Mathematical models of calcium and tight junctions in normal and reconstructed epidermis

This project investigated the calcium distributions of the skin, and the growth patterns of skin substitutes grown in the laboratory, using mathematical models. The research found that the calcium distribution in the upper layer of the skin is controlled by three different mechanisms, not one as previously thought. The research also suggests that tight junctions, which are adhesions between neighbouring skin cells, cannot be solely responsible for the differences in the growth patterns of skin substitutes and normal skin.

Second-order quantile methods for experts and combinatorial games

We aim to design strategies for sequential decision making that adjust to the difficulty of the learning problem. We study this question both in the setting of prediction with expert advice, and for more general combinatorial decision tasks. We are not satisfied with just guaranteeing minimax regret rates, but we want our algorithms to perform significantly better on easy data. Two popular ways to formalize such adaptivity are second-order regret bounds and quantile bounds. The underlying notions of 'easy data', which may be paraphrased as "the learning problem has small variance" and "multiple decisions are useful", are synergetic. But even though there are sophisticated algorithms that exploit one of the two, no existing algorithm is able to adapt to both. In this paper we outline a new method for obtaining such adaptive algorithms, based on a potential function that aggregates a range of learning rates (which are essential tuning parameters). By choosing the right prior we construct efficient algorithms and show that they reap both benefits by proving the first bounds that are both second-order and incorporate quantiles.

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.

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.

Differences in trunk accelerometry between frail and non-frail elderly persons in functional tasks

Background Physical conditions through gait and other functional task are parameters to consider for frailty detection. The aim of the present study is to measure and describe the variability of acceleration, angular velocity and trunk displacement in the ten meter Extended Timed Get-Up-and-Go test in two groups of frail and non-frail elderly people through instrumentation with the iPhone4® smartphone. Secondly, to analyze the differences and performance of the variance between the study groups (frail and non-frail). This is a cross-sectional study of 30 subjects aged over 65 years, 14 frail subjects and 16 non-frail subjects. Results The highest difference between groups in the Sit-to-Stand and Stand-to-Sit subphases was in the y axis (vertical vector). The minimum acceleration in the Stand-to-Sit phase was -2.69 (-4.17 / -0.96) m/s2 frail elderly versus -8.49 (-12.1 / -5.23) m/s2 non-frail elderly, p < 0.001. In the Gait Go and Gait Come subphases the biggest differences found between the groups were in the vertical axis: -2.45 (-2.77 /-1.89) m/s2 frail elderly versus -5.93 (-6.87 / -4.51) m/s2 non-frail elderly, p < 0.001. Finally, with regards to the turning subphase, the statistically significant differences found between the groups were greater in the data obtained from the gyroscope than from the accelerometer (the gyroscope data for the mean maximum peak value for Yaw movement angular velocity in the frail elderly was specifically 25.60°/s, compared to 112.8°/s for the non-frail elderly, p < 0.05). Conclusions The inertial sensor fitted in the iPhone4® is capable of studying and analyzing the kinematics of the different subphases of the Extended Timed Up and Go test in frail and non-frail elderly people. For the Extended Timed Up and Go test, this device allows more sensitive differentiation between population groups than the traditionally used variable, namely time.

Deficits on self ordered tasks associated with hyperostosis frontalis interna

A 74 year old patient, EW, with dorsolateral frontal cortical compression due to hyperostosis frontalis interna, in the absence of the Morgagni or Stewart-Morel syndromes, is described. In addition to conventional neuropsychological measures EW was administered one nonspatial and two spatial self ordered working memory tasks, as well as a standard measure of fluid intelligence or g. She showed impaired performance on all three self ordered working memory tasks compared with a normal control group of 10 subjects matched for age, education, sex, and IQ. By contrast, her performance on the fluid intelligence test was comparable with that of the controls. It is concluded that the compression of dorsolateral frontal cortex accompanying hyperostosis frontalis interna may produce selective cognitive impairment.

A dynamic real time scheduling methodology for the emergency department

This project constructs a scheduling solution for the Emergency Department. The schedules are generated in real-time to adapt to new patient arrivals and changing conditions. An integrated scheduling formulation assigns patients to beds and treatment tasks to resources. The schedule efficiency is assessed using waiting time and total care time experienced by patients. The solution algorithm incorporates dispatch rules, meta-heuristics and a new extended disjunctive graph formulation which provide high quality solutions in a fast time-frame for real time decision support. This algorithm can be implemented in an electronic patient management system to improve patient flow in the Emergency Department.

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.

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.

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.