The Genetic Code as a Function of Multiple-Valued Logic Over the Field of Complex Numbers and its Learning using Multilayer Neural Network Based on Multi-Valued Neurons

It is shown in this paper that a model of multiplevalued logic over the field of complex numbers is the most appropriate for the representation of the genetic code as a multiple-valued function. The genetic code is considered as a partially defined multiple-valued function of three variables. The genetic code is the four-letter nucleic acid code, and it is translated into a 20-letter amino acid code from proteins (each of 20 amino acids is coded by the triplet of four nucleic acids). Thus, it is possible to consider the genetic code as a partially defined multiple-valued function of a 20-valued logic. Consideration of the genetic code within the proposed mathematical model makes it possible to learn the code using a multilayer neural network based on multi-valued neurons (MLMVN). MLMVN is a neural network with traditional feedforward architecture, but with a highly efficient derivativefree learning algorithm and higher functionality than the one of the traditional feedforward neural networks and a variety of kernel-based networks. It is shown that the genetic code multiple-valued function can be easily trained by a significantly * Based on "The Genetic Code as a Multiple-Valued Function and its Implementation Using Multilayer Neural Network based on Multi-Valued Neurons ", by Igor Aizenberg and Claudio Moraga which appeared in The Proceedings of 37 International Symposium on MultipleValued Logic (ISMVL-2007), © 2007 IEEE IGOR AIZENBERG AND CLAUDIO MORAGA, JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING, NO 4-6, NOVEMBER 2007, PP. 605-618 smaller MLMVN in comparison with a classical feedforward neural network.