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**1 - 8**of**8**### The Double-Helix Pattern of Prime Number Growth

"... Abstract—This paper is the result of analyzing the growth pattern of the first 500 prime numbers. The growth rate was found to be related to two characteristics – two parallel threads and the almost viral impact of the multiples of 6 on these two threads. When corresponding cause and effect of these ..."

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Abstract—This paper is the result of analyzing the growth pattern of the first 500 prime numbers. The growth rate was found to be related to two characteristics – two parallel threads and the almost viral impact of the multiples of 6 on these two threads. When corresponding cause and effect of these impacts are overlaid, a double-helix structure is the result. This concept and modeling approach is submitted with the hope of providing a model that helps connect the research benefits of bioinformatics and the potential impact of the prime number structure of the Riemann Hypothesis when applied by professionals in their scientific computing fields. Index Terms—Double-helix, gap, growth, prime numbers. I.

### Quantumlike Chaos in the Frequency Distributions of Bases A, C, G, T in Human Chromosome1 DNA

, 2004

"... Introduction DNA topology is of fundamental importance for a wide range of biological processes [1]. Since the topological state of genomic DNA is of importance for its replication, recombination and transcription, there is an immediate interest to obtain information about the supercoiled state fro ..."

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Introduction DNA topology is of fundamental importance for a wide range of biological processes [1]. Since the topological state of genomic DNA is of importance for its replication, recombination and transcription, there is an immediate interest to obtain information about the supercoiled state from sequence periodicities [2,3]. Identification of dominant periodicities in DNA sequence will help understand the important role of coherent structures in genome sequence organization [4,5]. Li [6] has discussed meaningful applications of spectral analyses in DNA sequence studies. Recent studies indicate that the DNA sequence of letters A, C, G and T exhibit the inverse power law form 1/f frequency spectrum where f is the frequency and a the exponent. It is possible, therefore, that the sequences have longrange order [7-14]. Inverse power-law form for power spectra of fractal space-time fluctuations is generic to dynamical systems in nature and is identified as self-organized criticality

### C. Roy Keys Inc.

"... this paper to derive the fundamental equation of the kinetic theory of ideal gases and the Maxwell's distribution of molecular speeds ..."

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this paper to derive the fundamental equation of the kinetic theory of ideal gases and the Maxwell's distribution of molecular speeds

### Universal Spectrum for DNA Base C+G Concentration Variability in Human Chromosome Y

"... Abstract:- The spatial distribution of DNA base sequence A, C, G and T exhibit selfsimilar fractal fluctuations and the corresponding power spectra follow inverse power law of the form 1/fα where f is the frequency and α the exponent. Inverse power law form for power spectra implies long-range spati ..."

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Abstract:- The spatial distribution of DNA base sequence A, C, G and T exhibit selfsimilar fractal fluctuations and the corresponding power spectra follow inverse power law of the form 1/fα where f is the frequency and α the exponent. Inverse power law form for power spectra implies long-range spatial correlations of the eddy fluctuations. Multifractal structure to space-time fluctuations and the associated inverse power law form for power spectra is generic to spatially extended dynamical systems in nature and is a signature of self-organized criticality. The exact physical mechanism for the observed self-organized criticality is not yet identified. The author has developed a general systems theory where quantum mechanical laws emerge as self-consistent explanations for the observed long-range space-time correlations, i.e. the apparently chaotic fractal fluctuations are signatures of quantum-like chaos in dynamical systems. The model also provides unique quantification for the observed inverse power law form for power spectra in terms of the statistical normal distribution. In this paper it is shown that the frequency distribution of the bases C+G in all available contiguous sequences for Human chromosome Y DNA exhibit model predicted quantum-like chaos. Key-Words:- fractals, chaos, self-organized criticality, quasicrystalline structure, quantumlike chaos 1

### 1 Fractal space-time fluctuations: A signature of quantumlike chaos in dynamical systems

"... Dynamical systems in nature such as fluid flows, heart beat patterns, rainfall variability, stock market price fluctuations, etc. exhibit selfsimilar fractal fluctuations characterized by a zigzag (an increase followed by a decrease and vice-versa) curve on all scales in space and time. Power spectr ..."

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Dynamical systems in nature such as fluid flows, heart beat patterns, rainfall variability, stock market price fluctuations, etc. exhibit selfsimilar fractal fluctuations characterized by a zigzag (an increase followed by a decrease and vice-versa) curve on all scales in space and time. Power spectral analyses of fractal fluctuations exhibit inverse power law form indicating long-range space-time correlations, identified as self-organized criticality. Mathematical models for simulation and prediction of dynamical systems are nonlinear so that analytical solutions are not available. Finite precision computed solutions are sensitively dependent on initial conditions and give chaotic solutions, identified as deterministic chaos. The author has proposed a general systems theory, which predicts the observed fractal fluctuations as signatures of quantumlike chaos. The model visualizes the irregular fluctuations to result from the superimposition of a continuum of eddies where the dominant component

### in Human Chromosome1 DNA

"... Abstract:- Recent studies of DNA sequence of letters A, C, G and T exhibit the inverse power law form frequency spectrum. Inverse power-law form of the power spectra of fractal space-time fluctuations is generic to the dynamical systems in nature and is identified as self-organized criticality. In t ..."

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Abstract:- Recent studies of DNA sequence of letters A, C, G and T exhibit the inverse power law form frequency spectrum. Inverse power-law form of the power spectra of fractal space-time fluctuations is generic to the dynamical systems in nature and is identified as self-organized criticality. In this study it is shown that the power spectra of the frequency distributions of bases A, C, G, T in the Human chromosome 1 DNA exhibit self-organized criticality. DNA is a quasicrystal possessing maximum packing efficiency in a hierarchy of spirals or loops. Self-organized criticality implies that non-coding introns may not be redundant, but serve to organize the effective functioning of the coding exons in the DNA molecule as a complete unit.

### Universal spectrum for DNA base C+G frequency distribution in human

, 2008

"... Abstract. Power spectra of human DNA base C+G frequency distribution in all available contiguous sections exhibit the universal inverse power law form of the statistical normal distribution for the 24 chromosomes. Inverse power law form for power spectra of space-time fluctuations is generic to dyna ..."

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Abstract. Power spectra of human DNA base C+G frequency distribution in all available contiguous sections exhibit the universal inverse power law form of the statistical normal distribution for the 24 chromosomes. Inverse power law form for power spectra of space-time fluctuations is generic to dynamical systems in na-ture and indicate long-range space-time correlations. A recently developed general systems theory predicts the observed non-local connections as intrinsic to quantumlike chaos governing space-time fluctuations of dynamical systems. The model predicts the following. (1) The quasiperiodic Penrose tiling pattern for the nested coiled structure of the DNA molecule in the chromosome resulting in maximum packing efficiency. (2) The DNA molecule functions as a unified whole fuzzy logic network with ordered two-way signal trans-mission between the coding and non-coding regions. Recent studies indicate influence of non-coding regions on functions of coding regions in the DNA molecule.