2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/85155What determines the caliber of axonal branches? We pursue the hypothesis that the axonal caliber has evolved to minimize signal propagation delays, while keeping arbor volume to a minimum. We show that for a general cost function the optimal diameters of mother ($d_0$) and daughter ($d_1$, $d_2$) branches at a bifurcation obey a branching law: $d_{0}^{ν+2}=d_{1}^{ν+2} + d_{2}^{ν+2}$. The derivation relies on the fact that the conduction speed scales with the axon diameter to the power $ν$ ($ν=1$ for myelinated axons and $ν=0.5$ for non-myelinated axons). We test the branching law on the available experimental data and find a reasonable agreement.8 pages, 4 figuresBiological PhysicsCondensed MatterGeneral PhysicsNeurons and Cognitiontext