TSuNAMi: Time Series Network Animal Modelling. Our proposal is motivated by and based upon the successful representation of time series as a network (or graph). We construct an abstract representation of a system from measurements of its changing behaviour over time. Properties of that structure (the network) then allow us to infer diagnostic information of the system. Specifically, we propose to apply this to livestock welfare during transport. By measuring the biological and environment condi ....TSuNAMi: Time Series Network Animal Modelling. Our proposal is motivated by and based upon the successful representation of time series as a network (or graph). We construct an abstract representation of a system from measurements of its changing behaviour over time. Properties of that structure (the network) then allow us to infer diagnostic information of the system. Specifically, we propose to apply this to livestock welfare during transport. By measuring the biological and environment condition of the animal we construct a network representation of that system. Geometric features of that network can then be used to infer health or duress of the subject. This proposal will develop the generic mathematical machinery to connect geometric features of the network with system behaviour. Read moreRead less
Optimising disease surveillance to support decision-making. COVID-19 has demonstrated the critical role of epidemic data and analytics in guiding government response to pandemic threats, reducing disease and saving lives. The demand for epidemic analytics for response to threats of national significance will only grow. The goals of this project are to 1) determine the combination(s) of surveillance methods that provide the most useful data for epidemic analysis and 2) translate these findings in ....Optimising disease surveillance to support decision-making. COVID-19 has demonstrated the critical role of epidemic data and analytics in guiding government response to pandemic threats, reducing disease and saving lives. The demand for epidemic analytics for response to threats of national significance will only grow. The goals of this project are to 1) determine the combination(s) of surveillance methods that provide the most useful data for epidemic analysis and 2) translate these findings into the blueprint for a next-generation infectious disease surveillance system for Australia. We will use a simulation-evaluation approach, coupling methods from infectious disease modelling with those from information theory optimal design. Outcomes will enable more tailored and effective pandemic response.Read moreRead less
Predicting strength of porous materials. This project aims to develop a predictive theory of strength for unflawed, low-ductile porous materials – an unsolved problem in computational solid mechanics. Three-dimensional printing of lightweight, porous materials is used in industry, medicine and science. The project will develop the theory and conduct experiments on porous metallic and polymeric samples made using additive manufacturing, which require understanding and optimisation of the building ....Predicting strength of porous materials. This project aims to develop a predictive theory of strength for unflawed, low-ductile porous materials – an unsolved problem in computational solid mechanics. Three-dimensional printing of lightweight, porous materials is used in industry, medicine and science. The project will develop the theory and conduct experiments on porous metallic and polymeric samples made using additive manufacturing, which require understanding and optimisation of the building of fine scale features. Understanding strength should improve design of stronger materials, by using and extending the capabilities of three-dimensional printing. These advances will further provide a much-needed basis for a fundamental understanding of fracture in other porous materials important to society such as concrete, rocks, porous ceramics and bone implants.Read moreRead less
Cooperative control of networked systems with constraints. This project aims to address the challenge of networked systems in deploying teams of robotic agents. Control of the networked system is extremely difficult due to real world constraints imposed on each agent. This project will focus on motion constraints, equipment/capability constraints, and spatial constraints. In addition to theoretical advances, the wider scientific community will benefit directly, because the control algorithms dev ....Cooperative control of networked systems with constraints. This project aims to address the challenge of networked systems in deploying teams of robotic agents. Control of the networked system is extremely difficult due to real world constraints imposed on each agent. This project will focus on motion constraints, equipment/capability constraints, and spatial constraints. In addition to theoretical advances, the wider scientific community will benefit directly, because the control algorithms developed are expected to allow straightforward deployment of robotic teams. There are myriad applications for cooperative robotic agents, ranging from surveillance, to environmental monitoring using underwater and aerial drone formations – with an array of benefits and impacts including economic, commercial and societal. The results are intended to ensure and cement Australia’s front-line position in the current technological revolution known as “Industry 4.0”.Read moreRead less
Development of a novel best approximation theory with applications . The aim of this project is to develop an innovative best approximation theory for complex fractional boundary value problems with discontinuities and with no compactness, and then apply the theory to study two classes of complex partial differential equation boundary value problems with industrial applications. The work will lead to the development of a new theory and a suite of innovative analytical and computational methods f ....Development of a novel best approximation theory with applications . The aim of this project is to develop an innovative best approximation theory for complex fractional boundary value problems with discontinuities and with no compactness, and then apply the theory to study two classes of complex partial differential equation boundary value problems with industrial applications. The work will lead to the development of a new theory and a suite of innovative analytical and computational methods for solving a wide range of nonlinear problems with singularities and non-local properties. The expected outcomes of the project will significantly advance our methods for the modelling and control of many industrial systems and processes.
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Exceptionally symmetric combinatorial designs. Advances in digital technologies are underpinned by powerful mathematics; use of symmetry greatly simplifies complex problems. This project aims to exploit the mathematical theory of groups to advance our understanding of combinatorial designs with exceptional symmetry. New designs have become prominent through links with networks and error correcting codes. The project expects to generate constructions and classifications in these areas by utilisin ....Exceptionally symmetric combinatorial designs. Advances in digital technologies are underpinned by powerful mathematics; use of symmetry greatly simplifies complex problems. This project aims to exploit the mathematical theory of groups to advance our understanding of combinatorial designs with exceptional symmetry. New designs have become prominent through links with networks and error correcting codes. The project expects to generate constructions and classifications in these areas by utilising powerful group theory. As well as innovative methods for studying designs with symmetry based on group actions, expected outcomes include enhanced international collaboration, and highly trained combinatorial mathematicians to strengthen Australia’s research standing in fundamental science. Read moreRead less
The synchronisation hierarchy of permutation groups. This project aims to make significant advances in understanding finite primitive permutation groups, which are the basic building blocks of the mathematical study of symmetry. A recently-developed perspective, inspired by the notion of a synchronising automaton, has revealed that these groups fall into a natural hierarchy. While the outline of this synchronisation hierarchy is known, many questions remain about exactly which primitive groups l ....The synchronisation hierarchy of permutation groups. This project aims to make significant advances in understanding finite primitive permutation groups, which are the basic building blocks of the mathematical study of symmetry. A recently-developed perspective, inspired by the notion of a synchronising automaton, has revealed that these groups fall into a natural hierarchy. While the outline of this synchronisation hierarchy is known, many questions remain about exactly which primitive groups lie in which layers. Answering these questions using techniques from group theory, graph theory and finite geometry will substantially deepen our understanding. The benefits of this include new knowledge and enhanced insight into this fundamental class of groups and new tools for their analysis.Read moreRead less
Graph symmetry and simple groups. This project aims to use knowledge of finite simple groups to tackle problems in graph symmetry. The symmetry of an object is encoded by a group, and this allows tools from algebra to be used to study graphs. The main impact will be in areas of pure mathematics such as graph theory and group theory by obtaining new classifications and constructions. Expected outcomes include providing new constructions and classifications of highly symmetric graphs, and an impro ....Graph symmetry and simple groups. This project aims to use knowledge of finite simple groups to tackle problems in graph symmetry. The symmetry of an object is encoded by a group, and this allows tools from algebra to be used to study graphs. The main impact will be in areas of pure mathematics such as graph theory and group theory by obtaining new classifications and constructions. Expected outcomes include providing new constructions and classifications of highly symmetric graphs, and an improved knowledge and understanding of local symmetries for graphs of higher valencies so that they become as well understood as the valency three case.Read moreRead less
Symmetry: Groups, Graphs, Number Fields and Loops. Exploiting symmetry can greatly simplify complex mathematical problems. This project aims to apply the powerful Classification of Finite Simple Groups to advance our understanding of the internal structure of number fields, highly symmetric graphs, and algebraic structures associated with Latin squares. The project expects to generate new constructions and classifications utilising group theory. Expected outcomes include resolutions of major ope ....Symmetry: Groups, Graphs, Number Fields and Loops. Exploiting symmetry can greatly simplify complex mathematical problems. This project aims to apply the powerful Classification of Finite Simple Groups to advance our understanding of the internal structure of number fields, highly symmetric graphs, and algebraic structures associated with Latin squares. The project expects to generate new constructions and classifications utilising group theory. Expected outcomes include resolutions of major open problems in each area as well as innovative methods for studying algebraic and combinatorial structures based on group actions. Expected benefits include enhanced international collaboration, and highly trained mathematicians to strengthen Australia’s research standing in fundamental science.Read moreRead less
Inequality, Trade, and Technology. This project aims to improve our understanding of the causes of rising income inequality in the world economy and in Australia since the early 1980s. We focus on the increasing building costs and imports of machinery as significant contributors to the increasing inequality. We hypothesize 1) that the increasing costs of buildings have reduced the demand for workers that are complementary to non-residential building capital; thus, reducing real wages; and 2) tha ....Inequality, Trade, and Technology. This project aims to improve our understanding of the causes of rising income inequality in the world economy and in Australia since the early 1980s. We focus on the increasing building costs and imports of machinery as significant contributors to the increasing inequality. We hypothesize 1) that the increasing costs of buildings have reduced the demand for workers that are complementary to non-residential building capital; thus, reducing real wages; and 2) that the marked increase in imports of machinery since the 1960s has reduced the demand for unskilled labour and widened the employment and wage gap between skilled and unskilled labour. Both factors may have driven the increasing inequality in Australia.
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