Computational methods for population-size-dependent branching processes. Branching processes are the primary mathematical tool used to model populations that evolve randomly in time. Most key results in the theory are derived under the simplifying assumption that individuals reproduce and die independently of each other. However, this assumption fails in most real-life situations, in particular when the environment has limited resources or when the habitat has a restricted capacity. This project ....Computational methods for population-size-dependent branching processes. Branching processes are the primary mathematical tool used to model populations that evolve randomly in time. Most key results in the theory are derived under the simplifying assumption that individuals reproduce and die independently of each other. However, this assumption fails in most real-life situations, in particular when the environment has limited resources or when the habitat has a restricted capacity. This project aims to develop novel and effective algorithmic techniques and statistical methods for a class of branching processes with dependences. We will use these results to study significant problems in the conservation of endangered island bird populations in Oceania, and to help inform their conservation management.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE200100200
Funder
Australian Research Council
Funding Amount
$418,398.00
Summary
Next generation causal inference methods for biological data. This project aims to develop next generation causal inference methods for analysing biological data especially the single cell sequencing data and their applications in cell biology. Although Artificial Intelligence and Statistical Machine Learning have been applied successfully in many fields, including biological research, there is still a serious lack of methods for interpreting and reasoning about the mechanism of biological syste ....Next generation causal inference methods for biological data. This project aims to develop next generation causal inference methods for analysing biological data especially the single cell sequencing data and their applications in cell biology. Although Artificial Intelligence and Statistical Machine Learning have been applied successfully in many fields, including biological research, there is still a serious lack of methods for interpreting and reasoning about the mechanism of biological systems, the ultimate goal of research in many areas. Efficient data-driven causality discovery approaches developed by the project will be a timely and significant contribution to the knowledge of biology and statistics as well as the battle against health threats.
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Mathematical modelling of information flow in social networks. This proposal aims to develop new mathematical and statistical methods to understand information flow in social networks. By using novel information theoretic techniques, it will create new methods to characterise social information flow in social networks. These tools will allow derivation of fundamental limits of predictability for AI methods applied to digital data. New mathematics of information flow will produce insights into so ....Mathematical modelling of information flow in social networks. This proposal aims to develop new mathematical and statistical methods to understand information flow in social networks. By using novel information theoretic techniques, it will create new methods to characterise social information flow in social networks. These tools will allow derivation of fundamental limits of predictability for AI methods applied to digital data. New mathematics of information flow will produce insights into social influence in online social networks. Benefits include: better understanding of how echo chambers may form in social networks, predictive models for how misinformation can spread online such as during an emergency, and a framework for intercomparison of AI methods applied to digital data on individuals. Read moreRead less
Advanced mathematical models and methods for a randomly-varying world. This project aims to develop advanced stochastic models and novel techniques, to analytically obtain performance measures and to efficiently simulate the time evolution. This project also plans to apply new models and methods to address important problems in ecology and epidemiology. The outputs of this project will advance knowledge in mathematics as well as in the intended application areas, including ultimately in improved ....Advanced mathematical models and methods for a randomly-varying world. This project aims to develop advanced stochastic models and novel techniques, to analytically obtain performance measures and to efficiently simulate the time evolution. This project also plans to apply new models and methods to address important problems in ecology and epidemiology. The outputs of this project will advance knowledge in mathematics as well as in the intended application areas, including ultimately in improved understanding, modelling, and tracking of the spread of diseases.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE230101174
Funder
Australian Research Council
Funding Amount
$443,154.00
Summary
Harnessing life-course transitions to optimise time-use behaviour habits. At every stage of life, how we use our time is one of the greatest determinants of our happiness, productivity, social wellbeing and quality of life. Time-use habits, for better or worse, are entrenched in daily routines that are difficult to break. This project aims to use existing population datasets to identify when during their life people are most likely to change their time-use habits, and to describe who may be at g ....Harnessing life-course transitions to optimise time-use behaviour habits. At every stage of life, how we use our time is one of the greatest determinants of our happiness, productivity, social wellbeing and quality of life. Time-use habits, for better or worse, are entrenched in daily routines that are difficult to break. This project aims to use existing population datasets to identify when during their life people are most likely to change their time-use habits, and to describe who may be at greatest risk of making unfavourable changes (e.g., replacing physical activity with sedentary time, not getting enough sleep). Expected outcomes include new analytical methods to understand time-use routines and new knowledge to inform future time-use improvement strategies to enable Australians to live their best life.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE220101409
Funder
Australian Research Council
Funding Amount
$432,447.00
Summary
Quantifying trophic niches to measure the resilience of marine predators. This project aims to pair global movement with feeding ecology datasets to characterise relationships between space use and diet breadth, and tests the effects of marine industries on functional roles of marine predators. This expects to generate knowledge about population and individual specalisation using innovative biochemical approaches and shark’s unique dental anatomy. Expected outcomes include a biochemical database ....Quantifying trophic niches to measure the resilience of marine predators. This project aims to pair global movement with feeding ecology datasets to characterise relationships between space use and diet breadth, and tests the effects of marine industries on functional roles of marine predators. This expects to generate knowledge about population and individual specalisation using innovative biochemical approaches and shark’s unique dental anatomy. Expected outcomes include a biochemical database facilitating global collaborations, and a vulnerability scale to rank resilience to impacts based on relative specalisation. This should benefit managers by accounting for previously unknown effects of marine industries on specialists at elevated extinction risk, with limited resilience to local impacts and global change.Read moreRead less
Perturbations in Complex Systems and Games. This project aims to: advance the perturbation theory of dynamic and stochastic games; further develop approximations of infinite dimensional linear programs by their finite dimensional counterparts, and by finding asymptotic limits of spaces of occupational measures, by solution of successive layers of fundamental equations; explain and quantify the "exceptionality" of instances of systems that are genuinely difficult to solve; and, capitalise on the ....Perturbations in Complex Systems and Games. This project aims to: advance the perturbation theory of dynamic and stochastic games; further develop approximations of infinite dimensional linear programs by their finite dimensional counterparts, and by finding asymptotic limits of spaces of occupational measures, by solution of successive layers of fundamental equations; explain and quantify the "exceptionality" of instances of systems that are genuinely difficult to solve; and, capitalise on the outstanding performance of our Snakes-and-Ladders Heuristic (SLH) for the solution of the Hamiltonian cycle problem to identify its "fixed complexity orbits" and generalise this notion to other NP-complete problems.Read moreRead less