Constrained and Stable Solutions of Nonlinear and Semismooth Equations. In this project, comprehensive models for designing safe power system parameters will be proposed, efficient algorthms for solving these models will be constructed. The new models and algorithms in this project will provide efficient tools to prevent catastrophic events in power systems, which is related with national security. This project will also strengthen collaboration of Australian applied
mathematians with inter ....Constrained and Stable Solutions of Nonlinear and Semismooth Equations. In this project, comprehensive models for designing safe power system parameters will be proposed, efficient algorthms for solving these models will be constructed. The new models and algorithms in this project will provide efficient tools to prevent catastrophic events in power systems, which is related with national security. This project will also strengthen collaboration of Australian applied
mathematians with international researchers and engineering scientists. This is important for the advance of science and technology in
Australia.Read moreRead less
Doubly Stochastic Matrices & The Hamiltonian Cycle Problem. The classical hard problem of determining whether a given graph possesses a Hamiltonian cycle contains the essential difficulty of the famous 'Travelling Salesman Problem'. A characterisation of this difficulty in terms of variability of returns (to the initial state) in a controlled stochastic process will be a significant conceptual advance with repercussions in a number of fields including optimisation and theoretical computer scien ....Doubly Stochastic Matrices & The Hamiltonian Cycle Problem. The classical hard problem of determining whether a given graph possesses a Hamiltonian cycle contains the essential difficulty of the famous 'Travelling Salesman Problem'. A characterisation of this difficulty in terms of variability of returns (to the initial state) in a controlled stochastic process will be a significant conceptual advance with repercussions in a number of fields including optimisation and theoretical computer science. Algorithmic advances exploiting such a characterisation will significantly contribute to existing technologies for solving problems in applications ranging from logistics to cryptography. Since TSP describes certain efficient ways of routing its applicability to information networks is clear.Read moreRead less
Approximation, Cubature and Point Designs on Spheres. The sphere is important in fields ranging from geophysics to global climate modelling to chemistry to codes for modern communications. This project aims to strengthen and unify key areas of mathematics on the sphere and at the same time provide methods and constructiions of practical significance. The areas of focus are constructive approximation of functions on the sphere, numerical integration on the sphere, and well distributed sets of poi ....Approximation, Cubature and Point Designs on Spheres. The sphere is important in fields ranging from geophysics to global climate modelling to chemistry to codes for modern communications. This project aims to strengthen and unify key areas of mathematics on the sphere and at the same time provide methods and constructiions of practical significance. The areas of focus are constructive approximation of functions on the sphere, numerical integration on the sphere, and well distributed sets of points on the sphere, including spherical designs.Read moreRead less
Next-Generation OFDM Communication Systems: Analysis and Design for the Physical Layer. Next-generation orthogonal frequency-division multiplexed (OFDM) systems represent the future of broadband wireless access technology. Such systems are vital to Australia's future infrastructure and growing economy by providing more bandwidth with greater flexibility for new broadband applications. The research outcomes from this project will help enable future OFDM systems, and thus directly benefit Austra ....Next-Generation OFDM Communication Systems: Analysis and Design for the Physical Layer. Next-generation orthogonal frequency-division multiplexed (OFDM) systems represent the future of broadband wireless access technology. Such systems are vital to Australia's future infrastructure and growing economy by providing more bandwidth with greater flexibility for new broadband applications. The research outcomes from this project will help enable future OFDM systems, and thus directly benefit Australia. Development of cutting-edge information technology know-how will enhance Australia's international ICT reputation. Valuable research training of highly-skilled Australian students is another important benefit.Read moreRead less
Nonsmooth Optimization in Constrained Spline Interpolation. Traditional methods based on standard calculus may not work for optimization problems with constraints; however, such problems can be reformulated as nonsmooth problems that need special treatment. The project aims to approach several important problems in constrained spline interpolation and approximation, from the perspective of nonsmooth optimization. The research, which builds upon a recent breakthrough in the approach to the convex ....Nonsmooth Optimization in Constrained Spline Interpolation. Traditional methods based on standard calculus may not work for optimization problems with constraints; however, such problems can be reformulated as nonsmooth problems that need special treatment. The project aims to approach several important problems in constrained spline interpolation and approximation, from the perspective of nonsmooth optimization. The research, which builds upon a recent breakthrough in the approach to the convex best interpolation by the applicant and his collaborators, is expected to provide fundamental theory for Newton-type methods being used for these problems with a vast number of applications in data fitting and curve and surface design.Read moreRead less
Real-time scheduling of trains to control peak electricity demand. This project aims to develop new scheduling and control methods that will enable railways to reduce their demand for electricity during peak demand periods, without undue disruption to the timetable.
These new methods and systems will integrate with—and expand the capabilities of—an Australian train control system that is used by railways around the world. This will enable better management of electricity within a region and be ....Real-time scheduling of trains to control peak electricity demand. This project aims to develop new scheduling and control methods that will enable railways to reduce their demand for electricity during peak demand periods, without undue disruption to the timetable.
These new methods and systems will integrate with—and expand the capabilities of—an Australian train control system that is used by railways around the world. This will enable better management of electricity within a region and better use of renewable energy sources, with significant cost savings for railways and the wider community.Read moreRead less
Mathematical models for water management systems. The Australian community is currently talking about schemes to return water to the Murray-Darling river system to combat increased salinity and dramatically reduced river flow. Many believe that vastly improved water management policies are essential to maintain agricultural well-being in Australia. Salinity and water quality depend directly on flow rates and are also important in smaller catchments. In this study we will use statistical rainf ....Mathematical models for water management systems. The Australian community is currently talking about schemes to return water to the Murray-Darling river system to combat increased salinity and dramatically reduced river flow. Many believe that vastly improved water management policies are essential to maintain agricultural well-being in Australia. Salinity and water quality depend directly on flow rates and are also important in smaller catchments. In this study we will use statistical rainfall models and stochastic dynamic programming to find practical water management policies that minimise the risk to water supply. We will develop an interactive simulation and management tool using a modern computer graphics package.Read moreRead less
A graphical simulation package for optimal management and risk assessment in urban stormwater harvesting systems. We will develop a Scalar Vector Graphics (SVG) simulation tool for optimal management and risk assessment in urban stormwater harvesting and utilisation schemes. The generic model will be applied to existing and proposed schemes within the City of Salisbury (CoS) and will include a capture dam, one or more storage dams and an aquifer storage and recovery (ASR) facility. The discret ....A graphical simulation package for optimal management and risk assessment in urban stormwater harvesting systems. We will develop a Scalar Vector Graphics (SVG) simulation tool for optimal management and risk assessment in urban stormwater harvesting and utilisation schemes. The generic model will be applied to existing and proposed schemes within the City of Salisbury (CoS) and will include a capture dam, one or more storage dams and an aquifer storage and recovery (ASR) facility. The discrete state vector will be the content of each storage unit and the daily transition will be driven by a new stochastic rainfall model (SRM). The objective will be to find a practical management policy that minimises Conditional Value-at-Risk (CVaR).Read moreRead less
Fast, practical and effective algorithms for clustering with advice. To maintain a safe and healthy society, government and industry need high quality immunization and national security databases. Since we cannot afford to have duplicate, incomplete and conflicting records that refer to the same person, we unify them by identifying clusters of related records.
In the emerging field of functional genomics, diagnosis of certain diseases is enhanced by determining which genes act together. Diffe ....Fast, practical and effective algorithms for clustering with advice. To maintain a safe and healthy society, government and industry need high quality immunization and national security databases. Since we cannot afford to have duplicate, incomplete and conflicting records that refer to the same person, we unify them by identifying clusters of related records.
In the emerging field of functional genomics, diagnosis of certain diseases is enhanced by determining which genes act together. Different experimental runs might result in different clusterings of genes: we need one consensus clustering that summarizes the experimental outcomes.
Cleaning databases and combining clusterings by hand would require vast amounts of time. This project will result in faster and more accurate computational procedures.Read moreRead less
Graph isomorphism and quantisation of longest cycles by means of determinants and spectra. A characterisation of the difficulty of the Hamiltonian cycle problem and the graphs isomorphism problem will be a significant conceptual advancement with repercussions in a number of fields including combinatorial optimisation and theoretical computer science, in particular, the Google PageRank. Applications of tensor networks technique will lead to a design of a quantum computer that enumerates all Hamil ....Graph isomorphism and quantisation of longest cycles by means of determinants and spectra. A characterisation of the difficulty of the Hamiltonian cycle problem and the graphs isomorphism problem will be a significant conceptual advancement with repercussions in a number of fields including combinatorial optimisation and theoretical computer science, in particular, the Google PageRank. Applications of tensor networks technique will lead to a design of a quantum computer that enumerates all Hamiltonian cycles in a graph. Analysis of the determinant objective function in terms of the eigenvalues may lead to new spectral properties of stochastic matrices. Algorithmic advances exploiting such a characterisation will significantly contribute to existing technologies for solving problems in a wide range of applications.Read moreRead less