Rényi continuous entropy of DNA sequences

Journal of Theoretical Biology

Volumn 231, Issue 3, 2004, Pages 377-388

  Vinga, Susana ^a   Almeida, Jonas S ^a,b  

^a INSTITUTO DE TECNOLOGIA QUÍMICA E BIOLÓGICA   (Portugal)

^b Med Univ S Carolina 135 C   (United States)

Author keywords

CGR USM; DNA; Information theory; Parzen's method; R nyi entropy

Indexed keywords

DNA;

ARTICLE; DNA SEQUENCE; ENTROPY; INTERMETHOD COMPARISON; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; PRIORITY JOURNAL; RANDOMIZATION; SIMULATION;

ANIMALS; DNA; ENTROPY; MODELS, GENETIC;

EID: 6344221592     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jtbi.2004.06.030     Document Type: Article

References (48)

1. J.S. Almeida, and S. Vinga Universal sequence map (USM) of arbitrary discrete sequences BMC Bioinformatics 3 2002 6
2. J.S. Almeida, J.A. Carriço, A. Maretzek, P.A. Noble, and M. Fletcher Analysis of genomic sequences by chaos game representation Bioinformatics 17 2001 429 437
3. R.B. Ash Information Theory 1990 Dover Publications New York
4. M.F. Barnsley Fractals Everywhere 1998 Academic Press Boston
5. C.L. Berthelsen, J.A. Glazier, and M.H. Skolnick Global fractal dimension of human DNA sequences treated as pseudorandom walks Phys. Rev. A 45 12 1992 8902 8913
6. V.R. Chechetkin, and V.V. Lobzin Levels of ordering in coding and noncoding regions of DNA sequences Phys. Lett. A 22 1996 354 360 doi:10.1016/0375-9601(96)00672-X
7. T.M. Cover, and J.A. Thomas Elements of Information Theory 1991 Wiley New York
8. M. Crochemore, and R. Verin Zones of low entropy in genomic sequences Comput. Chem. 23 1999 275 282 doi:10.1016/S0097-8485(99)00009-1
9. P. Deschavanne, A. Giron, J. Vilain, G. Fagot, and B. Fertil Genomic signature characterization and classification of species assessed by chaos game representation of sequences Mol. Biol. Evol. 16 1999 1391 1399
10. M. Farach, M. Noordewier, S. Savari, L. Shepp, A. Wyner, and J. Ziv On the entropy of DNA algorithms and measurements based on memory and rapid convergence Proceedings of the Sixth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'95) 1995 SIAM San Francisco, CA 48 57
11. A. Gabrielian, and A. Bolshoy Sequence complexity and DNA curvature Comput. Chem. 23 1999 263 274 doi:10.1016/S0097-8485(99)00007-8
12. L.L. Gatlin Information Theory and the Living System 1972 Columbia University Press New York
13. Gokcay, E., Principe, J.C., 2000. A new clustering evaluation function using Renyi's information potential. IEEE Interntional Conference on Acoustic, Speech and Signal Processing (ICASSP'00).
14. E. Gokcay, and J.C. Principe Information theoretic clustering IEEE Trans. Pattern Anal. Mach. Intell. 24 2002 158 171
15. A. Hariri, B. Weber, and J. Olmsted 3rd. On the validity of Shannon-informatin calculations for molecular biological sequences J. Theor. Biol. 147 1990 235 254
16. J.D. Helmann Compilation and analysis of Bacillus subtilis sigma A-dependent promoter sequences evidence for extended contact between RNA polymerase and upstream promoter DNA Nucleic Acids Res. 23 1995 2351 2360
17. H. Herzel, and I. Grosse Measuring correlations in symbolic sequences Physica A 216 1995 518 542 doi:10.1016/0378-4371(95)00104-F
18. H. Herzel, W. Ebeling, and A.O. Schmitt Entropies of biosequences the role of repeats Phys. Rev. E 50 1994 5061 5071
19. H. Herzel, A.O. Schmitt, and W. Ebeling Finite sample effects in sequence analysis Chaos, Solitons Fractals 4 1994 97 113 doi:10.1016/0960-0779(94)90020- 5
20. H.J. Jeffrey Chaos game representation of gene structure Nucleic Acids Res. 18 1990 2163 2170
21. M.A. Jimenez-Montano, W. Ebeling, T. Pohl, and P.E. Rapp Entropy and complexity of finite sequences as fluctuating quantities Biosystems 64 2002 23 32 doi:10.1016/S0303-2647(01)00171-X
22. A.I. Khinchin Mathematical Foundations of Information Theory 1957 Dover Publications New York
23. A. Krishnamachari, V.M. Mandal, and Karmeshu Study of DNA binding sites using the Renyi parametric entropy measure J. Theor. Biol. 227 2004 429 436 doi:10.1016/j.jtbi.2003.11.026
24. J.K. Lanctot, M. Li, and E.H. Yang Estimating DNA sequence entropy Proceedings of 11th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'00) 2000 SIAM San Francisco, CA 409 418
25. P. Lio, A. Politi, M. Buiatti, and S. Ruffo High statistics block entropy measures of DNA sequences J. Theor. Biol. 180 1996 151 160 doi:10.1006/jtbi. 1996.0091
26. D. Loewenstern, and P.N. Yianilos Significantly lower entropy estimates for natural DNA sequences J. Comput. Biol. 6 1999 125 142
27. R.N. Mantegna, S.V. Buldyrev, A.L. Goldberger, S. Havlin, C.K. Peng, M. Simons, and H.E. Stanley Linguistic features of noncoding DNA sequences Phys. Rev. Lett. 73 1994 3169 3172
28. J.L. Oliver, P. Bernaola-Galvan, J. Guerrero-Garcia, and R. Roman-Roldan Entropic profiles of DNA sequences through chaos-game-derived images J. Theor. Biol. 160 1993 457 470 doi:10.1006/jtbi.1993.1030
29. Y.L. Orlov, V.P. Filippov, V.N. Potapov, and N.A. Kolchanov Complexity software tools for analysis of information measures of genetic texts 2002 Workshop on Genomic Signal Processing and Statistics (GENSIPS) Raleigh, North Carolina, USA
30. E. Parzen On estimation of a probability density function and mode Ann. Math. Stat. 33 1962 1065 1076
31. J.C. Principe, and D. Xu Information - theoretic learning using Renyi's quadratic entropy First International Workshop on Independent Component Analysis (ICA '99) 1999 Aussois France 407 412
32. J.C. Principe, D. Xu, and J.W.I. Fisher Information-theoretic learning S. Haykin Unsupervised Adaptive Filtering vol. 1 2000 Wiley New York 265 319
33. A. Rényi On measures of entropy and information Proceedings of the Fourth Berkeley Symposium on Mathematics, Statistics and Probability vol. 1 1961 University of California Press Berkeley, CA 547 561
34. A. Rényi Introduction a la théorie de l'information 1966 Calcul des probabilités. Dunod Paris
35. M.G. Sadovsky The method to compare nucleotide sequences based on the minimum entropy principle Bull. Math. Biol. 65 2003 309 322 doi:10.1016/S0092- 8240(02)00107-6
36. A.O. Schmitt, and H. Herzel Estimating the entropy of DNA sequences J. Theor. Biol. 188 1997 369 377 doi:10.1006/jtbi.1997.0493
37. Shannon, C.E., 1948. A mathematical theory of communication. Bell Syst. Tech. J. 27, 379-423, 623-656.
38. H.E. Stanley, S.V. Buldyrev, A.L. Goldberger, S. Havlin, C.K. Peng, and M. Simons Scaling features of noncoding DNA Physica A 273 1999 1 18 doi:10.1016/S0378-4371(99)00407-0
39. P. Tino Spatial representation of symbolic sequences through iterative function systems IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 29 1999 386 392
40. P. Tino Multifractal properties of Hao's geometric representations of DNA sequences Physica A 304 2002 480 494 doi:10.1016/S0378-4371(01)00574-X
41. P. Tino, and G. Dorffner Predicting the future of discrete sequences from fractal representations of the past Mach. Learn. 45 2001 187 217
42. O.G. Troyanskaya, O. Arbell, Y. Koren, G.M. Landau, and A. Bolshoy Sequence complexity profiles of prokaryotic genomic sequences a fast algorithm for calculating linguistic complexity Bioinformatics 18 2002 679 688
43. A. Vanet, L. Marsan, and M.-F. Sagot Promoter sequences and algorithmical methods for identifying them Res. Microbiol. 150 1999 779 799 doi:10.1016/S0923-2508(99)00115-1
44. S. Vinga, and J.S. Almeida Alignment-free sequence comparison - a review Bioinformatics 19 2003 513 523
45. S. Vinga, R. Gouveia-Oliveira, and J.S. Almeida Comparative evaluation of word composition distances for the recognition of SCOP relationships Bioinformatics 20 2004 206 215
46. O. Weiss, M.A. Jimenez-Montano, and H. Herzel Information content of protein sequences J. Theor. Biol. 206 2000 379 386 doi:10.1006/jtbi.2000.2138
47. M. Xiao, Z.Z. Zhu, J. Liu, and C.Y. Zhang A new method based on entropy theory for genomic sequence analysis Acta. Biotheor. 50 2002 155 165
48. Z.G. Yu, V. Anh, and K.S. Lau Chaos game representation of protein sequences based on the detailed HP model and their multifractal and correlation analyses J. Theor. Biol. 226 2004 341 348 doi:10.1016/j.jtbi.2003.09.009