Symmetries in Complex Networks

Science Series Part III

Have you got any outstanding promises? Some minor job or task, that you said you would do years ago, and never got round to? Every day you wake up thinking “Gosh, I really need to get that done, after all, I said I would - but not today...”.

Well - I really can’t help you there. But I can report that with this post I’ve managed to get one such promise done: in August 2018 I said I would write a third post completing my trilogy on nonlinear networks, which I started writing during my internship at the University of Maryland!

How did I finally get the inspiration to put through with a post on Nonlinear Networks in our Lab and their relation to Symmetries? I have to confess, I’ve been smart here, and taken a shortcut: I realised that after all this time, I had in effect already written such a post: after my internship, I published a chapter on my work in the proceedings of the 2018 International Conference on Applications of Nonlinear Dynamics with my kind supervisors J.D. Hart, R. Roy & T.E.M. Murphy.

The chapter gives a neat summary of what I worked on - and has finally relieved me of my promise. It is endearing looking back at this early work, where I had just discovered the great power of symmetry for analysing problems. In hindsight, this was a rather elementary observation - but the interesting thing here was that my theorem applied quite well to the data produced by our nonlinear, noisy, partially symmetric system!

You can find our contributed chapter here, and the preprint here.

“Revealing Network Symmetries Using Time-Series Data”,
van Woerkom E.T.H.A., Hart J.D., Murphy T.E., Roy R. (2019).
Proceedings of the 5th International Conference on Applications in Nonlinear Dynamics.

Do you have similar work waiting on your to-do list?