Lattice-free descriptions of collective motion with crowding and adhesion

Cell-to-cell adhesion is an important aspect of malignant spreading that is often observed in images from the experimental cell biology literature. Since cell-to-cell adhesion plays an important role in controlling the movement of individual malignant cells, it is likely that cell-to-cell adhesion also influences the spatial spreading of populations of such cells. Therefore, it is important for us to develop biologically realistic simulation tools that can mimic the key features of such collective spreading processes to improve our understanding of how cell-to-cell adhesion influences the spreading of cell populations. Previous models of collective cell spreading with adhesion have used lattice-based random walk frameworks which may lead to unrealistic results, since the agents in the random walk simulations always move across an artificial underlying lattice structure. This is particularly problematic in high-density regions where it is clear that agents in the random walk align along the underlying lattice, whereas no such regular alignment is ever observed experimentally. To address these limitations, we present a lattice-free model of collective cell migration that explicitly incorporates crowding and adhesion. We derive a partial differential equation description of the discrete process and show that averaged simulation results compare very well with numerical solutions of the partial differential equation.

Examining the potential for design and renewable energy to contribute to zero energy housing in Queensland

This was a comparative study of the possibility of a net zero energy house in Queensland, Australia. It examines the actual energy use and thermal comfort conditions of an occupied Brisbane home and compares performance with the 10 star scale rating scheme for Australian residential buildings. An adaptive comfort psychometric chart was developed for this analysis. The house's capacity for the use of the natural ventilation was studied by CFD modelling. This study showed that the house succeeded in achieving the definition of net zero energy on an annual and monthly basis for lighting, cooking and space heating / cooling and for 70% of days for lighting, hot water and cooking services.

The equity and efficiency of the Australian share market with respect to director trading

Purpose – The purpose of this paper is to investigate the extent of directors breaching the reporting requirements of the Australian Stock Exchange (ASX) and the Corporations Act in Australia. Further, it seeks to assess whether directors in Australia achieve abnormal returns from trades in their own companies. Design/methodology/approach – Using an event study approach on an Australian sample, abnormal returns for a range of situations were estimated. Findings – A total of 13 (seven) per cent of own‐company directors trades do not meet the ASX (Corporations Act) requirement of reporting within five (14) business days. Directors do achieve abnormal returns through trading in shares of their own companies. Ignoring transaction costs, outsiders can achieve abnormal returns by imitating directors' trades. Analysis of returns to directors after they trade but before they announce the trade to the market shows that directors are making small but statistically significant returns that are not available to the market. Analysis of returns to directors subsequent to the ASX reporting requirement up to the day the trade is reported shows that directors are making small but statistically significant returns that should be available to the market. Research limitations/implications – Future research should investigate the linkages between late reporting by directors and disadvantages to outside shareholders and the implementation of internal policies implemented to mitigate insider trading. Practical implications – Market participants should remain vigilant regarding the potential for late/non‐reporting of directors' trades. Originality/value – Uncovering breaches of reporting regulations are particularly important given that directors tend to purchase (sell) shares when the price is low (high), thereby achieving abnormal returns.

Combining ganglion cell topology and data of patients with glaucoma to determine a structure-function map

PURPOSE: To introduce techniques for deriving a map that relates visual field locations to optic nerve head (ONH) sectors and to use the techniques to derive a map relating Medmont perimetric data to data from the Heidelberg Retinal Tomograph. METHODS: Spearman correlation coefficients were calculated relating each visual field location (Medmont M700) to rim area and volume measures for 10 degrees ONH sectors (HRT III software) for 57 participants: 34 with glaucoma, 18 with suspected glaucoma, and 5 with ocular hypertension. Correlations were constrained to be anatomically plausible with a computational model of the axon growth of retinal ganglion cells (Algorithm GROW). GROW generated a map relating field locations to sectors of the ONH. The sector with the maximum statistically significant (P < 0.05) correlation coefficient within 40 degrees of the angle predicted by GROW for each location was computed. Before correlation, both functional and structural data were normalized by either normative data or the fellow eye in each participant. RESULTS: The model of axon growth produced a 24-2 map that is qualitatively similar to existing maps derived from empiric data. When GROW was used in conjunction with normative data, 31% of field locations exhibited a statistically significant relationship. This significance increased to 67% (z-test, z = 4.84; P < 0.001) when both field and rim area data were normalized with the fellow eye. CONCLUSIONS: A computational model of axon growth and normalizing data by the fellow eye can assist in constructing an anatomically plausible map connecting visual field data and sectoral ONH data.

Classification of Airborne LIDAR Intensity Data Using Statistical Analysis and Hough Transform with Application to Power Line Corridors

Light Detection and Ranging (LIDAR) has great potential to assist vegetation management in power line corridors by providing more accurate geometric information of the power line assets and vegetation along the corridors. However, the development of algorithms for the automatic processing of LIDAR point cloud data, in particular for feature extraction and classification of raw point cloud data, is in still in its infancy. In this paper, we take advantage of LIDAR intensity and try to classify ground and non-ground points by statistically analyzing the skewness and kurtosis of the intensity data. Moreover, the Hough transform is employed to detected power lines from the filtered object points. The experimental results show the effectiveness of our methods and indicate that better results were obtained by using LIDAR intensity data than elevation data.

Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion

Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A^(-α/2)b, where A ∈ ℝ^(n×n) is a large, sparse symmetric positive definite matrix and b ∈ ℝ^n is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LL^T is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L^(-T)z, with x = A^(-1/2)z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form ϕn = A^(-α/2)b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t^(-α/2) and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A^(-α/2)b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.