Reflected Backward Stochastic Difference Equations and Optimal Stopping Problems under g-expectation

In this paper, we study reflected backward stochastic difference equations (RBSDEs for short) with finitely many states in discrete time. The general existence and uniqueness result, as well as comparison theorems for the solutions, are established under mild assumptions. The connections between RBSDEs and optimal stopping problems are also given. Then we apply the obtained results to explore optimal stopping problems under $g$-expectation. Finally, we study the pricing of American contingent claims in our context.Comment: 29 page

The Grushko decomposition of a finite graph of finite rank free groups: an algorithm

A finitely generated group admits a decomposition, called its Grushko decomposition, into a free product of freely indecomposable groups. There is an algorithm to construct the Grushko decomposition of a finite graph of finite rank free groups. In particular, it is possible to decide if such a group is free.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper41.abs.htm

Impact of a case-management intervention for reducing emergency attendance on primary care: randomised control trial

BACKGROUND: The impact on primary care workload of case-management interventions to reduce emergency department (ED) attendances is unknown. AIM: To examine the impact of a telephone-based case-management intervention targeting people with high ED attendance on primary care use. DESIGN AND SETTING: A single-site data extract from a larger randomised control trial, using the patient-level data from primary care electronic health records (2015–2020), was undertaken. METHOD: A total of 363 patients at high risk of ED usage were randomised to receive a 6-month case-management intervention (253 patients) or standard care (110 patients). Poisson regression models were used to calculate monthly rates of primary care use over time for the 2 years post-randomisation, comparing both arms. Usage was subclassified into face-to-face, telephone, letter, and community and secondary care referrals, stratified by patient demographics. RESULTS: No significant difference was found in the mean annual rate of primary care events between the intervention and control arms (P = 0.70). Secondary care referrals saw a 26% reduction in the mean annual referral rate (incident rate ratio [IRR] 0.74, 95% confidence interval [CI] = 0.64 to 0.86, P<0.001) and letters sent increased by 6% in the intervention arm compared with the control arm (IRR 1.06, 95% CI = 1.01 to 1.11, P = 0.01). In the case-managed arm, in patients aged ≥80 years there was a 33% increase in primary care usage (IRR 1.33, 95% CI = 1.28 to 1.40, P<0.001); with a corresponding 10% decrease in patients aged <80 years when compared with controls (IRR 0.90, 95% CI = 0.87 to 0.92, P<0.001). CONCLUSION: A targeted case-management intervention to reduce ED attendances did not increase overall primary care use. Redistribution of usage is seen among some patient groups, particularly older people, which may have important implications for primary healthcare planning

The SEGUE Stellar Parameter Pipeline. IV. Validation with an Extended Sample of Galactic Globular and Open Clusters

Spectroscopic and photometric data for likely member stars of five Galactic globular clusters (M3, M53, M71, M92, and NGC 5053) and three open clusters (M35, NGC 2158, and NGC 6791) are processed by the current version of the SEGUE Stellar Parameter Pipeline (SSPP), in order to determine estimates of metallicities and radial velocities for the clusters. These results are then compared to values from the literature. We find that the mean metallicity () and mean radial velocity () estimates for each cluster are almost all within 2{\sigma} of the adopted literature values; most are within 1{\sigma}. We also demonstrate that the new version of the SSPP achieves small, but noteworthy, improvements in estimates at the extrema of the cluster metallicity range, as compared to a previous version of the pipeline software. These results provide additional confidence in the application of the SSPP for studies of the abundances and kinematics of stellar populations in the Galaxy.Comment: 98 pages, 31 figures; accepted for publication in A

A Survey of CN and CH Variations in Galactic Globular Clusters from SDSS Spectroscopy

We present a homogeneous survey of the CN and CH bandstrengths in eight Galactic globular clusters observed during the course of the Sloan Extension for Galactic Understanding and Exploration (SEGUE) sub-survey of the SDSS. We confirm the existence of a bimodal CN distribution among RGB stars in all of the clusters with metallicity greater than [Fe/H] = -1.7; the lowest metallicity cluster with an observed CN bimodality is M53, with [Fe/H] ~ -2.1. There is also some evidence for individual CN groups on the subgiant branches of M92, M2, and M13, and on the red giant branches of M92 and NGC 5053. Finally, we quantify the correlation between overall cluster metallicity and the slope of the CN bandstrength-luminosity plot as a means of further demonstrating the level of CN-enrichment in cluster giants. Our results agree well with previous studies reported in the literature.Comment: AJ submitted; 80 pages, 22 figure

Multi-Element Abundance Measurements from Medium-Resolution Spectra. II. Catalog of Stars in Milky Way Dwarf Satellite Galaxies

We present a catalog of Fe, Mg, Si, Ca, and Ti abundances for 2961 red giant stars that are likely members of eight dwarf satellite galaxies of the Milky Way (MW): Sculptor, Fornax, Leo I, Sextans, Leo II, Canes Venatici I, Ursa Minor, and Draco. For the purposes of validating our measurements, we also observed 445 red giants in MW globular clusters and 21 field red giants in the MW halo. The measurements are based on Keck/DEIMOS medium-resolution spectroscopy combined with spectral synthesis. We estimate uncertainties in [Fe/H] by quantifying the dispersion of [Fe/H] measurements in a sample of stars in monometallic globular clusters. We estimate uncertainties in Mg, Si, Ca, and Ti abundances by comparing our medium-resolution spectroscopic measurements to high-resolution spectroscopic abundances of the same stars. For this purpose, our DEIMOS sample included 132 red giants with published high-resolution spectroscopy in globular clusters, the MW halo field, and dwarf galaxies. The standard deviations of the differences in [Fe/H] and [alpha/Fe] (the average of [Mg/Fe], [Si/Fe], [Ca/Fe], and [Ti/Fe]) between the two samples is 0.15 and 0.16, respectively. This catalog represents the largest sample of multi-element abundances in dwarf galaxies to date. The next papers in this series draw conclusions on the chemical evolution, gas dynamics, and star formation histories from the catalog presented here. The wide range of dwarf galaxy luminosity reveals the dependence of dwarf galaxy chemical evolution on galaxy stellar mass.Comment: 26 pages, 22 figures, 4 machine-readable tables (available in the source file; click "Other formats"); accepted for publication in ApJ Supplements; updated acknowledgments in v

Do adults with high functioning autism or Asperger Syndrome differ in empathy and emotion recognition?

The present study examined whether adults with high functioning autism (HFA) showed greater difficulties in (i) their self-reported ability to empathise with others and/or (ii) their ability to read mental states in others’ eyes than adults with Asperger syndrome (AS). The Empathy Quotient (EQ) and ‘Reading the Mind in the Eyes’ Test (Eyes Test) were compared in 43 adults with AS and 43 adults with HFA. No significant difference was observed on EQ score between groups, while adults with AS performed significantly better on the Eyes Test than those with HFA. This suggests that adults with HFA may need more support, particularly in mentalizing and complex emotion recognition, and raises questions about the existence of subgroups within autism spectrum conditions

Single-particle motional oscillator powered by laser

An ion, atom, molecule or macro-particle in a trap can exhibit large motional oscillations due to the Doppler-affected radiation pressure by a laser, blue-detuned from an absorption line of a particle. This oscillator can be nearly thresholdless, but under certain conditions it may exhibit huge hysteretic excitation. Feasible applications include a "Foucault pendulum" in a trap, a rotation sensor, single atom spectroscopy, isotope separation, etc.Comment: 9 pages, 1 fig; v2: the latest revision for Optics Expres

Testing stellar population synthesis models with Sloan Digital Sky Survey colors of M31's globular clusters

Accurate stellar population synthesis models are vital in understanding the properties and formation histories of galaxies. In order to calibrate and test the reliability of these models, they are often compared with observations of star clusters. However, relatively little work has compared these models in the ugriz filters, despite the recent widespread use of this filter set. In this paper, we compare the integrated colors of globular clusters in the Sloan Digital Sky Survey (SDSS) with those predicted from commonly used simple stellar population (SSP) models. The colors are based on SDSS observations of M31's clusters and provide the largest population of star clusters with accurate photometry available from the survey. As such, it is a unique sample with which to compare SSP models with SDSS observations. From this work, we identify a significant offset between the SSP models and the clusters' g-r colors, with the models predicting colors which are too red by g-r\sim0.1. This finding is consistent with previous observations of luminous red galaxies in the SDSS, which show a similar discrepancy. The identification of this offset in globular clusters suggests that it is very unlikely to be due to a minority population of young stars. The recently updated SSP model of Maraston & Stromback better represents the observed g-r colors. This model is based on the empirical MILES stellar library, rather than theoretical libraries, suggesting an explanation for the g-r discrepancy.Comment: 8 pages, 4 figures, accepted for publication in Ap