Physics

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Complex systems are systems that, as a whole, are more than the sum of its parts. The best example I know is one I heard Thilo use: The molecules in a chicken, and the molecules in a can of chicken soup are pretty much the same. The difference between 'living' and 'ready-to-eatly dead' is not a difference in the constituents but rather a difference in their interaction. Living or dead are thus collective properties. Or, in the words of physics, 'emergent'.

A very exciting thing to do is to try understanding an emergent system-level property from the interactions of the microscopic constituent parts. That is where networks enter the stage: Networks consist of nodes, mirroring the constituents of a system, and links mirroring the interactions between them. Usually nodes and links are assigned with states, which change dynamically in time. Capturing both, the interaction structure (who is interacting with whom) as well as the interactive changes (how does x impinge on y), networks provide an excellent framework for hunting up the origin of emergent collective phenomena.

As often happens, the devil is in the details. In this case specifically: in the technical details. Classically, structure and dynamics, the two antithetical aspects of networks, are subject to different mathematical fields. Structure is typically studied in the framework of graph theory, dynamics in the framework of dynamical systems theory. Each of these theories comes with specific concepts, specific tools and a specific language. Trying to interlock them, to develop new analytical approaches and to apply these approaches for understanding collective phenomena in biological systems is what I do most of the day. And really enjoy doing.