  The purpose of this paper is to infer a global (collective) model of
time-varying responses of a set of nodes as a dynamic graph, where the
individual time series are respectively observed at each of the nodes. The
motivation of this work lies in the search for a connectome model which
properly captures brain functionality upon observing activities in different
regions of the brain and possibly of individual neurons. We formulate the
problem as a quadratic objective functional of observed node signals over short
time intervals, subjected to the proper regularization reflecting the graph
smoothness and other dynamics involving the underlying graph's Laplacian, as
well as the time evolution smoothness of the underlying graph. The resulting
joint optimization is solved by a continuous relaxation and an introduced novel
gradient-projection scheme. We apply our algorithm to a real-world dataset
comprising recorded activities of individual brain cells. The resulting model
is shown to not only be viable but also efficiently computable.
