The Hopfield neural network for optimization problems often falls into local minima. To escape from the local minima, the neuron unit in the neural network is modified to become an oscillatory unit by adding a simple self-feedback circuit. By combining the oscillatory unit with an energy-value extraction circuit, an oscillatory neural network is constructed. The network can repeatedly extract solutions, and can simultaneously evaluate them. In this paper, the network is applied to four NP-complete problems to demonstrate its generality and efficiency. The network can solve each problem and can obtain better solutions than the original Hopfield neural network and simple algorithms.

ZCZ sets are families of sequences, whose periodic auto/cross-correlation functions have zero correlation zone at the both side of the zero-shift. They can provide approximately synchronized CDMA systems without intra-cell interference for cellular mobile communications. This paper presents ternary ZCZ sets achieving a mathematical bound, and investigates the average interference parameters for the sets in order to evaluate inter-cell interference. It is shown that they can provide AS-CDMA systems with efficiency frequency usage.