Australian Research Council

Centre of Excellence for Mathematics

and Statistics of Complex Systems

Centre of Excellence for Mathematics

and Statistics of Complex Systems

Sunday 15 December 2019
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## INTRODUCTIONComplex systems play an integral role in providing society with a variety of amenities such as the internet, air traffic control, irrigation, robotics, power distribution, telecommunications, defence, manufacturing and finance. They also provide models for ecological and biological systems of all types. It is pivotal for society to have a greater understanding of complex systems and the ability to model and predict their behaviour.
In the ARCâ€™s definition of complex/intelligent systems, the following fields of research are specifically mentioned: system analysis and control theory, mathematical and statistical modelling, system and software engineering, software-hardware co-design, intelligent systems, and communications engineering. The boundaries between these fields are obviously blurred but they may still be thought of as lying along a continuum. This ranges from very analytical approaches, such as those embodied in mathematical and statistical modelling, to very practical approaches, such as those embodied in software engineering, software-hardware co-design and communications engineering. In all these research areas, mathematics plays an essential role as a provider of the modelling language and analysis tools, and as a source of new fruitful ideas. The Centre has situated itself toward the analytical end of the above-mentioned spectrum. Its mission has been to stimulate research activity in mathematical and statistical modelling of complex systems, and to encourage the cross-fertilisation of ideas and techniques from different areas of mathematics and statistics and apply them to the analysis of complex systems. The Centre's specific objectives are: - To formulate and analyse mathematical and statistical models for both natural and artificial complex systems
- To use these models to develop an understanding of the behaviour of these systems
- To incorporate this understanding into strategies for the management and control of complex systems.
The Centre is multinodal and spread across different mathematical and statistical disciplines. To draw these distributed aspects together, the Centre has defined a number of research themes, specifically chosen because of their impact on knowledge advancement or applicability to industry, and because they are amenable to attack by one or more of the mathematical and statistical disciplines covered by the Centre. The themes are: - Critical Phenomena
- Risk Modelling and Complex Networks
- Dynamical Systems
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