Discovery Early Career Researcher Award - Grant ID: DE120101113
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
Mathematical modelling of breast cancer immunity: guiding the development of preventative breast cancer vaccines. The project will apply various methods from mathematical modelling to simulate anti-breast cancer immune responses to incipient tumours. Results from simulation and analysis will help develop, assess, and optimise preventative breast cancer vaccines for further testing in future experimental studies.
Geometric methods in mathematical physiology. This project will develop new geometric methods for the analysis of multiple-scales models of physiological rhythms and patterns, and will design diagnostic tools to identify key parameters that cause and control these signals. Thus, this project will deliver powerful mathematics for detecting and understanding fundamental issues of physiological systems.
Dynamics of atherosclerotic plaque formation, growth and regression. This project aims to provide a mathematical framework to interpret plaque growth. Many biological processes contribute to the growth of atherosclerotic plaques inside arteries. Lipoproteins enter the artery walls and stimulate tissues to signal to cells which duly respond so that fatty streaks form and grow into dangerous plaques that cause heart attacks or stroke. These processes are often nonlinear and operate on widely varyi ....Dynamics of atherosclerotic plaque formation, growth and regression. This project aims to provide a mathematical framework to interpret plaque growth. Many biological processes contribute to the growth of atherosclerotic plaques inside arteries. Lipoproteins enter the artery walls and stimulate tissues to signal to cells which duly respond so that fatty streaks form and grow into dangerous plaques that cause heart attacks or stroke. These processes are often nonlinear and operate on widely varying time scales. The project plans to use systems of ordinary differential equations, partial differential equations with non-standard boundary conditions, and bifurcation theory to find how nonlinear processes shape plaque growth. The expected results may demonstrate the importance of bifurcations, dynamics and nonlinear systems in plaque growth and provide new models to interpret biological data.Read moreRead less
A probabilistic and geometric understanding of transport and metastability in mathematical geophysical flows. Complicated fluid flow is at the heart of physical oceanography and atmospheric science. This project will develop new mathematical technologies to reveal hidden transport barriers around which complicated fluid flow is organised. This project will lead to more accurate circulation predictions from ocean and atmosphere models.
Bodies in space. By investigating how a change in shape of the human body can produce a change in spatial orientation, the project will bring a fundamental advance of knowledge in the intersection of applied mathematics, sports science and mechanical engineering. These knowledge advances will lead to a novel theory regarding the control of the aerial dynamics of athletes, specifically springboard and platform divers. When applied in collaboration with world class Australian athletes, this theory ....Bodies in space. By investigating how a change in shape of the human body can produce a change in spatial orientation, the project will bring a fundamental advance of knowledge in the intersection of applied mathematics, sports science and mechanical engineering. These knowledge advances will lead to a novel theory regarding the control of the aerial dynamics of athletes, specifically springboard and platform divers. When applied in collaboration with world class Australian athletes, this theory will result in innovative platform and springboard diving techniques and improved performance. The reach of new insights generated by this work extends to many other fields, including robotics, spacecraft dynamics and nano technology.Read moreRead less
Extracting macroscopic variables and their dynamics in multiscale systems with metastable states. There are practical barriers to the simulation of complex systems such as molecular systems and the climate system because of the high-dimensionality of the models and the presence of multiscale dynamics. This project will lift these barriers by uncovering the most relevant variables and by creating innovative multiscale simulation algorithms.
Atomic Resolution Sensors for Imaging and Metrological Science. This project aims to create new sensing technologies for detecting motion on the atomic scale with Megahertz (MHz) bandwidth. Advanced signal processing and communication theory will be applied with the aim of developing new classes of capacitive, inductive and optical position sensors. The resolution and bandwidth are predicted to be a one-hundred fold improvement over the current state-of-the-art. Applications are expected to incl ....Atomic Resolution Sensors for Imaging and Metrological Science. This project aims to create new sensing technologies for detecting motion on the atomic scale with Megahertz (MHz) bandwidth. Advanced signal processing and communication theory will be applied with the aim of developing new classes of capacitive, inductive and optical position sensors. The resolution and bandwidth are predicted to be a one-hundred fold improvement over the current state-of-the-art. Applications are expected to include biomedical imaging, high-speed nanofabrication, high-resolution computer numerical control (CNC) machining, high-speed gas and chemical sensors, and ultra-precise seismometers and gyroscopes.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.
Discovery Early Career Researcher Award - Grant ID: DE220100284
Funder
Australian Research Council
Funding Amount
$444,000.00
Summary
Multiscale mathematical modelling to gain insights into hepatitis viruses. This project aims to use mathematical modelling to study hepatitis viruses at multiple levels. The project expects to develop complex yet analysable mathematical models to comprehend the fundamental biology of hepatitis viruses by elucidating longitudinal patterns in viral and immune markers at intracellular and cellular levels, and advance a new subfield in mathematical biology, i.e., modelling codependent human viruses. ....Multiscale mathematical modelling to gain insights into hepatitis viruses. This project aims to use mathematical modelling to study hepatitis viruses at multiple levels. The project expects to develop complex yet analysable mathematical models to comprehend the fundamental biology of hepatitis viruses by elucidating longitudinal patterns in viral and immune markers at intracellular and cellular levels, and advance a new subfield in mathematical biology, i.e., modelling codependent human viruses. Expected outcomes of the project include new generalized mathematical tools, biological insights that may aid research beyond the scope of this project, and strong interdisciplinary collaborations. Expected benefits include an increased capacity of the research community in Australia to use mathematical models in virology.Read moreRead less
Mathematical model reduction for complex networks. This project aims to develop new mathematical methodology to describe the collective behaviour of large networks of oscillators with parameters called collective coordinates. This will allow for the quantitative description of finite-size networks as well as chaotic dynamics, which are both out of reach for current model reduction methods. The project will apply methodology to understand the causes of, and ways to prevent, glitches and failure i ....Mathematical model reduction for complex networks. This project aims to develop new mathematical methodology to describe the collective behaviour of large networks of oscillators with parameters called collective coordinates. This will allow for the quantitative description of finite-size networks as well as chaotic dynamics, which are both out of reach for current model reduction methods. The project will apply methodology to understand the causes of, and ways to prevent, glitches and failure in the emerging modern decentralised power grids. This will develop a framework to address this question, tailored to deal with the hitherto uncharted case of finite-size networks.Read moreRead less