Fractional decomposition of graphs and the Nash-Williams conjecture. Nash-Williams' conjecture is a famous unsolved problem about decomposing graphs (abstract networks). Breakthrough results achieved in recent years have shown that the conjecture, along with other major graph decomposition problems, could be solved if only more were known about fractional decomposition. This project aims to clear this bottleneck to progress by dramatically expanding the state of knowledge on fractional decomposi ....Fractional decomposition of graphs and the Nash-Williams conjecture. Nash-Williams' conjecture is a famous unsolved problem about decomposing graphs (abstract networks). Breakthrough results achieved in recent years have shown that the conjecture, along with other major graph decomposition problems, could be solved if only more were known about fractional decomposition. This project aims to clear this bottleneck to progress by dramatically expanding the state of knowledge on fractional decomposition. Expected outcomes include major progress on Nash-Williams' conjecture and related graph decomposition problems. This should enhance Australia's research reputation in pure mathematics and provide benefits in downstream applications areas including statistics, data transmission, and fibre-optic networks.Read moreRead less
Unpacking the immune system with applied mathematics. This project aims to model immune interactions across cells and structures spanning scales of nanometres to millimetres. It expects to develop innovative mathematical insights, improve our understanding of immunology, and consolidate collaborations with top American and European laboratories and groups. Expected outcomes include cutting-edge techniques for multiscale biological modelling and improved prediction and analysis of immune dynami ....Unpacking the immune system with applied mathematics. This project aims to model immune interactions across cells and structures spanning scales of nanometres to millimetres. It expects to develop innovative mathematical insights, improve our understanding of immunology, and consolidate collaborations with top American and European laboratories and groups. Expected outcomes include cutting-edge techniques for multiscale biological modelling and improved prediction and analysis of immune dynamics. The project should provide benefits to industries where highly organised behaviours are important, for example those interested in robot swarming, optimal transportation, and epidemic management. It should also benefit Australian students and researchers with novel overseas training opportunities.Read moreRead less
Mathematical Modelling of the Mechanobiology of Arterial Plaque Growth. Plaque growth is a chronic inflammatory response induced by the interactions between endothelial cells, lipids, monocytes/macrophages, smooth muscle cells and platelets in the arteries. It involves many different biological processes, such as lipid deposition, inflammation and angiogenesis, and their interactions with the microcirculation. To understand the underlying mechanobiology, we propose to develop a mathematical mode ....Mathematical Modelling of the Mechanobiology of Arterial Plaque Growth. Plaque growth is a chronic inflammatory response induced by the interactions between endothelial cells, lipids, monocytes/macrophages, smooth muscle cells and platelets in the arteries. It involves many different biological processes, such as lipid deposition, inflammation and angiogenesis, and their interactions with the microcirculation. To understand the underlying mechanobiology, we propose to develop a mathematical model to interpret plaque growth by integrating these dynamic biological processes. It will offer a systematic rational understanding of plaque growth. New models will be provided to better interpret biological data and contribute to our knowledge in quantifying complex biological mechanisms during growth and development.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
Computational modelling of nanofluids for industrial applications. The use of nanoparticles in heat transfer fluids, then known as nanofluids, increases their specific heat and thermal conductivity. Recent experimental works highlight that anomalous transport phenomena are evident in nanofluids that cannot be adequately described by classical conservation laws. We will extend these conservation laws to incorporate fractional operators to capture the fluid memory effects and the impact of particl ....Computational modelling of nanofluids for industrial applications. The use of nanoparticles in heat transfer fluids, then known as nanofluids, increases their specific heat and thermal conductivity. Recent experimental works highlight that anomalous transport phenomena are evident in nanofluids that cannot be adequately described by classical conservation laws. We will extend these conservation laws to incorporate fractional operators to capture the fluid memory effects and the impact of particle clustering. Computational modelling and experimental investigations will be undertaken to identify the heat transfer mechanisms of various nanofluids. The outcomes of the work will increase knowledge on nanofluids and offer a significant opportunity to improve the efficiency of many thermal engineering systems.Read moreRead less
Reasonable Adjustments to Maths for Students with Intellectual Disabilities. Reasonable adjustments to secondary mathematics – parents want it, students need it, the Australian law requires it – but how do teachers achieve it? The aim of this project is to find ways to adjust, teach and assess secondary mathematics for students with intellectual and developmental disabilities. The significance of this study is in solving a problem facing teachers who are required by law to teach mathematics with ....Reasonable Adjustments to Maths for Students with Intellectual Disabilities. Reasonable adjustments to secondary mathematics – parents want it, students need it, the Australian law requires it – but how do teachers achieve it? The aim of this project is to find ways to adjust, teach and assess secondary mathematics for students with intellectual and developmental disabilities. The significance of this study is in solving a problem facing teachers who are required by law to teach mathematics without evidence informed approaches. Expected outcomes are an evidence-base for reasonable adjustments to secondary mathematics and approaches and strategies for teachers for inclusive practices. If ways for teaching year-level mathematics to learners with intellectual disability are developed, many more students may benefit.
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A new universal mechanism controlling body proportions in animals. This project aims to establish that a recently-discovered mechanism, the inhibitory cascade, determines the basic proportions of appendages and body segments in a diverse range of animal groups, particularly vertebrates and arthropods. The goals of the project are to reveal the molecular mechanisms in mice and insects, and build computer simulations to show how to manipulate the control of development by the inhibitory cascade. T ....A new universal mechanism controlling body proportions in animals. This project aims to establish that a recently-discovered mechanism, the inhibitory cascade, determines the basic proportions of appendages and body segments in a diverse range of animal groups, particularly vertebrates and arthropods. The goals of the project are to reveal the molecular mechanisms in mice and insects, and build computer simulations to show how to manipulate the control of development by the inhibitory cascade. The project should benefit bioengineering by establishing control mechanisms for the manipulation and regeneration of teeth and limbs.Read moreRead less
Developing feasible in situ control of mange disease in wombats. Our goal is the development of feasible in situ control of sarcoptic mange in wombat populations. Globally important, the Sarcoptes scabiei mite infects >100 mammal species and is among the 50 most common human diseases, causing health, welfare and population impacts. This infection is treatable, and we will test a new treatment (fluralaner), develop new models to guide management, and conduct replicated field trials. This will ena ....Developing feasible in situ control of mange disease in wombats. Our goal is the development of feasible in situ control of sarcoptic mange in wombat populations. Globally important, the Sarcoptes scabiei mite infects >100 mammal species and is among the 50 most common human diseases, causing health, welfare and population impacts. This infection is treatable, and we will test a new treatment (fluralaner), develop new models to guide management, and conduct replicated field trials. This will enable science-based guidelines, advancing disease control, local eradication, and regulatory approval for wombats. Our research framework is adaptable to other mange-impacted species, and advance methods and theory for control of treatable disease in wildlife.Read moreRead less
Fractional dynamic models for MRI to probe tissue microstructure. This project aims to develop new mathematical tools for mapping tissue microstructural properties via the use of space-time fractional calculus methods. In magnetic resonance imaging, mathematical models and their parameters play a key role in associating information between images and biology, with the overall aim of producing spatially resolved maps of tissue property variations. However, models which can inform on changes in mi ....Fractional dynamic models for MRI to probe tissue microstructure. This project aims to develop new mathematical tools for mapping tissue microstructural properties via the use of space-time fractional calculus methods. In magnetic resonance imaging, mathematical models and their parameters play a key role in associating information between images and biology, with the overall aim of producing spatially resolved maps of tissue property variations. However, models which can inform on changes in microscale tissue properties are lacking. The tools developed by this project will be used to generate new magnetic resonance image based maps to convey information on tissue microstructure changes in the human brain. Additionally, the mathematical tools developed will be transferable to other applications where diffusion and transport in heterogeneous porous media play a role.Read moreRead less