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In this paper we present a self-organizing neural network paradigm that is able to discriminate information locally using a strategy for information coding and processing inspired in recent findings in living neural systems. The proposed neural network uses: (1) neural signatures to identify each unit in the network; (2) local discrimination of input information during the processing; and (3) a multicoding mechanism for information propagation regarding the who and the what of the information. The local discrimination implies a distinct processing as a function of the neural signature recognition and a local transient memory. In the context of artificial neural networks none of these mechanisms has been analyzed in detail, and our goal is to demonstrate that they can be used to efficiently solve some specific problems. To illustrate the proposed paradigm, we apply it to the problem of multidimensional sorting, which can take advantage of the local information discrimination. In particular, we compare the results of this new approach with traditional methods to solve jigsaw puzzles and we analyze the situations where the new paradigm improves the performance.