Collective motion of dimers

We consider a discrete agent-based model on a one-dimensional lattice and a two-dimensional square lattice, where each agent is a dimer occupying two sites. Agents move by vacating one occupied site in favor of a nearest-neighbor site and obey either a strict simple exclusion rule or a weaker constraint that permits partial overlaps between dimers. Using indicator variables and careful probability arguments, a discrete-time master equation for these processes is derived systematically within a mean-field approximation. In the continuum limit, nonlinear diffusion equations that describe the average agent occupancy of the dimer population are obtained. In addition, we show that multiple species of interacting subpopulations give rise to advection-diffusion equations. Averaged discrete simulation data compares very well with the solution to the continuum partial differential equation models. Since many cell types are elongated rather than circular, this work offers insight into population-level behavior of collective cellular motion.

Bayesian models for spatio-temporal assessment of disease

This thesis has contributed to the advancement of knowledge in disease modelling by addressing interesting and crucial issues relevant to modelling health data over space and time. The research has led to the increased understanding of spatial scales, temporal scales, and spatial smoothing for modelling diseases, in terms of their methodology and applications. This research is of particular significance to researchers seeking to employ statistical modelling techniques over space and time in various disciplines. A broad class of statistical models are employed to assess what impact of spatial and temporal scales have on simulated and real data.

An investigation of the impact of various geographical scales for the specification of spatial dependence

Ecological studies are based on characteristics of groups of individuals, which are common in various disciplines including epidemiology. It is of great interest for epidemiologists to study the geographical variation of a disease by accounting for the positive spatial dependence between neighbouring areas. However, the choice of scale of the spatial correlation requires much attention. In view of a lack of studies in this area, this study aims to investigate the impact of differing definitions of geographical scales using a multilevel model. We propose a new approach -- the grid-based partitions and compare it with the popular census region approach. Unexplained geographical variation is accounted for via area-specific unstructured random effects and spatially structured random effects specified as an intrinsic conditional autoregressive process. Using grid-based modelling of random effects in contrast to the census region approach, we illustrate conditions where improvements are observed in the estimation of the linear predictor, random effects, parameters, and the identification of the distribution of residual risk and the aggregate risk in a study region. The study has found that grid-based modelling is a valuable approach for spatially sparse data while the SLA-based and grid-based approaches perform equally well for spatially dense data.

Bayesian hierarchical models for analysing spatial point-based data at a grid level: A comparison of approaches

Spatial data are now prevalent in a wide range of fields including environmental and health science. This has led to the development of a range of approaches for analysing patterns in these data. In this paper, we compare several Bayesian hierarchical models for analysing point-based data based on the discretization of the study region, resulting in grid-based spatial data. The approaches considered include two parametric models and a semiparametric model. We highlight the methodology and computation for each approach. Two simulation studies are undertaken to compare the performance of these models for various structures of simulated point-based data which resemble environmental data. A case study of a real dataset is also conducted to demonstrate a practical application of the modelling approaches. Goodness-of-fit statistics are computed to compare estimates of the intensity functions. The deviance information criterion is also considered as an alternative model evaluation criterion. The results suggest that the adaptive Gaussian Markov random field model performs well for highly sparse point-based data where there are large variations or clustering across the space; whereas the discretized log Gaussian Cox process produces good fit in dense and clustered point-based data. One should generally consider the nature and structure of the point-based data in order to choose the appropriate method in modelling a discretized spatial point-based data.

A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

A computationally efficient sequential Monte Carlo algorithm is proposed for the sequential design of experiments for the collection of block data described by mixed effects models. The difficulty in applying a sequential Monte Carlo algorithm in such settings is the need to evaluate the observed data likelihood, which is typically intractable for all but linear Gaussian models. To overcome this difficulty, we propose to unbiasedly estimate the likelihood, and perform inference and make decisions based on an exact-approximate algorithm. Two estimates are proposed: using Quasi Monte Carlo methods and using the Laplace approximation with importance sampling. Both of these approaches can be computationally expensive, so we propose exploiting parallel computational architectures to ensure designs can be derived in a timely manner. We also extend our approach to allow for model uncertainty. This research is motivated by important pharmacological studies related to the treatment of critically ill patients.

Coherent phonon decay and the boron isotope effect for MgB2

Ab-initio DFT calculations for the phonon dispersion (PD) and the Phonon Density Of States (PDOS) of the two isotopic forms (10B and 11B) of MgB2 demonstrate that use of a reduced symmetry super-lattice provides an improved approximation to the dynamical, phonon-distorted P6/mmm crystal structure. Construction of phonon frequency plots using calculated values for these isotopic forms gives linear trends with integer multiples of a base frequency that change in slope in a manner consistent with the isotope effect (IE). Spectral parameters inferred from this method are similar to that determined experimentally for the pure isotopic forms of MgB2. Comparison with AlB2 demonstrates that a coherent phonon decay down to acoustic modes is not possible for this metal. Coherent acoustic phonon decay may be an important contributor to superconductivity for MgB2.

A tag-based personalized item recommendation system using tensor modeling and topic model approaches

This research falls in the area of enhancing the quality of tag-based item recommendation systems. It aims to achieve this by employing a multi-dimensional user profile approach and by analyzing the semantic aspects of tags. Tag-based recommender systems have two characteristics that need to be carefully studied in order to build a reliable system. Firstly, the multi-dimensional correlation, called as tag assignment , should be appropriately modelled in order to create the user profiles [1]. Secondly, the semantics behind the tags should be considered properly as the flexibility with their design can cause semantic problems such as synonymy and polysemy [2]. This research proposes to address these two challenges for building a tag-based item recommendation system by employing tensor modeling as the multi-dimensional user profile approach, and the topic model as the semantic analysis approach. The first objective is to optimize the tensor model reconstruction and to improve the model performance in generating quality rec-ommendation. A novel Tensor-based Recommendation using Probabilistic Ranking (TRPR) method [3] has been developed. Results show this method to be scalable for large datasets and outperforming the benchmarking methods in terms of accuracy. The memory efficient loop implements the n-mode block-striped (matrix) product for tensor reconstruction as an approximation of the initial tensor. The probabilistic ranking calculates the probabil-ity of users to select candidate items using their tag preference list based on the entries generated from the reconstructed tensor. The second objective is to analyse the tag semantics and utilize the outcome in building the tensor model. This research proposes to investigate the problem using topic model approach to keep the tags nature as the “social vocabulary” [4]. For the tag assignment data, topics can be generated from the occurrences of tags given for an item. However there is only limited amount of tags availa-ble to represent items as collection of topics, since an item might have only been tagged by using several tags. Consequently, the generated topics might not able to represent the items appropriately. Furthermore, given that each tag can belong to any topics with various probability scores, the occurrence of tags cannot simply be mapped by the topics to build the tensor model. A standard weighting technique will not appropriately calculate the value of tagging activity since it will define the context of an item using a tag instead of a topic.

Deriving a preference-based utility measure for cancer patients from the European Organisation for the Research and Treatment of Cancer's Quality of Life Questionnaire C30 : a confirmatory versus exploratory approach

Background Multi attribute utility instruments (MAUIs) are preference-based measures that comprise a health state classification system (HSCS) and a scoring algorithm that assigns a utility value to each health state in the HSCS. When developing a MAUI from a health-related quality of life (HRQOL) questionnaire, first a HSCS must be derived. This typically involves selecting a subset of domains and items because HRQOL questionnaires typically have too many items to be amendable to the valuation task required to develop the scoring algorithm for a MAUI. Currently, exploratory factor analysis (EFA) followed by Rasch analysis is recommended for deriving a MAUI from a HRQOL measure. Aim To determine whether confirmatory factor analysis (CFA) is more appropriate and efficient than EFA to derive a HSCS from the European Organisation for the Research and Treatment of Cancer’s core HRQOL questionnaire, Quality of Life Questionnaire (QLQ-C30), given its well-established domain structure. Methods QLQ-C30 (Version 3) data were collected from 356 patients receiving palliative radiotherapy for recurrent/metastatic cancer (various primary sites). The dimensional structure of the QLQ-C30 was tested with EFA and CFA, the latter informed by the established QLQ-C30 structure and views of both patients and clinicians on which are the most relevant items. Dimensions determined by EFA or CFA were then subjected to Rasch analysis. Results CFA results generally supported the proposed QLQ-C30 structure (comparative fit index =0.99, Tucker–Lewis index =0.99, root mean square error of approximation =0.04). EFA revealed fewer factors and some items cross-loaded on multiple factors. Further assessment of dimensionality with Rasch analysis allowed better alignment of the EFA dimensions with those detected by CFA. Conclusion CFA was more appropriate and efficient than EFA in producing clinically interpretable results for the HSCS for a proposed new cancer-specific MAUI. Our findings suggest that CFA should be recommended generally when deriving a preference-based measure from a HRQOL measure that has an established domain structure.

High performance all-carbon thin film supercapacitors

We fabricated high performance supercapacitors by using all carbon electrodes, with volume energy in the order of 10−3 Whcm−3, comparable to Li-ion batteries, and power densities in the range of 10 Wcm−3, better than laser-scribed-graphene supercapacitors. All-carbon supercapacitor electrodes are made by solution processing and filtering electrochemically-exfoliated graphene sheets mixed with clusters of spontaneously entangled multiwall carbon nanotubes. We maximize the capacitance by using a 1:1 weight ratio of graphene to multi-wall carbon nanotubes and by controlling their packing in the electrode film so as to maximize accessible surface and further enhance the charge collection. This electrode is transferred onto a plastic-paper-supported double-wall carbon nanotube film used as current collector. These all-carbon thin films are combined with plastic paper and gelled electrolyte to produce solid-state bendable thin film supercapacitors. We assembled supercapacitor cells in series in a planar configuration to increase the operating voltage and find that the shape of our supercapacitor film strongly affects its capacitance. An in-line superposition of rectangular sheets is superior to a cross superposition in maintaining high capacitance when subject to fast charge/discharge cycles. The effect is explained by addressing the mechanism of ion diffusion into stacked graphene sheets.

Force controlled hexapod walking

This thesis is a study on controlling methods for six-legged robots. The study is based on mathematical modeling and simulation. A new joint controller is proposed and tested in simulation that uses joint angles and leg reaction force as inputs to generate a torque, and a method to optimise this controller is formulated and validated. Simulation shows that hexapod can walk on flat ground based on PID controllers with just four target configurations and a set of leg coordination rules, which provided the basis for the design of the new controller.

A new ambiguity acceptance test threshold determination method with controllable failure rate

The ambiguity acceptance test is an important quality control procedure in high precision GNSS data processing. Although the ambiguity acceptance test methods have been extensively investigated, its threshold determine method is still not well understood. Currently, the threshold is determined with the empirical approach or the fixed failure rate (FF-) approach. The empirical approach is simple but lacking in theoretical basis, while the FF-approach is theoretical rigorous but computationally demanding. Hence, the key of the threshold determination problem is how to efficiently determine the threshold in a reasonable way. In this study, a new threshold determination method named threshold function method is proposed to reduce the complexity of the FF-approach. The threshold function method simplifies the FF-approach by a modeling procedure and an approximation procedure. The modeling procedure uses a rational function model to describe the relationship between the FF-difference test threshold and the integer least-squares (ILS) success rate. The approximation procedure replaces the ILS success rate with the easy-to-calculate integer bootstrapping (IB) success rate. Corresponding modeling error and approximation error are analysed with simulation data to avoid nuisance biases and unrealistic stochastic model impact. The results indicate the proposed method can greatly simplify the FF-approach without introducing significant modeling error. The threshold function method makes the fixed failure rate threshold determination method feasible for real-time applications.

The Craving Experience Questionnaire : a brief, theory-based measure of consummatory desire and craving

Background and Aims Research into craving is hampered by lack of theoretical specification and a plethora of substance-specific measures. This study aimed to develop a generic measure of craving based on elaborated intrusion (EI) theory. Confirmatory factor analysis (CFA) examined whether a generic measure replicated the three-factor structure of the Alcohol Craving Experience (ACE) scale over different consummatory targets and time-frames. Design Twelve studies were pooled for CFA. Targets included alcohol, cigarettes, chocolate and food. Focal periods varied from the present moment to the previous week. Separate analyses were conducted for strength and frequency forms. Setting Nine studies included university students, with single studies drawn from an internet survey, a community sample of smokers and alcohol-dependent out-patients. Participants A heterogeneous sample of 1230 participants. Measurements Adaptations of the ACE questionnaire. Findings Both craving strength [comparative fit indices (CFI = 0.974; root mean square error of approximation (RMSEA) = 0.039, 95% confidence interval (CI) = 0.035–0.044] and frequency (CFI = 0.971, RMSEA = 0.049, 95% CI = 0.044–0.055) gave an acceptable three-factor solution across desired targets that mapped onto the structure of the original ACE (intensity, imagery, intrusiveness), after removing an item, re-allocating another and taking intercorrelated error terms into account. Similar structures were obtained across time-frames and targets. Preliminary validity data on the resulting 10-item Craving Experience Questionnaire (CEQ) for cigarettes and alcohol were strong. Conclusions The Craving Experience Questionnaire (CEQ) is a brief, conceptually grounded and psychometrically sound measure of desires. It demonstrates a consistent factor structure across a range of consummatory targets in both laboratory and clinical contexts.

Contributions to Bayesian experimental design

This thesis progresses Bayesian experimental design by developing novel methodologies and extensions to existing algorithms. Through these advancements, this thesis provides solutions to several important and complex experimental design problems, many of which have applications in biology and medicine. This thesis consists of a series of published and submitted papers. In the first paper, we provide a comprehensive literature review on Bayesian design. In the second paper, we discuss methods which may be used to solve design problems in which one is interested in finding a large number of (near) optimal design points. The third paper presents methods for finding fully Bayesian experimental designs for nonlinear mixed effects models, and the fourth paper investigates methods to rapidly approximate the posterior distribution for use in Bayesian utility functions.

A numerical method for the fractional Fitzhugh–Nagumo monodomain model

A fractional FitzHugh–Nagumo monodomain model with zero Dirichlet boundary conditions is presented, generalising the standard monodomain model that describes the propagation of the electrical potential in heterogeneous cardiac tissue. The model consists of a coupled fractional Riesz space nonlinear reaction-diffusion model and a system of ordinary differential equations, describing the ionic fluxes as a function of the membrane potential. We solve this model by decoupling the space-fractional partial differential equation and the system of ordinary differential equations at each time step. Thus, this means treating the fractional Riesz space nonlinear reaction-diffusion model as if the nonlinear source term is only locally Lipschitz. The fractional Riesz space nonlinear reaction-diffusion model is solved using an implicit numerical method with the shifted Grunwald–Letnikov approximation, and the stability and convergence are discussed in detail in the context of the local Lipschitz property. Some numerical examples are given to show the consistency of our computational approach.