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Links between topology and controllability

April 12, 2016
Presenters: Colin Campbell
Length: 24 minutes 17 seconds

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The topology of a network provides a substrate upon which dynamical processes may occur; understanding the manner in which topology constrains dynamics is therefore central to our ability to predict and influence the behavior of complex systems. Recent work has considered canonical linear dynamics, where the state variable associated with a node varies according to the summative influence of the node's regulators. Under these dynamics, the control-related properties of networks are differentiated only by their topological structure. As such, analyzing the relationships between network topology and control-related properties offers a rich avenue for characterizing networks in a way that complements traditional measures such as the degree distribution.

For instance, it has been shown that under these dynamics it is possible to drive a network to any state in finite time by directly controlling a (typically small) subset of its nodes. In a given network, how many nodes must be directly controlled to achieve complete control over the network? Are these nodes uniquely defined, or can multiple sets of nodes be used to populate the so-called minimal driver set? Where are these nodes located in the network? What about a network's topological structure determines the answers to these questions? This presentation will address these and related questions, with an emphasis on the unique control-related characteristics of different classes of synthetic and empirical networks.