Risk and Reliability in Stochastic Optimisation and Equilibrium. This project seeks to develop theory and methodology in optimisation which take advantage of recent progress in understanding and treating risk in decision making. Problems of optimisation in the face of uncertainty must confront the risk inherent in having to make reliable decisions before knowing the outcomes of crucial random variables on which costs and constraints may depend. Recent theoretical developments, featuring ‘measure ....Risk and Reliability in Stochastic Optimisation and Equilibrium. This project seeks to develop theory and methodology in optimisation which take advantage of recent progress in understanding and treating risk in decision making. Problems of optimisation in the face of uncertainty must confront the risk inherent in having to make reliable decisions before knowing the outcomes of crucial random variables on which costs and constraints may depend. Recent theoretical developments, featuring ‘measures of risk’ beyond just-expected values and quantiles offer hope of major new advances. This project aims to achieve such advances not only in optimisation but also in models of equilibrium that likewise have to deal with uncertainty. Extending current theory and methodology to such multi-stage stochastic models is a challenge. Besides taking up this challenge for its own sake, a major goal of this research will be to use the results in solution algorithms.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE200100988
Funder
Australian Research Council
Funding Amount
$425,333.00
Summary
From cells to whales: A mathematical framework to understand navigation. This project aims to understand what drives the navigation of small and large organisms. To achieve this, the project seeks to develop a mathematical framework that unifies models of navigation, communication and uncertainty, for the first time. This is significant as navigation underpins fundamental behaviour such as migration. Expected outcomes of this project include novel insights into the mechanisms underlying navigati ....From cells to whales: A mathematical framework to understand navigation. This project aims to understand what drives the navigation of small and large organisms. To achieve this, the project seeks to develop a mathematical framework that unifies models of navigation, communication and uncertainty, for the first time. This is significant as navigation underpins fundamental behaviour such as migration. Expected outcomes of this project include novel insights into the mechanisms underlying navigation, and new mathematical techniques required to construct the framework. The mathematical framework will be employed to explore and explain critical biological phenomena such as the impact of noise pollution on whale migration, and the conditions required for successful cellular navigation.Read moreRead less
System identification of microstructure in the brain using magnetic resonance. Magnetic Resonance Imaging technologies will be exploited to probe the microstructure of the brain, using powerful Bayesian optimisation techniques and innovative uses of magnetic resonance. The project will in particular develop non-invasive imaging methods to quantify iron content in the brain, important for research on dementia and Alzheimer's disease.
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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How microbes build their environments through evolutionary feedback. The fitness landscape, a key evolutionary concept, relates genes or traits to reproductive fitness. However, this has been challenged by organisms that distort the landscape by changing their environments. This project aims to develop a new mathematical model that restores the landscape concept by extending it to accommodate niche construction. This framework will be applied to microorganisms that alter their environments, for ....How microbes build their environments through evolutionary feedback. The fitness landscape, a key evolutionary concept, relates genes or traits to reproductive fitness. However, this has been challenged by organisms that distort the landscape by changing their environments. This project aims to develop a new mathematical model that restores the landscape concept by extending it to accommodate niche construction. This framework will be applied to microorganisms that alter their environments, for example, by provoking and subverting the host immune system, and by inducing behavioural change in hosts. These processes alter how natural selection operates on microbes and thus lead to important evolutionary feedback. The model will be used to examine antibiotic resistance, pathogen virulence and how microbiomes develop.Read moreRead less
Neural spike variability: unifying conflicting views of neural dynamics. The project aims to improve our understanding of neural dynamics. The brain represents and processes information by means of neural voltage spikes, which show great variability in their timing. Understanding the origin of such variable neural dynamics is a long-standing problem in neuroscience. The aim of this project is to develop a novel account of variable neural dynamics, unravelling their computational principles in th ....Neural spike variability: unifying conflicting views of neural dynamics. The project aims to improve our understanding of neural dynamics. The brain represents and processes information by means of neural voltage spikes, which show great variability in their timing. Understanding the origin of such variable neural dynamics is a long-standing problem in neuroscience. The aim of this project is to develop a novel account of variable neural dynamics, unravelling their computational principles in the brain, and unifying current leading but conflicting theories. The model developed in this project would be used to explain a range of empirical observations, and the principles unravelled would be applied to understand spike-timing based neural coding. The new knowledge gained in this project may have profound implications for designing brain-like computing devices.Read moreRead less
Novel techniques for statistical and mathematical analyses of sequence data. Algorithms will be developed for analysing and comparing the sequences of DNA letters and amino acids constantly being generated in massive quantities by biological research. The novel approach taken is based on the statistical frequency of occurrence of short words and is designed specifically for situations where current methods fail.
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.
Mathematical modelling of the dynamics of multi-layered biological tissues. The project intends to develop a mathematical model of the basic mechanisms that determine the self-organisation of cells into complex tissues during the development of the embryo. Tissue function requires a non-trivial tissue architecture often composed of multiple cell layers which exhibit a remarkable capacity for renewal and defect correction. A cardinal part of embryonic development involves robust shaping of multi- ....Mathematical modelling of the dynamics of multi-layered biological tissues. The project intends to develop a mathematical model of the basic mechanisms that determine the self-organisation of cells into complex tissues during the development of the embryo. Tissue function requires a non-trivial tissue architecture often composed of multiple cell layers which exhibit a remarkable capacity for renewal and defect correction. A cardinal part of embryonic development involves robust shaping of multi-layered tissue morphologies. The project plans to use mathematical models to determine how complex, three-dimensional structures arise from adaptive multicellular biomechanical interactions. It plans to develop a novel computational modelling framework to represent and analyse such systems, which may be applicable to a wide range of problems where tissue mechanics is a key factor such as bone remodelling and wound healing.Read moreRead less
How motor proteins contract the cell cortex and form a cell division ring. This project aims to develop a detailed physical model for motor proteins and filaments and, based on it, derive a fluid-type mean-field mathematical model, which will facilitate numerical simulations and lead to testable predictions. This study will also provide detailed quantitative information on how these processes can be controlled by modifying concentration and properties of structural and motor proteins. This has p ....How motor proteins contract the cell cortex and form a cell division ring. This project aims to develop a detailed physical model for motor proteins and filaments and, based on it, derive a fluid-type mean-field mathematical model, which will facilitate numerical simulations and lead to testable predictions. This study will also provide detailed quantitative information on how these processes can be controlled by modifying concentration and properties of structural and motor proteins. This has potential applications in tumour therapy, developmental biology and in the bioengineering of nanomaterials.Read moreRead less