Double symbolic joint entropy in nonlinear dynamic complexity analysis

Symbolizations, the base of symbolic dynamic analysis, are classified as global static and local dynamic approaches which are combined by joint entropy in our works for nonlinear dynamic complexity analysis. Two global static methods, symbolic transformations of Wessel N. symbolic entropy and base-scale entropy, and two local ones, namely symbolizations of permutation and differential entropy, constitute four double symbolic joint entropies that have accurate complexity detections in chaotic models, logistic and Henon map series. In nonlinear dynamical analysis of different kinds of heart rate variability, heartbeats of healthy young have higher complexity than those of the healthy elderly, and congestive heart failure (CHF) patients are lowest in heartbeats' joint entropy values. Each individual symbolic entropy is improved by double symbolic joint entropy among which the combination of base-scale and differential symbolizations have best complexity analysis. Test results prove that double symbolic joint entropy is feasible in nonlinear dynamic complexity analysis.Comment: 7 pages, 4 figure

Threshold distribution of equal states for quantitative amplitude fluctuations

Objective. The distribution of equal states (DES) quantifies amplitude fluctuations in biomedical signals. However, under certain conditions, such as a high resolution of data collection or special signal processing techniques, equal states may be very rare, whereupon the DES fails to measure the amplitude fluctuations. Approach. To address this problem, we develop a novel threshold DES (tDES) that measures the distribution of differential states within a threshold. To evaluate the proposed tDES, we first analyze five sets of synthetic signals generated in different frequency bands. We then analyze sleep electroencephalography (EEG) datasets taken from the public PhysioNet. Main results. Synthetic signals and detrend-filtered sleep EEGs have no neighboring equal values; however, tDES can effectively measure the amplitude fluctuations within these data. The tDES of EEG data increases significantly as the sleep stage increases, even with datasets covering very short periods, indicating decreased amplitude fluctuations in sleep EEGs. Generally speaking, the presence of more low-frequency components in a physiological series reflects smaller amplitude fluctuations and larger DES. Significance.The tDES provides a reliable computing method for quantifying amplitude fluctuations, exhibiting the characteristics of conceptual simplicity and computational robustness. Our findings broaden the application of quantitative amplitude fluctuations and contribute to the classification of sleep stages based on EEG data

Comparative analysis of the original and amplitude permutations

The original and amplitude permutations are two basic ordinal patterns; however, their relationship has received little attention. This paper compares the original and amplitude permutations used to characterize vector structures. To accurately convey the vector structure, we modify indexes of equal values in the permutations to be the same ones in each group of equalities. Comparative analysis suggests that the amplitude permutation, comprising the positions of the original values in the reordered vector, directly reflects the vector's temporal structure, whereas the original permutation, consisting of the indexes of reorganized values in the original vector, conveys the structural pattern of the reorganized vector. Moreover, we clarify the association of the original and amplitude permutations with timeand amplitude-symmetric vectors, thus contributing to the fields of symbolic analysis, topological data analysis, and so on.Comment: 7 pages, 3 figure

Depressed MEG causality analysis based on polynomial kernel Granger causality

In this study, we employ the Granger causality of a polynomial kernel to identify the coupling causality of depressed magnetoencephalography (MEG). We collect MEG under positive, neutral, and negative emotional stimuli and focus on the β-band activities. According to test results, depressed people display stronger left–right symmetrical interconnection in their prefrontal and occipital lobes under nonpositive stimuli(namely neutral and negative stimuli), indicating that they are more sensitive to nonpositive stimuli. The intensity of the right occipital information flow is higher in depressed people. We also see the Granger causality index increased in the occipital–frontal areas of depressed patients under negative stimuli. In general, detecting the polynomial kernel Granger causality of the MEG can effectively characterize the strength of the interconnected brain regions in depressed patients, which can be used as a clinical diagnosis aid