Methodology for assessing the vulnerability of multimodal transport networks and developing remedial measures to safeguard network performance. When transport networks fail, the effects on people and the economy can be devastating. The consequences for Hobart of the 1975 Tasman Bridge collapse provide a prime example. Failure may also result from extreme weather and natural disasters, traffic congestion and incidents, commercial failure, human error, or malevolence (such as sabotage). This proje ....Methodology for assessing the vulnerability of multimodal transport networks and developing remedial measures to safeguard network performance. When transport networks fail, the effects on people and the economy can be devastating. The consequences for Hobart of the 1975 Tasman Bridge collapse provide a prime example. Failure may also result from extreme weather and natural disasters, traffic congestion and incidents, commercial failure, human error, or malevolence (such as sabotage). This project will develop a methodology for auditing a transport network to identify where infrastructure failure will have the worst consequences for movement of people and goods. The research will provide tools for planners to determine critical network locations, and devise strategies and remedial measures to safeguard network performance.Read moreRead less
There and back again: operator algebras, algebras and dynamical systems. The aim of this project is to develop mathematics that enables us to transfer information back and forth between dynamical systems and algebras, including operator algebras. Dynamical systems - systems that change over time - are ubiquitous, and central to modern mathematics and its applications. In mathematics, dualities allow us to translate questions from one context to another in which they are easier to solve and then ....There and back again: operator algebras, algebras and dynamical systems. The aim of this project is to develop mathematics that enables us to transfer information back and forth between dynamical systems and algebras, including operator algebras. Dynamical systems - systems that change over time - are ubiquitous, and central to modern mathematics and its applications. In mathematics, dualities allow us to translate questions from one context to another in which they are easier to solve and then translate the answer back again. Expected outcomes include increased understanding of the relationship between operator algebras and the dynamical systems that they represent. Benefits include enhanced international collaboration, and increased Australian capacity in pure mathematics, particularly operator algebras.Read moreRead less
Symmetry in Differential Geometry. Differential geometry is a major branch of mathematics studying shape by using calculus and differential equations. This is a fundamental research project in this area, especially concerned with the interaction between geometry, differential equations, and symmetry. The mathematical notion of symmetry was already formalised early last century and nowadays lies at the very heart of mathematics and physics. Advances in this area provide essential tools in basic s ....Symmetry in Differential Geometry. Differential geometry is a major branch of mathematics studying shape by using calculus and differential equations. This is a fundamental research project in this area, especially concerned with the interaction between geometry, differential equations, and symmetry. The mathematical notion of symmetry was already formalised early last century and nowadays lies at the very heart of mathematics and physics. Advances in this area provide essential tools in basic science and unexpected technological benefits can easily arise (for example, in medical imaging). Fundamental mathematical research is absolutely necessary if Australia is to maintain a presence on the international scientific stage.
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Classification and Invariants in Complex Differential Geometry. Differential geometry is the study of shape using calculus and differential equations. This is a fundamental research project in this area. Complex differential geometry refers to geometry based on the complex numbers, generally a rich and intriguing setting. Geometries will be distinguished by the construction of suitable invariants, both algebraic and analytic. Classification problems will be solved by these means. Of particular i ....Classification and Invariants in Complex Differential Geometry. Differential geometry is the study of shape using calculus and differential equations. This is a fundamental research project in this area. Complex differential geometry refers to geometry based on the complex numbers, generally a rich and intriguing setting. Geometries will be distinguished by the construction of suitable invariants, both algebraic and analytic. Classification problems will be solved by these means. Of particular interest are geometries with a high degree of symmetry, a critical feature that pervades both mathematics and physics. Twistor theory provides the unifying theme for this project.Read moreRead less
Deformable Surfaces Supporting 3D Tactile Human Computer Interactions. This project will support Research Priority 3: Frontier Technologies for Building and Transforming Australian Industries. The results will provide information that will further build our understanding of human computer interactions. Digital Foam supports Smart Information Use by providing a new interaction paradigm for existing and new creative applications for digital technologies. The new form of interaction provides a new ....Deformable Surfaces Supporting 3D Tactile Human Computer Interactions. This project will support Research Priority 3: Frontier Technologies for Building and Transforming Australian Industries. The results will provide information that will further build our understanding of human computer interactions. Digital Foam supports Smart Information Use by providing a new interaction paradigm for existing and new creative applications for digital technologies. The new form of interaction provides a new computer interaction product in itself and the ability to make a more efficient creative environment for designers of 3D content, multi-media and manufacturing design. This technology supports the ability of organisations to operate virtually and collaborate across large distances in Australia and internationally.Read moreRead less
The Next Step in Intelligent Decision-Support Systems (IDSS): Systems that Learn and Adapt. This project will benefit Australia's scientific knowledge and technology base in the areas of evolutionary computation, business intelligence, and decision management. The outcomes will advance Australian companies and organisations, as many common yet complex business problems can be better addressed with systems that automatically learn and adapt to environmental changes. Such complex business problems ....The Next Step in Intelligent Decision-Support Systems (IDSS): Systems that Learn and Adapt. This project will benefit Australia's scientific knowledge and technology base in the areas of evolutionary computation, business intelligence, and decision management. The outcomes will advance Australian companies and organisations, as many common yet complex business problems can be better addressed with systems that automatically learn and adapt to environmental changes. Such complex business problems include dynamic scheduling (in the manufacturing sector), resource allocation optimisation (in the defence, mining, and agriculture sectors), and network design optimisation (in the telecommunications and energy sectors).Read moreRead less
Advanced planning systems for vertically integrated supply chain management. This project will integrate various algorithms into an adaptive, dynamic and intelligent system that deals with the vertically integrated supply chains. The outcomes include publications in the quality outlets, generation of intellectual property, and dissemination of this research amongst the research and business communities.
Normal forms and Chern-Moser connection in the study of Cauchy-Riemann Manifolds. This research project is aimed at a systematic study of Cauchy-Riemann manifolds, their holomorphic mappings and automorphisms, by means of a unifying approach based on
Chern-Moser type normal forms. The importance of Cauchy-Riemann manifolds stems from the fact that they bridge complex structure and holomorphy with the Riemannian nature of real manifolds. Construction of an analogue of the Chern-Moser normal form ....Normal forms and Chern-Moser connection in the study of Cauchy-Riemann Manifolds. This research project is aimed at a systematic study of Cauchy-Riemann manifolds, their holomorphic mappings and automorphisms, by means of a unifying approach based on
Chern-Moser type normal forms. The importance of Cauchy-Riemann manifolds stems from the fact that they bridge complex structure and holomorphy with the Riemannian nature of real manifolds. Construction of an analogue of the Chern-Moser normal form for multicodimensional Levi-nondegenerate CR-manifolds and extension of CR-mappings between them are major goals in complex analysis. Identification of Chern-Moser chains and equivariant linearisation of isotropy automorphisms are major goals in geometry.Read moreRead less
Continuous process improvement through workstation feedback for General Practice medicine using experts-in-the-loop data mining. This project investigates the iterative use of data mining results to allow experts to construct feedback to influence subsequent production work. We explore the problem in the context of General Practice medicine by having General Practitioners (GPs) review emerging patterns from their own practice's electronic medical records and author feedback to discourage undesi ....Continuous process improvement through workstation feedback for General Practice medicine using experts-in-the-loop data mining. This project investigates the iterative use of data mining results to allow experts to construct feedback to influence subsequent production work. We explore the problem in the context of General Practice medicine by having General Practitioners (GPs) review emerging patterns from their own practice's electronic medical records and author feedback to discourage undesirable patterns. The work will have immediate applicability to medical practice and will drive innovation in data mining method, notably for efficient identification of temporal and complex niche patterns. More broadly, the work will extend the way data mining is used to create new expectations of workstation behaviour.Read moreRead less
New Analytical Perspectives on the Algorithmic Complexity of the Hamiltonian Cycle Problem. Hamiltonian Cycle Problem (HCP), known - in the complexity theory of
algorithms -to be NP-hard is proposed for study, from three innovative,
separate (yet related) analytical perspectives: singularly perturbed
(controlled) Markov chains, that links the HCP with systems and control
theories; parametric nonconvex optimization, that links HCP with fast
interior point methods of modern optimization an ....New Analytical Perspectives on the Algorithmic Complexity of the Hamiltonian Cycle Problem. Hamiltonian Cycle Problem (HCP), known - in the complexity theory of
algorithms -to be NP-hard is proposed for study, from three innovative,
separate (yet related) analytical perspectives: singularly perturbed
(controlled) Markov chains, that links the HCP with systems and control
theories; parametric nonconvex optimization, that links HCP with fast
interior point methods of modern optimization and the spectral approach
based on a novel adaptation of Ihara-Selberg trace formula for regular
graphs. Our mathematical approach to this archetypal complex problem of graph
theory and discrete optimization promises to enhance the fundamental
understanding - and ultimate "managibility" - of the underlying
difficulty of HCP.
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