Mathematical modelling can provide vital information on the effectiveness and practical implementation of microbicides and vaccines against HIV. This project will produce mathematical models of the earliest stages of HIV infection suitable for investigation of the implementation of vaccines and microbicides. It will provide a framework to investigate why these interventions have performed poorly to date, and how these may be better implemented.
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
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
A geometric theory for travelling waves in advection-reaction-diffusion models. Cell migration patterns often develop distinct sharp interfaces between identifiably different cell populations within a tissue. This research will develop new geometric methods for the mathematical analysis of cell migration models, and will design diagnostic tools to identify key parameters that cause and control these patterns and interfaces.
Mathematical and Numerical Models of Piezoelectric Wave Energy Converters. The project will investigate piezoelectric wave energy converters. We will derive the equations of motion in a form suitable for use in marine engineering paradigms using variational methods and then solve these analytically and with smoothed particle hydrodynamics. Using these innovative techniques, this project will generate new knowledge capable of elucidating the multifaceted physical phenomena that occur when comple .... Mathematical and Numerical Models of Piezoelectric Wave Energy Converters. The project will investigate piezoelectric wave energy converters. We will derive the equations of motion in a form suitable for use in marine engineering paradigms using variational methods and then solve these analytically and with smoothed particle hydrodynamics. Using these innovative techniques, this project will generate new knowledge capable of elucidating the multifaceted physical phenomena that occur when complex fluid motion and deformable structures interact. The project outcomes include the development of mathematical and computation methods to handle intricate behaviours of piezoelectric elastic-fluids systems. These groundbreaking methods will allow these wave energy systems to be analysed and their effectiveness assessed.Read moreRead less
What predictions can I trust? Stability of chaotic random dynamical systems. This project aims to make significant progress on the intricate question of global stability of non-autonomous chaotic dynamical systems. Using ergodic theory, this project expects to determine when and how errors in dynamical models that are small and frequent, or large and infrequent, can cause dramatic changes in meaningful mathematical model outputs. Expected outcomes include the discovery of mathematical mechanisms ....What predictions can I trust? Stability of chaotic random dynamical systems. This project aims to make significant progress on the intricate question of global stability of non-autonomous chaotic dynamical systems. Using ergodic theory, this project expects to determine when and how errors in dynamical models that are small and frequent, or large and infrequent, can cause dramatic changes in meaningful mathematical model outputs. Expected outcomes include the discovery of mathematical mechanisms underlying large-scale (in)stability for time-dependent dynamical systems, and reliable numerical methods for detecting instabilities. This research is expected to lead to improved characterisations of shocks or collapse in externally driven dynamical systems and assist scientists to gauge which predictions they can trust.Read moreRead less
New mathematics to quantify fluctuations and extremes in dynamical systems. Many problems in the natural world result from the cumulative effect of extreme events in complex dynamical systems. Dynamical models of ecological and physical processes have internal variables that can combine to produce large observable changes. Quantitative estimation of the variability of these chaotic models is difficult because of the time dependence of the dynamics and their “long memory” due to significant deter ....New mathematics to quantify fluctuations and extremes in dynamical systems. Many problems in the natural world result from the cumulative effect of extreme events in complex dynamical systems. Dynamical models of ecological and physical processes have internal variables that can combine to produce large observable changes. Quantitative estimation of the variability of these chaotic models is difficult because of the time dependence of the dynamics and their “long memory” due to significant deterministic components. This project aims to develop mathematics and numerics to accurately quantify and assess these complicated variations. The project expects to provide powerful tools to predict harmful outcomes in biogeophysical systems, and assist with the development of mitigation strategies.Read moreRead less
Algorithmic engineering and complexity analysis of protocols for consensus. Opinions, rankings, observations, votes, gene sequences, sensor-networks in security systems or climate models. Massive datasets and the ability to share information at unprecedented speeds, makes finding the most central representative, the Consensus Problem, extremely complex. This research delivers new insights and new, efficient algorithms.
The Ethics of Voluntary Assisted Dying: Promoting Constructive Debate. This project aims to analyze core concepts that play key roles in emerging debates about the ethics of Voluntary Assisted Dying (VAD) in Australia. The project expects to make constructive contributions to these debates, promoting respectful dialogue and reducing polarization. Expected outcomes include a new model for managing VAD in Australia which is ethically appropriate and consistent with community values. This model wil ....The Ethics of Voluntary Assisted Dying: Promoting Constructive Debate. This project aims to analyze core concepts that play key roles in emerging debates about the ethics of Voluntary Assisted Dying (VAD) in Australia. The project expects to make constructive contributions to these debates, promoting respectful dialogue and reducing polarization. Expected outcomes include a new model for managing VAD in Australia which is ethically appropriate and consistent with community values. This model will also benefit other countries where the ethics of VAD is under consideration. The project will promote the dignity and autonomy of all and ensure that issues about the conscientious refusal of healthcare professionals to participate in the provision of VAD are handled in an ethically appropriate and effective manner.Read moreRead less
Determining principles for successful episode retrieval of repeated events. This project aims to develop the first-ever set of explanatory principles for how people successfully retain and retrieve individual episode memories from repeated experiences (e.g., one occurrence of a routine social encounter or job-related activity). By deepening our understanding of how memory works, this new knowledge is expected to lay the foundation for interview guidance and ongoing research aimed at enhancing th ....Determining principles for successful episode retrieval of repeated events. This project aims to develop the first-ever set of explanatory principles for how people successfully retain and retrieve individual episode memories from repeated experiences (e.g., one occurrence of a routine social encounter or job-related activity). By deepening our understanding of how memory works, this new knowledge is expected to lay the foundation for interview guidance and ongoing research aimed at enhancing the proficiency of investigations into matters that rely on detailed and accurate accounts of specific episodes. This includes workplace or traffic accident investigations, infectious disease contact tracing, as well as prosecution of repeated sexual offences.Read moreRead less