Inferring collective dynamical states from subsampled systems

When studying the dynamics of complex systems, one can rarely sample the state of all components. We show that this spatial subsampling typically leads to severe underestimation of the risk of instability in systems with propagation of events. We analytically derived a subsampling-invariant estimator and applied it to non-linear network simulations and case reports of various diseases, recovering a close relation between vaccination rate and spreading behavior. The estimator can be particularly useful in countries with unreliable case reports, and promises early warning if e.g. antibiotic resistant bacteria increase their infectiousness. In neuroscience, subsampling has led to contradictory hypotheses about the collective spiking dynamics: asynchronous-irregular or critical. With the novel estimator, we demonstrated for rat, cat and monkey that collective dynamics lives in a narrow subspace between the two. Functionally, this subspace can combine the different computational properties associated with the two states.