9 papers
Persistent local Laplacian prediction of protein-ligand binding affinities
Jian Liu, Hongsong Feng
Accurate prediction of protein-ligand binding affinity remains a central challenge in structure-based drug discovery. The effectiveness of machine learning models critically depend…
Local Laplacian: theory and models for data analysis
Jian Liu, Hongsong Feng, Kefeng Liu
While topological data analysis has emerged as a powerful paradigm for structural inference, its foundational tools, notably persistent homology and the persistent Laplacian, are f…
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…
Interaction Topological Transformer for Multiscale Learning in Porous Materials
Dong Chen, Jian Liu, Chun-Long Chen +1
Porous materials exhibit vast structural diversity and support critical applications in gas storage, separations, and catalysis. However, predictive modeling remains challenging du…
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.…
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…