4 papers
Weighted Hodge Laplacians on Manifolds with Boundary
Zhe Su, Yiying Tong, Guo-Wei Wei
The spectrum of the Hodge Laplacian on differential manifolds encodes rich topological and geometric information and thus provides a powerful tool for analyzing data on manifolds.…
Topological Learning Prediction of Virus-like Particle Stoichiometry and Stability
Xiang Liu, Xuefei Huang, Guo-Wei Wei
Understanding the stoichiometry and associated stability of virus-like particles (VLPs) is crucial for optimizing their assembly efficiency and immunogenic properties, which are es…
Topological Data Analysis and Topological Deep Learning Beyond Persistent Homology -- A Review
Zhe Su, Xiang Liu, Layal Bou Hamdan +4
Topological data analysis (TDA) is a rapidly evolving field in applied mathematics and data science that leverages tools from topology to uncover robust, shape-driven insights in c…
Manifold Topological Deep Learning for Biomedical Data
Xiang Liu, Zhe Su, Yongyi Shi +3
Recently, topological deep learning (TDL), which integrates algebraic topology with deep neural networks, has achieved tremendous success in processing point-cloud data, emerging a…