One-Dimensional Cellular Automaton Transitions and Integral Value Transformations Representing Deoxyribonucleic Acid Sequence Evolutions
Sreeya Ghosh
Electronics and Communications Sciences Unit, Indian Statistical Institute
Kolkata-700108, India
sreeya135@gmail.com
Sudhakar Sahoo
Institute of Mathematics and Applications
Bhubaneshwar-751029, India
sudhakar.sahoo@gmail.com
Sk. Sarif Hassan
Department of Mathematics, Pingla Thana Mahavidyalaya
Paschim Medinipur-721140, India
sksarifhassan@pinglacollege.ac.in
Jayanta Kumar Das
School of Medicine, Johns Hopkins University
MD-21287, USA
Applied Statistics Unit, Indian Statistical Institute
Kolkata-700108, India
dasjayantakumar89@gmail.com
Pabitra Pal Choudhury
Applied Statistics Unit, Indian Statistical Institute
Kolkata-700108, India
pabitrapalchoudhury@gmail.com
Antara Sengupta
Department of Computer Science and Engineering, University of Calcutta
Kolkata-700009, India
antara.sngpt@gmail.com
Abstract
The cellular automaton (CA) and an integral value transformation (IVT) evolving in discrete time steps are two mathematical models that are well established. Theoretically, it can be suggested that a CA possesses the capacity to produce varieties of evolutionary patterns. However, computing a CA in higher dimensions or computing a nonlinear CA may be complex. In such cases, an IVT can be conveniently used. This paper presents the relation between the transition functions of a one-dimensional CA and an IVT. It also highlights the algebraic structures on the basis of binary operations for a set of transition functions of a one-dimensional CA and for a set of IVTs. The suitability of using an IVT over a CA is discussed. Also, we present the evolutionary models of two deoxyribonucleic acid (DNA) sequences through IVTs and their spacetime diagrams. This can eventually bring out some characteristic features of the evolutionary sequences.
Keywords: CA; IVT; mutation and crossover operations; DNA sequence evolution
Cite this publication as:
S. Ghosh, S. Sahoo, Sk. S. Hassan, J. K. Das, P. P. Choudhury and A. Sengupta, “One-Dimensional Cellular Automaton Transitions and Integral Value Transformations Representing Deoxyribonucleic Acid Sequence Evolutions,” Complex Systems, 32(2), 2023 pp. 115–138.
https://doi.org/10.25088/ComplexSystems.32.2.115
