We are pursuing a wide range of research topics within the scope of mathematical and computational biology. Some typical methods that we use are given below.
Data assimilation, also known as model data fusion, involves combining data and mathematical models to produce optimal predictions. Historically, developed within the context of weather prediction, data assimilation techniques are now being used in health applications, such as real time prediction of optimal treatment strategies.
Mathematical modelling and analysis
Depending on the application, we use a broad range of mathematical modelling and techniques to take biological mechanisms and provide insight and predictions on behaviour.
Nonlinear time series techniques
We have expertise in various techniques for characterising the complexity of signals including the use of entropy methods and novel variants of Lempel-Ziv complexity. We are developing new methods to analyse physiological data based on the method of delays and Takens embedding theory.
Deployment and development of computational approaches for the analysis, integration and interpretation of data for furthering understanding of biological systems at the molecular level.
Examples include the handling and processing of –omics data, inference of molecular interaction networks, and identifying functional modules associated with a given status/response of a system.
Machine learning and artificial intelligence
Machine learning describes a collection of statistical and computational techniques for identifying patterns within data. More generally, other artificial intelligence techniques such as evolutionary algorithms, neural networks, and deep learning play an important role in identifying large scale networks or bioinformatics problems with small data. Members of our centre have expertise in:
- The identification of classifiers/predictors of clinical outcomes
- Attractor reconstruction methods for physiological data combined with machine learning
- Bayesian machine learning
- Evolutionary multi-objective machine learning
- Secure machine learning
- Advanced machine learning
- Neural networks and deep learning
- Ensemble learning and drop-out learning
- Evolutionary optimisation.
Mathematical modelling and analysis of biological systems
Mathematical models can be used to describe core biological mechanisms in order to help develop insight into the way that systems behave and predict behaviour. Ultimately, this may inform policy decisions, for example, when and who to vaccinate for infectious diseases, drug design or optimal light patterns for healthy circadian rhythmicity.
The kind of models that occur depend strongly on the nature of the research question and the particular system. Members of our centre have expertise in developing models in a variety of forms including ordinary differential equations, partial differential equations and agent-based models. Depending on the application, models may be deterministic or stochastic.
Models are analysed using a broad range of techniques including geometric singular perturbation methods, multiple spatial and/or time scale analysis, asymptotics and nonlinear dynamical systems techniques including bifurcation theory.
Members of our centre are also actively involved in developing novel numerical methods, for example for model data fusion (data assimilation).
Application areas include:
- Open quantum systems
- Population models
- Stem cell differentiation modelling
- Elasticity theory and mechanics of cell growth
- Sleep and circadian rhythms
- Systems pharmacology (PKPD)
- Evolutionary biology.
Statistical methods and time series analysis
Members have expertise in:
- Design of experiments, including design robustness against observation loss and fractional and fractional factorial experiments.
- Data analysis
- Bayesian statistics
- Monte Carlo methods
- Gaussian models
- Latent linear models
- Markov models
- The use of SQL/R-studio
- Descriptive statistics
- Medical statistics
- Computerised medical record systems,
- Attractor reconstruction methods for physiological data.