  Epidemics, neural cascades, power failures, and many other phenomena can be
described by a diffusion process on a network. To identify the causal origins
of a spread, it is often necessary to identify the triggering initial node.
Here we define a new morphological operator and use it to detect the origin of
a diffusive front, given the final state of a complex network. Our method
performs better than randomized trials as well as centrality based methods.
More importantly, our method is applicable regardless of the specifics of the
forward model, and therefore can be applied to a wide range of systems such as
identifying the patient zero in an epidemic, pinpointing the neuron that
triggers a cascade, identifying the original malfunction that causes a
catastrophic infrastructure failure, and inferring the ancestral species from
which a heterogeneous population evolves.
