1. Self-Assembly and Self-Organization in Complex Systems
Self-assembly is the fundamental process that creates the specific conditions under which atoms, molecules, or even galaxies spontaneously arrange themselves into a final entity (molecule, drug, universe, etc). On the other hand, self-organization is a process in which the components (or state) of a system increase in complexity without external intervention. In some cases, self-organizing systems could exhibit emergent behaviour. The aim of this project is use a range of algorithmic techniques to study and gain insight into the processes of self-assembly and self-organization for a wide range of systems.
2. Empirical Evaluation of a Model of Dynamical Synchronisation on Networks (in collaboration with Dr. Joseph Lizier, School of Civil Engineering)
The ability of distributed components of a system to synchronise their behaviour has been observed in a diverse range of fields, including swarms of flashing fireflies, clusters of pacemaker cells in our own heart, and electrons in a superconductor, making this phenomenon an important field of complex systems science. We have recently been able to analytically infer the synchronisability of a system from the underlying connectivity between its components (i.e. its network structure), for a specific type of dynamic activity on the network. This project seeks to model other types of dynamic behaviour to examine the extent to which those analytic findings remain applicable. Specifically, the project will investigate the effect of network structure on the accuracy of the model, whether the model is accurate at both a high and low level in the network, and accuracy of prediction of the robustness of the network to damage. Skills required: mathematical ability particularly in linear algebra; programming skills in Matlab/Octave primarily, and in Java also may be useful.
3. Constructing and Analysing Contact Networks of Dengue/Ross River Fever Epidemics in rural Australia (in collaboration with Dr. Mahendra Piraveenan, School of Civil Engineering)
This ambitious project seeks to understand the relationship between contact networks among people, and infection networks constructed based on the similarities in genetic material found in the virus strains on patients. To be undertaken in collaboration with local health authorities, the project will seek to establish best vaccination and resource allocation strategies by understanding the disparities between contact networks established prior to inspection spread on one hand, and infection networks constructed based on virus strains found on patients, after the infection has passed through, on the other hand. This potential project will involve collaboration with leading academics from US and other countries.
4. Developing Centrality Measures for Percolating Networks (in collaboration with Dr. Mahendra Piraveenan, School of Civil Engineering)
A number of centrality measures are available to determine the relative importance of a node in a complex network. Betweenness, Closeness, and Eigen value centrality are prominent among them. However, the existing centrality measures are not adequate in network percolation scenarios (for example, during infection transmission in a social network, or spread of virus in computer networks) because they do not account for the changing percolation states of individual nodes. In this project, the student will work on developing context specific centrality measures, which can be applied to determine the importance of nodes in a dynamic scenario. The project requires high level of proficiency in mathematics and programming. The student will work in collaboration with academics from United States and other countries.
5. Measuring Robustness and Attack Tolerance in Complex Networks (in collaboration with Dr. Mahendra Piraveenan, School of Civil Engineering)
Security concerns are increasingly at the forefront in today’s world. A complex network’s topology plays an important role in determining how the network can resist random and targeted attacks. It has been shown by prominent researchers that the so-called scale-free networks display high resilience to random attacks, and this is perhaps partly the reason for most of the ‘real world’ networks in any domain being scale free. Yet, scale free networks are vulnerable to targeted attacks. It is possible to design network topologies so that they display high levels of tolerance to both random and targeted attacks. However, quantifying the robustness and attack tolerance of a network topology is necessary to achieve this goal. This project will attempt to define robustness measures for complex networks which are particularly useful in sustained attack scenarios, and test their effectiveness in various domains, including computer networks, Internet and World Wide Web, social networks, and biological networks inside organisms. The project requires high level of proficiency in mathematics and programming.