9 citations · 19 across the 14 of their papers we have counts for
14 papers
Khovanov homology of tangles: algorithm and computation
Li Shen, Jian Liu, Guo-Wei Wei
Knot, link, and tangle theory is crucial in both mathematical theory and practical application, including quantum physics, molecular biology, and structural chemistry. Unlike knots…
Computing Khovanov homology of tangles
Li Shen, Jian Liu, Guo-Wei Wei
The computation of Khovanov homology for tangles has significant potential applications, yet explicit computational studies remain limited. In this work, we present a method for co…
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…
Topological Sequence Analysis of Genomes: Category theory Approaches
Jian Liu, Li Shen, Mushal Zia +1
Sequence data, such as DNA, RNA, and protein sequences, exhibit intricate, multi-scale structures that pose significant challenges for conventional analysis methods, particularly t…
Persistent Khovanov homology of tangles
Jian Liu, Li Shen, Guo-Wei Wei
Knot data analysis (KDA), which studies data with curve-type structures such as knots, links, and tangles, has emerging as a promising geometric topology approach in data science.…
Mayer-homology learning prediction of protein-ligand binding affinities
Hongsong Feng, Li Shen, Jian Liu +1
Artificial intelligence-assisted drug design is revolutionizing the pharmaceutical industry. Effective molecular features are crucial for accurate machine learning predictions, and…
Evolutionary Khovanov homology
Li Shen, Jian Liu, Guo-Wei Wei
Knot theory is a study of the embedding of closed circles into three-dimensional Euclidean space, motivated the ubiquity of knots in daily life and human civilization. However, the…
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…
Knot data analysis using multiscale Gauss link integral
Li Shen, Hongsong Feng, Fengling Li +3
In the past decade, topological data analysis (TDA) has emerged as a powerful approach in data science. The main technique in TDA is persistent homology, which tracks topological i…