ArticleJournal of computational chemistry2015
Persistent homology for the quantitative prediction of fullerene stability.
Article in Journal of computational chemistry, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 30 papers.
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Who cites it
30 citing papers in PubMed.
- Topology-enhanced machine learning for speech signal processing.Nature communications · 2026Article
- Topological data analysis and topological deep learning beyond persistent homology: a review.Artificial intelligence review · 2026Article
- A Review of Topological Data Analysis and Topological Deep Learning in Molecular Sciences.Journal of chemical information and modeling · 2025Review
- Superionic Ionic Conductor Discovery via Multiscale Topological Learning.Journal of the American Chemical Society · 2025Article
- Persistent Topological Laplacians-A Survey.Mathematics (Basel, Switzerland) · 2025Article
- A machine learning based classifier for topological quantum materials.Scientific reports · 2024Article
- Persistent Mayer Dirac.Journal of physics. Complexity · 2024Article
- Understanding Changes in the Topology and Geometry of Financial Market Correlations during a Market Crash.Entropy (Basel, Switzerland) · 2021Article
- EVOLUTIONARY DE RHAM-HODGE METHOD.Discrete and continuous dynamical systems. Series B · 2021Article
- Exact Probability Landscapes of Stochastic Phenotype Switching in Feed-Forward Loops: Phase Diagrams of Multimodality.Frontiers in genetics · 2021Article
- Evolutionary homology on coupled dynamical systems with applications to protein flexibility analysis.Journal of applied and computational topology · 2020Article
- Persistent spectral graph.International journal for numerical methods in biomedical engineering · 2020Article
- The de Rham-Hodge Analysis and Modeling of Biomolecules.Bulletin of mathematical biology · 2020Article
- Topology-Based Machine Learning Strategy for Cluster Structure Prediction.The journal of physical chemistry letters · 2020Article
- A review of mathematical representations of biomolecular data.Physical chemistry chemical physics : PCCP · 2020Review
- MathDL: mathematical deep learning for D3R Grand Challenge 4.Journal of computer-aided molecular design · 2020Article
- Mathematical deep learning for pose and binding affinity prediction and ranking in D3R Grand Challenges.Journal of computer-aided molecular design · 2019Article
- Generative network complex (GNC) for drug discovery.Communications in information and systems · 2019Article
- Improved understanding of aqueous solubility modeling through topological data analysis.Journal of cheminformatics · 2018Article
- Protein pocket detection via convex hull surface evolution and associated Reeb graph.Bioinformatics (Oxford, England) · 2018Article
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4 authors.
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Abstract
Persistent homology is a relatively new tool often used for qualitative analysis of intrinsic topological features in images and data originated from scientific and engineering applications. In this article, we report novel quantitative predictions of the energy and stability of fullerene molecules, the very first attempt in using persistent homology in this context. The ground-state structures of a series of small fullerene molecules are first investigated with the standard Vietoris-Rips complex. We decipher all the barcodes, including both short-lived local bars and long-lived global bars arising from topological invariants, and associate them with fullerene structural details. Using accumulated bar lengths, we build quantitative models to correlate local and global Betti-2 bars, respectively with the heat of formation and total curvature energies of fullerenes. It is found that the heat of formation energy is related to the local hexagonal cavities of small fullerenes, while the total curvature energies of fullerene isomers are associated with their sphericities, which are measured by the lengths of their long-lived Betti-2 bars. Excellent correlation coefficients (>0.94) between persistent homology predictions and those of quantum or curvature analysis have been observed. A correlation matrix based filtration is introduced to further verify our findings.
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