Mapping equivalence for symbolic sequences: Theory and applications

IEEE Transactions on Signal Processing

Volumn 57, Issue 12, 2009, Pages 4895-4905

  Wang, Liming ^a   Schonfeld, Dan ^a  

^a University of Illinois at Chicago   (United States)

Author keywords

DNA sequence analysis; Symbolic signal processing; Transform equivalence

Indexed keywords

ABSTRACT MAPPING; ALGEBRAIC FRAMEWORK; DNA SEQUENCE ANALYSIS; NUMERICAL REPRESENTATION; NUMERICAL SIGNALS; PROTEOMIC SEQUENCES; SCIENTIFIC LITERATURE; SIGNAL CORRELATION; SYMBOLIC DATA; SYMBOLIC SEQUENCE; THEORETICAL RESULT;

DNA; EQUIVALENCE CLASSES; GENES; MAPPING; NUCLEIC ACIDS; SIGNAL PROCESSING;

DATA PROCESSING;

EID: 70450225401     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2009.2026544     Document Type: Article

References (33)

1. P. Vaidyanathan, "Genomics and proteomics: A signal processor's tour," IEEE Circuits Syst. Mag., vol.4, no.4, pp. 6-29, 2004.
2. A. Agresti, Categorical Data Analysis. New York: Wiley, 1990.
3. A. Krogh, I. Mian, and D. Haussler, "A hidden Markov model that finds genes in E. coli DNA," Nucleic Acids Res., vol.22, no.22, pp. 4768-4778, 1994.
4. S. Salzberg, A. Delcher, S. Kasif, and O. White, "Microbial gene identification using interpolated Markov models," Nucleic Acids Res., vol.26, no.2, pp. 544-548, 1998.
5. S. Salzberg, D. Searls, and S. Kasif, Computational Methods in Molecular Biology. Amsterdam, The Netherlands: Elsevier Science & Technology, 1998.
6. A. Oppenheim and S. Nawab, Symbolic and Knowledge-Based Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1992.
7. H. Herzel and I. Große, "Measuring correlations in symbol sequences," Physica A, vol.216, no.4, pp. 518-542, 1995.
8. S. V. Buldyrev, A. L. Goldberger, S. Havlin, R. N. Mantegna, M. E. Matsa, C. K. Peng, M. Simons, and H. E. Stanley, "Long-range correlation properties of coding and noncoding DNA sequences: Genbank analysis," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol.51, pp. 5084-5091, 1995.
9. W. Li and K. Kaneko, "Long-range correlation and partial 1/f spectrum in a noncoding DNA sequence," Europhys. Lett., vol.17, p. 655, Feb. 1992.
10. R. F. Voss, "Evolution of long-range fractal correlations and 1/f noise in DNA base sequences," Phys. Rev. Lett., vol.68, pp. 3805-3808, 1992.
11. C. Berthelsen, J. Glazier, and M. Skolnick, "Global fractal dimension of human DNA sequences treated as pseudorandom walks," Phys. Rev. A, Gen. Phys., vol.45, no.12, pp. 8902-8913, 1992.
12. B. D. Silverman and R. Linsker, "A measure of DNA periodicity," J. Theoretic. Biol., vol.118, pp. 295-300, 1986.
13. P. Cristea, "Conversion of nucleotides sequences into genomic signals," J. Cellular Molecul. Med., vol.6, no.2, pp. 279-303, 2002.
14. D. Anastassiou, "Genomic signal processing," IEEE Signal Process. Mag., vol.18, no.4, pp. 8-20, Jul. 2001.
15. D. S. Stoffer, D. E. Tyler, and A. J. McDougall, "Spectral analysis for categorical time series: Scaling and the spectral envelope," Biometrika, vol.80, pp. 611-622, 1993.
16. W. Wang and D. H. Johnson, "Computing linear transforms of symbolic signals," IEEE Trans. Signal Process., vol.50, no.3, pp. 628-635, Mar. 2002.
17. A. Rushdi and J. Tuqan, "Gene identification using the Z-curve representation," in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing (ICASSP), 2006, vol.2, pp. II-II.
18. A. Rushdi and J. Tuqan, "The role of the symbolic-to-numerical mapping in the detection of DNA periodicities," in Proc. IEEE Int. Workshop Genomic Signal Processing Statistics, 2008, pp. 1-4.
19. C. K. Peng, S. V. Buldyrev, A. L. Goldberger, S. Havlin, F. Sciortino, M. Simons, and H. E. Stanley, "Long-range correlations in nucleotide sequences," Nature, vol.356, no.6365, pp. 168-170, Mar. 1992.
20. A. Arneodo, E. Bacry, P. V. Graves, and J. F. Muzy, "Characterizing long-range correlations in DNA sequences from wavelet analysis," Phys. Rev. Lett., vol.74, no.16, pp. 3293-3296, Apr. 1995.
21. P. Carpena, P. Bernaola-Galvan, A. V. Coronado, M. Hackenberg, and J. L. Oliver, "Identifying chracteristic scales in the human genome," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol.75, p. 032903, 2007.
22. N. Bouaynaya and D. Schonfeld, "Non-stationary analysis of DNA sequences," in Proc. IEEE/SP 14th Workshop Statistical Signal Processing, 2007, pp. 200-204.
23. N. Bouaynaya and D. Schonfeld, "Nonstationary analysis of coding and noncoding regions in nucleotide sequences," IEEE J. Sel. Topics Signal Process., vol.2, no.3, pp. 357-364, Jun. 2008.
24. L. J. Corwin and R. Szczarba, Calculus in Vector Spaces, 2nd ed. New York: Macel Dekker, 1994.
25. L. D. Lathauwer, "Signal processing based on multilinear algebra," Ph.D. dissertation, Electr. Eng. Dept.-ESAT, K.U. Leuven, Leuven, Belgium, 1997.
26. R. Larsen and M. Marx, An Introduction to Mathematical Statistics and its Applications. Englewood Cliffs, NJ: Prentice-Hall, 2005.
27. Y. Eidelman, V. Milman, and A. Tsolomitis, Functional Analysis. Providence, RI: Amer. Math. Soc., 2004.
28. G. Caire, R. Grossman, and H. Poor, "Wavelet transforms associated with finite cyclic groups," IEEE Trans. Inf. Theory, vol.39, no.4, pp. 1157-1166, Jul. 1993.
29. M. Swanson and A. Tewfik, "A binarywavelet decomposition of binary images," IEEE Trans. Image Process., vol.5, no.12, pp. 1637-1650, Dec. 1996.
30. M. Pueschel and J. Moura, "Algebraic signal processing theory," Arxiv Preprint Cs/0612077, 2006.
31. D. Dummit and R. Foote, Abstract Algebra. New York: Wiley, 2004.
32. R. A. Horn and C. R. Johnson, Matrix Analysis. New York: Cambridge Univ. Press, 1988.
33. F. R. Gantmacher, The Theory of Matrices. New York: Chelsea, 1959, vol.I and II, Reprinted by Amer. Math. Soc.