Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

Supplement : Efficient weak second-order stochastic Runge-Kutta methods for non-commutative Stratonvich stochastic differential equations

This paper gives a modification of a class of stochastic Runge–Kutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly.

Investigation of methods for increasing the energy efficiency on unmanned aerial vehicles (UAVS)

In recent years, development of Unmanned Aerial Vehicles (UAV) has become a significant growing segment of the global aviation industry. These vehicles are developed with the intention of operating in regions where the presence of onboard human pilots is either too risky or unnecessary. Their popularity with both the military and civilian sectors have seen the use of UAVs in a diverse range of applications, from reconnaissance and surveillance tasks for the military, to civilian uses such as aid relief and monitoring tasks. Efficient energy utilisation on an UAV is essential to its functioning, often to achieve the operational goals of range, endurance and other specific mission requirements. Due to the limitations of the space available and the mass budget on the UAV, it is often a delicate balance between the onboard energy available (i.e. fuel) and achieving the operational goals. This thesis presents an investigation of methods for increasing the energy efficiency on UAVs. One method is via the development of a Mission Waypoint Optimisation (MWO) procedure for a small fixed-wing UAV, focusing on improving the onboard fuel economy. MWO deals with a pre-specified set of waypoints by modifying the given waypoints within certain limits to achieve its optimisation objectives of minimising/maximising specific parameters. A simulation model of a UAV was developed in the MATLAB Simulink environment, utilising the AeroSim Blockset and the in-built Aerosonde UAV block and its parameters. This simulation model was separately integrated with a multi-objective Evolutionary Algorithm (MOEA) optimiser and a Sequential Quadratic Programming (SQP) solver to perform single-objective and multi-objective optimisation procedures of a set of real-world waypoints in order to minimise the onboard fuel consumption. The results of both procedures show potential in reducing fuel consumption on a UAV in a ight mission. Additionally, a parallel Hybrid-Electric Propulsion System (HEPS) on a small fixedwing UAV incorporating an Ideal Operating Line (IOL) control strategy was developed. An IOL analysis of an Aerosonde engine was performed, and the most efficient (i.e. provides greatest torque output at the least fuel consumption) points of operation for this engine was determined. Simulation models of the components in a HEPS were designed and constructed in the MATLAB Simulink environment. It was demonstrated through simulation that an UAV with the current HEPS configuration was capable of achieving a fuel saving of 6.5%, compared to the ICE-only configuration. These components form the basis for the development of a complete simulation model of a Hybrid-Electric UAV (HEUAV).

Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions

We consider time-space fractional reaction diffusion equations in two dimensions. This equation is obtained from the standard reaction diffusion equation by replacing the first order time derivative with the Caputo fractional derivative, and the second order space derivatives with the fractional Laplacian. Using the matrix transfer technique proposed by Ilic, Liu, Turner and Anh [Fract. Calc. Appl. Anal., 9:333--349, 2006] and the numerical solution strategy used by Yang, Turner, Liu, and Ilic [SIAM J. Scientific Computing, 33:1159--1180, 2011], the solution of the time-space fractional reaction diffusion equations in two dimensions can be written in terms of a matrix function vector product $f(A)b$ at each time step, where $A$ is an approximate matrix representation of the standard Laplacian. We use the finite volume method over unstructured triangular meshes to generate the matrix $A$, which is therefore non-symmetric. However, the standard Lanczos method for approximating $f(A)b$ requires that $A$ is symmetric. We propose a simple and novel transformation in which the standard Lanczos method is still applicable to find $f(A)b$, despite the loss of symmetry. Numerical results are presented to verify the accuracy and efficiency of our newly proposed numerical solution strategy.

A multi-resolution image alignment technique based on direct methods for pose estimation of aerial vehicles

In this paper, we seek to expand the use of direct methods in real-time applications by proposing a vision-based strategy for pose estimation of aerial vehicles. The vast majority of approaches make use of features to estimate motion. Conversely, the strategy we propose is based on a MR (Multi- Resolution) implementation of an image registration technique (Inverse Compositional Image Alignment ICIA) using direct methods. An on-board camera in a downwards-looking configuration, and the assumption of planar scenes, are the bases of the algorithm. The motion between frames (rotation and translation) is recovered by decomposing the frame-to-frame homography obtained by the ICIA algorithm applied to a patch that covers around the 80% of the image. When the visual estimation is required (e.g. GPS drop-out), this motion is integrated with the previous known estimation of the vehicles’ state, obtained from the on-board sensors (GPS/IMU), and the subsequent estimations are based only on the vision-based motion estimations. The proposed strategy is tested with real flight data in representative stages of a flight: cruise, landing, and take-off, being two of those stages considered critical: take-off and landing. The performance of the pose estimation strategy is analyzed by comparing it with the GPS/IMU estimations. Results show correlation between the visual estimation obtained with the MR-ICIA and the GPS/IMU data, that demonstrate that the visual estimation can be used to provide a good approximation of the vehicle’s state when it is required (e.g. GPS drop-outs). In terms of performance, the proposed strategy is able to maintain an estimation of the vehicle’s state for more than one minute, at real-time frame rates based, only on visual information.

Bilski v Kappos : The United States Supreme Court delivers mixed views on patenting non-physical inventions and business methods

The United States Supreme Court has handed down a once in a generation patent law decision that will have important ramifications for the patentability of non-physical methods, both internationally and in Australia. In Bilski v Kappos, the Supreme Court considered whether an invention must either be tied to a machine or apparatus, or transform an article into a different state or thing to be patentable. It also considered for the first time whether business methods are patentable subject matter. The decision will be of particular interest to practitioners who followed the litigation in Grant v Commissioner of Patents, a Federal Court decision in which a Brisbane-based inventor was denied a patent over a method of protecting an asset from the claims of creditors.

Prediction of structural integrity, robustness and service life using advanced finite element methods

Corrosion is a common phenomenon and critical aspects of steel structural application. It affects the daily design, inspection and maintenance in structural engineering, especially for the heavy and complex industrial applications, where the steel structures are subjected to hash corrosive environments in combination of high working stress condition and often in open field and/or under high temperature production environments. In the paper, it presents the actual engineering application of advanced finite element methods in the predication of the structural integrity and robustness at a designed service life for the furnaces of alumina production, which was operated in the high temperature, corrosive environments and rotating with high working stress condition.

Using Bayesian methods for the estimation of uncertainty in complex statistical models

The research objectives of this thesis were to contribute to Bayesian statistical methodology by contributing to risk assessment statistical methodology, and to spatial and spatio-temporal methodology, by modelling error structures using complex hierarchical models. Specifically, I hoped to consider two applied areas, and use these applications as a springboard for developing new statistical methods as well as undertaking analyses which might give answers to particular applied questions. Thus, this thesis considers a series of models, firstly in the context of risk assessments for recycled water, and secondly in the context of water usage by crops. The research objective was to model error structures using hierarchical models in two problems, namely risk assessment analyses for wastewater, and secondly, in a four dimensional dataset, assessing differences between cropping systems over time and over three spatial dimensions. The aim was to use the simplicity and insight afforded by Bayesian networks to develop appropriate models for risk scenarios, and again to use Bayesian hierarchical models to explore the necessarily complex modelling of four dimensional agricultural data. The specific objectives of the research were to develop a method for the calculation of credible intervals for the point estimates of Bayesian networks; to develop a model structure to incorporate all the experimental uncertainty associated with various constants thereby allowing the calculation of more credible credible intervals for a risk assessment; to model a single day’s data from the agricultural dataset which satisfactorily captured the complexities of the data; to build a model for several days’ data, in order to consider how the full data might be modelled; and finally to build a model for the full four dimensional dataset and to consider the timevarying nature of the contrast of interest, having satisfactorily accounted for possible spatial and temporal autocorrelations. This work forms five papers, two of which have been published, with two submitted, and the final paper still in draft. The first two objectives were met by recasting the risk assessments as directed, acyclic graphs (DAGs). In the first case, we elicited uncertainty for the conditional probabilities needed by the Bayesian net, incorporated these into a corresponding DAG, and used Markov chain Monte Carlo (MCMC) to find credible intervals, for all the scenarios and outcomes of interest. In the second case, we incorporated the experimental data underlying the risk assessment constants into the DAG, and also treated some of that data as needing to be modelled as an ‘errors-invariables’ problem [Fuller, 1987]. This illustrated a simple method for the incorporation of experimental error into risk assessments. In considering one day of the three-dimensional agricultural data, it became clear that geostatistical models or conditional autoregressive (CAR) models over the three dimensions were not the best way to approach the data. Instead CAR models are used with neighbours only in the same depth layer. This gave flexibility to the model, allowing both the spatially structured and non-structured variances to differ at all depths. We call this model the CAR layered model. Given the experimental design, the fixed part of the model could have been modelled as a set of means by treatment and by depth, but doing so allows little insight into how the treatment effects vary with depth. Hence, a number of essentially non-parametric approaches were taken to see the effects of depth on treatment, with the model of choice incorporating an errors-in-variables approach for depth in addition to a non-parametric smooth. The statistical contribution here was the introduction of the CAR layered model, the applied contribution the analysis of moisture over depth and estimation of the contrast of interest together with its credible intervals. These models were fitted using WinBUGS [Lunn et al., 2000]. The work in the fifth paper deals with the fact that with large datasets, the use of WinBUGS becomes more problematic because of its highly correlated term by term updating. In this work, we introduce a Gibbs sampler with block updating for the CAR layered model. The Gibbs sampler was implemented by Chris Strickland using pyMCMC [Strickland, 2010]. This framework is then used to consider five days data, and we show that moisture in the soil for all the various treatments reaches levels particular to each treatment at a depth of 200 cm and thereafter stays constant, albeit with increasing variances with depth. In an analysis across three spatial dimensions and across time, there are many interactions of time and the spatial dimensions to be considered. Hence, we chose to use a daily model and to repeat the analysis at all time points, effectively creating an interaction model of time by the daily model. Such an approach allows great flexibility. However, this approach does not allow insight into the way in which the parameter of interest varies over time. Hence, a two-stage approach was also used, with estimates from the first-stage being analysed as a set of time series. We see this spatio-temporal interaction model as being a useful approach to data measured across three spatial dimensions and time, since it does not assume additivity of the random spatial or temporal effects.

Methods used in cross-cultural comparisons of psychological symptoms and their determinants

This paper is the second in a series of reviews of cross-cultural studies of menopausal symptoms. The goal of this review is to compare and contrast methods which have been previously utilized in Cross-Cultural Midlife Women's Health Studies with a view to (1) identifying the challenges in measurement across cultures in psychological symptoms and (2) suggesting a set of unified questions and tools that can be used in future research in this area. This review also aims to examine the determinants of psychological symptoms and how those determinants were measured. The review included eight studies that explicitly compared symptoms in different countries or different ethnic groups in the same country and included: Australian/Japanese Midlife Women's Health Study (AJMWHS), Decisions At Menopause Study (DAMeS), Four Major Ethnic Groups (FMEG), Hilo Women's Health Survey (HWHS), Penn Ovarian Aging Study (POAS), Study of Women's Health Across the Nation (SWAN), Women's Health in Midlife National Study (WHiMNS), and the Women's International Study of Health and Sexuality (WISHeS). This review concludes that mental morbidity does affect vasomotor symptom prevalence across cultures and therefore should be measured. Based on the review of these eight studies it is recommended that the following items be included when measuring psychological symptoms across cultures, feeling tense or nervous, sleeping difficulty, difficulty in concentrating, depressed and irritability along with the CES-D Scale, and the Perceived Stress Scale. The measurement of these symptoms will provide an evidence based approach when forming any future menopause symptom list and allow for comparisons across studies.