Optimal-stopping control for airborne collision avoidance and return-to-course flight

This paper considers an aircraft collision avoidance design problem that also incorporates design of the aircraft’s return-to-course flight. This control design problem is formulated as a non-linear optimal-stopping control problem; a formulation that does not require a prior knowledge of time taken to perform the avoidance and return-to-course manoeuvre. A dynamic programming solution to the avoidance and return-to-course problem is presented, before a Markov chain numerical approximation technique is described. Simulation results are presented that illustrate the proposed collision avoidance and return-to-course flight approach.

Review of 'Speaking Out: Stopping Homophobic and Transphobic Abuse In Queensland'

Speaking Out documents the outcomes of the largest ever study to examine homophobic and transphobic abuse and reporting in Queensland, Australia. It reports the results of a quantitative survey on victimisation of lesbian, gay, bisexual, transgender, intersex, and queer (LGBTIQ) people and how this victimisation is reported to police. Follow-up qualitative interviews and focus groups were also conducted with LGBTIQ people to examine the impact of this abuse and the reporting to police. This research is timely as we can sometimes assume LGBTIQ victimisation is a historical problem and may be settled by the idea that relations with police are in good shape. This book clearly demonstrates that we have some way to go before we can be assured these issues have been resolved...

A microscopic simulation model to estimate Bus Rapid Transit (BRT) station service capacity with mixed stopping and non-stopping bus operation

Bus Rapid Transit (BRT) station is the interface between passenger and service. The station is crucial to line operation as it is typically the only location where buses can pass each other. Congestion may occur here when buses maneuvering into and out of the platform lane interfere with bus flow, or when a queue of buses forms upstream of the platform lane blocking the passing lane. However, some systems include operation where express buses pass the critical station, resulting in a proportion of non stopping buses. It is important to understand the operation of the critical busway station under this type of operation, as it affects busway line capacity. This study uses micro simulation to treat the BRT station operation and to analyze the relationship between station Limit state bus capacity (B_ls), Total Bus Capacity (B_ttl). First, the simulation model is developed for Limit state scenario and then a mathematical model is defined, calibrated for a specified range of controlled scenarios of mean and coefficient of variation of dwell time. Thereafter, the proposed B_ls model is extended to consider non stopping buses and B_ttlmodel is defined. The proposed models provides better understanding to the BRT line capacity and is useful for transit authorities for designing better BRT operation.

Enlarged stopping distance to improve vehicle discharge at urban signalised intersections

Normally, vehicles queued at an intersection reach maximum flow rate after the fourth vehicle and results in a start-up lost time. This research demonstrated that the Enlarged Stopping Distance (ESD) concept could assist in reducing the start-up time and therefore increase traffic flow capacity at signalised intersections. In essence ESD gives sufficient space for a queuing vehicle to accelerate simultaneously without having to wait for the front vehicle to depart, hence reducing start-up lost time. In practice, the ESD concept would be most effective when enlarged stopping distance between the first and second vehicle allowing faster clearance of the intersection.

Analyzing busway station potential capacity under mixed stopping and non-stopping operation

Busway stations are the interface between passengers and services. The station is crucial to line operation as it is typically the only location where buses can pass each other. Congestion may occur here when buses manoeuvring into and out of the platform lane interfere with bus flow, or when a queue of buses forms upstream of the platform lane blocking the passing lane. Further, some systems include operation where express buses do not observe the station, resulting in a proportion of non-stopping buses. It is important to understand the operation of the station under this type of operation and its effect on busway capacity. This study uses microscopic simulation to treat the busway station operation and to analyse the relationship between station potential capacity where all buses stop, and Mixed Potential Capacity where there is a mixture of stopping and non-stopping buses. First, the micro simulation technique is used to analyze the All Stopping Buses (ASB) scenario and then statistical model is tuned and calibrated for a specified range of controlled scenarios of dwell time characteristics Subsequently, a mathematical model is developed for Mixed Stopping Buses (MSB) Potential Capacity by introducing different proportions of express (or non-stopping) buses. The proposed models for a busway station bus capacity provide a better understanding of operation and are useful to transit agencies in busway planning, design and operation.

Analysing busway station capacity under mixed stopping and non-stopping operation

Busway stations are the interface between passengers and services. The station is crucial to line operation as it is typically the only location where buses can pass each other. Congestion may occur here when buses manoeuvring into and out of the platform lane interfere with bus flow, or when a queue of buses forms upstream of the platform lane blocking the passing lane. Further, some systems include operation where express buses do not observe the station, resulting in a proportion of non-stopping buses. It is important to understand the operation of the station under this type of operation and its effect on busway capacity. This study uses microscopic simulation to treat the busway station operation and to analyse the relationship between station potential capacity where all buses stop, and Mixed Potential Capacity where there is a mixture of stopping and non-stopping buses. First, the micro simulation technique is used to analyze the All Stopping Buses (ASB) scenario and then statistical model is tuned and calibrated for a specified range of controlled scenarios of dwell time characteristics Subsequently, a mathematical model is developed for Mixed Stopping Buses (MSB) Potential Capacity by introducing different proportions of express (or non-stopping) buses. The proposed models for a busway station bus capacity provide a better understanding of operation and are useful to transit agencies in busway planning, design and operation.

Modelling the BRT station capacity and queuing for all stopping busway operation

Stations on Bus Rapid Transit (BRT) lines ordinarily control line capacity because they act as bottlenecks. At stations with passing lanes, congestion may occur when buses maneuvering into and out of the platform stopping lane interfere with bus flow, or when a queue of buses forms upstream of the station blocking inflow. We contend that, as bus inflow to the station area approaches capacity, queuing will become excessive in a manner similar to operation of a minor movement on an unsignalized intersection. This analogy was used to treat BRT station operation and to analyze the relationship between station queuing and capacity. We conducted microscopic simulation to study and analyze operating characteristics of the station under near steady state conditions through output variables of capacity, degree of saturation and queuing. In the first of two stages, a mathematical model was developed for all stopping buses potential capacity with bus to bus interference and the model was validated. Secondly, a mathematical model was developed to estimate the relationship between average queue and degree of saturation and calibrated for a specified range of controlled scenarios of mean and coefficient of variation of dwell time.

Modelling busway operation with mixed stopping and non-stopping buses

This thesis investigated the complexity of busway operation with stopping and non-stopping buses using field data and microscopic simulation modelling. The proposed approach made significant recommendations to transit authorities to achieve the most practicable system capacity for existing and new busways. The empirical equations developed in this research and newly introduced analysis methods will be ideal tools for transit planners to achieve optimal reliability of busways.

Early stopping by using stochastic curtailment in a three-arm sequential trial

Summary. Interim analysis is important in a large clinical trial for ethical and cost considerations. Sometimes, an interim analysis needs to be performed at an earlier than planned time point. In that case, methods using stochastic curtailment are useful in examining the data for early stopping while controlling the inflation of type I and type II errors. We consider a three-arm randomized study of treatments to reduce perioperative blood loss following major surgery. Owing to slow accrual, an unplanned interim analysis was required by the study team to determine whether the study should be continued. We distinguish two different cases: when all treatments are under direct comparison and when one of the treatments is a control. We used simulations to study the operating characteristics of five different stochastic curtailment methods. We also considered the influence of timing of the interim analyses on the type I error and power of the test. We found that the type I error and power between the different methods can be quite different. The analysis for the perioperative blood loss trial was carried out at approximately a quarter of the planned sample size. We found that there is little evidence that the active treatments are better than a placebo and recommended closure of the trial.

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.

Modelling water droplet movement on a leaf surface

Modelling droplet movement on leaf surfaces is an important component in understanding how water, pesticide or nutrient is absorbed through the leaf surface. A simple mathematical model is proposed in this paper for generating a realistic, or natural looking trajectory of a water droplet traversing a virtual leaf surface. The virtual surface is comprised of a triangular mesh structure over which a hybrid Clough-Tocher seamed element interpolant is constructed from real-life scattered data captured by a laser scanner. The motion of the droplet is assumed to be affected by gravitational, frictional and surface resistance forces and the innovation of our approach is the use of thin-film theory to develop a stopping criterion for the droplet as it moves on the surface. The droplet model is verified and calibrated using experimental measurement; the results are promising and appear to capture reality quite well.

Ecology and bioprospecting

Bioprospecting is the exploration of biodiversity for new resources of social and commercial value. It is carried out by a wide range of established industries such as pharmaceuticals, manufacturing and agriculture as well as a wide range of comparatively new ones such as aquaculture, bioremediation, biomining, biomimetic engineering and nanotechnology. The benefits of bioprospecting have emerged from such a wide range of organisms and environments worldwide that it is not possible to predict what species or habitats will be critical to society, or industry, in the future. The benefits include an unexpected variety of products that include chemicals, genes, metabolic pathways, structures, materials and behaviours. These may provide physical blueprints or inspiration for new designs. Criticism aimed at bioprospecting has been addressed, in part, by international treaties and legal agreements aimed at stopping biopiracy and many activities are now funded by agencies that require capacity-building and economic benefits in host countries. Thus, much contemporary bioprospecting has multiple goals, including the conservation of biodiversity, the sustainable management of natural resources and economic development. Ecologists are involved in three vital ways: first, applying ecological principles to the discovery of new resources. In this context, natural history becomes a vast economic database. Second, carrying out field studies, most of them demographic, to help regulate the harvest of wild species. Third, emphasizing the profound importance of millions of mostly microscopic species to the global economy.

Alleviating ‘overfitting’ via genetically-regularised neural network

A hybrid genetic algorithm/scaled conjugate gradient regularisation method is designed to alleviate ANN `over-fitting'. In application to day-ahead load forecasting, the proposed algorithm performs better than early-stopping and Bayesian regularisation, showing promising initial results.

The conflict resolution in connected railway junctions

Purpose of study: Traffic conflicts occur when trains on different routes approach a converging junction in a railway network at the same time. To prevent collisions, a right-of-way assignment is needed to control the order in which the trains should pass the junction. Such control action inevitably requires the braking and/or stopping of trains, which lengthens their travelling times and leads to delays. Train delays cause a loss of punctuality and hence directly affect the quality of service. It is therefore important to minimise the delays by devising a suitable right-of-way assignment. One of the major difficulties in attaining the optimal right-of-way assignment is that the number of feasible assignments increases dramatically with the number of trains. Connected-junctions further complicate the problem. Exhaustive search for the optimal solution is time-consuming and infeasible for area control (multi-junction). Even with the more intelligent deterministic optimisation method revealed in [1], the computation demand is still considerable, which hinders real-time control. In practice, as suggested in [2], the optimality may be traded off by shorter computation time, and heuristic searches provide alternatives for this optimisation problem.