Maximizing Dimensional Efficiency With Minimal Cardinality Pattern Combinations. Making optimal use of dimensional capacity is often fundamental to the efficiency of processes in science and industry. Many important applications use combinations of patterns to achieve this. For example, in paper and in steel manufacturing, reels are divided lengthwise into cutting patterns, combined so as to minimize waste. In medicine, radiation patterns are combined to effectively treat cancerous tumours. ....Maximizing Dimensional Efficiency With Minimal Cardinality Pattern Combinations. Making optimal use of dimensional capacity is often fundamental to the efficiency of processes in science and industry. Many important applications use combinations of patterns to achieve this. For example, in paper and in steel manufacturing, reels are divided lengthwise into cutting patterns, combined so as to minimize waste. In medicine, radiation patterns are combined to effectively treat cancerous tumours. By addressing the common mathematical structure underlying pattern combination, this project will account for a hitherto neglected critical factor - the solution cardinality - making fully optimized solutions available for the first time to many applications in science and industry.Read moreRead less
New Theory and Algorithms for Nonsmooth Optimisation with Application to Integer Programming. Mathematical optimisation plays a key role in a wide variety of applications in business, industry, engineering and science. For example, airlines cannot fly and radiation treatment for cancer cannot be delivered without solving (a series of) optimisation problems. Some classes of optimisation problem are very well solved, with clear mathematical foundations, efficient algorithms, and reliable software ....New Theory and Algorithms for Nonsmooth Optimisation with Application to Integer Programming. Mathematical optimisation plays a key role in a wide variety of applications in business, industry, engineering and science. For example, airlines cannot fly and radiation treatment for cancer cannot be delivered without solving (a series of) optimisation problems. Some classes of optimisation problem are very well solved, with clear mathematical foundations, efficient algorithms, and reliable software implementations. Both nonsmooth and integer optimisation problems have a good mathematical basis, but there are "gaps"; existing methods cannot always solve real industrial problems. This project will deliver better methods, built on better theory, and so will yield better solutions for important applications.Read moreRead less
Doubly Stochastic Matrices & The Hamiltonian Cycle Problem. The classical hard problem of determining whether a given graph possesses a Hamiltonian cycle contains the essential difficulty of the famous 'Travelling Salesman Problem'. A characterisation of this difficulty in terms of variability of returns (to the initial state) in a controlled stochastic process will be a significant conceptual advance with repercussions in a number of fields including optimisation and theoretical computer scien ....Doubly Stochastic Matrices & The Hamiltonian Cycle Problem. The classical hard problem of determining whether a given graph possesses a Hamiltonian cycle contains the essential difficulty of the famous 'Travelling Salesman Problem'. A characterisation of this difficulty in terms of variability of returns (to the initial state) in a controlled stochastic process will be a significant conceptual advance with repercussions in a number of fields including optimisation and theoretical computer science. Algorithmic advances exploiting such a characterisation will significantly contribute to existing technologies for solving problems in applications ranging from logistics to cryptography. Since TSP describes certain efficient ways of routing its applicability to information networks is clear.Read moreRead less
Modelling patient flows through hospitals: optimizing effective use of resources. Hospitals are complex, dynamic systems confronted by increased demand in the face of shrinking real capacity. Managing such systems is currently undertaken with sub-optimal analytical support, particularly when demand and capacity are changing and resources must be manipulated to respond to such changes. In this project, the investigators will apply a mathematical modelling approach to the analysis of hospital pati ....Modelling patient flows through hospitals: optimizing effective use of resources. Hospitals are complex, dynamic systems confronted by increased demand in the face of shrinking real capacity. Managing such systems is currently undertaken with sub-optimal analytical support, particularly when demand and capacity are changing and resources must be manipulated to respond to such changes. In this project, the investigators will apply a mathematical modelling approach to the analysis of hospital patient flows. Furthermore, they will employ statistical process control methodologies to the problem of recognising and responding to changes in the flows, so that performance objectives are met. In doing this, they will give health service managers and clinicians a significant advantage in deciding how best to manage a constrained resource to maximize access, throughput and patient outcomes.Read moreRead less
Bayesian statistical models for understanding outcomes and improving decision-making for women screened for breast cancer. This project has two key benefits: (i) the development of frontier statistical methods for spatio-temporal analysis and data synthesis, which are imperative in a wide range of disciplines; and (ii) the application of these methods for improved understanding of breast cancer outcomes for women screened in Queensland. The project results will lead to direct health and financi ....Bayesian statistical models for understanding outcomes and improving decision-making for women screened for breast cancer. This project has two key benefits: (i) the development of frontier statistical methods for spatio-temporal analysis and data synthesis, which are imperative in a wide range of disciplines; and (ii) the application of these methods for improved understanding of breast cancer outcomes for women screened in Queensland. The project results will lead to direct health and financial benefits through targeted policies for increasing screening uptake and reducing cancer morbidity and mortality and therefore health spending in this area. Importantly, the project represents an excellent training opportunity to develop a PhD candidate into an experienced interdisciplinary researcher.Read moreRead less
WaterLog - A mathematical model to implement recommendations of The Wentworth Group. In 2003, The Wentworth Group of Concerned Scientists released their 'Blueprint for a national water plan' with the primary objective to 'protect river health and the rights of all Australians to clean usable water'. Currently, there are significant water restrictions in all the Australian mainland capital cities. In January 2007, the Prime Minister of Australia, announced a bold plan to rescue the Murray-Darling ....WaterLog - A mathematical model to implement recommendations of The Wentworth Group. In 2003, The Wentworth Group of Concerned Scientists released their 'Blueprint for a national water plan' with the primary objective to 'protect river health and the rights of all Australians to clean usable water'. Currently, there are significant water restrictions in all the Australian mainland capital cities. In January 2007, the Prime Minister of Australia, announced a bold plan to rescue the Murray-Darling Basin. The plan incorporates political management changes, and an investment of $10Bn. Now is the time to develop improved techniques for management of water storage systems. This project will develop the fundamental mathematical principles required for this improved management.Read moreRead less
Using Mathematics to Maximize the Efficiency of Shared Infrastructure in Australia's Coal Export Supply Chain. Port Waratah Coal Services operates the world's largest coal export terminal, servicing about 14 coal mining companies in the Hunter Valley, NSW. It is responsible for around $15 billion in annual export income for Australia. The coal supply chain is a complex operation, hampered by bottlenecks in critical shared infrastructure. Such limitations are estimated to cost Australia about $2 ....Using Mathematics to Maximize the Efficiency of Shared Infrastructure in Australia's Coal Export Supply Chain. Port Waratah Coal Services operates the world's largest coal export terminal, servicing about 14 coal mining companies in the Hunter Valley, NSW. It is responsible for around $15 billion in annual export income for Australia. The coal supply chain is a complex operation, hampered by bottlenecks in critical shared infrastructure. Such limitations are estimated to cost Australia about $2 billion pa in lost sales. This project will support the design of new infrastructure and processes to ensure an efficient supply chain. The new science resulting will benefit other coal operations in Australia, and potentially other bulk goods supply chains.Read moreRead less
Queueing systems and their application to telecommunication systems and dams. The aim of this project is to investigate the behaviour of large queueing systems under critical load conditions and solve problems related to large telecommunication systems, information technologies and dams. The project will have significant economic and social benefits. It will lead to the solution of high priority problems of optimal control of water resources, as well as problems in design technology of high spee ....Queueing systems and their application to telecommunication systems and dams. The aim of this project is to investigate the behaviour of large queueing systems under critical load conditions and solve problems related to large telecommunication systems, information technologies and dams. The project will have significant economic and social benefits. It will lead to the solution of high priority problems of optimal control of water resources, as well as problems in design technology of high speed telecommunication networks. It will suggest new more profitable approaches to known problems such as effective bandwidth problem, analysis and design of computer networks, optimal control of dams, and anticipate not ordinary results and solutions. It will contribute to the mathematical culture in Australia and worldwide. Read moreRead less
Problems of identification and inference for 'non-standard' models in complex systems with special reference to finance and teletraffic. The project is concerned with 'non-standard' models needed to deal with complex systems, such as those exhibiting scaling and fractal properties. There is a focus on methods for dealing with heavy tailed distributions and long range dependent observations, for which most standard statistical methods break down, and on applications in finance and telecommunicati ....Problems of identification and inference for 'non-standard' models in complex systems with special reference to finance and teletraffic. The project is concerned with 'non-standard' models needed to deal with complex systems, such as those exhibiting scaling and fractal properties. There is a focus on methods for dealing with heavy tailed distributions and long range dependent observations, for which most standard statistical methods break down, and on applications in finance and telecommunications. An important part of the project concerns model validation for Heyde's fractal activity time geometric Brownian motion model, a candidate minimal description risky asset model to replace the geometric Brownian motion paradigm.Read moreRead less
Channel Assignment in Cellular Communication Systems and Optical Networks. Due to the rapid growth in mobile communications, efficient management of the scarce radio spectrum has emerged as an important issue. To avoid interference various conditions need to be satisfied by channels assigned to the transmitters in a cellular communication network. This project targets optimal assignments under such constraints, and similar problems for optical networks. Its implementation will have potential app ....Channel Assignment in Cellular Communication Systems and Optical Networks. Due to the rapid growth in mobile communications, efficient management of the scarce radio spectrum has emerged as an important issue. To avoid interference various conditions need to be satisfied by channels assigned to the transmitters in a cellular communication network. This project targets optimal assignments under such constraints, and similar problems for optical networks. Its implementation will have potential applications in computer and telecommunication industries, and advance significantly our knowledge on relevant subjects of mathematics and operations research. Read moreRead less