Mathematical modelling of tumour-induced angiogenesis

The growth of solid tumours beyond a critical size is dependent upon angiogenesis, the formation of new blood vessels from an existing vasculature. Tumours may remain dormant at microscopic sizes for some years before switching to a mode in which growth of a supportive vasculature is initiated. The new blood vessels supply nutrients, oxygen, and access to routes by which tumour cells may travel to other sites within the host (metastasize). In recent decades an abundance of biological research has focused on tumour-induced angiogenesis in the hope that treatments targeted at the vasculature may result in a stabilisation or regression of the disease: a tantalizing prospect. The complex and fascinating process of angiogenesis has also attracted the interest of researchers in the field of mathematical biology, a discipline that is, for mathematics, relatively new. The challenge in mathematical biology is to produce a model that captures the essential elements and critical dependencies of a biological system. Such a model may ultimately be used as a predictive tool. In this thesis we examine a number of aspects of tumour-induced angiogenesis, focusing on growth of the neovasculature external to the tumour. Firstly we present a one-dimensional continuum model of tumour-induced angiogenesis in which elements of the immune system or other tumour-cytotoxins are delivered via the newly formed vessels. This model, based on observations from experiments by Judah Folkman et al., is able to show regression of the tumour for some parameter regimes. The modelling highlights a number of interesting aspects of the process that may be characterised further in the laboratory. The next model we present examines the initiation positions of blood vessel sprouts on an existing vessel, in a two-dimensional domain. This model hypothesises that a simple feedback inhibition mechanism may be used to describe the spacing of these sprouts with the inhibitor being produced by breakdown of the existing vessel's basement membrane. Finally, we have developed a stochastic model of blood vessel growth and anastomosis in three dimensions. The model has been implemented in C++, includes an openGL interface, and uses a novel algorithm for calculating proximity of the line segments representing a growing vessel. This choice of programming language and graphics interface allows for near-simultaneous calculation and visualisation of blood vessel networks using a contemporary personal computer. In addition the visualised results may be transformed interactively, and drop-down menus facilitate changes in the parameter values. Visualisation of results is of vital importance in the communication of mathematical information to a wide audience, and we aim to incorporate this philosophy in the thesis. As biological research further uncovers the intriguing processes involved in tumourinduced angiogenesis, we conclude with a comment from mathematical biologist Jim Murray, Mathematical biology is : : : the most exciting modern application of mathematics.

Learning English in an English speaking world : examining opportunities for intercultural understandings and connectedness through representations of identities in English language textbooks

With the recognition that language both reflects and constructs culture and English now widely acknowledged as an international language, the cul-tural content of language teaching materials is now being problematised. Through a quantitative analysis, this chapter focuses on opportunities for intercultural understanding and connectedness through representations of the identities that appear in two leading English language textbooks. The analyses reveal that the textbooks orientate towards British and western identities with representations of people from non-European/non-Western backgrounds being notable for their absence, while others are hidden from view. Indeed there would appear to be a neocolonialist orientation in oper-ation in the textbooks, one that aligns English with the West. The chapter proposes arguments for the consideration of cultural diversity in English language teaching (ELT) textbook design, and promoting intercultural awareness and acknowledging the contexts in which English is now being used. It also offers ways that teachers can critically reflect on existing ELT materials and proposes arguments for including different varieties of Eng-lish in order to ensure a level of intercultural understanding and connect-edness.

Mathematical modelling of the drying of sol gel microspheres

This thesis presents a mathematical model of the evaporation of colloidal sol droplets suspended within an atmosphere consisting of water vapour and air. The main purpose of this work is to investigate the causes of the morphologies arising within the powder collected from a spray dryer into which the precursor sol for Synroc™ is sprayed. The morphology is of significant importance for the application to storage of High Level Liquid Nuclear Waste. We begin by developing a model describing the evaporation of pure liquid droplets in order to establish a framework. This model is developed through the use of continuum mechanics and thermodynamic theory, and we focus on the specific case of pure water droplets. We establish a model considering a pure water vapour atmosphere, and then expand this model to account for the presence of an atmospheric gas such as air. We model colloidal particle-particle interactions and interactions between colloid and electrolyte using DLVO Theory and reaction kinetics, then incorporate these interactions into an expression for net interaction energy of a single particle with all other particles within the droplet. We account for the flow of material due to diffusion, advection, and interaction between species, and expand the pure liquid droplet models to account for the presence of these species. In addition, the process of colloidal agglomeration is modelled. To obtain solutions for our models, we develop a numerical algorithm based on the Control Volume method. To promote numerical stability, we formulate a new method of convergence acceleration. The results of a MATLAB™ code developed from this algorithm are compared with experimental data collected for the purposes of validation, and further analysis is done on the sensitivity of the solution to various controlling parameters.

Rights versus reality : the difficulty of providing 'access to English' in Queensland courts

This project reviewed the success of the Aboriginal English in the Courts booklet which was published by the Department of Justice and Attorney-General in 2000, with a view to improving access to the courts for speakers of Aboriginal English in Queensland. Surveys and interview were conducted with judges, magistrates, prosecutors, legal aid lawyers and courts registry staff. The feedback from the research has shown that the handbook has had little impact on ‘access to English’ in Queensland courts. The problems relate to the tension between protecting the rights of the accused under an adversarial system and legitimately introducing the issues of language uncertainty to the court in a non-prejudicial manner. In addition, the interviews have brought to light emerging language issues in remote communities that cannot be remedied under existing language policy mechanisms, such as the provision of interpreters or friends of court.

Meeting under the “Omei” Tree in the Torres Strait Islands : networks and funds of knowledge of mathematical ideas

This paper focuses on the turning point experiences that worked to transform the researcher during a preliminary consultation process to seek permission to conduct of a small pilot project on one Torres Strait Island. The project aimed to learn from parents how they support their children in their mathematics learning. Drawing on a community research design, a consultative meeting was held with one Torres Strait Islander community to discuss the possibility of piloting a small project that focused on working with parents and children to learn about early mathematics processes. Preliminary data indicated that parents use networks in their community. It highlighted the funds of knowledge of mathematics that exist in the community and which are used to teach their children. Such knowledges are situated within a community’s unique histories, culture and the voices of the people. “Omei” tree means the Tree of Wisdom in the Island community.

‘Personal Response’ and English Teaching

A case study relating to secondary education, examining the teacher student relationship as it operates within the English classroom is the topic of this paper. It describes how a certain conception of 'personal response' to literature provided a means for the teacher/counsellor to form the ethical capacities of children. 'Personal response' is usually associated with the moment in which the child is freed to be most natural. But for all the emphasis upon the irreducibly individual nature of the 'genuinely felt response', this pedagogic exercise finds its place within a series of strategies designed both to cherish and correct the child, to nurture and to scrutinise, to guide and to reconstruct.

Reading in the Australian curriculum English : describing the effects of structure and organisation on multimodal texts

The recently introduced Australian Curriculum: English Version 3.0 (Australian Curriculum, Assessment and Reporting Authority [ACARA], 2012) requires students to ‘read’ multimodal text and describe the effects of structure and organisation. We begin this article by tracing the variable understandings of what reading multimodal text might entail through the Framing Paper (National Curriculum Board, 2008), the Framing Paper Consultation Report (National Curriculum Board, 2009a), the Shaping Paper (National Curriculum Board, 2009b) and Version 3.0 of the Australian Curriculum English (ACARA, 2012). Our findings show that the theoretical and descriptive framework for doing so is implicit. Drawing together multiple but internally coherent theories from the field of semiotics, we suggest one way to work towards three Year 5 learning outcomes from the reading/writing mode. The affordances of assembling a broad but explicit technical metalanguage for an informed reading of the integrated design elements of multimodal texts are noted.

Numerical simulation of a fractional mathematical model for epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider numerical simulation of fractional model based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in advection and diffusion terms belong to the intervals (0; 1) or (1; 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of the Riemann-Liouville and Gr¨unwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

The relationship between listening and other language skills in International English Language Testing System

Listening comprehension is the primary channel of learning a language. Yet of the four dominant macro-skills (listening, speaking, reading and writing), it is often difficult and inaccessible for second and foreign language learners due to its implicit process. The secondary skill, speaking, proceeds listening cognitively. Aural/oral skills precede the graphic skills, such as reading and writing, as they form the circle of language learning process. However, despite the significant relationship with other language skills, listening comprehension is treated lightly in the applied linguistics research. Half of our daily conversation and three quarters of classroom interaction are virtually devoted to listening comprehension. To examine the relationship of listening skill with other language skills, the outcome of 1800 Iranian participants undertaking International English Language Testing System (IELTS) in Tehran indicates the close correlation between listening comprehension and the overall language proficiency.

Metacognitive strategy instruction in English as Foreign Language (EFL) listening skill

Listening skill is a critical part of language learning in general, and second, and foreign language learning, in particular. However, the process of this basic skill has been overlooked compared to other skills such as speaking, reading and writing, in terms of an explicit instruction, and the product of listening is instead mainly tested indirectly through comprehension questions in classrooms. Instruction of metacognitive strategies demonstrates the pivotal impact on second language listening skill development. In this vein, this study used a mixed method with an experimental male group (N = 30) listened to texts using process-approach pedagogy directed students through metacognitive strategies over a semester (10 weeks) in Iran. To investigate the impact of metacognitive strategy instruction, the following approaches were implemented. First, IELTS listening test was used to track any development of listening comprehension. Second, using Vandergrift et al. (2006) Metacognitive Awareness Listening Questionnaire (MALQ) helped examine students’ use of metacognitive strategies in listening comprehension. Finally, interviews were used to examine students’ use of strategies in listening. The results showed that students had a development in comprehension of IELTS listening test, but no statistical significant development of metacognitive awareness in listening was demonstrated. Students and teacher reported in the interviews students used multiple strategies to approach listening comprehension besides metacognitive strategies.

The impact of English as a Foreign Language (EFL) listening comprehension through first language (L1) listening strategy training

Listening is the basic and complementary skill in second language learning. The term listening is used in language teaching to refer to a complex process that allows us to understand spoken language. Listening, the most widely used language skill, is often used in conjunction with the other skills of speaking, reading and writing. Listening is not only a skill area in primary language performance (L1), but is also a critical means of acquiring a second language (L2). Listening is the channel in which we process language in real time – employing pacing, units of encoding and decoding (the 2 processes are central to interpretation and meaning making) and pausing (allows for reflection) that are unique to spoken language. Despite the wide range of areas investigated in listening strategies during training, there is a lack of research looking specifically at how effectively L1 listening strategy training may transfer to L2. To investigate the development of any such transfer patterns the instructional design and implementation of listening strategy of L1 will be critical.