Finite volume methods for simulating anomalous transport

In this thesis a new approach for solving a certain class of anomalous diffusion equations was developed. The theory and algorithms arising from this work will pave the way for more efficient and more accurate solutions of these equations, with applications to science, health and industry. The method of finite volumes was applied to discretise the spatial derivatives, and this was shown to outperform existing methods in several key respects. The stability and convergence of the new method were rigorously established.

Locally weighted learning methods for non-rigid robot control

This thesis develops a novel approach to robot control that learns to account for a robot's dynamic complexities while executing various control tasks using inspiration from biological sensorimotor control and machine learning. A robot that can learn its own control system can account for complex situations and adapt to changes in control conditions to maximise its performance and reliability in the real world. This research has developed two novel learning methods, with the aim of solving issues with learning control of non-rigid robots that incorporate additional dynamic complexities. The new learning control system was evaluated on a real three degree-of-freedom elastic joint robot arm with a number of experiments: initially validating the learning method and testing its ability to generalise to new tasks, then evaluating the system during a learning control task requiring continuous online model adaptation.

A survey: Error control methods used in bio-cryptography

Integration of biometrics is considered as an attractive solution for the issues associated with password based human authentication as well as for secure storage and release of cryptographic keys which is one of the critical issues associated with modern cryptography. However, the widespread popularity of bio-cryptographic solutions are somewhat restricted by the fuzziness associated with biometric measurements. Therefore, error control mechanisms must be adopted to make sure that fuzziness of biometric inputs can be sufficiently countered. In this paper, we have outlined such existing techniques used in bio-cryptography while explaining how they are deployed in different types of solutions. Finally, we have elaborated on the important facts to be considered when choosing appropriate error correction mechanisms for a particular biometric based solution.

Second-order quantile methods for experts and combinatorial games

We aim to design strategies for sequential decision making that adjust to the difficulty of the learning problem. We study this question both in the setting of prediction with expert advice, and for more general combinatorial decision tasks. We are not satisfied with just guaranteeing minimax regret rates, but we want our algorithms to perform significantly better on easy data. Two popular ways to formalize such adaptivity are second-order regret bounds and quantile bounds. The underlying notions of 'easy data', which may be paraphrased as "the learning problem has small variance" and "multiple decisions are useful", are synergetic. But even though there are sophisticated algorithms that exploit one of the two, no existing algorithm is able to adapt to both. In this paper we outline a new method for obtaining such adaptive algorithms, based on a potential function that aggregates a range of learning rates (which are essential tuning parameters). By choosing the right prior we construct efficient algorithms and show that they reap both benefits by proving the first bounds that are both second-order and incorporate quantiles.

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.

An introduction to education research methods: Exploring the learning journey of pre-service teachers in a transnational programme

Internationally there is interest in developing the research skills of pre-service teachers as a means of ongoing professional renewal with a distinct need for systematic and longitudinal investigation of student learning. The current study takes a unique perspective by exploring the research learning journey of pre-service teachers participating in a transnational degree programme. Using a case-study design that includes both a self-reported and direct measure of research knowledge, the results indicate a progression in learning, as well as evidence that this research knowledge is continued or maintained when the pre-service teachers return to their home university. The findings of this study have implications for both pre-service teacher research training and transnational programmes.

Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy

This article aims to fill in the gap of the second-order accurate schemes for the time-fractional subdiffusion equation with unconditional stability. Two fully discrete schemes are first proposed for the time-fractional subdiffusion equation with space discretized by finite element and time discretized by the fractional linear multistep methods. These two methods are unconditionally stable with maximum global convergence order of $O(\tau+h^{r+1})$ in the $L^2$ norm, where $\tau$ and $h$ are the step sizes in time and space, respectively, and $r$ is the degree of the piecewise polynomial space. The average convergence rates for the two methods in time are also investigated, which shows that the average convergence rates of the two methods are $O(\tau^{1.5}+h^{r+1})$. Furthermore, two improved algorithms are constrcted, they are also unconditionally stable and convergent of order $O(\tau^2+h^{r+1})$. Numerical examples are provided to verify the theoretical analysis. The comparisons between the present algorithms and the existing ones are included, which show that our numerical algorithms exhibit better performances than the known ones.

High order unconditionally stable difference schemes for the Riesz space-fractional telegraph equation

In this paper, a class of unconditionally stable difference schemes based on the Pad´e approximation is presented for the Riesz space-fractional telegraph equation. Firstly, we introduce a new variable to transform the original dfferential equation to an equivalent differential equation system. Then, we apply a second order fractional central difference scheme to discretise the Riesz space-fractional operator. Finally, we use (1, 1), (2, 2) and (3, 3) Pad´e approximations to give a fully discrete difference scheme for the resulting linear system of ordinary differential equations. Matrix analysis is used to show the unconditional stability of the proposed algorithms. Two examples with known exact solutions are chosen to assess the proposed difference schemes. Numerical results demonstrate that these schemes provide accurate and efficient methods for solving a space-fractional hyperbolic equation.

Numerical simulation of anomalous infiltration in porous media

Nonlinear time-fractional diffusion equations have been used to describe the liquid infiltration for both subdiffusion and superdiffusion in porous media. In this paper, some problems of anomalous infiltration with a variable-order timefractional derivative in porous media are considered. The time-fractional Boussinesq equation is also considered. Two computationally efficient implicit numerical schemes for the diffusion and wave-diffusion equations are proposed. Numerical examples are provided to show that the numerical methods are computationally efficient.

A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation

The fractional Fokker-Planck equation is an important physical model for simulating anomalous diffusions with external forces. Because of the non-local property of the fractional derivative an interesting problem is to explore high accuracy numerical methods for fractional differential equations. In this paper, a space-time spectral method is presented for the numerical solution of the time fractional Fokker-Planck initial-boundary value problem. The proposed method employs the Jacobi polynomials for the temporal discretization and Fourier-like basis functions for the spatial discretization. Due to the diagonalizable trait of the Fourier-like basis functions, this leads to a reduced representation of the inner product in the Galerkin analysis. We prove that the time fractional Fokker-Planck equation attains the same approximation order as the time fractional diffusion equation developed in [23] by using the present method. That indicates an exponential decay may be achieved if the exact solution is sufficiently smooth. Finally, some numerical results are given to demonstrate the high order accuracy and efficiency of the new numerical scheme. The results show that the errors of the numerical solutions obtained by the space-time spectral method decay exponentially.

Informing methods for preparing public health overviews of reviews: a comparison of public health overviews with Cochrane Overviews published between 1999 and 2014

Background: Overviews of systematic reviews (SRs) are useful for public health policy; however there is an absence of Cochrane Overviews covering public health (PH) topics. Objectives: We sought to analyze the methodological approaches used in existing Cochrane Overviews and Protocols for overviews (primarily clinical in nature), and compare these to the methods and approaches used in PH overviews (non-Cochrane). The intent was to identify issues that would be relevant for undertaking Cochrane overviews. Methods: We conducted a descriptive analysis of overviews published between 1999 and 2014. We searched the Cochrane Database of Systematic Reviews for Cochrane Protocols for overviews and Cochrane Overviews, and the HealthEvidence.org for PH overviews. The primary characteristics of the overviews and elements of the methodology were extracted and compared. Results: A total of 61 overviews of SRs were included in our analysis; specifically, this included 21 Cochrane Protocols for overviews, 15 Cochrane Overviews, and 27 non-Cochrane PH overviews. Amongst the overviews, the most significant differences are that PH overviews (non-Cochrane) tend to: include earlier and more reviews, greater number of participants, allow lower levels of evidence, use assessment tools other than AMSTAR (A Measurement Tool to Assess Systematic Reviews, i.e. a tool for assessing quality of SRs), not assess quality of evidence in reviews, search more databases overall, specify search limits including English-only reviews, and not consider recent primary studies for inclusion. Some of these differences clearly related to quality, however many relate to the nuances of PH interventions. Conclusions: The methodology in Cochrane overviews and PH overviews varies widely. Future PH overviews may benefit from the Cochrane methodology but the Cochrane approach requires modification to accommodate PH research methodology. Additionally, the use of databases that pre-screen and quality assess relevant PH systematic reviews may help expedite the search process.

Valuation of hospital bed-days released by infection control programs: A comparison of methods

We performed a contingent valuation survey to elicit the opportunity cost of bed-days consumed by healthcare-associated infections in 11 European hospitals. The opportunity cost of a bed-day was significantly lower than the accounting cost; median values were i72 and i929, respectively (P ! .001). Accounting methods overestimate the opportunity cost of bed-days...

A comparison of methods to estimate the extent of unlicensed driving: Literature review. Final report to Queensland Transport

Unlicensed driving is a serious problem in many countries, despite ongoing improvements in traffic law enforcement practices and technology. The term ‘unlicensed driver' is generally used to refer to people who operate a motor vehicle or motorcycle without a valid driver's licence, including those who: • have let their licence expire; • have been disqualified or suspended from driving; • hold an inappropriate class of licence for the vehicle they drive; • drive outside the restrictions of a special licence; • don’t currently hold a licence; or • have never held a licence.