Irreducible Specht modules for Iwahori-Hecke algebras of type B

We consider the problem of classifying irreducible Specht modules for the Iwahori-Hecke algebra of type B with parameters Q,q. We solve this problem completely in the case where q is not a root of unity, and in the case q=-1 we reduce the problem to the corresponding problem in type A

Analysing randomised controlled trials with missing data : Choice of approach affects conclusions

Copyright © 2012 Elsevier Inc. All rights reserved. PMID: 22265924 [PubMed - indexed for MEDLINE]Peer reviewedPostprin

(s,t)-cores: a weighted version of Armstrong's conjecture

The study of core partitions has been very active in recent years, with the study of $(s,t)$-cores - partitions which are both $s$- and $t$-cores - playing a prominent role. A conjecture of Armstrong, proved recently by Johnson, says that the average size of an $(s,t)$-core, when $s$ and $t$ are coprime positive integers, is $\frac1{24}(s-1)(t-1)(s+t-1)$. Armstrong also conjectured that the same formula gives the average size of a self-conjugate $(s,t)$-core; this was proved by Chen, Huang and Wang. In the present paper, we develop the ideas from the author's paper [J. Combin. Theory Ser. A 118 (2011) 1525-1539] studying actions of affine symmetric groups on the set of $s$-cores in order to give variants of Armstrong's conjectures in which each $(s,t)$-core is weighted by the reciprocal of the order of its stabiliser under a certain group action. Informally, this weighted average gives the expected size of the $t$-core of a random $s$-core

Predicting missing quality of life data that were later recovered : an empirical comparison of approaches

Peer reviewedPostprin

Implicit self-comparisons against others could bias quality of life assessments

Objectives: To explore how patient-reported health related quality of life (HRQL) and global health status are affected by use of differing personal reference frames. We hypothesised that implicit comparisons against self at an earlier time, against healthy peers or against ill patients would greatly affect patients’ response values. Study design and setting: Patients in a randomised trial for treatment of Paget’s disease completed annual HRQL questionnaires. Supplementary questions were appended, asking the patients whether they were aware of having made implicit comparisons. Results: The majority of patients reported considering themselves a year ago (31% at baseline), themselves before becoming ill (23%) or other healthy people (24%), with similar proportions during follow up. Mean HRQL scores varied substantially according to the declared frame of reference, with differences as big as 19% of the scale score, or a standardised mean effect size of 0.74 standard deviations. Conclusion: Reported reference frames were associated with effects of similar magnitude to the differences in HRQL that are regarded as clinically important. This may be of particular concern in trials that andomise patients to management in different settings, such as treatment at home / in hospital, or surgery / chemotherapy, and might bias or obscure HRQL differences