Electrical Kalmanson Metrics and the Positive Isotropic Grassmannian in Combinatorics
A geometric characterization of which Kalmanson metrics arise as the resistance metric of a circular electrical network. Students learn to read an electrical network's resistance and response matrices as a dissimilarity and a similarity function related by the Farris transform (Gromov product), to recognize that the resistance metric of a circular network is a Kalmanson metric, and to place these electrical Kalmanson metrics inside the full space of Kalmanson metrics through the geometry of the positive isotropic Grassmannian. The correspondence lets network-reconstruction methods for electrical networks be carried over to phylogenetic networks and split-based data analysis.
ELECTRICAL NETWORKS AND DATA ANALYSIS IN PHYLOGENETICS V. GORBOUNOV AND A. KAZAKOV Abstract. A
This paper studies electrical networks - graphs with positive edge conductances and a distinguished set of boundary nodes - through the lens of data analysis. Two functions on the nodes describe such…