Some novel techniques of parameter estimation for the dynamical models in biological systems

Inverse problems based on using experimental data to estimate unknown parameters of a system often arise in biological and chaotic systems. In this paper, we consider parameter estimation in systems biology involving linear and non-linear complex dynamical models, including the Michaelis–Menten enzyme kinetic system, a dynamical model of competence induction in Bacillus subtilis bacteria and a model of feedback bypass in B. subtilis bacteria. We propose some novel techniques for inverse problems. Firstly, we establish an approximation of a non-linear differential algebraic equation that corresponds to the given biological systems. Secondly, we use the Picard contraction mapping, collage methods and numerical integration techniques to convert the parameter estimation into a minimization problem of the parameters. We propose two optimization techniques: a grid approximation method and a modified hybrid Nelder–Mead simplex search and particle swarm optimization (MH-NMSS-PSO) for non-linear parameter estimation. The two techniques are used for parameter estimation in a model of competence induction in B. subtilis bacteria with noisy data. The MH-NMSS-PSO scheme is applied to a dynamical model of competence induction in B. subtilis bacteria based on experimental data and the model for feedback bypass. Numerical results demonstrate the effectiveness of our approach.

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.

Advanced Computational Intelligence System for inverse aeronautical design optimisation

Abstract—Computational Intelligence Systems (CIS) is one of advanced softwares. CIS has been important position for solving single-objective / reverse / inverse and multi-objective design problems in engineering. The paper hybridise a CIS for optimisation with the concept of Nash-Equilibrium as an optimisation pre-conditioner to accelerate the optimisation process. The hybridised CIS (Hybrid Intelligence System) coupled to the Finite Element Analysis (FEA) tool and one type of Computer Aided Design(CAD) system; GiD is applied to solve an inverse engineering design problem; reconstruction of High Lift Systems (HLS). Numerical results obtained by the hybridised CIS are compared to the results obtained by the original CIS. The benefits of using the concept of Nash-Equilibrium are clearly demonstrated in terms of solution accuracy and optimisation efficiency.

Development and validation of novel methods for microbial source tracking based on Escherichia coli as an indicator of water quality

Microbial pollution in water periodically affects human health in Australia, particularly in times of drought and flood. There is an increasing need for the control of waterborn microbial pathogens. Methods, allowing the determination of the origin of faecal contamination in water, are generally referred to as Microbial Source Tracking (MST). Various approaches have been evaluated as indicatorsof microbial pathogens in water samples, including detection of different microorganisms and various host-specific markers. However, until today there have been no universal MST methods that could reliably determine the source (human or animal) of faecal contamination. Therefore, the use of multiple approaches is frequently advised. MST is currently recognised as a research tool, rather than something to be included in routine practices. The main focus of this research was to develop novel and universally applicable methods to meet the demands for MST methods in routine testing of water samples. Escherichia coli was chosen initially as the object organism for our studies as, historically and globally, it is the standard indicator of microbial contamination in water. In this thesis, three approaches are described: single nucleotide polymorphism (SNP) genotyping, clustered regularly interspaced short palindromic repeats (CRISPR) screening using high resolution melt analysis (HRMA) methods and phage detection development based on CRISPR types. The advantage of the combination SNP genotyping and CRISPR genes has been discussed in this study. For the first time, a highly discriminatory single nucleotide polymorphism interrogation of E. coli population was applied to identify the host-specific cluster. Six human and one animal-specific SNP profile were revealed. SNP genotyping was successfully applied in the field investigations of the Coomera watershed, South-East Queensland, Australia. Four human profiles [11], [29], [32] and [45] and animal specific SNP profile [7] were detected in water. Two human-specific profiles [29] and [11] were found to be prevalent in the samples over a time period of years. The rainfall (24 and 72 hours), tide height and time, general land use (rural, suburban), seasons, distance from the river mouth and salinity show a lack of relashionship with the diversity of SNP profiles present in the Coomera watershed (p values > 0.05). Nevertheless, SNP genotyping method is able to identify and distinquish between human- and non-human specific E. coli isolates in water sources within one day. In some samples, only mixed profiles were detected. To further investigate host-specificity in these mixed profiles CRISPR screening protocol was developed, to be used on the set of E. coli, previously analysed for SNP profiles. CRISPR loci, which are the pattern of previous DNA coliphages attacks, were considered to be a promising tool for detecting host-specific markers in E. coli. Spacers in CRISPR loci could also reveal the dynamics of virulence in E. coli as well in other pathogens in water. Despite the fact that host-specificity was not observed in the set of E. coli analysed, CRISPR alleles were shown to be useful in detection of the geographical site of sources. HRMA allows determination of ‘different’ and ‘same’ CRISPR alleles and can be introduced in water monitoring as a cost-effective and rapid method. Overall, we show that the identified human specific SNP profiles [11], [29], [32] and [45] can be useful as marker genotypes globally for identification of human faecal contamination in water. Developed in the current study, the SNP typing approach can be used in water monitoring laboratories as an inexpensive, high-throughput and easy adapted protocol. The unique approach based on E. coli spacers for the search for unknown phage was developed to examine the host-specifity in phage sequences. Preliminary experiments on the recombinant plasmids showed the possibility of using this method for recovering phage sequences. Future studies will determine the host-specificity of DNA phage genotyping as soon as first reliable sequences can be acquired. No doubt, only implication of multiple approaches in MST will allow identification of the character of microbial contamination with higher confidence and readability.

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.

Deformation behaviours of coarse-grained and nanocrystalline Mg-5wt% Al alloys

Magnesium alloys have been of growing interest to various engineering applications, such as the automobile, aerospace, communication and computer industries due to their low density, high specific strength, good machineability and availability as compared with other structural materials. However, most Mg alloys suffer from poor plasticity due to their Hexagonal Close Packed structure. Grain refinement has been proved to be an effective method to enhance the strength and alter the ductility of the materials. Several methods have been proposed to produce materials with nanocrystalline grain structures. So far, most of the research work on nanocrystalline materials has been carried out on Face-Centered Cubic and Body-Centered Cubic metals. However, there has been little investigation of nanocrystalline Mg alloys. In this study, bulk coarse-grained and nanocrystalline Mg alloys were fabricated by a mechanical alloying method. The mixed powder of Mg chips and Al powder was mechanically milled under argon atmosphere for different durations of 0 hours (MA0), 10 hours (MA10), 20 hours (MA20), 30 hours (MA30) and 40 hours (MA40), followed by compaction and sintering. Then the sintered billets were hot-extruded into metallic rods with a 7 mm diameter. The obtained Mg alloys have a nominal composition of Mg–5wt% Al, with grain sizes ranging from 13 μm down to 50 nm, depending on the milling durations. The microstructure characterization and evolution after deformation were carried out by means of Optical microscopy, X-Ray Diffraction, Scanning Electron Microscopy, Transmission Electron Microscopy, Scanning Probe Microscopy and Neutron Diffraction techniques. Nanoindentaion, compression and micro-compression tests on micro-pillars were used to study the size effects on the mechanical behaviour of the Mg alloys. Two kinds of size effects on the mechanical behaviours and deformation mechanisms were investigated: grain size effect and sample size effect. The nanoindentation tests were composed of constant strain rate, constant loading rate and indentation creep tests. The normally reported indentation size effect in single crystal and coarse-grained crystals was observed in both the coarse-grained and nanocrystalline Mg alloys. Since the indentation size effect is correlated to the Geometrically Necessary Dislocations under the indenter to accommodate the plastic deformation, the good agreement between the experimental results and the Indentation Size Effect model indicated that, in the current nanocrystalline MA20 and MA30, the dislocation plasticity was still the dominant deformation mechanism. Significant hardness enhancement with decreasing grain size, down to 58 nm, was found in the nanocrystalline Mg alloys. Further reduction of grain size would lead to a drop in the hardness values. The failure of grain refinement strengthening with the relatively high strain rate sensitivity of nanocrystalline Mg alloys suggested a change in the deformation mechanism. Indentation creep tests showed that the stress exponent was dependent on the loading rate during the loading section of the indentation, which was related to the dislocation structures before the creep starts. The influence of grain size on the mechanical behaviour and strength of extruded coarse-grained and nanocrystalline Mg alloys were investigated using uniaxial compression tests. The macroscopic response of the Mg alloys transited from strain hardening to strain softening behaviour, with grain size reduced from 13 ìm to 50 nm. The strain hardening was related to the twinning induced hardening and dislocation hardening effect, while the strain softening was attributed to the localized deformation in the nanocrystalline grains. The tension–compression yield asymmetry was noticed in the nanocrystalline region, demonstrating the twinning effect in the ultra-fine-grained and nanocrystalline region. The relationship k tensions < k compression failed in the nanocrystalline Mg alloys; this was attributed to the twofold effect of grain size on twinning. The nanocrystalline Mg alloys were found to exhibit increased strain rate sensitivity with decreasing grain size, with strain rate ranging from 0.0001/s to 0.01/s. Strain rate sensitivity of coarse-grained MA0 was increased by more than 10 times in MA40. The Hall-Petch relationship broke down at a critical grain size in the nanocrystalline region. The breakdown of the Hall-Petch relationship and the increased strain rate sensitivity were due to the localized dislocation activities (generalization and annihilation at grain boundaries) and the more significant contribution from grain boundary mediated mechanisms. In the micro-compression tests, the sample size effects on the mechanical behaviours were studied on MA0, MA20 and MA40 micro-pillars. In contrast to the bulk samples under compression, the stress-strain curves of MA0 and MA20 micro-pillars were characterized with a number of discrete strain burst events separated by nearly elastic strain segments. Unlike MA0 and MA20, the stress-strain curves of MA40 micro-pillars were smooth, without obvious strain bursts. The deformation mechanisms of the MA0 and MA20 micro-pillars under micro-compression tests were considered to be initially dominated by deformation twinning, followed by dislocation mechanisms. For MA40 pillars, the deformation mechanisms were believed to be localized dislocation activities and grain boundary related mechanisms. The strain hardening behaviours of the micro-pillars suggested that the grain boundaries in the nanocrystalline micro-pillars would reduce the source (nucleation sources for twins/dislocations) starvation hardening effect. The power law relationship of the yield strength on pillar dimensions in MA0, MA20 supported the fact that the twinning mechanism was correlated to the pre-existing defects, which can promote the nucleation of the twins. Then, we provided a latitudinal comparison of the results and conclusions derived from the different techniques used for testing the coarse-grained and nanocrystalline Mg alloy; this helps to better understand the deformation mechanisms of the Mg alloys as a whole. At the end, we summarized the thesis and highlighted the conclusions, contributions, innovations and outcomes of the research. Finally, it outlined recommendations for future work.

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.