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This research aims to enhance the analysis of topological changes in evolving point clouds during dynamic phase transitions.

Beyond distance: quantifying point cloud dynamics with persistent homology and dynamic optimal transport

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This research aims to enhance the analysis of topological changes in evolving point clouds during dynamic phase transitions.
Introduced a hierarchical dynamic evaluation framework for analyzing topological structures.
Developed multi-scale indicators including topological distortion and persistence entropy.
Evaluated methods on various physical and biological dynamical systems.
The multi-scale indicators effectively captured significant structural reorganizations in the evaluated systems.
Macroscopic metrics showed global shifts while mesoscopic indicators revealed sensitive local rewirings.
Extensive evaluations validated the effectiveness of combining transport-based alignment with multi-scale entropy diagnostics.

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Randomized trial demonstrates new methods for analyzing dynamic point cloud structures, suggesting improved detection of transitions.

Wang et al. (2026) studied this question.

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