MASCOS, or the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, was established in 2003 with about $11 million in funding over five years from the Australian Research Council (ARC) to research Complex/Intelligent Systems.
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MASCOS’s overarching strategic vision is to be one of the world’s leading centres in the mathematical and statistical analysis, design and optimisation of complex systems, and to apply that research for scientific, economic, social and environmental benefit. The Centre 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. In 2008, it will have 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.
The underlying problem in complex systems science that guides MASCOS' work may be summed up thus: how do local or small-scale phenomena interact to create complex or chaotic behaviour?
MASCOS' work revolves around three flagship applications, all of which highlight real-world complex systems, which can be better understood and therefore, potentially, better controlled through the research conducted by MASCOS. These three flagship applications are:
These, and other applications (e.g. climate modelling) 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, a situation reflective of their interconnectedness and which maximise cross-pollination of ideas. These are the four themes:
The focus, scale and interconnectedness of MASCOS is greatly enhanced by the above-mentioned flagship applications, which are all dependent on the work done in some or all of the four themes. For example, the first application Accurate assessment of financial risk, is being tackled by Hall's classifiers, Borovkov's stochastic analysis, Sloan's Quasi-Monte Carlo tools and Thompson/Guttmann's Info-Gap work, all supported by the dynamical systems theme members’ studies of stability, and Brent's algorithmic expertise.
The second application, Security of large engineering grids, is being addressed by Hill’s stability theory, Froyland’s and Taylor’s optimisation algorithms, and Pollett’s and Taylor’s network techniques.
The third application, Control of emerging pests, diseases and pathogens, is being tackled by techniques from risk modelling, such as Pollett’s calibration of stochastic models from discrete-sampled infection data, from Taylor’s work in complex networks in which he develops models that account for spatial structure in the spread of infection, by Brak’s work in critical phenomena – determining conditions for endemicity and other stable regimes, and Froyland’s work in dynamical systems in which he assesses the relative stability of endemic and non-endemic states.
The generic nature of mathematics, where the same methodology can have a wide range of applications, leads to research activities with potentially very broad scale. The above research program harnesses and exploits this scale particularly well.
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.