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This paper presents a neural network with a novel neuron model. In this model, the neuron has two activation functions and exhibits a node-to-node relationship in the hidden layer. This neural network provides better performance than a traditional feedforward neural network, and fewer hidden nodes are needed. The parameters of the proposed neural network are tuned by a genetic algorithm with arithmetic crossover and nonuniform mutation. Some applications are given to show the merits of the proposed neural network.