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A generalized topological entropy for analyzing the complexity of DNA sequences.

ABSTRACT: Topological entropy is one of the most difficult entropies to be used to analyze the DNA sequences, due to the finite sample and high-dimensionality problems. In order to overcome these problems, a generalized topological entropy is introduced. The relationship between the topological entropy and the generalized topological entropy is compared, which shows the topological entropy is a special case of the generalized entropy. As an application the generalized topological entropy in introns, exons and promoter regions was computed, respectively. The results indicate that the entropy of introns is higher than that of exons, and the entropy of the exons is higher than that of the promoter regions for each chromosome, which suggest that DNA sequence of the promoter regions is more regular than the exons and introns.

SUBMITTER: Jin S

PROVIDER: S-EPMC3922877 | biostudies-literature | 2014

REPOSITORIES: biostudies-literature

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A generalized topological entropy for analyzing the complexity of DNA sequences.

Jin Shuilin S Tan Renjie R Jiang Qinghua Q Xu Li L Peng Jiajie J Wang Yong Y Wang Yadong Y

PloS one 20140212 2

Topological entropy is one of the most difficult entropies to be used to analyze the DNA sequences, due to the finite sample and high-dimensionality problems. In order to overcome these problems, a generalized topological entropy is introduced. The relationship between the topological entropy and the generalized topological entropy is compared, which shows the topological entropy is a special case of the generalized entropy. As an application the generalized topological entropy in introns, exons ...[more]

PMID: 24533097

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Project description:The Complexity-entropy causality plane (CECP) is a parsimonious representation space for time series. It has only two dimensions: normalized permutation entropy ([Formula: see text]) and Jensen-Shannon complexity ([Formula: see text]) of a time series. This two-dimensional representation allows for detection of slow or rapid drifts in the condition of mechanical components monitored through sensor measurements. The CECP representation can be used for both predictive analytics and visual monitoring of changes in component condition. This method requires minimal pre-processing of raw signals. Furthermore, it is insensitive to noise, stationarity, and trends. These desirable properties make CECP a good candidate for machine condition monitoring and fault diagnostics. In this work we study the effectiveness of CECP on three rotary component condition assessment applications. We use CECP representation of vibration signals to differentiate various machine component health conditions for rotary machine components, namely roller bearing and gears. The results confirm that the CECP representation is able to detect, with high accuracy, changes in underlying dynamics of machine component degradation states. From class separability perspective, the CECP representation is able to generate linearly separable classes for the classification of different fault states. This classification performance improves with increasing signal length. For signal length of 16,384 data points, the fault classification accuracy varies from 90% to 100% for bearing applications, and from 85% to 100% for gear applications. We observed that the optimum parameter for CECP representatino depends on the application. For bearing applications we found that embedding dimension D = 4, 5, 6, and embedding delay τ = 1, 2, 3 are suitable for good fault classification. For gear applications we find that embedding dimension D = 4, 5, and embedding delay τ = 1, 5 are suitable for fault classification.

Dataset Information

A generalized topological entropy for analyzing the complexity of DNA sequences.

Publications

A generalized topological entropy for analyzing the complexity of DNA sequences.

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