Wave-like behaviour in (0,1) binary sequences

Abstract

AbstractA comprehensive study of the properties of finite (0,1) binary systems from the mathematical viewpoint of quantum theory is presented. This is a quantum-inspired extension of the GenomeBits model to characterize observed genome sequences, where a complex wavefunction $$\psi _{n}$$ ψ n is considered as an analogous probability measure and it is related to an alternating (0,1) binary series having independent distributed terms. The real and imaginary spectrum of $$\psi _{n}$$ ψ n vs. the nucleotide base positions display characteristic features of sound waves. This approach represents a novel perspective for identifying and “observing” emergent properties of genome sequences in the form of wavefunctions via superposition states. The motivation is to develop a simple algorithm to perform wave calculations from binary sequences and to apply these wave functions to sonification.