![]() This is a remarkable result based on a simple algorithm of finite alternating sum series having independently distributed terms associated with just two indicators (0,1) for each of the nucleotide bases A, C, T or G. At any other point different from zero, the wavefunction with oscillatory behaviour for genome sequences is obtained. From the numerical point of view, these wavefunctions are here not quantum states of interest with a definite total physics energy, but rather an analogous mathematical construction. Since this wavefunction is discretized, one may think of it as a standing wave with zero nodes. These results are a consequence of factorizing the full wavefunction as the product of two different expressions i.e., a linear function proportional to the (0,1) binary sequences and a complex exponential form. Individually all the wavefunctions for a given n exhibit a set of zeros in their real and imaginary parts along the complete real \(1 \le k \le N\) axis. The arithmetic progression carries positive and negative signs \((-1)^=0\). For example, sonification algorithms based on biological rules for DNA sequence data use codons to generate strings of audio that are representative of ribonucleotides synthesized during transcription (see 9). The use of non-speech sounds in the biological context can be useful to identify trends in gene sequences and determinate its properties. Our motivation is to develop a simple algorithm to perform wave calculations from binary sequences and to apply these wave functions to sonification where inputs of zeros and ones are sufficient. The examples given in this context are selected as test for the mathematical conversion of binary sequences into isolate acoustic-like waves by appropriate formulas. the nucleotide bases display analogous features of sound waves. The real and imaginary parts of the longitudinal wavefunction vs. The complex wavefunction is seen as a mathematical description of an isolated, analogous quantum system. 4, the present approach is treated from the viewpoint of quantum theory as a measurement theory and not as being the atomic-level modelling of real quantum physical processes. We also compare results with random binary sequences.įollowing Ref. This novel approach allows to identify and ”observe” emergent properties of genome sequences in the form of wavefunctions via superposition states from a new perspective. It can reveal further unique imprints of the genome dynamics at the level of nucleotide ordering for different systems (or genome mutations) following experimental measures over N intervals. This quantum-based mathematical description is an extension of our previous GenomeBits model 7, 8. ![]() The purpose of this work is to introduce a wave-like function for complete genome sequences of pathogens represented by an alternating binary series having independently distributed terms associated with (0,1) binary indicators for the nucleotide bases. Motivated by these analogous representations, we apply in this work quantum formalism outside of physics to derive properties of binary sequences containing 0 and 1 distinct outcomes from a new perspective. Such parallel analyses have been useful to describe the rich complexity of diverse dynamical systems in terms of well-known physics phenomena and, therefore, best characterize the peculiarities of their behaviour. There exists also suggestive parallels between various aspects of number theory and physics phenomena 6. ![]() In 5, it has been argued how analogous Hawking radiation-like phenomena may arise in chaotic systems with exponential sensitivity to initial conditions (butterfly effect). ![]() In this study, biological functions such as psychological functions and epigenetic mutation are modelled in analogy with the physics of open quantum systems. A mathematical approach for the quantum information representation of biosystems has been introduced in 4. The thermodynamic interpretation of multifractality was established in 2, and an expression for an analogous specific heat in these systems was derived in 1.Īnother particularly interesting example is the 3D deformation of a compressible filament which has been modelled as the oscillation of a relativistic non-linear pendulum, where the compression modulus relates to the relativistic particle’s rest mass, and the bending modulus mimics the speed of light 3. These efforts have pursued analogies between stochastic models commonly used in the statistical physics of complex systems and stock market dynamics 1. This type of approach has been implemented in a wide range of applications, as for example in the domains of physics and finance. The derivation of analogous relationships between different disciplines has become increasingly popular in recent years.
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