I have many research interests, most of which can be placed under the umbrella of 'complex systems'. Some of the topics I am currently working on are:
Trophic structure of directed networks: Together with colleagues in Granada, I have recently studied a network property called 'trophic coherence', (Johnson et al, PNAS, 2014). This and subsequent work (with colleagues Miguel Ángel Muñoz, Virginia Dominguez, Janis Klaise and Nick Jones) has shown that trophic coherence is related to many aspects of complex systems, including the prevalence of cycles and feedback loops, ecological stability, motif distributions and spreading processes such as epidemics and neuronal avalanches. It has also opened several questions, such as: Does trophic coherence account for the existence of large, complex ecosystems? Can trophic structure be used to identify node function in systems like gene regulatory networks? is there a general theory relating feedback and stability in complex, dynamical systems.
Human ecology: Work with Weisi Guo, Xueke Lu and Guillem Mosquera has shown that the prevalence of violence around the world is related to the spatial distribution of cities according to a remarkably simple and robust law. We are currently looking into the causes of this effect though a combination of data analysis and agent based modelling and looking for ways in which our results can be applied.
Brain development: The neural network underlying all mental activity comes into being in a curious way: at birth it has a great many synapses (connections between neurons), about half of which are 'pruned' throughout infancy. Recent work with Ana Paula Millán, Joaquin Torres and Joaquin Marro describes a mechanism which could explain this phenomenon with a simple neural network model. We are now studying this process with more realistic neural modelling, looking into its effects in other complex systems.