Model selection and error estimation

We study model selection strategies based on penalized empirical loss minimization. We point out a tight relationship between error estimation and data-based complexity penalization: any good error estimate may be converted into a data-based penalty function and the performance of the estimate is governed by the quality of the error estimate. We consider several penalty functions, involving error estimates on independent test data, empirical VC dimension, empirical VC entropy, and margin-based quantities. We also consider the maximal difference between the error on the first half of the training data and the second half, and the expected maximal discrepancy, a closely related capacity estimate that can be calculated by Monte Carlo integration. Maximal discrepancy penalty functions are appealing for pattern classification problems, since their computation is equivalent to empirical risk minimization over the training data with some labels flipped.

The power of historical causal components involved in engaging at risk youth at three alternative schools

This article addresses the causal powers associated with the social phenomena of alternative schooling for youth at risk. It stems from a doctoral thesis, Alternative Schooling Programs for At Risk Youth – Three Case Studies which addresses wider issues integral to alternative schooling: youth at risk, alternative schooling models, and literacy. This article explores one aspect of alternative schooling: the historical causal factors involved in the establishment and continuance of three alternative case study models in Queensland, Australia. By adhering to Bhaskar’s transformational model of social activity (TMSA) , social structures and individuals will be analytically distinguished to uncover their separate causal powers and how these have effected the establishment and continuance of three alternative schools.

Modeling perceived collision risk in port water navigation

An increase in the likelihood of navigational collisions in port waters has put focus on the collision avoidance process in port traffic safety. The most widely used on-board collision avoidance system is the automatic radar plotting aid which is a passive warning system that triggers an alert based on the pilot’s pre-defined indicators of distance and time proximities at the closest point of approaches in encounters with nearby vessels. To better help pilot in decision making in close quarter situations, collision risk should be considered as a continuous monotonic function of the proximities and risk perception should be considered probabilistically. This paper derives an ordered probit regression model to study perceived collision risks. To illustrate the procedure, the risks perceived by Singapore port pilots were obtained to calibrate the regression model. The results demonstrate that a framework based on the probabilistic risk assessment model can be used to give a better understanding of collision risk and to define a more appropriate level of evasive actions.

Measuring the effect of motorcycle rider training on psychosocial influences for risk taking

Aim: Whilst motorcycle rider training is commonly incorporated into licensing programs in many developed nations, little empirical support has been found in previous research to prescribe it as an effective road safety countermeasure. It has been posited that the lack of effect of motorcycle rider training on crash reduction may, in part, be due to the predominant focus on skills-based training with little attention devoted to addressing attitudes and motives that influence subsequent risky riding. However, little past research has actually endeavoured to measure attitudinal and motivational factors as a function of rider training. Accordingly, this study was undertaken to assess the effect of a commercial motorcycle rider training program on psychosocial factors that have been shown to influence risk taking by motorcyclists. Method: Four hundred and thirty-eight motorcycle riders attending a competency-based licence training course in Brisbane, Australia, voluntarily participated in the study. A self-report questionnaire adapted from the Rider Risk Assessment Measure (RRAM) was administered to participants at the commencement of training, then again at the conclusion of training. Participants were informed of the independent nature of the research and that their responses would in no way effect their chance of obtaining a licence. To minimise potential demand characteristics, participants were instructed to seal completed questionnaires in envelopes and place them in a sealed box accessible only by the research team (i.e. not able to be viewed by instructors). Results: Significant reductions in the propensity for thrill seeking and intentions to engage in risky riding in the next 12 months were found at the end of training. In addition, a significant increase in attitudes to safety was found. Conclusions: These findings indicate that rider training may have a positive short-term influence on riders’ propensity for risk taking. However, such findings must be interpreted with caution in regard to the subsequent safety of riders as these factors may be subject to further influence once riders are licensed and actively engage with peers during on-road riding. This highlights a challenge for road safety education / training programs in regard to the adoption of safety practices and the need for behavioural follow-up over time to ascertain long-term effects. This study was the initial phase of an ongoing program of research into rider training and risk taking framed around Theory of Planned Behaviour concepts. A subsequent 12 month follow-up of the study participants has been undertaken with data analysis pending.

Navigational safety in port waters: Techniques for modeling collision risk

Navigational collisions are one of the major safety concerns for many seaports. Continuing growth of shipping traffic in number and sizes is likely to result in increased number of traffic movements, which consequently could result higher risk of collisions in these restricted waters. This continually increasing safety concern warrants a comprehensive technique for modeling collision risk in port waters, particularly for modeling the probability of collision events and the associated consequences (i.e., injuries and fatalities). A number of techniques have been utilized for modeling the risk qualitatively, semi-quantitatively and quantitatively. These traditional techniques mostly rely on historical collision data, often in conjunction with expert judgments. However, these techniques are hampered by several shortcomings, such as randomness and rarity of collision occurrence leading to obtaining insufficient number of collision counts for a sound statistical analysis, insufficiency in explaining collision causation, and reactive approach to safety. A promising alternative approach that overcomes these shortcomings is the navigational traffic conflict technique (NTCT), which uses traffic conflicts as an alternative to the collisions for modeling the probability of collision events quantitatively. This article explores the existing techniques for modeling collision risk in port waters. In particular, it identifies the advantages and limitations of the traditional techniques and highlights the potentials of the NTCT in overcoming the limitations. In view of the principles of the NTCT, a structured method for managing collision risk is proposed. This risk management method allows safety analysts to diagnose safety deficiencies in a proactive manner, which consequently has great potential for managing collision risk in a fast, reliable and efficient manner.

Numerical simulation of a fractional mathematical model for epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider numerical simulation of fractional model based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in advection and diffusion terms belong to the intervals (0; 1) or (1; 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of the Riemann-Liouville and Gr¨unwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

Risk-based approach to the management of on-site wastewater treatment facilities

Background On-site wastewater treatment system (OWTS) siting, design and management has traditionally been based on site specific conditions with little regard to the surrounding environment or the cumulative effect of other systems in the environment. The general approach has been to apply the same framework of standards and regulations to all sites equally, regardless of the sensitivity, or lack thereof, to the receiving environment. Consequently, this has led to the continuing poor performance and failure of on-site systems, resulting in environmental and public health consequences. As a result, there is increasing realisation that more scientifically robust evaluations in regard to site assessment and the underlying ground conditions are needed. Risk-based approaches to on-site system siting, design and management are considered the most appropriate means of improvement to the current standards and codes for on-site wastewater treatment systems. The Project Research in relation to this project was undertaken within the Gold Coast City Council region, the major focus being the semi-urban, rural residential and hinterland areas of the city that are not serviced by centralised treatment systems. The Gold Coast has over 15,000 on-site systems in use, with approximately 66% being common septic tank-subsurface dispersal systems. A recent study evaluating the performance of these systems within the Gold Coast area showed approximately 90% were not meeting the specified guidelines for effluent treatment and dispersal. The main focus of this research was to incorporate strong scientific knowledge into an integrated risk assessment process to allow suitable management practices to be set in place to mitigate the inherent risks. To achieve this, research was undertaken focusing on three main aspects involved with the performance and management of OWTS. Firstly, an investigation into the suitability of soil for providing appropriate effluent renovation was conducted. This involved detailed soil investigations, laboratory analysis and the use of multivariate statistical methods for analysing soil information. The outcomes of these investigations were developed into a framework for assessing soil suitability for effluent renovation. This formed the basis for the assessment of OWTS siting and design risks employed in the developed risk framework. Secondly, an assessment of the environmental and public health risks was performed specifically related the release of contaminants from OWTS. This involved detailed groundwater and surface water sampling and analysis to assess the current and potential risks of contamination throughout the Gold Coast region. Additionally, the assessment of public health risk incorporated the use of bacterial source tracking methods to identify the different sources of fecal contamination within monitored regions. Antibiotic resistance pattern analysis was utilised to determine the extent of human faecal contamination, with the outcomes utilised for providing a more indicative public health assessment. Finally, the outcomes of both the soil suitability assessment and ground and surface water monitoring was utilised for the development of the integrated risk framework. The research outcomes achieved through this project enabled the primary research aims and objects to be accomplished. This in turn would enable Gold Coast City Council to provide more appropriate assessment and management guidelines based on robust scientific knowledge which will ultimately ensure that the potential environmental and public health impacts resulting from on-site wastewater treatment is minimised. As part of the implementation of suitable management strategies, a critical point monitoring program (CPM) was formulated. This entailed the identification of the key critical parameters that contribute to the characterised risks at monitored locations within the study area. The CPM will allow more direct procedures to be implemented, targeting the specific hazards at sensitive areas throughout Gold Coast region.

Developing a predictive contractor satisfaction model (CoSMo) for construction projects

Over the last few decades, construction project performance has been evaluated due to the increase of delays, cost overruns and quality failures. Growing numbers of disputes, inharmonious working environments, conflict, blame cultures, and mismatches of objectives among project teams have been found to be contributory factors to poor project performance. Performance measurement (PM) approaches have been developed to overcome these issues, however, the comprehensiveness of PM as an overall approach is still criticised in terms of the iron triangle; namely time, cost, and quality. PM has primarily focused on objective measures, however, continuous improvement requires the inclusion of subjective measures, particularly contractor satisfaction (Co-S). It is challenging to deal with the two different groups of large and small-medium contractor satisfaction as to date, Co-S has not been extensively defined, primarily in developing countries such as Malaysia. Therefore, a Co-S model is developed in this research which aims to fulfil the current needs in the construction industry by integrating performance measures to address large and small-medium contractor perceptions. The positivist paradigm used in the research was adhered to by reviewing relevant literature and evaluating expert discussions on the research topic. It yielded a basis for the contractor satisfaction model (CoSMo) development which consists of three elements: contractor satisfaction (Co-S) dimensions; contributory factors and characteristics (project and participant). Using valid questionnaire results from 136 contractors in Malaysia lead to the prediction of several key factors of contractor satisfaction and to an examination of the relationships between elements. The relationships were examined through a series of sequential statistical analyses, namely correlation, one-way analysis of variance (ANOVA), t-tests and multiple regression analysis (MRA). Forward and backward MRAs were used to develop Co-S mathematical models. Sixteen Co-S models were developed for both large and small-medium contractors. These determined that the large contractor Malaysian Co-S was most affected by the conciseness of project scope and quality of the project brief. Contrastingly, Co-S for small-medium contractors was strongly affected by the efficiency of risk control in a project. The results of the research provide empirical evidence in support of the notion that appropriate communication systems in projects negatively contributes to large Co-S with respect to cost and profitability. The uniqueness of several Co-S predictors was also identified through a series of analyses on small-medium contractors. These contractors appear to be less satisfied than large contractors when participants lack effectiveness in timely authoritative decision-making and communication between project team members. Interestingly, the empirical results show that effective project health and safety measures are influencing factors in satisfying both large and small-medium contractors. The perspectives of large and small-medium contractors in respect to the performance of the entire project development were derived from the Co-S models. These were statistically validated and refined before a new Co-S model was developed. Developing such a unique model has the potential to increase project value and benefit all project participants. It is important to improve participant collaboration as it leads to better project performance. This study may encourage key project participants; such as client, consultant, subcontractor and supplier; to increase their attention to contractor needs in the development of a project. Recommendations for future research include investigating other participants‟ perspectives on CoSMo and the impact of the implementation of CoSMo in a project, since this study is focused purely on the contractor perspective.

Assessing Cardiovascular Risk in Regional Areas: The Healthy Hearts – Beyond City Limits Program

Background: Cardiovascular disease (CVD) is more prevalent in regional and remote Australia compared to metropolitan areas. The aim of Healthy Hearts was to determine age and sex specific CVD risk factor levels and the potential value of national risk clinics. Methods: Healthy Hearts was an observational research study conducted in four purposefully selected higher risk communities in regional Victoria, Australia. The main outcome measures were the proportion of participants with CVD risk factors with group comparisons to determine the adjusted likelihood of elevated risk factor levels. Trained personnel used a standardized protocol over four weeks per community to measure CVD risk factor levels, estimate absolute CVD risk and provide feedback and advice. Results: A total of 2125 self-selected participants were assessed (mean age 58 ± 15 years, 57% women). Overall, CVD risk factors were highly prevalent. More men than women had ≥ 2 modifiable CVD risk factors (76% vs. 68%, p < .001), pre-existing CVD (20 vs. 15%, p < .01) and a major ECG abnormality requiring follow-up (15% vs. 7%, p < .001) . Less men reported depressive symptoms compared to women (28% vs. 22%, p < .01). A higher proportion of women were obese (adjusted OR 1.36, 95% CI 1.13 to 1.63), and physically inactive (adjusted OR 1.32, 95% CI 1.07 to 1.63). Conclusions: High CVD risk factor levels were confirmed for regional Victoria. Close engagement with individuals and communities provides scope for the application of regional risk management clinics to reduce the burden of CVD risk in regional Australia.

Students’ approaches to learning a new mathematical model

In this article, we report on the findings of an exploratory study into the experience of undergraduate students as they learn new mathematical models. Qualitative and quanti- tative data based around the students’ approaches to learning new mathematical models were collected. The data revealed that students actively adopt three approaches to under- standing a new mathematical model: gathering information for the task of understanding the model, practising with and using the model, and finding interrelationships between elements of the model. We found that the students appreciate mathematical models that have a real world application and that this can be used to engage students in higher level learning approaches.

Contextual models and the non-Newtonian paradigm

Biological systems exhibit a wide range of contextual effects, and this often makes it difficult to construct valid mathematical models of their behaviour. In particular, mathematical paradigms built upon the successes of Newtonian physics make assumptions about the nature of biological systems that are unlikely to hold true. After discussing two of the key assumptions underlying the Newtonian paradigm, we discuss two key aspects of the formalism that extended it, Quantum Theory (QT). We draw attention to the similarities between biological and quantum systems, motivating the development of a similar formalism that can be applied to the modelling of biological processes.

Numerical techniques for simulating a fractional mathematical model of epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider the numerical simulation of a fractional mathematical model of epidermal wound healing (FMM-EWH), which is based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in the advection and diffusion terms belong to the intervals (0, 1) or (1, 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of Riemann-Liouville and Grünwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

Mathematical modelling of LiFePO4 cathodes

LiFePO4 is a commercially available battery material with good theoretical discharge capacity, excellent cycle life and increased safety compared with competing Li-ion chemistries. It has been the focus of considerable experimental and theoretical scrutiny in the past decade, resulting in LiFePO4 cathodes that perform well at high discharge rates. This scrutiny has raised several questions about the behaviour of LiFePO4 material during charge and discharge. In contrast to many other battery chemistries that intercalate homogeneously, LiFePO4 can phase-separate into highly and lowly lithiated phases, with intercalation proceeding by advancing an interface between these two phases. The main objective of this thesis is to construct mathematical models of LiFePO4 cathodes that can be validated against experimental discharge curves. This is in an attempt to understand some of the multi-scale dynamics of LiFePO4 cathodes that can be difficult to determine experimentally. The first section of this thesis constructs a three-scale mathematical model of LiFePO4 cathodes that uses a simple Stefan problem (which has been used previously in the literature) to describe the assumed phase-change. LiFePO4 crystals have been observed agglomerating in cathodes to form a porous collection of crystals and this morphology motivates the use of three size-scales in the model. The multi-scale model developed validates well against experimental data and this validated model is then used to examine the role of manufacturing parameters (including the agglomerate radius) on battery performance. The remainder of the thesis is concerned with investigating phase-field models as a replacement for the aforementioned Stefan problem. Phase-field models have recently been used in LiFePO4 and are a far more accurate representation of experimentally observed crystal-scale behaviour. They are based around the Cahn-Hilliard-reaction (CHR) IBVP, a fourth-order PDE with electrochemical (flux) boundary conditions that is very stiff and possesses multiple time and space scales. Numerical solutions to the CHR IBVP can be difficult to compute and hence a least-squares based Finite Volume Method (FVM) is developed for discretising both the full CHR IBVP and the more traditional Cahn-Hilliard IBVP. Phase-field models are subject to two main physicality constraints and the numerical scheme presented performs well under these constraints. This least-squares based FVM is then used to simulate the discharge of individual crystals of LiFePO4 in two dimensions. This discharge is subject to isotropic Li+ diffusion, based on experimental evidence that suggests the normally orthotropic transport of Li+ in LiFePO4 may become more isotropic in the presence of lattice defects. Numerical investigation shows that two-dimensional Li+ transport results in crystals that phase-separate, even at very high discharge rates. This is very different from results shown in the literature, where phase-separation in LiFePO4 crystals is suppressed during discharge with orthotropic Li+ transport. Finally, the three-scale cathodic model used at the beginning of the thesis is modified to simulate modern, high-rate LiFePO4 cathodes. High-rate cathodes typically do not contain (large) agglomerates and therefore a two-scale model is developed. The Stefan problem used previously is also replaced with the phase-field models examined in earlier chapters. The results from this model are then compared with experimental data and fit poorly, though a significant parameter regime could not be investigated numerically. Many-particle effects however, are evident in the simulated discharges, which match the conclusions of recent literature. These effects result in crystals that are subject to local currents very different from the discharge rate applied to the cathode, which impacts the phase-separating behaviour of the crystals and raises questions about the validity of using cathodic-scale experimental measurements in order to determine crystal-scale behaviour.

Mathematical modelling of tumour growth and interaction with host tissue and the immune system

In this thesis, three mathematical models describing the growth of solid tumour incorporating the host tissue and the immune system response are developed and investigated. The initial model describes the dynamics of the growing tumour and immune response before being extended in the second model by introducing a time-varying dendritic cell-based treatment strategy. Finally, in the third model, we present a mathematical model of a growing tumour using a hybrid cellular automata. These models can provide information to pre-experimental work to assist in designing more effective and efficient laboratory experiments related to tumour growth and interactions with the immune system and immunotherapy.

A data mining driven risk profiling method for road asset management

Road surface skid resistance has been shown to have a strong relationship to road crash risk, however, applying the current method of using investigatory levels to identify crash prone roads is problematic as they may fail in identifying risky roads outside of the norm. The proposed method analyses a complex and formerly impenetrable volume of data from roads and crashes using data mining. This method rapidly identifies roads with elevated crash-rate, potentially due to skid resistance deficit, for investigation. A hypothetical skid resistance/crash risk curve is developed for each road segment, driven by the model deployed in a novel regression tree extrapolation method. The method potentially solves the problem of missing skid resistance values which occurs during network-wide crash analysis, and allows risk assessment of the major proportion of roads without skid resistance values.