The Brain Connectivity Workshop is my first neuroscience excursion so I have been totally nerding out for the last two days. I am pleased to find such friendly and interesting people. My main interest here is network topology and dynamics. There has been a lot of talk about networks that display small world topological properties (i.e. small characteristic path length between any two nodes and a high cluster index in the network as a whole), as well as talk about the brains fractal and modular formation. As I am sure you are all aware these three properties are mutually compatible.
There was a very interesting talk today by Danielle Bassett form Cambridge University, who along with her colleagues has been studying network organisation properties in both artificial VLSI integrated computer circuits as well as animal brains. Her proposal is that all physical information processing systems share modular organisational properties. The brain was shown to display hierarchical formations which at each level can be modularised. Bassett also showed that the cost entailed in physical wiring was not strictly minimized, but that there is a trade off between this cost and topological complexity which gives rise to fractal and modular designs. In addition she illustrated how volume ratios between gray matter (which contain neural cell bodies) and white matter (which contains axonal connections) across a wide range of mammals remain similar. Interestingly VLSI circuits display an isometric scaling relationship between the number of connections and the number of processing elements. For more details read here.