Inference of Network Connectivity from Dynamics*

Many biological systems of interest can be represented as networks
of many nodes that interact with one another. Often these systems
are subject to external influence or noise. One challenging
problem is to infer the interaction pattern of the system or the
connectivity structure of the network from measurements. We have
developed methods that can infer the connectivity structure of the network
using only time-series measurements of the dynamics of the nodes.
Our methods are guided by noise-induced mathematical relations
between the network connectivity structure and quantities that can
be calculated using solely the time-series measurements of the
dynamics of the nodes. These mathematical relations show clearly
that statistical covariance or correlation is not the appropriate
indicator for connectivity or interaction. Instead, the relevant
quantity is the product of the time-lagged covariance matrix and
the inverse of the covariance matrix for general directed networks
with unidirectional coupling or the inverse of the covariance
matrix for undirected networks with bidirectional coupling. We
have tested and verified our methods using simulated data from
different networks and dynamics.