The Yamabe problem on non-compact manifolds of negative curvature type

We study existence and uniqueness results for the Yamabe problem on non-compact manifolds of negative curvature type. Our first existence and uniqueness result concerns those such manifolds which are asymptotically locally hyperbolic. In this context, our result requires only a partial C2 decay of the metric, namely the full decay of the metric in C1 and the decay of the scalar curvature. In particular, no decay of the Ricci curvature is assumed. In our second result we establish that a local volume ratio condition, when combined with negativity of the scalar curvature at infinity, is sufficient for existence of a solution

Existence and uniqueness for the non-compact Yamabe problem of negative curvature type

We study existence and uniqueness results for the Yamabe problem on non-compact manifolds of negative curvature type. Our first existence and uniqueness result concerns those such manifolds which are asymptotically locally hyperbolic. In this context, our result requires only a partial $C^2$ decay of the metric, namely the full decay of the metric in $C^1$ and the decay of the scalar curvature. In particular, no decay of the Ricci curvature is assumed. In our second result we establish that a local volume ratio condition, when combined with negativity of the scalar curvature at infinity, is sufficient for existence of a solution. Our volume ratio condition appears tight. This paper is based on the DPhil thesis of the first author.Comment: To appear in Analysis in Theory and Application

The Neutral Hydrogen Bridge between M31 and M33

The Green Bank Telescope has been used to search for 21cm HI emission over a large area between the galaxies M31 and M33 in an attempt to confirm at 9.1 arcmin angular resolution the detection by Braun and Thilker (2004) of a very extensive neutral gas "bridge" between the two systems at the level NHI approximately 10^{17} cm^{-2}. We detect HI emission at several locations up to 120 kpc in projected distance from M31, at least half the distance to M33, with velocities similar to that of the galaxies, confirming the essence of the Braun and Thilker discovery. The HI does not appear to be associated with the extraplanar high-velocity clouds of either galaxy. In two places we measure NHI > 3 x 10^{18} cm^{-2}, indicative of concentrations of HI with ~10^5 solar masses on scales <2 kpc, but over most of the field we have only 5sigma upper limits of NHI <= 1.4 x 10^{18} cm^{-2}. In very deep measurements in two directions HI lines were detected at a few 10^{17} cm^{-2}. The absence of emission at another location to a 5sigma limit NHI <= 1.5 x 10^{17} cm^{-2} suggests that the HI bridge is either patchy or confined to within ~125 kpc of M31. The measurements also cover two of M31's dwarf galaxies, And II and And XV, but in neither case is there evidence for associated HI at the 5sigma level of 1.4 x 10^4 solar masses of HI for And II, and 9.3 x 10^3 solar masses for And XV.Comment: Submitted to the Astronomical Journa

Structure of the Helicase Domain of DNA Polymerase Theta Reveals a Possible Role in the Microhomology-Mediated End-Joining Pathway

DNA polymerase theta (Polθ) has been identified as a crucial alternative non-homologous end-joining factor in mammalian cells. Polθ is upregulated in a range of cancer cell types defective in homologous recombination, and knockdown has been shown to inhibit cell survival in a subset of these, making it an attractive target for cancer treatment. We present crystal structures of the helicase domain of human Polθ in the presence and absence of bound nucleotides, and a characterization of its DNA-binding and DNA-stimulated ATPase activities. Comparisons with related helicases from the Hel308 family identify several unique features. Polθ exists as a tetramer both in the crystals and in solution. We propose a model for DNA binding to the Polθ helicase domain in the context of the Polθ tetramer, which suggests a role for the helicase domain in strand annealing of DNA templates for subsequent processing by the polymerase domain

Decline of an Ecotone Forest: 50 Years of Demography in the Southern Boreal Forest

Variation in tree recruitment, mortality, and growth can alter forest community composition and structure. Because tree recruitment and mortality events are generally infrequent, long‐time scales are needed to confirm trends in forests. We performed a 50‐yr demographic census of a forest plot located on the southern edge of the Canadian boreal forest, a region currently experiencing forest die‐back in response to direct and indirect effects of recent severe droughts. Here, we show that over the last 30 yr biomass, basal area, growth, and recruitment have decreased along with a precipitous rise in mortality across the dominant tree species. The stand experienced periods of drought in combination with multiple outbreaks of forest tent caterpillar (Malacosoma disstria) and bark beetles. These insect disturbances interacted to increase mortality rates within the stand and decrease stand density. The interaction of endogenous and exogenous factors may shift forests in this region onto novel successional trajectories with the possibility of changes in regional vegetation type

The Color Variability of Quasars

We quantify quasar color-variability using an unprecedented variability database - ugriz photometry of 9093 quasars from SDSS Stripe 82, observed over 8 years at ~60 epochs each. We confirm previous reports that quasars become bluer when brightening. We find a redshift dependence of this blueing in a given set of bands (e.g. g and r), but show that it is the result of the flux contribution from less-variable or delayed emission lines in the different SDSS bands at different redshifts. After correcting for this effect, quasar color-variability is remarkably uniform, and independent not only of redshift, but also of quasar luminosity and black hole mass. The color variations of individual quasars, as they vary in brightness on year timescales, are much more pronounced than the ranges in color seen in samples of quasars across many orders of magnitude in luminosity. This indicates distinct physical mechanisms behind quasar variability and the observed range of quasar luminosities at a given black hole mass - quasar variations cannot be explained by changes in the mean accretion rate. We do find some dependence of the color variability on the characteristics of the flux variations themselves, with fast, low-amplitude, brightness variations producing more color variability. The observed behavior could arise if quasar variability results from flares or ephemeral hot spots in an accretion disc.Comment: Accepted for publication in ApJ - in press, 17 pages, 14 figures - v2: abstract typo corrected & reference clean-u

Think Outside the Color Box: Probabilistic Target Selection and the SDSS-XDQSO Quasar Targeting Catalog

We present the SDSS-XDQSO quasar targeting catalog for efficient flux-based quasar target selection down to the faint limit of the Sloan Digital Sky Survey (SDSS) catalog, even at medium redshifts (2.5 <~ z <~ 3) where the stellar contamination is significant. We build models of the distributions of stars and quasars in flux space down to the flux limit by applying the extreme-deconvolution method to estimate the underlying density. We convolve this density with the flux uncertainties when evaluating the probability that an object is a quasar. This approach results in a targeting algorithm that is more principled, more efficient, and faster than other similar methods. We apply the algorithm to derive low-redshift (z < 2.2), medium-redshift (2.2 <= z 3.5) quasar probabilities for all 160,904,060 point sources with dereddened i-band magnitude between 17.75 and 22.45 mag in the 14,555 deg^2 of imaging from SDSS Data Release 8. The catalog can be used to define a uniformly selected and efficient low- or medium-redshift quasar survey, such as that needed for the SDSS-III's Baryon Oscillation Spectroscopic Survey project. We show that the XDQSO technique performs as well as the current best photometric quasar-selection technique at low redshift, and outperforms all other flux-based methods for selecting the medium-redshift quasars of our primary interest. We make code to reproduce the XDQSO quasar target selection publicly available

Association Between Community Social Vulnerability and Preventable Hospitalizations

Preventable hospitalizations are common and costly events that burden patients and our health care system. While research suggests that these events are strongly linked to ambulatory care access, emerging evidence suggests they may also be sensitive to a patient’s social, environmental, and economic conditions. This study examines the association between variations in social vulnerability and preventable hospitalization rates. We conducted a cross-sectional analysis of county-level preventable hospitalization rates for 33 states linked with data from the 2020 Social Vulnerability Index (SVI). Preventable hospitalizations were 40% higher in the most vulnerable counties compared with the least vulnerable. Adjusted regression results confirm the strong relationship between social vulnerability and preventable hospitalizations. Our results suggest wide variation in community-level preventable hospitalization rates, with robust evidence that variation is strongly related to a community’s social vulnerability. The human toll, societal cost, and preventability of these hospitalizations make understanding and mitigating these inequities a national priority