- Tutorial and Review Articles
- Current Priority Areas
- Selected Contributions
Although we work on a broad range of projects, including transdisciplinary projects with neuroscientists and biologists, our current research priority areas are Optimisation, Pulse Processing, Machine Learning and Time-series Prediction.
The common theme in our research is the application of mathematics and statistics to the study of systems and networks of systems. Whether these systems are living, social or engineered, the same fundamental principles apply.
The theoretical foundations underpinning our research often come from the following disciplines:
We are interested in fast (online) optimisation problems with guaranteed performance. In 2013 we proposed an Optimisation Geometry framework for such problems. We are now looking to apply this framework to specific problems. We are also pursuing the hypothesis that the nicest optimisation problems are not convex ones but certain classes of problems on compact manifolds.
Identifying the locations and amplitudes of slowly-decaying pulses in a noisy signal is difficult at high pulse-generation rates because two pulses sufficiently close together are indistinguishable from a single pulse. We are interested in deriving faster and more accurate algorithms as well as understanding theoretical limitations that must apply to all pulse-processing algorithms.
We are interested in analysing neural networks from a mathematical perspective using tools from both information theory and analysis. We are also interested in how to impose certain geometric constraints on a neural network, such as invariance or equivariance.
Building on our background in Statistical Signal Processing and Stochastic Filtering, we wish to return to a topic we looked briefly at over two decades ago: financial time-series analysis. We are interested in understanding how much information can be extracted from past observations, and how best to use past observations to determine the best course of action.