Research Topics

I am interested in Complex Systems. The patterns of connections and interactions between large numbers of things can give rise to unexpected and complex behaviour, that can't be understood by examining the parts in isolation.

These connections can often be represented as complex networks. I study the structure and function of these network systems, and the effects of interdependence on system functioning and stability.

Many of the systems I am interested in come from fields outside of traditional physics. I'm interested in social collective behaviour, particularly in linguistics, but also applications in areas such as technology, biology.

Language Change

Languages are continually changing. For example, new words are introduced, pronunciations change, meanings of words change, spellings may change. With Bill Croft, Richard Blythe and Alan McKane I have constructed a mathematical model3 of the process by which language changes occur, based on Bill's evolutionary account of language change. A distinguishing feature of this theory is that the driving force behind changes is the social interactions between speakers:

''...the empirical evidence indicates that linguistic selection is governed largely if not exclusively by social forces that have little or nothing to do with functional adaptiveness for communication.''
William Croft 'Explaining Language Change: An Evolutionary Approach', Longman 2000, p39.
In other words who says something is more important than any inherent features of what they say.

So far we have applied this model to:

  • Examine Trudgill's (P. Trudgill New Dialect Formation: The Inevitability of Colonial Englishes, Edinburgh University Press, 2004) explanation of the emergence of New Zealand English from the interaction of the different British and Irish dialects of the European immigrants in the 19th century7.
  • Consider what mechanisms may be responsible for the "adolescent peak" in an ongoing change, and differing distributions of individual behaviour during a collective change19.
  • Find under what model conditions one group may lead another through a chamge, in terms of different levels of receptiveness within and between groups, and social cohesion33.

Complex Network Theory

Networks are a useful way to describe the complex interactions in many real systems, such as social interactions, ecosystems and neurons in the brain.
With my colleagues in the Complex Networks group in Aveiro, I study the structure of networks and novel critical phenomena that occur in networks, and how this affects processes occurring on the network.

  • In systems with multiple interdependent layers, damage in one layer propagates to other layers, leading to avalanches. This can produce a discontinuous hybrid phase transition13 and other exotic critical phenomena 24,28 . With my colleagues, I have shown that the rules governing interactions between layers have a significant effect on the phenomena observed27,15.
  • Very similar critical phenomena appear in network processes with multiple dependencies, such as k-core percolation9,16 and bootstrap percolation8, a form of complex contagion.

The structure of the network can have a very strong effect on the processes which occur on the network. Recently I have been interested particularly on the effect of loops or cycles 21, and particularly clustering (also called transitivity) which is the presence of connections between nearest neighbours: the tendency for my friends to also be friends of each other.

I have helped to develop a new rapid method of generating random networks with high clustering. In the process we found that the networks generated exhibit very interesting structural critical phenomena 31.

Processes on Networks

There are many similarities between models that appear in opinion dynamics, disease spreading, population genetics, biodiversity and language change. All involve the competition between elements (alleles, language variants, opinions, species, contagions) that are copied from node to node in a network.

Besides my work on language change, I have studied several such models and applications:

Inference and Optimisation

Optimisation and inference problems appear very frequently in a huge variety of applications. I have shown that applying what we have learnt from studying complex networks to such problems can lead to effective and efficient algoriths for optimisation problems, such as finding the minimal damaging set in a multiplex network22, or inferring the causal relationships from variable data32.