9 citations · 19 across the 14 of their papers we have counts for
7 papers · 1 filter
Parametrization of Symmetry in Data
Jian Liu, Dong Chen, Guo-Wei Wei
Symmetry plays a fundamental role in understanding natural phenomena and mathematical structures. This work develops a comprehensive theory for studying the persistent symmetries a…
Topological Sequence Analysis of Genomes: Delta Complex approaches
Jian Liu, Li Shen, Dong Chen +1
Algebraic topology has been widely applied to point cloud data to capture geometric shapes and topological structures. However, its application to genome sequence analysis remains…
Persistent interaction topology in data analysis
Jian Liu, Dong Chen, Guo-Wei Wei
Topological data analysis, as a tool for extracting topological features and characterizing geometric shapes, has experienced significant development across diverse fields. Its key…
Persistent Mayer homology and persistent Mayer Laplacian
Li Shen, Jian Liu, Guo-Wei Wei
In algebraic topology, the differential (i.e., boundary operator) typically satisfies . However, the generalized differential for an integer has been s…
Persistent Topological Laplacians -- a Survey
Xiaoqi Wei, Guo-Wei Wei
Persistent topological Laplacians constitute a new class of tools in topological data analysis (TDA). They are motivated by the necessity to address challenges encountered in persi…
Interaction homotopy and interaction homology
Jian Liu, Dong Chen, Guo-Wei Wei
Interactions in complex systems are widely observed across various fields, drawing increased attention from researchers. In mathematics, efforts are made to develop various theorie…
ChatGPT for Computational Topology
Jian Liu, Li Shen, Guo-Wei Wei
ChatGPT represents a significant milestone in the field of artificial intelligence (AI), finding widespread applications across diverse domains. However, its effectiveness in mathe…