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Fractals and hidden symmetries in DNA. (English) Zbl 1189.92015
Summary: This paper deals with the digital complex representation of a DNA sequence and the analysis of existing correlations by wavelets. The symbolic DNA sequence is mapped into a nonlinear time series. By studying this time series the existence of fractal shapes and symmetries will be shown. At a first step, the indicator matrix enables us to recognize some typical patterns of nucleotide distributions. The DNA sequence of the influenza virus A (H1N1) is investigated by using the complex representation, together with the corresponding walks on DNA; in particular, it is shown that DNA walks are fractals. Finally, by using wavelet analysis, the existence of symmetries is proven.

MSC:
92C40 Biochemistry, molecular biology
28A80 Fractals
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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