Hodge-Laplacian of Brain Networks and Its Application to Modeling Cycles.
D. Vijay Anand, Moo Kwon Chung · arXiv (Cornell University) · 2021
Decoding the closed loops amidst a myriad of connections in a brain network is the key to understand the feedback and synchronization. The closed loops or cycles in a brain network embeds higher order signal transmission paths, which provide fundamental insights into the functioning of the brain. In this work, we propose an efficient algorithm for systematic identification and modeling of 1-cycles using persistent homology and the Hodge-Laplacian. We validate the our methods on simulation and apply to human brain networks obtained through the resting state functional magnetic resonance images. New statistical inference procedures on 1-cycles are developed for discriminating male and female brain networks.