Stability estimates for resolvents, eigenvalues and eigenfunctions of elliptic operators on variable domains

We consider general second order uniformly elliptic operators subject to homogeneous boundary conditions on open sets $\phi (\Omega)$ parametrized by Lipschitz homeomorphisms $\phi$ defined on a fixed reference domain $\Omega$. Given two open sets $\phi (\Omega)$, $\tilde \phi (\Omega)$ we estimate the variation of resolvents, eigenvalues and eigenfunctions via the Sobolev norm $\|\tilde \phi -\phi \|_{W^{1,p}(\Omega)}$ for finite values of $p$, under natural summability conditions on eigenfunctions and their gradients. We prove that such conditions are satisfied for a wide class of operators and open sets, including open sets with Lipschitz continuous boundaries. We apply these estimates to control the variation of the eigenvalues and eigenfunctions via the measure of the symmetric difference of the open sets. We also discuss an application to the stability of solutions to the Poisson problem.Comment: 34 pages. Minor changes in the introduction and the refercenes. Published in: Around the research of Vladimir Maz'ya II, pp23--60, Int. Math. Ser. (N.Y.), vol. 12, Springer, New York 201

The Trispectrum in the Multi-brid Inflation

The trispectrum is at least as important as the bispectrum and its size can be characterized by two parameters $\tau_{NL}$ and $g_{NL}$. In this short paper, we focus on the Multi-brid inflation, in particular the two-brid inflation model in arXiv.0805.0974, and find that $\tau_{NL}$ is always positive and roughly equals to $({6\over 5}f_{NL})^2$ for the low scale inflation, but $g_{NL}$ can be negative or positive and its order of magnitude can be the same as that of $\tau_{NL}$ or even largerComment: 12 pages; minor correction, refs added; further refs added, version for publication in JCA

A mathematical framework for critical transitions: normal forms, variance and applications

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio

Corrigendum: Delivery of crop pollination services is an insufficient argument for wild pollinator conservation

There is compelling evidence that more diverse ecosystems deliver greater benefits to people, and these ecosystem services have become a key argument for biodiversity conservation. However, it is unclear how much biodiversity is needed to deliver ecosystem services in a cost-effective way. Here we show that, while the contribution of wild bees to crop production is significant, service delivery is restricted to a limited subset of all known bee species. Across crops, years and biogeographical regions, crop-visiting wild bee communities are dominated by a small number of common species, and threatened species are rarely observed on crops. Dominant crop pollinators persist under agricultural expansion and many are easily enhanced by simple conservation measures, suggesting that cost-effective management strategies to promote crop pollination should target a different set of species than management strategies to promote threatened bees. Conserving the biological diversity of bees therefore requires more than just ecosystem-service-based arguments

An aggravated trajectory of depression and anxiety co-morbid with hepatitis C: : A 21 to 62 month follow-up study in 61 South Australian outpatients

BACKGROUND: This study aimed to explore the course of depression and anxiety in chronic hepatitis C patients. METHODS:   Data were combined from two studies: (1) Hospital Anxiety and Depression Scale (HADS) scores in 395 consecutive Australian outpatients from 2006 to 2010 formed the baseline measurement; and (2) Depression Anxiety Stress Scales (DASS) scores in a survey of a sub-sample of these patients in 2011 formed the follow-up measurement. After converting DASS to HADS scores, changes in symptom scores and rates of case-ness (≥8), and predictors of follow-up symptoms were assessed. RESULTS:   Follow-up data were available for 61 patients (70.5% male) whose age ranged from 24.5 to 74.6 years (M=45.6). The time to follow-up ranged from 20.7 to 61.9 months (M=43.8). Baseline rates of depression (32.8%) and anxiety (44.3%) increased to 62.3% and 67.2%, respectively. These findings were confirmed, independent of the conversion, by comparing baseline HADS and follow-up DASS scores with British community norms. Baseline anxiety and younger age predicted depression, while baseline anxiety, high school non-completion, and single relationship status predicted anxiety. CONCLUSION:  This study demonstrated a worsening trajectory of depression and anxiety. Further controlled and prospective research in a larger sample is required to confirm these findings

β-Klotho deficiency protects against obesity through a crosstalk between liver, microbiota, and brown adipose tissue.

β-Klotho (encoded by Klb) is the obligate coreceptor mediating FGF21 and FGF15/19 signaling. Klb-/- mice are refractory to beneficial action of pharmacological FGF21 treatment including stimulation of glucose utilization and thermogenesis. Here, we investigated the energy homeostasis in Klb-/- mice on high-fat diet in order to better understand the consequences of abrogating both endogenous FGF15/19 and FGF21 signaling during caloric overload. Surprisingly, Klb-/- mice are resistant to diet-induced obesity (DIO) owing to enhanced energy expenditure and BAT activity. Klb-/- mice exhibited not only an increase but also a shift in bile acid (BA) composition featured by activation of the classical (neutral) BA synthesis pathway at the expense of the alternative (acidic) pathway. High hepatic production of cholic acid (CA) results in a large excess of microbiota-derived deoxycholic acid (DCA). DCA is specifically responsible for activating the TGR5 receptor that stimulates BAT thermogenic activity. In fact, combined gene deletion of Klb and Tgr5 or antibiotic treatment abrogating bacterial conversion of CA into DCA both abolish DIO resistance in Klb-/- mice. These results suggested that DIO resistance in Klb-/- mice is caused by high levels of DCA, signaling through the TGR5 receptor. These data also demonstrated that gut microbiota can regulate host thermogenesis via conversion of primary into secondary BA. Pharmacologic or nutritional approaches to selectively modulate BA composition may be a promising target for treating metabolic disorders

Measurement of the polarisation of W bosons produced with large transverse momentum in pp collisions at sqrt(s) = 7 TeV with the ATLAS experiment

This paper describes an analysis of the angular distribution of W->enu and W->munu decays, using data from pp collisions at sqrt(s) = 7 TeV recorded with the ATLAS detector at the LHC in 2010, corresponding to an integrated luminosity of about 35 pb^-1. Using the decay lepton transverse momentum and the missing transverse energy, the W decay angular distribution projected onto the transverse plane is obtained and analysed in terms of helicity fractions f0, fL and fR over two ranges of W transverse momentum (ptw): 35 < ptw < 50 GeV and ptw > 50 GeV. Good agreement is found with theoretical predictions. For ptw > 50 GeV, the values of f0 and fL-fR, averaged over charge and lepton flavour, are measured to be : f0 = 0.127 +/- 0.030 +/- 0.108 and fL-fR = 0.252 +/- 0.017 +/- 0.030, where the first uncertainties are statistical, and the second include all systematic effects.Comment: 19 pages plus author list (34 pages total), 9 figures, 11 tables, revised author list, matches European Journal of Physics C versio

Observation of a new chi_b state in radiative transitions to Upsilon(1S) and Upsilon(2S) at ATLAS

The chi_b(nP) quarkonium states are produced in proton-proton collisions at the Large Hadron Collider (LHC) at sqrt(s) = 7 TeV and recorded by the ATLAS detector. Using a data sample corresponding to an integrated luminosity of 4.4 fb^-1, these states are reconstructed through their radiative decays to Upsilon(1S,2S) with Upsilon->mu+mu-. In addition to the mass peaks corresponding to the decay modes chi_b(1P,2P)->Upsilon(1S)gamma, a new structure centered at a mass of 10.530+/-0.005 (stat.)+/-0.009 (syst.) GeV is also observed, in both the Upsilon(1S)gamma and Upsilon(2S)gamma decay modes. This is interpreted as the chi_b(3P) system.Comment: 5 pages plus author list (18 pages total), 2 figures, 1 table, corrected author list, matches final version in Physical Review Letter

Search for displaced vertices arising from decays of new heavy particles in 7 TeV pp collisions at ATLAS

We present the results of a search for new, heavy particles that decay at a significant distance from their production point into a final state containing charged hadrons in association with a high-momentum muon. The search is conducted in a pp-collision data sample with a center-of-mass energy of 7 TeV and an integrated luminosity of 33 pb^-1 collected in 2010 by the ATLAS detector operating at the Large Hadron Collider. Production of such particles is expected in various scenarios of physics beyond the standard model. We observe no signal and place limits on the production cross-section of supersymmetric particles in an R-parity-violating scenario as a function of the neutralino lifetime. Limits are presented for different squark and neutralino masses, enabling extension of the limits to a variety of other models.Comment: 8 pages plus author list (20 pages total), 8 figures, 1 table, final version to appear in Physics Letters

Measurement of the inclusive isolated prompt photon cross-section in pp collisions at sqrt(s)= 7 TeV using 35 pb-1 of ATLAS data

A measurement of the differential cross-section for the inclusive production of isolated prompt photons in pp collisions at a center-of-mass energy sqrt(s) = 7 TeV is presented. The measurement covers the pseudorapidity ranges |eta|<1.37 and 1.52<=|eta|<2.37 in the transverse energy range 45<=E_T<400GeV. The results are based on an integrated luminosity of 35 pb-1, collected with the ATLAS detector at the LHC. The yields of the signal photons are measured using a data-driven technique, based on the observed distribution of the hadronic energy in a narrow cone around the photon candidate and the photon selection criteria. The results are compared with next-to-leading order perturbative QCD calculations and found to be in good agreement over four orders of magnitude in cross-section.Comment: 7 pages plus author list (18 pages total), 2 figures, 4 tables, final version published in Physics Letters