Spacetime Slices and Surfaces of Revolution

Under certain conditions, a $(1+1)$-dimensional slice $\hat{g}$ of a spherically symmetric black hole spacetime can be equivariantly embedded in $(2+1)$-dimensional Minkowski space. The embedding depends on a real parameter that corresponds physically to the surface gravity $\kappa$ of the black hole horizon. Under conditions that turn out to be closely related, a real surface that possesses rotational symmetry can be equivariantly embedded in 3-dimensional Euclidean space. The embedding does not obviously depend on a parameter. However, the Gaussian curvature is given by a simple formula: If the metric is written $g = \phi(r)^{-1} dr^2 + \phi(r) d\theta^2$, then \K_g=-{1/2}\phi''(r). This note shows that metrics $g$ and $\hat{g}$ occur in dual pairs, and that the embeddings described above are orthogonal facets of a single phenomenon. In particular, the metrics and their respective embeddings differ by a Wick rotation that preserves the ambient symmetry. Consequently, the embedding of $g$ depends on a real parameter. The ambient space is not smooth, and $\kappa$ is inversely proportional to the cone angle at the axis of rotation. Further, the Gaussian curvature of $\hat{g}$ is given by a simple formula that seems not to be widely known.Comment: 15 pages, added reference

LaTeX at Distributed Proofreaders and the Electronic Preservation of Mathematical Literature at Project Gutenberg

summary:A small but growing effort is underway at the volunteer web site Distributed Proofreaders (DP, at www.pgdp.net), with the goal of creating high-quality LaTeX files of selected public domain mathematical books for distribution by Project Gutenberg (PG). This article introduces DP and PG, describes how books are transcribed at DP, and gives an overview of current LaTeX coding strategies.summary:Snaha dobrovolníků vytvářejících web Distributed Proofreaders (DP, www.pgdp.net) je v plném proudu. Cílem webu je vytvořit vysoce kvalitní soubory v LaTeXu vybraných volně šiřitelných matematických knih pro distribuce v rámci projektu Gutenberg (PG). Článek představuje DP a PG a popisuje jak jsou knihy zpracovávány v DP. Dále ukazuje přehled současných kódovacích strategií LaTeXu

Motifs from the deep

Because of the increasing recognition of the importance of non-coding RNAs in gene regulation, there is considerable interest in identifying RNA motifs in genomic data. In a recent report in BMC Genomics, Breaker and colleagues describe a new algorithm for identifying functional noncoding RNAs in metagenomic sequences of marine organisms, a strategy that may be particularly effective for discovering new and unique riboswitches

Analgesic prescribing trends in a national sample of older veterans with osteoarthritis: 2012-2017

Few investigations examine patterns of opioid and nonopioid analgesic prescribing and concurrent pain intensity ratings before and after institution of safer prescribing programs such as the October 2013 Veterans Health Administration system-wide Opioid Safety Initiative (OSI) implementation. We conducted a quasi-experimental pre–post observational study of all older U.S. veterans (≥50 years old) with osteoarthritis of the knee or hip. All associated outpatient analgesic prescriptions and outpatient pain intensity ratings from January 1, 2012 to December 31, 2016, were analyzed with segmented regression of interrupted time series. Standardized monthly rates for each analgesic class (total, opioid, nonsteroidal anti-inflammatory drug, acetaminophen, and other study analgesics) were analyzed with segmented negative binomial regression models with overall slope, step, and slope change. Similarly, segmented linear regression was used to analyze pain intensity ratings and percentage of those reporting pain. All models were additionally adjusted for age, sex, and race. Before OSI implementation, total analgesic prescriptions showed a steady rise, abruptly decreasing to a flat trajectory after OSI implementation. This trend was primarily due to a decrease in opioid prescribing after OSI. Total prescribing after OSI implementation was partially compensated by continuing increased prescribing of other study analgesics as well as a significant rise in acetaminophen prescriptions (post-OSI). No changes in nonsteroidal anti-inflammatory drug prescribing were seen. A small rise in the percentage of those reporting pain but not mean pain intensity ratings continued over the study period with no changes associated with OSI. Changes in analgesic prescribing trends were not paralleled by changes in reported pain intensity for older veterans with osteoarthritis

Nonlinear terahertz metamaterials via field-enhanced carrier dynamics in GaAs

We demonstrate nonlinear metamaterial split ring resonators (SRRs) on GaAs at terahertz frequencies. For SRRs on doped GaAs films, incident terahertz radiation with peak fields of ~20 - 160 kV/cm drives intervalley scattering. This reduces the carrier mobility and enhances the SRR LC response due to a conductivity decrease in the doped thin film. Above ~160 kV/cm, electric field enhancement within the SRR gaps leads to efficient impact ionization, increasing the carrier density and the conductivity which, in turn, suppresses the SRR resonance. We demonstrate an increase of up to 10 orders of magnitude in the carrier density in the SRR gaps on semi-insulating GaAs substrate. Furthermore, we show that the effective permittivity can be swept from negative to positive values with increasing terahertz field strength in the impact ionization regime, enabling new possibilities for nonlinear metamaterials.Comment: 5 pages, 4 figure

Small‐Molecule Activators of Glucose‐6‐phosephate Dehydrogenase (G6PD) Bridging the Dimer Interface

We have recently identified AG1, a small-molecule activator that functions by promoting oligomerization of glucose-6- phosphate dehydrogenase (G6PD) to the catalytically competent forms. Biochemical experiments indicate activation of G6PD by the original hit molecule (AG1) is noncovalent and that one C2-symmetric region of the G6PD homodimer is important for ligand function. Consequently, the disulfide in AG1 is not required for activation of G6PD and a number of analogs were prepared without this reactive moiety. Our Study supports a mechanism of action whereby AG1 bridges the dimer interface at the structural nicotinamide adenine dinucleotide phosphate (NADP+)-binding sites of two interacting G6PD monomers. Small molecules that promote G6PD oligomerization have the potential to provide a first-in-class treatment for G6PD deficiency. This general strategy could be applied to other enzyme deficiencies where control of oligomerization can enhance enzymatic activity and/or stability

Analysis of representative elementary volume and through-plane regional characteristics of carbon-fiber papers: diffusivity, permeability and electrical/thermal conductivity

Understanding the transport processes that occur in carbon-fiber papers (CFPs) used in fuel cells, electrolyzers, and metal-air/redox flow batteries is necessary to help predict cell performance and durability, optimize materials and diagnose problems. The most common technique used to model these thin, heterogeneous, anisotropic porous media is the volume-averaged approximation based on the existence of a representative elementary volume (REV). However, the applicability of the continuum hypothesis to these materials has been questioned many times, and the error incurred in the predictions is yet to be quantified. In this work, the existence of a REV in CFPs is assessed in terms of dry effective transport properties: mass diffusivity, permeability and electrical/thermal conductivity. Multiple sub-samples with different widths and thicknesses are examined by combining the lattice Boltzmann method with X-ray tomography images of four uncompressed CFPs. The results show that a meaningful length scale can be defined in the material plane in the order of 1–2 mm, which is comparable to the rib/channel width used in the aforementioned devices. As for the through-plane direction, no distinctive length scale smaller than the thickness can be identified due to the lack of a well-defined separation between pore and volume-averaged scales in these inherently thin heterogeneous materials. The results also show that the highly porous surface region (amounting up to 20% of the thickness) significantly reduces the through-plane electrical/thermal conductivity. Overall, good agreement is found with previous experimental data of virtually uncompressed CFPs when approximately the full thickness is considered.The authors thank the support team of Calcul Quebec and Compute Canada for their help during the simulation campaign, as well as Dr. Dula Parkinson and Dr. Alastair MacDowell at the Advanced Light Source (ALS) for help in obtaining the tomographic images. This work was funded under the Fuel Cell Performance and Durability Consortium (FC-PAD), by the Fuel Cell Technologies Office (FCTO), Office of Energy Efficiency and Renewable Energy (EERE), of the U.S. Department of Energy under contract number DE-AC02-05CH11231, Project ENE2015-68703-C2-1-R (MINECO/FEDER, UE) and the research grant 'Ayudas a la Investigation en Energia y Medio Ambiente' awarded to the first author by the Spanish lberdrola Foundation. I.V. Zenyuk and A.D. Shum would like to acknowledge support from the National Science Foundation under CBET Award 1605159. X-ray tomography experiments were performed on beamline 8.3.2 at the ALS (Lawrence Berkeley National Laboratory), which is a national user facility funded by the Department of Energy, Office of Basic Energy Sciences under contract DE-ACO2-05CH11231. Numerical calculations were performed on the supercomputing clusters Briaree, Colosse, Guillimin and Mp2, managed by Calcul Quebec and Compute Canada. The operation of these supercomputers is funded by the Canada Foundation for Innovation (CFI), Ministere de l'Economie, de l'Innovation et des Exportations du Quebec (MEIE), RMGA and the Fonds de recherche du Quebec -Nature et technologies (FRQ-NT)