Hypergraph models for complex discrete systems. This project aims to better understand the structure and properties of very large hypergraphs of various kinds. Hypergraphs are very general mathematical objects which can be used to model complex discrete systems. They arise naturally in many areas such as ecology, chemistry and computer science. Despite this, our theoretical understanding of very large, or random, hypergraphs lags far behind the intensely-studied special case of graphs. This proj ....Hypergraph models for complex discrete systems. This project aims to better understand the structure and properties of very large hypergraphs of various kinds. Hypergraphs are very general mathematical objects which can be used to model complex discrete systems. They arise naturally in many areas such as ecology, chemistry and computer science. Despite this, our theoretical understanding of very large, or random, hypergraphs lags far behind the intensely-studied special case of graphs. This project will answer many fundamental questions about large, random hypergraphs. The expected outcomes of the project also include new tools for working with hypergraphs, such as efficient algorithms for sampling hypergraphs. These outcomes will benefit researchers who use hypergraphs in their work and will enhance Australia's reputation for research in this area.Read moreRead less
Guiding principles and guardrails for genetic association studies. This project aims to investigate deep connections between genetic structure (population genetic processes, linkage disequilibrium and population structure) and the ability to statistically detect genetic variants responsible for variation in traits. The project expects to generate new knowledge in the areas of statistics, mathematics and biology through an innovative, multidisciplinary approach that synthesises and extends founda ....Guiding principles and guardrails for genetic association studies. This project aims to investigate deep connections between genetic structure (population genetic processes, linkage disequilibrium and population structure) and the ability to statistically detect genetic variants responsible for variation in traits. The project expects to generate new knowledge in the areas of statistics, mathematics and biology through an innovative, multidisciplinary approach that synthesises and extends foundational disciplinary results. Expected outcomes of this project include principles and methodology that underpin future genetic association studies by supplying a framework for interpreting results. This should provide significant benefits by reducing false conclusions and their associated costs.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE200100056
Funder
Australian Research Council
Funding Amount
$403,019.00
Summary
Statistical shape analysis using persistent homology. Statistical shape analysis is the quantitative study of variation in geometric shape. An innovative approach applies concepts from algebraic topology in the form of the persistent homology transform. This project aims to prove mathematical theory relating to the persistent homology transform, to develop new statistical theory and methodology, and to apply this theory to a range of applications including the analysis of bird beaks, human skull ....Statistical shape analysis using persistent homology. Statistical shape analysis is the quantitative study of variation in geometric shape. An innovative approach applies concepts from algebraic topology in the form of the persistent homology transform. This project aims to prove mathematical theory relating to the persistent homology transform, to develop new statistical theory and methodology, and to apply this theory to a range of applications including the analysis of bird beaks, human skulls and boundary contours of stem cells. An anticipated goal is the generation of new and significant theoretical results in topological data analysis. Expected outcomes include a topologically motivated platform for shape analysis that is statistically rigorous and has firm mathematical foundations.
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Optimisation of piezoelectric metamaterials: Towards robotic stress sensors. This project aims to design new piezoelectric material microstructures that can enhance the measurement of complex local stress states within robotic limbs. The project expects to generate new knowledge of the achievable properties of multi-poled piezoelectric materials and develop computational tools for the analysis and structural optimisation of such materials. The designed microstructures may revolutionise piezoelec ....Optimisation of piezoelectric metamaterials: Towards robotic stress sensors. This project aims to design new piezoelectric material microstructures that can enhance the measurement of complex local stress states within robotic limbs. The project expects to generate new knowledge of the achievable properties of multi-poled piezoelectric materials and develop computational tools for the analysis and structural optimisation of such materials. The designed microstructures may revolutionise piezoelectric sensor technology. Expected outcomes include manufactured proof-of-concept sensors that enable measurement of local stress fields. This should provide significant benefits, such as improved future robot capability and reliability, and research training for next-generation Australian computational mathematicians. Read moreRead less
Regularisation methods of inverse problems: theory and computation. This project aims to investigate regularisation methods for inverse problems which are ill-posed in the sense that their solutions depend discontinuously on the data. When only noisy data is available, regularisation methods define stable approximate solutions by replacing the original inverse problem with a family of well-posed neighbouring problems monitored by a so-called regularisation parameter. The project expects to devel ....Regularisation methods of inverse problems: theory and computation. This project aims to investigate regularisation methods for inverse problems which are ill-posed in the sense that their solutions depend discontinuously on the data. When only noisy data is available, regularisation methods define stable approximate solutions by replacing the original inverse problem with a family of well-posed neighbouring problems monitored by a so-called regularisation parameter. The project expects to develop purely data-driven rules to choose the regularisation parameter and show how they work in theory, and in practice. It will also develop convex framework, acceleration strategies as well as preconditioning and splitting ideas to design efficient regularisation solvers.Read moreRead less
ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. The ARC Centre for the Mathematical Analysis of Cellular Systems aims to deliver the mathematics required to compute life. The Centre will deliver innovation in computational and mathematical biology and establish in silico biology alongside in vivo and in vitro biology. These models will allow us to understand the complexity of life at the cellu ....ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. The ARC Centre for the Mathematical Analysis of Cellular Systems aims to deliver the mathematics required to compute life. The Centre will deliver innovation in computational and mathematical biology and establish in silico biology alongside in vivo and in vitro biology. These models will allow us to understand the complexity of life at the cellular level and enable new ways of combining diverse and heterogenous data. This will allow us to understand the mechanisms underlying cellular behaviour, and to apply rational design engineering methods in order to control the dynamics of biological systems. Read moreRead less
Design of Real-time Optimisation Methods with Guaranteed Performance. The project aim is the development of a framework for the advancement of optimisation algorithms operating in real-time applications. This project expects to generate new knowledge in the area of systems theory and optimisation, and its application to time-varying problems. Expected outcomes of this project should lead to a new theoretical and practical framework that aims to ameliorate the shortcomings of the existing approac ....Design of Real-time Optimisation Methods with Guaranteed Performance. The project aim is the development of a framework for the advancement of optimisation algorithms operating in real-time applications. This project expects to generate new knowledge in the area of systems theory and optimisation, and its application to time-varying problems. Expected outcomes of this project should lead to a new theoretical and practical framework that aims to ameliorate the shortcomings of the existing approaches that struggle to rapidly respond to new information. This should provide significant benefits. Specifically, this project aims to facilitate a technological leap that generates smaller, faster, and more powerful embedded systems such as broadband services, mobile phones, medical imagining, radar and avionics.Read moreRead less
Industrial Transformation Training Centres - Grant ID: IC200100009
Funder
Australian Research Council
Funding Amount
$4,861,236.00
Summary
ARC Training Centre in Optimisation Technologies, Integrated Methodologies, and Applications (OPTIMA). OPTIMA addresses industry’s urgent need for decision-making tools for global competitiveness: reducing lead times, and financial and environmental costs, while improving efficiency, quality, and agility. Despite strong expertise in academia, industry is yet to fully benefit from optimisation technology due to its high barrier to entry. Connecting industry partners with world-leading interdiscip ....ARC Training Centre in Optimisation Technologies, Integrated Methodologies, and Applications (OPTIMA). OPTIMA addresses industry’s urgent need for decision-making tools for global competitiveness: reducing lead times, and financial and environmental costs, while improving efficiency, quality, and agility. Despite strong expertise in academia, industry is yet to fully benefit from optimisation technology due to its high barrier to entry. Connecting industry partners with world-leading interdisciplinary researchers and talented students, OPTIMA will advance an industry-ready optimisation toolkit, while training a new generation of industry practitioners and over 120 young researchers, vanguarding a highly skilled workforce of change agents for transformation of the advanced manufacturing, energy resources, and critical infrastructure sectors.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