Characterizing time series by extended complexity-entropy curves based on Tsallis, Rényi, and power spectral entropy

Dispersion complexity-entropy curves: An effective method to characterize the structures of nonlinear time series

The complexity-entropy curve (CEC) is a valuable tool for characterizing the structure of time series and finds broad application across various research fields. Despite its widespread usage, the original permutation complexity-entropy curve (PCEC), which is founded on permutation entropy (PE), exhibits a notable limitation: its inability to take the means and amplitudes of time series into considerations. This oversight can lead to inaccuracies in differentiating time series. In this paper, drawing inspiration from dispersion entropy (DE), we propose the dispersion complexity-entropy curve (DCEC) to enhance the capability of CEC in uncovering the concealed structures within nonlinear time series. Our approach initiates with simulated data including the logistic map, color noises, and various chaotic systems. The outcomes of our simulated experiments consistently showcase the effectiveness of DCEC in distinguishing nonlinear time series with diverse characteristics. Furthermore, we extend the application of DCEC to real-world data, thereby asserting its practical utility. A novel approach is proposed, wherein DCEC-based feature extraction is combined with multivariate support vector machine for the diagnosis of various types of bearing faults. This combination achieved a high accuracy rate in our experiments. Additionally, we employ DCEC to assess stock indices from different countries and periods, thereby facilitating an analysis of the complexity inherent in financial markets. Our findings reveal significant insights into the dynamic regularities and distinct structures of these indices, offering a novel perspective for analyzing financial time series. Collectively, these applications underscore the potential of DCEC as an effective tool for the nonlinear time series analysis.

Electrocardiogram-based sleep analysis for sleep apnea screening and diagnosis

PURPOSE

Despite the increasing number of research studies of cardiopulmonary coupling (CPC) analysis, an electrocardiogram-based technique, the use of CPC in underserved population remains underexplored. This study aimed to first evaluate the reliability of CPC analysis for the detection of obstructive sleep apnea (OSA) by comparing with polysomnography (PSG)-derived sleep outcomes.

METHODS

Two hundred five PSG data (149 males, age 46.8 ± 12.8 years) were used for the evaluation of CPC regarding the detection of OSA. Automated CPC analyses were based on ECG signals only. Respiratory event index (REI) derived from CPC and apnea-hypopnea index (AHI) derived from PSG were compared for agreement tests.

RESULTS

CPC-REI positively correlated with PSG-AHI (r = 0.851, p < 0.001). After adjusting for age and gender, CPC-REI and PSG-AHI were still significantly correlated (r = 0.840, p < 0.001). The overall results of sensitivity and specificity of CPC-REI were good.

CONCLUSION

Compared with the gold standard PSG, CPC approach yielded acceptable results among OSA patients. ECG recording can be used for the screening or diagnosis of OSA in the general population.

Langevin equations from experimental data: The case of rotational diffusion in granular media

A model has two main aims: predicting the behavior of a physical system and understanding its nature, that is how it works, at some desired level of abstraction. A promising recent approach to model building consists in deriving a Langevin-type stochastic equation from a time series of empirical data. Even if the protocol is based upon the introduction of drift and diffusion terms in stochastic differential equations, its implementation involves subtle conceptual problems and, most importantly, requires some prior theoretical knowledge about the system. Here we apply this approach to the data obtained in a rotational granular diffusion experiment, showing the power of this method and the theoretical issues behind its limits. A crucial point emerged in the dense liquid regime, where the data reveal a complex multiscale scenario with at least one fast and one slow variable. Identifying the latter is a major problem within the Langevin derivation procedure and led us to introduce innovative ideas for its solution.