Project Summary We will develop new large-scale dynamic embedding models of network data with a focus on dynamic connec- tivity matrices from non-stationary multivariate time series obtained from human functional magnetic resonance images (fMRI). We propose to model brain networks as 2D curved surfaces, where the surface geodesics give connectivity information. Our approach will bypass the use of parcellations and more accurately evaluate the evolutionary dynamics of functional brain networks at the voxel level. We propose to build dynamically changing functional brain networks from a dataset with 1206 subjects from the Human Connectome Project (HCP) database containing T1-weighted magnetic resonance images (MRI), diffusion MRI (dMRI) and task and resting-state functional MRI (fMRI). MRI and dMRI will be used in conjunction with fMRI in building more refined dynamic connectivity models. Using 243 pairs of twins in the HCP database, we will determine network phenotypes specific to behavior, cognition and their genetic associations. This study will provide the research community with the brain network heritability maps and as well as a versatile open-source toolbox of algorithms for modeling and visualizing dynamically changing large-scale brain networks.