Speaker
Description
Spatial biological networks derived from microscopy are commonly represented as embedded graphs whose topology reflects underlying organisation. Subtle precursor events often precede visible structural reorganisation: for example, branch migration preceding mitochondrial fission, local neurite remodelling in dendritic arbors, or early junction displacement in microvascular networks. Detecting these weak structural signals is challenging because vertex localisation uncertainty and geometric noise dilute graph‑distance comparisons as network size increases. We introduce ROSA, a geometric spectral lift that transforms a base graph distance into an integrated distance along a filtration that removes edges according to spectral sensitivity. By
accumulating metric variation along this path, ROSA amplifies localised structural edits that would otherwise be obscured by noise or scale. We prove that ROSA defines a metric under mild conditions and derive an anti‑dilution inequality showing that, for localised perturbations
on growing graphs, ROSA retains strictly stronger signal than the base distance. Symmetric geometries provide explicit regimes where amplification cannot occur. Experiments on spatial graph models and imaging‑derived networks—including mitochondrial
and vascular networks—demonstrate improved recovery of pre‑reorganisation signals under heavy vertex noise when ROSA is applied to spectral and diffusion‑based graph distances.
