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
Igor Aizenberg and Claudio Moraga
It is shown in this paper that a model of multiple-valued 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 derivative-free 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 smaller MLMVN in comparison with a classical feedforward neural network.