomy algebras: Riemannian manifolds; Lorentzian manifolds; pseudo-Riemannian manifolds with irreducible holonomy algebras; pseudo-Riemannian manifolds of neutral signature admitting two complementary parallel isotropic distributions.Comment: 13 pages, the final versio

Holonomy of Einstein Lorentzian manifolds

The classification of all possible holonomy algebras of Einstein and vacuum Einstein Lorentzian manifolds is obtained. It is shown that each such algebra appears as the holonomy algebra of an Einstein (resp., vacuum Einstein) Lorentzian manifold, the direct constructions are given. Also the holonomy algebras of totally Ricci-isotropic Lorentzian manifolds are classified. The classification of the holonomy algebras of Lorentzian manifolds is reviewed and a complete description of the spaces of curvature tensors for these holonomies is given.Comment: Dedicated to to Mark Volfovich Losik on his 75th birthday. This version is an extended part of the previous version; another part of the previous version is extended and submitted as arXiv:1001.444

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