Speaker
Description
Spatial networks reconstructed from microscopy such as mitochondrial, neuronal, and vascular networks are frequently modelled as embedded graphs whose edge weights depend on inter‑vertex distance. Uncertainty in vertex localisation arising from segmentation, registration, or temporal sampling introduces geometric perturbations that propagate nonlinearly into graph Laplacians. These perturbations induce structured spectral noise that is not captured by independent edge‑noise models.
We study the spectral effects of tempered heavy‑tailed vertex displacement in spatial graphs. We derive bounds showing that spectral fragility is governed by small geometric configurations:
extremal witness motifs saturate Weyl‑type eigenvalue inequalities and provide conservative envelopes on eigenvalue perturbations. This allows global sensitivity to be approximated through vertex‑disjoint motif tilings. To assess when spectral comparisons remain meaningful under geometric noise, we introduce stochastic spectral separation indices (S3I) that quantify whether observed spectral differences exceed noise‑induced variability. Experiments on spatial graph models and imaging‑derived networks reveal geometry‑dependent noise floors across organisational regimes ranging from sparse tubular mitochondrial networks to dense reticulated structures. These results identify when spectral differences reflect genuine biological reorganisation rather
than uncertainty in vertex localisation.
