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References
Anfinsen, C. (1973) Principles that govern the folding of protein chains. Science 181: 223–230.
Anh, V.V., Lau, K.S. and Yu, Z.G. (2001) Multifractal characterization of complete genomes. J. Phys. A: Math. Gene. 34: 7127–7139.
Anh, V.V., Lau, K.S. and Yu, Z.G., (2002) Recognition of an organism from fragments of its complete genome, Phys. Rev. E 66: 031910.
Balafas, J.S. and Dewey, T.G. (1995) Multifractal analysis of solvent accessibilities in proteins. Phys. Rev. E. 52: 880–887.
Barnsley, M.F. and Demko, S. (1985) Iterated function systems and the global construction of Fractals. Proc. R. Soc. Lond. A 399: 243–275.
Basu, S., Pan, A., Dutta, C. and Das, J. (1998) Chaos game representation of proteins. J. Mol. Graphics and Modeling 15: 279–289.
Berthelsen, C.L., Glazier, J.A. and Skolnick, M.H. (1992) Global fractal dimension of human DNA sequences treated as pseudorandom walks. Phys. Rev. A 45: 8902–8913.
Brown, T.A. (1998) Genetics (3rd Edition). CHAPMAN & HALL, London
Buldyrev, S.V., Dokholyan, N.V., Goldberger, A.L., Havlin, S., Peng, C.K., Stanley, H.E. and Visvanathan, G.M. (1998) Analysis of DNA sequences using method of statistical physics. Physica A 249: 430–438.
Buldyrev, S.V., Goldgerger, A.I., Havlin, S., Peng, C.K. and Stanley, H.E. (1994) in: Fractals in Science, Edited by A. Bunde and S. Havlin, Springer-verlag Berlin Heidelberg, Page 49–87.
Canessa, E. (2000) Multifractality in time series. J. Phys. A: Math. Gene. 33: 3637–3651.
Chothia, C. (1992) One thousand families for the molecular biologists. Nature (London) 357: 543–544.
Dewey, T.G. (1993) Protein structure and polymer collapse. J. Chem. Phys. 98: 2250–2257.
Dill, K.A. (1985) Theory for the folding and stability of globular proteins, Biochemistry 24: 1501–1509.
Falconer, K.J. (1990) Fractal geometry: Mathematical foundations and applications. John wiley & sons LTD.
Feder, J. (1988) Fractals. Plenum Press, New York, London..
Fedorov, B.A., Fedorov, B.B. and Schmidt, P.W. (1993) An analysis of the fractal properties of the surfaces of globular proteins, J. Chem. Phys. 99: 4076–4083.
Fiser, A., Tusnady, G.E., Simon, I. (1994) Chaos game representation of protein structures. J. Mol. Graphics 12: 302–304.
Fraser, C.M. et al. (1995) The minimal gene complement of Mycoplasma genitalium. Science 270: 397–404.
Grassberger, P. and Procaccia, I. (1983) Characterization of strange attractors. Phys. Rev. Lett. 50: 346–349.
Halsy, T., Jensen, M., Kadanoff, L., Procaccia, I. and Schraiman, B. (1986) Fractal measures and their singularities: the characterization of strange sets. Phys. Rev. A 33: 1141–1151.
Hao, B.L., Lee, H.C. and Zhang, S.Y. (2000) Fractals related to long DNA sequences and complete genomes. Chaos, Solitons and Fractals 11(6): 825–836.
Hao, B.L., Xie, H.M., Yu, Z.G. and Chen, G.Y. (2001) Factorizable language: from dynamics to bacterial complete genomes. Physica A 288: 10–20.
Jeffrey, H.J. (1990) Chaos game representation of gene structure. Nucleic Acids Research 18(8): 2163–2170.
Larhammar, D. and Chatzidimitriou-Dreismann, C.A. (1993) Biological origins of long-range correlations and compositional variations in DNA. Nucl. Acids Res. 21: 5167–5170.
Lewis, M., Rees, D.C. (1985) Fractal Surface of Proteins. Science 230: 1163–1165.
Li, H., Helling, R., Tang, C. and Wingreen, N.S. (1996) Emergence of Preferred Structures in a Simple Model of Protein Folding, Science 273: 666–669.
Li, W.H. and Graur, D. (1991) Fundamental of Molecular Evolution. Sinauer Associates, Inc. Sunderland, Massachusetts.
Lidar, D.A., Thirumalai, D., Elber, R. and Gerber, R.B. (1999) Fractal analysis of protein potential energy landscapes. Phys. Rev. E 59: 2231–2243.
Luo, L., Lee, W., Jia, L., Ji, F. and Lu, T. (1998) Statistical correlation of nucleotides in a DNA sequence. Phy. Rev. E 58(1): 861–871.
Luo, L. and Tsai, L. (1988) Fractal analysis of DNA walk. Chin. Phys. Lett. 5: 421–424.
Mandelbrot, B.B. (1982) The Fractal Geometry of Nature. W.H. Freeman, New York.
Micheletti, C., Banavar, J.R., Maritan, A. and Seno, F. (1998) Steric Constraints in Model Proteins, Phys. Rev. Lett. 80: 5683–5686.
Noonan, J. and Zeilberger, D. (1999) The Goulden-Jackson cluster method: extensions, applications and implementations, J. Difference Eq. Appl. 5, 355–377, http://www.math.rutgers.edu/~zeilberg/papers1.html.
Pande, V.S., Grosberg, A.Y. and Tanaka, T. (1994) Nonrandomness in Protein Sequences: Evidence for a Physically Driven Stage of Evolution? Proc. Natl. Acad. Sci. USA 91: 12972–12975
Peng, C.K., Buldyrev, S., Goldberg, A.L., Havlin, S., Sciortino, F., Simons, M. and Stanley, H.E. (1992) Long-range correlations in nucleotide sequences. Nature 356: 168–170.
Pfiefer, P., Welz, U. and Wipperman, H. (1985) Fractal surface dimension of proteins: Lysozyme. Chem. Phys. Lett. 2113: 535–540
Prabhu, V.V. and Claverie, J.M. (1992) Correlations in intronless DNA. Nature 359: 782–782.
Qi, J., Wang, B. and Hao, B.L. (2004) Prokaryote phylogeny based on complete genomes—tree construction without sequence alignment. J. Mol. Evol. 58: 1–11.
Russell, R.B. (2000) Classification of Protein Folds, in Protein structure prediction: Methods and Protocls, Eds, D. Webster, Humana Press Inc., Totowa, NJ.
Shih, C.T., Su, Z.Y., Gwan, J.F., Hao, B.L., Hsieh, C.H. and Lee, H.C. (2000) Mean-Field HP Model, Designability and Alpha-Helices in Protein Structures, Phys. Rev. Lett. 84(2): 386–389.
Shih, C.T., Su, Z.Y., Gwan, J.F., Hao, B.L., Hsieh, C.H., Lee, H.C. (2002) Geometric and statistical properties of the mean-field HP model, the LS model and real protein sequences. Phys. Rev. E 65: 041923.
Strait, B.J. and Dewey, T.G. (1995) Multifractals and decoded walks: Applications to protein sequence correlations, Phys. Rev. E. 52: 6588–6592.
Tino, P. (2001) Multifractal properties of Hao’s geometric representation of DNA sequences, Physica A 304: 480–494.
Vrscay, E.R. (1991) Iterated function systems: theory, applications and the inverse problem, in Fractal Geometry and analysis, Eds, J. Belair, NATO ASI series, Kluwer Academic Publishers.
Wang, B. and Yu, Z.G. (2000) One way to characterize the compact structures of lattice protein model. J. Chem. Phys. 112(13): 6084–6088
Wang, J. and Wang, W. (2000) Modeling study on the validity of a possibly simplified representation of proteins. Phys. Rev. E 61: 6981–6986.
Xie, H.M. (1996) Grammatical Complexity and One-Dimensional Dynamical Systems. World Scientific, Singapore.
Yu, Z.G., Anh, V.V. and Lau, K.S. (2001) Measure representation and multifractal analysis of complete genome. Phys. Rev. E 64: 031903.
Yu, Z.G., Anh, V.V. and Lau, K.S. (2003) Multifractal and correlation analysis of protein sequences from complete genome. Phys. Rev. E 68: 021913.
Yu, Z.G., Anh, V.V. and Lau, K.S. (2004) Fractal analysis of large proteins based on the Detailed HP model. Physica A (in press).
Yu, Z.G., Hao, B.L., Xie, H.M. and Chen, G.Y. (2000) Dimension of fractals related to language defined by tagged strings in complete genome. Chaos, Solitons and Fractals 11(14): 2215–2222.
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Yu, ZG., Anhl, V., Chen, YP.P. (2005). Visualization and Fractal Analysis of Biological Sequences. In: Chen, YP.P. (eds) Bioinformatics Technologies. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26888-X_11
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