Wondering what to do with your Sunday? I know just the very thing: complexity!
Nature Physics has an insights issue on the subject (vol. 8 no. 1), and I have heard that the articles are free of charge until February 1, 2012 (the Nature journals are unfortunately otherwise quite fond of paywalls). There’s quite a lot of things to read (though I cheated a bit – I got some through early access and did not read it all on [Sun]day).
First, there is a good Commentary by Albert-László Barabási – The network takeover (doi:10.1038/nphys2188) – arguing that while we may not be seeing the end of reductionism, the advent complexity science and network theory is an important part of a new trend where the structure of component relations is studied. I agree, I think more and more of natural science is turning to studying emergent behaviour, putting back together that what has been taken apart, and the rigorous theories developed over the years in mathematics, physics, and information theory are providing new ways in for instance in the social sciences.
There are also three good reviews in the issue, highlighting what perhaps are the main network science directions currently: the information theoretical view of a system, the analysis of structure in existing networks, and the simulation of dynamic systems as processes on networks.
Between order and chaos by James Crutchfield (doi:10.1038/nphys2190) address randomness and computational mechanics. Very nice review describing complexity from an information theoretical point of view, and therefore having a special place in my heart. Good if you are approaching the field, as I do, from that specific direction and have been telling yourself “Hey, this look awfully lot like computation to me.” It all comes down to -machines.
Communities, modules and large-scale structure in networks by M. E. J. Newman (doi:10.1038/nphys2162). Looking at structure, and communities in networks. Besides being an interesting problem, community detection has turned out to be a quite important problem in many applications (for example lumping you together with your social network friends in order to predict your behaviour — wait you did not think you were unique, did you?). Newman’s review is well written and I felt I knew the field better after reading it. Both the historic link to physics, the challenges, and the state of the research.
Modelling dynamical processes in complex socio-technical systems by Alessandro Vespignani (doi:10.1038/nphys2160) is an overview of what one may gain from viewing a complex system as a process on a network instead of as a compartmental model, and mean field approaches. Borrows the standard SI(R) examples from epidemiology, but it is of course the same process whether we talk about diffusion, epidemics, or memes on twitter.
The Insight issue also contain a progress article – Networks formed from interdependent networks by Gao et al. (doi:10.1038/nphys2180) – but I have to admit not having read it yet. It is more technical dealing with the issue of a network of networks. Something very interesting as I guess it may mean that some of the sub-networks are not any more in equilibrium, but also something I am not familiar with yet.
In any case, good stuff for a Sunday read, go grab the PDFs while you can!
If you still can’t get enough, or simply want a good introduction to the whole complexity thing, Newman has recently published another good general review Complex Systems: A Survey (properly in Am. J. Phys. 79, 800-810 (2011), I believe, but I took the liberty of linking to the arXiv.org preprint).