Stochastic linear multistep methods for the simulation of chemical kinetics

In this paper, we introduce the Stochastic Adams-Bashforth (SAB) and Stochastic Adams-Moulton (SAM) methods as an extension of the tau-leaping framework to past information. Using the theta-trapezoidal tau-leap method of weak order two as a starting procedure, we show that the k-step SAB method with k >= 3 is order three in the mean and correlation, while a predictor-corrector implementation of the SAM method is weak order three in the mean but only order one in the correlation. These convergence results have been derived analytically for linear problems and successfully tested numerically for both linear and non-linear systems. A series of additional examples have been implemented in order to demonstrate the efficacy of this approach.

Recurrence risk modelling of the genetic susceptibility to ankylosing spondylitis

Objectives - It has long been suspected that susceptibility to ankylosing spondylitis (AS) is influenced by genes lying distant to the major histocompatibility complex. This study compares genetic models of AS to assess the most likely mode of inheritance, using recurrence risk ratios in relatives of affected subjects. Methods - Recurrence risk ratios in different degrees of relatives were determined using published data from studies specifically designed to address the question. The methods of Risch were used to determine the expected recurrence risk ratios in different degrees of relatives, assuming equal first degree relative recurrence risk between models. Goodness of fit was determined by χ2 comparison of the expected number of affected subjects with the observed number, given equal numbers of each type of relative studied. Results - The recurrence risks in different degrees of relatives were: monozygotic (MZ) twins 63% (17/27), first degree relatives 8.2% (441/5390), second degree relatives 1.0% (8/834), and third degree relatives 0.7% (7/997). Parent-child recurrence risk (7.9%, 37/466) was not significantly different from the sibling recurrence risk (8.2%, 404/4924), excluding a significant dominance genetic component to susceptibility. Poor fitting models included single gene, genetic heterogeneity, additive, two locus multiplicative, and one locus and residual polygenes (χ2 > 32 (two degrees of freedom), p < 10-6 for all models). The best fitting model studied was a five locus model with multiplicative interaction between loci (χ2 = 1.4 (two degrees of freedom), p = 0.5). Oligogenic multiplicative models were the best fitting over a range of population prevalences and first degree recurrence risk rates. Conclusions - This study suggests that of the genetic models tested, the most likely model operating in AS is an oligogenic model with predominantly multiplicative interaction between loci.

Exploring accuracy factors in cost estimating practice towards implementing Building Information Modelling (BIM)

Cost estimating has been acknowledged as a crucial component of construction projects. Depending on available information and project requirements, cost estimates evolve in tandem with project lifecycle stages; conceptualisation, design development, execution and facility management. The premium placed on the accuracy of cost estimates is crucial to producing project tenders and eventually in budget management. Notwithstanding the initial slow pace of its adoption, Building Information Modelling (BIM) has successfully addressed a number of challenges previously characteristic of traditional approaches in the AEC, including poor communication, the prevalence of islands of information and frequent reworks. Therefore, it is conceivable that BIM can be leveraged to address specific shortcomings of cost estimation. The impetus for leveraging BIM models for accurate cost estimation is to align budgeted and actual cost. This paper hypothesises that the accuracy of BIM-based estimation, as more efficient, process-mirrors of traditional cost estimation methods, can be enhanced by simulating traditional cost estimation factors variables. Through literature reviews and preliminary expert interviews, this paper explores the factors that could potentially lead to more accurate cost estimates for construction projects. The findings show numerous factors that affect the cost estimates ranging from project information and its characteristic, project team, clients, contractual matters, and other external influences. This paper will make a particular contribution to the early phase of BIM-based project estimation.

Cost estimating practice incorporating Building Information Modelling (BIM): Malaysian Quantity Surveyors perspectives

Cost estimating is a key task within Quantity Surveyors’ (QS) offices. Provision of an accurate estimate is vital to ensure that the objectives of the client are met by staying within the client’s budget. Building Information Modelling (BIM) is an evolving technology that has gained attention in the construction industries all over the world. Benefits from the use of BIM include cost and time savings if the processes used by the procurement team are adapted to maximise the benefits of BIM. BIM can be used by QSs to automate aspects of quantity take-off and the preparation of estimates, decreasing turnaround time and assist in controlling errors and inaccuracies. The Malaysian government has decided to require the use of BIM for its projects beginning from 2016. However, slow uptake is reported in the use of BIM both within companies and to support collaboration within the Malaysian industry. It has been recommended that QSs to start evaluating the impact of BIM on their practices. This paper reviews the perspectives of QSs in Malaysia towards the use of BIM to achieve more dependable results in their cost estimating practice. The objectives of this paper include identifying strategies in improving practice and potential adoption drivers that lead QSs to BIM usage in their construction projects. From the expert interviews, it was found out that, despite still using traditional methods and not practising BIM, the interviewees still acquire limited knowledge related to BIM. There are some drivers that potentially motivate them to employ BIM in their practices. These include client demands, innovation in traditional methods, speed in estimating costs, reduced time and costs, improvement in practices and self-awareness, efficiency in projects, and competition from other companies. The findings of this paper identify the potential drivers in encouraging Malaysian Quantity Surveyors to exploit BIM in their construction projects.

Online hidden Markov model parameter estimation and minimax robust quickest change detection in uncertain stochastic processes

Stochastic (or random) processes are inherent to numerous fields of human endeavour including engineering, science, and business and finance. This thesis presents multiple novel methods for quickly detecting and estimating uncertainties in several important classes of stochastic processes. The significance of these novel methods is demonstrated by employing them to detect aircraft manoeuvres in video signals in the important application of autonomous mid-air collision avoidance.

Review and future options for computer modelling in the sugar industry

Computer modelling has been used extensively in some processes in the sugar industry to achieve significant gains. This paper reviews the investigations carried out over approximately the last twenty five years, including the successes but also areas where problems and delays have been encountered. In that time the capability of both hardware and software have increased dramatically. For some processes such as cane cleaning, cane billet preparation, and sugar drying, the application of computer modelling towards improved equipment design and operation has been quite limited. A particular problem has been the large number of particles and particle interactions in these…

Efficient simulation of stochastic chemical kinetics with the Stochastic Bulirsch-Stoer extrapolation method

Background Biochemical systems with relatively low numbers of components must be simulated stochastically in order to capture their inherent noise. Although there has recently been considerable work on discrete stochastic solvers, there is still a need for numerical methods that are both fast and accurate. The Bulirsch-Stoer method is an established method for solving ordinary differential equations that possesses both of these qualities. Results In this paper, we present the Stochastic Bulirsch-Stoer method, a new numerical method for simulating discrete chemical reaction systems, inspired by its deterministic counterpart. It is able to achieve an excellent efficiency due to the fact that it is based on an approach with high deterministic order, allowing for larger stepsizes and leading to fast simulations. We compare it to the Euler τ-leap, as well as two more recent τ-leap methods, on a number of example problems, and find that as well as being very accurate, our method is the most robust, in terms of efficiency, of all the methods considered in this paper. The problems it is most suited for are those with increased populations that would be too slow to simulate using Gillespie’s stochastic simulation algorithm. For such problems, it is likely to achieve higher weak order in the moments. Conclusions The Stochastic Bulirsch-Stoer method is a novel stochastic solver that can be used for fast and accurate simulations. Crucially, compared to other similar methods, it better retains its high accuracy when the timesteps are increased. Thus the Stochastic Bulirsch-Stoer method is both computationally efficient and robust. These are key properties for any stochastic numerical method, as they must typically run many thousands of simulations.

A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems

In order to simulate stiff biochemical reaction systems, an explicit exponential Euler scheme is derived for multidimensional, non-commutative stochastic differential equations with a semilinear drift term. The scheme is of strong order one half and A-stable in mean square. The combination with this and the projection method shows good performance in numerical experiments dealing with an alternative formulation of the chemical Langevin equation for a human ether a-go-go related gene ion channel mode

Generalizing the use of geographical weights in biodiversity modelling

Aim Determining how ecological processes vary across space is a major focus in ecology. Current methods that investigate such effects remain constrained by important limiting assumptions. Here we provide an extension to geographically weighted regression in which local regression and spatial weighting are used in combination. This method can be used to investigate non-stationarity and spatial-scale effects using any regression technique that can accommodate uneven weighting of observations, including machine learning. Innovation We extend the use of spatial weights to generalized linear models and boosted regression trees by using simulated data for which the results are known, and compare these local approaches with existing alternatives such as geographically weighted regression (GWR). The spatial weighting procedure (1) explained up to 80% deviance in simulated species richness, (2) optimized the normal distribution of model residuals when applied to generalized linear models versus GWR, and (3) detected nonlinear relationships and interactions between response variables and their predictors when applied to boosted regression trees. Predictor ranking changed with spatial scale, highlighting the scales at which different species–environment relationships need to be considered. Main conclusions GWR is useful for investigating spatially varying species–environment relationships. However, the use of local weights implemented in alternative modelling techniques can help detect nonlinear relationships and high-order interactions that were previously unassessed. Therefore, this method not only informs us how location and scale influence our perception of patterns and processes, it also offers a way to deal with different ecological interpretations that can emerge as different areas of spatial influence are considered during model fitting.

Two-scale computational modelling of water flow in unsaturated soils containing irregular-shaped inclusions

The focus of this paper is two-dimensional computational modelling of water flow in unsaturated soils consisting of weakly conductive disconnected inclusions embedded in a highly conductive connected matrix. When the inclusions are small, a two-scale Richards’ equation-based model has been proposed in the literature taking the form of an equation with effective parameters governing the macroscopic flow coupled with a microscopic equation, defined at each point in the macroscopic domain, governing the flow in the inclusions. This paper is devoted to a number of advances in the numerical implementation of this model. Namely, by treating the micro-scale as a two-dimensional problem, our solution approach based on a control volume finite element method can be applied to irregular inclusion geometries, and, if necessary, modified to account for additional phenomena (e.g. imposing the macroscopic gradient on the micro-scale via a linear approximation of the macroscopic variable along the microscopic boundary). This is achieved with the help of an exponential integrator for advancing the solution in time. This time integration method completely avoids generation of the Jacobian matrix of the system and hence eases the computation when solving the two-scale model in a completely coupled manner. Numerical simulations are presented for a two-dimensional infiltration problem.

Post-transcriptional regulation in the nucleus and cytoplasm: study of mean time to threshold (MTT) and narrow escape problem

Messenger RNAs (mRNAs) can be repressed and degraded by small non-coding RNA molecules. In this paper, we formulate a coarsegrained Markov-chain description of the post-transcriptional regulation of mRNAs by either small interfering RNAs (siRNAs) or microRNAs (miRNAs). We calculate the probability of an mRNA escaping from its domain before it is repressed by siRNAs/miRNAs via cal- culation of the mean time to threshold: when the number of bound siRNAs/miRNAs exceeds a certain threshold value, the mRNA is irreversibly repressed. In some cases,the analysis can be reduced to counting certain paths in a reduced Markov model. We obtain explicit expressions when the small RNA bind irreversibly to the mRNA and we also discuss the reversible binding case. We apply our models to the study of RNA interference in the nucleus, examining the probability of mRNAs escaping via small nuclear pores before being degraded by siRNAs. Using the same modelling framework, we further investigate the effect of small, decoy RNAs (decoys) on the process of post-transcriptional regulation, by studying regulation of the tumor suppressor gene, PTEN : decoys are able to block binding sites on PTEN mRNAs, thereby educing the number of sites available to siRNAs/miRNAs and helping to protect it from repression. We calculate the probability of a cytoplasmic PTEN mRNA translocating to the endoplasmic reticulum before being repressed by miRNAs. We support our results with stochastic simulations

One practical algorithm for both stochastic and adversarial bandits

We present an algorithm for multiarmed bandits that achieves almost optimal performance in both stochastic and adversarial regimes without prior knowledge about the nature of the environment. Our algorithm is based on augmentation of the EXP3 algorithm with a new control lever in the form of exploration parameters that are tailored individually for each arm. The algorithm simultaneously applies the “old” control lever, the learning rate, to control the regret in the adversarial regime and the new control lever to detect and exploit gaps between the arm losses. This secures problem-dependent “logarithmic” regret when gaps are present without compromising on the worst-case performance guarantee in the adversarial regime. We show that the algorithm can exploit both the usual expected gaps between the arm losses in the stochastic regime and deterministic gaps between the arm losses in the adversarial regime. The algorithm retains “logarithmic” regret guarantee in the stochastic regime even when some observations are contaminated by an adversary, as long as on average the contamination does not reduce the gap by more than a half. Our results for the stochastic regime are supported by experimental validation.

Do motor vehicle crashes arise from single or multiple unique risk processes? An inquiry into crash causes and modelling

Crashes at any particular transport network location consist of a chain of events arising from a multitude of potential causes and/or contributing factors whose nature is likely to reflect geometric characteristics of the road, spatial effects of the surrounding environment, and human behavioural factors. It is postulated that these potential contributing factors do not arise from the same underlying risk process, and thus should be explicitly modelled and understood. The state of the practice in road safety network management applies a safety performance function that represents a single risk process to explain crash variability across network sites. This study aims to elucidate the importance of differentiating among various underlying risk processes contributing to the observed crash count at any particular network location. To demonstrate the principle of this theoretical and corresponding methodological approach, the study explores engineering (e.g. segment length, speed limit) and unobserved spatial factors (e.g. climatic factors, presence of schools) as two explicit sources of crash contributing factors. A Bayesian Latent Class (BLC) analysis is used to explore these two sources and to incorporate prior information about their contribution to crash occurrence. The methodology is applied to the state controlled roads in Queensland, Australia and the results are compared with the traditional Negative Binomial (NB) model. A comparison of goodness of fit measures indicates that the model with a double risk process outperforms the single risk process NB model, and thus indicating the need for further research to capture all the three crash generation processes into the SPFs.

Robust iris recognition using decision fusion and degradation modelling

This thesis investigates the use of fusion techniques and mathematical modelling to increase the robustness of iris recognition systems against iris image quality degradation, pupil size changes and partial occlusion. The proposed techniques improve recognition accuracy and enhance security. They can be further developed for better iris recognition in less constrained environments that do not require user cooperation. A framework to analyse the consistency of different regions of the iris is also developed. This can be applied to improve recognition systems using partial iris images, and cancelable biometric signatures or biometric based cryptography for privacy protection.

Estimating the parameters of stochastic volatility models using option price data

This article describes a maximum likelihood method for estimating the parameters of the standard square-root stochastic volatility model and a variant of the model that includes jumps in equity prices. The model is fitted to data on the S&P 500 Index and the prices of vanilla options written on the index, for the period 1990 to 2011. The method is able to estimate both the parameters of the physical measure (associated with the index) and the parameters of the risk-neutral measure (associated with the options), including the volatility and jump risk premia. The estimation is implemented using a particle filter whose efficacy is demonstrated under simulation. The computational load of this estimation method, which previously has been prohibitive, is managed by the effective use of parallel computing using graphics processing units (GPUs). The empirical results indicate that the parameters of the models are reliably estimated and consistent with values reported in previous work. In particular, both the volatility risk premium and the jump risk premium are found to be significant.