The Conformal Willmore Functional: a Perturbative Approach

The conformal Willmore functional (which is conformal invariant in general Riemannian manifold $(M,g)$) is studied with a perturbative method: the Lyapunov-Schmidt reduction. Existence of critical points is shown in ambient manifolds $(\mathbb{R}^3, g_\epsilon)$ -where $g_\epsilon$ is a metric close and asymptotic to the euclidean one. With the same technique a non existence result is proved in general Riemannian manifolds $(M,g)$ of dimension three.Comment: 34 pages; Journal of Geometric Analysis, on line first 23 September 201

Does black-hole growth depend on the cosmic environment?

It is well known that environment affects galaxy evolution, which is broadly related to supermassive black hole (SMBH) growth. We investigate whether SMBH evolution also depends on host-galaxy local (sub-Mpc) and global (≈1–10 Mpc) environment. We construct the surface-density field (local environment) and cosmic web (global environment) in the Cosmic Evolution Survey (COSMOS) field at z = 0.3–3.0. The environments in COSMOS range from the field to clusters (Mhalo ≲ 1014 M⊙), covering the environments where ≈99 per cent of galaxies in the Universe reside. We measure sample-averaged SMBH accretion rate ( BHAR¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ) from X-ray observations, and study its dependence on overdensity and cosmic-web environment at different redshifts while controlling for galaxy stellar mass (M⋆). Our results show that BHAR¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ does not significantly depend on overdensity or cosmic-web environment once M⋆ is controlled, indicating that environment-related physical mechanisms (e.g. tidal interaction and ram-pressure stripping) might not significantly affect SMBH growth. We find that BHAR¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ is strongly related to host-galaxy M⋆, regardless of environment

On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree

In our recent works [R. Szmytkowski, J. Phys. A 39 (2006) 15147; corrigendum: 40 (2007) 7819; addendum: 40 (2007) 14887], we have investigated the derivative of the Legendre function of the first kind, $P_{\nu}(z)$, with respect to its degree $\nu$. In the present work, we extend these studies and construct several representations of the derivative of the associated Legendre function of the first kind, $P_{\nu}^{\pm m}(z)$, with respect to the degree $\nu$, for $m\in\mathbb{N}$. At first, we establish several contour-integral representations of $\partial P_{\nu}^{\pm m}(z)/\partial\nu$. They are then used to derive Rodrigues-type formulas for $[\partial P_{\nu}^{\pm m}(z)/\partial\nu]_{\nu=n}$ with $n\in\mathbb{N}$. Next, some closed-form expressions for $[\partial P_{\nu}^{\pm m}(z)/\partial\nu]_{\nu=n}$ are obtained. These results are applied to find several representations, both explicit and of the Rodrigues type, for the associated Legendre function of the second kind of integer degree and order, $Q_{n}^{\pm m}(z)$; the explicit representations are suitable for use for numerical purposes in various regions of the complex $z$-plane. Finally, the derivatives $[\partial^{2}P_{\nu}^{m}(z)/\partial\nu^{2}]_{\nu=n}$, $[\partial Q_{\nu}^{m}(z)/\partial\nu]_{\nu=n}$ and $[\partial Q_{\nu}^{m}(z)/\partial\nu]_{\nu=-n-1}$, all with $m>n$, are evaluated in terms of $[\partial P_{\nu}^{-m}(\pm z)/\partial\nu]_{\nu=n}$.Comment: LateX, 40 pages, 1 figure, extensive referencin

A vitamin D, calcium and leucine-enriched whey protein nutritional supplement improves measures of bone health in sarcopenic non-malnourished older adults: The PROVIDE study

Alterations in musculoskeletal health with advanced age contribute to sarcopenia and decline in bone mineral density (BMD) and bone strength. This decline may be modifiable via dietary supplementation. To test the hypothesis that a specific oral nutritional supplement can result in improvements in measures of bone health. Participants (n 380) were participants of the PROVIDE study, a 13-week, multicenter, randomized, controlled, double-blind, 2 parallel-group study among non-malnourished older participants (≥ 65 years) with sarcopenia [determined by Short Physical Performance Battery (SPPB; 0-12) scores between 4 and 9, and a low skeletal muscle mass index (SMI; skeletal muscle mass/BW × 100) ≤ 37% in men and ≤ 28% in women using bioelectric impedance analysis] Supplementation of a vitamin D, calcium and leucine-enriched whey protein drink that comprises a full range of micronutrients (active; 2/day) was compared with an iso-caloric control. Serum 25-hydroxyvitamin D [25(OH)D], parathyroid hormone (PTH), biochemical markers of bone formation (osteocalcin; OC, procollagen type 1 amino-terminal propeptide; P1NP) and resorption (carboxy-terminal collagen crosslinks; CTX), insulin like growth factor 1 (IGF-1) and total-body BMD were analysed pre- and post-intervention. Serum 25(OH)D concentrations increased from 51.1 ± 22.9 nmol/L (mean ± SD) to 78.9 ± 21.1 nmol/L in the active group (p < 0.001 vs. control). Serum PTH showed a significant treatment difference (p < 0.001) with a decline in the active group, and increase in the control group. Serum IGF-1 increased in the active group (p < 0.001 vs. control). Serum CTX showed a greater decline in the active group (p = 0.001 vs. control). There were no significant differences in serum OC or P1NP between groups during the intervention. Total body BMD showed a small (0.02 g/cm2; ~ 2%) but significant increase in the active group after supplementation (p = 0.033 vs. control). Consuming a vitamin D, calcium and leucine-enriched whey protein supplement for 13 weeks improved 25(OH)D, suppressed PTH and had small but positive effects on BMD, indicative of improved bone health, in sarcopenic non-malnourished older adults

Black Hole Growth Is Mainly Linked to Host-galaxy Stellar Mass Rather Than Star Formation Rate

We investigate the dependence of black-hole accretion rate (BHAR) on host-galaxy star formation rate (SFR) and stellar mass (M∗) in the CANDELS/GOODS-South field in the redshift range of 0.5≤z<2.0. Our sample consists of ≈18000 galaxies, allowing us to probe galaxies with 0.1≲SFR≲100 M⊙ yr−1 and/or 108≲M∗≲1011 M⊙. We use sample-mean BHAR to approximate long-term average BHAR. Our sample-mean BHARs are derived from the Chandra Deep Field-South 7 Ms observations, while the SFRs and M∗ have been estimated by the CANDELS team through SED fitting. The average BHAR is correlated positively with both SFR and M∗, and the BHAR-SFR and BHAR-M∗ relations can both be described acceptably by linear models with a slope of unity. However, BHAR appears to be correlated more strongly with M∗ than SFR. This result indicates that M∗ is the primary host-galaxy property related to black-hole growth, and the apparent BHAR-SFR relation is largely a secondary effect due to the star-forming main sequence. Among our sources, massive galaxies (M∗≳1010M⊙) have significantly higher BHAR/SFR ratios than less-massive galaxies, indicating the former have higher black-hole fueling efficiency and/or higher SMBH occupation fraction than the latter. Our results can naturally explain the observed proportionality between MBH and M∗ for local giant ellipticals, and suggest their MBH/M∗ is higher than that of local star-forming galaxies. Among local star-forming galaxies, massive systems might have higher MBH/M∗ compared to dwarfs

Study protocol; Thyroid hormone Replacement for Untreated older adults with Subclinical hypothyroidism - a randomised placebo controlled Trial (TRUST).

Subclinical hypothyroidism (SCH) is a common condition in elderly people, defined as elevated serum thyroid-stimulating hormone (TSH) with normal circulating free thyroxine (fT4). Evidence is lacking about the effect of thyroid hormone treatment. We describe the protocol of a large randomised controlled trial (RCT) of Levothyroxine treatment for SCH. Participants are community-dwelling subjects aged ≥65 years with SCH, diagnosed by elevated TSH levels (≥4.6 and ≤19.9 mU/L) on a minimum of two measures ≥ three months apart, with fT4 levels within laboratory reference range. The study is a randomised double-blind placebo-controlled parallel group trial, starting with levothyroxine 50 micrograms daily (25 micrograms in subjects &lt;50Kg body weight or known coronary heart disease) with titration of dose in the active treatment group according to TSH level, and a mock titration in the placebo group. The primary outcomes are changes in two domains (hypothyroid symptoms and fatigue / vitality) on the thyroid-related quality of life questionnaire (ThyPRO) at one year. The study has 80% power (at p = 0.025, 2-tailed) to detect a change with levothyroxine treatment of 3.0% on the hypothyroid scale and 4.1% on the fatigue / vitality scale with a total target sample size of 750 patients. Secondary outcomes include general health-related quality of life (EuroQol), fatal and non-fatal cardiovascular events, handgrip strength, executive cognitive function (Letter Digit Coding Test), basic and instrumental activities of daily living, haemoglobin, blood pressure, weight, body mass index and waist circumference. Patients are monitored for specific adverse events of interest including incident atrial fibrillation, heart failure and bone fracture. This large multicentre RCT of levothyroxine treatment of subclinical hypothyroidism is powered to detect clinically relevant change in symptoms / quality of life and is likely to be highly influential in guiding treatment of this common condition. Clinicaltrials.gov NCT01660126 ; registered 8th June 2012

Run-Time Assertion Checking of Data- and Protocol-Oriented Properties of Java Programs: An Industrial Case Study

htmlabstractRun-time assertion checking is one of the useful techniques for detecting faults, and can be applied during any program execution context, including debugging, testing, and production. In general, however, it is limited to checking state-based properties. We introduce SAGA, a general framework that provides a smooth integration of the specification and the run-time checking of both data- and protocol-oriented properties of Java classes and interfaces. We evaluate SAGA, which combines several state-of-the art tools, by conducting an industrial case study from an eCommerce software company Fredhopper

The NuSTAR Serendipitous Survey: Hunting for the Most Extreme Obscured AGN at >10 keV

We identify sources with extremely hard X-ray spectra (i.e., with photon indices of ${\rm{\Gamma }}\lesssim 0.6$) in the 13 deg2 NuSTAR serendipitous survey, to search for the most highly obscured active galactic nuclei (AGNs) detected at $\gt 10\,\mathrm{keV}$. Eight extreme NuSTAR sources are identified, and we use the NuSTAR data in combination with lower-energy X-ray observations (from Chandra, Swift XRT, and XMM-Newton) to characterize the broadband (0.5–24 keV) X-ray spectra. We find that all of the extreme sources are highly obscured AGNs, including three robust Compton-thick (CT; ${N}_{{\rm{H}}}\gt 1.5\times {10}^{24}$ cm−2) AGNs at low redshift ($z\lt 0.1$) and a likely CT AGN at higher redshift (z = 0.16). Most of the extreme sources would not have been identified as highly obscured based on the low-energy ($\lt 10$ keV) X-ray coverage alone. The multiwavelength properties (e.g., optical spectra and X-ray–mid-IR luminosity ratios) provide further support for the eight sources being significantly obscured. Correcting for absorption, the intrinsic rest-frame 10–40 keV luminosities of the extreme sources cover a broad range, from $\approx 5\times {10}^{42}$ to 1045 erg s−1. The estimated number counts of CT AGNs in the NuSTAR serendipitous survey are in broad agreement with model expectations based on previous X-ray surveys, except for the lowest redshifts ($z\lt 0.07$), where we measure a high CT fraction of ${f}_{\mathrm{CT}}^{\mathrm{obs}}={30}_{-12}^{+16} \%$. For the small sample of CT AGNs, we find a high fraction of galaxy major mergers (50% ± 33%) compared to control samples of "normal" AGNs

Dark Energy and Gravity

I review the problem of dark energy focusing on the cosmological constant as the candidate and discuss its implications for the nature of gravity. Part 1 briefly overviews the currently popular `concordance cosmology' and summarises the evidence for dark energy. It also provides the observational and theoretical arguments in favour of the cosmological constant as the candidate and emphasises why no other approach really solves the conceptual problems usually attributed to the cosmological constant. Part 2 describes some of the approaches to understand the nature of the cosmological constant and attempts to extract the key ingredients which must be present in any viable solution. I argue that (i)the cosmological constant problem cannot be satisfactorily solved until gravitational action is made invariant under the shift of the matter lagrangian by a constant and (ii) this cannot happen if the metric is the dynamical variable. Hence the cosmological constant problem essentially has to do with our (mis)understanding of the nature of gravity. Part 3 discusses an alternative perspective on gravity in which the action is explicitly invariant under the above transformation. Extremizing this action leads to an equation determining the background geometry which gives Einstein's theory at the lowest order with Lanczos-Lovelock type corrections. (Condensed abstract).Comment: Invited Review for a special Gen.Rel.Grav. issue on Dark Energy, edited by G.F.R.Ellis, R.Maartens and H.Nicolai; revtex; 22 pages; 2 figure

System Size and Energy Dependence of Jet-Induced Hadron Pair Correlation Shapes in Cu+Cu and Au+Au Collisions at sqrt(s_NN) = 200 and 62.4 GeV

We present azimuthal angle correlations of intermediate transverse momentum (1-4 GeV/c) hadrons from {dijets} in Cu+Cu and Au+Au collisions at sqrt(s_NN) = 62.4 and 200 GeV. The away-side dijet induced azimuthal correlation is broadened, non-Gaussian, and peaked away from \Delta\phi=\pi in central and semi-central collisions in all the systems. The broadening and peak location are found to depend upon the number of participants in the collision, but not on the collision energy or beam nuclei. These results are consistent with sound or shock wave models, but pose challenges to Cherenkov gluon radiation models.Comment: 464 authors from 60 institutions, 6 pages, 3 figures, 2 tables. Submitted to Physical Review Letters. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm