Networks can be used to describe many ways that humans (and many other agents) interact, enabling researchers to identify potential disease spread on a network of people meeting, or identify groups of neurons that perform some cognitive task and so are linked together in a brain, or make efficient supply chains for companies that manufacture objects from components made by other companies.
Many interesting networks have been identified as having useful structure, such as the surprising number of people with huge numbers of friends on Facebook (who turn the network into a ‘scale-free’ network) and the short paths that exist between parts of the brain that seem unconnected, making it act as a ‘small world’.
In this project, we will ask two important and related questions about these networks: (1) what are the underlying reasons for these extra features, and (2) how can we utilise them to produce more efficient algorithms on networks of these types? For example, a scale-free network has nodes of very high degree (hubs) and so routing algorithms that produce short paths can be made by connecting nodes to hubs, which connect to other hubs, which then connect to the destination node. However, if the hubs are deluged with traffic, this might become inefficient. We will study these questions for a variety of real-world complex networks, such as biological networks, human interactions, and digital humanities.
The project will suit an applied mathematician interested in algorithms. The successful applicant will have the chance to work with a variety of researchers across Te Pūnaha Matatini with interest in several different areas of application as well as the underlying theory.
The three-year scholarship covers PhD tuition fees plus a non-taxed living allowance of NZ$27,300 per annum. The starting date can be anytime from 1 November 2017.
How to apply
For further information and to apply, please contact:
Prof Stephen Marsland
School of Mathematics and Statistics
Victoria University of Wellington