CLEARMIND: Closed-Form Laplacian Embeddings of Arakelov-Green Resistance for Morphological Intrinsic Neuronal Distances

Excerpt

arXiv:2608.04460v2 Announce Type: replace-cross Abstract: Tropical geometry turns a metric graph into a flat torus, its tropical Jacobian, and measures distances between the images of its points by a closest vector problem on the period lattice. We prove that for points of the graph this problem is solved by geodesics: the squared tropical polarization distance equals the path metric minus the Arakelov-Green (AG) distance, an effective-resistance kernel given in closed form by the Laplacian pseu