Title: The topological inference and learning for cycles in networks

Abstract: Cycles or loops in a network embeds higher-order interactions beyond dyadic relations. The cycles are essential for the parallel processing of information and enable feedback loops. Despite the fundamental importance of cycles in networks, identifying and extracting them are computationally prohibitive. In this talk, we propose an efficient algorithm for the systematic identification and modeling of cycles using the persistent homology and the Hodge Laplacian. The method is applied to modeling human brain networks obtained from resting-state functional magnetic resonance imaging (MRI). The talk is based on Anand et al. 2022 (arXiv:2110.14599) and Songdechakraiwut and Chung 2022 (arXiv:2012.00675).

Shortbio:  Moo K. Chung, Ph.D. is an Associate Professor in the Department of Biostatistics and Medical Informatics at the University of Wisconsin-Madison (http://www.stat.wisc.edu/~mchung). He is also affiliated with the Waisman Laboratory for Brain Imaging and Behavior and the Department of Statistics. He participated in the World Class University Project at Seoul National University as a faulty between 2009-2013. Dr. Chung’s research focuses on topological data analysis, spectral geometry, computational neuroimaging and brain network analysis. His research concentrates on the methodological development required for quantifying and contrasting brain functional, anatomical shape and network variations in both normal and clinical populations using various mathematical, statistical and computational techniques. He has published three books on neuroimage computation including Brain Network Analysis that was published through Cambridge University Press in 2019.