Student identities in a mathematical community of practice : radical visible pedagogy and the teacher collective

This study investigated the practices of two teachers in a school that was successful in enabling the mathematical learning of students in Years 1 and 2, including those from backgrounds associated with low mathematical achievement. The study explained how the practices of the teachers constituted a radical visible pedagogy that enabled equitable outcomes. The study also showed that teachers’ practices have collective power to shape students’ mathematical identities. The role of the principal in the school was pivotal because she structured curriculum delivery so that students experienced the distinct practices of both teachers.

Mathematical modelling of soft callus formation in early murine bone repair

Fracture healing is a complicated coupling of many processes. Yet despite the apparent complexity, fracture repair is usually effective. There is, however, no comprehensive mathematical model addressing the multiple interactions of cells, cytokines and oxygen that includes extra-cellular matrix production and that results in the formation of the early stage soft callus. This thesis develops a one dimensional continuum transport model in the context of early fracture healing. Although fracture healing is a complex interplay of many local factors, critical components are identified and used to construct an hypothesis about regulation of the evolution of early callus formation. Multiple cell lines, cellular differentiation, oxygen levels and cytokine concentrations are examined as factors affecting this model of early bone repair. The model presumes diffusive and chemotactic cell migration mechanisms. It is proposed that the initial signalling regime and oxygen availability arising as consequences of bone fracture, are sufficient to determine the quantity and quality of early soft callus formation. Readily available software and purpose written algorithms have been used to obtain numerical solutions representative of various initial conditions. These numerical distributions of cellular populations reflect available histology obtained from murine osteotomies. The behaviour of the numerical system in response to differing initial conditions can be described by alternative in vivo healing pathways. An experimental basis, as illustrated in murine fracture histology, has been utilised to validate the mathematical model outcomes. The model developed in this thesis has potential for future extension, to incorporate processes leading to woven bone deposition, while maintaining the characteristics that regulate early callus formation.

Fully Bayesian experimental design for pharmacokinetic studies

Utility functions in Bayesian experimental design are usually based on the posterior distribution. When the posterior is found by simulation, it must be sampled from for each future data set drawn from the prior predictive distribution. Many thousands of posterior distributions are often required. A popular technique in the Bayesian experimental design literature to rapidly obtain samples from the posterior is importance sampling, using the prior as the importance distribution. However, importance sampling will tend to break down if there is a reasonable number of experimental observations and/or the model parameter is high dimensional. In this paper we explore the use of Laplace approximations in the design setting to overcome this drawback. Furthermore, we consider using the Laplace approximation to form the importance distribution to obtain a more efficient importance distribution than the prior. The methodology is motivated by a pharmacokinetic study which investigates the effect of extracorporeal membrane oxygenation on the pharmacokinetics of antibiotics in sheep. The design problem is to find 10 near optimal plasma sampling times which produce precise estimates of pharmacokinetic model parameters/measures of interest. We consider several different utility functions of interest in these studies, which involve the posterior distribution of parameter functions.

Gemcitabine reactivates epigenetically silenced genes and functions as a DNA methyltransferase inhibitor

Gemcitabine is indicated in combination with cisplatin as first-line therapy for solid tumours including non-small cell lung cancer (NSCLC), bladder cancer and mesothelioma. Gemcitabine is an analogue of pyrimidine cytosine and functions as an anti-metabolite. Structurally, however, gemcitabine has similarities to 5-aza-2-deoxycytidine (decitabine/Dacogen®), a DNA methyltransferase inhibitor (DNMTi). NSCLC, mesothelioma and prostate cancer cell lines were treated with decitabine and gemcitabine. Reactivation of epigenetically silenced genes was examined by RT-PCR/qPCR. DNA methyltransferase activity in nuclear extracts and recombinant proteins was measured using a DNA methyltransferase assay, and alterations in DNA methylation status were examined using methylation-specific PCR (MS-PCR) and pyrosequencing. We observe a reactivation of several epigenetically silenced genes including GSTP1, IGFBP3 and RASSF1A. Gemcitabine functionally inhibited DNA methyltransferase activity in both nuclear extracts and recombinant proteins. Gemcitabine dramatically destabilised DNMT1 protein. However, DNA CpG methylation was for the most part unaffected by gemcitabine. In conclusion, gemcitabine both inhibits and destabilises DNA methyltransferases and reactivates epigenetically silenced genes having activity equivalent to decitabine at concentrations significantly lower than those achieved in the treatment of patients with solid tumours. This property may contribute to the anticancer activity of gemcitabine.

A RBF meshless approach for modeling a fractal mobile/immobile transport model

A fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBFs) to discretize the space variable. In contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example which is presented to describe a fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating fractional differential equations, and it has good potential in the development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

Mathematical modelling of counter flow v-grove solar air collector

Double-pass counter flow v-grove collector is considered one of the most efficient solar air-collectors. In this design of the collector, the inlet air initially flows at the top part of the collector and changes direction once it reaches the end of the collector and flows below the collector to the outlet. A mathematical model is developed for this type of collector and simulation is carried out using MATLAB programme. The simulation results were verified with three distinguished research results and it was found that the simulation has the ability to predict the performance of the air collector accurately as proven by the comparison of experimental data with simulation. The difference between the predicted and experimental results is, at maximum, approximately 7% which is within the acceptable limit considering some uncertainties in the input parameter values to allow comparison. A parametric study was performed and it was found that solar radiation, inlet air temperature, flow rate and length have a significant effect on the efficiency of the air collector. Additionally, the results are compared with single flow V-groove collector.

Rich and purposeful mathematical knowledge of mothers and children in a Torres Strait Islander community

This paper focuses on a pilot study that explored the situated mathematical knowledge of mothers and children in one Torres Strait Islander community in Australia. The community encouraged parental involvement in their children’s learning and schooling. The study explored parents’ understandings of mathematics and how their children came to learn about it on the island. A funds of knowledge approach was used in the study. This approach is based on the premise that people are competent and have knowledge that has been historically and culturally accumulated into a body of knowledge and skills essential for their functioning and well-being (Moll, 1992). The participants, three adults and one child are featured in this paper. Three separate events are described with epiphanic or illuminative moments analysed to ascertain the features that enabled an understanding of the nature of the mathematical events. The study found that Indigenous ways of knowing of mathematics were deeply embedded in rich cultural practices that were tied to the community. This finding has implications for teachers of children in the early years. Where school mathematics is often presented as disembodied and isolated facts with children seeing little relevance, learning a different perspective of mathematics that is tied to the resources and practices of children’s lives and facilitated through social relationships, may go a long way to improving the engagement of children and their parents in learning and schooling.

Sampling designs on stream networks using the pseudo-Bayesian approach

Monitoring stream networks through time provides important ecological information. The sampling design problem is to choose locations where measurements are taken so as to maximise information gathered about physicochemical and biological variables on the stream network. This paper uses a pseudo-Bayesian approach, averaging a utility function over a prior distribution, in finding a design which maximizes the average utility. We use models for correlations of observations on the stream network that are based on stream network distances and described by moving average error models. Utility functions used reflect the needs of the experimenter, such as prediction of location values or estimation of parameters. We propose an algorithmic approach to design with the mean utility of a design estimated using Monte Carlo techniques and an exchange algorithm to search for optimal sampling designs. In particular we focus on the problem of finding an optimal design from a set of fixed designs and finding an optimal subset of a given set of sampling locations. As there are many different variables to measure, such as chemical, physical and biological measurements at each location, designs are derived from models based on different types of response variables: continuous, counts and proportions. We apply the methodology to a synthetic example and the Lake Eacham stream network on the Atherton Tablelands in Queensland, Australia. We show that the optimal designs depend very much on the choice of utility function, varying from space filling to clustered designs and mixtures of these, but given the utility function, designs are relatively robust to the type of response variable.

Identifying Core Functions of Asset Management

It is widely acknowledged that effective asset management requires an interdisciplinary approach, in which synergies should exist between traditional disciplines such as: accounting, engineering, finance, humanities, logistics, and information systems technologies. Asset management is also an important, yet complex business practice. Business process modelling is proposed as an approach to manage the complexity of asset management through the modelling of asset management processes. A sound foundation for the systematic application and analysis of business process modelling in asset management is, however, yet to be developed. Fundamentally, a business process consists of activities (termed functions), events/states, and control flow logic. As both events/states and control flow logic are somewhat dependent on the functions themselves, it is a logical step to first identify the functions within a process. This research addresses the current gap in knowledge by developing a method to identify functions common to various industry types (termed core functions). This lays the foundation to extract such functions, so as to identify both commonalities and variation points in asset management processes. This method describes the use of a manual text mining and a taxonomy approach. An example is presented.

Mathematical investigation of the interactions between the inflammatory response and mechanical aspects of dermal wound repair

Dermal wound repair involves complex interactions between cells, cytokines and mechanics to close injuries to the skin. In particular, we investigate the contribution of fibroblasts, myofibroblasts, TGFβ, collagen and local tissue mechanics to wound repair in the human dermis. We develop a morphoelastic model where a realistic representation of tissue mechanics is key, and a fibrocontractive model that involves a reasonable approximation to the true kinetics of the important bioactive species. We use each of these descriptions to elucidate the mechanisms that generate pathologies such as hypertrophic scars, contractures and keloids. We find that for hypertrophic scar and contracture development, factors regulating the myofibroblast phenotype are critical, with heightened myofibroblast activation, reduced myofibroblast apoptosis or prolonged inflammation all predicted as mediators for scar hypertrophy and contractures. Prevention of these pathologies is predicted when myofibroblast apoptosis is induced, myofibroblast activation is blocked or TGFβ is neutralised. To investigate keloid invasion, we develop a caricature representation of the fibrocontractive model and find that TGFβ spread is the driving factor behind keloid growth. Blocking activation of TGFβ is found to cause keloid regression. Thus, we recommend myofibroblasts and TGFβ as targets for clinicians when developing intervention strategies for prevention and cure of fibrotic scars.

A multiscale road map of cancer spheroids : incorporating experimental and mathematical modelling to understand cancer progression

Computational models represent a highly suitable framework, not only for testing biological hypotheses and generating new ones but also for optimising experimental strategies. As one surveys the literature devoted to cancer modelling, it is obvious that immense progress has been made in applying simulation techniques to the study of cancer biology, although the full impact has yet to be realised. For example, there are excellent models to describe cancer incidence rates or factors for early disease detection, but these predictions are unable to explain the functional and molecular changes that are associated with tumour progression. In addition, it is crucial that interactions between mechanical effects, and intracellular and intercellular signalling are incorporated in order to understand cancer growth, its interaction with the extracellular microenvironment and invasion of secondary sites. There is a compelling need to tailor new, physiologically relevant in silico models that are specialised for particular types of cancer, such as ovarian cancer owing to its unique route of metastasis, which are capable of investigating anti-cancer therapies, and generating both qualitative and quantitative predictions. This Commentary will focus on how computational simulation approaches can advance our understanding of ovarian cancer progression and treatment, in particular, with the help of multicellular cancer spheroids, and thus, can inform biological hypothesis and experimental design.

Mathematical relationships for metal build-up on urban road surfaces based on traffic and land use characteristics

The study investigated the influence of traffic and land use parameters on metal build-up on urban road surfaces. Mathematical relationships were developed to predict metals originating from fuel combustion and vehicle wear. The analysis undertaken found that nickel and chromium originate from exhaust emissions, lead, copper and zinc from vehicle wear, cadmium from both exhaust and wear and manganese from geogenic sources. Land use does not demonstrate a clear pattern in relation to the metal build-up process, though its inherent characteristics such as traffic activities exert influence. The equation derived for fuel related metal load has high cross-validated coefficient of determination (Q2) and low Standard Error of Cross-Validation (SECV) values indicates that the model is reliable, while the equation derived for wear-related metal load has low Q2 and high SECV values suggesting its use only in preliminary investigations. Relative Prediction Error values for both equations are considered to be well within the error limits for a complex system such as an urban road surface. These equations will be beneficial for developing reliable stormwater treatment strategies in urban areas which specifically focus on mitigation of metal pollution.

Mechanism based emulation of dynamic simulation models : concept and application in hydrology

Many model-based investigation techniques, such as sensitivity analysis, optimization, and statistical inference, require a large number of model evaluations to be performed at different input and/or parameter values. This limits the application of these techniques to models that can be implemented in computationally efficient computer codes. Emulators, by providing efficient interpolation between outputs of deterministic simulation models, can considerably extend the field of applicability of such computationally demanding techniques. So far, the dominant techniques for developing emulators have been priors in the form of Gaussian stochastic processes (GASP) that were conditioned with a design data set of inputs and corresponding model outputs. In the context of dynamic models, this approach has two essential disadvantages: (i) these emulators do not consider our knowledge of the structure of the model, and (ii) they run into numerical difficulties if there are a large number of closely spaced input points as is often the case in the time dimension of dynamic models. To address both of these problems, a new concept of developing emulators for dynamic models is proposed. This concept is based on a prior that combines a simplified linear state space model of the temporal evolution of the dynamic model with Gaussian stochastic processes for the innovation terms as functions of model parameters and/or inputs. These innovation terms are intended to correct the error of the linear model at each output step. Conditioning this prior to the design data set is done by Kalman smoothing. This leads to an efficient emulator that, due to the consideration of our knowledge about dominant mechanisms built into the simulation model, can be expected to outperform purely statistical emulators at least in cases in which the design data set is small. The feasibility and potential difficulties of the proposed approach are demonstrated by the application to a simple hydrological model.

A stochastic neighborhood conditional autoregressive model for spatial data

A spatial process observed over a lattice or a set of irregular regions is usually modeled using a conditionally autoregressive (CAR) model. The neighborhoods within a CAR model are generally formed deterministically using the inter-distances or boundaries between the regions. An extension of CAR model is proposed in this article where the selection of the neighborhood depends on unknown parameter(s). This extension is called a Stochastic Neighborhood CAR (SNCAR) model. The resulting model shows flexibility in accurately estimating covariance structures for data generated from a variety of spatial covariance models. Specific examples are illustrated using data generated from some common spatial covariance functions as well as real data concerning radioactive contamination of the soil in Switzerland after the Chernobyl accident.

An improved chemically inducible gene switch that functions in the monocotyledonous plant sugar cane

Chemically inducible gene switches can provide precise control over gene expression, enabling more specific analyses of gene function and expanding the plant biotechnology toolkit beyond traditional constitutive expression systems. The alc gene expression system is one of the most promising chemically inducible gene switches in plants because of its potential in both fundamental research and commercial biotechnology applications. However, there are no published reports demonstrating that this versatile gene switch is functional in transgenic monocotyledonous plants, which include some of the most important agricultural crops. We found that the original alc gene switch was ineffective in the monocotyledonous plant sugar cane, and describe a modified alc system that is functional in this globally significant crop. A promoter consisting of tandem copies of the ethanol receptor inverted repeat binding site, in combination with a minimal promoter sequence, was sufficient to give enhanced sensitivity and significantly higher levels of ethanol inducible gene expression. A longer CaMV 35S minimal promoter than was used in the original alc gene switch also substantially improved ethanol inducibility. Treating the roots with ethanol effectively induced the modified alc system in sugar cane leaves and stem, while an aerial spray was relatively ineffective. The extension of this chemically inducible gene expression system to sugar cane opens the door to new opportunities for basic research and crop biotechnology.