Harmonic analysis of homogeneous networks.

We introduce a generalization of mutually inhibitory networks called homogeneous networks. Such networks have symmetric connection strength matrices that are circulant (one-dimensional case) or block circulant with circulant blocks (two-dimensional case). Fourier harmonics provide universal eigenvectors, and we apply them to several homogeneous examples: k-wta, k-cluster, on/center off/surround, and the assignment problem. We also analyze one nonhomogeneous case: the subset-sum problem. We present the results of 10000 trials on a 50-node k-cluster problem and 100 trials on a 25-node subset-sum problem.