Computational methods for population-size-dependent branching processes. Branching processes are the primary mathematical tool used to model populations that evolve randomly in time. Most key results in the theory are derived under the simplifying assumption that individuals reproduce and die independently of each other. However, this assumption fails in most real-life situations, in particular when the environment has limited resources or when the habitat has a restricted capacity. This project ....Computational methods for population-size-dependent branching processes. Branching processes are the primary mathematical tool used to model populations that evolve randomly in time. Most key results in the theory are derived under the simplifying assumption that individuals reproduce and die independently of each other. However, this assumption fails in most real-life situations, in particular when the environment has limited resources or when the habitat has a restricted capacity. This project aims to develop novel and effective algorithmic techniques and statistical methods for a class of branching processes with dependences. We will use these results to study significant problems in the conservation of endangered island bird populations in Oceania, and to help inform their conservation management.Read moreRead less
ARC Centre of Excellence for Mathematical and Statistical Frontiers of Big Data, Big Models, New Insights. In today's world, massive amounts of data in a variety of forms are collected daily from a multitude of sources. Many of the resulting data sets have the potential to make vital contributions to society, business and government, as well as impact on international developments, but are so large or complex that they are difficult to process and analyse using traditional tools. The aim of this ....ARC Centre of Excellence for Mathematical and Statistical Frontiers of Big Data, Big Models, New Insights. In today's world, massive amounts of data in a variety of forms are collected daily from a multitude of sources. Many of the resulting data sets have the potential to make vital contributions to society, business and government, as well as impact on international developments, but are so large or complex that they are difficult to process and analyse using traditional tools. The aim of this Centre is to create innovative mathematical and statistical models that can uncover the knowledge concealed within the size and complexity of these big data sets, with a focus on using the models to deliver insight into problems vital to the Centre's Collaborative Domains: Healthy People, Sustainable Environments and Prosperous Societies.Read moreRead less
Improving Choice Models: Multiple Goal Pursuit and Multi-Stage Decision Processes. This project aims to develop new econometric models of choice behaviour that recognise individuals adopt “how to decide” strategies when choosing between alternatives. Existing models simplistically assume that people evaluate all goods and choose the best of them, when in fact they ignore some goods, select what information is relevant, pursue multiple goals, and otherwise deviate from the assumptions commonly ma ....Improving Choice Models: Multiple Goal Pursuit and Multi-Stage Decision Processes. This project aims to develop new econometric models of choice behaviour that recognise individuals adopt “how to decide” strategies when choosing between alternatives. Existing models simplistically assume that people evaluate all goods and choose the best of them, when in fact they ignore some goods, select what information is relevant, pursue multiple goals, and otherwise deviate from the assumptions commonly made in econometric models. Filling in this significant gap in the choice modelling literature constitutes a significant contribution to improving our understanding of human decision making and policy analysis in every area of human endeavour.Read moreRead less
Accounting for preference seperability in stated choice experiments. This project aims to unite three separate streams of applied economic research into a single framework in order to develop a micro-economically consistent framework for demand forecasting and analysis. Forecasting demand to improve product performance or policy impacts requires realistic representations of how humans actually make choices. Combining theories of preference separability with recent developments in both activity a ....Accounting for preference seperability in stated choice experiments. This project aims to unite three separate streams of applied economic research into a single framework in order to develop a micro-economically consistent framework for demand forecasting and analysis. Forecasting demand to improve product performance or policy impacts requires realistic representations of how humans actually make choices. Combining theories of preference separability with recent developments in both activity and time use modelling and stated choice techniques, the project plans to develop new insights into consumer equilibrium as well as new econometric methods to test for the assumption of preference separability. Project outcomes would lead to an improved understanding of consumer behaviour as well as demand forecasting, with benefits to studies involving the need for benefit cost comparisons.Read moreRead less
Optimal electromaterial structures for energy applications. This project aims to develop new mathematical and modelling approaches to determine optimal configurations and parameters for material structures created from three-dimensional printing of combined metals and electromaterials. Electromaterials are needed for sustainable energy, but solving coupled-systems of highly nonlinear governing equations is needed for optimal control of spatial arrangement and composition in nano and micro-struct ....Optimal electromaterial structures for energy applications. This project aims to develop new mathematical and modelling approaches to determine optimal configurations and parameters for material structures created from three-dimensional printing of combined metals and electromaterials. Electromaterials are needed for sustainable energy, but solving coupled-systems of highly nonlinear governing equations is needed for optimal control of spatial arrangement and composition in nano and micro-structural domains. Dealing with this mathematical complexity is critical to developing high efficiency energy generation and gas storage systems. This is expected to enhance transport mechanisms within electrochemical devices and create opportunities for industry to use electrofunctional materials.Read moreRead less
Risk Measures and Management in Finance and Actuarial Science Under Regime-Switching Models. New models for assessing and managing risk of financial products will place Australia at the forefront of risk management. The work will also sustain the competitive edge of Australia as one of the major financial centres in the Asia-Pacific region through enhancing both the theory and practice of financial risk management. The project outcome will also benefit to the country in other areas of risk, for ....Risk Measures and Management in Finance and Actuarial Science Under Regime-Switching Models. New models for assessing and managing risk of financial products will place Australia at the forefront of risk management. The work will also sustain the competitive edge of Australia as one of the major financial centres in the Asia-Pacific region through enhancing both the theory and practice of financial risk management. The project outcome will also benefit to the country in other areas of risk, for example, environment risk, climate change, and energy and security problems.Read moreRead less
Transitioning to a water-secure future in the Basin. Increased water scarcity threatens the viability of the Murray-Darling Basin. There has been little analysis conducted of the consequences of water market impediments. The economic dimensions of trade impediments, water management, water market intervention and the net social benefits of water markets are at the core of this project. In particular, this project aims to explore: the impact of impediments and policy in water markets; how further ....Transitioning to a water-secure future in the Basin. Increased water scarcity threatens the viability of the Murray-Darling Basin. There has been little analysis conducted of the consequences of water market impediments. The economic dimensions of trade impediments, water management, water market intervention and the net social benefits of water markets are at the core of this project. In particular, this project aims to explore: the impact of impediments and policy in water markets; how further water market products may increase water market efficiency; and, the nature and sources of transactions costs in markets. Benefits from this project will enhance resilience and adaptation of irrigators to future climate change and water shortages, as well as providing future policy guidance.Read moreRead less
Real-time scheduling of trains to control peak electricity demand. This project aims to develop new scheduling and control methods that will enable railways to reduce their demand for electricity during peak demand periods, without undue disruption to the timetable.
These new methods and systems will integrate with—and expand the capabilities of—an Australian train control system that is used by railways around the world. This will enable better management of electricity within a region and be ....Real-time scheduling of trains to control peak electricity demand. This project aims to develop new scheduling and control methods that will enable railways to reduce their demand for electricity during peak demand periods, without undue disruption to the timetable.
These new methods and systems will integrate with—and expand the capabilities of—an Australian train control system that is used by railways around the world. This will enable better management of electricity within a region and better use of renewable energy sources, with significant cost savings for railways and the wider community.Read moreRead less
The implications for greying Australia of international property market interlinkages. Recent events in global financial markets have had a major effect on the retirement plans of Australians and the living standards of retirees. This research will permit pension fund managers to better gauge the fundamental links that exist across international property markets, as well as provide a better understanding for both academics and practitioners on the driving forces that link international real est ....The implications for greying Australia of international property market interlinkages. Recent events in global financial markets have had a major effect on the retirement plans of Australians and the living standards of retirees. This research will permit pension fund managers to better gauge the fundamental links that exist across international property markets, as well as provide a better understanding for both academics and practitioners on the driving forces that link international real estate markets together. The research will benefit all Australians as the outcomes will result in improved risk and return performance for superannuation funds, leading to a better standard of living for all retirees.Read moreRead less
Perturbations in Complex Systems and Games. This project aims to: advance the perturbation theory of dynamic and stochastic games; further develop approximations of infinite dimensional linear programs by their finite dimensional counterparts, and by finding asymptotic limits of spaces of occupational measures, by solution of successive layers of fundamental equations; explain and quantify the "exceptionality" of instances of systems that are genuinely difficult to solve; and, capitalise on the ....Perturbations in Complex Systems and Games. This project aims to: advance the perturbation theory of dynamic and stochastic games; further develop approximations of infinite dimensional linear programs by their finite dimensional counterparts, and by finding asymptotic limits of spaces of occupational measures, by solution of successive layers of fundamental equations; explain and quantify the "exceptionality" of instances of systems that are genuinely difficult to solve; and, capitalise on the outstanding performance of our Snakes-and-Ladders Heuristic (SLH) for the solution of the Hamiltonian cycle problem to identify its "fixed complexity orbits" and generalise this notion to other NP-complete problems.Read moreRead less