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Measuring correlations in symbol sequences

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  • Herzel, Hanspeter
  • Große, Ivo

Abstract

The paper is devoted to relations between correlation functions and mutual information. It is shown that, in sequences over an alphabet of λ symbols, statistical dependences are measured by (λ − 1)2 independent parameters. However, not all of them can be determined by autocorrelation functions. Appropriate sets of correlation functions (including crosscorrelations) are introduced, which allow the detection of all dependences. The results are exemplified for binary, ternary, and quaternary symbol sequences. As an application, it is discussed that a nonuniform codon usage in protein-coding DNA sequences introduces periodic correlations even at distances in the order of 1000 base pairs.

Suggested Citation

  • Herzel, Hanspeter & Große, Ivo, 1995. "Measuring correlations in symbol sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 216(4), pages 518-542.
    • Handle: RePEc:eee:phsmap:v:216:y:1995:i:4:p:518-542
    DOI: 10.1016/0378-4371(95)00104-F
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    1. Leven, Charles L, 1986. "Analysis and Policy Implications of Regional Decline," American Economic Review, American Economic Association, vol. 76(2), pages 308-312, May.
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    Cited by:

    1. Ciorsac, Alecu & Craciun, Dana & Ostafe, Vasile & Isvoran, Adriana, 2011. "Nonlinear correlations in the hydrophobicity and average flexibility along the glycolytic enzymes sequences," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 191-197.
    2. Giovanni Villani, 2022. "Affinity and Correlation in DNA," J, MDPI, vol. 5(2), pages 1-18, April.
    3. Michael Schauperl & Julian E Fuchs & Birgit J Waldner & Roland G Huber & Christian Kramer & Klaus R Liedl, 2015. "Characterizing Protease Specificity: How Many Substrates Do We Need?," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-17, November.
    4. Rosenblum, Michael & Kurths, Jürgen, 1995. "A model of neural control of the heart rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 215(4), pages 439-450.
    5. Craciun, Dana & Isvoran, Adriana & Avram, N.M., 2009. "Long range correlation of hydrophilicity and flexibility along the calcium binding protein chains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4609-4618.
    6. Chapeau-Blondeau, François, 2007. "Autocorrelation versus entropy-based autoinformation for measuring dependence in random signal," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 1-18.
    7. Dehnert, M. & Helm, W.E. & Hütt, M.-Th., 2003. "A discrete autoregressive process as a model for short-range correlations in DNA sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 327(3), pages 535-553.
    8. Z S Hua & B Zhang & J Yang & D S Tan, 2007. "A new approach of forecasting intermittent demand for spare parts inventories in the process industries," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(1), pages 52-61, January.

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