  A key question in modern neuroscience is how cognitive changes in a human
brain can be quantified and captured by functional connectomes (FC) . A
systematic approach to measure pairwise functional distance at different brain
states is lacking. This would provide a straight-forward way to quantify
differences in cognitive processing across tasks; also, it would help in
relating these differences in task-based FCs to the underlying structural
network. Here we propose a framework, based on the concept of Jensen-Shannon
divergence, to map the task-rest connectivity distance between tasks and
resting-state FC. We show how this information theoretical measure allows for
quantifying connectivity changes in distributed and centralized processing in
functional networks. We study resting-state and seven tasks from the Human
Connectome Project dataset to obtain the most distant links across tasks. We
investigate how these changes are associated to different functional brain
networks, and use the proposed measure to infer changes in the information
processing regimes. Furthermore, we show how the FC distance from resting state
is shaped by structural connectivity, and to what extent this relationship
depends on the task. This framework provides a well grounded mathematical
quantification of connectivity changes associated to cognitive processing in
large-scale brain networks.
