How can cultural innovations trigger the emergence of new diseases? This project aims to develop new mathematical and computational models to examine whether cultural innovations creates conditions for the emergence of new diseases. It will combine elements of microbial evolution and cultural evolution to advance a new modelling framework to consider their joint dynamics. The expected outcome is an enhanced understanding of how human behaviour influences the emergence of infections. This will br ....How can cultural innovations trigger the emergence of new diseases? This project aims to develop new mathematical and computational models to examine whether cultural innovations creates conditions for the emergence of new diseases. It will combine elements of microbial evolution and cultural evolution to advance a new modelling framework to consider their joint dynamics. The expected outcome is an enhanced understanding of how human behaviour influences the emergence of infections. This will bring benefits of computational models for broad use in understanding complex population processes, and training to maintain mathematical and computational skills in the Australian workforce.
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The mathematics of stochastic transport and signalling in cells. The project aims to develop new stochastic mathematical models of the dynamics of protein transport and cell signalling. The mathematics will link macro scale biological observations to micro scale molecular movements to characterise the relative role that different components and processes play. Expected outcomes are robust mathematical analyses of the transient dynamics of closed, finite capacity queueing networks and biological ....The mathematics of stochastic transport and signalling in cells. The project aims to develop new stochastic mathematical models of the dynamics of protein transport and cell signalling. The mathematics will link macro scale biological observations to micro scale molecular movements to characterise the relative role that different components and processes play. Expected outcomes are robust mathematical analyses of the transient dynamics of closed, finite capacity queueing networks and biological insight into the major control mechanisms in cellular insulin signalling. The project should provide significant benefits via the delivery of new mathematical tools and analysis for stochastic networks, impacting our understanding of metabolic transport, and providing interdisciplinary research training.Read moreRead less
Sinusoidal voltage protocols for characterisation of ion channel kinetics. This project aims to implement an innovative approach to modelling ion channel behaviour that employs short, information-rich datasets and parameter inference. Using the hERG potassium channel as a test case, the project will show that this approach is more efficient than current methods and outperforms all published models in independent validations. The project aims to extend on initial implementation to probe the therm ....Sinusoidal voltage protocols for characterisation of ion channel kinetics. This project aims to implement an innovative approach to modelling ion channel behaviour that employs short, information-rich datasets and parameter inference. Using the hERG potassium channel as a test case, the project will show that this approach is more efficient than current methods and outperforms all published models in independent validations. The project aims to extend on initial implementation to probe the thermodynamics and pharmacology of ion channel gating. The anticipated outcomes are to grow fundamental knowledge of ion channel biophysics and ability to probe ion channel function in silico. The project will build on an emerging collaboration between international leaders in physiology, pharmacology, mathematics and computer modelling. The methodology and fundamental knowledge generated will significantly advance our understanding of the physiology and biophysics of ion channels, while the application of the method will have direct impact in the pharmaceutical industry and regulatory science.Read moreRead less
Mathematical modelling unravels the impact of social dynamics on evolution. This project aims to mathematically model human evolution as a dynamical process. The anticipated goal is to quantitatively analyse theories of human origins. The project expects to develop innovative mathematical models, improve our understanding of the evolutionary process, and advance a unique area of interdisciplinary collaboration: applied mathematics and anthropology. Expected outcomes include refined methods fo ....Mathematical modelling unravels the impact of social dynamics on evolution. This project aims to mathematically model human evolution as a dynamical process. The anticipated goal is to quantitatively analyse theories of human origins. The project expects to develop innovative mathematical models, improve our understanding of the evolutionary process, and advance a unique area of interdisciplinary collaboration: applied mathematics and anthropology. Expected outcomes include refined methods for mathematical modelling of human evolution and improved techniques for analysing such models. It should provide benefits, such as increasing research in mathematical biology, an important growth area of science in Australia, and advancing mathematical approaches to engaging questions arising from anthropology.Read moreRead less
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
Space, time and boundary conditions: Mathematics for evolving plaques. This project aims to create new mathematical theory to model the morphology of atherosclerotic plaques, which cause heart attacks and strokes, as plaques grow or regress. The project expects to devise new mathematical tools for formulating novel spatial models for cellular processes inside the plaque. These should give a new window into plaque growth and spatial structures . Expected outcomes include powerful and reliable mat ....Space, time and boundary conditions: Mathematics for evolving plaques. This project aims to create new mathematical theory to model the morphology of atherosclerotic plaques, which cause heart attacks and strokes, as plaques grow or regress. The project expects to devise new mathematical tools for formulating novel spatial models for cellular processes inside the plaque. These should give a new window into plaque growth and spatial structures . Expected outcomes include powerful and reliable mathematical models, new tools to understand plaque evolution, 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.
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A coordinate-independent theory for multi-time-scale dynamical systems. Biochemical reaction networks operate inherently on many disparate timescales, and identifying this temporal hierarchy is key to understanding biological behaviour. Currently, the existing dynamical systems theory is not able to rigorously analyse many important biological systems and networks due to this inherent non-standard multi-time-scale splitting. This project aims to remove these stumbling blocks and develop a coordi ....A coordinate-independent theory for multi-time-scale dynamical systems. Biochemical reaction networks operate inherently on many disparate timescales, and identifying this temporal hierarchy is key to understanding biological behaviour. Currently, the existing dynamical systems theory is not able to rigorously analyse many important biological systems and networks due to this inherent non-standard multi-time-scale splitting. This project aims to remove these stumbling blocks and develop a coordinate-independent mathematical theory that weaves together results from geometric singular perturbation theory, differential and algebraic geometry and reaction network theory to decompose and explain the structure in the dynamic hierarchy of events in non-standard multi-time-scale systems and networks.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
New mathematics for multi-extremal optimization and diffusion tensor imaging. This project aims to establish numerically certifiable mathematical theory and methods for semi-algebraic optimisation problems. Numerically certifiable optimisation principles and techniques are vital for the practical use of optimisation technologies because they can be readily implemented by common computer models and algorithms. Yet no such methodologies exist for multi-extremal, semi-algebraic optimisation problem ....New mathematics for multi-extremal optimization and diffusion tensor imaging. This project aims to establish numerically certifiable mathematical theory and methods for semi-algebraic optimisation problems. Numerically certifiable optimisation principles and techniques are vital for the practical use of optimisation technologies because they can be readily implemented by common computer models and algorithms. Yet no such methodologies exist for multi-extremal, semi-algebraic optimisation problems which are common in modern science and medicine. The expected outcomes of this project include enhanced optimisation methods for diffusion tensor imaging, an emerging technology in brain sciences.Read moreRead less
Microcantilevers for multifrequency atomic force microscopy. This project aims to design a microcantilever with high-performing sensors more sensitive and with better noise performance than the typical optical system used in commercial Atomic Force Microscopes (AFMs). The AFM, a nanotechnology instrument, uses a microcantilever (with an extremely shape probe) to interrogate a sample surface. It has made important discoveries in nanotechnology, life sciences, nanomachining, material science and d ....Microcantilevers for multifrequency atomic force microscopy. This project aims to design a microcantilever with high-performing sensors more sensitive and with better noise performance than the typical optical system used in commercial Atomic Force Microscopes (AFMs). The AFM, a nanotechnology instrument, uses a microcantilever (with an extremely shape probe) to interrogate a sample surface. It has made important discoveries in nanotechnology, life sciences, nanomachining, material science and data storage systems. Despite its success, the technique’s spatial resolution and quantitative measurements are limited. This project could lead to breakthrough technologies such as atomic force spectroscopy to study elastic modulus of nanostructures, and establish Australia's prominence in this emerging field.Read moreRead less