Topological Metric Detects Hidden Order in Disordered Media
| Autor: | Boya Song, Hannah Jeckel, Joern Dunkel, Dominic J. Skinner, Knut Drescher, Eric Jelli |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Computer science
Entropy General Physics and Astronomy Non-equilibrium thermodynamics FOS: Physical sciences Condensed Matter - Soft Condensed Matter Topology 01 natural sciences Imaging data Models Biological Biophysical Phenomena Pattern Recognition Automated 0103 physical sciences Image Interpretation Computer-Assisted Animals Colloids 010306 general physics Condensed Matter - Statistical Mechanics Statistical Mechanics (cond-mat.stat-mech) Cryoelectron Microscopy Epithelial Cells Disordered Systems and Neural Networks (cond-mat.dis-nn) Condensed Matter - Disordered Systems and Neural Networks Models Theoretical Hidden order Graph Models Chemical Soft Condensed Matter (cond-mat.soft) RNA Drosophila Algorithms |
| Zdroj: | Physical Review Letters |
| Popis: | Recent advances in microscopy techniques make it possible to study the growth, dynamics, and response of complex biophysical systems at single-cell resolution, from bacterial communities to tissues and organoids. In contrast to ordered crystals, it is less obvious how one can reliably distinguish two amorphous yet structurally different cellular materials. Here, we introduce a topological earth mover's (TEM) distance between disordered structures that compares local graph neighborhoods of the microscopic cell-centroid networks. Leveraging structural information contained in the neighborhood motif distributions, the TEM metric allows an interpretable reconstruction of equilibrium and non-equilibrium phase spaces and embedded pathways from static system snapshots alone. Applied to cell-resolution imaging data, the framework recovers time-ordering without prior knowledge about the underlying dynamics, revealing that fly wing development solves a topological optimal transport problem. Extending our topological analysis to bacterial swarms, we find a universal neighborhood size distribution consistent with a Tracy-Widom law. Comment: 23 pages, 25 figures. Fly wing analysis extended; new bacterial swarming example added; co-authors added |
| Databáze: | OpenAIRE |
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