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
Distinguishing heterogeneity from model misspecification
Deterministic mathematical models are widely applied to describe phenomena throughout the natural sciences and beyond. Allowing model parameters to vary according to probability distributions enables deterministic models to capture the sometimes significant variability between individuals. Given a specific mathematical model, it is, in many cases, possible to infer these individual-level distributions from population-level data. Many models are, however, likely to be misspecified (i.e., not an accurate representation of reality) to some extent. This project will explore whether it is ever possible to distinguish variability between individuals from model misspecification. Depending on student interests, this project can involve either or both of analytical work (based on calculus, analysis, and Taylor series expansions) or computational work.
Contact: Alexander Browning alex.browning@unimelb.edu.au and Adriana Zanca adriana.zanca@unimelb.edu.au
Multiscale modelling in biology
Many biological processes evolve over multiple scales, from molecular interactions within a cell to the dynamics of entire populations. Modelling such systems, and calibrating these models to data, is an open challenge. Various projects are available in this area that will use stochastic dynamical modelling, Bayesian inference and machine learning methods.
Contact: Tom Kimpson tom.kimpson@unimelb.edu.au and Jennifer Flegg jennifer.flegg@unimelb.edu.au
Multicellular Systems Biology
My research is on the interface between applied mathematics numerical methods scientific computing and biology. We use theoretical tools to try to get a better understanding of organ and tissue development and disease.
Due to recent increases in the amount and quality of cell level imaging data, and matching advances in computational power, multicellular modelling has become ever more popular. Multicellular modelling considers cells as discrete entities and represents their interactions using mathematical formalisms, both stochastic and mechanics based. This allows tissues to be simulated, with tissue level behaviour and properties being emergent rather than imposed.
Various projects are available focusing on modelling and on numerical methods. See my website for examples of my work.
Contact: James Osborne jmosborne@unimelb.edu.au
Go with the flow: mathematically modelling hormonal fluctuations throughout the menstrual cycle
No one menstrual cycle looks exactly like another. How a person experiences their period is influenced by how their hormones fluctuate throughout the menstrual cycle. Understanding a person’s unique menstrual cycle is crucial to monitoring health outcomes and assessing the efficacy of hormonal contraception at an individual level.
Previous mathematical studies of the menstrual cycle have often neglected the individual experience. This project aims to explore how we can model the hormonal fluctuations throughout a menstrual cycle, and how these fluctuations are impacted by individual menstrual cycle characteristics.
Contact: Adriana Zanca adriana.zanca@unimelb.edu.au, James Osborne jmosborne@unimelb.edu.au, and Isobel Abell isobel.abell@unimelb.edu.au