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Centre of Excellence for Mathematics

时间:2010-08-13 13:15:35  来源:  作者:

http://www.complex.org.au/

MASCOS, or the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, was established in 2003 and operates from five nodes: The University of Melbourne, Australian National University, The University of New South Wales, The University of Queensland and La Trobe University. It presently has 14 Chief Investigators and 1 Professorial Fellow, all of whom have international reputations for their research in mathematics and statistics.

Complex systems play a key role in a vast range of societal activities– climate, the internet, traffic control, power distribution, agriculture, defence, manufacturing, engineering, water management, finance and many more. In any system, be it physical, biological or social, collective phenomena occur as the number of components increase. Analysing the behaviour of any individual component gives no indication as to how the system as a whole behaves, but understanding entire systems can lead to the prediction and subsequently the control and optimisation of their behaviour. The mathematical and statistical techniques developed to understand these entire complex systems form the basis for the research being undertaken by MASCOS, which in turn has many potential applications to real world problems.

MASCOS’ vision is to be one of the world’s leading centres in mathematical and statistical analysis, design and optimisation of complex systems, and to apply that research for scientific, economic, social and environmental benefit.

The Centre also aims to reinforce the importance of mathematics and statistics across the spectrum of Australia’s scientific and technological development by maintaining an extensive and vigorous outreach program, encompassing schools, commerce and industry, and the broader research community in Australia.

MASCOS Strategic Vision

Flagship Applications

Themes

MASCOS' Legacy


STRATEGIC VISION
Our vision is to be a world leading centre in the mathematical and statistical analysis, design and optimisation of complex systems, and to apply our research for scientific, economic, social and environmental benefit.

In all our work towards this vision, we attack the underlying problem in complex systems science, which is: how do local or small-scale phenomena interact to create complex or chaotic behaviour?

Our research will address a number of key problems that are of relevance, both immediate and long-term, to the development, protection and wellbeing of the Australian people.

The research program at MASCOS comprises four themes, critical phenomena, risk modelling, dynamical systems and complex networks, all directed and supported by the core of key problems, the flagship applications.


FLAGSHIP APPLICATIONS
Real-world complex systems are highlighted within MASCOS by the following three flagship applications:

1. Accurate assessment of financial risk.
The sub-prime loan disaster of 2007 is a reminder of the complex networks that link banks. Even in stable times the daily fluctuation of interest rates makes the calculation of risk a major challenge.

2. Security of large engineering grids.
Power grids, the internet and traffic flow can all be described as networks that are prone to dynamic collapse, as occurred in North American and European power grids in 2003. Security measures are important tools for maintaining system integrity in the face of such critical behaviour.

3. Control of emerging pests, diseases and pathogens.
Australia has a persistent problem with the introduction of foreign pests or diseases – such as equine flu in 2007.

THEMES
MASCOS' flagship applications draw upon a variety of mathematical and statistical techniques, which MASCOS has now grouped into four themes. At the mathematical level, each of the themes constitutes a concerted push towards the central problem of the relationship between local behaviour and global complexity. Within each theme, clearly identifiable goals are set and a range of projects is tackled. These projects are stepping stones in the solution of the flagship applications described above. Regular workshops are held around eachtheme, at which agreed projects are developed and reviewed. Each theme has a leader and a deputy leader. Almost all members of MASCOS are associated with at least two themes.


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Critical phenomena
Leader: Aleks Owczarek
Deputy Leader: Richard Brak
Critical phenomena are universal features of complex systems displaying emergent behaviour. This describes the phenomenon whereby macroscopic behaviour emerges from interactions between simpler, microscopic components.

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