Operator-Analytic Methods in Telecommunication Systems. Many systems in information technology and telecommunications evolve under conditions of uncertainty. In this context, mathematical modelling is an essential component of the design process. We shall provide techniques for analysing a class of mathematical models, called operator-analytic models, which can be used to study many of the above-mentioned systems, such as the Internet. This project will deliver efficient numerical algorithms tha ....Operator-Analytic Methods in Telecommunication Systems. Many systems in information technology and telecommunications evolve under conditions of uncertainty. In this context, mathematical modelling is an essential component of the design process. We shall provide techniques for analysing a class of mathematical models, called operator-analytic models, which can be used to study many of the above-mentioned systems, such as the Internet. This project will deliver efficient numerical algorithms that will make possible practical analysis of operator-analytic models.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
Characterisation of Internet Traffic Matrices. The benefits to the community of characterisation of Internet traffic matrices arise because this information is used in the design of efficient and reliable networks. This is a genuine example of using the data we have more cleverly, rather than throwing money at a problem. Better information will result in the Internet becoming more efficient, and therefore cheaper, and at the same time more reliable.
Ensuring the Robustness of IP Routing. The Internet is by its nature international, and so any such effort to model and understand it must be somewhat international. However, Australia has longer network paths to the rest of the world and the routing protocols' operation depends on this latency. This emphasizes why Australia must participate in such research: to ensure that Australian issues are considered when Internet protocols are designed. This project will directly deliver a more robust Int ....Ensuring the Robustness of IP Routing. The Internet is by its nature international, and so any such effort to model and understand it must be somewhat international. However, Australia has longer network paths to the rest of the world and the routing protocols' operation depends on this latency. This emphasizes why Australia must participate in such research: to ensure that Australian issues are considered when Internet protocols are designed. This project will directly deliver a more robust Internet for Australia, international exposure in an area of general interest, the potential for patents, and the development of commercially valuable expertise and measurement infrastructure.Read moreRead less
The use of stochastic fluid models for the evaluation of applications-driven sample path integrals. The major technical goal of this project is the production of novel methodologies which can be used to model and solve real-world problems of considerable engineering and/or environmental significance. The research for this project will serve to enhance further Australia's reputation as a country which makes major contributions, both theoretical and practical, to this field. The activities of the ....The use of stochastic fluid models for the evaluation of applications-driven sample path integrals. The major technical goal of this project is the production of novel methodologies which can be used to model and solve real-world problems of considerable engineering and/or environmental significance. The research for this project will serve to enhance further Australia's reputation as a country which makes major contributions, both theoretical and practical, to this field. The activities of the Stochastic Modelling, Analysis and Optimisation group at the University of Adelaide and the School of Mathematics at the University of Tasmania will receive further impetus, consequently maintaining a dynamic research environment for staff and students at both universities. Links between the two groups will be strengthened.Read moreRead less
WaterLog - A mathematical model to implement recommendations of The Wentworth Group. In 2003, The Wentworth Group of Concerned Scientists released their 'Blueprint for a national water plan' with the primary objective to 'protect river health and the rights of all Australians to clean usable water'. Currently, there are significant water restrictions in all the Australian mainland capital cities. In January 2007, the Prime Minister of Australia, announced a bold plan to rescue the Murray-Darling ....WaterLog - A mathematical model to implement recommendations of The Wentworth Group. In 2003, The Wentworth Group of Concerned Scientists released their 'Blueprint for a national water plan' with the primary objective to 'protect river health and the rights of all Australians to clean usable water'. Currently, there are significant water restrictions in all the Australian mainland capital cities. In January 2007, the Prime Minister of Australia, announced a bold plan to rescue the Murray-Darling Basin. The plan incorporates political management changes, and an investment of $10Bn. Now is the time to develop improved techniques for management of water storage systems. This project will develop the fundamental mathematical principles required for this improved management.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
Saddlepoint approximation, likelihood analysis and ancestral graphs for strong and weak natural selection, genetic drift and population subdivision. Building new research strength in theoretical population genetics and related statistical techniques will enhance Australia's capability in harnessing the power of post-genomic information. Sophisticated statistical techniques that make smart use of genetic data are being developed in this project. The extent to which natural selection and migrati ....Saddlepoint approximation, likelihood analysis and ancestral graphs for strong and weak natural selection, genetic drift and population subdivision. Building new research strength in theoretical population genetics and related statistical techniques will enhance Australia's capability in harnessing the power of post-genomic information. Sophisticated statistical techniques that make smart use of genetic data are being developed in this project. The extent to which natural selection and migration affect current genetic polymorphism on a population level can be quantified using these new methods. New modeling provides a rigorous foundation with which to construct inference techniques currently beyond computational approaches to the data. Assessing selective effects on genetic mutations associated with human disease will be a consequence of this new statistical methodology.Read moreRead less
Perturbation and approximation methods for linear operators with applications to train control, water resource management and evolution of physical systems. Linear equations are used to solve practical problems. In realistic problems the equations and their solutions depend on parameters obtained by measurement of physical quantities and on data derived from observations and experiments. Changes to the values of the key parameters will lead to changes in the solutions. This project will devel ....Perturbation and approximation methods for linear operators with applications to train control, water resource management and evolution of physical systems. Linear equations are used to solve practical problems. In realistic problems the equations and their solutions depend on parameters obtained by measurement of physical quantities and on data derived from observations and experiments. Changes to the values of the key parameters will lead to changes in the solutions. This project will develop methods to better understand the relationships between the key parameters and the solutions and will apply the new insights to practical problems such as the minimization of fuel consumption in trains, optimal resource management in water supply systems and the evolution of physical systems.Read moreRead less
Aggregating Generalised Stochastic Petri Nets for improved Performance Analysis. Australia's economy is very dependent on the operation of complex man-made systems. Important examples are telecommunication networks and services (e.g. the Internet), manufacturing plants, organisational processes, military logistics and transport systems (e.g. air traffic control). The performance of these systems is critical to their success. Thus being able to predict performance before systems are implemented i ....Aggregating Generalised Stochastic Petri Nets for improved Performance Analysis. Australia's economy is very dependent on the operation of complex man-made systems. Important examples are telecommunication networks and services (e.g. the Internet), manufacturing plants, organisational processes, military logistics and transport systems (e.g. air traffic control). The performance of these systems is critical to their success. Thus being able to predict performance before systems are implemented is very important in their design. This project will develop leading-edge performance analysis techniques and tools for an important class of practical systems. There is potential to commercialise the resulting tools and methodology and to transfer the expertise to industry.Read moreRead less