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

TL;DR

This paper explores wave-like properties in binary (0,1) sequences inspired by quantum theory, extending genome sequence analysis with a complex wavefunction model that reveals sound wave characteristics.

Contribution

It introduces a quantum-inspired model for binary sequences, linking genome data to wave phenomena and analyzing spectral features related to nucleotide positions.

Findings

Binary sequences exhibit wave-like spectral features.

Real and imaginary spectra resemble sound waves.

Model extends genome analysis with quantum-inspired wavefunctions.

Abstract

This work presents a comprehensive study of the properties of finite (0,1) binary systems from the mathematical viewpoint of quantum theory where a complex wavefunction $\psi_{n}$ is considered as an analogous probability measure. This is a quantum-inspired extension of the GenomeBits model to characterise observed genome sequences, where $\psi_{n}$ is related to an alternating (0,1) binary series having independent distributed terms. The real and imaginary spectrum of $\psi_{n}$ {\emph vs.} the nucleotide base positions display characteristic features of sound waves.