Advanced mathematical models and methods for a randomly-varying world. This project aims to develop advanced stochastic models and novel techniques, to analytically obtain performance measures and to efficiently simulate the time evolution. This project also plans to apply new models and methods to address important problems in ecology and epidemiology. The outputs of this project will advance knowledge in mathematics as well as in the intended application areas, including ultimately in improved ....Advanced mathematical models and methods for a randomly-varying world. This project aims to develop advanced stochastic models and novel techniques, to analytically obtain performance measures and to efficiently simulate the time evolution. This project also plans to apply new models and methods to address important problems in ecology and epidemiology. The outputs of this project will advance knowledge in mathematics as well as in the intended application areas, including ultimately in improved understanding, modelling, and tracking of the spread of diseases.Read moreRead less
New methods for integrating population structure and stochasticity into models of disease dynamics. Epidemics, such as the 2007 equine 'flu outbreak and 2009 swine 'flu pandemic, highlight the need to make informed decisive responses. This project will develop new methods that incorporate two important aspects of disease dynamics---host structure and chance---into mathematical models, and determine their impact in terms of controlling infections.
Developing mathematical models and statistical methods to understand the dynamics of infectious diseases: stochasticity, structure and inference. Infectious diseases remain a major contributor to mortality and illness worldwide. The potential for future severe pandemics also continues to present a substantial threat to our health and well-being. Mathematics and statistics are increasingly becoming part of the arsenal used by governments to combat the invasion and spread of infectious diseases. I ....Developing mathematical models and statistical methods to understand the dynamics of infectious diseases: stochasticity, structure and inference. Infectious diseases remain a major contributor to mortality and illness worldwide. The potential for future severe pandemics also continues to present a substantial threat to our health and well-being. Mathematics and statistics are increasingly becoming part of the arsenal used by governments to combat the invasion and spread of infectious diseases. In such work, three themes have emerged as having the potential to revolutionise the modelling of infectious diseases: stochasticity, structure (both age and spatial), and inference. This project will develop state-of-the-art techniques, at the interface of these themes, of critical importance to understanding the dynamics of infectious diseases.Read moreRead less
Operator-Analytic Methods in Telecommunication Systems. Many systems in information technology and telecommunications evolve under conditions of uncertainty. In this context, mathematical modelling is an essential component of the design process. We shall provide techniques for analysing a class of mathematical models, called operator-analytic models, which can be used to study many of the above-mentioned systems, such as the Internet. This project will deliver efficient numerical algorithms tha ....Operator-Analytic Methods in Telecommunication Systems. Many systems in information technology and telecommunications evolve under conditions of uncertainty. In this context, mathematical modelling is an essential component of the design process. We shall provide techniques for analysing a class of mathematical models, called operator-analytic models, which can be used to study many of the above-mentioned systems, such as the Internet. This project will deliver efficient numerical algorithms that will make possible practical analysis of operator-analytic models.Read moreRead less
Strategic integration of renewable energy systems into the electricity grid. The Intergovernmental Panel on Climate Change states that 'warming of the climate system is unequivocal' and there is high probability it is anthropogenic. In response to the growing awareness of climate change, there is an expansion in Australia in the use of renewable energy resources in electricity generation, albeit from a low base. The various renewable energy systems have differing patterns of availability and vol ....Strategic integration of renewable energy systems into the electricity grid. The Intergovernmental Panel on Climate Change states that 'warming of the climate system is unequivocal' and there is high probability it is anthropogenic. In response to the growing awareness of climate change, there is an expansion in Australia in the use of renewable energy resources in electricity generation, albeit from a low base. The various renewable energy systems have differing patterns of availability and volatility, and it is difficult to determine the right mixture to best match the demand. It is imperative that future growth be structured so that both maximum grid penetration, and required greenhouse gas reductions be attained. 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
Advanced matrix-analytic methods with applications. Over the last twenty-five years, matrix-analytic methods have proved to be very successful in formulating and analysing certain classes of stochastic models. Motivated by applications, this project will investigate more advanced matrix-analytic methods than have hitherto been studied.
The use of stochastic fluid models for the evaluation of applications-driven sample path integrals. The major technical goal of this project is the production of novel methodologies which can be used to model and solve real-world problems of considerable engineering and/or environmental significance. The research for this project will serve to enhance further Australia's reputation as a country which makes major contributions, both theoretical and practical, to this field. The activities of the ....The use of stochastic fluid models for the evaluation of applications-driven sample path integrals. The major technical goal of this project is the production of novel methodologies which can be used to model and solve real-world problems of considerable engineering and/or environmental significance. The research for this project will serve to enhance further Australia's reputation as a country which makes major contributions, both theoretical and practical, to this field. The activities of the Stochastic Modelling, Analysis and Optimisation group at the University of Adelaide and the School of Mathematics at the University of Tasmania will receive further impetus, consequently maintaining a dynamic research environment for staff and students at both universities. Links between the two groups will be strengthened.Read moreRead less
Mathematical models for water management systems. The Australian community is currently talking about schemes to return water to the Murray-Darling river system to combat increased salinity and dramatically reduced river flow. Many believe that vastly improved water management policies are essential to maintain agricultural well-being in Australia. Salinity and water quality depend directly on flow rates and are also important in smaller catchments. In this study we will use statistical rainf ....Mathematical models for water management systems. The Australian community is currently talking about schemes to return water to the Murray-Darling river system to combat increased salinity and dramatically reduced river flow. Many believe that vastly improved water management policies are essential to maintain agricultural well-being in Australia. Salinity and water quality depend directly on flow rates and are also important in smaller catchments. In this study we will use statistical rainfall models and stochastic dynamic programming to find practical water management policies that minimise the risk to water supply. We will develop an interactive simulation and management tool using a modern computer graphics package.Read moreRead less
A graphical simulation package for optimal management and risk assessment in urban stormwater harvesting systems. We will develop a Scalar Vector Graphics (SVG) simulation tool for optimal management and risk assessment in urban stormwater harvesting and utilisation schemes. The generic model will be applied to existing and proposed schemes within the City of Salisbury (CoS) and will include a capture dam, one or more storage dams and an aquifer storage and recovery (ASR) facility. The discret ....A graphical simulation package for optimal management and risk assessment in urban stormwater harvesting systems. We will develop a Scalar Vector Graphics (SVG) simulation tool for optimal management and risk assessment in urban stormwater harvesting and utilisation schemes. The generic model will be applied to existing and proposed schemes within the City of Salisbury (CoS) and will include a capture dam, one or more storage dams and an aquifer storage and recovery (ASR) facility. The discrete state vector will be the content of each storage unit and the daily transition will be driven by a new stochastic rainfall model (SRM). The objective will be to find a practical management policy that minimises Conditional Value-at-Risk (CVaR).Read moreRead less