Much of the recent interest in complex networks has been driven by the prospect that network optimization will help us understand the workings of evolutionary pressure in natural systems and the design of efficient engineered systems. In this talk, I will reflect on unanticipated attributes and artifacts in three classes of network optimization problems. First, I will discuss implications of optimization for the metabolic activity of living cells and its role in giving rise to the recently discovered phenomenon of synthetic rescues. Then I will comment on the problem of controlling network dynamics and show that theoretical results on optimizing the number of driver nodes/variables often only offer a conservative lower bound to the number actually needed in practice. Finally, I will discuss the sensitive dependence of network dynamics on network structure that emerges in the optimization of network topology for dynamical processes governed by eigenvalue spectra, such as synchronization and consensus processes. Optimization is a double-edged sword for which desired and adverse effects can be exacerbated in complex network systems due to the high dimensionality of their dynamics.
- Industrial and Applied Mathematics Seminar