Layered Networks

Laura Kang
Laura Negrin

David Ingerman introduced a characterization for Dirichlet-to-Neumann
maps of discrete layered networks in terms of their eigenvalues.  Here
we introduce an alternate characterization for Dirichlet-to-Neumann
maps of layered networks with 7 radial lines and 2 layers, also in
terms of their eigenvalues, which we find much simpler to evaluate, if
less general.  We also explicitly show that the characterization
givien in Ingerman's paper holds for layered networks with n radial
lines and 1 layer.

1. Introduction
1.1 Discrete layered networks and the eigenvalues of their Dirichlet-to-Neumann
    maps
1.2 Characterization of the Dirichlet-to-Neumann maps
2. \Lambda_\gamma for D(7,2) and D*(7,2)
2.1 rank 2 condition on L_1 and L_2
2.2 Characterization of \Lambda_\gamma for D(7,2) and D*(7,2)
3. D(n,1) and D*(n,1)