A framework for integrating disadvantaged analysis into transportation planning models

This research paper aims to develop a method to explore the travel behaviour differences between disadvantaged and non-disadvantaged populations. It also aims to develop a modelling approach or a framework to integrate disadvantage analysis into transportation planning models (TPMs). The methodology employed identifies significantly disadvantaged groups through a cluster analysis and the paper presents a disadvantage-integrated TPM. This model could be useful in determining areas with concentrated disadvantaged population and also developing and formulating relevant disadvantage sensitive policies. (a) For the covering entry of this conference, please see ITRD abstract no. E214666.

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.

Timing of births and endometrial cancer risk in Swedish women

While a protective long-term effect of parity on endometrial cancer risk is well established, the impact of timing of births is not fully understood. We examined the relationship between endometrial cancer risk and reproductive characteristics in a population-based cohort of 2,674,465 Swedish women, 20–72 years of age. During follow-up from 1973 through 2004, 7,386 endometrial cancers were observed. Compared to uniparous women, nulliparous women had a significantly elevated endometrial cancer risk (hazard ratio [HR] = 1.32, 95% confidence interval [CI], 1.22–1.42). Endometrial cancer risk decreased with increasing parity; compared to uniparous women, women with ≥4 births had a HR=0.66 (95% CI, 0.59–0.74); p-trend < 0.001. Among multiparous women, we observed no relationship of risk with age at first birth after adjustment for other reproductive factors. While we initially observed a decreased risk with later ages at last birth, this appeared to reflect a stronger relationship with time since last birth, with women with shorter times being at lowest risk. In models for multiparous women that included number of births, age at first and last birth, and time since last birth, age at last birth was not associated with endometrial cancer risk, while shorter time since last birth and increased parity were associated with statistically significantly reduced endometrial cancer risks. The HR was 3.95 (95%CI; 2.17–7.20; p-trend=<0.0001) for women with ≥25 years since a last birth compared to women having given birth within 4 years. Our findings support that clearance of initiated cells during delivery may be important in endometrial carcinogenesis. Keywords: endometrial carcinoma, parity, registry, reproductive factors

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.

Navigational Safety in Port Waters : Proactive Management of Collision Risk Using Traffic Conflicts

Traditionally navigational safety analyses rely on historical collision data which is often hampered because of low collision counts, insufficiency in explaining collision causation, and reactive approach to safety. A promising alternative approach that overcomes these problems is using navigational traffic conflicts or near-misses as an alternative to the collision data. This book discusses how traffic conflicts can effectively be used in modeling of port water collision risks. Techniques for measuring and predicting collision risks in fairways, intersections, and anchorages are discussed by utilizing advanced statistical models. Risk measurement models, which quantitatively measure collision risks in waterways, are discussed. To predict risks, a hierarchical statistical modeling technique is discussed which identifies the factors influencing the risks. The modeling techniques are illustrated for Singapore port data. Results showed that traffic conflicts are an ethically appealing alternative to collision data for fast, reliable and effective safety assessment, thus possessing great potential for managing collision risks in port waters.

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.

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.

Evaluation of the potential impact of the global economic crisis on HIV epidemics in Southeast Asia

Economic conditions around the world are likely to deteriorate in the short to medium term. The potential impact of this crisis on the spread of HIV is not clear. Government revenues and aid flows from international donors may face constraints, possibly leading to reductions in funding for HIV programs. Economic conditions (leading to increases in unemployment, for example) may also have an indirect impact on HIV epidemics by affecting the behaviour of individual people. Some behavioural changes may influence the rate of HIV transmission. This report presents findings from a study that investigates the potential impact of the economic crisis on HIV epidemics through the use of mathematical modelling. The potential epidemiological impacts of changes in the economy are explored for two distinctly characterised HIV epidemics: (i) a well-defined, established, and generalised HIV epidemic (specifically Cambodia, where incidence is declining); (ii) an HIV epidemic in its early expansion phase (specifically Papua New Guinea, where incidence has not yet peaked). Country-specific data are used for both settings and the models calibrated to accurately reflect the unique HIV epidemics in each population in terms of both incidence and prevalence. Models calibrated to describe the past and present epidemics are then used to forecast epidemic trajectories over the next few years under assumptions that behavioural or program conditions may change due to economic conditions. It should be noted that there are very limited solid data on how HIV/AIDS program funds may decrease or how social determinants related to HIV risk may change due to the economic crisis. Potential changes in key relevant factors were explored, along with sensitivity ranges around these assumptions, based on extensive discussions with in-country and international experts and stakeholders. As with all mathematical models, assumptions should be reviewed critically and results interpreted cautiously.

Mathematical modelling of intramembranous bone formation during fracture healing

During fracture healing, many complex and cryptic interactions occur between cells and bio-chemical molecules to bring about repair of damaged bone. In this thesis two mathematical models were developed, concerning the cellular differentiation of osteoblasts (bone forming cells) and the mineralisation of new bone tissue, allowing new insights into these processes. These models were mathematically analysed and simulated numerically, yielding results consistent with experimental data and highlighting the underlying pattern formation structure in these aspects of fracture healing.

Feature selection using expected attainable discrimination

We propose expected attainable discrimination (EAD) as a measure to select discrete valued features for reliable discrimination between two classes of data. EAD is an average of the area under the ROC curves obtained when a simple histogram probability density model is trained and tested on many random partitions of a data set. EAD can be incorporated into various stepwise search methods to determine promising subsets of features, particularly when misclassification costs are difficult or impossible to specify. Experimental application to the problem of risk prediction in pregnancy is described.

Quantifying uncertainty in parameter estimates for stochastic models of collective cell spreading using approximate Bayesian computation

Wound healing and tumour growth involve collective cell spreading, which is driven by individual motility and proliferation events within a population of cells. Mathematical models are often used to interpret experimental data and to estimate the parameters so that predictions can be made. Existing methods for parameter estimation typically assume that these parameters are constants and often ignore any uncertainty in the estimated values. We use approximate Bayesian computation (ABC) to estimate the cell diffusivity, D, and the cell proliferation rate, λ, from a discrete model of collective cell spreading, and we quantify the uncertainty associated with these estimates using Bayesian inference. We use a detailed experimental data set describing the collective cell spreading of 3T3 fibroblast cells. The ABC analysis is conducted for different combinations of initial cell densities and experimental times in two separate scenarios: (i) where collective cell spreading is driven by cell motility alone, and (ii) where collective cell spreading is driven by combined cell motility and cell proliferation. We find that D can be estimated precisely, with a small coefficient of variation (CV) of 2–6%. Our results indicate that D appears to depend on the experimental time, which is a feature that has been previously overlooked. Assuming that the values of D are the same in both experimental scenarios, we use the information about D from the first experimental scenario to obtain reasonably precise estimates of λ, with a CV between 4 and 12%. Our estimates of D and λ are consistent with previously reported values; however, our method is based on a straightforward measurement of the position of the leading edge whereas previous approaches have involved expensive cell counting techniques. Additional insights gained using a fully Bayesian approach justify the computational cost, especially since it allows us to accommodate information from different experiments in a principled way.