Novel techniques for statistical and mathematical analyses of sequence data. Algorithms will be developed for analysing and comparing the sequences of DNA letters and amino acids constantly being generated in massive quantities by biological research. The novel approach taken is based on the statistical frequency of occurrence of short words and is designed specifically for situations where current methods fail.
Rogue waves in realistic situations. Rapid progress in rogue wave research internationally requires the further development of an accurate theory of extreme waves in deep water and in optical fibers. Such progress is a necessity for our ability to predict their appearance in the ocean or their use in optics. This project will enhance the modelling of extreme waves by taking into account higher order effects such as third order dispersion, self-steepening and time delayed response, as well as dis ....Rogue waves in realistic situations. Rapid progress in rogue wave research internationally requires the further development of an accurate theory of extreme waves in deep water and in optical fibers. Such progress is a necessity for our ability to predict their appearance in the ocean or their use in optics. This project will enhance the modelling of extreme waves by taking into account higher order effects such as third order dispersion, self-steepening and time delayed response, as well as dissipative and higher order nonlinear terms. These are essential for a precise description of both giant waves in the ocean and strong pulses in optics. Read moreRead less
Topological data analysis for enhanced modelling of the physical properties of complex micro-structured materials. The way water flows through sandstone depends on the connectivity of its pores, the balance of forces in a grain silo on the contacts between individual grains, and the impact resistance of metal foam in a car door on the arrangement of its cells. These structural properties are described mathematically by topology. Advanced three-dimensional X-ray imaging can now reveal the interna ....Topological data analysis for enhanced modelling of the physical properties of complex micro-structured materials. The way water flows through sandstone depends on the connectivity of its pores, the balance of forces in a grain silo on the contacts between individual grains, and the impact resistance of metal foam in a car door on the arrangement of its cells. These structural properties are described mathematically by topology. Advanced three-dimensional X-ray imaging can now reveal the internal detail of micro-structured materials. Recent developments in image analysis mean it is possible to compute accurate topological information from such images. This project aims to investigate how fundamental measures of shape influence the physical properties of complex materials and clarifies the mathematics that underpins these relationships.Read moreRead less
Stabilisation of nonlinear quantum feedback control systems. One of the most exciting technological developments of this century promises to be the development of quantum technology. Quantum feedback systems will play a key part of this technology and this project will develop the underlying fundamental theory which will be crucial to the systematic design of quantum feedback control systems.
Coherent Feedback Synchronisation and Stabilisation of Quantum Systems. The aim of this project is to address a range of fundamental problems of stabilisation and coherent synchronisation in quantum feedback control systems, leading to new systematic methods of designing controllers for the interacting quantum systems arising in emerging areas of quantum technology. Quantum feedback control systems will be at the heart of emerging areas of quantum technology and stability is essential for their ....Coherent Feedback Synchronisation and Stabilisation of Quantum Systems. The aim of this project is to address a range of fundamental problems of stabilisation and coherent synchronisation in quantum feedback control systems, leading to new systematic methods of designing controllers for the interacting quantum systems arising in emerging areas of quantum technology. Quantum feedback control systems will be at the heart of emerging areas of quantum technology and stability is essential for their operation. Standard control system methods do not take into account the special features of quantum systems and there is a need for new control theories that deal with stabilisation and synchronisation as quantum technologies become more advanced. Read moreRead less
Mathematical models of diseases with complex transmission routes. This project aims to model diseases that spread via a mixture of routes including food, water, the environment, and direct spread between individuals. Key diseases include: avian influenza, which causes massive disruption to the poultry industry; gastroenteritis, which costs Australia $1,250 million each year; and leptospirosis, which causes one million severe illnesses each year globally. This project will develop mathematical a ....Mathematical models of diseases with complex transmission routes. This project aims to model diseases that spread via a mixture of routes including food, water, the environment, and direct spread between individuals. Key diseases include: avian influenza, which causes massive disruption to the poultry industry; gastroenteritis, which costs Australia $1,250 million each year; and leptospirosis, which causes one million severe illnesses each year globally. This project will develop mathematical and statistical tools to better estimate risk, analyse outbreak data, and provide guidance for disease control. This research will improve policy and enhance our ability to respond to disease outbreaks.Read moreRead less
Solving inverse problems with Iterative regularisation and convex penalties. This project aims to develop and investigate new computational procedures for the solution of inverse problems which do not have the usual smoothness properties (or source conditions) required for the traditional regularisation methods. Examples of such inverse problems are very common and include image restoration, photo-acoustic tomography and spectroscopy. It is anticipated that this project will substantially extend ....Solving inverse problems with Iterative regularisation and convex penalties. This project aims to develop and investigate new computational procedures for the solution of inverse problems which do not have the usual smoothness properties (or source conditions) required for the traditional regularisation methods. Examples of such inverse problems are very common and include image restoration, photo-acoustic tomography and spectroscopy. It is anticipated that this project will substantially extend the toolbox of methods for such problems utilising ideas from Banach spaces, convex analysis, parallel computing and optimisation. This project is expected to make a substantial contribution to a better understanding of inverse problems and their solution procedures.Read moreRead less
Generalised Energy Based Robust and Nonlinear Control Systems. This project aims to develop new energy-based theories of robust stability analysis and controller design for both linear and nonlinear systems, building on passivity and negative imaginary system theories and their physical interpretations along with stochastic optimal control theory. These control theories would allow for a wide range of plant dynamics in the design of high-performance robust control systems, enabling advances in e ....Generalised Energy Based Robust and Nonlinear Control Systems. This project aims to develop new energy-based theories of robust stability analysis and controller design for both linear and nonlinear systems, building on passivity and negative imaginary system theories and their physical interpretations along with stochastic optimal control theory. These control theories would allow for a wide range of plant dynamics in the design of high-performance robust control systems, enabling advances in emerging technologies including nanopositioning, micro-electromechanical systems and opto-mechatronics. The project plans to combine these theoretical advances with numerical methods involving advanced optimisation tools and the experimental implementation of nanopositioning control systems in atomic force microscopy.Read moreRead less
Information consensus and coordination of multiagent systems. Revolutions in information and communication technologies create a complex 'network of everything'. This project will develop advanced control techniques for such networks, to make the nation's power systems safer, to fly formations of unmanned airborne vehicles, and to extract key information from networks of environmental monitoring sensors.
Navigating tipping points in complex dynamical systems. This project aims to use applied mathematics to investigate the onset of tipping points in dynamical systems. Working with clinicians and practicing engineers, the project aims to contribute to the development of new treatment regimes for dynamical diseases and develop improved management strategies for resource focussed engineering industries. This should provide significant benefit to many areas, including the personalised treatment of di ....Navigating tipping points in complex dynamical systems. This project aims to use applied mathematics to investigate the onset of tipping points in dynamical systems. Working with clinicians and practicing engineers, the project aims to contribute to the development of new treatment regimes for dynamical diseases and develop improved management strategies for resource focussed engineering industries. This should provide significant benefit to many areas, including the personalised treatment of disease.Read moreRead less