Wavelet-based multifractal analysis of DNA sequences by using chaos-game representation |
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Authors: | Han Jia-Jing and Fu Wei-Juan |
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Institution: | Surface Physics Laboratory (National Key Laboratory) and Physics Department, Fudan University, Shanghai 200433, China |
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Abstract: | Chaos game representation (CGR) is proposed as a
scale-independent representation for DNA sequences and provides
information about the statistical distribution of oligonucleotides
in a DNA sequence. CGR images of DNA sequences represent some kinds of
fractal patterns, but the common multifractal analysis based on the
box counting method cannot deal with CGR images perfectly. Here, the
wavelet transform modulus maxima (WTMM) method is applied to the
multifractal analysis of CGR images. The results show that the
scale-invariance range of CGR edge images can be extended to three
orders of magnitude, and complete singularity spectra can be
calculated. Spectrum parameters such as the singularity spectrum
span are extracted to describe the statistical character of DNA
sequences. Compared with the singularity spectrum span, exon
sequences with a minimal spectrum span have the most uniform
fractal structure. Also, the singularity spectrum parameters are
related to oligonucleotide length, sequence component and species,
thereby providing a method of studying the length polymorphism of
repeat oligonucleotides. |
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Keywords: | chaos game representation (CGR) multifractal wavelet
transform modulus maxima(WTMM) singularity spectrum |
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