Abstract
In previous studies for nuclear reactor kinetics0, the author developed a mathematical formulation for special form of binomial expansion which introduced a new mathematical representation of nuclear reactor kinetics. Further research by the author introduced a generalization of the developed expansion which is named the Embedded Pascal Triangles (EPTs) expansion which has applications in different disciplines. It is the objective of this paper to extend the applications of the introduced expansion from neutronics to genomics applications. Hence, the paper explores the attempt to reduce the representation complexity of the DNA sequencing of genomes which then minimizes computer storage. Also the paper presents an attempt for providing a generating function of the DNA sequencing of genomes via the use of the EPTs expansion. The result of the attempt established a generating function which is capable of providing the number of A, T, C, and G nucleotides in the genome, along with a number representing all the possible sequences of those nucleotides, of which only one corresponds to the complete nucleotides sequence of the genome in concern. Four numbers which are called the four genomic numbers (n, k, k', k") are used in the generating function to represent the number of nucleotides presented in the genome, and are used, as well, to represent the number of sequences (T) of those nucleotides, one of which corresponds to the complete sequence of the genome in consideration. Such T-number which is generated from the four genomic numbers, and the four genomic numbers themselves can be used for tagging of the genome in concern. Simple example was used to demonstrate the concept, and a tagging of the complete DNA sequence of the Hepatitis B Virus genome, using the tagger: T(n, k, k', k") is presented in this paper.