Modelling, Identification and Control of Complex Networks. Australia has been well known for its leading research in systems and control and many real-world applications in, for instance, telecommunications, defence, power grids and life sciences. This project will further promote Australia's leading position in the emerging new research field - complex networks by theoretical breakthrough in modelling, identification and control of complex networks, and cutting-edge platform technology that can ....Modelling, Identification and Control of Complex Networks. Australia has been well known for its leading research in systems and control and many real-world applications in, for instance, telecommunications, defence, power grids and life sciences. This project will further promote Australia's leading position in the emerging new research field - complex networks by theoretical breakthrough in modelling, identification and control of complex networks, and cutting-edge platform technology that can help Australian energy industry to reduce greenhouse emissions. It will also result in education of the next generation research leaders in this emerging field.Read moreRead less
Service-oriented negotiation and coordination in multi-agent systems. Australia has a strong competitive advantage in the area of agent software. The outcomes of this project will provide an improved platform for services in application areas such as finance, e-commerce, tourism, and multi-platform media. More broadly, the work proposed here will enable the IT industry in Australia, and Melbourne specifically, to adopt and utilise agent-technology in developing the complex software that is inc ....Service-oriented negotiation and coordination in multi-agent systems. Australia has a strong competitive advantage in the area of agent software. The outcomes of this project will provide an improved platform for services in application areas such as finance, e-commerce, tourism, and multi-platform media. More broadly, the work proposed here will enable the IT industry in Australia, and Melbourne specifically, to adopt and utilise agent-technology in developing the complex software that is increasingly required to meet the needs of the software-driven knowledge economy of the 21st century.Read moreRead less
HOLOMORPHIC CURVES, REEB FLOWS AND CONTACT TOPOLOGY. Motion of a satellite is one of many examples of a Reeb dynamical system. The aim of the project is to deepen our understanding of Reeb flows. The Reeb flows, in particular, include Hamiltonian flows on three-dimensional contact type energy surfaces. To study the behaviour of Reeb flows we construct systems of global surfaces of section and study the iterates of the Poincare map, which is obtained by following the flow until it hits a surface. ....HOLOMORPHIC CURVES, REEB FLOWS AND CONTACT TOPOLOGY. Motion of a satellite is one of many examples of a Reeb dynamical system. The aim of the project is to deepen our understanding of Reeb flows. The Reeb flows, in particular, include Hamiltonian flows on three-dimensional contact type energy surfaces. To study the behaviour of Reeb flows we construct systems of global surfaces of section and study the iterates of the Poincare map, which is obtained by following the flow until it hits a surface. The main tools in constructing systems of global surfaces of section are holomorphic curves in symplectization, which are defined on punctured Riemann surfaces and solve nonlinear Cauchy-Riemann type operator. These curves are also main ingredients of new invariants of contact and symplectic manifolds.
These new invariants are now known as Contact Homology and Symplectic Field Theory. In the second part of the project we develop analytical foundations for these theories.Read moreRead less
Modelling and estimation methods for discrete multi-dimensional systems. Multi-dimensional signal processing plays a role in a variety of application areas, ranging from remote sensing for environmental monitoring and geological mapping, to medical imaging and the automatic control of industrial processes. The success of the project will provide mathematical tools for the advancement of the state-of-the-art in these broad areas.
Complexity-manageable methodologies and efficient computational tools for analysis and design of large-scale systems. The tools to be developed in this project have impact on a broad range of disciplines, including system analysis, feedback control technology, signal processing, communication network, and information theory. Practically, the success of this project will create cutting edge technologies applicable to design and management of important infrastructures of the modern society such as ....Complexity-manageable methodologies and efficient computational tools for analysis and design of large-scale systems. The tools to be developed in this project have impact on a broad range of disciplines, including system analysis, feedback control technology, signal processing, communication network, and information theory. Practically, the success of this project will create cutting edge technologies applicable to design and management of important infrastructures of the modern society such as communication networks, transportation systems, electrical power grids, and collaborative intelligent machines, and water distribution networks. Success of this project will bring novel methodologies and computational tools which help engineers to systematically design and validate the performance of their engineering systems.Read moreRead less
Robustness Analysis and Control Design of Distributed and Networked Systems. The theory and computational tools to be developed in this project have impact on a broad range of areas, including various engineering disciplines, biology, and medical and environmental sciences. In terms of practical interests, this project will create cutting edge technologies which are applicable to important infrastructures of the modern society such as communication networks, transportation systems, electrical po ....Robustness Analysis and Control Design of Distributed and Networked Systems. The theory and computational tools to be developed in this project have impact on a broad range of areas, including various engineering disciplines, biology, and medical and environmental sciences. In terms of practical interests, this project will create cutting edge technologies which are applicable to important infrastructures of the modern society such as communication networks, transportation systems, electrical power grids, collaborative intelligent machines, and water distribution networks. Read moreRead less
Modelling, Analysis and Synthesis Tools for Multi-Dimensional Signal Processing Systems. Multi-dimensional signal processing plays a role in a variety of application areas, ranging from remote sensing for environmental monitoring and geological mapping, to medical imaging and the automatic control of industrial processes. The success of this project will provide mathematical tools for the advancement of the state-of-the-art in these broad areas.
Eclectic problems in topology, geometry and dynamics. This project aims to resolve a number of problems across several broad areas of pure mathematics. The problems all have a geometric or topological flavour, and some deal with dynamics in the qualitative sense. The problems share two common themes: they have group theoretic aspects and homological aspects. Specifically, the problems lie in the following areas:
1. finite dimensional Lie algebras and their cohomology,
2. low dimensional combin ....Eclectic problems in topology, geometry and dynamics. This project aims to resolve a number of problems across several broad areas of pure mathematics. The problems all have a geometric or topological flavour, and some deal with dynamics in the qualitative sense. The problems share two common themes: they have group theoretic aspects and homological aspects. Specifically, the problems lie in the following areas:
1. finite dimensional Lie algebras and their cohomology,
2. low dimensional combinatorial geometry: graph drawings on surfaces,
3. topological dynamics of group actions,
4. differentiable group actions and foliation theory.
The most significant aims are to resolve two well known conjectures: Halperin's toral rank conjecture and Conway's thrackle conjecture.
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Derivative free algorithms for large scale nonsmooth and global optimization and their applications. The outcomes expected from this research fall broadly into two categories: 1) the development of a new class of effective readily implementable derivative free techniques for large scale non-smooth and global optimisation and 2) the development of new algorithms based on derivative free optimization techniques for solving data mining, resource allocation problems and some problems in bioinformati ....Derivative free algorithms for large scale nonsmooth and global optimization and their applications. The outcomes expected from this research fall broadly into two categories: 1) the development of a new class of effective readily implementable derivative free techniques for large scale non-smooth and global optimisation and 2) the development of new algorithms based on derivative free optimization techniques for solving data mining, resource allocation problems and some problems in bioinformatics. In particular, the application of these techniques to molecular biology and cluster analysis will be very important for the development of competitive technologies for Australia.
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Patient-specific Computational Tools for Diagnosing and Treating Gait Disorders in Children with Cerebral Palsy. This proposal addresses one of the most fundamental and difficult questions related to the treatment of children with cerebral palsy: Why do these children walk in a crouched position, with excessively bent hips and knees? High-fidelity, patient-specific computer simulations of walking can help to answer this question and, in so doing, can improve the outcomes of orthopaedic surgeries ....Patient-specific Computational Tools for Diagnosing and Treating Gait Disorders in Children with Cerebral Palsy. This proposal addresses one of the most fundamental and difficult questions related to the treatment of children with cerebral palsy: Why do these children walk in a crouched position, with excessively bent hips and knees? High-fidelity, patient-specific computer simulations of walking can help to answer this question and, in so doing, can improve the outcomes of orthopaedic surgeries designed to correct movement abnormalities in these patients. Realistic computer simulations of human movement can play a pivotal role in healthcare through patient rehabilitation; in sports, through the development of personalized training programs for elite athletes; and in entertainment, through the creation of video games and animated films.Read moreRead less