Sunday 19 January 2020
Research Theme: Complex Networks
Theme Leader: Peter Taylor (UM)
Deputy Leader: Phil Pollett (UQ)
CIs: Kostya Borovkov (UM)
Complexity typically arises from interconnectedness in large-scale systems which can be modelled as a network.
Goal: To develop advanced methods for optimisation, inference, stability and control of such networks.
Illustrative problem: How to scale methodologies that work for smaller systems to the massive networks of networks structures existing in natural and modern infrastructure systems. For example, there are opportunities for exploiting system structure in overcoming the so-called “curse of dimensionality” in customized optimisation.
Applications: There are numerous possibilities in transport, energy systems, teletraffic and ecological networks. A typical one is how to derive indicators of proximity to collapse situations in large power networks.
The current list of major projects was confirmed at the recent Theme Workshop, held in connection with the Annual Meeting of the Australian Mathematical Society, La Trobe University, Friday 28th September 2007. They are as follows:
• Spatially realistic structured population networks;
• Limiting behaviour in stochastic network models for populations;
• Capacity configuration in telecommunication networks;
• Parameter and property inference, e.g. loss, delays, on networks including by using active probing experiments;
• Connectivity in sensor networks;
• Optimisation under uncertainty including bad data and events;
• Scheduling algorithms in applications to port handling and power systems control;
• Stability theory for switched networks;
• Security control for large power networks.
There is a lot of common underlying core mathematics in all these projects coming mainly from network science, graph theory, dynamical systems, stochastic processes, stability theory and optimization. Further, there are strong connections to all the other themes. Critical phenomena in networks is a recent trend to understanding phase transitions; risk analysis in large infrastructure networks is a vitally important area and the network models of interest are dynamical requiring analysis techniques of dynamical systems.
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