The dynamics of viral latency in chronic infection. Although many acute infections can now be controlled, we still suffer from a large number of chronic infections such as HIV or herpes that cannot be eradicated. Many of these infections persist because they can lie dormant in a 'latent' state. How this latent state is established, and how long it lasts are important to understand if we want to control these infections. We have assembled a team of mathematicians, immunologists and virologists in ....The dynamics of viral latency in chronic infection. Although many acute infections can now be controlled, we still suffer from a large number of chronic infections such as HIV or herpes that cannot be eradicated. Many of these infections persist because they can lie dormant in a 'latent' state. How this latent state is established, and how long it lasts are important to understand if we want to control these infections. We have assembled a team of mathematicians, immunologists and virologists in order to study latent infection at the cellular level, and within infected monkeys. This will provide the first insights into the dynamics of latency - how these cells are produced and die - and should lead to novel approaches to controlling chronic infection.Read moreRead less
Green functions, correlation functions and differential equations. Classical and quantum exact solutions are established cornerstones in Australian applied mathematical research. In this project, we will:- 1). Address long standing open problems, whose resolution will add to mathematical knowledge and enhance Australia's reputation as a leading contributor to these topics; 2). List concrete and tractable sub-projects that will engage young scientists, whose training we are particularly keen on, ....Green functions, correlation functions and differential equations. Classical and quantum exact solutions are established cornerstones in Australian applied mathematical research. In this project, we will:- 1). Address long standing open problems, whose resolution will add to mathematical knowledge and enhance Australia's reputation as a leading contributor to these topics; 2). List concrete and tractable sub-projects that will engage young scientists, whose training we are particularly keen on, in vigorous and internationally competitive research; 3). Facilitate collaborations between various Australian research groups, all of whom are very well positioned to contribute to it; 4). Bring leading scientists to visit Australia to the benefit of the entire Australian mathematical community.Read moreRead less
Complexity in a mesoscopic model of brain dynamics. Research into how the brain work remains at the frontier of human knowledge. We possess only the vaguest idea how the brain is able to generate memories, perceptions and behaviour. This research proposal concerns new approaches aimed at bridging this gap in our understanding by developing and studying detailed theories of the brain's electrical activity. The outcomes of this work will not only suggest improved diagnostic methods and treatments ....Complexity in a mesoscopic model of brain dynamics. Research into how the brain work remains at the frontier of human knowledge. We possess only the vaguest idea how the brain is able to generate memories, perceptions and behaviour. This research proposal concerns new approaches aimed at bridging this gap in our understanding by developing and studying detailed theories of the brain's electrical activity. The outcomes of this work will not only suggest improved diagnostic methods and treatments but contribute vital knowledge about how to control and predict the behaviour of complex systems.Read moreRead less
Emergence of modular structure in complex systems. Complex systems pervade our world, but are still poorly understood. Self-contained modules provide the most widespread and effective way of reducing and managing complexity, but the way they form in natural systems remains largely a mystery. This study investigates mechanisms that contribute to module formation in complex networks, including adaptation, clustering, enslavement, feedback, phase change and synchronisation. Outcomes will include in ....Emergence of modular structure in complex systems. Complex systems pervade our world, but are still poorly understood. Self-contained modules provide the most widespread and effective way of reducing and managing complexity, but the way they form in natural systems remains largely a mystery. This study investigates mechanisms that contribute to module formation in complex networks, including adaptation, clustering, enslavement, feedback, phase change and synchronisation. Outcomes will include insights into the organisation and functioning of many complex systems, including the Internet, ecological communities and genetic networks. Practical outcomes will include new modelling tools and applications both to evolutionary computation and the design and control of large information networks.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
Realising the promise of neural networks for practical optimisation: improving their efficiency and effectivess through chaotic dynamics and hardware implementation. Combinatorial optimisation problems such as transportation routing and assembly-line scheduling are critical to the efficiency of many industries, but their combinatorial explosion makes rapid solution difficult. Neural networks (NNs) hold much potential for rapid solution though hardware implementation, but we need to improve the q ....Realising the promise of neural networks for practical optimisation: improving their efficiency and effectivess through chaotic dynamics and hardware implementation. Combinatorial optimisation problems such as transportation routing and assembly-line scheduling are critical to the efficiency of many industries, but their combinatorial explosion makes rapid solution difficult. Neural networks (NNs) hold much potential for rapid solution though hardware implementation, but we need to improve the quality of their solutions before developing hardware. We have previously shown that the rich dynamics of chaos can improve the efficiency and effectiveness of NNs. We aim to develop new chaotic NN models, rigorously evaluate them on industrially significant problems such as those arising in manufacturing, logistics and telecommunications, and demonstrate their speed through hardware acceleration.Read moreRead less
Wavelet approaches for solving nonlinear dynamic systems in process engineering. The success of the proposed project will enable us to obtain more accurate numerical solutions for the nonlinear dynamical systems arising from process engineering. This ensures the potential for understanding and optimising industrial and engineering processes. Hence, a wide range of processing industries in Australia, such as agricultural chemicals, mineral processing, food, detergents, pharmaceuticals, ceramics ....Wavelet approaches for solving nonlinear dynamic systems in process engineering. The success of the proposed project will enable us to obtain more accurate numerical solutions for the nonlinear dynamical systems arising from process engineering. This ensures the potential for understanding and optimising industrial and engineering processes. Hence, a wide range of processing industries in Australia, such as agricultural chemicals, mineral processing, food, detergents, pharmaceuticals, ceramics and specialty chemicals will benefit from the results of this project. This will ensure globally competitive production and, therefore, greater contributions to the Australian economy.Read moreRead less
Neurobiological computation using self organization. Despite their phenomenal power and speed there are many simple things that computers still cannot do, that humans, and indeed many animals, are able to perform effortlessly. The research outlined in this proposal aims to develop new, biologically inspired, computational approaches that attempt to bridge this gap. This research will help place Australia, despite its relatively small size, as a leading research community in the development of ....Neurobiological computation using self organization. Despite their phenomenal power and speed there are many simple things that computers still cannot do, that humans, and indeed many animals, are able to perform effortlessly. The research outlined in this proposal aims to develop new, biologically inspired, computational approaches that attempt to bridge this gap. This research will help place Australia, despite its relatively small size, as a leading research community in the development of the next wave of computing devices. The development of new and "more natural" approaches to computing will deliver large dividends to a range of social, economic and environmental problems.Read moreRead less
Stochastic Geometry for Multi-sensor Data Fusion System. The aim of this project is to develop efficient algorithms for tracking and sensor management in a multi-sensor multi-target environment. Finite random set theory provides a natural way of representing a random number of (random) object states, an issue that has been largely ignored in the tracking literature until recently. Although a satisfactory foundation for multiple object filtering has been provided by random set theory, in this ear ....Stochastic Geometry for Multi-sensor Data Fusion System. The aim of this project is to develop efficient algorithms for tracking and sensor management in a multi-sensor multi-target environment. Finite random set theory provides a natural way of representing a random number of (random) object states, an issue that has been largely ignored in the tracking literature until recently. Although a satisfactory foundation for multiple object filtering has been provided by random set theory, in this early stage no algorithm capable of tracking many targets has emerged from this framework. We are confident that efficient algorithms can be developed by exploiting the insights and mathematical tools of stochastic geometryRead moreRead less
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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