A generative design system based on evolutionary and mathematical functions

Previous work by Professor John Frazer on Evolutionary Architecture provides a basis for the development of a system evolving architectural envelopes in a generic and abstract manner. Recent research by the authors has focused on the implementation of a virtual environment for the automatic generation and exploration of complex forms and architectural envelopes based on solid modelling techniques and the integration of evolutionary algorithms, enhanced computational and mathematical models. Abstract data types are introduced for genotypes in a genetic algorithm order to develop complex models using generative and evolutionary computing techniques. Multi-objective optimisation techniques are employed for defining the fitness function in the evaluation process.

Exploratory spatial analysis of social and environmental factors associated with the incidence of Ross River Virus in Brisbane, Australia

We used geographic information systems and a spatial analysis approach to explore the pattern of Ross River virus (RRV) incidence in Brisbane, Australia. Climate, vegetation and socioeconomic data in 2001 were obtained from the Australian Bureau of Meteorology, the Brisbane City Council and the Australian Bureau of Statistics, respectively. Information on the RRV cases was obtained from the Queensland Department of Health. Spatial and multiple negative binomial regression models were used to identify the socioeconomic and environmental determinants of RRV transmission. The results show that RRV activity was primarily concentrated in the northeastern, northwestern, and southeastern regions in Brisbane. Multiple negative binomial regression models showed that the spatial pattern of RRV disease in Brisbane seemed to be determined by a combination of local ecologic, socioeconomic, and environmental factors.

Chlamydial infection and spatial ascension of the female genital tract : a novel hybrid cellular automata and continuum mathematical model

Sexually transmitted chlamydial infection initially establishes in the endocervix in females, but if the infection ascends the genital tract, significant disease, including infertility, can result. Many of the mechanisms associated with chlamydial infection kinetics and disease ascension are unknown. We attempt to elucidate some of these processes by developing a novel mathematical model, using a cellular automata–partial differential equation model. We matched our model outputs to experimental data of chlamydial infection of the guinea-pig cervix and carried out sensitivity analyses to determine the relative influence of model parameters. We found that the rate of recruitment and action of innate immune cells to clear extracellular chlamydial particles and the rate of passive movement of chlamydial particles are the dominant factors in determining the early course of infection, magnitude of the peak chlamydial time course and the time of the peak. The rate of passive movement was found to be the most important factor in determining whether infection would ascend to the upper genital tract. This study highlights the importance of early innate immunity in the control of chlamydial infection and the significance of motility-diffusive properties and the adaptive immune response in the magnitude of infection and in its ascension.

Group metacognition during mathematical problem solving

Although various studies have shown that groups are more productive than individuals in complex mathematical problem solving, not all groups work together cooperatively. This review highlights that addressing organisational and cognitive factors to help scaffold group mathematical problem solving is necessary but not sufficient. Successful group problem solving also needs to incorporate metacognitive factors in order for groups to reflect on the organisational and cognitive factors influencing their group mathematical problem solving.

Promoting interdisciplinarity through mathematical modelling

This article presents one approach to addressing the important issue of interdisciplinarity in the primary school mathematics curriculum, namely, through realistic mathematical modelling problems. Such problems draw upon other disciplines for their contexts and data. The article initially considers the nature of modelling with complex systems and discusses how such experiences differ from existing problem-solving activities in the primary mathematics curriculum. Principles for designing interdisciplinary modelling problems are then addressed, with reference to two mathematical modelling problems— one based in the scientific domain and the other in the literary domain. Examples of the models children have created in solving these problems follow. A reflection on the differences in the diversity and sophistication of these models raises issues regarding the design of interdisciplinary modelling problems. The article concludes with suggested opportunities for generating multidisciplinary projects within the regular mathematics curriculum.

A fully Bayesian approach to inference for Coxian phase-type distributions with covariate dependent mean

Phase-type distributions represent the time to absorption for a finite state Markov chain in continuous time, generalising the exponential distribution and providing a flexible and useful modelling tool. We present a new reversible jump Markov chain Monte Carlo scheme for performing a fully Bayesian analysis of the popular Coxian subclass of phase-type models; the convenient Coxian representation involves fewer parameters than a more general phase-type model. The key novelty of our approach is that we model covariate dependence in the mean whilst using the Coxian phase-type model as a very general residual distribution. Such incorporation of covariates into the model has not previously been attempted in the Bayesian literature. A further novelty is that we also propose a reversible jump scheme for investigating structural changes to the model brought about by the introduction of Erlang phases. Our approach addresses more questions of inference than previous Bayesian treatments of this model and is automatic in nature. We analyse an example dataset comprising lengths of hospital stays of a sample of patients collected from two Australian hospitals to produce a model for a patient's expected length of stay which incorporates the effects of several covariates. This leads to interesting conclusions about what contributes to length of hospital stay with implications for hospital planning. We compare our results with an alternative classical analysis of these data.

Scaffolding students’ thinking in mathematical investigations

This article describes some of the issues that teachers might encounter when scaffolding students’ thinking during mathematical investigations. It describes four episodes where a teacher’s scaffolding failed to support students’ mathematical thinking and explores the reasons why the scaffolding was ineffective. Understanding what is ineffective and why is one way to improve pedagogical practice. As a background to these episodes, we first provide an overview of the mathematical investigation. Our paper concludes with some recommendations for judicious scaffolding during investigations.

Mixing colours: An ICT tool based on a semiotic framework for mathematical meaning-makng about ratio and fractions

This paper reports on the research and development of an ICT tool to facilitate the learning of ratio and fractions by adult prisoners. The design of the ICT tool was informed by a semiotic framework for mathematical meaning-making. The ICT tool thus employed multiple semiotic resources including topological, typological, and social-actional resources. The results showed that individual semiotic resource could only represent part of the mathematical concept, while at the same time it might signify something else to create a misconception. When multiple semiotic resources were utilised the mathematical ideas could be better learnt.

Mathematical models for describing the shape of the in vitro unstretched human crystalline lens

We developed orthogonal least-squares techniques for fitting crystalline lens shapes, and used the bootstrap method to determine uncertainties associated with the estimated vertex radii of curvature and asphericities of five different models. Three existing models were investigated including one that uses two separate conics for the anterior and posterior surfaces, and two whole lens models based on a modulated hyperbolic cosine function and on a generalized conic function. Two new models were proposed including one that uses two interdependent conics and a polynomial based whole lens model. The models were used to describe the in vitro shape for a data set of twenty human lenses with ages 7–82 years. The two-conic-surface model (7 mm zone diameter) and the interdependent surfaces model had significantly lower merit functions than the other three models for the data set, indicating that most likely they can describe human lens shape over a wide age range better than the other models (although with the two-conic-surfaces model being unable to describe the lens equatorial region). Considerable differences were found between some models regarding estimates of radii of curvature and surface asphericities. The hyperbolic cosine model and the new polynomial based whole lens model had the best precision in determining the radii of curvature and surface asphericities across the five considered models. Most models found significant increase in anterior, but not posterior, radius of curvature with age. Most models found a wide scatter of asphericities, but with the asphericities usually being positive and not significantly related to age. As the interdependent surfaces model had lower merit function than three whole lens models, there is further scope to develop an accurate model of the complete shape of human lenses of all ages. The results highlight the continued difficulty in selecting an appropriate model for the crystalline lens shape.

Elicitator : an expert elicitation tool for regression in ecology

Expert elicitation is the process of retrieving and quantifying expert knowledge in a particular domain. Such information is of particular value when the empirical data is expensive, limited, or unreliable. This paper describes a new software tool, called Elicitator, which assists in quantifying expert knowledge in a form suitable for use as a prior model in Bayesian regression. Potential environmental domains for applying this elicitation tool include habitat modeling, assessing detectability or eradication, ecological condition assessments, risk analysis, and quantifying inputs to complex models of ecological processes. The tool has been developed to be user-friendly, extensible, and facilitate consistent and repeatable elicitation of expert knowledge across these various domains. We demonstrate its application to elicitation for logistic regression in a geographically based ecological context. The underlying statistical methodology is also novel, utilizing an indirect elicitation approach to target expert knowledge on a case-by-case basis. For several elicitation sites (or cases), experts are asked simply to quantify their estimated ecological response (e.g. probability of presence), and its range of plausible values, after inspecting (habitat) covariates via GIS.

Spatial analysis of notified cryptosporidiosis infections in Brisbane, Australia

Purpose: This study explored the spatial distribution of notified cryptosporidiosis cases and identified major socioeconomic factors associated with the transmission of cryptosporidiosis in Brisbane, Australia. Methods: We obtained the computerized data sets on the notified cryptosporidiosis cases and their key socioeconomic factors by statistical local area (SLA) in Brisbane for the period of 1996 to 2004 from the Queensland Department of Health and Australian Bureau of Statistics, respectively. We used spatial empirical Bayes rates smoothing to estimate the spatial distribution of cryptosporidiosis cases. A spatial classification and regression tree (CART) model was developed to explore the relationship between socioeconomic factors and the incidence rates of cryptosporidiosis. Results: Spatial empirical Bayes analysis reveals that the cryptosporidiosis infections were primarily concentrated in the northwest and southeast of Brisbane. A spatial CART model shows that the relative risk for cryptosporidiosis transmission was 2.4 when the value of the social economic index for areas (SEIFA) was over 1028 and the proportion of residents with low educational attainment in an SLA exceeded 8.8%. Conclusions: There was remarkable variation in spatial distribution of cryptosporidiosis infections in Brisbane. Spatial pattern of cryptosporidiosis seems to be associated with SEIFA and the proportion of residents with low education attainment.