- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 507056, 31 pages
Fractals and Hidden Symmetries in DNA
Department of Pharmaceutical Sciences, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy
Received 27 January 2010; Accepted 8 March 2010
Academic Editor: Cristian Toma
Copyright © 2010 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.
- J. P. Fitch and B. Sokhansanj, “Genomic engineering: moving beyond DNA sequence to function,” Proceedings of the IEEE, vol. 88, no. 12, pp. 1949–1971, 2000.
- H. Gee, “A journey into the genome: what's there,” Nature, 2001, http://www.nature.com/nsu/010215/010215-3.html.
- National Center for Biotechnology Information, http://www.ncbi.nlm.nih.gov/genbank/.
- Genome Browser, http://genome.ucsc.edu/.
- European Informatics Institute, http://www.ebi.ac.uk/.
- Ensembl, http://www.ensembl.org.
- C. Cattani and J. J. Rushchitsky, Wavelet and Wave Analysis as Applied to Materials with Micro or Nanostructure, vol. 74 of Series on Advances in Mathematics for Applied Sciences, World Scientific, Singapore, 2007.
- P. D. Cristea, “Large scale features in DNA genomic signals,” Signal Processing, vol. 83, no. 4, pp. 871–888, 2003.
- 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.
- C. Cattani, “Complex representation of DNA sequences,” in Proceedings of the 2nd International Conference Bioinformatics Research and Development (BIRD '08), M. Elloumi, et al., Ed., vol. 13 of Communications in Computer and Information Science, pp. 528–537, Springer, Vienna, Austria, July 2008.
- 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, Wiley-Blackwell, New York, NY, USA, 2010.
- R. F. Voss, “Evolution of long-range fractal correlations and noise in DNA base sequences,” Physical Review Letters, vol. 68, no. 25, pp. 3805–3808, 1992.
- F. Voss, “Long-range fractal correlations in DNA introns and exons,” Fractals, vol. 2, pp. 1–6, 1992.
- C. Cattani, “Haar wavelet-based technique for sharp jumps classification,” Mathematical and Computer Modelling, vol. 39, no. 2-3, pp. 255–278, 2004.
- C. Cattani, “Haar wavelets based technique in evolution problems,” Proceedings of the Estonian Academy of Sciences, Physics and Mathematics, vol. 53, no. 1, pp. 45–63, 2004.
- 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.
- M. Altaiski, O. Mornev, and R. Polozov, “Wavelet analysis of DNA sequences,” Genetic Analysis, vol. 12, no. 5-6, pp. 165–168, 1996.
- 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.
- 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.
- C. Cattani, “Harmonic wavelet approximation of random, fractal and high frequency signals,” Telecommunication Systems, vol. 43, no. 3-4, pp. 207–217, 2010.
- M. Li, “Fractal time series—a tutorial review,” Mathematical Problems in Engineering, vol. 2010, Article ID 157264, 26 pages, 2010.
- M. Li and J.-Y. Li, “On the predictability of long-range dependent series,” Mathematical Problems in Engineering, vol. 2010, Article ID 397454, 9 pages, 2010.
- M. Li and S. C. Lim, “Power spectrum of generalized Cauchy process,” Telecommunication Systems, vol. 43, no. 3-4, pp. 219–222, 2010.
- 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.
- B. Audit, C. Vaillant, A. Arneodo, Y. D'Aubenton-Carafa, and C. Thermes, “Long-range correlations between DNA bending sites: relation to the structure and dynamics of nucleosomes,” Journal of Molecular Biology, vol. 316, no. 4, pp. 903–918, 2002.
- B. Borstnik, D. Pumpernik, and D. Lukman, “Analysis of apparent spectrum in DNA sequences,” Europhysics Letters, vol. 23, pp. 389–394, 1993.
- S. V. Buldyrev, A. L. Goldberger, S. Havlin, et al., “Long-range correlation properties of coding and noncoding DNA sequences: GenBank analysis,” Physical Review E, vol. 51, no. 5, pp. 5084–5091, 1995.
- H. Herzel, E. N. Trifonov, O. Weiss, and I. Große, “Interpreting correlations in biosequences,” Physica A, vol. 249, no. 1–4, pp. 449–459, 1998.
- W. Li, “The study of correlation structures of DNA sequences: a critical review,” Computers and Chemistry, vol. 21, no. 4, pp. 257–271, 1997.
- W. Li and K. Kaneko, “Long-range correlations and partial spectrum in a noncoding DNA sequence,” Europhysics Letters, vol. 17, pp. 655–660, 1992.
- C.-K. Peng, S. V. Buldyrev, A. L. Goldberger, et al., “Long-range correlations in nucleotide sequences,” Nature, vol. 356, no. 6365, pp. 168–170, 1992.
- C.-K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley, and A. L. Goldberger, “Mosaic organization of DNA nucleotides,” Physical Review E, vol. 49, no. 2, pp. 1685–1689, 1994.
- O. Weiss and H. Herzel, “Correlations in protein sequences and property codes,” Journal of Theoretical Biology, vol. 190, no. 4, pp. 341–353, 1998.
- Z.-G. Yu, V. V. Anh, and B. Wang, “Correlation property of length sequences based on global structure of the complete genome,” Physical Review E, vol. 63, no. 1, Article ID 011903, 8 pages, 2001.
- P. P. Vaidyanathan and B.-J. Yoon, “The role of signal-processing concepts in genomics and proteomics,” Journal of the Franklin Institute, vol. 341, no. 1-2, pp. 111–135, 2004.
- P. Bernaola-Galván, R. Román-Roldán, and J. L. Oliver, “Compositional segmentation and long-range fractal correlations in DNA sequences,” Physical Review E, vol. 53, no. 5, pp. 5181–5189, 1996.
- W. Li, “The complexity of DNA: the measure of compositional heterogenity in DNA sequence and measures of complexity,” Complexity, vol. 3, pp. 33–37, 1997.
- S. Karlin and V. Brendel, “Patchiness and correlations in DNA sequences,” Science, vol. 259, no. 5095, pp. 677–680, 1993.
- D. Anastassiou, “Frequency-domain analysis of biomolecular sequences,” Bioinformatics, vol. 16, no. 12, pp. 1073–1081, 2000.
- S. S.-T. Yau, J. Wang, A. Niknejad, C. Lu, N. Jin, and Y.-K. Ho, “DNA sequence representation without degeneracy,” Nucleic Acids Research, vol. 31, no. 12, pp. 3078–3080, 2003.
- G. Dodin, P. Vandergheynst, P. Levoir, C. Cordier, and L. Marcourt, “Fourier and wavelet transform analysis, a tool for visualizing regular patterns in DNA sequences,” Journal of Theoretical Biology, vol. 206, no. 3, pp. 323–326, 2000.
- 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.
- E. Coward, “Equivalence of two Fourier methods for biological sequences,” Journal of Mathematical Biology, vol. 36, no. 1, pp. 64–70, 1997.
- 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.
- I. Daubechies, Ten Lectures on Wavelets, vol. 61 of CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics, Philadelphia, Pa, USA, 1992.