Correlation between detrended fluctuation analysis and the Lempel-Ziv complexity in nonlinear time series analysis

We study the correlation between detrended fluctuation analysis（DFA） and the Lempel-Ziv complexity（LZC） in nonlinear time series analysis in this paper.Typical dynamic systems including a logistic map and a Duffing model are investigated.Moreover,the influence of Gaussian random noise on both the DFA and LZC are analyzed.The results show a high correlation between the DFA and LZC,which can quantify the non-stationarity and the nonlinearity of the time series,respectively.With the enhancement of the random component,the exponent α and the normalized complexity index C show increasing trends.In addition,C is found to be more sensitive to the fluctuation in the nonlinear time series than α.Finally,the correlation between the DFA and LZC is applied to the extraction of vibration signals for a reciprocating compressor gas valve,and an effective fault diagnosis result is obtained.

Harmonicity Spectrum

Perceiving harmonic information (especially weak harmonic information) in time series has important scientific and engineering significance. Fourier spectrum and time-frequency spectrum are commonly used tools for perceiving harmonic information, but they are often ineffective in perceiving weak harmonic signals because they are based on energy or amplitude analysis. Based on the theory of Normal time-frequency transform (NTFT) and complex correlation coefficient, a new type of spectrum, the Harmonicity Spectrum (HS), is developed to perceive harmonic information in time series. HS is based on the degree of signal harmony rather than energy or amplitude analysis, and can therefore perceive very weak harmonic information in signals sensitively. Simulation examples show that HS can detect harmonic information that cannot be detected by Fourier spectrum or time-frequency spectrum. Acoustic data analysis shows that HS has better resolution than traditional LOFAR spectrum.

Measuring air traffic complexity based on small samples

Air traffic complexity is an objective metric for evaluating the operational condition of the airspace. It has several applications, such as airspace design and traffic flow management.Therefore, identifying a reliable method to accurately measure traffic complexity is important. Considering that many factors correlate with traffic complexity in complicated nonlinear ways,researchers have proposed several complexity evaluation methods based on machine learning models which were trained with large samples. However, the high cost of sample collection usually results in limited training set. In this paper, an ensemble learning model is proposed for measuring air traffic complexity within a sector based on small samples. To exploit the classification information within each factor, multiple diverse factor subsets（FSSs） are generated under guidance from factor noise and independence analysis. Then, a base complexity evaluator is built corresponding to each FSS. The final complexity evaluation result is obtained by integrating all results from the base evaluators. Experimental studies using real-world air traffic operation data demonstrate the advantages of our model for small-sample-based traffic complexity evaluation over other stateof-the-art methods.

Natural variation of hormone levels in Arabidopsis roots and correlations with complex root architecture

Studies on natural variation are an important tool to unravel the genetic basis of quantitative traits in plants. Despite the significant roles of phytohormones in plant development, including root architecture, hardly any studies have been done to investigate natural variation in endogenous hormone levels in plants. Therefore, in the present study a range of hormones were quantified in root extracts of thirteen Arabidopsis thaliana accessions using a ultra performance liquid chromatography triple quadrupole mass spectrometer. Root system architecture of the set of accessions was quantified, using a new parameter （mature root unit） for complex root systems, and correlated with the phytohormone data. Significant variations in phytohormone levels among the accessions were detected, but were remarkably small, namely less than three-fold difference between extremes. For cytokinins, relatively larger variations were found for ribosides and glucosides, as compared to the free bases. For root phenotyping, length-related traits--lateral root length and total root length--showed larger variations than lateral root number-related ones. For root architecture, antagonistic interactions between hormones, for example, indole-3-acetic acid to trans-zeatin were detected in correlation analysis. These findings provide conclusive evidence for the presence of natural variation in phytohormone levels in Arabidopsis roots, suggesting that quantitative genetic analyses are feasible.