Our project began in 1st April 2005 and was to run until 31st January 2009; we have been granted a no cost extension until 31st March 2009 because our research assistant Rui Carvalho left December 31st 2007 and we did not appoint a replacement until September 1st 2008. The person who is now the RA is Paolo Masucci who came from Brunel and has published papers on transport and related networks which he is continuing to work on for this project.
The original proposal was that the UCL group would work on scaling in the geographical distribution of citations and also on geographical networks involving flows such as citations and traffic. In the event we did not make much progress on flows of citations largely because of difficulties over getting such data and after our preliminary quest to focus on citations using the Arxiv and also CiteSeer, I moved the project to examine size distributions in cities and transport networks where the focus has been on scaling.
Our project within SECSE is now organised into four parts, which deal with
In essence, we have looked at size distributions and scaling in network links and nodes, with perhaps a stronger emphasis on nodes. Our work on citations has confirmed that there is strong scaling in geographical distributions but that there is considerable path dependence in that places that attract researchers in particular and people in general and gain some initial advantage, tend to dominate all subsequent distributions. We have not looked at the dynamics of scaling for citation networks but we have for cities, firms and even plant species and these show remarkable volatility within the scaling envelop, suggesting that the competitive ethic of scaling which dominates all such systems provides a hidden constraint on the extent to which systems develop. In fact from this, we would suggest a new definition of complex systems or even complexity as “systems which are characterised by volatility at micro scales which transform to continued stability at macro scales”. These concepts mesh well with ideas about hierarchy and emergence which are key to the complexity sciences. They also seem to explain the sort of complexity we see in financial and economic systems. We are also examining transport networks which are essentially embedded in geographical space and looking at the transition to topological less constrained space. Scaling rarely occurs in networks which are embedded in this way but variants of their relations do show scaling and we are tracking how we can use the results of network science to make sense of the topology and geometry of such networks. This is the last part of our research project and we hope to write a number of key papers on this area within the next months.