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proof of Borodin's product expression for their generating functions, that can be regarded as a limiting case of an unpublished proof by Krattenthaler.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

A computer code for calculations in the algebraic collective model of the atomic nucleus

A Maple code is presented for algebraic collective model (ACM) calculations. The ACM is an algebraic version of the Bohr model of the atomic nucleus, in which all required matrix elements are derived by exploiting the model's SU(1,1) x SO(5) dynamical group. This paper reviews the mathematical formulation of the ACM, and serves as a manual for the code. The code enables a wide range of model Hamiltonians to be analysed. This range includes essentially all Hamiltonians that are rational functions of the model's quadrupole moments $q_M$ and are at most quadratic in the corresponding conjugate momenta $\pi_N$ ($-2\le M,N\le 2$). The code makes use of expressions for matrix elements derived elsewhere and newly derived matrix elements of the operators $[\pi\otimes q \otimes\pi]_0$ and $[\pi\otimes\pi]_{LM}$. The code is made efficient by use of an analytical expression for the needed SO(5)-reduced matrix elements, and use of SO(5)$\,\supset\,$SO(3) Clebsch-Gordan coefficients obtained from precomputed data files provided with the code.Comment: REVTEX4. v2: Minor improvements and corrections. v3: Introduction rewritten, references added, Appendix B.4 added illustrating efficiencies obtained using modified basis, Appendix E added summarising computer implementation, and other more minor improvements. 43 pages. Manuscript and program to be published in Computer Physics Communications (2016

Fletcher-Turek Model Averaged Profile Likelihood Confidence Intervals

We evaluate the model averaged profile likelihood confidence intervals proposed by Fletcher and Turek (2011) in a simple situation in which there are two linear regression models over which we average. We obtain exact expressions for the coverage and the scaled expected length of the intervals and use these to compute these quantities in particular situations. We show that the Fletcher-Turek confidence intervals can have coverage well below the nominal coverage and expected length greater than that of the standard confidence interval with coverage equal to the same minimum coverage. In these situations, the Fletcher-Turek confidence intervals are unfortunately not better than the standard confidence interval used after model selection but ignoring the model selection process

A photospheric metal line profile analysis of hot DA white dwarfs with circumstellar material

Some hot DA white dwarfs have circumstellar high ion absorption features in their spectra, in addition to those originating in the photosphere. In many cases, the line profiles of these absorbing components are unresolved. Given the importance of the atmospheric composition of white dwarfs to studies of stellar evolution, extra-solar planetary systems and the interstellar medium, we examine the effect of including circumstellar line profiles in the abundance estimates of photospheric metals in six DA stars. The photospheric C and Si abundances are reduced in five cases where the circumstellar contamination is strong, though the relative weakness of the circumstellar Si IV absorption introduces minimal contamination, resulting in a small change in abundance. The inability of previous, approximate models to reproduce the photospheric line profiles here demonstrates the need for a technique that accounts for the physical line profiles of both the circumstellar and photospheric lines when modelling these blended absorption features.Comment: 7 pages, 5 figues, 3 tables, accepted for publication in MNRA

'For the bibliographers at UCL': A Humument and the lessons it teaches 21st century librarians

Object-based learning lies at the heart of teaching in both Historical Bibliography and Cataloguing classes on the MA Library and Information Studies at UCL. Tom Phillips’s work A Humument and the novel he chose to use as his canvas, W.H. Mallock’s A Human Document provide memorable ‘object lessons’ with scope for students to synthesize and evaluate their pre-existing learning from inside and outside the modules. It is important that the examples used in class are simple enough to illustrate the strengths of any conceptual model yet complex enough to highlight its limits. It is also ideal if examples can be beautiful as well as useful. A Humument fulfills all these criteria and, for students with no background in Art or Art Librarianship, also introduces the artists’ book as a genre and artists themselves as an important and interesting user group within information services

MarcEdit for Mac and the rare books researcher

This methodological communication discusses the use of MarcEdit in a recent research project and foregrounds how a tool designed for the library community to manipulate catalogue data has been repurposed within an academic methodology. As such, it discusses solutions to the research problem generated by difficulties in outputting MARC records highlighted at CIG 2014 (Welsh, 2014) and the IFLA Rare Books and Special Collections Section’s Conference A Common International Standard for Rare Materials: Why? And How? (Welsh, 2016b) and in articles published in Catalogue and Index (Welsh, 2015) and Cataloging and Classification Quarterly (Welsh, 2016a). In doing so, it suggests ways in which metadata for a particular set of rare materials – the catalogue records for the Working Library of Walter de la Mare (Senate House Library [WdlM]) – have been incorporated in the research database and thereby moved beyond Wilson’s (1968) idea of the “descriptive power” of bibliographic control to the second, greater power he defined – “exploitative power,” summarized by Smiraglia (2008, 35) as “the power of a scholar to make the best possible use of recorded knowledge,” and which I have previously argued is a larger purpose than those solely of applying international standards and creating linked data (Welsh, 2016a)