Robot architectures and design paradigms
William J. Wolfe, Wendell H. Chun · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1993
We introduce a generalization of mutually inhibitory networks, and call them homogeneous networks, and provide the harmonic analysis for all such networks. The critical features of such networks are (1) the connection strength matrix is a circulant, symmetric, Toeplitz matrix; and (2) the discrete fourier transform of the first row of the connection strength matrix provides the eigenvalues of the matrix; and (3) the corresponding eigenspaces are spanned by the discrete harmonics from fourier analysis. We apply these ideas to k-winner, k-cluster, on- center off-surround, and knapsack problems, with some thoughts about how to generalize the results to 2 dimensions for problems such as the Assignment Problem and the Traveling Salesman Problem.