Unsupervised learning applied to an unstructured neural network can give approximate solutions to the traveling salesman problem. For 50 cities in the plane this algorithm performs like the elasticâ€¦ (More)

The paper reviews some of the existing exact bounds to the maximum clique of a graph and successively presents a new upper and a new lower bound. The new upper bound is !6 n âˆ’ rank 1 A=2, where 1 Aâ€¦ (More)

combinatorial optimization is an active field of research in Neural Networks. Since the first attempts to solve the travelling salesman problem with Hopfield nets several progresses have been made. Iâ€¦ (More)

A self-organizing feature map (Von der Malsburg 1973; Kohonen 1984) sorts n real numbers in O(n) time apparently violating the O(n log n) bound. Detailed analysis shows that the net takes advantageâ€¦ (More)

The classical Cover results on linear separability of points in Rd are a milestone in neural network theory. Nevertheless they are not valid for digital input networks because in this case the pointsâ€¦ (More)

We present a new formulation of the maximum clique problem of a graph in complex space. We start observing that the adjacency matrix A of a graph can always be written in the form A = B where B is aâ€¦ (More)

In his seminal paper Cover used geometrical arguments to compute the probabilityofseparatingtwosetsof patterns witha perceptron. We extend these ideastofeedfonvard networks with hidden layers. Thereâ€¦ (More)

After a brief discussion of the computational complexity of Clifford algebras, we present a new basis for even Clifford algebra Cl 2m that simplifies greatly the actual calculations and, withoutâ€¦ (More)

The convex hull of any subset o f vertices of an n-dimensional hypercube contains no other vertex of the hypercube. This result permits the application of some theorems of n-dimensional geometry loâ€¦ (More)