Quantifying time irreversibility using probabilistic differences between symmetric permutations

Abstract

To simplify the quantification of time irreversibility, we employ order patterns instead of the raw multidimension vectors in time series, and considering the existence of forbidden permutation, we propose a subtraction-based parameter, Y S , to measure the probabilistic differences between symmetric permutations for time irreversibility. Two chaotic models, the logistic and Henon systems, and reversible Gaussian process and their surrogate data are used to validate the time-irreversible measure, and time irreversibility of epileptic EEGs from Nanjing General Hospital is detected by the parameter. Test results prove that it is promising to quantify time irreversibility by measuring the subtraction-based probabilistic differences between symmetric order patterns, and our findings highlight the manifestation of nonlinearity of whether healthy or diseased EEGs and suggest that the epilepsy leads to a decline in the nonlinearity of brain electrical activities during seize-free intervals.

Networked information interactions of epileptic EEG based on symbolic transfer entropy

“…The neurological disease of epilepsy have long-term effects to the brain dynamical interactions based on our findings although the epileptics during seizure-free intervals have no significant difference in daily behaviors and brain activities. In the related reports of the present authors [30,32,27], the epileptic EEGs have lower nonlinearity from low-dimension dynamics, which is further verified by our networked analysis. In the nonlinearity of time irreversibility analysis [30], epileptic brain activities showed lower nonlinear dynamics especially in the brain areas of parietal lobes, which is close to the most distinct occipital lobe of O1 in our informational exchanges.…”

“…1. This order pattern scheme, inheriting the causal information without any further model assumptions, is widely adopted to simplify time series analysis [29,30,31]. for EEG collection [27,30,32].…”

“…This order pattern scheme, inheriting the causal information without any further model assumptions, is widely adopted to simplify time series analysis [29,30,31]. for EEG collection [27,30,32]. Following the standard 10-20 system, we locate 16 scalp electrodes, namely Fp1, Fp2, F3, F4, C3, C4, P3, P4, O1, O2, F7, F8, T3, T4, T5 To detect the information exchanges or causal links between different brain areas contributes to explore the brain modulation mechanism.…”

“…Our findings, however, challenge the reports and suggest the healthy subjects should have more dynamical activities than the epileptics in their seizure-free intervals. A tentative explanation to the different findings could be circadian and circaseptan rhythms in human epilepsy [30,39] that abnormally firing nerves during seizures lead to long-term damage to the brain and the epileptic seizure-free brain activities (about 20 to 30 days from the latest seizures) decrease interactions or synchronization of the brain networks, which reduce information exchanges between different brain regions and the degree of brain activities.…”

Equal heartbeat intervals and their effects on the nonlinearity of permutation-based time irreversibility in heart rate

“…J. Martinez et al [28] detect time reversibility by measuring the Jensen-Shannon divergence of time forward as well as its time-reversed counterpart by means of permutation, and M. Zanin et al [29] adopt the KL divergence to compare the probability distributions of symmetric order patterns. Considering the existence of forbidden permutation, W. Yao et al [30] propose a subtraction-based parameter to measure the probabilistic difference between order patterns for the time irreversibility. These simplified approaches have been gaining growing popularity for the features of fast, simplicity, noise insensitivity and so on.…”