Professor Natashia Boland |

In recent years, there has been increasing attention on improving the robustness of airline schedules. One sense in which this can occur is that the probability that flights are delayed is reduced. This can be achieved by re-timing flights, to move slack in the schedule to "most vulnerable" areas, by re-routing aircraft to a similar end, and through a number of measures in crew scheduling. Re-distributing slack to minimize measures such as the probability of delays in excess of 15 minutes, leads to models in which probability distributions along routes must be computed with multiplicative operations to calculate the objective value. Surprisingly, these can be modelled as linear optimization problems, with nice properties that can be exploited in solution algorithms.

A/Professor Andrew Francis |

University of Western Sydney |

Wherever there are symmetries in nature, group theory can have a role. Some important rearrangements of bacterial chromosomes (such as inversions) can be modelled using groups, and hopefully some of the theoretical development of the last century can be brought to bear. In this talk I will describe some progress in that direction using the affine symmetric group.

Australian National University |

Many diseases have distinct seasonal patterns. Examples include influenza and respiratory syncytial virus (RSV) with peaks in winter months in temperate climates and dengue fever with peaks during the wet season in tropical climates. In addition diseases have a natural frequency governed by waning immunity and incoming susceptibles (for example births). Due to these multiple frequencies, complex behaviour in outbreaks is possible. Examples of simple models for RSV and dengue demonstrating this complex behaviour such as period doubling and chaos will be explored.