Subdegree growth rates of infinite primitive permutation groups

A transitive group $G$ of permutations of a set $\Omega$ is primitive if the only $G$-invariant equivalence relations on $\Omega$ are the trivial and universal relations. If $\alpha \in \Omega$, then the orbits of the stabiliser $G_\alpha$ on $\Omega$ are called the $\alpha$-suborbits of $G$; when $G$ acts transitively the cardinalities of these $\alpha$-suborbits are the subdegrees of $G$. If $G$ acts primitively on an infinite set $\Omega$, and all the suborbits of $G$ are finite, Adeleke and Neumann asked if, after enumerating the subdegrees of $G$ as a non-decreasing sequence $1 = m_0 \leq m_1 \leq ...$, the subdegree growth rates of infinite primitive groups that act distance-transitively on locally finite distance-transitive graphs are extremal, and conjecture there might exist a number $c$ which perhaps depends upon $G$, perhaps only on $m$, such that $m_r \leq c(m-2)^{r-1}$. In this paper it is shown that such an enumeration is not desirable, as there exist infinite primitive permutation groups possessing no infinite subdegree, in which two distinct subdegrees are each equal to the cardinality of infinitely many suborbits. The examples used to show this provide several novel methods for constructing infinite primitive graphs. A revised enumeration method is then proposed, and it is shown that, under this, Adeleke and Neumann's question may be answered, at least for groups exhibiting suitable rates of growth.Comment: 41 page

Sustainability in the theology curriculum

This is the author's PDF version of a book chapter available in Sustainability education: Perspectives and practice across higher education. Edited by Paula Jones, David Selby, and Stephen Sterling. London: Earthscan, 2010. This book chapter was reproduced with the kind permission of EasthScan.This book chapter discusses how theology has the potential to contribute to education for sustainable development

Formal ontology for biomedical knowledge systems integration

The central hypothesis of the collaboration between Language and Computing (L&C) and the Institute for Formal Ontology and Medical Information Science (IFOMIS) is that the methodology and conceptual rigor of a philosophically inspired formal ontology will greatly benefit software application ontologies. To this end LinKBase®, L&C’s ontology, which is designed to integrate and reason across various external databases simultaneously, has been submitted to the conceptual demands of IFOMIS’s Basic Formal Ontology (BFO). With this, we aim to move beyond the level of controlled vocabularies to yield an ontology with the ability to support reasoning applications

Ontological theory for ontological engineering: Biomedical systems information integration

Software application ontologies have the potential to become the keystone in state-of-the-art information management techniques. It is expected that these ontologies will support the sort of reasoning power required to navigate large and complex terminologies correctly and efficiently. Yet, there is one problem in particular that continues to stand in our way. As these terminological structures increase in size and complexity, and the drive to integrate them inevitably swells, it is clear that the level of consistency required for such navigation will become correspondingly difficult to maintain. While descriptive semantic representations are certainly a necessary component to any adequate ontology-based system, so long as ontology engineers rely solely on semantic information, without a sound ontological theory informing their modeling decisions, this goal will surely remain out of reach. In this paper we describe how Language and Computing nv (L&C), along with The Institute for Formal Ontology and Medical Information Sciences (IFOMIS), are working towards developing and implementing just such a theory, combining the open software architecture of L&C’s LinkSuiteTM with the philosophical rigor of IFOMIS’s Basic Formal Ontology. In this way we aim to move beyond the more or less simple controlled vocabularies that have dominated the industry to date

The relevance and sustainability of Investors in People

Title: The relevance and sustainability of Investors in People. Purpose: The purpose of this research project is to explore and challenge the relevance and sustainability of Investors in People (IIP) involvement and recognition within seven case studies. Research design: Seven in-depth case studies combining thirty-eight semi-structured interviews are used to gather the appropriate insights. Findings: In essence, it is the studied organizations themselves that generate what the Leitch Report describes as the “untapped and vast” potential of their employees, not IIP involvement or recognition. The data collected challenges the direct relationship frequently proposed between IIP recognition and increases in business performance. The sample organizations have delivered performance improvements and success independently of IIP consideration, raising serious questions over the relevance and sustainability of the standard. These insights are supported by the lack of knowledge and understanding of the standard within the workforce. In addition, other quality improvement tools and techniques and industry standards are found to have a significant detrimental influence on the standing of IIP. Other influences are also found to impact negatively on the standing. Thus, this research project questions what contribution IIP can make towards national competitiveness when the standard is so withdrawn from the business performance improvements integrated. Even as a badge or plaque of external recognition, the assumptions surrounding the perceptual value of IIP are questioned when the impact of the standard’s logo/ symbols is considered to be nominal. A theoretical framework and alternative definition for IIP are developed to represent the findings within the seven organizations studied. Research limitations: Research is needed beyond the case samples studied to further explore and generalize the rhetoric and realities concerning the insights developed. Practical implications: HR practitioners and managers need to exhibit caution before considering IIP involvement and recognition. Indeed, practitioners need to consider that the asserted benefits associated with IIP may not match their expectations and provide the impact they seek. Originality/value: This research project provides HR practitioners and managers with a valuable and timely alternative discourse and perspective when considering employee development towards IIP recognition and the possibility of improved business performance and customer/employee perceptual value. In addition, the theoretical exemplars developed from the data set provide visual representations that can be used as pragmatic comparisons to develop the field of IIP further

Signs and wonders: Exploring the effects and impact of the Investors in People logo and symbols

This article is (c) Emerald Group Publishing and permission has been granted for this version to appear herehttp://www.emeraldinsight.com/doi/full/10.1108/EJTD-11-2014-0074 . Emerald does not grant permission for this article to be further copied/distributed or hosted elsewhere without the express permission from Emerald Group Publishing LimitedPurpose – This paper aims to examine and assess the reputational impact of the logo and symbols of the UK Standard Investors in People (IiP). The extant literature highlights differing opinions in terms of the likely benefits that IiP generates following achievement of the Standard. This paper focuses specifically on the perceptions of reputational claims made regarding existing employees, potential employees and customers. Design/methodology/approach – The debate is explored through 38 interviews using the perceptions of managers and frontline employees within six IiP-accredited firms and one non-accredited firm. Findings – The study indicates that the logo and symbols of the Standard have minimal meaning and significance for the interviewees and their outlook on potential employees and customers. There were some indications, however, that the wider reputational implications of carrying the logo may have some potentially beneficial effects. Originality/value – The paper concludes that the overarching findings present a potentially serious issue for IiP, and that there is a need to understand further the impact and value of the logo and symbols