Semi-classical analysis of non self-adjoint transfer matrices in statistical mechanics. I

We propose a way to study one-dimensional statistical mechanics models with complex-valued action using transfer operators. The argument consists of two steps. First, the contour of integration is deformed so that the associated transfer operator is a perturbation of a normal one. Then the transfer operator is studied using methods of semi-classical analysis. In this paper we concentrate on the second step, the main technical result being a semi-classical estimate for powers of an integral operator which is approximately normal.Comment: 28 pp, improved the presentatio

Accuracy of diagnosing atrial fibrillation on electrocardiogram by primary care practitioners and interpretative diagnostic software: analysis of data from screening for atrial fibrillation in the elderly (SAFE) trial

Objective To assess the accuracy of general practitioners, practice nurses, and interpretative software in the use of different types of electrocardiogram to diagnose atrial fibrillation. Design Prospective comparison with reference standard of assessment of electrocardiograms by two independent specialists. Setting 49 general practices in central England. Participants 2595 patients aged 65 or over screened for atrial fibrillation as part of the screening for atrial fibrillation in the elderly (SAFE) study; 49 general practitioners and 49 practice nurses. Interventions All electrocardiograms were read with the Biolog interpretative software, and a random sample of 12 lead, limb lead, and single lead thoracic placement electrocardiograms were assessed by general practitioners and practice nurses independently of each other and of the Biolog assessment. Main outcome measures Sensitivity, specificity, and positive and negative predictive values. Results General practitioners detected 79 out of 99 cases of atrial fibrillation on a 12 lead electrocardiogram (sensitivity 80%, 95% confidence interval 71% to 87%) and misinterpreted 114 out of 1355 cases of sinus rhythm as atrial fibrillation (specificity 92%, 90% to 93%). Practice nurses detected a similar proportion of cases of atrial fibrillation (sensitivity 77%, 67% to 85%), but had a lower specificity (85%, 83% to 87%). The interpretative software was significantly more accurate, with a specificity of 99%, but missed 36 of 215 cases of atrial fibrillation (sensitivity 83%). Combining general practitioners' interpretation with the interpretative software led to a sensitivity of 92% and a specificity of 91%. Use of limb lead or single lead thoracic placement electrocardiograms resulted in some loss of specificity. Conclusions Many primary care professionals cannot accurately detect atrial fibrillation on an electrocardiogram, and interpretative software is not sufficiently accurate to circumvent this problem, even when combined with interpretation by a general practitioner. Diagnosis of atrial fibrillation in the community needs to factor in the reading of electrocardiograms by appropriately trained peopl

Screening versus routine practice in detection of atrial fibrillation in patients aged 65 or over: Screening versus routine practice in detection cluster randomised controlled trial

Objectives : To assess whether screening improves the detection of atrial fibrillation (cluster randomisation) and to compare systematic and opportunistic screening. Design : Multicentred cluster randomised controlled trial, with subsidiary trial embedded within the intervention arm. Setting : 50 primary care centres in England, with further individual randomisation of patients in the intervention practices. Participants : 14,802 patients aged 65 or over in 25 intervention and 25 control practices. Interventions : Patients in intervention practices were randomly allocated to systematic screening (invitation for electrocardiography) or opportunistic screening (pulse taking and invitation for electrocardiography if the pulse was irregular). Screening took place over 12 months in each practice from October 2001 to February 2003. No active screening took place in control practices. Main outcome measure : Newly identified atrial fibrillation. Results : The detection rate of new cases of atrial fibrillation was 1.63% a year in the intervention practices and 1.04% in control practices (difference 0.59%, 95% confidence interval 0.20% to 0.98%). Systematic and opportunistic screening detected similar numbers of new cases (1.62% v 1.64%, difference 0.02%, −0.5% to 0.5%). Conclusion : Active screening for atrial fibrillation detects additional cases over current practice. The preferred method of screening in patients aged 65 or over in primary care is opportunistic pulse taking with follow-up electrocardiography. Trial registration Current Controlled Trials ISRCTN19633732

Black Hole Thermodynamics in Horava Lifshitz Gravity and the Related Geometry

Recently, Ho$\breve{r}$ava proposed a non-relativistic renormalizable theory of gravity which is essentially a field theoretic model for a UV complete theory of gravity and reduces to Einstein gravity with a non-vanishing cosmological constant in IR. Also the theory admits a Lifshitz scale-invariance in time and space with broken Lorentz symmetry at short scale. On the other hand, at large distances higher derivative terms do not contribute and the theory coincides with general relativity. Subsequently, Cai and his collaborators and then Catiuo et al have obtained black hole solutions in this gravity theory and studied the thermodynamic properties of the black hole solution. In the present paper, we have investigated the black hole thermodynamic for two choices of the entropy function - a classical and a topological in nature. Finally, it is examined whether a phase transition is possible or not.Comment: 8 figure

The peculiar motions of early-type galaxies in two distant regions - V. The Mg-sigma relation, age and metallicity

We have examined the Mg-sigma relation for early-type galaxies in the EFAR sample and its dependence on cluster properties. A comprehensive maximum likelihood treatment of the sample selection and measurement errors gives fits to the global Mg-sigma relation of Mg b^'=0.131 log sigma -0.131 and Mg_2=0.257 log sigma -0.305. The slope of these relations is 25 per cent steeper than that obtained by most other authors owing to the reduced bias of our fitting method. The intrinsic scatter in the global Mg- sigma relation is estimated to be 0.016 mag in Mg b^' and 0.023 mag in Mg_2. The Mg- sigma relation for cD galaxies has a higher zero-point than for E and S0 galaxies, implying that cDs are older and/or more metal-rich than other early-type galaxies with the same velocity dispersion. We investigate the variation in the zero-point of the Mg- sigma relation between clusters. We find that it is consistent with the number of galaxies observed per cluster and the intrinsic scatter between galaxies in the global Mg-sigma relation. We find no significant correlation between the Mg-sigma zero-point and the cluster velocity dispersion, X-ray luminosity or X-ray temperature over a wide range in cluster mass. These results provide constraints for models of the formation of elliptical galaxies. However, the Mg-sigma relation on its own does not place strong limits on systematic errors in Fundamental Plane (FP) distance estimates resulting from stellar population differences between clusters. We compare the intrinsic scatter in the Mg-sigma and Fundamental Plane relations with stellar population models in order to constrain the dispersion in ages, metallicities and M/L ratios for early-type galaxies at fixed velocity dispersion. We find that variations in age or metallicity alone cannot explain the measured intrinsic scatter in both Mg- sigma and the FP. We derive the joint constraints on the dispersion in age and metallicity implied by the scatter in the Mg-sigma and FP relations for a simple Gaussian model. We find upper limits on the dispersions in age and metallicity at fixed velocity dispersion of 32 per cent in delta t/t and 38 per cent in delta Z/Z if the variations in age and metallicity are uncorrelated; only strongly anticorrelated variations lead to significantly higher upper limits. The joint distribution of residuals from the Mg- sigma and FP relations is only marginally consistent with a model having no correlation between age and metallicity, and is better matched by a model in which age and metallicity variations are moderately anticorrelated (delta t/t ~ 40 per cent, delta Z/Z ~ 50 per cent and rho ~ -0.5), with younger galaxies being more metal-rich

Insight into the Scalar Mesons from a Lattice Calculation

We study the possibility that the light scalar mesons are (qbar qbar q q) states rather than (qbar q). We perform a lattice QCD calculation of pseudoscalar meson scattering amplitudes, ignoring quark loops and quark annihilation, and find indications that for sufficiently heavy quarks there is a stable four-quark bound state with J^{PC}=0^{++} and non-exotic flavor quantum numbers.Comment: 16 pages, revtex, with eps figure

The peculiar motions of early-type galaxies in two distant regions - II. The spectroscopic data

We present the spectroscopic data for the galaxies studied in the EFAR project, which is designed to measure the properties and peculiar motions of early-type galaxies in two distant regions. We have obtained 1319 spectra of 714 early-type galaxies over 33 observing runs on 10 different telescopes. We describe the observations and data reductions used to measure redshifts, velocity dispersions and the Mgb and Mg_2 Lick linestrength indices. Detailed simulations and intercomparison of the large number of repeat observations lead to reliable error estimates for all quantities. The measurements from different observing runs are calibrated to a common zero-point or scale before being combined, yielding a total of 706 redshifts, 676 velocity dispersions, 676 Mgb linestrengths and 582 Mg_2 linestrengths. The median estimated errors in the combined measurements are Delta cz=20 km s^-1, Delta sigma sigma =9.1 per cent, Delta Mgb Mgb=7.2 per cent and Delta Mg_2=0.015 mag. Comparison of our measurements with published data sets shows no systematic errors in the redshifts or velocity dispersions, and only small zero-point corrections to bring our linestrengths on to the standard Lick system. We have assigned galaxies to physical clusters by examining the line-of-sight velocity distributions based on EFAR and ZCAT redshifts, together with the projected distributions on the sky. We derive mean redshifts and velocity dispersions for these clusters, which will be used in estimating distances and peculiar velocities and to test for trends in the galaxy population with cluster mass. The spectroscopic parameters presented here for 706 galaxies combine high-quality data, uniform reduction and measurement procedures, and detailed error analysis. They form the largest single set of velocity dispersions and linestrengths for early-type galaxies published to date

Sharp Trace Hardy-Sobolev-Maz'ya Inequalities and the Fractional Laplacian

In this work we establish trace Hardy and trace Hardy-Sobolev-Maz'ya inequalities with best Hardy constants, for domains satisfying suitable geometric assumptions such as mean convexity or convexity. We then use them to produce fractional Hardy-Sobolev-Maz'ya inequalities with best Hardy constants for various fractional Laplacians. In the case where the domain is the half space our results cover the full range of the exponent $s \in (0,1)$ of the fractional Laplacians. We answer in particular an open problem raised by Frank and Seiringer \cite{FS}.Comment: 42 page

The SAURON project – XVII. Stellar population analysis of the absorption line strength maps of 48 early-type galaxies

The definitive version can be found at: http://onlinelibrary.wiley.com/ Copyright Royal Astronomical SocietyWe present a stellar population analysis of the absorption line strength maps for 48 early-type galaxies from the SAURON sample. Using the line strength index maps of Hβ, Fe5015 and Mg b, measured in the Lick/IDS system and spatially binned to a constant signal-to-noise ratio, together with predictions from up-to-date stellar population models, we estimate the simple stellar population-equivalent (SSP-equivalent) age, metallicity and abundance ratio [α/Fe] over a two-dimensional field extending up to approximately one effective radius. A discussion of calibrations and differences between model predictions is given. Maps of SSP-equivalent age, metallicity and abundance ratio [α/Fe] are presented for each galaxy. We find a large range of SSP-equivalent ages in our sample, of which ∼40 per cent of the galaxies show signs of a contribution from a young stellar population. The most extreme cases of post-starburst galaxies, with SSP-equivalent ages of ≤3 Gyr observed over the full field-of-view, and sometimes even showing signs of residual star formation, are restricted to low-mass systems (σe≤ 100 km s−1 or ∼2 × 1010 M⊙). Spatially restricted cases of young stellar populations in circumnuclear regions can almost exclusively be linked to the presence of star formation in a thin, dusty disc/ring, also seen in the near-UV or mid-IR on top of an older underlying stellar population. The flattened components with disc-like kinematics previously identified in all fast rotators are shown to be connected to regions of distinct stellar populations. These range from the young, still star-forming circumnuclear discs and rings with increased metallicity preferentially found in intermediate-mass fast rotators, to apparently old structures with extended disc-like kinematics, which are observed to have an increased metallicity and mildly depressed [α/Fe] ratio compared to the main body of the galaxy. The slow rotators, often harbouring kinematically decoupled components (KDC) in their central regions, generally show no stellar population signatures over and above the well-known metallicity gradients in early-type galaxies and are largely consistent with old (≥10 Gyr) stellar populations. Using radially averaged stellar population gradients we find in agreement with Spolaor et al. a mass–metallicity gradient relation where low-mass fast rotators form a sequence of increasing metallicity gradient with increasing mass. For more massive systems (above ∼3.5 × 1010 M⊙) there is an overall downturn such that metallicity gradients become shallower with increased scatter at a given mass leading to the most massive systems being slow rotators with relatively shallow metallicity gradients. The observed shallower metallicity gradients and increased scatter could be a consequence of the competition between different star formation and assembly scenarios following a general trend of diminishing gas fractions and more equal-mass mergers with increasing mass, leading to the most massive systems being devoid of ordered motion and signs of recent star formation.Peer reviewe