arXiv subjects

Wenpo Yao

Publications and source records attributed to Wenpo Yao.

10 recordsLinked to original sources

arXiv2025

Fuzzy permutation time irreversibility for nonequilibrium analysis of complex system

Permutation time irreversibility is an important method to quantify nonequilibrium characteristics of complex systems; however, ordinal pattern is a coarse-graining alternative of temporal structure and cannot accurately represent detailed structural information. This study aims to propose a fuzzy permutation time irreversibility (fpTIR) by measuring the difference between vector elements based on a negative exponential function. The amplitude permutation of vector is constructed and its membership degree is calculated; then, the difference in probability distribution between the forward and backward sequences is measured for fpTIR. To compare and measure the system's complexity, the Shannon entropy is calculated as the average amount of information in the fuzzy permutation probability distribution, i.e., fuzzy permutation entropy (fPEn). According to the surrogate theory, mode series are generated using logistic, Henon, and first-order autoregressive systems to verify the fpTIR, which is then used to analyze the heartbeats of patients with congestive heart failure and healthy elderly and young participants from the PhysioNet database. Results suggest that the fpTIR effectively measures the system's nonequilibrium characteristics, thus improving the accuracy of heartbeat analysis. However, in analyzing probability distributions, the fpTIR and fPEn exhibit discrepancies in the chaotic series and even opposite results in the heartbeats, wherein the results of fpTIR are consistent with the theory of complexity loss in aging and disease. Overall, the fpTIR accurately characterizes the structure of the sequences and enhances the accuracy of the nonequilibrium analysis of complex systems, providing a theoretical basis for exploring complex systems from the perspectives of nonequilibrium dynamics and entropy complexity.

physics.data-an↗

arXiv2024

Permutation time irreversibility in sleep electroencephalograms: Dependence on sleep stage and the effect of equal values

Time irreversibility (TIR) refers to the manifestation of nonequilibrium brain activity influenced by various physiological conditions; however, the influence of sleep on electroencephalogram (EEG) TIR has not been sufficiently investigated. In this paper, a comprehensive study on permutation TIR (pTIR) of EEG data under different sleep stages is conducted. Two basic ordinal patterns (i.e., the original and amplitude permutations) are distinguished to simplify sleep EEGs, and then the influences of equal values and forbidden permutation on pTIR are elucidated. To detect pTIR of brain electric signals, 5 groups of EEGs in the awake, stages I, II, III, and rapid eye movement (REM) stages are collected from the public Polysomnographic Database in PhysioNet. Test results suggested that the pTIR of sleep EEGs significantly decreases as the sleep stage increases (p<0.001), with the awake and REM EEGs, demonstrating greater differences than others. Comparative analysis and numerical simulations support the importance of equal values. Distribution of equal states, a simple quantification of amplitude fluctuations, significantly increases with the sleep stage (p<0.001). If these equalities are ignored, incorrect probabilistic differences may arise in the forward-backward and symmetric permutations of TIR, leading to contradictory results; moreover, the ascending and descending orders for symmetric permutations also lead different outcomes in sleep EEGs. Overall, pTIR in sleep EEGs contributes to our understanding of quantitative TIR and classification of sleep EEGs.

stat.CO↗

arXiv2022

Comparative analysis of time irreversibility and amplitude irreversibility based on joint permutation

Although time irreversibility (TIR) and amplitude irreversibility (AIR) are relevant concepts for nonequilibrium analysis, their association has received little attention. This paper conducts a systematic comparative analysis of the relationship between TIR and AIR based on statistical descriptions and numerical simulations. To simplify the quantification of TIR and AIR, the amplitude permutation and global information of the associated vector are combined to produce a joint probability estimation. Chaotic logistic, Henon, and Lorenz series are generated to evaluate TIR and AIR according to surrogate theory, and the distributions of joint permutations for these model series are measured to compare the degree of TIR and AIR. The joint permutation TIR and AIR are then used to investigate nonequilibrium pathological features in epileptic electroencephalography data. Test results suggest that epileptic brain electrical activities, particular those during the onset of seizure, manifest higher nonequilibrium characteristics. According to the statistical definitions and targeted pairs of joint permutations in the chaotic model data, TIR and AIR are fundamentally different nonequilibrium descriptors from time- and amplitude-reversibility, respectively, and thus require different forms of numerical analysis. At the same time, TIR and AIR both provide measures for fluctuation theorems associated with nonequilibrium processes, and have similar probabilistic differences in the pairs of joint permutations and consistent outcomes when used to analyze both the model series and real-world signals. Overall, comparative analysis of TIR and AIR contributes to our understanding of nonequilibrium features and broadens the scope of quantitative nonequilibrium measures. Additionally, the construction of joint permutations contributes to the development of symbolic time series analysis.

stat.CO↗

arXiv2022

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.

stat.OT↗

arXiv2021

A novel parameter for nonequilibrium analysis in reconstructed state spaces

Kernel methods are widely used for probability estimation by measuring the distribution of low-passed vector distances in reconstructed state spaces. However, the information conveyed by the vector distances that are greater than the threshold has received little attention. In this paper, we consider the probabilistic difference of the kernel transformation in reconstructed state spaces, and derive a novel nonequilibrium descriptor by measuring the fluctuations of the vector distance with respect to the tolerance. We verify the effectiveness of the proposed kernel probabilistic difference using three chaotic series (logistic, Henon, and Lorenz) and a first-order autoregressive series according to the surrogate theory, and we use the kernel parameter to analyze real-world heartbeat data. In the heartbeat analysis, the kernel probabilistic difference, particularly that based on the Kullback--Leibler divergence, effectively characterizes the physiological complexity loss related to reduced cardiac dynamics in the elderly and diseased heartbeat data. Overall, the kernel probabilistic difference provides a novel method for the quantification of nonequilibria by characterizing the fluctuation theorem in reconstructed state spaces, and enables reliable detection of cardiac physiological and pathological information from heart rates.

physics.data-an↗

arXiv2020

Time irreversibility and amplitude irreversibility measures for nonequilibrium processes

Time irreversibility, which characterizes nonequilibrium processes, can be measured based on the probabilistic differences between symmetric vectors. To simplify the quantification of time irreversibility, symmetric permutations instead of symmetric vectors have been employed in some studies. However, although effective in practical applications, this approach is conceptually incorrect. Time irreversibility should be measured based on the permutations of symmetric vectors rather than symmetric permutations, whereas symmetric permutations can instead be employed to determine the quantitative amplitude irreversibility -- a novel parameter proposed in this paper for nonequilibrium calculated by means of the probabilistic difference in amplitude fluctuations. Through theoretical and experimental analyses, we highlight the strong similarities and close associations between the time irreversibility and amplitude irreversibility measures. Our paper clarifies the connections of and the differences between the two types of permutation-based parameters for quantitative nonequilibrium, and by doing so, we bridge the concepts of amplitude irreversibility and time irreversibility and broaden the selection of quantitative tools for studying nonequilibrium processes in complex systems.

eess.SP↗

arXiv2019

Effects of controlling parameter on symbolic nonlinear complexity detection

Symbolic transformation, a coarse-graining process, is a crucial prerequisite for and has evidential influence to the symbolic time series analysis. We employ Shannon entropy for a parameter-dependent symbolization, KW (Kurths-Wessel) symbolic method, to test the effects of controlling parameter on its symbolic nonlinear complexity detection. Two chaotic models, logistic and Henon series, and heartbeats of CHF (Congestive Heart Failure) patients, healthy young and elderly subjects from PhysioNet are applied to test the KW symbolic entropy. The complexity-loss theory about aging and diseases in heart rates is validated and reasons that may account for some paradoxes in nonlinear analysis are discussed. Tests results suggest that due to different structural or dynamical properties of different nonlinear systems, controlling parameter of the KW symbolization should be adjusted accordingly to have reliable symbolic nonlinear analysis.

physics.bio-ph↗

arXiv2018

Quantifying time irreversibility using probabilistic differences between symmetric permutations

To simplify the quantification of time irreversibility, we employ order patterns instead of the raw multi-dimension vectors in time series, and considering the existence of forbidden permutation, we propose a subtraction-based parameter, Ys, 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.

physics.med-ph↗

arXiv2018

Differential symbolic entropy in nonlinear dynamics complexity analysis

Differential symbolic entropy, a measure for nonlinear dynamics complexity, is proposed in our contribution. With flexible controlling parameter, the chaotic deterministic measure takes advantage of local nonlinear dynamical information among three adjacent elements to extract nonlinear complexity. In nonlinear complexity detections of chaotic logistic series, DSEn (differential symbolic entropy) has satisfied complexity extractions with the changes of chaotic features of logistic map. In nonlinear analysis of real-world physiological heart signals, three kinds of heart rates are significantly distinguished by DSEn in statistics, healthy young subjects > healthy elderly people > CHF (congestive heart failure) patients, highlighting the complex-losing theory of aging and heart diseases in cardiac nonlinearity. Moreover, DSEn does not have high demand on data length and can extract nonlinear complexity at short data sets; therefore, it is an efficient parameter to characterize nonlinear dynamic complexity.

physics.data-an↗

arXiv2018

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.

physics.data-an↗