Australian Research Council

Centre of Excellence for Mathematics

and Statistics of Complex Systems

Centre of Excellence for Mathematics

and Statistics of Complex Systems

Saturday 26 September 2020
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## About MASCOS and Complex SystemsMASCOS, or the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, was established in 2003 and operates from three nodes: The University of Melbourne, The University of Queensland and La Trobe University. It presently has 10 Chief Investigators, 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. 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. 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. 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 each theme, 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.
Critical phenomenaLeader: Richard Brak Deputy Leader: Aleks Owczarek 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.Risk modelling & Complex networksLeader: Kostya Borovkov All complex systems are subject to operational risks, especially those associated with extreme behaviour. The analysis and prediction of extreme behaviour emerges from the influence of small scale phenomena on large scale behaviour. Complexity typically arises from interconnectedness in large-scale systems which can be modelled as a network. Dynamical systemsLeader: Reinout Quispel Deputy Leader: John Roberts The complex systems in the flagship applications all involve non-linear dynamical systems. The analysis and prediction of extreme behaviour emerges from the influence of small scale phenomena on large scale behaviour. An important contribution is the legacy or longer term benefit that the MASCOS research program will provide, and it is here that the mathematical sciences, by their nature, provide broad benefits, even in areas beyond the current scope of MASCOS.There is a body of common core mathematics and statistics which can be identified as important to solving problems in complex systems such as our flagship applications. The themes are underpinned by a unified mathematical framework which consists of dynamical systems, graph theory, network science, stability theory and stochastic processes that can be used to tackle a wide variety of complex systems problems. The themes are strongly inter-linked. Critical phenomena is being applied to networks to understand transitions, risk analysis is used in studying the reliability of large networks, and dynamical systems theory is used to determine the stability of networks. These links create mathematical synergies toward development of a powerful approach to managing complexity that will be of lasting value to Australian science. Thus, for instance, while working on risk classifiers for the first flagship application, Hall's work on classifiers will include improved ways of discriminating among different forms of cancer using genetic data, better ways of detecting covert signals, making the best decisions for important meteorological problems, and so forth. The second flagship application will lead to broader ideas on coordinated control that have applications in numerous areas of importance to Australia’s infrastructure. Similarly, work done in the third will be of lasting benefit to Australia, not only for its immediate relevance to biosecurity issues, but also because the techniques developed can be applied directly wherever interaction and flow are salient features of the system in question: for example, the control of populations of native fauna, the management of fish stocks, and the propagation of memes in social networks. More examples of the potential inherent in this approach exist. For instance, improved data assimilation techniques will be essential for extending existing techniques in meteorology to apply to the wider range of scale and complexity that will arise when developing a new generation of climate models for the Southern Hemisphere. The development of the critical dimension of dynamical systems is finding application in coding theory, and Quispel’s bifurcation analysis of the model of the human cortex has already received favourable reactions from both mathematically- and medically-oriented research teams. Clinical implementation of control strategies suggested by this work is still at a preliminary stage, but earlier work by collaborator David Liley, based on the same model equations, has already led to a patented EEG reading device. Additionally, complex networks research undertaken by MASCOS for Patrick Corporation is already being incorporated into Patrick’s software to significantly increase the efficiency of new container handling infrastructure at Port Botany, Sydney. This research will have a lasting impact on Australia's international trade at Port Botany with the potential to be adopted at other major ports around Australia. While this initial research is embedded in Patrick’s systems, MASCOS continues to hold discussions with Patrick for a second major stage of research Thus, MASCOS’s legacy extends substantially beyond the solution of the flagship applications and key problems– important though they are. Created by: system last modification: Wednesday 03 of June, 2015 [05:57:54 UTC] by kerry |