New mathematics for lipids and cells: structured models for atherosclerosis. The project aims to create new mathematical theory for immune cell behaviour which leads to heart attacks and strokes. This includes formulation and analysis of new types of mathematical models for atherosclerotic plaque development, leading to the creation of new mathematical tools to investigate cell fate in plaques and to generate new hypotheses for experimental research. Expected outcomes of this project include po ....New mathematics for lipids and cells: structured models for atherosclerosis. The project aims to create new mathematical theory for immune cell behaviour which leads to heart attacks and strokes. This includes formulation and analysis of new types of mathematical models for atherosclerotic plaque development, leading to the creation of new mathematical tools to investigate cell fate in plaques and to generate new hypotheses for experimental research. Expected outcomes of this project include powerful and reliable mathematical models ready for application, and national and international collaborations with scientists and mathematicians. This should provide significant benefits including increased capacity to use mathematical models in vascular biology and training young researchers in interdisciplinary methods.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
A Novel Geometric Approach to Shocks in Reaction-Nonlinear Diffusion Models. Reaction-nonlinear diffusion models play a vital role in the study of cell migration and population dynamics. However, the presence of aggregation, or backward diffusion, leads to the formation of shock waves - distinct, sharp interfaces between different populations of densities of cells - and the breakdown of the model. This project will develop new geometric methods to explain the formation and temporal evolution of ....A Novel Geometric Approach to Shocks in Reaction-Nonlinear Diffusion Models. Reaction-nonlinear diffusion models play a vital role in the study of cell migration and population dynamics. However, the presence of aggregation, or backward diffusion, leads to the formation of shock waves - distinct, sharp interfaces between different populations of densities of cells - and the breakdown of the model. This project will develop new geometric methods to explain the formation and temporal evolution of these shock waves, while simultaneously unifying existing regularisation techniques under a single, geometric banner. It will devise innovative tools in singular perturbation theory and stability analysis that will identify key parameters in the creation of shock waves, as well as their dynamic behaviour.Read moreRead less
ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. The ARC Centre for the Mathematical Analysis of Cellular Systems aims to deliver the mathematics required to compute life. The Centre will deliver innovation in computational and mathematical biology and establish in silico biology alongside in vivo and in vitro biology. These models will allow us to understand the complexity of life at the cellu ....ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. The ARC Centre for the Mathematical Analysis of Cellular Systems aims to deliver the mathematics required to compute life. The Centre will deliver innovation in computational and mathematical biology and establish in silico biology alongside in vivo and in vitro biology. These models will allow us to understand the complexity of life at the cellular level and enable new ways of combining diverse and heterogenous data. This will allow us to understand the mechanisms underlying cellular behaviour, and to apply rational design engineering methods in order to control the dynamics of biological systems. Read moreRead less
Two-price quantitative finance. This project aims to establish a novel field, namely two-price quantitative finance, and explore its applications. The new field will integrate two major schools for modelling and explain the presence of two prices, the buying and selling prices, widely observed in the real-world markets, and the equilibrium approach from the fundamental law of one price. The outcomes would deepen our understanding of the fundamental relationship among liquidity, prices, risk and ....Two-price quantitative finance. This project aims to establish a novel field, namely two-price quantitative finance, and explore its applications. The new field will integrate two major schools for modelling and explain the presence of two prices, the buying and selling prices, widely observed in the real-world markets, and the equilibrium approach from the fundamental law of one price. The outcomes would deepen our understanding of the fundamental relationship among liquidity, prices, risk and the economy. This project expects to bring about long-term impact on quantitative finance and related applications through providing a deep understanding of, and a new perspective for, the design, risk and fairness of the finance, property and insurance markets.Read moreRead less
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
There and back again: operator algebras, algebras and dynamical systems. The aim of this project is to develop mathematics that enables us to transfer information back and forth between dynamical systems and algebras, including operator algebras. Dynamical systems - systems that change over time - are ubiquitous, and central to modern mathematics and its applications. In mathematics, dualities allow us to translate questions from one context to another in which they are easier to solve and then ....There and back again: operator algebras, algebras and dynamical systems. The aim of this project is to develop mathematics that enables us to transfer information back and forth between dynamical systems and algebras, including operator algebras. Dynamical systems - systems that change over time - are ubiquitous, and central to modern mathematics and its applications. In mathematics, dualities allow us to translate questions from one context to another in which they are easier to solve and then translate the answer back again. Expected outcomes include increased understanding of the relationship between operator algebras and the dynamical systems that they represent. Benefits include enhanced international collaboration, and increased Australian capacity in pure mathematics, particularly operator algebras.Read moreRead less
Implications of Global Economic Forces for Domestic Monetary Policy. The project aims to quantify and understand the extent to which international factors affect key macroeconomic variables such as inflation and interest rates in open economies. The aims will be achieved through the development and application of new macroeconomic and econometric models. Expected outcomes are new insights and policy recommendations on how to appropriately conduct monetary policy for an open economy such as Austr ....Implications of Global Economic Forces for Domestic Monetary Policy. The project aims to quantify and understand the extent to which international factors affect key macroeconomic variables such as inflation and interest rates in open economies. The aims will be achieved through the development and application of new macroeconomic and econometric models. Expected outcomes are new insights and policy recommendations on how to appropriately conduct monetary policy for an open economy such as Australia. This should provide significant benefits to the broader Australian economy through the conduct of suitable policy by institutions such as the Reserve Bank of Australia.Read moreRead less
Situational Assessment as a Marker of Cognitive Skill Decay. The aim of this study is to test how differences in exposure to complex tasks change the capacity for situational assessment. Amongst drivers, pilots and electricity controllers, the capacity to assess and respond effectively to changes in the operational environment are critical in sustaining performance and ensuring the safety and security of the public. Establishing the nature of this relationship will enable, for the first time, ob ....Situational Assessment as a Marker of Cognitive Skill Decay. The aim of this study is to test how differences in exposure to complex tasks change the capacity for situational assessment. Amongst drivers, pilots and electricity controllers, the capacity to assess and respond effectively to changes in the operational environment are critical in sustaining performance and ensuring the safety and security of the public. Establishing the nature of this relationship will enable, for the first time, objective measures of cognitive skill decay. In evaluating cognitive skill decay more accurately, we will provide a cost-effective, easily administered tool, enabling practitioners to identify and address areas of development and providing data to anticipate when cognitive skill decay is most likely to occur.Read moreRead less
Empowering next-generation sea-ice models with wave–ice mathematics. Sea ice is a crucial part of the Australian and global climate systems, and the most sensitive indicator of the alarming climate changes in motion. This project aims to deliver a vital component in next-generation sea-ice models, by modelling ocean waves in the ice-covered ocean, and implementing it in the leading large-scale sea-ice model. The waves-in-ice model will be accurate for the range of possible wave–ice conditions, u ....Empowering next-generation sea-ice models with wave–ice mathematics. Sea ice is a crucial part of the Australian and global climate systems, and the most sensitive indicator of the alarming climate changes in motion. This project aims to deliver a vital component in next-generation sea-ice models, by modelling ocean waves in the ice-covered ocean, and implementing it in the leading large-scale sea-ice model. The waves-in-ice model will be accurate for the range of possible wave–ice conditions, using understanding derived from state-of-the-art experimental measurements. Powerful mathematical approximation methods will be developed to generate model efficiency. The outcomes will create a new standard in sea-ice modelling, with significant benefits for sea-ice forecasting and climate studies.Read moreRead less