Confidence Intervals and Upper Bounds for Small Signals in the Presence of Background Noise

We discuss a new method for setting limits on small signals in the presence of background noise. The method is based on a combination of a two dimensional confidence region and the large sample approximation to the likelihood ratio test statistic. It automatically quotes upper limits for small signals and two-sided confidence intervals for larger samples. We show that this method gives the correct coverage and also has good power.Comment: Document was created by Sciword V3.0, it consists of one main document (lrt.tex), eight figures (figure1.eps - figure8.eps) and one table (table.tex). Paper was revised after being accepted for publication in NIM A Paper was revised after being accepted for publication in NIM

Limits and Confidence Intervals in the Presence of Nuisance Parameters

We study the frequentist properties of confidence intervals computed by the method known to statisticians as the Profile Likelihood. It is seen that the coverage of these intervals is surprisingly good over a wide range of possible parameter values for important classes of problems, in particular whenever there are additional nuisance parameters with statistical or systematic errors. Programs are available for calculating these intervals.Comment: 6 figure

New optical and near-infrared Surface Brightness Fluctuations models. A primary distance indicator ranging from Globular Clusters to distant galaxies?

We present new theoretical models for Surface Brightness Fluctuations (SBF) both for optical and near-infrared bands in standard ground-based and Hubble Space Telescope filter systems. Simple Stellar Population simulations are adopted. Models cover the age and metallicity ranges from $t=5$ to $15~Gyr$ and from $Z=0.0001$ to 0.04 respectively. Effects due to the variation of the Initial Mass Function and the stellar color-temperature relations are explored. Particular attention is devoted to very bright stars in the color-magnitude diagram and to investigate the effects of mass loss along the Red Giant Branch (RGB) and the Asymptotic Giant Branch (AGB). It is found that $U$ and $B$ bands SBF amplitudes are powerful diagnostics for the morphology of the Horizontal Branch and the Post-AGB stars population. We point out that a careful treatment of mass loss process along the RGB and AGB is fundamental in determining reliable SBF evaluations. The SBF measurements are used to give robust constraints on the evolution of AGB stars, suggesting that mass loss activity on AGB stars should be twice more efficient than on the RGB stars. Our models are able to reproduce the absolute SBF magnitudes of the Galactic Globular Clusters and of galaxies, and their integrated colors. New calibrations of absolute SBF magnitude in $V$, $R$, $I$, and $K$ photometric filters are provided, which appear reliable enough to directly gauge distances bypassing other distance indicators. The SBF technique is also used as stellar population tracer to derive age and metallicity of a selected sample of galaxies of known distances. Finally, {\it SBF color} versus {\it integrated color} diagrams are proposed as particularly useful in removing the well known {\it age-metallicity degeneracy} affecting our knowledge of remote stellar systems.Comment: AJ accepted, 46 pages, 21 figures, 10 tables, uses aastex.cl

Spectral identification and quantification of salts in the Atacama Desert

This work was part-funded by a Research Incentive Grant from The Carnegie Trust (REF: 70335) and a Royal Society of Edinburgh Research Fellowship to C. Cousins. J, Harris acknowledges funding from STFC (consolidated grant ST/N000528/1).Salt minerals are an important natural resource. The ability to quickly and remotely identify and quantify salt deposits and salt contaminated soils and sands is therefore a priority goal for the various industries and agencies that utilise salts. The advent of global hyperspectral imagery from instruments such as Hyperion on NASA’s Earth-Observing 1 satellite has opened up a new source of data that can potentially be used for just this task. This study aims to assess the ability of Visible and Near Infrared (VNIR) spectroscopy to identify and quantify salt minerals through the use of spectral mixture analysis. The surface and near-surface soils of the Atacama Desert in Chile contain a variety of well-studied salts, which together with low cloud coverage, and high aridity, makes this region an ideal testbed for this technique. Two forms of spectral data ranging 0.35 – 2.5 μm were collected: laboratory spectra acquired using an ASD FieldSpec Pro instrument on samples from four locations in the Atacama desert known to have surface concentrations of sulfates, nitrates, chlorides and perchlorates; and images from the EO-1 satellite’s Hyperion instrument taken over the same four locations. Mineral identifications and abundances were confirmed using quantitative XRD of the physical samples. Spectral endmembers were extracted from within the laboratory and Hyperion spectral datasets and together with additional spectral library endmembers fed into a linear mixture model. The resulting identification and abundances from both dataset types were verified against the sample XRD values. Issues of spectral scale, SNR and how different mineral spectra interact are considered, and the utility of VNIR spectroscopy and Hyperion in particular for mapping specific salt concentrations in desert environments is established. Overall, SMA was successful at estimating abundances of sulfate minerals, particularly calcium sulfate, from both hyperspectral image and laboratory sample spectra, while abundance estimation of other salt phase spectral end-members was achieved with a higher degree of error.Publisher PD

Correcting the Minimization Bias in Searches for Small Signals

We discuss a method for correcting the bias in the limits for small signals if those limits were found based on cuts that were chosen by minimizing a criterion such as sensitivity. Such a bias is commonly present when a "minimization" and an "evaluation" are done at the same time. We propose to use a variant of the bootstrap to adjust the limits. A Monte Carlo study shows that these new limits have correct coverage.Comment: 14 pages, 5 figue

Nonlinear modal coupling in a high-stress doubly-clamped nanomechanical resonator

We present results from a study of the nonlinear intermodal coupling between different flexural vibrational modes of a single high-stress, doubly-clamped silicon nitride nanomechanical beam. The measurements were carried out at 100 mK and the beam was actuated using the magnetomotive technique. We observed the nonlinear behavior of the modes individually and also measured the coupling between them by driving the beam at multiple frequencies. We demonstrate that the different modes of the resonator are coupled to each other by the displacement induced tension in the beam, which also leads to the well known Duffing nonlinearity in doubly-clamped beams.Comment: 15 pages, 7 figure

A Photometric Technique to Search for Be Stars in Open Clusters

We describe a technique to identify Be stars in open clusters using Stromgren b, y, and narrow-band Halpha photometry. We first identify the B-type stars of the cluster using a theoretical isochrone fit to the (b-y, y) color-magnitude diagram. The strongest Be stars are easily identified in a (b-y, y-Halpha) color-color diagram, but those with weaker Halpha emission (classified as possible Be star detections) may be confused with evolved or foreground stars. Here we present such photometry plus Halpha spectroscopy of members of the cluster NGC 3766 to demonstrate the accuracy of our technique. Statistical results on the relative numbers of Be and B-type stars in additional clusters will be presented in a future paper.Comment: 15 pages, 6 figures, 1 table. Accepted by Ap

The outsourcing of social care in Britain : what does it mean for voluntary sector workers?

While recent decades have witnessed a growth in the outsourcing of public services in Britain, the post-1997 UK Labour governments have sought to put in place mechanisms aimed at encouraging long-term collaborative contracting relationships marked by less reliance on cost-based competition. This article explores empirically how far these mechanisms have achieved their aims and thereby acted to protect the employment conditions of staff, and links this exploration to debates concerning the employment implications of organizational reforms within public sectors internationally. It concludes that in terms of bringing income security to the voluntary sector and stability to employment terms and conditions these efforts have been unsuccessful, and consequently casts doubts on more optimistic interpretations of the employment effects of organizational restructuring in the British public sector

Spectroscopy and Time Variability of Absorption Lines in the Direction of the Vela Supernova Remnant

We present high resolution (R~75,000), high signal-to-noise (S/N~100) Ca II $\lambda$3933.663 and Na I $\lambda\lambda$5889.951, 5895.924 spectra of 68 stars in the direction of the Vela supernova remnant. The spectra comprise the most complete high resolution, high S/N, optical survey of early type stars in this region of the sky. A subset of the sight lines has been observed at multiple epochs, 1993/1994 and 1996. Of the thirteen stars observed twice, seven have spectra revealing changes in the equivalent width and/or velocity structure of lines, most of which arise from remnant gas. Such time variability has been reported previously for the sight lines towards HD 72089 and HD 72997 by Danks & Sembach (1995) and for HD 72127 by Hobbs et al. (1991). We have confirmed the ongoing time variability of these spectra and present new evidence of variability in the spectra of HD 73658, HD 74455, HD 75309 and HD 75821. We have tabulated Na I and Ca II absorption line information for the sight lines in our sample to serve as a benchmark for further investigations of the dynamics and evolution of the Vela SNR.Comment: 8 pages of text, 4 tables, 16 pages of figures Accepted and to be published in ApJ