Proposed Corrections for the Quantification of Coupling Patterns by Recurrence Plots

A study of EEG non-stationarity on inducing false memory in different emotional states

False memory leads to inaccurate decisions and unnecessary challenges. Researchers have conventionally used electroencephalography (EEG) to study false memory under different emotional states. However, EEG non-stationarity has scarcely been investigated. To address this problem, this study utilized the nonlinear method of recursive quantitative analysis to analyze the non-stationarity of EEG signals. Deese-Roediger-McDermott paradigm experiments were used to induce false memory wherein semantic words were highly correlated. The EEG signals of 48 participants with false memory associated with different emotional states were collected. Recurrence rate (RR), determination rate (DET), and entropy recurrence (ENTR) data were generated to characterize EEG non-stationarity. Behavioral outcomes exhibited significantly higher false-memory rates in the positive group than in the negative group. The prefrontal, temporal, and parietal regions yielded significantly higher RR, DET, and ENTR values than other brain regions in the positive group. However, only the prefrontal region had significantly higher values than other brain regions in the negative group. Therefore, positive emotions enhance non-stationarity in brain regions associated with semantics compared with negative emotions, leading to a higher false-memory rate. This suggests that non-stationary alterations in brain regions under different emotional states are correlated with false memory.

Alternate Entropy Computations by Applying Recurrence Matrix Masking

In practicality, recurrence analyses of dynamical systems can only process short sections of signals that may be infinitely long. By necessity, the recurrence plot and its quantifications are constrained within a truncated triangle that clips the signals at its borders. Recurrence variables defined within these confining borders can be influenced more or less by truncation effects depending upon the system under evaluation. In this study, the question being asked is what if the boundary borders were tilted, what would be the effect on all recurrence variables? This question was prompted by the observation that line entropy values are maximized for highly periodic systems in which the infinitely long line elements are truncated to different unique lengths. However, by redefining the recurrence plot area to a 45-degree tilted box within the triangular area, the diagonal lines would consequently be truncated to identical lengths. Such masking would minimize the line entropy to 0.000 bits/bin. However, what new truncation influences would be imposed on the other recurrence variables? This question is examined by comparing recurrence variables computed with the triangular recurrence area versus boxed recurrence area. Examples include the logistic equation (mathematical series), the Dow Jones Industrial Average over a decade (real-word data), and a square wave pulse (toy series). Good agreement among the variables in terms of timing and amplitude was found for most, but not all variables. These important results are discussed.

Entropy of weighted recurrence plots

The Shannon entropy of a time series is a standard measure to assess the complexity of a dynamical process and can be used to quantify transitions between different dynamical regimes. An alternative way of quantifying complexity is based on state recurrences, such as those available in recurrence quantification analysis. Although varying definitions for recurrence-based entropies have been suggested so far, for some cases they reveal inconsistent results. Here we suggest a method based on weighted recurrence plots and show that the associated Shannon entropy is positively correlated with the largest Lyapunov exponent. We demonstrate the potential on a prototypical example as well as on experimental data of a chemical experiment.

A new heart rate variability analysis method by means of quantifying the variation of nonlinear dynamic patterns

A new heart rate variability (HRV) analysis method, quantifying the variation of nonlinear dynamic pattern (VNDP) in heart rate series, is proposed and validated against the age stratified Fantasia database. The method is based on three processes: (1) a recurrence quantification analysis (RQA) to quantify the dynamic patterns, (2) the use of mutual information (MI) and the entropy (EN) to characterize the VNDP, and 3) linear discriminant analysis to exploit the associations within MI and EN measures. Practically, the VNDP method overcomes the nonstationarity problem and exploits the nonstationary properties in HRV analyses. Physiologically, the VNDP reflects the properties of the fundamental short-term HRV dynamic system and the external associations of the system within the autonomous nervous system (ANS). The characteristic probability density peaks portrayed by VNDP plots indicate the quantum-like heart dynamics, which may provide valuable insights into the control of the ANS. The discrimination results of the reduced pattern dynamic range due to aging, from a new perspective, display the reduction in HRV. The significantly improved discriminatory power, compared to conventional RQA analyses, shows that the VNDP analysis can practically quantify the nonstationary nonlinear dynamics for ANS assessments.