Table of Contents Author Guidelines Submit a Manuscript
Computational and Mathematical Methods in Medicine
Volume 2012, Article ID 673934, 21 pages
http://dx.doi.org/10.1155/2012/673934
Research Article

On the Existence of Wavelet Symmetries in Archaea DNA

Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy

Received 13 September 2011; Revised 27 October 2011; Accepted 29 October 2011

Academic Editor: Sheng-yong Chen

Copyright © 2012 Carlo Cattani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. C. Cattani, “Complex representation of DNA sequences,” in Proceedings of the Bioinformatics Research and Development Second International Conference, M. Elloumi et al., Ed., Springer, Vienna, Austria, July 2008.
  2. C. Cattani, “Complex representation of DNA sequences,” Communications in Computer and Information Science, vol. 13, pp. 528–537, 2008. View at Google Scholar
  3. C. Cattani, “Wavelet Algorithms for DNA Analysis,” in Algorithms in Computational Molecular Biology: Techniques, Approaches and Applications, M. Elloumi and A. Y. Zomaya, Eds., Wiley Series in Bioinformatics, chapter 35, pp. 799–842, John Wiley & Sons, New York, NY, USA, 2010. View at Google Scholar
  4. C. Cattani, “Fractals and hidden symmetries in DNA,” Mathematical Problems in Engineering, vol. 2010, Article ID 507056, pp. 1–31, 2010. View at Publisher · View at Google Scholar · View at Scopus
  5. C. Cattani and G. Pierro, “Complexity on acute myeloid leukemia mRNA transcript variant,” Mathematical Problems in Engineering, vol. 2011, pp. 1–16, 2011. View at Publisher · View at Google Scholar
  6. C. Cattani, G. Pierro, and G. Altieri, “Entropy and multi-fractality for the myeloma multiple TET 2 gene,” Mathematical Problems in Engineering, vol. 2011, pp. 1–17, 2011. View at Publisher · View at Google Scholar
  7. C. Cattani and J. J. Rushchitsky, Wavelet and Wave Analysis as applied to Materials with Micro or Nanostructure, Series on Advances in Mathematics for Applied Sciences, vol. 74, World Scientific, Singapore, 2007.
  8. K. B. Murray, D. Gorse, and J. M. Thornton, “Wavelet transforms for the characterization and detection of repeating motifs,” Journal of Molecular Biology, vol. 316, no. 2, pp. 341–363, 2002. View at Publisher · View at Google Scholar · View at Scopus
  9. A. A. Tsonis, P. Kumar, J. B. Elsner, and P. A. Tsonis, “Wavelet analysis of DNA sequences,” Physical Review E, vol. 53, no. 2, pp. 1828–1834, 1996. View at Google Scholar · View at Scopus
  10. M. Altaiski, O. Mornev, and R. Polozov, “Wavelet analysis of DNA sequences,” Genetic Analysis—Biomolecular Engineering, vol. 12, no. 5-6, pp. 165–168, 1996. View at Publisher · View at Google Scholar · View at Scopus
  11. A. Arneodo, Y. D'Aubenton-Carafa, E. Bacry, P. V. Graves, J. F. Muzy, and C. Thermes, “Wavelet based fractal analysis of DNA sequences,” Physica D, vol. 96, no. 1–4, pp. 291–320, 1996. View at Google Scholar · View at Scopus
  12. M. Zhang, “Exploratory analysis of long genomic DNA sequences using the wavelet transform: examples using polyomavirus genomes,” in Proceedings of the 6th Genome Sequencing and Analysis Conference, pp. 72–85, 1995.
  13. C. Cattani, “Haar wavelet-based technique for sharp jumps classification,” Mathematical and Computer Modelling, vol. 39, no. 2-3, pp. 255–278, 2004. View at Google Scholar · View at Scopus
  14. C. Cattani, “Harmonic wavelet approximation of random, fractal and high frequency signals,” Telecommunication Systems, vol. 43, no. 3-4, pp. 207–217, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. M. Li, “Fractal time series-a tutorial review,” Mathematical Problems in Engineering, vol. 2010, Article ID 157264, pp. 1–26, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. M. Li and J. Y. Li, “On the predictability of long-range dependent series,” Mathematical Problems in Engineering, vol. 2010, Article ID 397454, pp. 1–9, 2010. View at Publisher · View at Google Scholar · View at Scopus
  17. M. Li and S. C. Lim, “Power spectrum of generalized Cauchy process,” Telecommunication Systems, vol. 43, no. 3-4, pp. 219–222, 2010. View at Publisher · View at Google Scholar · View at Scopus
  18. National Center for Biotechnology Information, http://www.ncbi.nlm.nih.gov/genbank.
  19. Genome Browser, http://genome.ucsc.edu.
  20. European Informatics Institute, http://www.ebi.ac.uk.
  21. Ensembl, http://www.ensembl.org.
  22. J. L. Howland, The Surprising Archaea, Oxford University Press, New York, NY, USA, 2000.
  23. C. R. Woese and G. E. Fox, “Phylogenetic structure of the prokaryotic domain: the primary kingdoms,” Proceedings of the National Academy of Sciences of the United States of America, vol. 74, no. 11, pp. 5088–5090, 1977. View at Google Scholar · View at Scopus
  24. M. T. Madigan and B. L. Marrs, “Extremophiles,” Scientific American, vol. 276, no. 4, pp. 82–87, 1997. View at Google Scholar · View at Scopus
  25. R. F. Voss, “Evolution of long-range fractal correlations and 1/f noise in DNA base sequences,” Physical Review Letters, vol. 68, no. 25, pp. 3805–3808, 1992. View at Publisher · View at Google Scholar · View at Scopus
  26. J. P. Eckmann, S. O. Kamphorst, and D. Ruelle, “Recurrence plots of dynamical systems,” Europhysics Letters, vol. 5, pp. 973–977, 1987. View at Google Scholar
  27. J. Szczepański and T. Michałek, “Random fields approach to the study of DNA chains,” Journal of Biological Physics, vol. 29, no. 1, pp. 39–54, 2003. View at Publisher · View at Google Scholar
  28. M. Stein and S. M. Ulam, “An observation on the distribution of primes,” American Mathematical Monthly, vol. 74, no. 1, p. 4344, 1967. View at Google Scholar
  29. C. Cattani, “Complexity and Simmetries in DNA sequences,” in Handbook of Biological Discovery, M. Elloumi and A. Y. Zomaya, Eds., Wiley Series in Bioinformatics, chapter 22, pp. 700–742, John Wiley & Sons, New York, NY, USA, 2012. View at Google Scholar
  30. M. A. Gates, “Simpler DNA sequence representations,” Nature, vol. 316, no. 6025, p. 219, 1985. View at Publisher · View at Google Scholar · View at Scopus
  31. M. A. Gates, “A simple way to look at DNA,” Journal of Theoretical Biology, vol. 119, no. 3, pp. 319–328, 1986. View at Google Scholar
  32. E. Hamori and J. Ruskin, “H curves, a novel method of representation of nucleotide series especially suited for long DNA sequences,” Journal of Biological Chemistry, vol. 258, no. 2, pp. 1318–1327, 1983. View at Google Scholar · View at Scopus
  33. J. A. Berger, S. K. Mitra, M. Carli, and A. Neri, “Visualization and analysis of DNA sequences using DNA walks,” Journal of the Franklin Institute, vol. 341, no. 1-2, pp. 37–53, 2004. View at Publisher · View at Google Scholar · View at Scopus
  34. P. Bernaola-Galván, R. Román-Roldán, and J. L. Oliver, “Compositional segmentation and long-range fractal correlations in DNA sequences,” Physical Review E, vol. 55, no. 5, pp. 5181–5189, 1996. View at Google Scholar · View at Scopus
  35. C. L. Berthelsen, J. A. Glazier, and M. H. Skolnick, “Global fractal dimension of human DNA sequences treated as pseudorandom walks,” Physical Review A, vol. 45, no. 12, pp. 8902–8913, 1992. View at Publisher · View at Google Scholar · View at Scopus
  36. P. R. Aldrich, R. K. Horsley, and S. M. Turcic, “Symmetry in the language of gene expression: a survey of gene promoter networks in multiple bacterial species and non-σ regulons,” Symmetry, vol. 3, pp. 1–20, 2011. View at Google Scholar
  37. R. Ferrer-I-Cancho and N. Forns, “The self-organization of genomes,” Complexity, vol. 15, no. 5, pp. 34–36, 2010. View at Publisher · View at Google Scholar · View at Scopus
  38. T. Misteli, “Self-organization in the genome,” Proceedings of the National Academy of Sciences of the United States of America, vol. 106, no. 17, pp. 6885–6886, 2009. View at Publisher · View at Google Scholar · View at Scopus
  39. C. E. Shannon, “A mathematical theory of communication,” The Bell System Technical Journal, vol. 27, pp. 379–423, 1948. View at Google Scholar
  40. C. E. Shannon, “A mathematical theory of communication,” The Bell System Technical Journal, vol. 27, pp. 623–656, 1948. View at Google Scholar
  41. R. V. Solé, “Genome size, self-organization and DNA's dark matter,” Complexity, vol. 16, no. 1, pp. 20–23, 2010. View at Publisher · View at Google Scholar · View at Scopus
  42. R. M. Yulmetyev, N. A. Emelyanova, and F. M. Gafarov, “Dynamical Shannon entropy and information Tsallis entropy in complex systems,” Physica A, vol. 341, no. 1–4, pp. 649–676, 2004. View at Publisher · View at Google Scholar · View at Scopus
  43. A. Arneodo, E. Bacry, P. V. Graves, and J. F. Muzy, “Characterizing long-range correlations in DNA sequences from wavelet analysis,” Physical Review Letters, vol. 74, no. 16, pp. 3293–3296, 1995. View at Publisher · View at Google Scholar · View at Scopus
  44. A. Arneodo, Y. D'Aubenton-Carafa, B. Audit, E. Bacry, J. F. Muzy, and C. Thermes, “What can we learn with wavelets about DNA sequences?” Physica A, vol. 249, no. 1–4, pp. 439–448, 1998. View at Google Scholar · View at Scopus
  45. W. Li, “The study of correlation structures of DNA sequences: a critical review,” Computers and Chemistry, vol. 21, no. 4, pp. 257–271, 1997. View at Google Scholar · View at Scopus
  46. C. Cattani, “Haar wavelets based technique in evolution problems,” Proceedings of the Estonian Academy of Sciences: Physics & Mathematics, vol. 53, no. 1, pp. 45–63, 2004. View at Google Scholar