  Recent studies have shown that functional brain brainwork is dynamic even
during rest. A common approach to modeling the brain network in whole brain
resting-state fMRI is to compute the correlation between anatomical regions via
sliding windows. However, the direct use of the sample correlation matrices is
not reliable due to the image acquisition, processing noises and the use of
discrete windows that often introduce spurious high-frequency fluctuations and
the zig-zag pattern in the estimated time-varying correlation measures. To
address the problem and obtain more robust correlation estimates, we propose
the heat kernel based dynamic correlations. We demonstrate that the proposed
heat kernel method can smooth out the unwanted high-frequency fluctuations in
correlation estimations and achieve higher accuracy in identifying dynamically
changing distinct states. The method is further used in determining if such
dynamic state change is genetically heritable using a large-scale twin study.
Various methodological challenges for analyzing paired twin dynamic networks
are addressed.
