Cylindric partitions, W_r characters and the Andrews-Gordon-Bressoud identities

We study the Andrews-Gordon-Bressoud (AGB) generalisations of the Rogers-Ramanujan q-series identities in the context of cylindric partitions. We recall the definition of r-cylindric partitions, and provide a simple proof of Borodin's product expression for their generating functions, that can be regarded as a limiting case of an unpublished proof by Krattenthaler. We also recall the relationships between the r-cylindric partition generating functions, the principal characters of affine sl_r algebras, the M^{r, r+d}_r minimal model characters of W_r algebras, and the r-string abaci generating functions, as well as the relationships between them, providing simple proofs for each. We then set r=2, and use 2-cylindric partitions to re-derive the AGB identities as follows. Firstly, we use Borodin's product expression for the generating functions of the 2-cylindric partitions with infinitely-long parts, to obtain the product sides of the AGB identities, times a factor (q; q)_{\infty}^{-1}, which is the generating function of ordinary partitions. Next, we obtain a bijection from the 2-cylindric partitions, via 2-string abaci, into decorated versions of Bressoud's restricted lattice paths. Extending Bressoud's method of transforming between restricted paths that obey different restrictions, we obtain sum expressions with manifestly non-negative coefficients for the generating functions of the 2-cylindric partitions which contains a factor (q; q)_{\infty}^{-1}. Equating the product and sum expressions of the same 2-cylindric partitions, and canceling a factor of (q; q)_{\infty}^{-1} on each side, we obtain the AGB identities.Comment: 38 page

Particles in RSOS paths

We introduce a new representation of the paths of the Forrester-Baxter RSOS models which represents the states of the irreducible modules of the minimal models M(p',p). This representation is obtained by transforming the RSOS paths, for the cases p> 2p'-2, to new paths for which horizontal edges are allowed at certain heights. These new paths are much simpler in that their weight is nothing but the sum of the position of the peaks. This description paves the way for the interpretation of the RSOS paths in terms of fermi-type charged particles out of which the fermionic characters could be obtained constructively. The derivation of the fermionic character for p'=2 and p=kp'+/- 1 is outlined. Finally, the particles of the RSOS paths are put in relation with the kinks and the breathers of the restricted sine-Gordon model.Comment: 15 pages, few typos corrected, version publishe

Awareness Of Racial And Ethnic Health Disparities Has Improved Only Modestly Over A Decade

Abstract available at publisher's web site.http://dx.doi.org/10.1377/hlthaff.2010.070

On a Site of X-ray Emission in AE Aquarii

An analysis of recently reported results of XMM-Newton observations of AE Aqr within a hypothesis that the detected X-ray source is located inside the Roche lobe of the white dwarf is presented. I show this hypothesis to be inconsistent with the currently adopted model of mass-transfer in the system. Possible solutions of this problem are briefly discussed.Comment: 4 pages, accepted for publication in ApJ Letter

Higher spin vertex models with domain wall boundary conditions

We derive determinant expressions for the partition functions of spin-k/2 vertex models on a finite square lattice with domain wall boundary conditions.Comment: 14 pages, 12 figures. Minor corrections. Version to appear in JSTA

Hubble Space Telescope Observations of UV Oscillations in WZ Sagittae During the Decline from Outburst

We present a time series analysis of Hubble Space Telescope observations of WZ Sge obtained in 2001 September, October, November and December as WZ Sge declined from its 2001 July superoutburst. Previous analysis of these data showed the temperature of the white dwarf decreased from ~29,000 K to ~18,000 K. In this study we binned the spectra over wavelength to yield ultraviolet light curves at each epoch that were then analyzed for the presence of the well-known 27.87 s and 28.96 s oscillations. We detect the 29 s periodicity at all four epochs, but the 28 s periodicity is absent. The origin of these oscillations has been debated since their discovery in the 1970s and competing hypotheses are based on either white dwarf non-radial g-mode pulsations or magnetically-channelled accretion onto a rotating white dwarf. By analogy with the ZZ Ceti stars, we argue that the non-radial g-mode pulsation model demands a strong dependence of pulse period on the white dwarf's temperature. However, these observations show the 29 s oscillation is independent of the white dwarf's temperature. Thus we reject the white dwarf non-radial g-mode pulsation hypothesis as the sole origin of the oscillations. It remains unclear if magnetically-funnelled accretion onto a rapidly rotating white dwarf (or belt on the white dwarf) is responsible for producing the oscillations. We also report the detection of a QPO with period ~18 s in the September light curve. The amplitudes of the 29 s oscillation and the QPO vary erratically on short timescales and are not correlated with the mean system brightness nor with each other.Comment: 20 pages, 3 figures, 1 table; accepted for publication in Ap

New path description for the M(k+1,2k+3) models and the dual Z_k graded parafermions

We present a new path description for the states of the non-unitary M(k+1,2k+3) models. This description differs from the one induced by the Forrester-Baxter solution, in terms of configuration sums, of their restricted-solid-on-solid model. The proposed path representation is actually very similar to the one underlying the unitary minimal models M(k+1,k+2), with an analogous Fermi-gas interpretation. This interpretation leads to fermionic expressions for the finitized M(k+1,2k+3) characters, whose infinite-length limit represent new fermionic characters for the irreducible modules. The M(k+1,2k+3) models are also shown to be related to the Z_k graded parafermions via a (q to 1/q) duality transformation.Comment: 43 pages (minor typo corrected and minor rewording in the introduction

Identification of a nearby stellar association in the Hipparcos catalog: implications for recent, local star formation

The TW Hydrae Association (~55 pc from Earth) is the nearest known region of recent star formation. Based primarily on the Hipparcos catalog, we have now identified a group of 9 or 10 co-moving star systems at a common distance (~45 pc) from Earth that appear to comprise another, somewhat older, association (``the Tucanae Association''). Together with ages and motions recently determined for some nearby field stars, the existence of the Tucanae and TW Hydrae Associations suggests that the Sun is now close to a region that was the site of substantial star formation only 10-40 million years ago. The TW Hydrae Association represents a final chapter in the local star formation history.Comment: 5 pages incl figs and table

Copeptin and the risk of incident stroke, CHD and cardiovascular mortality in older men with and without diabetes: The British Regional Heart Study.

AIMS/HYPOTHESIS: This study aimed to examine the association between copeptin (a surrogate marker of arginine vasopressin) and incident stroke, CHD and cardiovascular mortality in older men with and without diabetes. METHODS: We conducted a prospective study of 3536 men aged 60-79 years who were followed for an average of 13 years. During this period, there were 437 major CHD events (fatal and non-fatal myocardial infarction [MI]), 323 stroke events (fatal and non-fatal) and 497 cardiovascular disease (CVD) deaths. Prevalent diabetes was defined on the basis of a history of doctor-diagnosed diabetes or fasting blood glucose ≥7.0 mmol or HbA1c ≥6.5% (48 mmol/mol) (n = 428). RESULTS: No association was seen between copeptin and incident stroke or CVD mortality in men without diabetes after adjustment for conventional cardiovascular risk factors, renal dysfunction, and insulin and N-terminal pro B-type natriuretic peptide levels. In contrast, elevated copeptin levels were associated with an increased risk of stroke and CVD mortality in men with diabetes after these adjustments. Compared with those in the lowest tertile of copeptin, men in the top tertile had adjusted relative HRs for stroke and CVD death of 2.34 (95% CI 1.04, 5.27) and 2.21 (1.12, 4.36), respectively. The risk of stroke and CVD mortality remained increased after the exclusion of men with prevalent stroke or MI. Higher levels of copeptin were associated with increased risk of CHD in the diabetic and non-diabetic groups, but these associations were attenuated after exclusion of individuals with a previous stroke or MI. CONCLUSIONS/INTERPRETATION: Copeptin was independently associated with an increased risk of incident stroke and CVD mortality in men with diabetes, but not in men without diabetes. Targeting the arginine vasopressin system might have beneficial effects on CVD mortality and stroke risk in older men with diabetes