The African Institute for Mathematical Sciences

Its mission is to promote Mathematics and Science in Africa and to provide a focal point for Mathematics university training in Africa. It offers scholarships for up to 50 students to come and study for a period of nine months. Of the 50 students, about 15 positions are reserved for females. In the 2006/2007 intake there were over 250 applicants. The students are housed and fed and their return travel from their home town is fully funded. Lecturers also stay at AIMS and share their meals with the students, so that a rapport quickly develops. The students are away from their families and friends for nine months and are absolutely committed to the discipline of Mathematics. When they first arrive, some of them have little ability in English but since all tuition is in English they quickly learn. Some find the transitions difficult but they all support one another and at the end of their time their English skills are very good. The students do a series of subjects that last for about three weeks each, consisting of 30 contact hours, as well as a thesis/project. Each course has a number of assignments associated with it and these get evaluated. AIMS has seven or eight teaching assistants who help with the tutorials, marking, advice, and who are a vital component of AIMS.

Evolving noisy oscillatory dynamics in genetic regulatory networks

We introduce a genetic programming (GP) approach for evolving genetic networks that demonstrate desired dynamics when simulated as a discrete stochastic process. Our representation of genetic networks is based on a biochemical reaction model including key elements such as transcription, translation and post-translational modifications. The stochastic, reaction-based GP system is similar but not identical with algorithmic chemistries. We evolved genetic networks with noisy oscillatory dynamics. The results show the practicality of evolving particular dynamics in gene regulatory networks when modelled with intrinsic noise.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

A mathematical model for genetic regulation of the lactose operon

In this paper we construct a mathematical model for the genetic regulatory network of the lactose operon. This mathematical model contains transcription and translation of the lactose permease (LacY) and a reporter gene GFP. The probability of transcription of LacY is determined by 14 binding states out of all 50 possible binding states of the lactose operon based on the quasi-steady-state assumption for the binding reactions, while we calculate the probability of transcription for the reporter gene GFP based on 5 binding states out of 19 possible binding states because the binding site O2 is missing for this reporter gene. We have tested different mechanisms for the transport of thio-methylgalactoside (TMG) and the effect of different Hill coefficients on the simulated LacY expression levels. Using this mathematical model we have realized one of the experimental results with different LacY concentrations, which are induced by different concentrations of TMG.

Modelling word meaning using efficient tensor representations

Models of word meaning, built from a corpus of text, have demonstrated success in emulating human performance on a number of cognitive tasks. Many of these models use geometric representations of words to store semantic associations between words. Often word order information is not captured in these models. The lack of structural information used by these models has been raised as a weakness when performing cognitive tasks. This paper presents an efficient tensor based approach to modelling word meaning that builds on recent attempts to encode word order information, while providing flexible methods for extracting task specific semantic information.

An improved genetic algorithm and graph theory based method for optimal sectionalizer switch placement in distribution networks with DG

In this paper a new graph-theory and improved genetic algorithm based practical method is employed to solve the optimal sectionalizer switch placement problem. The proposed method determines the best locations of sectionalizer switching devices in distribution networks considering the effects of presence of distributed generation (DG) in fitness functions and other optimization constraints, providing the maximum number of costumers to be supplied by distributed generation sources in islanded distribution systems after possible faults. The proposed method is simulated and tested on several distribution test systems in both cases of with DG and non DG situations. The results of the simulations validate the proposed method for switch placement of the distribution network in the presence of distributed generation.

Business process management : theory on progression and maturity

Business Process Management (BPM) is a topic that continues to grow in significance as organisations seek to gain and sustain competitive advantage in an increasingly global environment. Despite anecdotal evidence of organisations improving performance by pursuing a BPM approach, there is little theory that explains and substantiates this relationship. This study provides the first theory on the progression and maturity of BPM Initiatives within organisations and provides a vital starting block upon which future research in this area can build. The Researcher starts by clearly defining three key terms (BPM Initiative, BPM Progression and BPM Maturity), showing the relationship between these three concepts and proposing their relationship with Organisational Performance. The Researcher then combines extant literature and use of the Delphi Technique and the case study method to explore the progression and measurement of the BPM Initiatives within organisations. The study builds upon the principles of general theories including the Punctuated Equilibrium Model and Dynamic Capabilities to present theory on BPM Progression and BPM Maturity. Using the BPM Capability Framework developed through an international Delphi study series, the Researcher shows how the specific organisational context influences which capability areas an organisation chooses to progress. By comparing five separate organisations over an extended time the Researcher is able to show that, despite this disparity, there is some evidence of consistency with regard to the capability areas progressed. This suggests that subsequent identification of progression paths may be possible. The study also shows that the approach and scope taken to BPM within each organisation is a likely predictor of such paths. These outcomes result in the proposal of a formative model for measuring BPM Maturity.

A preliminary theory of dark network resilience

A crucial contemporary policy question for governments across the globe is how to cope with international crime and terrorist networks. Many such “dark” networks—that is, networks that operate covertly and illegally—display a remarkable level of resilience when faced with shocks and attacks. Based on an in-depth study of three cases (MK, the armed wing of the African National Congress in South Africa during apartheid; FARC, the Marxist guerrilla movement in Colombia; and the Liberation Tigers of Tamil Eelam, LTTE, in Sri Lanka), we present a set of propositions to outline how shocks impact dark network characteristics (resources and legitimacy) and networked capabilities (replacing actors, linkages, balancing integration and differentiation) and how these in turn affect a dark network's resilience over time. We discuss the implications of our findings for policymakers.

A communitarian theory of the education rights of students with disabilities

There is a lack of writing on the issue of the education rights of people with disabilities by authors of any theoretical persuasion. While the deficiency of theory may be explained by a variety of historical, philosophical and practical considerations, it is a deficiency which must be addressed. Otherwise, any statement of rights rings out as hollow rhetoric unsupported by sound reason and moral rectitude. This paper attempts to address this deficiency in education rights theory by postulating a communitarian theory of the education rights of people with disabilities. The theory is developed from communitarian writings on the role of education in democratic society. The communitarian school, like the community within which it nests, is inclusive. Schools both reflect and model the shape of communitarian society and have primary responsibility for teaching the knowledge and virtues which will allow citizens to belong to and function within society. Communitarians emphasise responsibilities, however, as the corollary of rights and require the individual good to yield to community good when the hard cases arise. The article not only explains the basis of the right to an inclusive education, therefore, but also engages with the difficult issue of when such a right may not be enforceable.

Re-thinking how we plan to address technically complex problems : drawing on planning theory to guide practice in revision of land use plans in coastal high hazard zones

Queensland's new State Planning Policy for Coastal Protection, released in March and approved in April 2011 as part of the Queensland Coastal Plan, stipulates that local governments prepare and implement adaptation strategies for built up areas projected to be subject to coastal hazards between present day and 2100. Urban localities within the delineated coastal high hazard zone (as determined by models incorporating a 0.8 meter rise in sea level and a 10% increase in the maximum cyclone activity) will be required to re-evaluate their plans to accommodate growth, revising land use plans to minimise impacts of anticipated erosion and flooding on developed areas and infrastructure. While implementation of such strategies would aid in avoidance or minimisation of risk exposure, communities are likely to face significant challenges in such implementation, especially as development in Queensland is so intensely focussed upon its coasts with these new policies directing development away from highly desirable waterfront land. This paper examines models of planning theory to understand how we plan when faced with technically complex problems towards formulation of a framework for evaluating and improving practice.

Knowledge-based urban development redefined : from theory to practice knowledge-based development of cities

The concept of knowledge-based urban development has first come to the urban planning and development agenda during the very last years of the 20th century as a promising paradigm to support the transformation process of cities into knowledge cities and their societies into knowledge societies. However, soon after the exponentially rapid advancements experienced, during the first decade of the 21st century, particularly, in the domains of economy, society, management and technology along with the severe impacts of climate change, have made the redefinition of the term a necessity. This paper, first, reports the findings of the review of the relatively short but dynamic history of urbanisation experiences of our cities around the globe. The paper, then, focuses on the 21st century urbanisation context and discusses the conceptual base of the knowledge-based development of cities and how this concept found application ground in many parts of the world. Following this, the paper speculates development of future cities by particularly highlighting potential challenges and opportunities that previously have not been fully considered. This paper, lastly, introduces and elaborates how relevant theories support the better conceptualisation of this relatively new, but rapidly emerging paradigm, and redefines it accordingly.

A grounded theory of protest movement continuity

Using a thematic story telling approach which draws on ethnographic method, a grounded theory of protest movement continuity is presented. The grounded theory draws from theories and activist stories relating to the facilitative role of movement networks, social contagion theory and the cultural experience of activism. It highlights the contagious influence of protest networks in maintaining protest continuity over time and how this leads to common perceptions of development risk and opportunity within communities. It also reveals how communities use collective values and identity, social capital, emotional dynamics and symbolic artifacts to maintain protest continuity.

To bound or not to bound: preliminary Theory of Time Bounds Specification in strategic alliances

This article augments Resource Dependence Theory with Real Options reasoning in order to explain time bounds specification in strategic alliances. Whereas prior work has found about a 50/50 split between alliances that are time bound and those that are open-ended, their substantive differences and antecedents are ill understood. To address this, we suggest that the two alliance modes present different real options trade-offs in adaptation to environmental uncertainty: ceteris paribus, time-bound alliances are likely to provide abandonment options over open-ended alliances, but require additional investments to extend the alliance when this turns out to be desirable after formation. Open-ended alliances are likely to provide growth options over open-ended alliances, but they demand additional effort to abandon the alliance if post-formation circumstances so desire. Therefore, we expect time bounds specification to be a function of environmental uncertainty: organizations in more uncertain environments will be relatively more likely to place time bounds on their strategic alliances. Longitudinal archival and survey data collected amongst 39 industry clusters provides empirical support for our claims, which contribute to the recent renaissance of resource dependence theory by specifying the conditions under which organizations choose different time windows in strategic partnering.

Converting theory to practice : university-school collaboration on devising strategies for mentoring pedagogical knowledge

There appears no shortage of theorists for preservice teacher education; however many ideas are abandoned without practical applications. Indeed, it can take years for theories to materialise into practice, if they materialise at all. The quality of preservice teacher education is central for enhancing an education system, and mentors’ roles can assist to shape preservice teachers’ development within the school context. Yet mentoring can be haphazard without being underpinned by a theoretical framework. A mentoring model (personal attributes, system requirements, pedagogical knowledge, modelling, and feedback) has emerged from research and the literature to guide mentors’ practices. This qualitative study investigates mentors’ pedagogical knowledge as one factor crucial to the mentoring process. More specifically, this study involves a questionnaire and audio-recorded focus group meetings with experienced mentors (n=14) who deliberated on devising practical applications for mentoring pedagogical knowledge. Findings revealed that these experienced mentors pinpointed practical applications around a mentor’s role for providing pedagogical knowledge to the mentee. These strategies were varied and demonstrated that any one mentoring practice may be approached from a number of different angles. Nevertheless, there were core mentoring practices in pedagogical knowledge such as showing the mentee how to plan for teaching, articulating classroom management approaches, and talking about how to connect learning to assessment. Mentors may require education on current mentoring practices with practical strategies that are linked to theoretical underpinnings.

An evaluation of the pattern and structure mathematics awareness program in the early school years

This paper reports a 2-year longitudinal study on the effectiveness of the Pattern and Structure Mathematical Awareness Program (PASMAP) on students’ mathematical development. The study involved 316 Kindergarten students in 17 classes from four schools in Sydney and Brisbane. The development of the PASA assessment interview and scale are presented. The intervention program provided explicit instruction in mathematical pattern and structure that enhanced the development of students’ spatial structuring, multiplicative reasoning, and emergent generalisations. This paper presents the initial findings of the impact of the PASMAP and illustrates students’ structural development.