Emerging applications of advanced computational methods and discrete mathematics. Ongoing improvements in computer performance are revolutionising research in combinatorial discrete mathematics, and leading to exciting new applications in information technology and the biological and chemical sciences. As a result, substantial international research effort, both at universities and in commercial and industrial organisations, is being channelled into high-performance computation and theoretical p ....Emerging applications of advanced computational methods and discrete mathematics. Ongoing improvements in computer performance are revolutionising research in combinatorial discrete mathematics, and leading to exciting new applications in information technology and the biological and chemical sciences. As a result, substantial international research effort, both at universities and in commercial and industrial organisations, is being channelled into high-performance computation and theoretical problems in combinatorial mathematics. Our aim is to develop and apply advanced computational methods through the study of several unsolved theoretical problems in design theory and practical problems in exact matrix computation and drug design.Read moreRead less
Asymptotic Geometric Analysis and Machine Learning. Phenomena in large dimensions appear in a number of domains of Mathematics and adjacent domains of science (e.g. Computer Science), dealing with functions of infinitely growing number of parameters. Here, we focus on several questions naturally linked to Asymptotic Geometric Analysis which have natural applications to Statistical Learning Theory. We intend to use geometric, probabilistic and combinatorial methods to investigate these problems, ....Asymptotic Geometric Analysis and Machine Learning. Phenomena in large dimensions appear in a number of domains of Mathematics and adjacent domains of science (e.g. Computer Science), dealing with functions of infinitely growing number of parameters. Here, we focus on several questions naturally linked to Asymptotic Geometric Analysis which have natural applications to Statistical Learning Theory. We intend to use geometric, probabilistic and combinatorial methods to investigate these problems, with an emphasis on modern tools in Empirical Processes Theory and the theory of Random Matrices.Read moreRead less
Cross-Entropy Methods in Complex Biological Systems. The Cross-Entropy method provides a powerful new way to find superior solutions to complicated optimisation problems in biology, ranging from better design and implementation of medical treatments to an increased understanding of complex ecosystems.
Adapting the Bulk Synchronous Parallel processing model to Peer-to-Peer Networked Computing. Advances in distributed computing have shown that data parallel and parametric applications domains are amenable to wide area distribution. The project will advance the Bulk Synchronous Parallel processing model to describe innovative applications from the loosely synchronous domain, e.g. fluid dynamics, strategy algorithms and N-body problems are challenges that have significant scientific and industria ....Adapting the Bulk Synchronous Parallel processing model to Peer-to-Peer Networked Computing. Advances in distributed computing have shown that data parallel and parametric applications domains are amenable to wide area distribution. The project will advance the Bulk Synchronous Parallel processing model to describe innovative applications from the loosely synchronous domain, e.g. fluid dynamics, strategy algorithms and N-body problems are challenges that have significant scientific and industrial value. The project specializes the exciting peer-to-peer paradigm, a frontier of inter-networking technology. By using the latest techniques and taking advantage of the technology implosion caused by low cost parallel infrastructure, the project outcomes will give Australia a strong position in the future of parallel technology.Read moreRead less
Control of Markov jumping processes with constraints. The project outcomes will constitute the set of tools for modelling and optimisation of complex stochastic systems and will lead to new and more precise characterisations of optimal behaviour of complex controllable systems arising in Resource Management, Engineering and Telecommunications. Therefore, the project fits to the research priority areas Breakthrough Science and Frontier Technologies in the topic of mathematical modelling and optim ....Control of Markov jumping processes with constraints. The project outcomes will constitute the set of tools for modelling and optimisation of complex stochastic systems and will lead to new and more precise characterisations of optimal behaviour of complex controllable systems arising in Resource Management, Engineering and Telecommunications. Therefore, the project fits to the research priority areas Breakthrough Science and Frontier Technologies in the topic of mathematical modelling and optimisation of Complex Systems.Read moreRead less
Computer Assisted Research Mathematics and its Applications. The mathematics community will benefit from infusion of new computer-assisted techniques and modalities for research and training post-graduate students, both from my pure research project and through development of an associated research centre. Ultimately, this should also help more school students learn mathematics well and so play a part in addressing Australia's skill shortage. Also, the work on optimization algorithms promises to ....Computer Assisted Research Mathematics and its Applications. The mathematics community will benefit from infusion of new computer-assisted techniques and modalities for research and training post-graduate students, both from my pure research project and through development of an associated research centre. Ultimately, this should also help more school students learn mathematics well and so play a part in addressing Australia's skill shortage. Also, the work on optimization algorithms promises to improve the performance and quality of many practical signal reconstruction methods. These are used by varied Australian industries from telecommunication to mining and by researchers in the digital arts and fields such as astronomy, physics, chemistry, bioscience, geoscience, engineering and medicine.Read moreRead less
Secure and Efficient Cryptographic Hashing. This project will enhance information security, which is absolutely crucial for rapidly growing e-commerce, e-government services and for national security (Priority 4 -Safeguarding Australia - Protection against Terrorism and Crime). The project will strengthen international collaboration by reciprocal exchange of researchers and postgraduate students leading to more attractive and productive research environment. At the same time, the project will he ....Secure and Efficient Cryptographic Hashing. This project will enhance information security, which is absolutely crucial for rapidly growing e-commerce, e-government services and for national security (Priority 4 -Safeguarding Australia - Protection against Terrorism and Crime). The project will strengthen international collaboration by reciprocal exchange of researchers and postgraduate students leading to more attractive and productive research environment. At the same time, the project will help to maintain high research profile of Australian researchers, to increase the capacity for consultancy and contract work, and provide a cutting-edge information technology for the Australian telecommunications industry, business and government (Priority 3 - Frontier Technologies). Read moreRead less
Implementing Feferman-Landin Logic. The objective of this project is to utilise computer based verification tools (such as PVS and Rewritting Logic) to develop a software engineering environment for specifying and verifying systems written in high-level programming languages such as Java, Scheme, and ML. The project will thus subtantially advance the use of formal computer based tools to develop reliable programs and specifications for life-critical systems. The project will also develop form ....Implementing Feferman-Landin Logic. The objective of this project is to utilise computer based verification tools (such as PVS and Rewritting Logic) to develop a software engineering environment for specifying and verifying systems written in high-level programming languages such as Java, Scheme, and ML. The project will thus subtantially advance the use of formal computer based tools to develop reliable programs and specifications for life-critical systems. The project will also develop formally
based interoperability between the PVS and Maude systems, two widely
used computer tools for reasoning about complex systems.Read moreRead less
Multiscale stochastic modelling of genetic regulatory mechanisms. The completion of the human genome marked the culmination of one hundred years of reductionist science in cell biology. Although further bioinformatics analysis will continue, the focus is shifting towards synthesis and understanding how the regulatory genetic components dynamically interact to form functional phenotypes. The key to this is the understanding of the roles of stochasticity in cellular processes. This project will ex ....Multiscale stochastic modelling of genetic regulatory mechanisms. The completion of the human genome marked the culmination of one hundred years of reductionist science in cell biology. Although further bioinformatics analysis will continue, the focus is shifting towards synthesis and understanding how the regulatory genetic components dynamically interact to form functional phenotypes. The key to this is the understanding of the roles of stochasticity in cellular processes. This project will explore these roles and will develop an integrated complex systems modelling, simulation and visualisation framework for exploring and validating genetic regulatory models in general. This will be used on an exemplar application for understanding the induction process in lambda phage.Read moreRead less
Adaptive and Integrated Resource Allocation. By leveraging progress in communication technologies, adaptive and integrated optimization systems will open innovative application areas critical to Australia, yet outside the scope of existing optimization technology. For instance, they will dispatch and reallocate ambulances in real time, help contain pandemics, allocate resources dynamically to extinguish bushfires, and assist in failure recovery of energy infrastrutures. These systems will also s ....Adaptive and Integrated Resource Allocation. By leveraging progress in communication technologies, adaptive and integrated optimization systems will open innovative application areas critical to Australia, yet outside the scope of existing optimization technology. For instance, they will dispatch and reallocate ambulances in real time, help contain pandemics, allocate resources dynamically to extinguish bushfires, and assist in failure recovery of energy infrastrutures. These systems will also solve existing logistics and manufacturing applications better, making these industries more effective and reactive. The project also aims at establishing a center of excellence in optimization in Melbourne with an international reputation in research, teaching, and industrial collaboration.Read moreRead less