  We consider the inverse boundary value problem in the case of discrete
electrical networks containing nonlinear (non-ohmic) resistors. Generalizing
work of Curtis, Ingerman, Morrow, Colin de Verdiere, Gitler, and Vertigan, we
characterize the circular planar graphs for which the inverse boundary value
problem has a solution in this generalized non-linear setting. The answer is
the same as in the linear setting. Our method of proof never requires that the
resistors behave in a continuous or monotone fashion; this allows us to recover
signed conductances in many cases. We apply this to the problem of recovery in
graphs that are not circular planar. We also use our results to make a
frivolous knot-theoretic statement, and to slightly generalize a fact proved by
Lam and Pylyavskyy about factorization schemes in their electrical linear
group.
