The mathematical modelling of cheese ripening

A mathematical model is developed for the ripening of cheese. Such models may assist predicting final cheese quality using measured initial composition. The main constituent chemical reactions are described with ordinary differential equations. Numerical solutions to the model equations are found using Matlab. Unknown parameter values have been fitted using experimental data available in the literature. The results from the numerical fitting are in good agreement with the data. Statistical analysis is performed on near infrared data provided to the MISG. However, due to the inhomogeneity and limited nature of the data, not many conclusions can be drawn from the analysis. A simple model of the potential changes in acidity of cheese is also considered. The results from this model are consistent with cheese manufacturing knowledge, in that the pH of cheddar cheese does not significantly change during ripening.

Enhancing the teaching and learning of mathematical visual images

The literacy demands of mathematics are very different to those in other subjects (Gough, 2007; O'Halloran, 2005; Quinnell, 2011; Rubenstein, 2007) and much has been written on the challenges that literacy in mathematics poses to learners (Abedi and Lord, 2001; Lowrie and Diezmann, 2007, 2009; Rubenstein, 2007). In particular, a diverse selection of visuals typifies the field of mathematics (Carter, Hipwell and Quinnell, 2012), placing unique literacy demands on learners. Such visuals include varied tables, graphs, diagrams and other representations, all of which are used to communicate information.

The Australian Qualifications Framework for bachelor degree in property economics

The Australian Qualifications Framework (AQF) requires every course in Australia to be reviewed and compliant by 2015. This paper compares the difference between AQF level 7 and level 8 and outlines the paradigm shift in course development, improvement and quality assurance. The AQF requires an outcome oriented process which influences the development, monitoring and implementation of AQF courses. Firstly the graduate profile is defined to underscore the direction of the property course development. Required graduate attributes are then defined, together with course learning outcomes. Each unit/subject assessment is then designed to reflect the desired learning outcomes, and then finally the unit/subject content is backfilled. This reverse engineered process will ensure that all students have been taught and assessed on the graduate attributes which will form the graduate profile. Therefore, monitoring the inclusion of learning outcomes on unit/subject level during course restructure and development is crucial to achieve the course learning outcomes. This paper recommends that further evaluation needs to be conducted in the course development phases by involving professional accreditation bodies, industry representatives, students and recent graduates in this course development process. It also discusses challenges for developing an undergraduate property course.

A behavioural economics inquiry into inequality in education: Three empirical essays

This thesis investigates behavioural processes for inequality in education and solutions to mitigate such effects, applying conceptual and methodological insights from behavioural and experimental economics. It explores relative age differences in economic preferences of young individuals, the influence of stereotypes and positive discrimination on performance, and evaluates a program that offers strong encouragement for educational achievement of indigenous high school students.

Statistical, electrical and mathematical analysis of water treed cross-linked polyethylene cable insulation

This work examined a new method of detecting small water filled cracks in underground insulation ('water trees') using data from commecially available non-destructive testing equipment. A testing facility was constructed and a computer simulation of the insulation designed in order to test the proposed ageing factor - the degree of non-linearity. This was a large industry-backed project involving an ARC linkage grant, Ergon Energy and the University of Queensland, as well as the Queensland University of Technology.

Scoring rules and abnormally low bids criteria in construction tenders: A taxonomic review

In the global construction context, the Best Value or Most Economically Advantageous Tender is becoming a widespread approach for contractor selection, as an alternative to other traditional awarding criteria such as the Lowest Price. In these multi-attribute tenders, the owner or auctioneer solicits proposals containing both a price bid and additional technical features. Once the proposals are received, each bidder's price bid is given an economic score according to a scoring rule, generally called an Economic Scoring Formula (ESF) and a technical score according to pre-specified criteria. Eventually, the contract is awarded to the bidder with the highest weighted overall score (economic + technical). However, Economic Scoring Formula selection by auctioneers is invariably and paradoxically a highly intuitive process in practice, involving few theoretical or empirical considerations, despite having being considered traditionally and mistakenly as objective, due to its mathematical nature. This paper provides a taxonomic classification of a wide variety of ESF and Abnormally Low Bid Criteria (ALBC) gathered in several countries with different tendering approaches. Practical implications concern the optimal design of price scoring rules in construction contract tenders, as well as future analyses of the effects of ESF and ALBC on competitive bidding behaviour.

Mathematical modelling of gas production and compositional shift of a CSG (coal seam gas) field: Local model development

In this work we discuss the development of a mathematical model to predict the shift in gas composition observed over time from a producing CSG (coal seam gas) well, and investigate the effect that physical properties of the coal seam have on gas production. A detailed (local) one-dimensional, two-scale mathematical model of a coal seam has been developed. The model describes the competitive adsorption and desorption of three gas species (CH4, CO2 and N2) within a microscopic, porous coal matrix structure. The (diffusive) flux of these gases between the coal matrices (microscale) and a cleat network (macroscale) is accounted for in the model. The cleat network is modelled as a one-dimensional, volume averaged, porous domain that extends radially from a central well. Diffusive and advective transport of the gases occurs within the cleat network, which also contains liquid water that can be advectively transported. The water and gas phases are assumed to be immiscible. The driving force for the advection in the gas and liquid phases is taken to be a pressure gradient with capillarity also accounted for. In addition, the relative permeabilities of the water and gas phases are considered as functions of the degree of water saturation.

Mathematical models for collective cell spreading

Collective cell spreading is frequently observed in development, tissue repair and disease progression. Mathematical modelling used in conjunction with experimental investigation can provide key insights into the mechanisms driving the spread of cell populations. In this study, we investigated how experimental and modelling frameworks can be used to identify several key features underlying collective cell spreading. In particular, we were able to independently quantify the roles of cell motility and cell proliferation in a spreading cell population, and investigate how these roles are influenced by factors such as the initial cell density, type of cell population and the assay geometry.

Submission to Senate Economics References Committee, An Inquiry in to Affordable Housing

Developer paid fees or infrastructure charges are a commonly used mechanism for local governments to pay for new infrastructure. However, property developers claim that these costs are merely passed on to home buyers, with adverse effects to housing affordability. Despite numerous government reports and many years of industry advocacy, there remains no empirical evidence in Australia to confirm or quantify this passing on effect to home buyers and the consequent effect on housing affordability. Hence there remains no data from which governments can base policy decision on, and the debate continues. This research examines the question of the impact of infrastructure charges on housing affordability in Australia. It employs hedonic regression methods to estimate the impact of infrastructure charges on house prices and vacant lot prices in Brisbane, Australia during 2005-2011, using a data set of 29,752 house sales, comprising 4,699 new house sales and 25,053 existing house sales and 13,739 lot sales. The regression results for the effect of infrastructure charges on house prices in Brisbane indicated that for every $1.00 of infrastructure charge levied on developers, all house prices increase by $3.69 or a 369% overpassing of these government levies onto home buyers. Thus, this one government levy could be responsible for $877 per month on home owner mortgage repayments in Brisbane, Queensland. This research is consistent with international findings, that support the proposition that developer paid infrastructure charges are passed on to home buyers and are a significant contributor to increasing house prices and reduced housing affordability. Understanding who really pays for urban infrastructure is critical to both the housing affordability and infrastructure funding debates in Australia and this research provides the first empirical data for policy makers to assess their policy objectives and outcomes against.

Interaction design for tablet based edutainment systems for mathematical education of primary student

Mathematics has been perceived as the core area of learning in most educational systems around the world including Sri Lanka. Unfortunately, it is clearly visible that a majority of Sri Lankan students are failing in their basic mathematics when the recent grade five scholarship examination and ordinary level exam marks are analysed. According to Department of Examinations Sri Lanka , on average, over 88 percent of the students are failing in the grade 5 scholarship examinations where mathematics plays a huge role while about 50 percent of the students fail in there ordinary level mathematics examination. Poor or lack of basic mathematics skills has been identified as the root cause.

Early mathematical learning: Number processing skills and executive function at 5 and 8 years of age

This research investigated differences and associations in performance in number processing and executive function for children attending primary school in a large Australian metropolitan city. In a cross-sectional study, performance of 25 children in the first full-time year of school, (Prep; mean age = 5.5 years) and 21 children in Year 3 (mean age = 8.5 years) completed three number processing tasks and three executive function tasks. Year 3 children consistently outperformed the Prep year children on measures of accuracy and reaction time, on the tasks of number comparison, calculation, shifting, and inhibition but not on number line estimation. The components of executive function (shifting, inhibition, and working memory) showed different patterns of correlation to performance on number processing tasks across the early years of school. Findings could be used to enhance teachers’ understanding about the role of the cognitive processes employed by children in numeracy learning, and so inform teachers’ classroom practices.

A mathematical model for intermittent microwave convective (IMCD) drying of food materials

Intermittent microwave convective drying (IMCD) is an advanced technology that improves both energy efficiency and food quality in drying. Modelling of IMCD is essential to understand the physics of this advanced drying process and to optimize the microwave power level and intermittency during drying. However, there is still a lack of modelling studies dedicated to IMCD. In this study, a mathematical model for IMCD was developed and validated with experimental data. The model showed that the interior temperature of the material was higher than the surface in IMCD, and that the temperatures fluctuated and redistributed due to the intermittency of the microwave power. This redistribution of temperature could significantly contribute to the improvement of product quality during IMCD. Limitations when using Lambert's Law for microwave heat generation were identified and discussed.

On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process

Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration.

Mathematical modeling for improved greenhouse gas balances, agro-ecosystems, and policy development: Lessons from the Australian experience

If the land sector is to make significant contributions to mitigating anthropogenic greenhouse gas (GHG) emissions in coming decades, it must do so while concurrently expanding production of food and fiber. In our view, mathematical modeling will be required to provide scientific guidance to meet this challenge. In order to be useful in GHG mitigation policy measures, models must simultaneously meet scientific, software engineering, and human capacity requirements. They can be used to understand GHG fluxes, to evaluate proposed GHG mitigation actions, and to predict and monitor the effects of specific actions; the latter applications require a change in mindset that has parallels with the shift from research modeling to decision support. We compare and contrast 6 agro-ecosystem models (FullCAM, DayCent, DNDC, APSIM, WNMM, and AgMod), chosen because they are used in Australian agriculture and forestry. Underlying structural similarities in the representations of carbon flows though plants and soils in these models are complemented by a diverse range of emphases and approaches to the subprocesses within the agro-ecosystem. None of these agro-ecosystem models handles all land sector GHG fluxes, and considerable model-based uncertainty exists for soil C fluxes and enteric methane emissions. The models also show diverse approaches to the initialisation of model simulations, software implementation, distribution, licensing, and software quality assurance; each of these will differentially affect their usefulness for policy-driven GHG mitigation prediction and monitoring. Specific requirements imposed on the use of models by Australian mitigation policy settings are discussed, and areas for further scientific development of agro-ecosystem models for use in GHG mitigation policy are proposed.

5-year Chlamydia vaccination programme could reverse disease-related koala population decline: Predictions from a mathematical model using field data

BACKGROUND Many koala populations around Australia are in serious decline, with a substantial component of this decline in some Southeast Queensland populations attributed to the impact of Chlamydia. A Chlamydia vaccine for koalas is in development and has shown promise in early trials. This study contributes to implementation preparedness by simulating vaccination strategies designed to reverse population decline and by identifying which age and sex category it would be most effective to target. METHODS We used field data to inform the development and parameterisation of an individual-based stochastic simulation model of a koala population endemic with Chlamydia. The model took into account transmission, morbidity and mortality caused by Chlamydia infections. We calibrated the model to characteristics of typical Southeast Queensland koala populations. As there is uncertainty about the effectiveness of the vaccine in real-world settings, a variety of potential vaccine efficacies, half-lives and dosing schedules were simulated. RESULTS Assuming other threats remain constant, it is expected that current population declines could be reversed in around 5-6 years if female koalas aged 1-2 years are targeted, average vaccine protective efficacy is 75%, and vaccine coverage is around 10% per year. At lower vaccine efficacies the immunological effects of boosting become important: at 45% vaccine efficacy population decline is predicted to reverse in 6 years under optimistic boosting assumptions but in 9 years under pessimistic boosting assumptions. Terminating a successful vaccination programme at 5 years would lead to a rise in Chlamydia prevalence towards pre-vaccination levels. CONCLUSION For a range of vaccine efficacy levels it is projected that population decline due to endemic Chlamydia can be reversed under realistic dosing schedules, potentially in just 5 years. However, a vaccination programme might need to continue indefinitely in order to maintain Chlamydia prevalence at a sufficiently low level for population growth to continue.