演講者：胡全燊博士 ( 新加坡南洋理工大學數理科學院 )

日   期：2025 年 08 月 25 日（星期一）13:30

地   點：國立高雄大學理學院 408 室

講   題：A Sheaf-Theoretic Perspective on Normal Mode Analysis

摘   要：

Normal mode analysis (NMA) characterizes intrinsic molecular dynamics by identifying normal modes—eigenvectors of the Hessian matrix—whose small non-zero eigenvalues often correspond to functional motions. Building on the anisotropic network model (ANM), we establish a sheaf-theoretic framework by defining an anisotropic sheaf on undirected, simple graphs, where the conventional Hessian is interpreted as the sheaf Laplacian of this cellular sheaf. In this formulation, zero-eigenvalue modes correspond exactly to a basis of global sections, offering a direct topological interpretation of rigid body motions. We analyze the dimension of the global section space under standard NMA assumptions, linking it to the harmonic signal space of the sheaf. Furthermore, we propose a streamlined, Delaunay triangulation–based graph construction that preserves the correct number of zero modes while improving computational efficiency. This connection between NMA and sheaf theory provides a rigorous topological foundation for interpreting and optimizing ANM computations, with potential for topology-aware strategies in biomolecular modeling.