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Schlagwörter:
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Zusammenfassung:
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 nonequilibrium 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.
