Psychology

My research in Psychology has mainly focussed on how humans detect patterns in sequences of events. This is known in the field as `sequential effects'. I believe sequential effects are related to some form of resonance or synchronisation in the brain. It is well known that the brain is capable of spontaneously generating geometric patterns, and this must be telling us something fundamental about how the brain works. One the other hand, animal locomotion is thought to rely on simple oscillatory patterns formed by coupled oscillators in the peripheral nervous system. My belief is that this pattern formation is the overall theme of how the brain works, from low-level locomotion up to higher level cognition, at which point the patterns become extremely complex. Extended into the empty regions of time and space, these patterns help us predict the future, i.e. what will happen next, where it will happen, and when. Attempting to answer questions such as these has led me to doing research in pattern formation in dynamical systems.

Mathematics

After my PhD I decided to do an MSc in Mathematics. This has led me to work with Prof. Ian Stewart, a legend in the field of pattern formation. Together we published two articles on pattern formation in networks of coupled dynamical systems. This is fairly abstract mathematics but it can be understood in a fairly simple way. Consider a network, which is a set of nodes and edged, and assume for the moment that all nodes and edges are equivalent. Imagine all nodes are coloured white; now take a subset of nodes and colour them a different colour (say yellow). Will the network support a state in which all the white nodes are synchronised with each other, and all the yellow nodes are synchronised too? To answer this question you only have to look at one thing: take a white node and look at all the nodes connecting to it. Does every white node have the same number of white and yellow nodes connecting to it? And does every yellow node have the same number of white and yellow nodes connecting to it? If the answer to both questions is `yes', the colouring is considered to be `balanced', and the network supports the synchronisation mode. My research, together with Prof. Stewart, consisted of finding all the possible balanced colourings of a square and an hexagonal lattice, specifically those colourings which are determined by the symmetries of the network.