Uniformity in association schemes and coherent configurations: cometric Q-antipodal schemes and linked systems

Inspired by some intriguing examples, we study uniform association schemes and uniform coherent configurations, including cometric Q-antipodal association schemes. After a review of imprimitivity, we show that an imprimitive association scheme is uniform if and only if it is dismantlable, and we cast these schemes in the broader context of certain --- uniform --- coherent configurations. We also give a third characterization of uniform schemes in terms of the Krein parameters, and derive information on the primitive idempotents of such a scheme. In the second half of the paper, we apply these results to cometric association schemes. We show that each such scheme is uniform if and only if it is Q-antipodal, and derive results on the parameters of the subschemes and dismantled schemes of cometric Q-antipodal schemes. We revisit the correspondence between uniform indecomposable three-class schemes and linked systems of symmetric designs, and show that these are cometric Q-antipodal. We obtain a characterization of cometric Q-antipodal four-class schemes in terms of only a few parameters, and show that any strongly regular graph with a ("non-exceptional") strongly regular decomposition gives rise to such a scheme. Hemisystems in generalized quadrangles provide interesting examples of such decompositions. We finish with a short discussion of five-class schemes as well as a list of all feasible parameter sets for cometric Q-antipodal four-class schemes with at most six fibres and fibre size at most 2000, and describe the known examples. Most of these examples are related to groups, codes, and geometries.Comment: 42 pages, 1 figure, 1 table. Published version, minor revisions, April 201

Professorial roles: a study of the professorial populations within nursing and midwifery, social work and allied health professions

The professorial populations in nursing/midwifery, social work and allied health are relatively new in academia compared to longer established professions such as medicine and dentistry. Less is known about the roles, career pathways, characteristics and career aspirations of the professoriate within these emerging professions. A survey was undertaken from sample populations in each of the three professorial groups in order to obtain qualitative and quantitative data on professorial roles and activities, career pathway information and support mechanisms for professorial positions. This paper discusses the findings of the survey which relate specifically to professorial roles and activities and whether the identified roles reflect the professorial activities proposed by the National Conference of University Professors (NCUP) Other aspects of this survey including career pathways, findings relating to gender and support mechanisms will form the basis of future papers. Result