Mathematical Biology

Listed on this page are current research projects being offered for the Vacation Scholarship Program.

For more information on this research group see: Mathematical Biology

Viscoplastic biofluids: active mixing of yield-stress fluids

Active fluid flows occur in a range of systems from coral reefs and the human respiratory tract to engineered systems and micro-robots. This project will investigate the structure of flows in unbounded and confined geometries, and assess how flow fields are modified by non-Newtonian rheology (e.g., yield stress fluid). The project will draw on skills across multiple domains, including analytical modelling, dynamical systems, asymptotic analysis and numerical simulations.

Contact: Edward Hinton edward.hinton@unimelb.edu.au

Applying deep learning to problems in genetic epidemiology

In phylogenetics, we use genomic data from pathogens to study infectious disease. In this project the student will investigate using neural networks to tackle computational problems in phylogenetics.

Contact: Alex Zarebski azarebski@unimelb.edu.au

A portrait of intercellular communication in Waddington’s landscape

Waddington’s epigenetic landscape is an illustrative metaphor proposed by the biologist C.H. Waddington in the mid-20th century to describe cell development. The metaphor suggests that cell development is analogous to a marble rolling down a hill. As a marble will descend down a hill until eventually coming to rest in a (local) valley, so too will a cell develop along trajectories of an epigenetic landscape until it has become a fully differentiated (or ‘developed’) cell. The features (peaks and troughs) of the epigenetic landscape are determined by the gene expression of the cell. Traditional mathematical models of the Waddington landscape used a deterministic approach that can only feasibly be applied to low-dimensional gene regulatory networks that are known in advance. These models did not account for stochasticity, nor the influence of intercellular communication on gene expression — both of which are crucial for determining a cell’s future state, or fate. To address these limitations (and more!), this project will use a statistical mechanics approach to describe Waddington’s epigenetic landscape.

Contact:  Michael Stumpf mstumpf@unimelb.edu.au