Novel solutions for a model of wound healing angiogenesis

We prove the existence of novel, shock-fronted travelling wave solutions to a model of wound healing angiogenesis studied in Pettet et al (2000 IMA J. Math. App. Med. 17 395–413) assuming two conjectures hold. In the previous work, the authors showed that for certain parameter values, a heteroclinic orbit in the phase plane representing a smooth travelling wave solution exists. However, upon varying one of the parameters, the heteroclinic orbit was destroyed, or rather cut-off, by a wall of singularities in the phase plane. As a result, they concluded that under this parameter regime no travelling wave solutions existed. Using techniques from geometric singular perturbation theory and canard theory, we show that a travelling wave solution actually still exists for this parameter regime. We construct a heteroclinic orbit passing through the wall of singularities via a folded saddle canard point onto a repelling slow manifold. The orbit leaves this manifold via the fast dynamics and lands on the attracting slow manifold, finally connecting to its end state. This new travelling wave is no longer smooth but exhibits a sharp front or shock. Finally, we identify regions in parameter space where we expect that similar solutions exist. Moreover, we discuss the possibility of more exotic solutions.

Canards in advection-reaction-diffusion systems in one spatial dimension

This thesis contains a mathematical investigation of the existence of travelling wave solutions to singularly perturbed advection-reaction-diffusion models of biological processes. An enhanced mathematical understanding of these solutions and models is gained via the identification of canards (special solutions of fast/slow dynamical systems) and their role in the existence of the most biologically relevant, shock-like solutions. The analysis focuses on two existing models. A new proof of existence of a whole family of travelling waves is provided for a model describing malignant tumour invasion, while new solutions are identified for a model describing wound healing angiogenesis.

Butterfly catastrophe for fronts in a three-component reaction–diffusion system

We study the dynamics of front solutions in a three-component reaction–diffusion system via a combination of geometric singular perturbation theory, Evans function analysis, and center manifold reduction. The reduced system exhibits a surprisingly complicated bifurcation structure including a butterfly catastrophe. Our results shed light on numerically observed accelerations and oscillations and pave the way for the analysis of front interactions in a parameter regime where the essential spectrum of a single front approaches the imaginary axis asymptotically.

Characterization of alluvial formation by stochastic modelling of paleo-fluvial processes: The concept and method

Modelling fluvial processes is an effective way to reproduce basin evolution and to recreate riverbed morphology. However, due to the complexity of alluvial environments, deterministic modelling of fluvial processes is often impossible. To address the related uncertainties, we derive a stochastic fluvial process model on the basis of the convective Exner equation that uses the statistics (mean and variance) of river velocity as input parameters. These statistics allow for quantifying the uncertainty in riverbed topography, river discharge and position of the river channel. In order to couple the velocity statistics and the fluvial process model, the perturbation method is employed with a non-stationary spectral approach to develop the Exner equation as two separate equations: the first one is the mean equation, which yields the mean sediment thickness, and the second one is the perturbation equation, which yields the variance of sediment thickness. The resulting solutions offer an effective tool to characterize alluvial aquifers resulting from fluvial processes, which allows incorporating the stochasticity of the paleoflow velocity.

Influences of Allee effects in the spreading of malignant tumours

A recent study by Korolev et al. [Nat. Rev. Cancer, 14:371–379, 2014] evidences that the Allee effect—in its strong form, the requirement of a minimum density for cell growth—is important in the spreading of cancerous tumours. We present one of the first mathematical models of tumour invasion that incorporates the Allee effect. Based on analysis of the existence of travelling wave solutions to this model, we argue that it is an improvement on previous models of its kind. We show that, with the strong Allee effect, the model admits biologically relevant travelling wave solutions, with well-defined edges. Furthermore, we uncover an experimentally observed biphasic relationship between the invasion speed of the tumour and the background extracellular matrix density.

Application of a continuum theory to vertical vibrations of a layer of granular material

Many interesting phenomena have been observed in layers of granular materials subjected to vertical oscillations; these include the formation of a variety of standing wave patterns, and the occurrence of isolated features called oscillons, which alternately form conical heaps and craters oscillating at one-half of the forcing frequency. No continuum-based explanation of these phenomena has previously been proposed. We apply a continuum theory, termed the double-shearing theory, which has had success in analyzing various problems in the flow of granular materials, to the problem of a layer of granular material on a vertically vibrating rigid base undergoing vertical oscillations in plane strain. There exists a trivial solution in which the layer moves as a rigid body. By investigating linear perturbations of this solution, we find that at certain amplitudes and frequencies this trivial solution can bifurcate. The time dependence of the perturbed solution is governed by Mathieu’s equation, which allows stable, unstable and periodic solutions, and the observed period-doubling behaviour. Several solutions for the spatial velocity distribution are obtained; these include one in which the surface undergoes vertical velocities that have sinusoidal dependence on the horizontal space dimension, which corresponds to the formation of striped standing waves, and is one of the observed patterns. An alternative continuum theory of granular material mechanics, in which the principal axes of stress and rate-of-deformation are coincident, is shown to be incapable of giving rise to similar instabilities.

Mesenchymal stem cells in osteoarthritis therapy : current status of theory, technology, and applications

Osteoarthritis (OA) is a chronic, non-inflammatory type of arthritis, which usually affects the movable and weight bearing joints of the body. It is the most common joint disease in human beings and common in elderly people. Till date, there are no safe and effective diseases modifying OA drugs (DMOADs) to treat the millions of patients suffering from this serious and debilitating disease. However, recent studies provide strong evidence for the use of mesenchymal stem cell (MSC) therapy in curing cartilage related disorders. Due to their natural differentiation properties, MSCs can serve as vehicles for the delivery of effective, targeted treatment to damaged cartilage in OA disease. In vitro, MSCs can readily be tailored with transgenes with anti-catabolic or pro-anabolic effects to create cartilage-friendly therapeutic vehicles. On the other hand, tissue engineering constructs with scaffolds and biomaterials holds promising biological cartilage therapy. Many of these strategies have been validated in a wide range of in vitro and in vivo studies assessing treatment feasibility or efficacy. In this review, we provide an outline of the rationale and status of stem-cell-based treatments for OA cartilage, and we discuss prospects for clinical implementation and the factors crucial for maintaining the drive towards this goal.

Self-determination theory as applied to the design of a software learning system using whole-body controls

Whole-body computer control interfaces present new opportunities to engage children with games for learning. Stomp is a suite of educational games that use such a technology, allowing young children to use their whole body to interact with a digital environment projected on the floor. To maximise the effectiveness of this technology, tenets of self-determination theory (SDT) are applied to the design of Stomp experiences. By meeting user needs for competence, autonomy, and relatedness our aim is to increase children's engagement with the Stomp learning platform. Analysis of Stomp's design suggests that these tenets are met. Observations from a case study of Stomp being used by young children show that they were highly engaged and motivated by Stomp. This analysis demonstrates that continued application of SDT to Stomp will further enhance user engagement. It also is suggested that SDT, when applied more widely to other whole-body multi-user interfaces, could instil similar positive effects.

The guide to the project management body of knowledge (PMBOK Guide) : applicability and contribution to project success in Australia

The PMBOK Guide is one of the most influential publications concerning the knowledge of the project manangement. Moreover, the pervasion of this guide seems to be set to increase as the basis of accreditation - in conjunction with the increasing global trend toward obtaining project management professional status. However, despite the influence and strengthening profile of this guide, reports continue to be published that detail numerous project failures in a wide range of different industries. The PMBOK Guide comprises mainly declarative (know-what) and procedural (know-how) information. In this sense, the guide is largely normative and provides a very good example of the limitations of this approach as highlighted by proponents of a move to the genuine application of positibe theory in project management.----- The aim of this paper is to determine the applicability of the guide in Australia and to determine the extent to which project success can be attributed to the guide. Project Managers from a variety of organisations were surveyed. This postal survey yielded 48 replies. Descriptive statistics was used to assess the incidence and effectivieness of all the processes in the guide. The results indicate that there were no processes that could be considered as peripheral or as a candidate for elimination from the guide. More specifically, all the processes were identified as either a key routine process or a key selective process and positively related to the level of project success. However, the results also indicated that other major factors pertaining to causal knowledge (know-why) are, at least, equally important determinants of project success. It is concluded that declarative, procedural and causal knowledge are all valuable, and given the preponderance of the first two types of knowledge, there seems to be an urgent need to now ensure an equal quest for causal knowledge. In terms of developing causal knowledge, a good starting point would appear to be both positive theory from production and economics.

Increased body temperature following subarachnoid haemorrhage : a retrospective correlational study

Introduction: Nursing clinicians are primarily responsible for the monitoring and treatment of increased body temperature. The body temperature of patients during their acute care hospital stay is measured at regular repeated intervals. In the event a patient is assessed with an elevated temperature, a multitude of decisions are required. The action of instigating temperature reducing strategies is based upon the assumption that elevated temperature is harmful and that the strategy employed will have some beneficial effect. Background and Significance: The potential harmful effects of increased body temperature (fever, hyperthermia) following neurological insult are well recognised. Although few studies have investigated this phenomenon in the diagnostic population of non-traumatic subarachnoid haemorrhage, it has been demonstrated that increased body temperature occurs in 41 to 72% of patients with poor clinical outcome. However, in the Australian context the frequency, or other characteristics of increased body temperature, as well as the association between increased body temperature with poor clinical outcome has not been established. Design: This study used a correlational study design to: describe the frequency, duration and timing of increased body temperature; determine the association between increased body temperature and clinical outcome; and describe the clinical interventions used to manage increased body temperature in patients with non-traumatic subarachnoid haemorrhage. A retrospective clinical chart audit was conducted on 43 patients who met the inclusion criteria. Findings: The major findings of this study were: increased body temperature occurred frequently; persisted for a long time; and onset did not occur until 20 hours after primary insult; increased body temperature was associated with death or dependent outcome; and no intervention was recorded in many instances. Conclusion: This study has quantified in a non-traumatic subarachnoid haemorrhage patient population the characteristics of increased body temperature, established an association between increased body temperature with death or dependent outcome and described the current management of elevated temperatures in the Australian context to improve nursing practice, education and research.

An investigation into the use of a blended model of learning in a first year accounting subject

The weaknesses of ‗traditional‘ modes of instruction in accounting education have been widely discussed. Many contend that the traditional approach limits the ability to provide opportunities for students to raise their competency level and allow them to apply knowledge and skills in professional problem solving situations. However, the recent body of literature suggests that accounting educators are indeed actively experimenting with ‗non-traditional‘ and ‗innovative‘ instructional approaches, where some authors clearly favour one approach over another. But can one instructional approach alone meet the necessary conditions for different learning objectives? Taking into account the ever changing landscape of not only business environments, but also the higher education sector, the premise guiding the collaborators in this research is that it is perhaps counter productive to promote competing dichotomous views of ‗traditional‘ and ‗non-traditional‘ instructional approaches to accounting education, and that the notion of ‗blended learning‘ might provide a useful framework to enhance the learning and teaching of accounting. This paper reports on the first cycle of a longitudinal study, which explores the possibility of using blended learning in first year accounting at one campus of a large regional university. The critical elements of blended learning which emerged in the study are discussed and, consistent with the design-based research framework, the paper also identifies key design modifications for successive cycles of the research.

Achieving better stewardship of major infrastructure assets through configuration of governance arrangements utilising Stewardship Theory

Major infrastructure assets are often governed by a mix of public and private organizations, each fulfilling a specific and separate role i.e. policy, ownership, operation or maintenance. This mix of entities is a legacy of Public Choice Theory influenced NPM reforms of the late 20th century. The privatization of the public sector has resulted in agency theory based ‘self-interest’ relationships and governance arrangements for major infrastructure assets which emphasize economic efficiency but which do not do not advance non-economic public values and the collective Public Interest. The community is now requiring that governments fulfill their stewardship role of also satisfying non-economic public values such as sustainability and intergenerational responsibility. In the 21st century governance arrangements which minimize individual self-interest alone and look to also pursue the interests of other stakeholders have emerged. Relational contracts, Public-Private Partnerships (PPP’s) and hybrid mixes of organizations from the state, market and network modes (Keast et al 2006) provide options for governance which better meet the interests of contractors, government and the community there is emerging a body of research which extends the consideration of the immediate governance configuration to the metagovernance environment constituted by hierarchy, regulation, industry standards, trust, culture and values. Stewardship theory has reemerged as a valuable aid in the understanding of the features of governance configurations which establish relationships between principal and agent which maximize the agent acting in the interests of the principal, even to the detriment of the agent. This body of literature suggests that an improved stewardship outcome from infrastructure governance configurations can be achieved by the application of the emerging options as to the immediate governance configuration, and the surrounding metagovernance environment. Stewardship theory provides a framework for the design of the relationships within that total governance environment, focusing on the achievement of a better, complete stewardship outcome. This paper explores the directions future research might take in seeking to improve the understanding of the design of the governance of major, critical infrastructure assets.

Theory and its role in mathematics education

The increased recognition of the theory in mathematics education is evident in numerous handbooks, journal articles, and other publications. For example, Silver and Herbst (2007) examined ―Theory in Mathematics Education Scholarship‖ in the Second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007) while Cobb (2007) addressed ―Putting Philosophy to Work: Coping with Multiple Theoretical Perspectives‖ in the same handbook. And a central component of both the first and second editions of the Handbook of International Research in Mathematics Education (English, 2002; 2008) was ―advances in theory development.‖ Needless to say, the comprehensive second edition of the Handbook of Educational Psychology (Alexander & Winne, 2006) abounds with analyses of theoretical developments across a variety of disciplines and contexts. Numerous definitions of ―theory‖ appear in the literature (e.g., see Silver & Herbst, in Lester, 2007). It is not our intention to provide a ―one-size-fits-all‖ definition of theory per se as applied to our discipline; rather we consider multiple perspectives on theory and its many roles in improving the teaching and learning of mathematics in varied contexts.

A 'deleterious' effect? : Australian legal education and the production of the legal identity

A body of critical legal scholarship argues that, by the time they have completed their studies, students who enter legal education holding social ideals and intending to use their legal education to achieve social change, have become cynical about the ability of the law to do so and no longer possess such ideals. This is explained by critical scholars to be the result of a process of ideological indoctrination, aimed at ensuring that graduates uphold the narrow and conservative interests of the legal profession and capitalist society, being exercised by law schools acting as adjuncts of the legal profession, and exercised upon the passive body of the law student. By using Foucault’s work on knowledge, power, and the subject to interrogate the assumptions upon which this narrative is based, this thesis intends to suggest a way of thinking differently to the approach taken by many critical legal scholars. It then uses an analytics of government (based on Foucault’s notion of ‘governmentality’) to consider the construction of the legal identity differently. It examines the ways in which the governance of the legal identity is rationalised, programmed, and implemented, in three Queensland law schools. It also looks at the way that five prescriptive texts to ‘surviving’ law school suggest students establish and practise a relation to themselves in order to construct their own legal identities. Overall, this analysis shows that governance is not simply conducted in the profession’s interests, but occurs due to a complex arrangement of different practices, which can lead to the construction of skilled legal professional identities as well as ethical lawyer-citizens that hold an interest in justice. The implications of such an analytics provide the basis for original ways of understanding legal education, and legal education scholarship.