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.

A mathematical framework for expanding a railway’s theoretical capacity

Analytical techniques for measuring and planning railway capacity expansion activities have been considered in this article. A preliminary mathematical framework involving track duplication and section sub divisions is proposed for this task. In railways these features have a great effect on network performance and for this reason they have been considered. Additional motivations have also arisen from the limitations of prior models that have not included them.

An integrated mathematical approach to measure the capacity of MMTS

This article focusses upon multi-modal transportation systems (MMTS) and the issues surrounding the determination of system capacity. For that purpose a multi-objective framework is advocated that integrates all the different modes and many different competing capacity objectives. This framework is analytical in nature and facilitates a variety of capacity querying and capacity expansion planning.

Simplified Mathematical Model for Effects of Freezing on the Low-Temperature Performance of the Lead-Acid Battery

Discharge periods of lead-acid batteries are significantly reduced at subzero centigrade temperatures. The reduction is more than what can he expected due to decreased rates of various processes caused by a lowering of temperature and occurs despite the fact that active materials are available for discharge. It is proposed that the major cause for this is the freezing of the electrolyte. The concentration of acid decreases during battery discharge with a consequent increase in the freezing temperature. A battery freezes when the discharge temperature falls below the freezing temperature. A mathematical model is developed for conditions where charge-transfer reaction is the rate-limiting step. and Tafel kinetics are applicable. It is argued that freezing begins from the midplanes of electrodes and proceeds toward the reservoir in-between. Ionic conduction stops when one of the electrodes freezes fully and the time taken to reach that point, namely the discharge period, is calculated. The predictions of the model compare well to observations made at low current density (C/5) and at -20 and -40 degrees C. At higher current densities, however, diffusional resistances become important and a more complicated moving boundary problem needs to be solved to predict the discharge periods. (C) 2009 The Electrochemical Society.

Mathematical model of arterial stenosis

A mathematical model for pulsatile flow in a partially occluded tube is presented. The problem has applications in studying the effects of blood flow characteristics on atherosclerotic development. The model brings out the importance of the pulsatility of blood flow on separation and the stress distribution. The results obtained show fairly good agreement with the available experimental results.

Mathematical modelling of the impaction and spreading of spray droplets on leaves

This thesis concerns the development of mathematical models to describe the interactions that occur between spray droplets and leaves. Models are presented that not only provide a contribution to mathematical knowledge in the field of fluid dynamics, but are also of utility within the agrichemical industry. The thesis is presented in two parts. First, thin film models are implemented with efficient numerical schemes in order to simulate droplets on virtual leaf surfaces. Then the interception event is considered, whereby energy balance techniques are employed to instantaneously predict whether an impacting droplet will bounce, splash, or adhere to a leaf.

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.

Application of Mathematical Programming to the Plywood Design and Manufacturing Problem

Plywood manufacture includes two fundamental stages. The first is to peel or separate logs into veneer sheets of different thicknesses. The second is to assemble veneer sheets into finished plywood products. At the first stage a decision must be made as to the number of different veneer thicknesses to be peeled and what these thicknesses should be. At the second stage, choices must be made as to how these veneers will be assembled into final products to meet certain constraints while minimizing wood loss. These decisions present a fundamental management dilemma. Costs of peeling, drying, storage, handling, etc. can be reduced by decreasing the number of veneer thicknesses peeled. However, a reduced set of thickness options may make it infeasible to produce the variety of products demanded by the market or increase wood loss by requiring less efficient selection of thicknesses for assembly. In this paper the joint problem of veneer choice and plywood construction is formulated as a nonlinear integer programming problem. A relatively simple optimal solution procedure is developed that exploits special problem structure. This procedure is examined on data from a British Columbia plywood mill. Restricted to the existing set of veneer thicknesses and plywood designs used by that mill, the procedure generated a solution that reduced wood loss by 79 percent, thereby increasing net revenue by 6.86 percent. Additional experiments were performed that examined the consequences of changing the number of veneer thicknesses used. Extensions are discussed that permit the consideration of more than one wood species.

Mathematical model of an arterial stenosis, allowing for tethering

Closed-form solutions are presented for approximate equations governing the pulsatile flow of blood through models of mild axisymmetric arterial stenosis, taking into account the effect of arterial distensibility. Results indicate the existence of back-flow regions and the phenomenon of flow-reversal in the cross-sections. The effects of pulsatility of flow and elasticity of vessel wall for arterial blood flow through stenosed vessels are determined.

Mathematical modelling of human corneal oxygenation and cell kinetics in corneal epithelial wound healing

Healthy transparent cornea depends upon the regulation of fluid, nutrient and oxygen transport through the tissue to sustain cell metabolism and other critical processes for normal functioning. This research considers the corneal geometry and investigates oxygen distribution using a two-dimensional Monod kinetic model, showing that previous studies make assumptions that lead to predictions of near-anoxic levels of oxygen tension in the limbal regions of the cornea. It also considers the comparison of experimental spatial and temporal data with the predictions of novel mathematical models with respect to distributed mitotic rates during corneal epithelial wound healing.