Hierarchical models for 2D presence/absence data having ambiguous zeroes: With a biogeographical case study on dingo behaviour

This dissertation is primarily an applied statistical modelling investigation, motivated by a case study comprising real data and real questions. Theoretical questions on modelling and computation of normalization constants arose from pursuit of these data analytic questions. The essence of the thesis can be described as follows. Consider binary data observed on a two-dimensional lattice. A common problem with such data is the ambiguity of zeroes recorded. These may represent zero response given some threshold (presence) or that the threshold has not been triggered (absence). Suppose that the researcher wishes to estimate the effects of covariates on the binary responses, whilst taking into account underlying spatial variation, which is itself of some interest. This situation arises in many contexts and the dingo, cypress and toad case studies described in the motivation chapter are examples of this. Two main approaches to modelling and inference are investigated in this thesis. The first is frequentist and based on generalized linear models, with spatial variation modelled by using a block structure or by smoothing the residuals spatially. The EM algorithm can be used to obtain point estimates, coupled with bootstrapping or asymptotic MLE estimates for standard errors. The second approach is Bayesian and based on a three- or four-tier hierarchical model, comprising a logistic regression with covariates for the data layer, a binary Markov Random field (MRF) for the underlying spatial process, and suitable priors for parameters in these main models. The three-parameter autologistic model is a particular MRF of interest. Markov chain Monte Carlo (MCMC) methods comprising hybrid Metropolis/Gibbs samplers is suitable for computation in this situation. Model performance can be gauged by MCMC diagnostics. Model choice can be assessed by incorporating another tier in the modelling hierarchy. This requires evaluation of a normalization constant, a notoriously difficult problem. Difficulty with estimating the normalization constant for the MRF can be overcome by using a path integral approach, although this is a highly computationally intensive method. Different methods of estimating ratios of normalization constants (N Cs) are investigated, including importance sampling Monte Carlo (ISMC), dependent Monte Carlo based on MCMC simulations (MCMC), and reverse logistic regression (RLR). I develop an idea present though not fully developed in the literature, and propose the Integrated mean canonical statistic (IMCS) method for estimating log NC ratios for binary MRFs. The IMCS method falls within the framework of the newly identified path sampling methods of Gelman & Meng (1998) and outperforms ISMC, MCMC and RLR. It also does not rely on simplifying assumptions, such as ignoring spatio-temporal dependence in the process. A thorough investigation is made of the application of IMCS to the three-parameter Autologistic model. This work introduces background computations required for the full implementation of the four-tier model in Chapter 7. Two different extensions of the three-tier model to a four-tier version are investigated. The first extension incorporates temporal dependence in the underlying spatio-temporal process. The second extensions allows the successes and failures in the data layer to depend on time. The MCMC computational method is extended to incorporate the extra layer. A major contribution of the thesis is the development of a fully Bayesian approach to inference for these hierarchical models for the first time. Note: The author of this thesis has agreed to make it open access but invites people downloading the thesis to send her an email via the 'Contact Author' function.

Modelling of some biological materials using continuum mechanics

Continuum mechanics provides a mathematical framework for modelling the physical stresses experienced by a material. Recent studies show that physical stresses play an important role in a wide variety of biological processes, including dermal wound healing, soft tissue growth and morphogenesis. Thus, continuum mechanics is a useful mathematical tool for modelling a range of biological phenomena. Unfortunately, classical continuum mechanics is of limited use in biomechanical problems. As cells refashion the �bres that make up a soft tissue, they sometimes alter the tissue's fundamental mechanical structure. Advanced mathematical techniques are needed in order to accurately describe this sort of biological `plasticity'. A number of such techniques have been proposed by previous researchers. However, models that incorporate biological plasticity tend to be very complicated. Furthermore, these models are often di�cult to apply and/or interpret, making them of limited practical use. One alternative approach is to ignore biological plasticity and use classical continuum mechanics. For example, most mechanochemical models of dermal wound healing assume that the skin behaves as a linear viscoelastic solid. Our analysis indicates that this assumption leads to physically unrealistic results. In this thesis we present a novel and practical approach to modelling biological plasticity. Our principal aim is to combine the simplicity of classical linear models with the sophistication of plasticity theory. To achieve this, we perform a careful mathematical analysis of the concept of a `zero stress state'. This leads us to a formal de�nition of strain that is appropriate for materials that undergo internal remodelling. Next, we consider the evolution of the zero stress state over time. We develop a novel theory of `morphoelasticity' that can be used to describe how the zero stress state changes in response to growth and remodelling. Importantly, our work yields an intuitive and internally consistent way of modelling anisotropic growth. Furthermore, we are able to use our theory of morphoelasticity to develop evolution equations for elastic strain. We also present some applications of our theory. For example, we show that morphoelasticity can be used to obtain a constitutive law for a Maxwell viscoelastic uid that is valid at large deformation gradients. Similarly, we analyse a morphoelastic model of the stress-dependent growth of a tumour spheroid. This work leads to the prediction that a tumour spheroid will always be in a state of radial compression and circumferential tension. Finally, we conclude by presenting a novel mechanochemical model of dermal wound healing that takes into account the plasticity of the healing skin.

On the data consumption benefits of accepting increased uncertainty

In the context of learning paradigms of identification in the limit, we address the question: why is uncertainty sometimes desirable? We use mind change bounds on the output hypotheses as a measure of uncertainty, and interpret ‘desirable’ as reduction in data memorization, also defined in terms of mind change bounds. The resulting model is closely related to iterative learning with bounded mind change complexity, but the dual use of mind change bounds — for hypotheses and for data — is a key distinctive feature of our approach. We show that situations exists where the more mind changes the learner is willing to accept, the lesser the amount of data it needs to remember in order to converge to the correct hypothesis. We also investigate relationships between our model and learning from good examples, set-driven, monotonic and strong-monotonic learners, as well as class-comprising versus class-preserving learnability.

On model typing

Where object-oriented languages deal with objects as described by classes, model-driven development uses models, as graphs of interconnected objects, described by metamodels. A number of new languages have been and continue to be developed for this model- based paradigm, both for model transformation and for general programming using models. Many of these use single-object approaches to typing, derived from solutions found in object-oriented systems, while others use metamodels as model types, but without a clear notion of polymorphism. Both of these approaches lead to brittle and overly restrictive reuse characteristics. In this paper we propose a simple extension to object-oriented typing to better cater for a model-oriented context, including a simple strategy for typing models as a collection of interconnected objects. We suggest extensions to existing type system formalisms to support these concepts and their manipulation. Using a simple example we show how this extended approach permits more flexible reuse, while preserving type safety.

Contracting bubbles in Hele-Shaw cells with a power-law fluid

The problem of bubble contraction in a Hele-Shaw cell is studied for the case in which the surrounding fluid is of power-law type. A small perturbation of the radially symmetric problem is first considered, focussing on the behaviour just before the bubble vanishes, it being found that for shear-thinning fluids the radially symmetric solution is stable, while for shear-thickening fluids the aspect ratio of the bubble boundary increases. The borderline (Newtonian) case considered previously is neutrally stable, the bubble boundary becoming elliptic in shape with the eccentricity of the ellipse depending on the initial data. Further light is shed on the bubble contraction problem by considering a long thin Hele-Shaw cell: for early times the leading-order behaviour is one-dimensional in this limit; however, as the bubble contracts its evolution is ultimately determined by the solution of a Wiener-Hopf problem, the transition between the long-thin limit and the extinction limit in which the bubble vanishes being described by what is in effect a similarity solution of the second kind. This same solution describes the generic (slit-like) extinction behaviour for shear-thickening fluids, the interface profiles that generalise the ellipses that characterise the Newtonian case being constructed by the Wiener-Hopf calculation.

Linear stern waves in finite depth channels

This paper formulates an analytically tractable problem for the wake generated by a long flat bottom ship by considering the steady free surface flow of an inviscid, incompressible fluid emerging from beneath a semi-infinite rigid plate. The flow is considered to be irrotational and two-dimensional so that classical potential flow methods can be exploited. In addition, it is assumed that the draft of the plate is small compared to the depth of the channel. The linearised problem is solved exactly using a Fourier transform and the Wiener-Hopf technique, and it is shown that there is a family of subcritical solutions characterised by a train of sinusoidal waves on the downstream free surface. The amplitude of these waves decreases as the Froude number increases. Supercritical solutions are also obtained, but, in general, these have infinite vertical velocities at the trailing edge of the plate. Consideration of further terms in the expansions suggests a way of canceling the singularity for certain values of the Froude number.

Perturbation solutions for flow through symmetrical hoppers with inserts and asymmetrical wedge hoppers

Under certain circumstances, an industrial hopper which operates under the "funnel-flow" regime can be converted to the "mass-flow" regime with the addition of a flow-corrective insert. This paper is concerned with calculating granular flow patterns near the outlet of hoppers that incorporate a particular type of insert, the cone-in-cone insert. The flow is considered to be quasi-static, and governed by the Coulomb-Mohr yield condition together with the non-dilatant double-shearing theory. In two dimensions, the hoppers are wedge-shaped, and as such the formulation for the wedge-in-wedge hopper also includes the case of asymmetrical hoppers. A perturbation approach, valid for high angles of internal friction, is used for both two-dimensional and axially symmetric flows, with analytic results possible for both leading order and correction terms. This perturbation scheme is compared with numerical solutions to the governing equations, and is shown to work very well for angles of internal friction in excess of 45 degree.

Robust tracking control of autonomous underwater vehicles in the presence of disturbance inputs

An autonomous underwater vehicle (AUV) is expected to operate in an ocean in the presence of poorly known disturbance forces and moments. The uncertainties of the environment makes it difficult to apply open-loop control scheme for the motion planning of the vehicle. The objective of this paper is to develop a robust feedback trajectory tracking control scheme for an AUV that can track a prescribed trajectory amidst such disturbances. We solve a general problem of feedback trajectory tracking of an AUV in SE(3). The feedback control scheme is derived using Lyapunov-type analysis. The results obtained from numerical simulations confirm the asymptotic tracking properties of the feedback control law. We apply the feedback control scheme to different mission scenarios, with the disturbances being initial errors in the state of the AUV.

Optimal fluid injection strategies for in situ mineral leaching in two-dimensions

This paper examines the ground-water flow problem associated with the injection and recovery of certain corrosive fluids into mineral bearing rock. The aim is to dissolve the minerals in situ, and then recover them in solution. In general, it is not possible to recover all the injected fluid, which is of concern economically and environmentally. However, a new strategy is proposed here, that allows all the leaching fluid to be recovered. A mathematical model of the situation is solved approximately using an asymptotic solution, and exactly using a boundary integral approach. Solutions are shown for two-dimensional flow, which is of some practical interest as it is achievable in old mine tunnels, for example.

Management [4th Asia Pacific Edition]

The fourth edition of this popular text has been throughly updated, continuing its strong emphasis on the importance of the Asian region to contemporary Australian and New Zealand organizations. Many Asian case examples are featured to illustrate key management concepts. ----- ----- ----- Joining the author team for this edition and enhancing this edition's critical analysis of management theory and applications are the best-selling authors from another of Wiley's undergraduate introductory management texts - Management: Core Concepts and Applications, 2nd Australasian edition (Davidson et al.).----- ----- ----- This new edition also discusses the impact of recent events such as the global financial crisis on the management of organisations, both during the crisis and in its aftermath.----- ----- ----- Of course, Management, 4th Asia- Pacific edition also retains the features that made it so popular with students and lecturers in the earlier editions: a balanced coverage of small to medium-sized enterprises and larger multinational corporations an emphasis on the need for business activities to be sustainable in terms of preserving the welfare of future generations the Career Readiness Workbook at the end of the book, which includes a range of individual and group activities to encourage the practical applications of management theory. With its clear insights into dynamics of management in the workplace of today and the future, Management, 4th Asia-Pacific edition provides a sound basis for the contemporary undergraduate study of introductory management.

In vitro and in vivo evaluation of adenovirus combined silk fibroin scaffolds for BMP-7 gene delivery

Introduction and aims: For a scaffold material to be considered effective and efficient for tissue engineering it must be biocompatible as well as bioinductive. Silk fiber is a natural biocompatible material suitable for scaffold fabrication; however, silk is tissue-conductive and lacks tissue-inductive properties. One proposed method to make the scaffold tissue-inductive is to introduce plasmids or viruses encoding a specific growth factor into the scaffold. In this study, we constructed adenoviruses encoding bone morphogenetic protein-7 (BMP-7) and incorporated these into silk scaffolds. The osteo-inductive and new bone formation properties of these constructs were assessed in vivo in a critical-sized skull defect animal model. Materials and methods: Silk fibroin scaffolds containing adenovirus particles coding BMP-7 were prepared. The release of the adenovirus particles from the scaffolds was quantified by tissue-culture infective dose (TCID50) and the bioactivity of the released viruses was evaluated on human bone marrow mesenchymal stromal cells (BMSCs). To demonstrate the in vivo bone forming ability of the virus-carrying silk fibroin scaffold, the scaffold constructs were implanted into calvarial defects in SCID mice. Results: In vitro studies demonstrated that the virus-carrying silk fibroin scaffold released virus particles over a 3 week period while preserving their bioactivity. In vivo test of the scaffold constructs in critical-sized skull defect areas revealed that silk scaffolds were capable of delivering the adenovirus encoding BMP-7, resulting significantly enhanced new bone formation. Conclusions: Silk scaffolds carrying BMP-7 encoding adenoviruses can effectively transfect cells and enhance both in vitro and in vivo osteogenesis. The findings of this study indicate silk fibroin is a promising biomaterial for gene delivery to repair critical-sized bone defects.

Numerical solution to the Saffman-Taylor finger problem with kinetic undercooling regularisation

The Saffman-Taylor finger problem is to predict the shape and,in particular, width of a finger of fluid travelling in a Hele-Shaw cell filled with a different, more viscous fluid. In experiments the width is dependent on the speed of propagation of the finger, tending to half the total cell width as the speed increases. To predict this result mathematically, nonlinear effects on the fluid interface must be considered; usually surface tension is included for this purpose. This makes the mathematical problem suffciently diffcult that asymptotic or numerical methods must be used. In this paper we adapt numerical methods used to solve the Saffman-Taylor finger problem with surface tension to instead include the effect of kinetic undercooling, a regularisation effect important in Stefan melting-freezing problems, for which Hele-Shaw flow serves as a leading order approximation when the specific heat of a substance is much smaller than its latent heat. We find the existence of a solution branch where the finger width tends to zero as the propagation speed increases, disagreeing with some aspects of the asymptotic analysis of the same problem. We also find a second solution branch, supporting the idea of a countably infinite number of branches as with the surface tension problem.

The molecular mechanisms utilised by mesenchymal stem cells in migration to acute myocardial infarction

Heart damage caused by acute myocardial infarction (AMI) is a leading cause of death and disability in Australia. Novel therapies are still required for the treatment of this condition due to the poor reparative ability of the heart. As such, cellular therapies that assist in the recovery of heart muscle are of great current interest. Culture expanded mesenchymal stem cells (MSC) represent a stem and progenitor cell population that has been shown to promote tissue recovery in pre-clinical studies of AMI. For MSC-based therapies in the clinic, an intravenous route of administration would ideally be used due to the low cost, ease of delivery and relative safety. The study of MSC migration is therefore clinically relevant for a minimally invasive cell therapy to promote regeneration of damaged tissue. C57BL/6, UBI-GFP-BL/6 and CD44-/-/GFP+/+ mice were utilised to investigate mMSC migration. To assist in murine models of MSC migration, a novel method was used for the isolation of murine MSC (mMSC). These mMSC were then expanded in culture and putative mMSC were positive for Sca-1, CD90.2, and CD44 and were negative for CD45 and CD11b. Furthermore, mMSC from C57BL/6 and UBI-GFP-BL/6 mice were shown to differentiate into cells of the mesodermal lineage. Cells from CD44-/-/GFP+/+ mice were positive for Sca-1 and CD90.2, and negative for CD44, CD45 and CD11b however, these cells were unable to differentiate into adipocytes and chondrocytes and express lineage specific genes, PLIN and ACAN. Analysis of mMSC chemokine receptor (CR) expression showed that although mMSC do express chemokine receptors, (including those specific for chemokines released after AMI), these were low or undetectable by mRNA. However, protein expression could be detected, which was predominantly cytoplasmic. It was further shown that in both healthy (unperturbed) and inflamed tissues, mMSC had very little specific migration and engraftment after intravenous injection. To determine if poor mMSC migration was due to the inability of mMSC to respond to chemotactic stimuli, chemokine expression in bone marrow, skin injury and hearts (healthy and after AMI) was analysed at various time points by quantitative real-time PCR (qRT PCR). Many chemokines were up-regulated after skin biopsy and AMI, but the highest acute levels were found for CXCL12 and CCL7. Due to their high expression in infarcted hearts, the chemokines CXCL12 and CCL7 were tested for their effect on mMSC migration. Despite CR expression at both protein and mRNA levels, migration in response to CXCL12 and CCL7 was low in mMSC cultured on Nunclon plastic. A novel tissue culture plastic technology (UpCellTM) was then used that allowed gentle non-enzymatic dissociation of mMSC, thus preserving surface expression of the CRs. Despite this the in vitro data indicated that CXCL12 fails to induce significant migration ability of mMSC, while CCL7 induces significant, but low-level migration. We speculated this may be because of low levels of surface expression of chemokine receptors. In a strategy to increase cell surface expression of mMSC chemokine receptors and enhance their in vitro and in vivo migration capacity, mMSC were pre-treated with pro-inflammatory cytokines. Increased levels of both mRNA and surface protein expression were found for CRs by pre-treating mMSC with pro-inflammatory cytokines including TNF-á, IFN-ã, IL-1á and IL-6. Furthermore, the chemotactic response of mMSC to CXCL12 and CCL7 was significantly higher with these pretreated cells. Finally, the effectiveness of this type of cell manipulation was demonstrated in vivo, where mMSC pre-treated with TNF-á and IFN-ã showed significantly increased migration in skin injury and AMI models. Therefore this thesis has demonstrated, using in vitro and in vivo models, the potential for prior manipulation of MSC as a possible means for increasing the utility of intravenously delivery for MSC-based cellular therapies.