Chemical abundances in Galactic planetary nebulae with Spitzer spectra

We present new low-resolution (R~800) optical spectra of 22 Galactic PNe with Spitzer spectra. These data are combined with recent optical spectroscopic data available in the literature to construct representative samples of compact (and presumably young) Galactic disc and bulge PNe with Spitzer spectra. Attending to the nature of the dust features seen in their Spitzer spectra, Galactic disc and bulge PNe are classified according to four major dust types (oxygen chemistry or OC, carbon chemistry or CC, double chemistry or DC, featureless or F) and subtypes (amorphous and crystalline, and aliphatic and aromatic). Nebular gas abundances of He, N, O, Ne, S, Cl, and Ar, as well as plasma parameters (e.g. Ne, Te) are homogeneously derived and we study the median chemical abundances and nebular properties in Galactic disc and bulge PNe depending on their Spitzer dust types and subtypes. A comparison of the derived median abundance patterns with AGB nucleosynthesis predictions show mainly that i) DC PNe, both with amorphous and crystalline silicates, display high-metallicity (solar/supra-solar) and the highest He abundances and N/O ratios, suggesting relatively massive (~3-5 M_sun) hot bottom burning AGB stars as progenitors; ii) PNe with O-rich and C-rich unevolved dust (amorphous and aliphatic) seem to evolve from subsolar metallicity (z~0.008) and lower mass (<3 M_sun) AGB stars; iii) a few O-rich PNe and a significant fraction of C-rich PNe with more evolved dust (crystalline and aromatic, respectively) display chemical abundances similar to DC PNe, suggesting that they are related objects. A comparison of the derived nebular properties with predictions from models combining the theoretical central star evolution with a simple nebular model is also presented. Finally, a possible link between the Spitzer dust properties, chemical abundances, and evolutionary status is discussed.Comment: Accepted for publication in Astronomy & Astrophysics (45 pages, 17 figures, and 14 tables); final version (language corrected

Langlands duality for finite-dimensional representations of quantum affine algebras

We describe a correspondence (or duality) between the q-characters of finite-dimensional representations of a quantum affine algebra and its Langlands dual in the spirit of q-alg/9708006 and 0809.4453. We prove this duality for the Kirillov-Reshetikhin modules and their irreducible tensor products. In the course of the proof we introduce and construct "interpolating (q,t)-characters" depending on two parameters which interpolate between the q-characters of a quantum affine algebra and its Langlands dual.Comment: 40 pages; several results and comments added. Accepted for publication in Letters in Mathematical Physic

Foreword

This Foreword provides an overview of Fifty Years of Loving v. Virginia and the Continued Pursuit of Racial Equality, a symposium hosted by the Fordham Law Review and cosponsored by the Fordham Law School Center on Race, Law & Justice. Even fifty years later, Loving provides ample foundation for an inquiry into the operation of race and racial inequality in the United States, which touches on the queries outlined above, as well as many others. In our view, a symposium focused on Loving makes a significant contribution by deepening scholarly analysis of that decision and by explicating the kinds of issues and concerns that should be at the heart of research concerning racial equality today

The relationship between EQ-5D, HAQ and pain in patients with rheumatoid arthritis: further validation and development of the limited dependent variable, mixture model approach

Objective To provide robust estimates of EQ-5D as a function of the Health Assessment Questionnaire (HAQ) and pain in patients with rheumatoid arthritis. Method Repeated observations of patients diagnosed with RA in a US observational cohort (n=100,398 observations) who provided data on HAQ, pain on a visual analogue scale and the EQ-5D questionnaire. We use a bespoke mixture modelling approach to appropriately reflect the characteristics of the EQ-5D instrument and compare this to results from linear regression. Results The addition of pain alongside HAQ as an explanatory variable substantially improves explanatory power. The preferred model is a four component mixture. Unlike the linear regression it exhibits very good fit to the data, does not suffer from problems of bias or predict values outside the feasible range. Conclusions It is appropriate to model the relationship between HAQ and EQ-5D but only if suitable statistical methods are applied. Linear models underestimate the QALY benefits, and therefore the cost effectiveness, of therapies. The bespoke mixture model approach outlined here overcomes this problem. The addition of pain as an explanatory variable greatly improves the estimates